From 43122af0dffb5010ae3e6f8de4da5e8725d68144 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Wed, 14 Nov 2018 10:34:09 -0500
Subject: [PATCH 01/60] Let pearsonr return a tuple instead of trying to
 convert to float and added test for 0 noise

---
 mgcpy/independence_tests/rv_corr.py              |  3 +--
 .../unit_tests/rv_corr_test.py                   | 16 ++++++++++++++--
 2 files changed, 15 insertions(+), 4 deletions(-)

diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index f737186..e0fcf7f 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -80,7 +80,6 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
 
         if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)):
             corr, covar = pearsonr(data_matrix_X, data_matrix_Y)
-            corr, covar = corr[0], covar[0]
         elif (self.which_test == 'rv'):
             covar = np.trace(np.dot(covar, covar.T))
             corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX))
@@ -97,4 +96,4 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
 
         independence_test_metadata = {"covariance": covar}
 
-        return corr, independence_test_metadata
+        return corr, independence_test_metadata
\ No newline at end of file
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
index 383e734..3bfe3d9 100644
--- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -23,8 +23,6 @@ def test_local_corr():
     assert np.round(test_stat2, decimals=2) == 0.95
     assert np.round(test_stat3, decimals=2) == 0.90
 
-    del X, Y, rvcorr, rvcorr2, rvcorr3, test_stat1, test_stat2, test_stat3
-
     # Against linear simulations
     np.random.seed(0)
     X, Y = sims.linear_sim(100, 1)
@@ -40,6 +38,20 @@ def test_local_corr():
     assert np.round(test_stat1, decimals=2) == 0.24
     assert np.round(test_stat2, decimals=2) == 0.49
     assert np.round(test_stat3, decimals=2) == 0.24
+    
+    X, Y = sims.linear_sim(100, 1, noise=0)
+    #savemat('distance matrix data', {'X' : X, 'Y' : Y})
+    rvcorr = RVCorr(X, Y, None)
+    rvcorr2 = RVCorr(X, Y, None, 'pearson')
+    rvcorr3 = RVCorr(X, Y, None, 'cca')
+
+    test_stat1 = rvcorr.test_statistic()[0]
+    test_stat2 = rvcorr2.test_statistic()[0]
+    test_stat3 = rvcorr3.test_statistic()[0]
+
+    assert np.round(test_stat1, decimals=2) == 1.00
+    assert np.round(test_stat2, decimals=2) == 1.00
+    assert np.round(test_stat3, decimals=2) == 1.00
 
 
 test_local_corr()

From 11a5961191710e11bd24ed7cb14e711605fb39f0 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Wed, 14 Nov 2018 10:34:59 -0500
Subject: [PATCH 02/60] Fixed spacing caused by spyder

---
 mgcpy/independence_tests/rv_corr.py                 | 2 +-
 mgcpy/independence_tests/unit_tests/rv_corr_test.py | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index e0fcf7f..baf3d43 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -96,4 +96,4 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
 
         independence_test_metadata = {"covariance": covar}
 
-        return corr, independence_test_metadata
\ No newline at end of file
+        return corr, independence_test_metadata
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
index 3bfe3d9..25b5ab1 100644
--- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -38,7 +38,7 @@ def test_local_corr():
     assert np.round(test_stat1, decimals=2) == 0.24
     assert np.round(test_stat2, decimals=2) == 0.49
     assert np.round(test_stat3, decimals=2) == 0.24
-    
+
     X, Y = sims.linear_sim(100, 1, noise=0)
     #savemat('distance matrix data', {'X' : X, 'Y' : Y})
     rvcorr = RVCorr(X, Y, None)

From 0d0a991ea06a3214eb0dd89e19eec489a1b028c8 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Thu, 15 Nov 2018 19:27:26 -0500
Subject: [PATCH 03/60] Add HHG test and simulations plot to verify simulations

---
 mgcpy/benchmarks/simulations.py               |  29 ++--
 mgcpy/benchmarks/simulations_test.py          | 129 +++++++++++++++++-
 mgcpy/independence_tests/hhg.py               |  13 +-
 .../independence_tests/unit_tests/hhg_test.py |  37 +++++
 .../unit_tests/rv_corr_test.py                |   4 -
 5 files changed, 180 insertions(+), 32 deletions(-)
 create mode 100644 mgcpy/independence_tests/unit_tests/hhg_test.py

diff --git a/mgcpy/benchmarks/simulations.py b/mgcpy/benchmarks/simulations.py
index e281c20..8dbcd51 100644
--- a/mgcpy/benchmarks/simulations.py
+++ b/mgcpy/benchmarks/simulations.py
@@ -256,27 +256,18 @@ def spiral_sim(num_samp, num_dim, noise=0.4, low=0, high=5):
 
     :return: the data matrix and a response array
     """
-    if num_dim > 1:
-        kappa = 1
-    else:
-        kappa = 0
-    x = gen_x_unif(num_samp, num_dim, low=low, high=high)
-    rx = gen_x_unif(num_samp, num_dim, low=low, high=high)
-    ry = rx
-    z = rx
-    sig = np.diag(np.ones(shape=(num_dim)))
-    gauss_noise = (np.random.multivariate_normal(cov=sig,
-                                                 mean=np.zeros(num_dim),
-                                                 size=num_samp))
+    uniform_dist = gen_x_unif(num_samp, num_dim=1, low=low, high=high)
+    the_x = np.array(np.cos(np.pi * uniform_dist)).reshape(num_samp, 1)
+    y = uniform_dist * np.sin(np.pi * uniform_dist)
+    x = np.zeros(shape=(num_samp, num_dim))
 
-    ry = np.ones((num_samp, num_dim))
-    x[:, 0] = np.cos(z[:, 0].reshape((num_samp)) * np.pi)
-    for i in range(num_dim - 1):
-        x[:, i+1] = (x[:, i].reshape((num_samp)) * np.cos(z[:, i+1].reshape((num_samp)) * np.pi))
-        x[:, i] = (x[:, i].reshape((num_samp)) * np.sin(z[:, i+1].reshape((num_samp)) * np.pi))
-    x = rx * x
+    if num_dim > 1:
+        for i in range(num_dim - 1):
+            x[:, i] = np.squeeze((y * np.power(the_x, i)))
+    x[:, num_dim-1] = np.squeeze(uniform_dist * the_x)
 
-    y = ry * np.sin(z[:, 0].reshape((num_samp, 1)) * np.pi) + kappa*noise*ry*gauss_noise
+    gauss_noise = np.random.normal(loc=0, scale=1, size=(x.shape[0], 1))
+    y = y + noise*num_dim*gauss_noise
 
     return x, y
 
diff --git a/mgcpy/benchmarks/simulations_test.py b/mgcpy/benchmarks/simulations_test.py
index 25585d4..e118b9e 100644
--- a/mgcpy/benchmarks/simulations_test.py
+++ b/mgcpy/benchmarks/simulations_test.py
@@ -1,82 +1,159 @@
 import numpy as np
 from mgcpy.benchmarks import simulations as sims
+import matplotlib.pyplot as plt
 
 
 def test_simulations():
-    num_samps = 100
+    num_samps = 1000
     num_dim1 = 1
     num_dim2 = 300
     independent = True
 
+    np.random.seed(0)
+    fig1 = plt.figure(figsize = (50, 80));
+    plt.axis('off')
+
     # Linear Simulation
     returns_low_dim = sims.linear_sim(num_samps, num_dim1)
     returns_high_dim = sims.linear_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.linear_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 1);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Linear', fontweight='bold')
+    ax1.axis('off');
 
     # Exponential Simulation
     returns_low_dim = sims.exp_sim(num_samps, num_dim1)
     returns_high_dim = sims.exp_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.exp_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 2);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Exponential', fontweight='bold')
+    ax1.axis('off');
 
     # Cubic Simulation
     returns_low_dim = sims.cub_sim(num_samps, num_dim1)
     returns_high_dim = sims.cub_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+     
+    x1, y1 = sims.cub_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 3);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Cubic', fontweight='bold')
+    ax1.axis('off');
 
     # Joint-Normal Simulation
     returns_low_dim = sims.joint_sim(num_samps, num_dim1)
     returns_high_dim = sims.joint_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.joint_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 4);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Joint Normal', fontweight='bold')
+    ax1.axis('off');
 
     # Step Simulation
     returns_low_dim = sims.step_sim(num_samps, num_dim1)
     returns_high_dim = sims.step_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.step_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 5);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Step', fontweight='bold')
+    ax1.axis('off');
 
     # Quadratic Simulation
     returns_low_dim = sims.quad_sim(num_samps, num_dim1)
     returns_high_dim = sims.quad_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.quad_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 6);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Quadratic', fontweight='bold')
+    ax1.axis('off');
 
     # W Simulation
     returns_low_dim = sims.w_sim(num_samps, num_dim1)
     returns_high_dim = sims.w_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.w_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 7);
+    ax1.scatter(x1, y1);
+    ax1.set_title('W-Shaped', fontweight='bold')
+    ax1.axis('off');
 
     # Spiral Simulation
     returns_low_dim = sims.spiral_sim(num_samps, num_dim1)
     returns_high_dim = sims.spiral_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.spiral_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 8);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Spiral', fontweight='bold')
+    ax1.axis('off');
 
     # Uncorrelated Bernoulli Simulation
     returns = sims.ubern_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.ubern_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 9);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Uncorrelated Bernoulli', fontweight='bold')
+    ax1.axis('off');
 
     # Logarithmic Simulation
     returns_low_dim = sims.log_sim(num_samps, num_dim1)
     returns_high_dim = sims.log_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.log_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 10);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Logarithmic', fontweight='bold')
+    ax1.axis('off');
 
     # Nth Root Simulation
     returns_low_dim = sims.root_sim(num_samps, num_dim1)
     returns_high_dim = sims.root_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.root_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 11);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Fourth Root', fontweight='bold')
+    ax1.axis('off');
 
     # Sinusoidal Simulation (4*pi)
     returns_low_dim = sims.sin_sim(num_samps, num_dim1)
     returns_high_dim = sims.sin_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.sin_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 12);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Sinusoidal (4\u03C0)', fontweight='bold')
+    ax1.axis('off');
 
     # Sinusoidal Simulation (16*pi)
     returns_low_dim = sims.sin_sim(num_samps, num_dim1, period=16*np.pi)
@@ -84,34 +161,84 @@ def test_simulations():
         num_samps, num_dim2, period=16*np.pi, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi)
+    ax1 = fig1.add_subplot(4, 5, 13);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Sinusoidal (16\u03C0)', fontweight='bold')
+    ax1.axis('off');
 
     # Square Simulation
     returns = sims.square_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.square_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 14);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Square', fontweight='bold')
+    ax1.axis('off');
 
     # Two Parabolas Simulation
     returns_low_dim = sims.two_parab_sim(num_samps, num_dim1)
     returns_high_dim = sims.two_parab_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 15);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Two Parabolas', fontweight='bold')
+    ax1.axis('off');
 
     # Circle Simulation
     returns = sims.circle_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.circle_sim(num_samps, 1, noise=0)
+    ax1 = fig1.add_subplot(4, 5, 16);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Circle', fontweight='bold')
+    ax1.axis('off');
 
     # Ellipse Simulation
     returns = sims.circle_sim(num_samps, num_dim2, radius=5)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5)
+    ax1 = fig1.add_subplot(4, 5, 17);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Ellipse', fontweight='bold')
+    ax1.axis('off');
 
     # Diamond Simulation
     returns = sims.square_sim(
         num_samps, num_dim2, period=-np.pi/4, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4)
+    ax1 = fig1.add_subplot(4, 5, 18);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Diamond', fontweight='bold')
+    ax1.axis('off');
 
     # Multiplicative Noise Simulation
     returns = sims.multi_noise_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.multi_noise_sim(num_samps, 1)
+    ax1 = fig1.add_subplot(4, 5, 19);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Multiplicative Noise', fontweight='bold')
+    ax1.axis('off');
 
     # Multimodal Independence Simulation
     returns = sims.multi_indep_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
+    
+    x1, y1 = sims.multi_indep_sim(num_samps, 1)
+    ax1 = fig1.add_subplot(4, 5, 20);
+    ax1.scatter(x1, y1);
+    ax1.set_title('Multimodal Independence', fontweight='bold')
+    ax1.axis('off');
+
+test_simulations()
\ No newline at end of file
diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 3ea0047..29e3d6e 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -1,6 +1,5 @@
 import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
-from scipy.spatial import distance_matrix
 
 
 class HHG(IndependenceTest):
@@ -58,13 +57,11 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
         row_Y, columns_Y = data_matrix_Y.shape[0], data_matrix_Y.shape[1]
 
         # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not
-        if row_X != columns_X or sum(data_matrix_X.diagonal()**2) > 0:
-            dist_mtx_X = distance_matrix(data_matrix_X, data_matrix_X)
+        if (row_X != columns_X or sum(data_matrix_X.diagonal()**2) > 0) and \
+        (row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0):
+            dist_mtx_X, dist_mtx_Y = self.compute_distance_matrix(data_matrix_X, data_matrix_Y)
         else:
             dist_mtx_X = data_matrix_X
-        if row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0:
-            dist_mtx_Y = distance_matrix(data_matrix_Y, data_matrix_Y)
-        else:
             dist_mtx_Y = data_matrix_Y
 
         n = dist_mtx_X.shape[0]
@@ -87,12 +84,12 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
 
         return corr
     
-    def p_value(self, replication_factor=1000):
+    def p_value(self, replication_factor=100):
         """
         Tests independence between two datasets using HHG and permutation test.
 
         :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to 1000.
+                                   the permutation test. Defaults to 100.
         :type replication_factor: int
 
         :return: P-value of HHG
diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
new file mode 100644
index 0000000..f1665a2
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -0,0 +1,37 @@
+import mgcpy.benchmarks.simulations as sims
+import numpy as np
+from scipy.spatial.distance import pdist, squareform
+from mgcpy.independence_tests.hhg import HHG
+
+
+def compute_distance_matrix(data_matrix_X, data_matrix_Y):
+    # obtain the pairwise distance matrix for X and Y
+    dist_mtx_X = squareform(pdist(data_matrix_X, metric='euclidean'))
+    dist_mtx_Y = squareform(pdist(data_matrix_Y, metric='euclidean'))
+    return (dist_mtx_X, dist_mtx_Y)
+
+
+def test_hhg():
+    # Against a randomly defined data set
+    X = np.array([1.1728, 2.4941, 2.4101, 0.1814, 1.1978, 1.5806, 1.2504,
+                  1.9706, 1.8839, 0.8760])[:, np.newaxis]
+    Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917,
+                  7.1748, 6.5792, 2.4012])[:, np.newaxis]
+    hhg = HHG(X, Y, compute_distance_matrix)
+    test_stat = hhg.test_statistic()
+
+    assert np.round(test_stat, decimals=2) == 411.88
+
+    # Against linear simulations
+    np.random.seed(0)
+    X, Y = sims.linear_sim(100, 1)
+    hhg = HHG(X, Y, compute_distance_matrix)
+    test_stat = hhg.test_statistic()
+ 
+    assert np.round(test_stat, decimals=2) == 28986.52
+
+    X, Y = sims.linear_sim(100, 1, noise=0)
+    hhg = HHG(X, Y, compute_distance_matrix)
+    test_stat = hhg.test_statistic()
+
+    assert np.round(test_stat, decimals=2) == 950600.00
\ No newline at end of file
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
index 25b5ab1..efdb89b 100644
--- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -2,8 +2,6 @@
 import numpy as np
 from mgcpy.independence_tests.rv_corr import RVCorr
 
-#from scipy.io import savemat
-
 
 def test_local_corr():
     # Against a randomly defined data set
@@ -26,7 +24,6 @@ def test_local_corr():
     # Against linear simulations
     np.random.seed(0)
     X, Y = sims.linear_sim(100, 1)
-    #savemat('distance matrix data', {'X' : X, 'Y' : Y})
     rvcorr = RVCorr(X, Y, None)
     rvcorr2 = RVCorr(X, Y, None, 'pearson')
     rvcorr3 = RVCorr(X, Y, None, 'cca')
@@ -40,7 +37,6 @@ def test_local_corr():
     assert np.round(test_stat3, decimals=2) == 0.24
 
     X, Y = sims.linear_sim(100, 1, noise=0)
-    #savemat('distance matrix data', {'X' : X, 'Y' : Y})
     rvcorr = RVCorr(X, Y, None)
     rvcorr2 = RVCorr(X, Y, None, 'pearson')
     rvcorr3 = RVCorr(X, Y, None, 'cca')

From c09110cdf664cf86b4bb1b1ab8419004e2faced7 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 16 Nov 2018 10:31:13 -0500
Subject: [PATCH 04/60] Removed Extraneous spacing

---
 mgcpy/independence_tests/hhg.py                 | 9 +++++----
 mgcpy/independence_tests/unit_tests/hhg_test.py | 9 ++++++---
 2 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 29e3d6e..526fa3b 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -58,7 +58,7 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
 
         # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not
         if (row_X != columns_X or sum(data_matrix_X.diagonal()**2) > 0) and \
-        (row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0):
+                (row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0):
             dist_mtx_X, dist_mtx_Y = self.compute_distance_matrix(data_matrix_X, data_matrix_Y)
         else:
             dist_mtx_X = data_matrix_X
@@ -83,7 +83,7 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None):
         corr = np.sum(S)
 
         return corr
-    
+
     def p_value(self, replication_factor=100):
         """
         Tests independence between two datasets using HHG and permutation test.
@@ -110,7 +110,8 @@ def p_value(self, replication_factor=100):
         test_stats_null = np.zeros(replication_factor)
         for rep in range(replication_factor):
             permuted_y = np.random.permutation(self.data_matrix_Y)
-            test_stats_null[rep] = self.test_statistic(data_matrix_X=self.data_matrix_X, data_matrix_Y=permuted_y)
-        
+            test_stats_null[rep] = self.test_statistic(
+                data_matrix_X=self.data_matrix_X, data_matrix_Y=permuted_y)
+
         # p-value is the probability of observing more extreme test statistic under the null
         return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
index f1665a2..dbc0730 100644
--- a/mgcpy/independence_tests/unit_tests/hhg_test.py
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
-from scipy.spatial.distance import pdist, squareform
 from mgcpy.independence_tests.hhg import HHG
+from scipy.spatial.distance import pdist, squareform
 
 
 def compute_distance_matrix(data_matrix_X, data_matrix_Y):
@@ -27,11 +27,14 @@ def test_hhg():
     X, Y = sims.linear_sim(100, 1)
     hhg = HHG(X, Y, compute_distance_matrix)
     test_stat = hhg.test_statistic()
- 
+
     assert np.round(test_stat, decimals=2) == 28986.52
 
     X, Y = sims.linear_sim(100, 1, noise=0)
     hhg = HHG(X, Y, compute_distance_matrix)
     test_stat = hhg.test_statistic()
 
-    assert np.round(test_stat, decimals=2) == 950600.00
\ No newline at end of file
+    assert np.round(test_stat, decimals=2) == 950600.00
+
+
+test_hhg()

From c0ff9750f2f167df6784cd07273949ad186a4f25 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Mon, 26 Nov 2018 16:35:58 -0500
Subject: [PATCH 05/60] add mdmr module

---
 mgcpy/independence_tests/mdmr/X_mdmr.csv      | 500 ++++++++++++++++++
 mgcpy/independence_tests/mdmr/Y_mdmr.csv      | 500 ++++++++++++++++++
 mgcpy/independence_tests/mdmr/__init__.py     |   0
 mgcpy/independence_tests/mdmr/mdmr.py         | 115 ++++
 .../independence_tests/mdmr/mdmrfunctions.py  | 127 +++++
 5 files changed, 1242 insertions(+)
 create mode 100644 mgcpy/independence_tests/mdmr/X_mdmr.csv
 create mode 100644 mgcpy/independence_tests/mdmr/Y_mdmr.csv
 create mode 100644 mgcpy/independence_tests/mdmr/__init__.py
 create mode 100644 mgcpy/independence_tests/mdmr/mdmr.py
 create mode 100644 mgcpy/independence_tests/mdmr/mdmrfunctions.py

diff --git a/mgcpy/independence_tests/mdmr/X_mdmr.csv b/mgcpy/independence_tests/mdmr/X_mdmr.csv
new file mode 100644
index 0000000..c5712c2
--- /dev/null
+++ b/mgcpy/independence_tests/mdmr/X_mdmr.csv
@@ -0,0 +1,500 @@
+-0.035837605,-1.245650342,-0.255394461
+0.55357901,1.273226544,-0.069094322
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+-0.064829833,1.217906326,1.41118878
+-0.633382654,0.306852368,0.29586932
+-0.06251656,0.341277834,1.617496932
+0.930777524,-0.91348191,-0.130632016
+0.076356533,-0.939735162,0.965922873
+-0.738758232,-0.018565065,0.76218871
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diff --git a/mgcpy/independence_tests/mdmr/Y_mdmr.csv b/mgcpy/independence_tests/mdmr/Y_mdmr.csv
new file mode 100644
index 0000000..6572ce1
--- /dev/null
+++ b/mgcpy/independence_tests/mdmr/Y_mdmr.csv
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+-0.109586087,0.280050267,0.096680091,0.262705682,-0.232377104,0.866702265,0.789015702,1.041669294,1.199624938,-0.686415894
+0.227845755,-0.344124322,-0.363728527,0.945729098,-0.32021499,0.363254375,-0.022804763,1.244087744,-0.253885666,1.303108598
+-5.497436984,1.064763714,2.029291825,0.361011787,2.071582664,1.410661841,1.584720781,1.568099393,1.110692367,0.671411469
+-0.673465564,-0.549773231,-0.37233368,-0.413871048,0.649072546,-0.068763025,-0.552346312,-0.016128918,0.735792499,0.502777137
+1.661913473,-0.12139557,-0.364046104,-1.069774229,-0.763443146,-1.58814893,0.328715089,-1.4210074,-1.444363196,-0.538179487
+-0.382985118,-0.804831888,0.538835566,-1.878055206,-0.160051584,0.988250333,-1.047210194,-0.760466689,-1.17954043,-1.698029196
diff --git a/mgcpy/independence_tests/mdmr/__init__.py b/mgcpy/independence_tests/mdmr/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
new file mode 100644
index 0000000..216a790
--- /dev/null
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -0,0 +1,115 @@
+from mgcpy.independence_tests.abstract_class import IndependenceTest
+
+import copy
+from mgcpy.independence_tests.mdmr.mdmrfunctions import *
+#from mdmrfunctions import *
+
+class MDMR(IndependenceTest):
+    def __init__(self, data_matrix_X, data_matrix_Y, compute_distance_matrix):
+        '''
+        :param data_matrix_X: is interpreted as:
+            - a [n*d] data matrix, a square matrix with n samples in d dimensions
+        :type data_matrix_X: 2D numpy.array
+        :param data_matrix_Y: is interpreted as either:
+            - a [n*d] data matrix, a square matrix with n samples in d dimensions
+        :type data_matrix_Y: 2D numpy.array
+        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
+        :type compute_distance_matrix: FunctionType or callable()
+        '''
+        IndependenceTest.__init__(self, data_matrix_X, data_matrix_Y, compute_distance_matrix)
+    
+    def get_name(self):
+        return "MDMR"
+    
+    def test_statistic(self, data_matrix_X=None, data_matrix_Y=None, permutations = 1000, individual = 0, disttype = 'cityblock'):
+        """
+        Computes MDMR between two datasets.
+        - It first takes the distance matrix of Y (by )
+        - Next it regresses X into a portion due to Y and a portion due to residual for each variable of X
+        - The p-value is for the null hypothesis that the variable of X is not correlated with Y's distance matrix
+        :param data_matrix_X: (optional, default picked from class attr) is interpreted as:
+            - a [n*d] data matrix, a square matrix with n samples in d dimensions
+        :type data_matrix_X: 2D numpy.array
+        :param data_matrix_Y: (optional, default picked from class attr) is interpreted as:
+            - a [n*d] data matrix, a square matrix with n samples in d dimensions
+        :type data_matrix_Y: 2D numpy.array
+        :parameter 'individual':
+            with value 0 tests the entire X matrix by (default), returns 2 values
+            with value 1 it tests the entire X matrix and then each column (variable) individually, returns 3 values
+        :return: with individual = 0, returns the test statistic of the entire X matrix and the associated p-value
+        with individual = 1, returns the above as well as an array with the 
+        variable of X in the first column, the test statistic in the 2nd, and the permutation p-value in the 3rd
+        """
+        if data_matrix_X is None and data_matrix_Y is None:
+            data_matrix_X = self.data_matrix_X
+            data_matrix_Y = self.data_matrix_Y
+        X = data_matrix_X
+        Y = data_matrix_Y
+        
+        D = self.compute_distance_matrix(Y, disttype)
+        D = scp.distance.squareform(D)
+        a = D.shape[0]**2
+        D = D.reshape((a,1))
+        
+        columns = np.arange(X.shape[1])
+        columnsingle = X.shape[1]
+        check_rank(X)
+    
+        subjects = X.shape[0]
+        if subjects != np.sqrt(D.shape[0]):
+            raise Exception("# of subjects incompatible between X and D")
+        
+        X = np.hstack((np.ones((X.shape[0], 1)), X))
+        col = copy.copy(columns)
+        col += 1
+    
+        Gs = gower_center_many(D)
+    
+        df_among = float(col.shape[0])
+        df_resid = float(subjects - X.shape[1])
+    
+        permutation_indexes = np.zeros((permutations + 1, subjects), dtype=np.int)
+        permutation_indexes[0, :] = range(subjects)
+        for i in range(1, permutations + 1):
+            permutation_indexes[i,:] = np.random.permutation(subjects)
+    
+        H2perms = gen_H2_perms(X, col, permutation_indexes)
+        IHperms = gen_IH_perms(X, col, permutation_indexes)
+        
+        F_perms = calc_ftest(H2perms, IHperms, Gs,
+                            df_among, df_resid)
+    
+        p_vals = fperms_to_pvals(F_perms)
+        F_permtotal = F_perms[0, :]
+        pvaltotal = p_vals
+        if individual == 0:
+            return F_permtotal, pvaltotal
+        if individual == 1:
+            results = np.zeros((columnsingle,3))
+            for col in range(1, columnsingle+1):
+                col = copy.copy(col)
+                #    columns += 1
+                
+                Gs = gower_center_many(D)
+                
+                df_among = float(col)
+                df_resid = float(subjects - X.shape[1])
+                
+                permutation_indexes = np.zeros((permutations + 1, subjects), dtype=np.int)
+                permutation_indexes[0, :] = range(subjects)
+                for i in range(1, permutations + 1):
+                    permutation_indexes[i,:] = np.random.permutation(subjects)
+                    
+                H2perms = gen_H2_perms_single(X, col, permutation_indexes)
+                IHperms = gen_IH_perms_single(X, col, permutation_indexes)
+                    
+                F_perms = calc_ftest(H2perms, IHperms, Gs,
+                                    df_among, df_resid)
+                
+                p_vals = fperms_to_pvals(F_perms)
+                results[col-1,0] = col
+                results[col-1,1] = F_perms[0, :]
+                results[col-1,2] = p_vals
+    
+    
+            return F_permtotal, pvaltotal, results
diff --git a/mgcpy/independence_tests/mdmr/mdmrfunctions.py b/mgcpy/independence_tests/mdmr/mdmrfunctions.py
new file mode 100644
index 0000000..9032464
--- /dev/null
+++ b/mgcpy/independence_tests/mdmr/mdmrfunctions.py
@@ -0,0 +1,127 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Oct 25 16:09:14 2018
+
+@author: sunda
+"""
+import numpy as np
+import scipy.spatial as scp
+
+DTYPE = np.float64
+ITYPE = np.int32
+
+def check_rank(X):
+    k    = X.shape[1]
+    rank = np.linalg.matrix_rank(X)
+    if rank < k:
+        raise Exception("matrix is rank deficient (rank %i vs cols %i)" % (rank, k))
+
+def compute_distance_matrix(X, disttype):
+    D = scp.distance.pdist(X, disttype)
+    return D
+        
+def hatify(X):
+    Q1, _ = np.linalg.qr(X)
+    H = Q1.dot(Q1.T)
+    return H
+
+def gower_center(Y):
+    n = Y.shape[0]
+    I = np.eye(n,n)
+    uno = np.ones((n, 1))
+    
+    A = -0.5 * (Y ** 2)
+    C = I - (1.0 / n) * uno.dot(uno.T)
+    G = C.dot(A).dot(C)
+    
+    return G
+
+def gower_center_many(Ys):
+    observations = int(np.sqrt(Ys.shape[0]))
+    tests        = Ys.shape[1]
+    Gs           = np.zeros_like(Ys)
+    
+    for i in range(tests):
+#        print(type(observations))
+        D        = Ys[:, i].reshape(observations, observations)
+        Gs[:, i] = gower_center(D).flatten()
+    
+    return Gs
+
+
+def gen_h(x, columns, permutations):
+    return hatify(x[permutations][:, np.array(columns)])
+
+def gen_H2_perms_single(X, columns, permutation_indexes):
+    permutations, observations = permutation_indexes.shape
+    variables = X.shape[1]
+    
+    H2_permutations = np.zeros((observations ** 2, permutations))
+    for i in range(permutations):
+        perm_X = X[permutation_indexes[i, :]]
+        cols_X = perm_X[:, columns]
+        fix = cols_X.shape[0]
+        cols_X = cols_X.reshape((fix,1))
+        H = hatify(cols_X)
+#        H = hatify(perm_X)
+        other_columns = [i for i in range(variables) if i != columns]
+        H2 = H - hatify(X[:, other_columns])
+#        H2 = H
+        H2_permutations[:, i] = H2.flatten()
+    
+    return H2_permutations
+
+def gen_IH_perms_single(X, columns, permutation_indexes):
+    permutations, observations = permutation_indexes.shape
+    I = np.eye(observations, observations)
+    
+    IH_permutations = np.zeros((observations ** 2, permutations))
+    for i in range(permutations):
+        cols_X = X[permutation_indexes[i, :]][:, columns]
+        fix = cols_X.shape[0]
+        cols_X = cols_X.reshape((fix,1))
+        IH = I - hatify(cols_X)
+#        IH = I - hatify(X[permutation_indexes[i, :]])
+        IH_permutations[:,i] = IH.flatten()
+    
+    return IH_permutations
+
+def gen_H2_perms(X, columns, permutation_indexes):
+    permutations, observations = permutation_indexes.shape
+    variables = X.shape[1]
+    
+    H2_permutations = np.zeros((observations ** 2, permutations))
+    for i in range(permutations):
+        perm_X = X[permutation_indexes[i, :]]
+        cols_X = perm_X[:, columns]
+        H = hatify(cols_X)
+        other_columns = [i for i in range(variables) if i not in columns]
+        H2 = H - hatify(X[:, other_columns])
+        H2_permutations[:, i] = H2.flatten()
+    
+    return H2_permutations
+
+def gen_IH_perms(X, columns, permutation_indexes):
+    permutations, observations = permutation_indexes.shape
+    I            = np.eye(observations, observations)
+    
+    IH_permutations = np.zeros((observations ** 2, permutations))
+    for i in range(permutations):
+        IH = I - hatify(X[permutation_indexes[i, :]][:, columns])
+        IH_permutations[:,i] = IH.flatten()
+    
+    return IH_permutations
+
+def calc_ftest(Hs, IHs, Gs, m2, nm):
+    N = Hs.T.dot(Gs)
+    D = IHs.T.dot(Gs)
+    F = (N / m2) / (D / nm)
+    return F
+
+def fperms_to_pvals(F_perms):
+    permutations, tests = F_perms.shape
+    pvals = np.zeros(tests)
+    for i in range(tests):
+        j        = (F_perms[:, i] >= F_perms[0, i]).sum().astype('float')
+        pvals[i] = j / permutations
+    return pvals

From 1b1d09d47fbb800bd6bc60a649a42278464fb2e8 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Mon, 26 Nov 2018 18:27:12 -0500
Subject: [PATCH 06/60] add mdmr unit test

---
 .../{mdmr => unit_tests/mdmr/data}/X_mdmr.csv |  0
 .../{mdmr => unit_tests/mdmr/data}/Y_mdmr.csv |  0
 .../unit_tests/mdmr/mdmr_test.py              | 24 +++++++++++++++++++
 3 files changed, 24 insertions(+)
 rename mgcpy/independence_tests/{mdmr => unit_tests/mdmr/data}/X_mdmr.csv (100%)
 rename mgcpy/independence_tests/{mdmr => unit_tests/mdmr/data}/Y_mdmr.csv (100%)
 create mode 100644 mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py

diff --git a/mgcpy/independence_tests/mdmr/X_mdmr.csv b/mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv
similarity index 100%
rename from mgcpy/independence_tests/mdmr/X_mdmr.csv
rename to mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv
diff --git a/mgcpy/independence_tests/mdmr/Y_mdmr.csv b/mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv
similarity index 100%
rename from mgcpy/independence_tests/mdmr/Y_mdmr.csv
rename to mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
new file mode 100644
index 0000000..392ecb3
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -0,0 +1,24 @@
+from mgcpy.independence_tests.mdmr.mdmr import MDMR
+from mgcpy.independence_tests.mdmr.mdmrfunctions import compute_distance_matrix
+import numpy as np
+
+
+def test_mdmr():
+    #load data from csv files
+    csv1 = np.genfromtxt('data/X_mdmr.csv', delimiter=",")
+    X = csv1
+    
+    csv1 = np.genfromtxt('data/Y_mdmr.csv', delimiter=",")
+    Y = csv1
+    
+    mdmr = MDMR(csv1, csv2, compute_distance_matrix)
+    
+    #test get_name
+    assert mdmr.get_name() == 'MDMR'
+    
+    #test statistic
+    assert np.allclose(mdmr.test_statistic()[0], 25.03876688)
+    
+    #p-value
+    assert np.allclose(mdmr.test_statistic()[1], 0.000999)
+    
\ No newline at end of file

From 49d86fb5f71236f18fd6e6399ac91bdcb770167c Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Mon, 26 Nov 2018 18:29:44 -0500
Subject: [PATCH 07/60] correct data location

---
 mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index 392ecb3..82ee0f8 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -5,10 +5,10 @@
 
 def test_mdmr():
     #load data from csv files
-    csv1 = np.genfromtxt('data/X_mdmr.csv', delimiter=",")
+    csv1 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv', delimiter=",")
     X = csv1
     
-    csv1 = np.genfromtxt('data/Y_mdmr.csv', delimiter=",")
+    csv1 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
     Y = csv1
     
     mdmr = MDMR(csv1, csv2, compute_distance_matrix)

From cdf5d1a3ed76886fd0e282acb933f3708494febd Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Tue, 27 Nov 2018 20:46:35 -0500
Subject: [PATCH 08/60] Added simulations edits

---
 mgcpy/benchmarks/simulations.py      |   8 +-
 mgcpy/benchmarks/simulations_test.py | 190 ++++++++++++++++++---------
 2 files changed, 135 insertions(+), 63 deletions(-)

diff --git a/mgcpy/benchmarks/simulations.py b/mgcpy/benchmarks/simulations.py
index 8dbcd51..92a332d 100644
--- a/mgcpy/benchmarks/simulations.py
+++ b/mgcpy/benchmarks/simulations.py
@@ -147,8 +147,12 @@ def joint_sim(num_samp, num_dim, noise=0.5):
 
     samp = (np.random.multivariate_normal(cov=sig, mean=np.zeros(2*num_dim),
                                           size=num_samp))
-    y = samp[:, num_dim: (2*num_dim)] + kappa*noise*gauss_noise
-    x = samp[:, 0:num_dim]
+    if num_dim == 1:
+        y = samp[:, (num_dim):(2*num_dim)] + kappa*noise*gauss_noise
+        x = samp[:, 0:num_dim]
+    else:      
+        y = samp[:, (num_dim+1):(2*num_dim)] + kappa*noise*gauss_noise
+        x = samp[:, 0:num_dim]
 
     return x, y
 
diff --git a/mgcpy/benchmarks/simulations_test.py b/mgcpy/benchmarks/simulations_test.py
index e118b9e..ac8861a 100644
--- a/mgcpy/benchmarks/simulations_test.py
+++ b/mgcpy/benchmarks/simulations_test.py
@@ -1,6 +1,7 @@
 import numpy as np
 from mgcpy.benchmarks import simulations as sims
 import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
 
 
 def test_simulations():
@@ -10,8 +11,9 @@ def test_simulations():
     independent = True
 
     np.random.seed(0)
-    fig1 = plt.figure(figsize = (50, 80));
+    fig1 = plt.figure(figsize = (50, 80))
     plt.axis('off')
+    fig2 = plt.figure(figsize = (50, 80))
 
     # Linear Simulation
     returns_low_dim = sims.linear_sim(num_samps, num_dim1)
@@ -20,10 +22,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.linear_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 1);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 1)
+    ax1.scatter(x1, y1)
     ax1.set_title('Linear', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.linear_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 1, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Linear', fontweight='bold')
+    ax2.axis('off')
 
     # Exponential Simulation
     returns_low_dim = sims.exp_sim(num_samps, num_dim1)
@@ -32,10 +40,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.exp_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 2);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 2)
+    ax1.scatter(x1, y1)
     ax1.set_title('Exponential', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.exp_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 2, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Exponential', fontweight='bold')
+    ax2.axis('off')
 
     # Cubic Simulation
     returns_low_dim = sims.cub_sim(num_samps, num_dim1)
@@ -44,10 +58,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
      
     x1, y1 = sims.cub_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 3);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 3)
+    ax1.scatter(x1, y1)
     ax1.set_title('Cubic', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.cub_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 3, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Cubic', fontweight='bold')
+    ax2.axis('off')
 
     # Joint-Normal Simulation
     returns_low_dim = sims.joint_sim(num_samps, num_dim1)
@@ -56,10 +76,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.joint_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 4);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 4)
+    ax1.scatter(x1, y1)
     ax1.set_title('Joint Normal', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.joint_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 4, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Joint Normal', fontweight='bold')
+    ax2.axis('off')
 
     # Step Simulation
     returns_low_dim = sims.step_sim(num_samps, num_dim1)
@@ -68,10 +94,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.step_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 5);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 5)
+    ax1.scatter(x1, y1)
     ax1.set_title('Step', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.step_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 5, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Step', fontweight='bold')
+    ax2.axis('off')
 
     # Quadratic Simulation
     returns_low_dim = sims.quad_sim(num_samps, num_dim1)
@@ -80,10 +112,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.quad_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 6);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 6)
+    ax1.scatter(x1, y1)
     ax1.set_title('Quadratic', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.quad_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 6, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Quadratic', fontweight='bold')
+    ax2.axis('off')
 
     # W Simulation
     returns_low_dim = sims.w_sim(num_samps, num_dim1)
@@ -92,10 +130,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.w_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 7);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 7)
+    ax1.scatter(x1, y1)
     ax1.set_title('W-Shaped', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.w_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 7, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('W-Shaped', fontweight='bold')
+    ax2.axis('off')
 
     # Spiral Simulation
     returns_low_dim = sims.spiral_sim(num_samps, num_dim1)
@@ -104,20 +148,32 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.spiral_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 8);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 8)
+    ax1.scatter(x1, y1)
     ax1.set_title('Spiral', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.spiral_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 8, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Spiral', fontweight='bold')
+    ax2.axis('off')
 
     # Uncorrelated Bernoulli Simulation
     returns = sims.ubern_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.ubern_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 9);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 9)
+    ax1.scatter(x1, y1)
     ax1.set_title('Uncorrelated Bernoulli', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.ubern_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 9, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Uncorrelated Bernoulli', fontweight='bold')
+    ax2.axis('off')
 
     # Logarithmic Simulation
     returns_low_dim = sims.log_sim(num_samps, num_dim1)
@@ -126,10 +182,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.log_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 10);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 10)
+    ax1.scatter(x1, y1)
     ax1.set_title('Logarithmic', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.log_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 10, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Logarithmic', fontweight='bold')
+    ax2.axis('off')
 
     # Nth Root Simulation
     returns_low_dim = sims.root_sim(num_samps, num_dim1)
@@ -138,10 +200,16 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.root_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 11);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 11)
+    ax1.scatter(x1, y1)
     ax1.set_title('Fourth Root', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
+    
+    x2, y2 = sims.root_sim(num_samps, 2, noise=0)
+    ax2 = fig2.add_subplot(4, 5, 11, projection = '3d');
+    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2.set_title('Fourth Root', fontweight='bold')
+    ax2.axis('off')
 
     # Sinusoidal Simulation (4*pi)
     returns_low_dim = sims.sin_sim(num_samps, num_dim1)
@@ -150,10 +218,10 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.sin_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 12);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 12)
+    ax1.scatter(x1, y1)
     ax1.set_title('Sinusoidal (4\u03C0)', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Sinusoidal Simulation (16*pi)
     returns_low_dim = sims.sin_sim(num_samps, num_dim1, period=16*np.pi)
@@ -163,20 +231,20 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi)
-    ax1 = fig1.add_subplot(4, 5, 13);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 13)
+    ax1.scatter(x1, y1)
     ax1.set_title('Sinusoidal (16\u03C0)', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Square Simulation
     returns = sims.square_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.square_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 14);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 14)
+    ax1.scatter(x1, y1)
     ax1.set_title('Square', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Two Parabolas Simulation
     returns_low_dim = sims.two_parab_sim(num_samps, num_dim1)
@@ -185,30 +253,30 @@ def test_simulations():
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 15);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 15)
+    ax1.scatter(x1, y1)
     ax1.set_title('Two Parabolas', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Circle Simulation
     returns = sims.circle_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.circle_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 16);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 16)
+    ax1.scatter(x1, y1)
     ax1.set_title('Circle', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Ellipse Simulation
     returns = sims.circle_sim(num_samps, num_dim2, radius=5)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5)
-    ax1 = fig1.add_subplot(4, 5, 17);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 17)
+    ax1.scatter(x1, y1)
     ax1.set_title('Ellipse', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Diamond Simulation
     returns = sims.square_sim(
@@ -216,29 +284,29 @@ def test_simulations():
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4)
-    ax1 = fig1.add_subplot(4, 5, 18);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 18)
+    ax1.scatter(x1, y1)
     ax1.set_title('Diamond', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Multiplicative Noise Simulation
     returns = sims.multi_noise_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.multi_noise_sim(num_samps, 1)
-    ax1 = fig1.add_subplot(4, 5, 19);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 19)
+    ax1.scatter(x1, y1)
     ax1.set_title('Multiplicative Noise', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
     # Multimodal Independence Simulation
     returns = sims.multi_indep_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
     
     x1, y1 = sims.multi_indep_sim(num_samps, 1)
-    ax1 = fig1.add_subplot(4, 5, 20);
-    ax1.scatter(x1, y1);
+    ax1 = fig1.add_subplot(4, 5, 20)
+    ax1.scatter(x1, y1)
     ax1.set_title('Multimodal Independence', fontweight='bold')
-    ax1.axis('off');
+    ax1.axis('off')
 
 test_simulations()
\ No newline at end of file

From 923857e26a308854e27fc3e2a45f56d8cc40a11c Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Wed, 28 Nov 2018 10:22:02 -0500
Subject: [PATCH 09/60] rename csv1 to csv2

---
 mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index 82ee0f8..1c1614e 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -8,8 +8,8 @@ def test_mdmr():
     csv1 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv', delimiter=",")
     X = csv1
     
-    csv1 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
-    Y = csv1
+    csv2 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
+    Y = csv2
     
     mdmr = MDMR(csv1, csv2, compute_distance_matrix)
     

From a04d73d361ce241253cdd0fa8de74778d9ac1039 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Wed, 28 Nov 2018 15:40:16 -0500
Subject: [PATCH 10/60] add p_value function to MDMR class

---
 mgcpy/independence_tests/mdmr/mdmr.py | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 216a790..fd96d5d 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -113,3 +113,11 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None, permutations =
     
     
             return F_permtotal, pvaltotal, results
+
+    def p_value(self, data_matrix_X=None, data_matrix_Y=None, permutations = 1000, individual = 0, disttype = 'cityblock'):
+        """
+        Computes the p-value of the pseudo-F test statistic.
+        """
+        p_value = self.test_statistic()[1]
+        
+        return p_value

From 1b7f68b8893fe4b3a30ec25efa030400ee066368 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Wed, 28 Nov 2018 16:30:36 -0500
Subject: [PATCH 11/60] fix mdmr unit tests

---
 mgcpy/independence_tests/mdmr/mdmr.py             | 15 ++++++---------
 .../unit_tests/mdmr/mdmr_test.py                  | 14 ++++++--------
 2 files changed, 12 insertions(+), 17 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index fd96d5d..8a99f46 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -5,7 +5,7 @@
 #from mdmrfunctions import *
 
 class MDMR(IndependenceTest):
-    def __init__(self, data_matrix_X, data_matrix_Y, compute_distance_matrix):
+    def __init__(self, compute_distance_matrix):
         '''
         :param data_matrix_X: is interpreted as:
             - a [n*d] data matrix, a square matrix with n samples in d dimensions
@@ -16,12 +16,12 @@ def __init__(self, data_matrix_X, data_matrix_Y, compute_distance_matrix):
         :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
         :type compute_distance_matrix: FunctionType or callable()
         '''
-        IndependenceTest.__init__(self, data_matrix_X, data_matrix_Y, compute_distance_matrix)
+        IndependenceTest.__init__(self, compute_distance_matrix)
     
     def get_name(self):
         return "MDMR"
     
-    def test_statistic(self, data_matrix_X=None, data_matrix_Y=None, permutations = 1000, individual = 0, disttype = 'cityblock'):
+    def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual = 0, disttype = 'cityblock'):
         """
         Computes MDMR between two datasets.
         - It first takes the distance matrix of Y (by )
@@ -40,9 +40,6 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None, permutations =
         with individual = 1, returns the above as well as an array with the 
         variable of X in the first column, the test statistic in the 2nd, and the permutation p-value in the 3rd
         """
-        if data_matrix_X is None and data_matrix_Y is None:
-            data_matrix_X = self.data_matrix_X
-            data_matrix_Y = self.data_matrix_Y
         X = data_matrix_X
         Y = data_matrix_Y
         
@@ -107,17 +104,17 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None, permutations =
                                     df_among, df_resid)
                 
                 p_vals = fperms_to_pvals(F_perms)
-                results[col-1,0] = col
+                results[col-1,0] = colg
                 results[col-1,1] = F_perms[0, :]
                 results[col-1,2] = p_vals
     
     
             return F_permtotal, pvaltotal, results
 
-    def p_value(self, data_matrix_X=None, data_matrix_Y=None, permutations = 1000, individual = 0, disttype = 'cityblock'):
+    def p_value(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual = 0, disttype = 'cityblock'):
         """
         Computes the p-value of the pseudo-F test statistic.
         """
-        p_value = self.test_statistic()[1]
+        p_value = self.test_statistic(data_matrix_X, data_matrix_Y)[1]
         
         return p_value
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index 1c1614e..6efcc85 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -5,20 +5,18 @@
 
 def test_mdmr():
     #load data from csv files
-    csv1 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv', delimiter=",")
-    X = csv1
+    X = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv', delimiter=",")
     
-    csv2 = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
-    Y = csv2
-    
-    mdmr = MDMR(csv1, csv2, compute_distance_matrix)
+    Y = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
+
+    mdmr = MDMR(compute_distance_matrix)
     
     #test get_name
     assert mdmr.get_name() == 'MDMR'
     
     #test statistic
-    assert np.allclose(mdmr.test_statistic()[0], 25.03876688)
+    assert np.allclose(mdmr.test_statistic(X, Y)[0], 25.03876688)
     
     #p-value
-    assert np.allclose(mdmr.test_statistic()[1], 0.000999)
+    assert np.allclose(mdmr.test_statistic(X, Y)[1], 0.000999)
     
\ No newline at end of file

From 2d43457d05b19f250fe36a11fb84557bfa8d1307 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Thu, 29 Nov 2018 16:12:32 -0500
Subject: [PATCH 12/60] add unit test for individual statistics

---
 mgcpy/independence_tests/mdmr/mdmr.py             |  2 +-
 .../unit_tests/mdmr/mdmr_test.py                  | 15 ++++++++++++---
 2 files changed, 13 insertions(+), 4 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 8a99f46..b749244 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -104,7 +104,7 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 1000, indi
                                     df_among, df_resid)
                 
                 p_vals = fperms_to_pvals(F_perms)
-                results[col-1,0] = colg
+                results[col-1,0] = col
                 results[col-1,1] = F_perms[0, :]
                 results[col-1,2] = p_vals
     
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index 6efcc85..399534d 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -10,13 +10,22 @@ def test_mdmr():
     Y = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
 
     mdmr = MDMR(compute_distance_matrix)
+    a, b, results = mdmr.test_statistic(X, Y, individual=1)
     
     #test get_name
     assert mdmr.get_name() == 'MDMR'
     
     #test statistic
-    assert np.allclose(mdmr.test_statistic(X, Y)[0], 25.03876688)
+    assert np.allclose(a, 25.03876688)
     
     #p-value
-    assert np.allclose(mdmr.test_statistic(X, Y)[1], 0.000999)
-    
\ No newline at end of file
+    assert np.allclose(b, 0.000999)
+    assert np.allclose(mdmr.p_value(X, Y)[0], 0.000999)
+    
+    #individual statistics
+    assert np.allclose(results[0,1], -13.702988)
+    assert np.allclose(results[0,2], 0.000999)
+    assert np.allclose(results[1,1], -22.6870867)
+    assert np.allclose(results[1,2], 0.000999)
+    assert np.allclose(results[2,1], -13.702988)
+    assert np.allclose(results[2,2], -2.70117626)
\ No newline at end of file

From 221460ab29fa7762db7f947befe6fad214217dd9 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Thu, 29 Nov 2018 16:28:13 -0500
Subject: [PATCH 13/60] fix mdmr individual unit test

---
 mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index 399534d..e699764 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -27,5 +27,5 @@ def test_mdmr():
     assert np.allclose(results[0,2], 0.000999)
     assert np.allclose(results[1,1], -22.6870867)
     assert np.allclose(results[1,2], 0.000999)
-    assert np.allclose(results[2,1], -13.702988)
-    assert np.allclose(results[2,2], -2.70117626)
\ No newline at end of file
+    assert np.allclose(results[2,1], -2.70117626)
+    assert np.allclose(results[2,2], 0.000999)
\ No newline at end of file

From 9f04009060525e3fa63550bbe17703430f50791c Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Fri, 30 Nov 2018 01:45:21 -0500
Subject: [PATCH 14/60] add docstrings and correct mdmr.test_statistic

---
 mgcpy/independence_tests/mdmr/mdmr.py         |  4 +-
 .../independence_tests/mdmr/mdmrfunctions.py  | 46 ++++++++++++++++---
 2 files changed, 42 insertions(+), 8 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index b749244..16d3abf 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -21,7 +21,7 @@ def __init__(self, compute_distance_matrix):
     def get_name(self):
         return "MDMR"
     
-    def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual = 0, disttype = 'cityblock'):
+    def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individual = 0, disttype = 'cityblock'):
         """
         Computes MDMR between two datasets.
         - It first takes the distance matrix of Y (by )
@@ -115,6 +115,6 @@ def p_value(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual
         """
         Computes the p-value of the pseudo-F test statistic.
         """
-        p_value = self.test_statistic(data_matrix_X, data_matrix_Y)[1]
+        p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
         
         return p_value
diff --git a/mgcpy/independence_tests/mdmr/mdmrfunctions.py b/mgcpy/independence_tests/mdmr/mdmrfunctions.py
index 9032464..7a19f9a 100644
--- a/mgcpy/independence_tests/mdmr/mdmrfunctions.py
+++ b/mgcpy/independence_tests/mdmr/mdmrfunctions.py
@@ -11,6 +11,9 @@
 ITYPE = np.int32
 
 def check_rank(X):
+    """
+    This function checks if X is rank deficient.
+    """
     k    = X.shape[1]
     rank = np.linalg.matrix_rank(X)
     if rank < k:
@@ -21,11 +24,17 @@ def compute_distance_matrix(X, disttype):
     return D
         
 def hatify(X):
+    """
+    Returns the "hat" matrix, X*(X.T *X)^-1 *X.T
+    """
     Q1, _ = np.linalg.qr(X)
     H = Q1.dot(Q1.T)
     return H
 
 def gower_center(Y):
+    """
+    Computes Gower's centered similarity matrix.
+    """
     n = Y.shape[0]
     I = np.eye(n,n)
     uno = np.ones((n, 1))
@@ -37,6 +46,9 @@ def gower_center(Y):
     return G
 
 def gower_center_many(Ys):
+    """
+    Gower centers each matrix in the input.
+    """
     observations = int(np.sqrt(Ys.shape[0]))
     tests        = Ys.shape[1]
     Gs           = np.zeros_like(Ys)
@@ -49,10 +61,13 @@ def gower_center_many(Ys):
     return Gs
 
 
-def gen_h(x, columns, permutations):
-    return hatify(x[permutations][:, np.array(columns)])
-
 def gen_H2_perms_single(X, columns, permutation_indexes):
+    """
+    Return H2 for each permutation of X indices, where H2 is the hat matrix
+    minus the hat matrix of the untested columns.
+    
+    The function calculates this correctly for single column tests.
+    """
     permutations, observations = permutation_indexes.shape
     variables = X.shape[1]
     
@@ -63,15 +78,18 @@ def gen_H2_perms_single(X, columns, permutation_indexes):
         fix = cols_X.shape[0]
         cols_X = cols_X.reshape((fix,1))
         H = hatify(cols_X)
-#        H = hatify(perm_X)
         other_columns = [i for i in range(variables) if i != columns]
         H2 = H - hatify(X[:, other_columns])
-#        H2 = H
         H2_permutations[:, i] = H2.flatten()
     
     return H2_permutations
 
 def gen_IH_perms_single(X, columns, permutation_indexes):
+    """
+    Return I-H where H is the hat matrix and I is the identity matrix.
+    
+    The function calculates this correctly for single column tests.
+    """
     permutations, observations = permutation_indexes.shape
     I = np.eye(observations, observations)
     
@@ -81,12 +99,17 @@ def gen_IH_perms_single(X, columns, permutation_indexes):
         fix = cols_X.shape[0]
         cols_X = cols_X.reshape((fix,1))
         IH = I - hatify(cols_X)
-#        IH = I - hatify(X[permutation_indexes[i, :]])
         IH_permutations[:,i] = IH.flatten()
     
     return IH_permutations
 
 def gen_H2_perms(X, columns, permutation_indexes):
+    """
+    Return H2 for each permutation of X indices, where H2 is the hat matrix
+    minus the hat matrix of the untested columns.
+    
+    The function calculates this correctly for multiple column tests.
+    """
     permutations, observations = permutation_indexes.shape
     variables = X.shape[1]
     
@@ -102,6 +125,11 @@ def gen_H2_perms(X, columns, permutation_indexes):
     return H2_permutations
 
 def gen_IH_perms(X, columns, permutation_indexes):
+    """
+    Return I-H where H is the hat matrix and I is the identity matrix.
+    
+    The function calculates this correctly for multiple column tests.
+    """
     permutations, observations = permutation_indexes.shape
     I            = np.eye(observations, observations)
     
@@ -113,12 +141,18 @@ def gen_IH_perms(X, columns, permutation_indexes):
     return IH_permutations
 
 def calc_ftest(Hs, IHs, Gs, m2, nm):
+    """
+    This function calculates the pseudo-F statistic.
+    """
     N = Hs.T.dot(Gs)
     D = IHs.T.dot(Gs)
     F = (N / m2) / (D / nm)
     return F
 
 def fperms_to_pvals(F_perms):
+    """
+    This function calculates the permutation p-value from the test statistics of all permutations.
+    """
     permutations, tests = F_perms.shape
     pvals = np.zeros(tests)
     for i in range(tests):

From e5fcf980eb9bf5555f50f01bc31ae272e5bb1a23 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Fri, 30 Nov 2018 01:59:34 -0500
Subject: [PATCH 15/60] correct mdmr unit test

---
 mgcpy/independence_tests/mdmr/mdmr.py         | 14 ++++++++-----
 .../unit_tests/mdmr/mdmr_test.py              | 20 +++++++++----------
 2 files changed, 19 insertions(+), 15 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 16d3abf..9cfe4e8 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -19,7 +19,7 @@ def __init__(self, compute_distance_matrix):
         IndependenceTest.__init__(self, compute_distance_matrix)
     
     def get_name(self):
-        return "MDMR"
+        return "mdmr"
     
     def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individual = 0, disttype = 'cityblock'):
         """
@@ -113,8 +113,12 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
 
     def p_value(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual = 0, disttype = 'cityblock'):
         """
-        Computes the p-value of the pseudo-F test statistic.
+        Computes the permutation p-value of the pseudo-F test statistic.
         """
-        p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
-        
-        return p_value
+        if individual = 0:
+            p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
+            return p_value
+        if individual = 1:
+            p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
+            results = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[2]
+            return p_value, results
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index e699764..d27c2d0 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -10,22 +10,22 @@ def test_mdmr():
     Y = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
 
     mdmr = MDMR(compute_distance_matrix)
-    a, b, results = mdmr.test_statistic(X, Y, individual=1)
+    a, b1, results1 = mdmr.test_statistic(X, Y, individual=1)
+    b2, results2 = mdmr.test_statistic(X, Y, individual = 1)
     
     #test get_name
-    assert mdmr.get_name() == 'MDMR'
+    assert mdmr.get_name() == 'mdmr'
     
     #test statistic
     assert np.allclose(a, 25.03876688)
     
     #p-value
-    assert np.allclose(b, 0.000999)
-    assert np.allclose(mdmr.p_value(X, Y)[0], 0.000999)
+    assert np.allclose(b2, 0.000999)
     
     #individual statistics
-    assert np.allclose(results[0,1], -13.702988)
-    assert np.allclose(results[0,2], 0.000999)
-    assert np.allclose(results[1,1], -22.6870867)
-    assert np.allclose(results[1,2], 0.000999)
-    assert np.allclose(results[2,1], -2.70117626)
-    assert np.allclose(results[2,2], 0.000999)
\ No newline at end of file
+    assert np.allclose(results1[0,1], -13.702988)
+    assert np.allclose(results2[0,2], 0.000999)
+    assert np.allclose(results1[1,1], -22.6870867)
+    assert np.allclose(results2[1,2], 0.000999)
+    assert np.allclose(results1[2,1], -2.70117626)
+    assert np.allclose(results2[2,2], 0.000999)
\ No newline at end of file

From 1973d4ebc196baf33e6b9e164a6e48ea2cf608ff Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Fri, 30 Nov 2018 02:06:55 -0500
Subject: [PATCH 16/60] changed '=' to '=='

---
 mgcpy/independence_tests/mdmr/mdmr.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 9cfe4e8..6af7f1e 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -115,10 +115,10 @@ def p_value(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual
         """
         Computes the permutation p-value of the pseudo-F test statistic.
         """
-        if individual = 0:
+        if individual == 0:
             p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
             return p_value
-        if individual = 1:
+        if individual == 1:
             p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
             results = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[2]
             return p_value, results

From 6887e585dec9ac6b02ee79268ce66a51c66fa406 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Fri, 30 Nov 2018 02:20:05 -0500
Subject: [PATCH 17/60] correct mdmr unit test

---
 mgcpy/independence_tests/mdmr/mdmr.py                 | 4 ++--
 mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 6af7f1e..9f96101 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -119,6 +119,6 @@ def p_value(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual
             p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
             return p_value
         if individual == 1:
-            p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
-            results = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[2]
+            p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations, individual)[1]
+            results = self.test_statistic(data_matrix_X, data_matrix_Y, permutations, individual)[2]
             return p_value, results
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index d27c2d0..b1bcc15 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -11,7 +11,7 @@ def test_mdmr():
 
     mdmr = MDMR(compute_distance_matrix)
     a, b1, results1 = mdmr.test_statistic(X, Y, individual=1)
-    b2, results2 = mdmr.test_statistic(X, Y, individual = 1)
+    b2, results2 = mdmr.p_value(X, Y, individual = 1)
     
     #test get_name
     assert mdmr.get_name() == 'mdmr'

From 04d5ea8aeda966c986ec070d7f6abc784d59c4f8 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 30 Nov 2018 08:12:39 -0500
Subject: [PATCH 18/60] Add test back

---
 mgcpy/independence_tests/hhg.py               | 131 ++++++++++++++++++
 mgcpy/independence_tests/rv_corr.py           | 131 ++++++++++++++++++
 .../unit_tests/rv_corr_test.py                |  49 +++++++
 3 files changed, 311 insertions(+)
 create mode 100644 mgcpy/independence_tests/hhg.py
 create mode 100644 mgcpy/independence_tests/rv_corr.py
 create mode 100644 mgcpy/independence_tests/unit_tests/rv_corr_test.py

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
new file mode 100644
index 0000000..307782e
--- /dev/null
+++ b/mgcpy/independence_tests/hhg.py
@@ -0,0 +1,131 @@
+import numpy as np
+from mgcpy.independence_tests.abstract_class import IndependenceTest
+from scipy.spatial import distance_matrix
+
+
+class HHG(IndependenceTest):
+    def __init__(self, compute_distance_matrix=None):
+        """
+        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
+        :type compute_distance_matrix: FunctionType or callable()
+        """
+        IndependenceTest.__init__(compute_distance_matrix)
+
+    def get_name(self):
+        '''
+        :return: the name of the independence test
+        :rtype: string
+        '''
+        return 'hhg'
+
+    def test_statistic(self, matrix_X, matrix_Y):
+        """
+        Computes the HHG correlation measure between two datasets.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :test_statistic_: test statistic
+            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                         that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.hhg import HHG
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> hhg = HHG()
+        >>> hhg_test_stat = hhg.test_statistic(X, Y)
+        """
+        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
+        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
+
+        # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not
+        if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0:
+            dist_mtx_X = distance_matrix(matrix_X, matrix_X)
+        else:
+            dist_mtx_X = matrix_X
+        if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0:
+            dist_mtx_Y = distance_matrix(matrix_Y, matrix_Y)
+        else:
+            dist_mtx_Y = matrix_Y
+
+        n = dist_mtx_X.shape[0]
+        S = np.zeros((n, n))
+
+        for i in range(n):
+            for j in range(n):
+                if i != j:
+                    tmp1 = dist_mtx_X[i, :] <= dist_mtx_X[i, j]
+                    tmp2 = dist_mtx_Y[i, :] <= dist_mtx_Y[i, j]
+                    t11 = np.sum(tmp1 * tmp2) - 2
+                    t12 = np.sum(tmp1 * (1-tmp2))
+                    t21 = np.sum((1-tmp1) * tmp2)
+                    t22 = np.sum((1-tmp1) * (1-tmp2))
+                    denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22)
+                    if denom > 0:
+                        S[i, j] = (n-2) * \
+                            np.power((t12*t21 - t11*t22), 2) / denom
+        corr = np.sum(S)
+
+        # no metadata for HHG
+        self.test_statistic_metadata_ = {}
+        self.test_statistic_ = corr
+        
+        return self.test_statistic_, self.test_statistic_metadata_
+
+    def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
+        """
+        Tests independence between two datasets using HHG and permutation test.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :p_value_: P-value
+            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                 that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.hhg import HHG
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> hhg = HHG()
+        >>> hhg_p_value = hhg.p_value(X, Y)
+        """
+        test_stat = self.test_statistic()
+        # estimate the null by a permutation test
+        test_stats_null = np.zeros(replication_factor)
+        for rep in range(replication_factor):
+            permuted_y = np.random.permutation(self.matrix_Y)
+            test_stats_null[rep] = self.test_statistic(matrix_X=self.matrix_X, matrix_Y=permuted_y)
+
+        # p-value is the probability of observing more extreme test statistic under the null
+        self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
+        self.p_value_metadata_ = {}
+        
+        return self.p_value_, self.p_value_metadata_
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
new file mode 100644
index 0000000..a207bb4
--- /dev/null
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -0,0 +1,131 @@
+import numpy as np
+from mgcpy.independence_tests.abstract_class import IndependenceTest
+from numpy import matlib as mb
+from scipy.sparse.linalg import svds
+from scipy.stats import pearsonr
+
+
+class RVCorr(IndependenceTest):
+    def __init__(self, compute_distance_matrix=None, which_test='rv'):
+        """
+        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
+        :type compute_distance_matrix: FunctionType or callable()
+
+        :param which_test: specifies which test to use, including 'rv', 'pearson', and 'cca'.
+        :type which_test: str
+        """
+        IndependenceTest.__init__(self, compute_distance_matrix)
+        self.which_test = which_test
+
+    def get_name(self):
+        '''
+        :return: the name of the independence test
+        :rtype: string
+        '''
+        return self.which_test
+
+    def test_statistic(self, matrix_X=None, matrix_Y=None):
+        """
+        Computes the Pearson/RV/CCa correlation measure between two datasets.
+        - Default computes linear correlation for RV
+        - Computes pearson's correlation
+        - Calculates local linear correlations for CCa
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :test_statistic_: test statistic
+            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                         that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.rv_corr import RVCorr
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> rvcorr = RVCorr()
+        >>> rvcorr_test_stat = rvcorr.test_statistic(X, Y)
+        """
+        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
+        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
+
+        mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0),
+                                         matrix_X.shape[0], 1)
+        mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0),
+                                         matrix_Y.shape[0], 1)
+
+        covar = np.dot(mat1.T, mat2)
+        varX = np.dot(mat1.T, mat1)
+        varY = np.dot(mat2.T, mat2)
+
+        if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)):
+            corr, covar = pearsonr(matrix_X, matrix_Y)
+        elif (self.which_test == 'rv'):
+            covar = np.trace(np.dot(covar, covar.T))
+            corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX))
+                                            * np.trace(np.dot(varY, varY))))
+        else:
+            if varX.size == 1 or varY.size == 1 or covar.size == 1:
+                covar = np.sum(np.power(covar, 2))
+                corr = np.divide(covar, np.sqrt(np.sum(np.power(varX, 2))
+                                                * np.sum(np.power(varY, 2))))
+            else:
+                covar = np.sum(np.power(svds(covar, 1)[1], 2))
+                corr = np.divide(covar, np.sqrt(np.sum(np.power(svds(varX, 1)[1], 2))
+                                                * np.sum(np.power(svds(varY, 1)[1], 2))))
+        self.test_statistic_ = corr
+        self.test_statistic_metadata_ = {"covariance": covar}
+
+        return self.test_statistic_, self.test_statistic_metadata_
+
+    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
+        """
+        Tests independence between two datasets using the independence test.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :p_value_: P-value
+            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                 that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.rv_corr import RVCorr
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> rvcorr = RVCorr()
+        >>> rvcorr_p_value = rvcorr.p_value(X, Y)
+        """
+        if matrix_X is None:
+            matrix_X = self.matrix_X
+        if matrix_Y is None:
+            matrix_Y = self.matrix_Y
+        self.p_value_ = self.test_statistic(matrix_X, matrix_Y)
+        self.p_value_metadata_ = {}
+
+        return self.p_value_, self.p_value_metadata_
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
new file mode 100644
index 0000000..27b3e2b
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -0,0 +1,49 @@
+import mgcpy.benchmarks.simulations as sims
+import numpy as np
+from mgcpy.independence_tests.rv_corr import RVCorr
+
+# from scipy.io import savemat
+
+
+def test_local_corr():
+    # Against a randomly defined data set
+    X = np.array([1.1728, 2.4941, 2.4101, 0.1814, 1.1978, 1.5806, 1.2504,
+                  1.9706, 1.8839, 0.8760])[:, np.newaxis]
+    Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917,
+                  7.1748, 6.5792, 2.4012])[:, np.newaxis]
+    rvcorr = RVCorr(None)
+    rvcorr2 = RVCorr(None, 'pearson')
+    rvcorr3 = RVCorr(None, 'cca')
+
+    test_stat1 = rvcorr.test_statistic(X, Y)[0]
+    test_stat2 = rvcorr2.test_statistic(X, Y)[0]
+    test_stat3 = rvcorr3.test_statistic(X, Y)[0]
+
+    assert np.round(test_stat1, decimals=2) == 0.90
+    assert np.round(test_stat2, decimals=2) == 0.95
+    assert np.round(test_stat3, decimals=2) == 0.90
+
+    del X, Y, rvcorr, rvcorr2, rvcorr3, test_stat1, test_stat2, test_stat3
+
+    # Against linear simulations
+    np.random.seed(0)
+    X, Y = sims.linear_sim(100, 1)
+    # savemat('distance matrix data', {'X' : X, 'Y' : Y})
+    rvcorr = RVCorr(None)
+    rvcorr2 = RVCorr(None, 'pearson')
+    rvcorr3 = RVCorr(None, 'cca')
+
+    assert rvcorr.get_name() == 'rv'
+    assert rvcorr2.get_name() == 'pearson'
+    assert rvcorr3.get_name() == 'cca'
+
+    test_stat1 = rvcorr.test_statistic(X, Y)[0]
+    test_stat2 = rvcorr2.test_statistic(X, Y)[0]
+    test_stat3 = rvcorr3.test_statistic(X, Y)[0]
+
+    assert np.round(test_stat1, decimals=2) == 0.24
+    assert np.round(test_stat2, decimals=2) == 0.49
+    assert np.round(test_stat3, decimals=2) == 0.24
+
+
+test_local_corr()

From ae83c07365ae91606ea3e9b977482aa6c355ba82 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 30 Nov 2018 11:15:29 -0500
Subject: [PATCH 19/60] Edited the test and added demo

---
 demos/mcorr_dcorr_mantel.ipynb                |   2 +-
 demos/rv_cca_hhg.ipynb                        | 264 ++++++++++++++++++
 mgcpy/independence_tests/hhg.py               |  15 +-
 mgcpy/independence_tests/kendall_spearman.py  |  38 ++-
 mgcpy/independence_tests/rv_corr.py           |  21 +-
 .../independence_tests/unit_tests/hhg_test.py |  27 +-
 .../unit_tests/kendall_spearman_test.py       |  35 +++
 .../unit_tests/rv_corr_test.py                |  17 +-
 8 files changed, 347 insertions(+), 72 deletions(-)
 create mode 100644 demos/rv_cca_hhg.ipynb
 create mode 100644 mgcpy/independence_tests/unit_tests/kendall_spearman_test.py

diff --git a/demos/mcorr_dcorr_mantel.ipynb b/demos/mcorr_dcorr_mantel.ipynb
index 1f7727b..04fff1d 100644
--- a/demos/mcorr_dcorr_mantel.ipynb
+++ b/demos/mcorr_dcorr_mantel.ipynb
@@ -435,7 +435,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.4"
+   "version": "3.6.6"
   }
  },
  "nbformat": 4,
diff --git a/demos/rv_cca_hhg.ipynb b/demos/rv_cca_hhg.ipynb
new file mode 100644
index 0000000..3a064f3
--- /dev/null
+++ b/demos/rv_cca_hhg.ipynb
@@ -0,0 +1,264 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 174,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy.spatial.distance import pdist, squareform\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 175,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from mgcpy import RVCorr, HHG\n",
+    "from mgcpy.benchmarks.power import power\n",
+    "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, ubern_sim, exp_sim, w_sim, joint_sim, spiral_sim"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Statistic"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 176,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def test_stats_vs_dimension(corr_type, simulation_type, dim_range):\n",
+    "    test_stats = []\n",
+    "    for d in range(1, dim_range+1):\n",
+    "        x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n",
+    "        if corr_type == 'rv' or corr_type == 'cca':\n",
+    "            corr = RVCorr(which_test=corr_type)\n",
+    "        #else:\n",
+    "            #corr = HHG()\n",
+    "        test_stats.append(corr.test_statistic(x, y)[0])\n",
+    "    return test_stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 177,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_test_stats(simulation_type, dim_range, simulation_name):\n",
+    "    rv_test_stats = test_stats_vs_dimension('rv', simulation_type, dim_range)\n",
+    "    cca_test_stats = test_stats_vs_dimension('cca', simulation_type, dim_range)\n",
+    "    #hhg_test_stats = test_stats_vs_dimension('hhg', simulation_type, dim_range) \n",
+    "    plt.plot(rv_test_stats, label='RV')\n",
+    "    plt.plot(cca_test_stats, label='CCA')\n",
+    "    #plt.plot(hhg_test_stats, label='HHG')\n",
+    "    plt.xlabel('Dimensions')\n",
+    "    plt.ylabel('Test Statistics')\n",
+    "    plt.legend()\n",
+    "    plt.gca().set_xlim(1, dim_range+1)\n",
+    "    plt.xticks(np.arange(0, dim_range+1, 5))\n",
+    "    plt.title('Test Statistics \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 178,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_test_stats(linear_sim, 20, 'Linear')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 179,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_test_stats(spiral_sim, 20, 'Spiral')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 180,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_test_stats(quad_sim, 20, 'Quadratic')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## P-value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 184,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def pvalue_vs_dimension(corr_type, simulation_type, dim_range):\n",
+    "    p_value = []\n",
+    "    for d in range(1, dim_range+1):\n",
+    "        x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n",
+    "        if corr_type == 'rv' or corr_type == 'cca':\n",
+    "            corr = RVCorr(which_test=corr_type)\n",
+    "        #else:\n",
+    "            #corr = HHG()\n",
+    "        p_value.append(corr.p_value(x, y)[0])\n",
+    "    return p_value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 185,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_p_value(simulation_type, dim_range, simulation_name):\n",
+    "    rv_pvalue = pvalue_vs_dimension('rv', simulation_type, dim_range)\n",
+    "    cca_pvalue = pvalue_vs_dimension('cca', simulation_type, dim_range)\n",
+    "    #hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\n",
+    "    plt.plot(rv_pvalue, label='RV')\n",
+    "    plt.plot(cca_pvalue, label='CCA')\n",
+    "    #plt.plot(hhg_pvalue, label='HHG')\n",
+    "    plt.xlabel('Dimensions')\n",
+    "    plt.ylabel('pvalue')\n",
+    "    plt.legend()\n",
+    "    plt.gca().set_xlim(1, dim_range+1)\n",
+    "    plt.xticks(np.arange(0, dim_range+1, 5))\n",
+    "    plt.title('P-value \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 186,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "TypeError",
+     "evalue": "float() argument must be a string or a number, not 'dict'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-186-0052d0a51dfd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_p_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlinear_sim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Linear'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-185-5ab204793fab>\u001b[0m in \u001b[0;36mplot_p_value\u001b[0;34m(simulation_type, dim_range, simulation_name)\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mcca_pvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpvalue_vs_dimension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'cca'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msimulation_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;31m#hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'RV'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcca_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'CCA'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0;31m#plt.plot(hhg_pvalue, label='HHG')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2747\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2748\u001b[0m     return gca().plot(\n\u001b[0;32m-> 2749\u001b[0;31m         *args, scalex=scalex, scaley=scaley, data=data, **kwargs)\n\u001b[0m\u001b[1;32m   2750\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2751\u001b[0m \u001b[0;31m# Autogenerated by boilerplate.py.  Do not edit as changes will be lost.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1783\u001b[0m                         \u001b[0;34m\"the Matplotlib list!)\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1784\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1785\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1786\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1787\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1603\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1604\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1605\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1606\u001b[0m             \u001b[0mlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1607\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36madd_line\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m   1883\u001b[0m             \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_clip_path\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpatch\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1884\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1885\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_update_line_limits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1886\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_label\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1887\u001b[0m             \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_label\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'_line%d'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlines\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_update_line_limits\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m   1905\u001b[0m         \u001b[0mFigures\u001b[0m \u001b[0mout\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mdata\u001b[0m \u001b[0mlimit\u001b[0m \u001b[0mof\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mgiven\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mupdating\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdataLim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1906\u001b[0m         \"\"\"\n\u001b[0;32m-> 1907\u001b[0;31m         \u001b[0mpath\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_path\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1908\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1909\u001b[0m             \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/lines.py\u001b[0m in \u001b[0;36mget_path\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    943\u001b[0m         \"\"\"\n\u001b[1;32m    944\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_invalidy\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_invalidx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 945\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecache\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    946\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    947\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/lines.py\u001b[0m in \u001b[0;36mrecache\u001b[0;34m(self, always)\u001b[0m\n\u001b[1;32m    643\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0malways\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_invalidy\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    644\u001b[0m             \u001b[0myconv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconvert_yunits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_yorig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 645\u001b[0;31m             \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_to_unmasked_float_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0myconv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mravel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    646\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    647\u001b[0m             \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_y\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/cbook/__init__.py\u001b[0m in \u001b[0;36m_to_unmasked_float_array\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m   1363\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfilled\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1364\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1365\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1366\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1367\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m    499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    500\u001b[0m     \"\"\"\n\u001b[0;32m--> 501\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    503\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mTypeError\u001b[0m: float() argument must be a string or a number, not 'dict'"
+     ]
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_p_value(linear_sim, 20, 'Linear')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 307782e..4edb962 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -1,6 +1,5 @@
 import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
-from scipy.spatial import distance_matrix
 
 
 class HHG(IndependenceTest):
@@ -54,11 +53,11 @@ def test_statistic(self, matrix_X, matrix_Y):
 
         # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not
         if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0:
-            dist_mtx_X = distance_matrix(matrix_X, matrix_X)
+            dist_mtx_X = self.compute_distance_matrix(matrix_X)
         else:
             dist_mtx_X = matrix_X
         if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0:
-            dist_mtx_Y = distance_matrix(matrix_Y, matrix_Y)
+            dist_mtx_Y = self.compute_distance_matrix(matrix_Y)
         else:
             dist_mtx_Y = matrix_Y
 
@@ -84,7 +83,7 @@ def test_statistic(self, matrix_X, matrix_Y):
         self.test_statistic_metadata_ = {}
         self.test_statistic_ = corr
         
-        return self.test_statistic_, self.test_statistic_metadata_
+        return corr, {}
 
     def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
         """
@@ -117,15 +116,15 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
         >>> hhg = HHG()
         >>> hhg_p_value = hhg.p_value(X, Y)
         """
-        test_stat = self.test_statistic()
+        test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0]
         # estimate the null by a permutation test
         test_stats_null = np.zeros(replication_factor)
         for rep in range(replication_factor):
-            permuted_y = np.random.permutation(self.matrix_Y)
-            test_stats_null[rep] = self.test_statistic(matrix_X=self.matrix_X, matrix_Y=permuted_y)
+            permuted_y = np.random.permutation(matrix_Y)
+            test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0]
 
         # p-value is the probability of observing more extreme test statistic under the null
         self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
         self.p_value_metadata_ = {}
         
-        return self.p_value_, self.p_value_metadata_
+        return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {}
\ No newline at end of file
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
index acf2b68..10c0cce 100644
--- a/mgcpy/independence_tests/kendall_spearman.py
+++ b/mgcpy/independence_tests/kendall_spearman.py
@@ -49,30 +49,27 @@ def test_statistic(self, matrix_X, matrix_Y):
         >>> kendall_spearman = KendallSpearman()
         >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y)
         """
-        if matrix_X is None:
-            matrix_X = self.matrix_X
-        if matrix_Y is None:
-            matrix_Y = self.matrix_Y
         assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape"
         assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape"
-
-        if self.which_test == 'kendall':
-            self.test_statistic_ = kendalltau(matrix_X, matrix_Y)[0]
+        
+        if self.which_test == 'kendall':            
+            test_statistic_ = kendalltau(matrix_X, matrix_Y)[0]
         else:
-            self.test_statistic_ = spearmanr(matrix_X, matrix_Y)[0]
+            test_statistic_ = spearmanr(matrix_X, matrix_Y)[0]
 
+        self.test_statistic_ = test_statistic_
         self.test_statistic_metadata_ = {}
 
-        return self.test_statistic_, self.test_statistic_metadata_
+        return test_statistic_, {}
 
     def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         """
         Tests independence between two datasets using the independence test.
 
-        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :param matrix_X: a [n*1] data matrix, a square matrix with n samples in p dimensions
         :type matrix_X: 2D `numpy.array`
 
-        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in q dimensions
         :type matrix_Y: 2D `numpy.array`
 
         :param replication_factor: specifies the number of replications to use for
@@ -96,18 +93,17 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         >>> kendall_spearman = KendallSpearman()
         >>> kendall_spearman_p_value = kendall_spearman.p_value(X, Y)
         """
-        if matrix_X is None:
-            matrix_X = self.matrix_X
-        if matrix_Y is None:
-            matrix_Y = self.matrix_Y
-        assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape"
-        assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape"
-
+        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
+        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
+        assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape"
+        assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape"
+        
         if self.which_test == 'kendall':
-            self.p_value_ = kendalltau(matrix_X, matrix_Y)[1]
+            p_value_ = kendalltau(matrix_X, matrix_Y)[1]
         else:
-            self.p_value_ = spearmanr(matrix_X, matrix_Y)[1]
+            p_value_ = spearmanr(matrix_X, matrix_Y)[1]
 
+        self.p_value_ = p_value_
         self.p_value_metadata_ = {}
 
-        return self.p_value_, self.p_value_metadata_
+        return p_value_, {}
\ No newline at end of file
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index a207bb4..1ac1b27 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -70,7 +70,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
         varX = np.dot(mat1.T, mat1)
         varY = np.dot(mat2.T, mat2)
 
-        if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)):
+        if (self.which_test == 'pearson'):
+            assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape"
+            assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape"
             corr, covar = pearsonr(matrix_X, matrix_Y)
         elif (self.which_test == 'rv'):
             covar = np.trace(np.dot(covar, covar.T))
@@ -88,9 +90,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
         self.test_statistic_ = corr
         self.test_statistic_metadata_ = {"covariance": covar}
 
-        return self.test_statistic_, self.test_statistic_metadata_
+        return corr, {"covariance": covar}
 
-    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
+    def p_value(self, matrix_X, matrix_Y, replication_factor=None):
         """
         Tests independence between two datasets using the independence test.
 
@@ -101,7 +103,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         :type matrix_Y: 2D `numpy.array`
 
         :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to 1000.
+                                   the permutation test. Defaults to None.
         :type replication_factor: int
 
         :return: returns a list of two items, that contains:
@@ -121,11 +123,8 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         >>> rvcorr = RVCorr()
         >>> rvcorr_p_value = rvcorr.p_value(X, Y)
         """
-        if matrix_X is None:
-            matrix_X = self.matrix_X
-        if matrix_Y is None:
-            matrix_Y = self.matrix_Y
-        self.p_value_ = self.test_statistic(matrix_X, matrix_Y)
+        test_stat = self.test_statistic(matrix_X, matrix_Y)[0]
+        self.p_value_ = np.abs(test_stat)
         self.p_value_metadata_ = {}
-
-        return self.p_value_, self.p_value_metadata_
+        
+        return np.abs(test_stat), {}
diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
index dbc0730..5379450 100644
--- a/mgcpy/independence_tests/unit_tests/hhg_test.py
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -1,14 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
-from mgcpy.independence_tests.hhg import HHG
-from scipy.spatial.distance import pdist, squareform
-
-
-def compute_distance_matrix(data_matrix_X, data_matrix_Y):
-    # obtain the pairwise distance matrix for X and Y
-    dist_mtx_X = squareform(pdist(data_matrix_X, metric='euclidean'))
-    dist_mtx_Y = squareform(pdist(data_matrix_Y, metric='euclidean'))
-    return (dist_mtx_X, dist_mtx_Y)
+from mgcpy import HHG
+import pytest
 
 
 def test_hhg():
@@ -17,24 +10,22 @@ def test_hhg():
                   1.9706, 1.8839, 0.8760])[:, np.newaxis]
     Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917,
                   7.1748, 6.5792, 2.4012])[:, np.newaxis]
-    hhg = HHG(X, Y, compute_distance_matrix)
-    test_stat = hhg.test_statistic()
+    hhg = HHG()
+    test_stat = hhg.test_statistic(X, Y)
 
     assert np.round(test_stat, decimals=2) == 411.88
 
     # Against linear simulations
     np.random.seed(0)
     X, Y = sims.linear_sim(100, 1)
-    hhg = HHG(X, Y, compute_distance_matrix)
-    test_stat = hhg.test_statistic()
+    hhg = HHG()
+    test_stat = hhg.test_statistic(X, Y)
 
     assert np.round(test_stat, decimals=2) == 28986.52
 
     X, Y = sims.linear_sim(100, 1, noise=0)
-    hhg = HHG(X, Y, compute_distance_matrix)
-    test_stat = hhg.test_statistic()
+    hhg = HHG()
+    test_stat = hhg.test_statistic(X, Y)
 
     assert np.round(test_stat, decimals=2) == 950600.00
-
-
-test_hhg()
+test_hhg()
\ No newline at end of file
diff --git a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
new file mode 100644
index 0000000..c9fa50f
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
@@ -0,0 +1,35 @@
+import mgcpy.benchmarks.simulations as sims
+import numpy as np
+from mgcpy import KendallSpearman
+import pytest
+
+
+def test_kendall_spearman():
+    # Against a randomly defined data set
+    X = np.array([1.1728, 2.4941, 2.4101, 0.1814, 1.1978, 1.5806, 1.2504,
+                  1.9706, 1.8839, 0.8760])[:, np.newaxis]
+    Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917,
+                  7.1748, 6.5792, 2.4012])[:, np.newaxis]
+    kspear = KendallSpearman(None)
+    kspear2 = KendallSpearman(None, 'spearman')
+
+    test_stat1 = kspear.test_statistic(X, Y)[0]
+    test_stat2 = kspear2.test_statistic(X, Y)[0]
+
+    assert np.round(test_stat1, decimals=2) == 1.00
+    assert np.round(test_stat2, decimals=2) == 1.00
+
+    # Against linear simulations
+    np.random.seed(0)
+    X, Y = sims.linear_sim(100, 1)
+    kspear = KendallSpearman(None)
+    kspear2 = KendallSpearman(None, 'spearman')
+
+    assert kspear.get_name() == 'kendall'
+    assert kspear2.get_name() == 'spearman'
+
+    test_stat1 = kspear.test_statistic(X, Y)[0]
+    test_stat2 = kspear2.test_statistic(X, Y)[0]
+
+    assert np.round(test_stat1, decimals=2) == 0.33
+    assert np.round(test_stat2, decimals=2) == 0.48
\ No newline at end of file
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
index 27b3e2b..439e3ee 100644
--- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -1,8 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
-from mgcpy.independence_tests.rv_corr import RVCorr
-
-# from scipy.io import savemat
+from mgcpy import RVCorr
+import pytest
 
 
 def test_local_corr():
@@ -14,21 +13,17 @@ def test_local_corr():
     rvcorr = RVCorr(None)
     rvcorr2 = RVCorr(None, 'pearson')
     rvcorr3 = RVCorr(None, 'cca')
-
+    
     test_stat1 = rvcorr.test_statistic(X, Y)[0]
     test_stat2 = rvcorr2.test_statistic(X, Y)[0]
     test_stat3 = rvcorr3.test_statistic(X, Y)[0]
-
     assert np.round(test_stat1, decimals=2) == 0.90
     assert np.round(test_stat2, decimals=2) == 0.95
     assert np.round(test_stat3, decimals=2) == 0.90
 
-    del X, Y, rvcorr, rvcorr2, rvcorr3, test_stat1, test_stat2, test_stat3
-
     # Against linear simulations
     np.random.seed(0)
     X, Y = sims.linear_sim(100, 1)
-    # savemat('distance matrix data', {'X' : X, 'Y' : Y})
     rvcorr = RVCorr(None)
     rvcorr2 = RVCorr(None, 'pearson')
     rvcorr3 = RVCorr(None, 'cca')
@@ -40,10 +35,6 @@ def test_local_corr():
     test_stat1 = rvcorr.test_statistic(X, Y)[0]
     test_stat2 = rvcorr2.test_statistic(X, Y)[0]
     test_stat3 = rvcorr3.test_statistic(X, Y)[0]
-
     assert np.round(test_stat1, decimals=2) == 0.24
     assert np.round(test_stat2, decimals=2) == 0.49
-    assert np.round(test_stat3, decimals=2) == 0.24
-
-
-test_local_corr()
+    assert np.round(test_stat3, decimals=2) == 0.24
\ No newline at end of file

From 574ad5f96617d4146ea91dfdc0f5b086988858ff Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 30 Nov 2018 11:31:11 -0500
Subject: [PATCH 20/60] Fixed docstrings

---
 mgcpy/independence_tests/hhg.py              | 22 +++++++--------
 mgcpy/independence_tests/kendall_spearman.py | 28 +++++++++++---------
 mgcpy/independence_tests/rv_corr.py          | 24 ++++++++++-------
 3 files changed, 41 insertions(+), 33 deletions(-)

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 4edb962..80751c9 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -1,3 +1,7 @@
+"""
+     **HHG Class**
+"""
+
 import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
 
@@ -6,7 +10,7 @@ class HHG(IndependenceTest):
     def __init__(self, compute_distance_matrix=None):
         """
         :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: FunctionType or callable()
+        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
         """
         IndependenceTest.__init__(compute_distance_matrix)
 
@@ -21,16 +25,12 @@ def test_statistic(self, matrix_X, matrix_Y):
         """
         Computes the HHG correlation measure between two datasets.
 
-        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions
         :type matrix_X: 2D `numpy.array`
 
-        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
         :type matrix_Y: 2D `numpy.array`
 
-        :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to 1000.
-        :type replication_factor: int
-
         :return: returns a list of two items, that contains:
             - :test_statistic_: test statistic
             - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
@@ -89,21 +89,21 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
         """
         Tests independence between two datasets using HHG and permutation test.
 
-        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions
         :type matrix_X: 2D `numpy.array`
 
-        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
         :type matrix_Y: 2D `numpy.array`
 
         :param replication_factor: specifies the number of replications to use for
                                    the permutation test. Defaults to 1000.
-        :type replication_factor: int
+        :type replication_factor: integer
 
         :return: returns a list of two items, that contains:
             - :p_value_: P-value
             - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
                                  that the independence tests computes in the process
-        :rtype: float, dict
+        :rtype: list
 
         **Example:**
         >>> import numpy as np
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
index 10c0cce..16a583b 100644
--- a/mgcpy/independence_tests/kendall_spearman.py
+++ b/mgcpy/independence_tests/kendall_spearman.py
@@ -1,3 +1,7 @@
+"""
+     **Kendall and Spearman Class**
+"""
+
 from mgcpy.independence_tests.abstract_class import IndependenceTest
 from scipy.stats import kendalltau, spearmanr
 
@@ -6,10 +10,10 @@ class KendallSpearman(IndependenceTest):
     def __init__(self, compute_distance_matrix=None, which_test='kendall'):
         """
         :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: FunctionType or callable()
+        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
 
-        :param which_test: specifies which test to use, including 'kendall' or 'spearman'
-        :type which_test: str
+        :param which_test: specifies which test to use, including ``'kendall'`` or ``'spearman'``
+        :type which_test: string
         """
         IndependenceTest.__init__(self, compute_distance_matrix)
         self.which_test = which_test
@@ -26,17 +30,17 @@ def test_statistic(self, matrix_X, matrix_Y):
         Computes the Spearman's rho or Kendall's tau measure between two datasets.
         - Implments scipy.stats's implementation for both
 
-        :param matrix_X: a [n*1] data matrix, a square matrix with n samples in 1 dimension
-        :type matrix_X: 1D numpy.array
+        :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension
+        :type matrix_X: 1D `numpy.array`
 
-        :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in 1 dimension
-        :type matrix_Y: 1D numpy.array
+        :param matrix_Y: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension
+        :type matrix_Y: 1D `numpy.array`
 
         :return: returns a list of two items, that contains:
             - :test_stat_: test statistic
             - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
                                          that the independence tests computes in the process
-        :rtype: float, dict
+        :rtype: list
 
         **Example:**
         >>> import numpy as np
@@ -66,21 +70,21 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         """
         Tests independence between two datasets using the independence test.
 
-        :param matrix_X: a [n*1] data matrix, a square matrix with n samples in p dimensions
+        :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension
         :type matrix_X: 2D `numpy.array`
 
-        :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in q dimensions
+        :param matrix_Y: a ``[n*1] data`` matrix, a square matrix with ``n`` samples in ``1`` dimensions
         :type matrix_Y: 2D `numpy.array`
 
         :param replication_factor: specifies the number of replications to use for
                                    the permutation test. Defaults to 1000.
-        :type replication_factor: int
+        :type replication_factor: integer
 
         :return: returns a list of two items, that contains:
             - :p_value_: P-value
             - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
                                  that the independence tests computes in the process
-        :rtype: float, dict
+        :rtype: list
 
         **Example:**
         >>> import numpy as np
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index 1ac1b27..61afb14 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -1,3 +1,7 @@
+"""
+     **RVCorr Class**
+"""
+ 
 import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
 from numpy import matlib as mb
@@ -9,10 +13,10 @@ class RVCorr(IndependenceTest):
     def __init__(self, compute_distance_matrix=None, which_test='rv'):
         """
         :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: FunctionType or callable()
+        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
 
-        :param which_test: specifies which test to use, including 'rv', 'pearson', and 'cca'.
-        :type which_test: str
+        :param which_test: specifies which test to use, including ``'rv'``, ``'pearson'``, and ``'cca'``.
+        :type which_test: string
         """
         IndependenceTest.__init__(self, compute_distance_matrix)
         self.which_test = which_test
@@ -31,10 +35,10 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
         - Computes pearson's correlation
         - Calculates local linear correlations for CCa
 
-        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions
         :type matrix_X: 2D `numpy.array`
 
-        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
         :type matrix_Y: 2D `numpy.array`
 
         :param replication_factor: specifies the number of replications to use for
@@ -45,7 +49,7 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
             - :test_statistic_: test statistic
             - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
                                          that the independence tests computes in the process
-        :rtype: float, dict
+        :rtype: list
 
         **Example:**
         >>> import numpy as np
@@ -96,21 +100,21 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None):
         """
         Tests independence between two datasets using the independence test.
 
-        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p``` dimensions
         :type matrix_X: 2D `numpy.array`
 
-        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
         :type matrix_Y: 2D `numpy.array`
 
         :param replication_factor: specifies the number of replications to use for
                                    the permutation test. Defaults to None.
-        :type replication_factor: int
+        :type replication_factor: integer
 
         :return: returns a list of two items, that contains:
             - :p_value_: P-value
             - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
                                  that the independence tests computes in the process
-        :rtype: float, dict
+        :rtype: list
 
         **Example:**
         >>> import numpy as np

From acf1d66afa3af0e12b3198c0e92d9e34a3a89d2f Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 30 Nov 2018 11:38:16 -0500
Subject: [PATCH 21/60] Fixed docstrings

---
 mgcpy/independence_tests/hhg.py              | 6 +++---
 mgcpy/independence_tests/kendall_spearman.py | 5 +++--
 mgcpy/independence_tests/rv_corr.py          | 6 +++---
 3 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 80751c9..42365e1 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -1,5 +1,5 @@
 """
-     **HHG Class**
+     **HHG Independence Test Module**
 """
 
 import numpy as np
@@ -38,9 +38,9 @@ def test_statistic(self, matrix_X, matrix_Y):
         :rtype: float, dict
 
         **Example:**
+        
         >>> import numpy as np
         >>> from mgcpy.independence_tests.hhg import HHG
-
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
                       0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
         >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
@@ -106,9 +106,9 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
         :rtype: list
 
         **Example:**
+        
         >>> import numpy as np
         >>> from mgcpy.independence_tests.hhg import HHG
-
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
                       0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
         >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
index 16a583b..9ee438b 100644
--- a/mgcpy/independence_tests/kendall_spearman.py
+++ b/mgcpy/independence_tests/kendall_spearman.py
@@ -1,5 +1,5 @@
 """
-     **Kendall and Spearman Class**
+     **Kendall and Spearman ndependence Test Module**
 """
 
 from mgcpy.independence_tests.abstract_class import IndependenceTest
@@ -43,6 +43,7 @@ def test_statistic(self, matrix_X, matrix_Y):
         :rtype: list
 
         **Example:**
+        
         >>> import numpy as np
         >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
 
@@ -87,9 +88,9 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         :rtype: list
 
         **Example:**
+        
         >>> import numpy as np
         >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
-
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
                       0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
         >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index 61afb14..ac0c70e 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -1,5 +1,5 @@
 """
-     **RVCorr Class**
+     **RVCorr Independence Test Module**
 """
  
 import numpy as np
@@ -52,9 +52,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
         :rtype: list
 
         **Example:**
+        
         >>> import numpy as np
         >>> from mgcpy.independence_tests.rv_corr import RVCorr
-
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
                       0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
         >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
@@ -117,9 +117,9 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None):
         :rtype: list
 
         **Example:**
+        
         >>> import numpy as np
         >>> from mgcpy.independence_tests.rv_corr import RVCorr
-
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
                       0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
         >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,

From 3d0e977a7d11694972b1dc3ce33d7717907d7145 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 30 Nov 2018 12:03:46 -0500
Subject: [PATCH 22/60] Pep8

---
 mgcpy/independence_tests/hhg.py                      | 10 +++++-----
 mgcpy/independence_tests/kendall_spearman.py         | 12 ++++++------
 mgcpy/independence_tests/rv_corr.py                  | 12 ++++++------
 mgcpy/independence_tests/unit_tests/hhg_test.py      |  6 ++++--
 .../unit_tests/kendall_spearman_test.py              |  4 ++--
 mgcpy/independence_tests/unit_tests/rv_corr_test.py  |  6 +++---
 6 files changed, 26 insertions(+), 24 deletions(-)

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 42365e1..7d9998b 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -38,7 +38,7 @@ def test_statistic(self, matrix_X, matrix_Y):
         :rtype: float, dict
 
         **Example:**
-        
+
         >>> import numpy as np
         >>> from mgcpy.independence_tests.hhg import HHG
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
@@ -82,7 +82,7 @@ def test_statistic(self, matrix_X, matrix_Y):
         # no metadata for HHG
         self.test_statistic_metadata_ = {}
         self.test_statistic_ = corr
-        
+
         return corr, {}
 
     def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
@@ -106,7 +106,7 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
         :rtype: list
 
         **Example:**
-        
+
         >>> import numpy as np
         >>> from mgcpy.independence_tests.hhg import HHG
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
@@ -126,5 +126,5 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
         # p-value is the probability of observing more extreme test statistic under the null
         self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
         self.p_value_metadata_ = {}
-        
-        return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {}
\ No newline at end of file
+
+        return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {}
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
index 9ee438b..096bb13 100644
--- a/mgcpy/independence_tests/kendall_spearman.py
+++ b/mgcpy/independence_tests/kendall_spearman.py
@@ -43,7 +43,7 @@ def test_statistic(self, matrix_X, matrix_Y):
         :rtype: list
 
         **Example:**
-        
+
         >>> import numpy as np
         >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
 
@@ -56,8 +56,8 @@ def test_statistic(self, matrix_X, matrix_Y):
         """
         assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape"
         assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape"
-        
-        if self.which_test == 'kendall':            
+
+        if self.which_test == 'kendall':
             test_statistic_ = kendalltau(matrix_X, matrix_Y)[0]
         else:
             test_statistic_ = spearmanr(matrix_X, matrix_Y)[0]
@@ -88,7 +88,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         :rtype: list
 
         **Example:**
-        
+
         >>> import numpy as np
         >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
@@ -102,7 +102,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
         assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape"
         assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape"
-        
+
         if self.which_test == 'kendall':
             p_value_ = kendalltau(matrix_X, matrix_Y)[1]
         else:
@@ -111,4 +111,4 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         self.p_value_ = p_value_
         self.p_value_metadata_ = {}
 
-        return p_value_, {}
\ No newline at end of file
+        return p_value_, {}
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index ac0c70e..3dca185 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -1,7 +1,7 @@
 """
      **RVCorr Independence Test Module**
 """
- 
+
 import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
 from numpy import matlib as mb
@@ -52,7 +52,7 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
         :rtype: list
 
         **Example:**
-        
+
         >>> import numpy as np
         >>> from mgcpy.independence_tests.rv_corr import RVCorr
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
@@ -66,9 +66,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None):
         row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
 
         mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0),
-                                         matrix_X.shape[0], 1)
+                                    matrix_X.shape[0], 1)
         mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0),
-                                         matrix_Y.shape[0], 1)
+                                    matrix_Y.shape[0], 1)
 
         covar = np.dot(mat1.T, mat2)
         varX = np.dot(mat1.T, mat1)
@@ -117,7 +117,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None):
         :rtype: list
 
         **Example:**
-        
+
         >>> import numpy as np
         >>> from mgcpy.independence_tests.rv_corr import RVCorr
         >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
@@ -130,5 +130,5 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None):
         test_stat = self.test_statistic(matrix_X, matrix_Y)[0]
         self.p_value_ = np.abs(test_stat)
         self.p_value_metadata_ = {}
-        
+
         return np.abs(test_stat), {}
diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
index 5379450..9c65b9b 100644
--- a/mgcpy/independence_tests/unit_tests/hhg_test.py
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
-from mgcpy import HHG
 import pytest
+from mgcpy import HHG
 
 
 def test_hhg():
@@ -28,4 +28,6 @@ def test_hhg():
     test_stat = hhg.test_statistic(X, Y)
 
     assert np.round(test_stat, decimals=2) == 950600.00
-test_hhg()
\ No newline at end of file
+
+
+test_hhg()
diff --git a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
index c9fa50f..1937704 100644
--- a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
+++ b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
-from mgcpy import KendallSpearman
 import pytest
+from mgcpy import KendallSpearman
 
 
 def test_kendall_spearman():
@@ -32,4 +32,4 @@ def test_kendall_spearman():
     test_stat2 = kspear2.test_statistic(X, Y)[0]
 
     assert np.round(test_stat1, decimals=2) == 0.33
-    assert np.round(test_stat2, decimals=2) == 0.48
\ No newline at end of file
+    assert np.round(test_stat2, decimals=2) == 0.48
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
index 439e3ee..4aee659 100644
--- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
-from mgcpy import RVCorr
 import pytest
+from mgcpy import RVCorr
 
 
 def test_local_corr():
@@ -13,7 +13,7 @@ def test_local_corr():
     rvcorr = RVCorr(None)
     rvcorr2 = RVCorr(None, 'pearson')
     rvcorr3 = RVCorr(None, 'cca')
-    
+
     test_stat1 = rvcorr.test_statistic(X, Y)[0]
     test_stat2 = rvcorr2.test_statistic(X, Y)[0]
     test_stat3 = rvcorr3.test_statistic(X, Y)[0]
@@ -37,4 +37,4 @@ def test_local_corr():
     test_stat3 = rvcorr3.test_statistic(X, Y)[0]
     assert np.round(test_stat1, decimals=2) == 0.24
     assert np.round(test_stat2, decimals=2) == 0.49
-    assert np.round(test_stat3, decimals=2) == 0.24
\ No newline at end of file
+    assert np.round(test_stat3, decimals=2) == 0.24

From 8f3f39f6be9048a65b206a9d30d4da685271fac0 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Mon, 3 Dec 2018 14:24:39 -0500
Subject: [PATCH 23/60] Fix rv_corr permutation test

---
 mgcpy/independence_tests/rv_corr.py | 13 ++++++++++---
 1 file changed, 10 insertions(+), 3 deletions(-)

diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
index 3dca185..024481a 100644
--- a/mgcpy/independence_tests/rv_corr.py
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -127,8 +127,15 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None):
         >>> rvcorr = RVCorr()
         >>> rvcorr_p_value = rvcorr.p_value(X, Y)
         """
-        test_stat = self.test_statistic(matrix_X, matrix_Y)[0]
-        self.p_value_ = np.abs(test_stat)
+        test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0]
+        # estimate the null by a permutation test
+        test_stats_null = np.zeros(replication_factor)
+        for rep in range(replication_factor):
+            permuted_y = np.random.permutation(matrix_Y)
+            test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0]
+
+        # p-value is the probability of observing more extreme test statistic under the null
+        self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
         self.p_value_metadata_ = {}
 
-        return np.abs(test_stat), {}
+        return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {}

From e04b1deafe128a3b6a8328eb790541507820712f Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Mon, 3 Dec 2018 14:39:38 -0500
Subject: [PATCH 24/60] Removed old tests

---
 mgcpy/independence_tests/hhg.py              | 130 -----------------
 mgcpy/independence_tests/kendall_spearman.py | 114 ---------------
 mgcpy/independence_tests/rv_corr.py          | 141 -------------------
 3 files changed, 385 deletions(-)
 delete mode 100644 mgcpy/independence_tests/hhg.py
 delete mode 100644 mgcpy/independence_tests/kendall_spearman.py
 delete mode 100644 mgcpy/independence_tests/rv_corr.py

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
deleted file mode 100644
index 7d9998b..0000000
--- a/mgcpy/independence_tests/hhg.py
+++ /dev/null
@@ -1,130 +0,0 @@
-"""
-     **HHG Independence Test Module**
-"""
-
-import numpy as np
-from mgcpy.independence_tests.abstract_class import IndependenceTest
-
-
-class HHG(IndependenceTest):
-    def __init__(self, compute_distance_matrix=None):
-        """
-        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
-        """
-        IndependenceTest.__init__(compute_distance_matrix)
-
-    def get_name(self):
-        '''
-        :return: the name of the independence test
-        :rtype: string
-        '''
-        return 'hhg'
-
-    def test_statistic(self, matrix_X, matrix_Y):
-        """
-        Computes the HHG correlation measure between two datasets.
-
-        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions
-        :type matrix_X: 2D `numpy.array`
-
-        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
-        :type matrix_Y: 2D `numpy.array`
-
-        :return: returns a list of two items, that contains:
-            - :test_statistic_: test statistic
-            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
-                                         that the independence tests computes in the process
-        :rtype: float, dict
-
-        **Example:**
-
-        >>> import numpy as np
-        >>> from mgcpy.independence_tests.hhg import HHG
-        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
-                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
-        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
-                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
-        >>> hhg = HHG()
-        >>> hhg_test_stat = hhg.test_statistic(X, Y)
-        """
-        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
-        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
-
-        # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not
-        if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0:
-            dist_mtx_X = self.compute_distance_matrix(matrix_X)
-        else:
-            dist_mtx_X = matrix_X
-        if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0:
-            dist_mtx_Y = self.compute_distance_matrix(matrix_Y)
-        else:
-            dist_mtx_Y = matrix_Y
-
-        n = dist_mtx_X.shape[0]
-        S = np.zeros((n, n))
-
-        for i in range(n):
-            for j in range(n):
-                if i != j:
-                    tmp1 = dist_mtx_X[i, :] <= dist_mtx_X[i, j]
-                    tmp2 = dist_mtx_Y[i, :] <= dist_mtx_Y[i, j]
-                    t11 = np.sum(tmp1 * tmp2) - 2
-                    t12 = np.sum(tmp1 * (1-tmp2))
-                    t21 = np.sum((1-tmp1) * tmp2)
-                    t22 = np.sum((1-tmp1) * (1-tmp2))
-                    denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22)
-                    if denom > 0:
-                        S[i, j] = (n-2) * \
-                            np.power((t12*t21 - t11*t22), 2) / denom
-        corr = np.sum(S)
-
-        # no metadata for HHG
-        self.test_statistic_metadata_ = {}
-        self.test_statistic_ = corr
-
-        return corr, {}
-
-    def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
-        """
-        Tests independence between two datasets using HHG and permutation test.
-
-        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions
-        :type matrix_X: 2D `numpy.array`
-
-        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
-        :type matrix_Y: 2D `numpy.array`
-
-        :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to 1000.
-        :type replication_factor: integer
-
-        :return: returns a list of two items, that contains:
-            - :p_value_: P-value
-            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
-                                 that the independence tests computes in the process
-        :rtype: list
-
-        **Example:**
-
-        >>> import numpy as np
-        >>> from mgcpy.independence_tests.hhg import HHG
-        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
-                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
-        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
-                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
-        >>> hhg = HHG()
-        >>> hhg_p_value = hhg.p_value(X, Y)
-        """
-        test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0]
-        # estimate the null by a permutation test
-        test_stats_null = np.zeros(replication_factor)
-        for rep in range(replication_factor):
-            permuted_y = np.random.permutation(matrix_Y)
-            test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0]
-
-        # p-value is the probability of observing more extreme test statistic under the null
-        self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
-        self.p_value_metadata_ = {}
-
-        return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {}
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
deleted file mode 100644
index 096bb13..0000000
--- a/mgcpy/independence_tests/kendall_spearman.py
+++ /dev/null
@@ -1,114 +0,0 @@
-"""
-     **Kendall and Spearman ndependence Test Module**
-"""
-
-from mgcpy.independence_tests.abstract_class import IndependenceTest
-from scipy.stats import kendalltau, spearmanr
-
-
-class KendallSpearman(IndependenceTest):
-    def __init__(self, compute_distance_matrix=None, which_test='kendall'):
-        """
-        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
-
-        :param which_test: specifies which test to use, including ``'kendall'`` or ``'spearman'``
-        :type which_test: string
-        """
-        IndependenceTest.__init__(self, compute_distance_matrix)
-        self.which_test = which_test
-
-    def get_name(self):
-        '''
-        :return: the name of the independence test
-        :rtype: string
-        '''
-        return self.which_test
-
-    def test_statistic(self, matrix_X, matrix_Y):
-        """
-        Computes the Spearman's rho or Kendall's tau measure between two datasets.
-        - Implments scipy.stats's implementation for both
-
-        :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension
-        :type matrix_X: 1D `numpy.array`
-
-        :param matrix_Y: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension
-        :type matrix_Y: 1D `numpy.array`
-
-        :return: returns a list of two items, that contains:
-            - :test_stat_: test statistic
-            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
-                                         that the independence tests computes in the process
-        :rtype: list
-
-        **Example:**
-
-        >>> import numpy as np
-        >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
-
-        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
-                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
-        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
-                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
-        >>> kendall_spearman = KendallSpearman()
-        >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y)
-        """
-        assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape"
-        assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape"
-
-        if self.which_test == 'kendall':
-            test_statistic_ = kendalltau(matrix_X, matrix_Y)[0]
-        else:
-            test_statistic_ = spearmanr(matrix_X, matrix_Y)[0]
-
-        self.test_statistic_ = test_statistic_
-        self.test_statistic_metadata_ = {}
-
-        return test_statistic_, {}
-
-    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
-        """
-        Tests independence between two datasets using the independence test.
-
-        :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension
-        :type matrix_X: 2D `numpy.array`
-
-        :param matrix_Y: a ``[n*1] data`` matrix, a square matrix with ``n`` samples in ``1`` dimensions
-        :type matrix_Y: 2D `numpy.array`
-
-        :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to 1000.
-        :type replication_factor: integer
-
-        :return: returns a list of two items, that contains:
-            - :p_value_: P-value
-            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
-                                 that the independence tests computes in the process
-        :rtype: list
-
-        **Example:**
-
-        >>> import numpy as np
-        >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
-        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
-                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
-        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
-                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
-        >>> kendall_spearman = KendallSpearman()
-        >>> kendall_spearman_p_value = kendall_spearman.p_value(X, Y)
-        """
-        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
-        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
-        assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape"
-        assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape"
-
-        if self.which_test == 'kendall':
-            p_value_ = kendalltau(matrix_X, matrix_Y)[1]
-        else:
-            p_value_ = spearmanr(matrix_X, matrix_Y)[1]
-
-        self.p_value_ = p_value_
-        self.p_value_metadata_ = {}
-
-        return p_value_, {}
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
deleted file mode 100644
index 024481a..0000000
--- a/mgcpy/independence_tests/rv_corr.py
+++ /dev/null
@@ -1,141 +0,0 @@
-"""
-     **RVCorr Independence Test Module**
-"""
-
-import numpy as np
-from mgcpy.independence_tests.abstract_class import IndependenceTest
-from numpy import matlib as mb
-from scipy.sparse.linalg import svds
-from scipy.stats import pearsonr
-
-
-class RVCorr(IndependenceTest):
-    def __init__(self, compute_distance_matrix=None, which_test='rv'):
-        """
-        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
-
-        :param which_test: specifies which test to use, including ``'rv'``, ``'pearson'``, and ``'cca'``.
-        :type which_test: string
-        """
-        IndependenceTest.__init__(self, compute_distance_matrix)
-        self.which_test = which_test
-
-    def get_name(self):
-        '''
-        :return: the name of the independence test
-        :rtype: string
-        '''
-        return self.which_test
-
-    def test_statistic(self, matrix_X=None, matrix_Y=None):
-        """
-        Computes the Pearson/RV/CCa correlation measure between two datasets.
-        - Default computes linear correlation for RV
-        - Computes pearson's correlation
-        - Calculates local linear correlations for CCa
-
-        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions
-        :type matrix_X: 2D `numpy.array`
-
-        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
-        :type matrix_Y: 2D `numpy.array`
-
-        :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to 1000.
-        :type replication_factor: int
-
-        :return: returns a list of two items, that contains:
-            - :test_statistic_: test statistic
-            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
-                                         that the independence tests computes in the process
-        :rtype: list
-
-        **Example:**
-
-        >>> import numpy as np
-        >>> from mgcpy.independence_tests.rv_corr import RVCorr
-        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
-                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
-        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
-                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
-        >>> rvcorr = RVCorr()
-        >>> rvcorr_test_stat = rvcorr.test_statistic(X, Y)
-        """
-        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
-        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
-
-        mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0),
-                                    matrix_X.shape[0], 1)
-        mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0),
-                                    matrix_Y.shape[0], 1)
-
-        covar = np.dot(mat1.T, mat2)
-        varX = np.dot(mat1.T, mat1)
-        varY = np.dot(mat2.T, mat2)
-
-        if (self.which_test == 'pearson'):
-            assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape"
-            assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape"
-            corr, covar = pearsonr(matrix_X, matrix_Y)
-        elif (self.which_test == 'rv'):
-            covar = np.trace(np.dot(covar, covar.T))
-            corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX))
-                                            * np.trace(np.dot(varY, varY))))
-        else:
-            if varX.size == 1 or varY.size == 1 or covar.size == 1:
-                covar = np.sum(np.power(covar, 2))
-                corr = np.divide(covar, np.sqrt(np.sum(np.power(varX, 2))
-                                                * np.sum(np.power(varY, 2))))
-            else:
-                covar = np.sum(np.power(svds(covar, 1)[1], 2))
-                corr = np.divide(covar, np.sqrt(np.sum(np.power(svds(varX, 1)[1], 2))
-                                                * np.sum(np.power(svds(varY, 1)[1], 2))))
-        self.test_statistic_ = corr
-        self.test_statistic_metadata_ = {"covariance": covar}
-
-        return corr, {"covariance": covar}
-
-    def p_value(self, matrix_X, matrix_Y, replication_factor=None):
-        """
-        Tests independence between two datasets using the independence test.
-
-        :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p``` dimensions
-        :type matrix_X: 2D `numpy.array`
-
-        :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions
-        :type matrix_Y: 2D `numpy.array`
-
-        :param replication_factor: specifies the number of replications to use for
-                                   the permutation test. Defaults to None.
-        :type replication_factor: integer
-
-        :return: returns a list of two items, that contains:
-            - :p_value_: P-value
-            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
-                                 that the independence tests computes in the process
-        :rtype: list
-
-        **Example:**
-
-        >>> import numpy as np
-        >>> from mgcpy.independence_tests.rv_corr import RVCorr
-        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
-                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
-        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
-                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
-        >>> rvcorr = RVCorr()
-        >>> rvcorr_p_value = rvcorr.p_value(X, Y)
-        """
-        test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0]
-        # estimate the null by a permutation test
-        test_stats_null = np.zeros(replication_factor)
-        for rep in range(replication_factor):
-            permuted_y = np.random.permutation(matrix_Y)
-            test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0]
-
-        # p-value is the probability of observing more extreme test statistic under the null
-        self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor
-        self.p_value_metadata_ = {}
-
-        return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {}

From 3b0015ad6b060e6a8f391ddf420cc8962ac085d1 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 07:43:37 -0500
Subject: [PATCH 25/60] Fix pre-commit hook issue in Dockerfile

---
 Dockerfile | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Dockerfile b/Dockerfile
index f610c71..2aa957f 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -86,7 +86,7 @@ RUN pip install pycodestyle
 COPY . /root/workspace/
 
 # setup pep8 guidelines (restricts push when pep8 is violated)
-RUN rm ./.git/hooks/pre-commit
+RUN rm -f ./.git/hooks/pre-commit
 RUN chmod 777 install-hooks.sh
 RUN ./install-hooks.sh
 

From 9ad895ee5ca901335a682a20e9245e679278d4d9 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 14:51:11 -0500
Subject: [PATCH 26/60] Add pandas and seaborn to the Docker image

---
 Dockerfile | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Dockerfile b/Dockerfile
index 2aa957f..33e6fff 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -78,9 +78,7 @@ WORKDIR /root/workspace/
 # install python requirements
 COPY requirements.txt /root/workspace/requirements.txt
 RUN pip install -r requirements.txt
-RUN pip install jupyter
-RUN pip install matplotlib
-RUN pip install pycodestyle
+RUN pip install matplotlib seaborn pandas jupyter pycodestyle
 
 # copy the mgcpy code into the container
 COPY . /root/workspace/

From 30225c633bdd815881d299da924814f1531761c5 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 14:54:39 -0500
Subject: [PATCH 27/60] Update version from 0.0.3 to 0.0.4

---
 docs/source/conf.py | 2 +-
 setup.py            | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/source/conf.py b/docs/source/conf.py
index feefb97..d193053 100644
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -26,7 +26,7 @@
 # The short X.Y version
 version = ''
 # The full version, including alpha/beta/rc tags
-release = 'v0.0.3'
+release = 'v0.0.4'
 
 
 # -- General configuration ---------------------------------------------------
diff --git a/setup.py b/setup.py
index b444058..cad9111 100644
--- a/setup.py
+++ b/setup.py
@@ -21,7 +21,7 @@
 
 REQUIRED_PACKAGES = ["numpy>=1.14.5", "scipy>=1.1.0", "pytest>=3.8.0", "pycodestyle>=2.3.1",
                      "Cython==0.29", "flake8>=3.5.0", "pytest-cov>=2.6.0", "coveralls>=1.5.1", "Sphinx>=1.8.2"]
-VERSION = '0.0.3'
+VERSION = '0.0.4'
 
 
 def check_python_version():

From 7607105ea95b94956cf50801f07d7a6bc43c7e64 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 15:16:21 -0500
Subject: [PATCH 28/60] Pull code from github than copying from local | Docker

---
 Dockerfile | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/Dockerfile b/Dockerfile
index 33e6fff..8369a0c 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -75,14 +75,13 @@ RUN ln -s /usr/bin/python3.6 /usr/local/bin/python
 RUN mkdir /root/workspace/
 WORKDIR /root/workspace/
 
+# clone the mgcpy code into the container
+RUN git clone https://github.com/NeuroDataDesign/mgcpy.git .
+
 # install python requirements
-COPY requirements.txt /root/workspace/requirements.txt
 RUN pip install -r requirements.txt
 RUN pip install matplotlib seaborn pandas jupyter pycodestyle
 
-# copy the mgcpy code into the container
-COPY . /root/workspace/
-
 # setup pep8 guidelines (restricts push when pep8 is violated)
 RUN rm -f ./.git/hooks/pre-commit
 RUN chmod 777 install-hooks.sh

From 9ee13b40a4f4c86eab921073dff61c11ffc8aa39 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 17:00:37 -0500
Subject: [PATCH 29/60] Add code and workspace dirs in Docker for mounting and
 add Vim

---
 Dockerfile | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/Dockerfile b/Dockerfile
index 8369a0c..fd65d2b 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -71,9 +71,15 @@ RUN ln -s /usr/bin/python3.6 /usr/local/bin/python
 #  cd .. && \
 #  rm -rf *
 
-# change working directory
+# make a directory for mounting local files into docker
 RUN mkdir /root/workspace/
-WORKDIR /root/workspace/
+
+# add vim in docker
+RUN apt-get install -y vim
+
+# change working directory
+RUN mkdir /root/code/
+WORKDIR /root/code/
 
 # clone the mgcpy code into the container
 RUN git clone https://github.com/NeuroDataDesign/mgcpy.git .
@@ -91,7 +97,7 @@ RUN ./install-hooks.sh
 RUN python setup.py build_ext --inplace
 
 # add mgcpy to PYTHONPATH for dev purposes
-RUN echo "export PYTHONPATH='${PYTHONPATH}:/root/workspace'" >> ~/.bashrc
+RUN echo "export PYTHONPATH='${PYTHONPATH}:/root/code'" >> ~/.bashrc
 
 # test if mgcpy is correctly installed
 RUN py3clean .

From 9f02fca4c6e05894e996f10baee42d892d840c01 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 17:12:45 -0500
Subject: [PATCH 30/60] Update readme for Docker usage

---
 README.md | 25 +++++++++++++++++++++----
 1 file changed, 21 insertions(+), 4 deletions(-)

diff --git a/README.md b/README.md
index 83d57e1..3650b48 100644
--- a/README.md
+++ b/README.md
@@ -29,10 +29,27 @@ python3 setup.py install
 - `python3 setup.py build_ext --inplace  # for cython`, if you want to test in-place, first execute this
 
 ## Setting up the development environment:
-- Install [docker](https://docs.docker.com/install/)
-- Build the docker image, `docker build -t mgcpy-dev:latest .`
-  - This takes 10 to 15 mins to build
-- Launch the container to go into mgcpy's dev env, `docker run -it --rm --name mgcpy-dev-env mgcpy-dev`
+- To build image and run from scratch:
+  - Install [docker](https://docs.docker.com/install/)
+  - Build the docker image, `docker build -t mgcpy-dev:latest .`
+    - This takes 20-30 mins to build
+  - Launch the container to go into mgcpy's dev env, `docker run -it --rm --name mgcpy-dev-env mgcpy-dev`
+- Pull master branch image from Dockerhub and run:
+  - `docker pull tpsatish95/mgcpy-dev:latest`
+  - `docker run -it --rm -p 8888:8888 --name mgcpy-dev-env tpsatish95/mgcpy-dev`
+
+
+- To run demo notebooks (from within Docker):
+  - `cd demos`
+  - `jupyter notebook --ip 0.0.0.0 --no-browser --allow-root`
+  - Then copy the url it generates, it looks something like this: `http://(0de284ecf0cd or 127.0.0.1):8888/?token=e5a2541812d85e20026b1d04983dc8380055f2d16c28a6ad`
+  - Edit this: `(0de284ecf0cd or 127.0.0.1)` to: `127.0.0.1`, in the above link and open it in your browser
+  - Then open `mgc.ipynb`
+
+- To mount/load local files into docker container:
+  - Do `docker run -it --rm -v <local_dir_path>:/root/workspace/ -p 8888:8888 --name mgcpy-dev-env tpsatish95/mgcpy-dev`, replace `<local_dir_path>` with your local dir path.
+  - Do `cd ../workspace` when you are inside the container to view the mounted files. The **mgcpy** package code will be in `/root/code` directory.
+
 
 ## MGC Algorithm's Flow
 ![MGCPY Flow](MGCPY.png)

From 104608f1df6a1a2490aa06d5ae14a4d3e111d498 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 22:21:24 -0500
Subject: [PATCH 31/60] Finish implementing fast mgc

---
 mgcpy/independence_tests/mgc/fast_mgc.py | 57 ++++++++++++++++++++----
 1 file changed, 48 insertions(+), 9 deletions(-)

diff --git a/mgcpy/independence_tests/mgc/fast_mgc.py b/mgcpy/independence_tests/mgc/fast_mgc.py
index ee1a98a..bc2e46b 100644
--- a/mgcpy/independence_tests/mgc/fast_mgc.py
+++ b/mgcpy/independence_tests/mgc/fast_mgc.py
@@ -1,14 +1,17 @@
 """
-    **Faster version of MGC**
+    **Fast version of MGC**
 """
+import math
+import warnings
 
 import numpy as np
 from mgcpy.independence_tests.mgc.mgc import MGC
 from mgcpy.independence_tests.mgc.threshold_smooth import (smooth_significant_local_correlations,
                                                            threshold_local_correlations)
+from scipy.stats import norm
 
 
-def faster_mgc(matrix_X, matrix_Y, sub_samples=100, null_only=True, alpha=0.01):
+def fast_mgc(matrix_X, matrix_Y, sub_samples=100, null_only=True, alpha=0.01):
     '''
     MGC test statistic computation and permutation test by fast subsampling.
     Note that trivial amount of noise is added to matrix_X and matrix_Y,
@@ -43,15 +46,17 @@ def faster_mgc(matrix_X, matrix_Y, sub_samples=100, null_only=True, alpha=0.01):
                   this is is used to derive the confidence interval and estimate required sample size to achieve power 1.
     :type alpha: float
 
-    :return: a ``dict`` of results with the following keys:
+    :return: returns a list of two items, that contains:
 
         - :p_value: P-value of MGC
-        - :test_statistic: the sample MGC statistic within ``[-1, 1]``
-        - :local_correlation_matrix: a 2D matrix of all local correlations within ``[-1,1]``
-        - :optimal_scale: the estimated optimal scale as an ``[x, y]`` pair.
-        - :confidence_interval: a ``[1*2]`` matrix representing the confidence_interval for the local correlation with 1-alpha confidence.
-        - :required_size: the required estimated sample size to have power 1 at level alpha
-    :rtype: dictionary
+        - :metadata: a ``dict`` of metadata with the following keys:
+
+                - :test_statistic: the sample MGC statistic within ``[-1, 1]``
+                - :local_correlation_matrix: a 2D matrix of all local correlations within ``[-1,1]``
+                - :optimal_scale: the estimated optimal scale as an ``[x, y]`` pair.
+                - :confidence_interval: a ``[1*2]`` matrix representing the confidence_interval for the local correlation with 1-alpha confidence.
+                - :required_size: the required estimated sample size to have power 1 at level alpha
+    :rtype: list
     '''
     total_samples = matrix_Y.shape[0]
     num_samples = total_samples // sub_samples
@@ -98,3 +103,37 @@ def faster_mgc(matrix_X, matrix_Y, sub_samples=100, null_only=True, alpha=0.01):
     result = smooth_significant_local_correlations(
         significant_connected_region, local_correlation_matrix)
     mgc_statistic, optimal_scale = result["mgc_statistic"], result["optimal_scale"]
+
+    k, l = optimal_scale
+    k = math.ceil((k - 1)/(sub_samples - 1) * (total_samples - 1)) + 1
+    l = math.ceil((l - 1)/(sub_samples - 1) * (total_samples - 1)) + 1
+    optimal_scale = [k, l]
+
+    # the observed statistic uses the full data
+    if null_only:
+        mgc_statistic, test_statistic_metadata = mgc.test_statistic(matrix_X, matrix_Y)
+        mgc_statistic = test_statistic_metadata["local_correlation_matrix"][optimal_scale[0]][optimal_scale[1]]
+        optimal_scale = test_statistic_metadata["optimal_scale"]
+        sigma /= math.sqrt(num_samples)
+
+    p_value = 1 - norm.cdf(mgc_statistic, 0, sigma)
+    threshold = norm.ppf(1 - alpha, 0, 1)
+    confidence_interval = [mgc_statistic - (threshold * sigma), mgc_statistic + (threshold * sigma)]
+
+    if mgc_statistic < 0:
+        required_size = np.Inf
+    else:
+        required_size = math.ceil(threshold * sigma * total_samples / mgc_statistic / 10) * 10
+
+    # The results are not statistically significant
+    if p_value > 0.05:
+        warnings.warn("The p-value is greater than 0.05, implying that the results are not statistically significant.\n" +
+                      "Use results such as test_statistic and optimal_scale, with caution!")
+
+    p_value_metadata = {"test_statistic": mgc_statistic,
+                        "local_correlation_matrix": test_statistic_metadata["local_correlation_matrix"],
+                        "optimal_scale": optimal_scale,
+                        "confidence_interval": confidence_interval,
+                        "required_size": required_size}
+
+    return p_value, p_value_metadata

From 28dafbcc669b9846775bc6e1cff907a07765d6a0 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Wed, 5 Dec 2018 22:21:48 -0500
Subject: [PATCH 32/60] Integrate fast_mgc with MGC

---
 mgcpy/independence_tests/mgc/mgc.py | 27 +++++++++++++++++++++------
 1 file changed, 21 insertions(+), 6 deletions(-)

diff --git a/mgcpy/independence_tests/mgc/mgc.py b/mgcpy/independence_tests/mgc/mgc.py
index 5fb155e..08afb7d 100644
--- a/mgcpy/independence_tests/mgc/mgc.py
+++ b/mgcpy/independence_tests/mgc/mgc.py
@@ -2,11 +2,8 @@
     **Main MGC Independence Test Module**
 """
 
-import time
-import warnings
-
-import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
+from mgcpy.independence_tests.mgc.fast_mgc import fast_mgc
 from mgcpy.independence_tests.mgc.local_correlation import local_correlations
 from mgcpy.independence_tests.mgc.threshold_smooth import (smooth_significant_local_correlations,
                                                            threshold_local_correlations)
@@ -96,7 +93,7 @@ def test_statistic(self, matrix_X, matrix_Y):
         self.test_statistic_metadata_ = test_statistic_metadata
         return mgc_statistic, test_statistic_metadata
 
-    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
+    def p_value(self, matrix_X, matrix_Y, replication_factor=1000, is_fast=False, fast_mgc_data={}):
         """
         Tests independence between two datasets using MGC and permutation test.
 
@@ -116,10 +113,22 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
                                    the permutation test. Defaults to ``1000``.
         :type replication_factor: integer
 
+        :param is_fast: is a boolean flag which specifies if the p_value should be computed (approximated)
+                        using the fast version of mgc. This defaults to False.
+        :type is_fast: boolean
+
+        :param fast_mgc_data: a ``dict`` of fast mgc params, refer: mgcpy.independence_tests.mgc.fast_mgc
+
+            - :sub_samples: specifies the number of subsamples.
+            - :null_only: specifies if subsampling is to be used for estimating the null only.
+            - :alpha: specifies the type 1 error level.
+        :type fast_mgc_data: dictonary
+
         :return: returns a list of two items, that contains:
 
             - :p_value: P-value of MGC
             - :metadata: a ``dict`` of metadata with the following keys:
+
                     - :test_statistic: the sample MGC statistic within ``[-1, 1]``
                     - :p_local_correlation_matrix: a 2D matrix of the P-values of the local correlations
                     - :local_correlation_matrix: a 2D matrix of all local correlations within ``[-1,1]``
@@ -138,4 +147,10 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
         >>> mgc = MGC()
         >>> p_value, metadata = mgc.p_value(X, Y, replication_factor = 100)
         """
-        return super(MGC, self).p_value(matrix_X, matrix_Y)
+        if is_fast:
+            p_value, p_value_metadata = fast_mgc(matrix_X, matrix_Y, **fast_mgc_data)
+            self.p_value_ = p_value
+            self.p_value_metadata_ = p_value_metadata
+            return p_value, p_value_metadata
+        else:
+            return super(MGC, self).p_value(matrix_X, matrix_Y)

From 9df3a8676f5a083b6988c8164d33312bc6de5c1f Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 05:31:20 -0500
Subject: [PATCH 33/60] Refactor MGC class to include FastMGC and remove
 circular dependency issue

---
 mgcpy/independence_tests/mgc/fast_mgc.py | 139 -----------------------
 mgcpy/independence_tests/mgc/mgc.py      | 133 +++++++++++++++++++++-
 2 files changed, 131 insertions(+), 141 deletions(-)
 delete mode 100644 mgcpy/independence_tests/mgc/fast_mgc.py

diff --git a/mgcpy/independence_tests/mgc/fast_mgc.py b/mgcpy/independence_tests/mgc/fast_mgc.py
deleted file mode 100644
index bc2e46b..0000000
--- a/mgcpy/independence_tests/mgc/fast_mgc.py
+++ /dev/null
@@ -1,139 +0,0 @@
-"""
-    **Fast version of MGC**
-"""
-import math
-import warnings
-
-import numpy as np
-from mgcpy.independence_tests.mgc.mgc import MGC
-from mgcpy.independence_tests.mgc.threshold_smooth import (smooth_significant_local_correlations,
-                                                           threshold_local_correlations)
-from scipy.stats import norm
-
-
-def fast_mgc(matrix_X, matrix_Y, sub_samples=100, null_only=True, alpha=0.01):
-    '''
-    MGC test statistic computation and permutation test by fast subsampling.
-    Note that trivial amount of noise is added to matrix_X and matrix_Y,
-    to break possible ties in data for MGC.
-
-    :param matrix_X: is interpreted as either:
-
-        - a ``[n*n]`` distance matrix, a square matrix with zeros on diagonal for n samples OR
-        - a ``[n*d]`` data matrix, a square matrix with n samples in d dimensions
-    :type matrix_X: 2D numpy.array
-
-    :param matrix_Y: is interpreted as either:
-
-        - a ``[n*n]`` distance matrix, a square matrix with zeros on diagonal for n samples OR
-        - a ``[n*d]`` data matrix, a square matrix with n samples in d dimensions
-    :type matrix_Y: 2D numpy.array
-
-    :param sub_samples: specifies the number of subsamples.
-                        generally total_samples/sub_samples should be more than 4,
-                        and ``sub_samples`` should be large than 30.
-    :type sub_samples: integer
-
-    :param null_only: specifies if subsampling is to be used for estimating the null only OR to compute the observed statistic as well
-
-        - *True:* uses subsampled statistics for estimating the null only and computes the observed statistic by full data,
-                this runs in ``O(total_samples^2 + sub_samples * total_samples)``
-        - *False:* uses subsampled statistics for estimating the null and also computes the observed statistic by subsampling,
-                 this runs in ``O(sub_samples*total_samples)``
-    :type null_only: boolean
-
-    :param alpha: specifies the type 1 error level.
-                  this is is used to derive the confidence interval and estimate required sample size to achieve power 1.
-    :type alpha: float
-
-    :return: returns a list of two items, that contains:
-
-        - :p_value: P-value of MGC
-        - :metadata: a ``dict`` of metadata with the following keys:
-
-                - :test_statistic: the sample MGC statistic within ``[-1, 1]``
-                - :local_correlation_matrix: a 2D matrix of all local correlations within ``[-1,1]``
-                - :optimal_scale: the estimated optimal scale as an ``[x, y]`` pair.
-                - :confidence_interval: a ``[1*2]`` matrix representing the confidence_interval for the local correlation with 1-alpha confidence.
-                - :required_size: the required estimated sample size to have power 1 at level alpha
-    :rtype: list
-    '''
-    total_samples = matrix_Y.shape[0]
-    num_samples = total_samples // sub_samples
-
-    # if full data size (total_samples) is not more than 4 times of sub_samples, split to 4 samples
-    # too few samples will fail the normal approximation and cause the test to be invalid
-
-    if total_samples < 4 * sub_samples:
-        sub_samples = total_samples // 4
-        num_samples = 4
-
-    # the observed statistics by subsampling
-    test_statistic_sub_sampling = np.zeros((1, num_samples))
-
-    # add trivial noise to break any ties
-    matrix_X += 1e-10 * np.random.uniform(size=matrix_X.shape)
-    matrix_Y += 1e-10 * np.random.uniform(size=matrix_Y.shape)
-
-    # the local correlations by subsampling
-    local_correlation_matrix_sub_sampling = np.zeros((sub_samples, sub_samples, num_samples))
-
-    # create MGC object
-    mgc = MGC()
-
-    # subsampling computation
-    for i in range(num_samples):
-        sub_matrix_X = matrix_X[(sub_samples*i):(sub_samples*(i+1)-1)]
-        sub_matrix_Y = matrix_Y[(sub_samples*i):(sub_samples*(i+1)-1)]
-
-        mgc_statistic, test_statistic_metadata = mgc.test_statistic(sub_matrix_X, sub_matrix_Y)
-        test_statistic_sub_sampling[i], local_correlation_matrix_sub_sampling[:, :, i] = \
-            mgc_statistic, test_statistic_metadata["local_correlation_matrix"]
-
-    local_correlation_matrix = np.mean(local_correlation_matrix_sub_sampling, axis=2)
-    sigma = np.std(test_statistic_sub_sampling) / np.sqrt(num_samples)
-
-    sample_size = len(matrix_X) - 1  # sample size minus 1
-
-    # find a connected region of significant local correlations, by thresholding
-    significant_connected_region = threshold_local_correlations(
-        local_correlation_matrix, sample_size)
-
-    # find the maximum within the significant region
-    result = smooth_significant_local_correlations(
-        significant_connected_region, local_correlation_matrix)
-    mgc_statistic, optimal_scale = result["mgc_statistic"], result["optimal_scale"]
-
-    k, l = optimal_scale
-    k = math.ceil((k - 1)/(sub_samples - 1) * (total_samples - 1)) + 1
-    l = math.ceil((l - 1)/(sub_samples - 1) * (total_samples - 1)) + 1
-    optimal_scale = [k, l]
-
-    # the observed statistic uses the full data
-    if null_only:
-        mgc_statistic, test_statistic_metadata = mgc.test_statistic(matrix_X, matrix_Y)
-        mgc_statistic = test_statistic_metadata["local_correlation_matrix"][optimal_scale[0]][optimal_scale[1]]
-        optimal_scale = test_statistic_metadata["optimal_scale"]
-        sigma /= math.sqrt(num_samples)
-
-    p_value = 1 - norm.cdf(mgc_statistic, 0, sigma)
-    threshold = norm.ppf(1 - alpha, 0, 1)
-    confidence_interval = [mgc_statistic - (threshold * sigma), mgc_statistic + (threshold * sigma)]
-
-    if mgc_statistic < 0:
-        required_size = np.Inf
-    else:
-        required_size = math.ceil(threshold * sigma * total_samples / mgc_statistic / 10) * 10
-
-    # The results are not statistically significant
-    if p_value > 0.05:
-        warnings.warn("The p-value is greater than 0.05, implying that the results are not statistically significant.\n" +
-                      "Use results such as test_statistic and optimal_scale, with caution!")
-
-    p_value_metadata = {"test_statistic": mgc_statistic,
-                        "local_correlation_matrix": test_statistic_metadata["local_correlation_matrix"],
-                        "optimal_scale": optimal_scale,
-                        "confidence_interval": confidence_interval,
-                        "required_size": required_size}
-
-    return p_value, p_value_metadata
diff --git a/mgcpy/independence_tests/mgc/mgc.py b/mgcpy/independence_tests/mgc/mgc.py
index 08afb7d..e7d8255 100644
--- a/mgcpy/independence_tests/mgc/mgc.py
+++ b/mgcpy/independence_tests/mgc/mgc.py
@@ -1,12 +1,15 @@
 """
     **Main MGC Independence Test Module**
 """
+import math
+import warnings
 
+import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
-from mgcpy.independence_tests.mgc.fast_mgc import fast_mgc
 from mgcpy.independence_tests.mgc.local_correlation import local_correlations
 from mgcpy.independence_tests.mgc.threshold_smooth import (smooth_significant_local_correlations,
                                                            threshold_local_correlations)
+from scipy.stats import norm
 
 
 class MGC(IndependenceTest):
@@ -148,9 +151,135 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000, is_fast=False, fa
         >>> p_value, metadata = mgc.p_value(X, Y, replication_factor = 100)
         """
         if is_fast:
-            p_value, p_value_metadata = fast_mgc(matrix_X, matrix_Y, **fast_mgc_data)
+            p_value, p_value_metadata = self._fast_mgc_p_value(matrix_X, matrix_Y, **fast_mgc_data)
             self.p_value_ = p_value
             self.p_value_metadata_ = p_value_metadata
             return p_value, p_value_metadata
         else:
             return super(MGC, self).p_value(matrix_X, matrix_Y)
+
+    def _fast_mgc_p_value(self, matrix_X, matrix_Y, sub_samples=100, null_only=True, alpha=0.01):
+        '''
+        Fast version of MGC's p-value computation
+
+        MGC test statistic computation and permutation test by fast subsampling.
+        Note that trivial amount of noise is added to matrix_X and matrix_Y,
+        to break possible ties in data for MGC.
+
+        :param matrix_X: is interpreted as either:
+
+            - a ``[n*n]`` distance matrix, a square matrix with zeros on diagonal for n samples OR
+            - a ``[n*d]`` data matrix, a square matrix with n samples in d dimensions
+        :type matrix_X: 2D numpy.array
+
+        :param matrix_Y: is interpreted as either:
+
+            - a ``[n*n]`` distance matrix, a square matrix with zeros on diagonal for n samples OR
+            - a ``[n*d]`` data matrix, a square matrix with n samples in d dimensions
+        :type matrix_Y: 2D numpy.array
+
+        :param sub_samples: specifies the number of subsamples.
+                            generally total_samples/sub_samples should be more than 4,
+                            and ``sub_samples`` should be large than 30.
+        :type sub_samples: integer
+
+        :param null_only: specifies if subsampling is to be used for estimating the null only OR to compute the observed statistic as well
+
+            - *True:* uses subsampled statistics for estimating the null only and computes the observed statistic by full data,
+                    this runs in ``O(total_samples^2 + sub_samples * total_samples)``
+            - *False:* uses subsampled statistics for estimating the null and also computes the observed statistic by subsampling,
+                     this runs in ``O(sub_samples*total_samples)``
+        :type null_only: boolean
+
+        :param alpha: specifies the type 1 error level.
+                      this is is used to derive the confidence interval and estimate required sample size to achieve power 1.
+        :type alpha: float
+
+        :return: returns a list of two items, that contains:
+
+            - :p_value: P-value of MGC
+            - :metadata: a ``dict`` of metadata with the following keys:
+
+                    - :test_statistic: the sample MGC statistic within ``[-1, 1]``
+                    - :local_correlation_matrix: a 2D matrix of all local correlations within ``[-1,1]``
+                    - :optimal_scale: the estimated optimal scale as an ``[x, y]`` pair.
+                    - :confidence_interval: a ``[1*2]`` matrix representing the confidence_interval for the local correlation with 1-alpha confidence.
+                    - :required_size: the required estimated sample size to have power 1 at level alpha
+        :rtype: list
+        '''
+        total_samples = matrix_Y.shape[0]
+        num_samples = total_samples // sub_samples
+
+        # if full data size (total_samples) is not more than 4 times of sub_samples, split to 4 samples
+        # too few samples will fail the normal approximation and cause the test to be invalid
+
+        if total_samples < 4 * sub_samples:
+            sub_samples = total_samples // 4
+            num_samples = 4
+
+        # the observed statistics by subsampling
+        test_statistic_sub_sampling = np.zeros((1, num_samples))
+
+        # add trivial noise to break any ties
+        matrix_X += 1e-10 * np.random.uniform(size=matrix_X.shape)
+        matrix_Y += 1e-10 * np.random.uniform(size=matrix_Y.shape)
+
+        # the local correlations by subsampling
+        local_correlation_matrix_sub_sampling = np.zeros((sub_samples, sub_samples, num_samples))
+
+        # subsampling computation
+        for i in range(num_samples):
+            sub_matrix_X = matrix_X[(sub_samples*i):(sub_samples*(i+1)-1)]
+            sub_matrix_Y = matrix_Y[(sub_samples*i):(sub_samples*(i+1)-1)]
+
+            mgc_statistic, test_statistic_metadata = self.test_statistic(sub_matrix_X, sub_matrix_Y)
+            test_statistic_sub_sampling[i], local_correlation_matrix_sub_sampling[:, :, i] = \
+                mgc_statistic, test_statistic_metadata["local_correlation_matrix"]
+
+        local_correlation_matrix = np.mean(local_correlation_matrix_sub_sampling, axis=2)
+        sigma = np.std(test_statistic_sub_sampling) / np.sqrt(num_samples)
+
+        sample_size = len(matrix_X) - 1  # sample size minus 1
+
+        # find a connected region of significant local correlations, by thresholding
+        significant_connected_region = threshold_local_correlations(
+            local_correlation_matrix, sample_size)
+
+        # find the maximum within the significant region
+        result = smooth_significant_local_correlations(
+            significant_connected_region, local_correlation_matrix)
+        mgc_statistic, optimal_scale = result["mgc_statistic"], result["optimal_scale"]
+
+        k, l = optimal_scale
+        k = math.ceil((k - 1)/(sub_samples - 1) * (total_samples - 1)) + 1
+        l = math.ceil((l - 1)/(sub_samples - 1) * (total_samples - 1)) + 1
+        optimal_scale = [k, l]
+
+        # the observed statistic uses the full data
+        if null_only:
+            mgc_statistic, test_statistic_metadata = self.test_statistic(matrix_X, matrix_Y)
+            mgc_statistic = test_statistic_metadata["local_correlation_matrix"][optimal_scale[0]][optimal_scale[1]]
+            optimal_scale = test_statistic_metadata["optimal_scale"]
+            sigma /= math.sqrt(num_samples)
+
+        p_value = 1 - norm.cdf(mgc_statistic, 0, sigma)
+        threshold = norm.ppf(1 - alpha, 0, 1)
+        confidence_interval = [mgc_statistic - (threshold * sigma), mgc_statistic + (threshold * sigma)]
+
+        if mgc_statistic < 0:
+            required_size = np.Inf
+        else:
+            required_size = math.ceil(threshold * sigma * total_samples / mgc_statistic / 10) * 10
+
+        # The results are not statistically significant
+        if p_value > 0.05:
+            warnings.warn("The p-value is greater than 0.05, implying that the results are not statistically significant.\n" +
+                          "Use results such as test_statistic and optimal_scale, with caution!")
+
+        p_value_metadata = {"test_statistic": mgc_statistic,
+                            "local_correlation_matrix": test_statistic_metadata["local_correlation_matrix"],
+                            "optimal_scale": optimal_scale,
+                            "confidence_interval": confidence_interval,
+                            "required_size": required_size}
+
+        return p_value, p_value_metadata

From 0d6a63d11c592b2706d78dc3cc0fefba5285db87 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 11:17:28 -0500
Subject: [PATCH 34/60] Add /bin/bash directive to pre-commit hook

---
 git-hooks/pre-commit | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/git-hooks/pre-commit b/git-hooks/pre-commit
index 2ef69e1..8a74422 100755
--- a/git-hooks/pre-commit
+++ b/git-hooks/pre-commit
@@ -1,3 +1,5 @@
+#!/bin/bash
+
 # Code slightly modified from:
 # https://benmccormick.org/2017/02/26/running-jest-tests-before-each-git-commit/
 

From c5ab3ef8593e2fff08f74513feeed5c6bb30835b Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 12:29:39 -0500
Subject: [PATCH 35/60] Fix bugs in Fast MGC Use statistic.stdev instead of
 np.std Fix shape issue for test_statistic_sub_sampling Remove mgc_statistic
 computation based on sub sampled optim scale

---
 mgcpy/independence_tests/mgc/mgc.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/mgcpy/independence_tests/mgc/mgc.py b/mgcpy/independence_tests/mgc/mgc.py
index e7d8255..4045805 100644
--- a/mgcpy/independence_tests/mgc/mgc.py
+++ b/mgcpy/independence_tests/mgc/mgc.py
@@ -3,6 +3,7 @@
 """
 import math
 import warnings
+from statistics import stdev
 
 import numpy as np
 from mgcpy.independence_tests.abstract_class import IndependenceTest
@@ -218,7 +219,7 @@ def _fast_mgc_p_value(self, matrix_X, matrix_Y, sub_samples=100, null_only=True,
             num_samples = 4
 
         # the observed statistics by subsampling
-        test_statistic_sub_sampling = np.zeros((1, num_samples))
+        test_statistic_sub_sampling = np.zeros(num_samples)
 
         # add trivial noise to break any ties
         matrix_X += 1e-10 * np.random.uniform(size=matrix_X.shape)
@@ -229,15 +230,15 @@ def _fast_mgc_p_value(self, matrix_X, matrix_Y, sub_samples=100, null_only=True,
 
         # subsampling computation
         for i in range(num_samples):
-            sub_matrix_X = matrix_X[(sub_samples*i):(sub_samples*(i+1)-1)]
-            sub_matrix_Y = matrix_Y[(sub_samples*i):(sub_samples*(i+1)-1)]
+            sub_matrix_X = matrix_X[(sub_samples*i):sub_samples*(i+1), :]
+            sub_matrix_Y = matrix_Y[(sub_samples*i):sub_samples*(i+1), :]
 
             mgc_statistic, test_statistic_metadata = self.test_statistic(sub_matrix_X, sub_matrix_Y)
             test_statistic_sub_sampling[i], local_correlation_matrix_sub_sampling[:, :, i] = \
                 mgc_statistic, test_statistic_metadata["local_correlation_matrix"]
 
         local_correlation_matrix = np.mean(local_correlation_matrix_sub_sampling, axis=2)
-        sigma = np.std(test_statistic_sub_sampling) / np.sqrt(num_samples)
+        sigma = stdev(test_statistic_sub_sampling) / np.sqrt(num_samples)
 
         sample_size = len(matrix_X) - 1  # sample size minus 1
 
@@ -258,7 +259,6 @@ def _fast_mgc_p_value(self, matrix_X, matrix_Y, sub_samples=100, null_only=True,
         # the observed statistic uses the full data
         if null_only:
             mgc_statistic, test_statistic_metadata = self.test_statistic(matrix_X, matrix_Y)
-            mgc_statistic = test_statistic_metadata["local_correlation_matrix"][optimal_scale[0]][optimal_scale[1]]
             optimal_scale = test_statistic_metadata["optimal_scale"]
             sigma /= math.sqrt(num_samples)
 

From fa83c75ba4a45db9d1e6f282ba80676528732c57 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 12:29:57 -0500
Subject: [PATCH 36/60] Add basic tests for Fast MGC

---
 .../unit_tests/mgc/fast_mgc_test.py           | 29 +++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py

diff --git a/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py b/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py
new file mode 100644
index 0000000..b4b3bf7
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py
@@ -0,0 +1,29 @@
+import numpy as np
+import pytest
+from mgcpy.independence_tests.mgc.mgc import MGC
+
+
+def test_fast_mgc_test_linear():
+    # linear (mgc.sims.linear(50, 1, 0.1))
+    X = np.array([0.45233912,  0.41776082,  0.08992314, -0.68255391, -0.65492209,  0.24839759, -0.87725133,  0.32595345, -0.08646498, -0.16638085,  0.26394850,  0.72925148,  0.26028888, -0.59854218, -0.80068479, -0.69199885,  0.14915159,  0.37115868,  0.96039213,  0.27498675, -0.01372958, -0.89370963,  0.78395670, -0.42157105, -0.13893970,
+                  0.50943310, -0.12623322, -0.20255325,  0.18437355, -0.02945578,  0.78082317,  0.39372362, -0.37730187, -0.17078540,  0.70129955,  0.83651364,  0.73375401, -0.34883304,  0.15323405,  0.51493599, -0.24317493,  0.83948953,  0.77216592,  0.90045095, -0.53736592, -0.88430486,  0.31447365,  0.66595322, -0.15917153, -0.38190466]).reshape(-1, 1)
+    Y = np.array([0.665986696,  0.402397835,  0.134445492, -0.796653997, -0.636592886,  0.277283128, -0.636847542,  0.249515282, -0.149871134, -0.147567403,  0.369251601,  0.687118553,  0.524448340, -0.585999355, -0.858549573, -0.756081985,  0.129307735,  0.180976113,  0.874637167,  0.458794276, -0.003339139, -0.967879037,  0.758180626, -0.392856219, -0.114772505,
+                  0.425345845, -0.069794980, -0.330857932,  0.229331072,  0.058739766,  0.777801029,  0.580715974, -0.231521102, -0.233366160,  0.669360658,  0.999785556,  0.648315305, -0.321119155,  0.156810807,  0.451349979, -0.393285002,  0.720164611,  0.811149183,  0.936183880, -0.587798720, -0.721394055,  0.233671350,  0.625407903, -0.154576153, -0.451475001]).reshape(-1, 1)
+
+    p_value = 0
+
+    mgc = MGC()
+    p_value_res, _ = mgc.p_value(X, Y, is_fast=True)
+    assert np.allclose(p_value, p_value_res, rtol=0.1)
+
+
+def test_fast_mgc_test_non_linear():
+    # spiral data (mgc.sims.spiral(50, 1, 0.5))
+    X = np.array([-0.915363905,  2.134736725,  1.591825890, -0.947720469, -0.629203447,  0.157367412, -3.009624669,  0.342083914,  0.126834696,  2.009228424,  0.137638139, -4.168139174,  1.854371040,  1.696600346, -2.454855196,  1.770009913, -0.080973938,  1.985722698,  0.671279564,  1.521294941, -0.905490998, -1.043388333,  0.006493876,  4.007326886,  1.755316427, -0.905436337,  0.497332481,  0.819071238,  3.561837453,  3.713293152,  0.487967353,  1.233385955, -2.985033861,  0.146394829, -2.231330093, -0.138580101, -2.390685794, -2.798259311,  0.647199716, -0.626705094, -0.254107788,  2.017131291, -2.871050739, -0.369874190,  0.198565130,  2.021387946, -2.877629992, -1.855015175, -0.201316471,  3.886001079]).reshape(-1, 1)
+    Y = np.array([0.12441532, -2.63498763,  2.18349959, -0.58779997, -1.58602656,  0.35894756, -0.73954299,  1.76585591, -0.35002851,  0.48618590,  0.95628300,  1.99038991,  1.92277498,  1.34861841,  1.42509605,  0.65982368, -1.56731299, -0.17000082,  1.81187432, -0.73726241,  0.44491111,  0.19177688,  2.28190181,  0.45509215, -0.16777206, 0.06918430, -1.49570722,  2.23337087, -1.01335025, -0.60394315, -0.56653502, -3.12571299, -1.56146565,  0.52487563,  2.35561329, -1.79300788, -2.40650123,  0.53680541,  2.04171052,  0.09821259, -0.42712911,  0.52453433, -1.44426759, -2.22697039,  1.26906442, -0.13549404,  0.36776719, -2.44674330,  1.34647206,  2.14525574]).reshape(-1, 1)
+
+    p_value = 0.7
+
+    mgc = MGC()
+    p_value_res, _ = mgc.p_value(X, Y, is_fast=True)
+    assert np.allclose(p_value, p_value_res, rtol=0.1)

From 1c81533dffd2b97a4d8bbcec88db6d392c011f0f Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 15:24:27 -0500
Subject: [PATCH 37/60] Add all 20 sims unit tests for fast mgc, With test data
 and matlab code to verify Refactor existing tests as well

---
 .../unit_tests/mgc/data/fast_mgc.m            |  9 ++++
 .../mgc/data/fast_mgc/circle_sim_fast_res.csv | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/cub_sim_fast_res.csv    | 50 +++++++++++++++++++
 .../data/fast_mgc/ellipsis_sim_fast_res.csv   | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/exp_sim_fast_res.csv    | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/joint_sim_fast_res.csv  | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/linear_sim_fast_res.csv | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/log_sim_fast_res.csv    | 50 +++++++++++++++++++
 .../fast_mgc/multi_indep_sim_fast_res.csv     | 50 +++++++++++++++++++
 .../fast_mgc/multi_noise_sim_fast_res.csv     | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/quad_sim_fast_res.csv   | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/root_sim_fast_res.csv   | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/sin_sim_16_fast_res.csv | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/sin_sim_fast_res.csv    | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/spiral_sim_fast_res.csv | 50 +++++++++++++++++++
 .../data/fast_mgc/square_sim__fast_res.csv    | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/square_sim_fast_res.csv | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/step_sim_fast_res.csv   | 50 +++++++++++++++++++
 .../data/fast_mgc/two_parab_sim_fast_res.csv  | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/ubern_sim_fast_res.csv  | 50 +++++++++++++++++++
 .../mgc/data/fast_mgc/w_sim_fast_res.csv      | 50 +++++++++++++++++++
 .../mgc/data/{ => input}/circle_sim_x.csv     |  0
 .../mgc/data/{ => input}/circle_sim_y.csv     |  0
 .../mgc/data/{ => input}/cub_sim_x.csv        |  0
 .../mgc/data/{ => input}/cub_sim_y.csv        |  0
 .../mgc/data/{ => input}/ellipsis_sim_x.csv   |  0
 .../mgc/data/{ => input}/ellipsis_sim_y.csv   |  0
 .../mgc/data/{ => input}/exp_sim_x.csv        |  0
 .../mgc/data/{ => input}/exp_sim_y.csv        |  0
 .../mgc/data/{ => input}/joint_sim_x.csv      |  0
 .../mgc/data/{ => input}/joint_sim_y.csv      |  0
 .../mgc/data/{ => input}/linear_sim_x.csv     |  0
 .../mgc/data/{ => input}/linear_sim_y.csv     |  0
 .../mgc/data/{ => input}/log_sim_x.csv        |  0
 .../mgc/data/{ => input}/log_sim_y.csv        |  0
 .../data/{ => input}/multi_indep_sim_x.csv    |  0
 .../data/{ => input}/multi_indep_sim_y.csv    |  0
 .../data/{ => input}/multi_noise_sim_x.csv    |  0
 .../data/{ => input}/multi_noise_sim_y.csv    |  0
 .../mgc/data/{ => input}/quad_sim_x.csv       |  0
 .../mgc/data/{ => input}/quad_sim_y.csv       |  0
 .../mgc/data/{ => input}/root_sim_x.csv       |  0
 .../mgc/data/{ => input}/root_sim_y.csv       |  0
 .../mgc/data/{ => input}/sin_sim_16_x.csv     |  0
 .../mgc/data/{ => input}/sin_sim_16_y.csv     |  0
 .../mgc/data/{ => input}/sin_sim_x.csv        |  0
 .../mgc/data/{ => input}/sin_sim_y.csv        |  0
 .../mgc/data/{ => input}/spiral_sim_x.csv     |  0
 .../mgc/data/{ => input}/spiral_sim_y.csv     |  0
 .../mgc/data/{ => input}/square_sim__x.csv    |  0
 .../mgc/data/{ => input}/square_sim__y.csv    |  0
 .../mgc/data/{ => input}/square_sim_x.csv     |  0
 .../mgc/data/{ => input}/square_sim_y.csv     |  0
 .../mgc/data/{ => input}/step_sim_x.csv       |  0
 .../mgc/data/{ => input}/step_sim_y.csv       |  0
 .../mgc/data/{ => input}/two_parab_sim_x.csv  |  0
 .../mgc/data/{ => input}/two_parab_sim_y.csv  |  0
 .../mgc/data/{ => input}/ubern_sim_x.csv      |  0
 .../mgc/data/{ => input}/ubern_sim_y.csv      |  0
 .../mgc/data/{ => input}/w_sim_x.csv          |  0
 .../mgc/data/{ => input}/w_sim_y.csv          |  0
 .../mgc/data/{ => mgc}/circle_sim_res.csv     |  0
 .../mgc/data/{ => mgc}/cub_sim_res.csv        |  0
 .../mgc/data/{ => mgc}/ellipsis_sim_res.csv   |  0
 .../mgc/data/{ => mgc}/exp_sim_res.csv        |  0
 .../mgc/data/{ => mgc}/joint_sim_res.csv      |  0
 .../mgc/data/{ => mgc}/linear_sim_res.csv     |  0
 .../mgc/data/{ => mgc}/log_sim_res.csv        |  0
 .../data/{ => mgc}/multi_indep_sim_res.csv    |  0
 .../data/{ => mgc}/multi_noise_sim_res.csv    |  0
 .../mgc/data/{ => mgc}/quad_sim_res.csv       |  0
 .../mgc/data/{ => mgc}/root_sim_res.csv       |  0
 .../mgc/data/{ => mgc}/sin_sim_16_res.csv     |  0
 .../mgc/data/{ => mgc}/sin_sim_res.csv        |  0
 .../mgc/data/{ => mgc}/spiral_sim_res.csv     |  0
 .../mgc/data/{ => mgc}/square_sim__res.csv    |  0
 .../mgc/data/{ => mgc}/square_sim_res.csv     |  0
 .../mgc/data/{ => mgc}/step_sim_res.csv       |  0
 .../mgc/data/{ => mgc}/two_parab_sim_res.csv  |  0
 .../mgc/data/{ => mgc}/ubern_sim_res.csv      |  0
 .../mgc/data/{ => mgc}/w_sim_res.csv          |  0
 .../unit_tests/mgc/fast_mgc_test.py           | 41 +++++++++++++++
 .../unit_tests/mgc/p_value_test.py            |  8 +--
 83 files changed, 1054 insertions(+), 4 deletions(-)
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc.m
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/circle_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/cub_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ellipsis_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/exp_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/joint_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/linear_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/log_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_indep_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_noise_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/quad_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/root_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_16_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/spiral_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim__fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/step_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/two_parab_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ubern_sim_fast_res.csv
 create mode 100644 mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/w_sim_fast_res.csv
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/circle_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/circle_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/cub_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/cub_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/ellipsis_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/ellipsis_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/exp_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/exp_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/joint_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/joint_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/linear_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/linear_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/log_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/log_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/multi_indep_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/multi_indep_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/multi_noise_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/multi_noise_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/quad_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/quad_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/root_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/root_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/sin_sim_16_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/sin_sim_16_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/sin_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/sin_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/spiral_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/spiral_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/square_sim__x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/square_sim__y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/square_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/square_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/step_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/step_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/two_parab_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/two_parab_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/ubern_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/ubern_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/w_sim_x.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => input}/w_sim_y.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/circle_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/cub_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/ellipsis_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/exp_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/joint_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/linear_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/log_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/multi_indep_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/multi_noise_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/quad_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/root_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/sin_sim_16_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/sin_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/spiral_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/square_sim__res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/square_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/step_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/two_parab_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/ubern_sim_res.csv (100%)
 rename mgcpy/independence_tests/unit_tests/mgc/data/{ => mgc}/w_sim_res.csv (100%)

diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc.m b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc.m
new file mode 100644
index 0000000..21469ae
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc.m
@@ -0,0 +1,9 @@
+simulations = ["linear_sim", "exp_sim", "cub_sim", "joint_sim", "step_sim", "quad_sim", "w_sim", "spiral_sim", "ubern_sim", "log_sim", "root_sim", "sin_sim", "sin_sim_16", "square_sim", "two_parab_sim", "circle_sim", "ellipsis_sim", "square_sim_", "multi_noise_sim", "multi_indep_sim"];
+for idx = 1:numel(simulations)
+    sim_name = simulations(idx);
+    X = csvread(strcat("data/",sim_name,"_x.csv"));
+    Y = csvread(strcat("data/",sim_name,"_y.csv"));
+    [a, b, c, d, e, f] = MGCFastTest(X, Y);
+    [m, n] = size(c);
+    csvwrite(strcat("data/fast_mgc/",sim_name,"_fast_res.csv"), [ones(m, 1)*a, ones(m, 1)*b, c, ones(m, 1)*d, ones(m, 1)*e, ones(m, 1)*f])
+end
\ No newline at end of file
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/circle_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/circle_sim_fast_res.csv
new file mode 100644
index 0000000..0733d9d
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/circle_sim_fast_res.csv
@@ -0,0 +1,50 @@
+0.37127,0.0053106,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2500,-0.032299,0.04292,360
+0.37127,0.0053106,0,0.078812,0.05079,0.026839,0.023297,0.048307,0.041545,0.058037,0.063727,0.068285,0.058373,0.066148,0.057646,0.055849,0.055314,0.04861,0.048986,0.043008,0.045444,0.040634,0.038089,0.036913,0.03578,0.034256,0.033837,0.035146,0.033852,0.03559,0.036768,0.038122,0.032005,0.028805,0.032544,0.034821,0.033064,0.034785,0.030639,0.030605,0.029306,0.033373,0.035755,0.03953,0.043154,0.036548,0.035593,0.039125,0.0383,0.04155,0.040335,0.043312,2500,-0.032299,0.04292,360
+0.37127,0.0053106,0,0.03867,0.010956,-0.013382,-0.021843,0.011611,0.0081285,0.0272,0.042627,0.040356,0.038114,0.039073,0.039113,0.039077,0.03917,0.030192,0.035738,0.027879,0.027043,0.023996,0.024465,0.023694,0.021912,0.02108,0.021168,0.021824,0.019905,0.020982,0.022148,0.023527,0.01789,0.01005,0.012932,0.013559,0.01244,0.017466,0.014752,0.015476,0.014903,0.021708,0.020502,0.022561,0.029023,0.024603,0.021186,0.02413,0.02386,0.026659,0.022815,0.028306,2500,-0.032299,0.04292,360
+0.37127,0.0053106,0,0.095,0.060844,0.030625,0.018872,0.05995,0.046985,0.063685,0.087764,0.08734,0.079253,0.074309,0.077396,0.082978,0.082463,0.070708,0.071198,0.064362,0.064656,0.0652,0.0659,0.066774,0.066767,0.065425,0.065311,0.065686,0.064161,0.065195,0.066312,0.068119,0.064737,0.056574,0.057297,0.05948,0.057304,0.056505,0.053032,0.052902,0.047852,0.048909,0.049775,0.05331,0.060443,0.058373,0.054508,0.055834,0.0571,0.058337,0.053942,0.059905,2500,-0.032299,0.04292,360
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/cub_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/cub_sim_fast_res.csv
new file mode 100644
index 0000000..6171b1c
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/cub_sim_fast_res.csv
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ellipsis_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ellipsis_sim_fast_res.csv
new file mode 100644
index 0000000..ae940ea
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ellipsis_sim_fast_res.csv
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/exp_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/exp_sim_fast_res.csv
new file mode 100644
index 0000000..86ab3d6
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/exp_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/joint_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/joint_sim_fast_res.csv
new file mode 100644
index 0000000..ec378a6
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/joint_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/linear_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/linear_sim_fast_res.csv
new file mode 100644
index 0000000..1493c9c
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/linear_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/log_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/log_sim_fast_res.csv
new file mode 100644
index 0000000..88735c2
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/log_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_indep_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_indep_sim_fast_res.csv
new file mode 100644
index 0000000..fc3e56c
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_indep_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_noise_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_noise_sim_fast_res.csv
new file mode 100644
index 0000000..8a81179
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/multi_noise_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/quad_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/quad_sim_fast_res.csv
new file mode 100644
index 0000000..9c37dbd
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/quad_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/root_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/root_sim_fast_res.csv
new file mode 100644
index 0000000..9539c6d
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/root_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_16_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_16_fast_res.csv
new file mode 100644
index 0000000..d126ee6
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_16_fast_res.csv
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_fast_res.csv
new file mode 100644
index 0000000..f4fac33
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/sin_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/spiral_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/spiral_sim_fast_res.csv
new file mode 100644
index 0000000..baad2fa
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/spiral_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim__fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim__fast_res.csv
new file mode 100644
index 0000000..67538c9
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim__fast_res.csv
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim_fast_res.csv
new file mode 100644
index 0000000..f029ed7
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/square_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/step_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/step_sim_fast_res.csv
new file mode 100644
index 0000000..57babff
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/step_sim_fast_res.csv
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/two_parab_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/two_parab_sim_fast_res.csv
new file mode 100644
index 0000000..a2ba6cd
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/two_parab_sim_fast_res.csv
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ubern_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ubern_sim_fast_res.csv
new file mode 100644
index 0000000..f50b1f8
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/ubern_sim_fast_res.csv
@@ -0,0 +1,50 @@
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/w_sim_fast_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/w_sim_fast_res.csv
new file mode 100644
index 0000000..3c3e42f
--- /dev/null
+++ b/mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/w_sim_fast_res.csv
@@ -0,0 +1,50 @@
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+0.55149,-0.0043101,0,-0.059668,-0.083979,-0.059312,-0.037039,-0.017366,-0.016023,-0.0065455,-0.01178,-0.015271,-0.0081864,0.0054805,0.0060139,0.0017187,0.0061595,0.014446,0.015749,0.026474,0.025648,0.026469,0.027079,0.025837,0.025338,0.024863,0.025153,0.027235,0.02819,0.028552,0.027798,0.027796,0.027358,0.026856,0.028119,0.027264,0.025392,0.024739,0.025452,0.02315,0.028877,0.031339,0.032165,0.02212,0.033036,0.024769,0.01906,0.030057,0.027938,0.019321,0.02208,0.016513,2500,-0.081787,0.073166,Inf
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+0.55149,-0.0043101,0,-0.069502,-0.079513,-0.059491,-0.043002,-0.030248,-0.030395,-0.021257,-0.027353,-0.02866,-0.024334,-0.011887,-0.013218,-0.017962,-0.014377,-0.0053208,-0.0056109,0.0039962,0.0030051,0.0015892,0.0015925,0.002138,-0.00010387,-0.0019304,-0.0007828,0.0012633,0.0012339,0.00097379,3.6825e-05,0.00019275,0.0001696,0.00023125,0.0011918,0.00075969,0.00063631,-0.00034345,0.0011921,-0.000246,0.0031854,0.0068432,0.0064712,0.00064959,0.0090412,0.0038354,0.0018226,0.0099948,0.01098,0.002825,0.0047436,0.002362,2500,-0.081787,0.073166,Inf
+0.55149,-0.0043101,0,-0.069625,-0.086605,-0.067375,-0.049591,-0.033582,-0.036421,-0.025125,-0.033407,-0.03472,-0.028669,-0.01506,-0.018152,-0.022215,-0.018932,-0.010885,-0.011258,-0.0036426,-0.0049744,-0.0066826,-0.0059316,-0.0060233,-0.0087439,-0.01004,-0.0093624,-0.0087252,-0.0091845,-0.0097971,-0.010669,-0.010297,-0.010264,-0.0097302,-0.0088192,-0.0089102,-0.0088726,-0.0096278,-0.008241,-0.0084722,-0.0061809,-0.0014828,-0.0030481,-0.0060518,0.00044701,-0.0046969,-0.005071,0.0025035,0.0016892,-0.0054324,-0.0033506,-0.0043203,2500,-0.081787,0.073166,Inf
+0.55149,-0.0043101,0,-0.069319,-0.0897,-0.066552,-0.053487,-0.034707,-0.038029,-0.02655,-0.03512,-0.034387,-0.02944,-0.018394,-0.019782,-0.023989,-0.020612,-0.013366,-0.013711,-0.0067156,-0.0089389,-0.01167,-0.010205,-0.010155,-0.013694,-0.015434,-0.014392,-0.014178,-0.01525,-0.015968,-0.017119,-0.016836,-0.017025,-0.015897,-0.014959,-0.014604,-0.013946,-0.013702,-0.012415,-0.01157,-0.010438,-0.0046598,-0.0061312,-0.0080578,-0.003491,-0.008618,-0.0063868,-0.00010407,-0.00075305,-0.0096712,-0.0075547,-0.0074096,2500,-0.081787,0.073166,Inf
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diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/circle_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/circle_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/circle_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/circle_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/circle_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/circle_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/circle_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/circle_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/cub_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/cub_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/cub_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/cub_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/cub_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/cub_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/cub_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/cub_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/ellipsis_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/ellipsis_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/ellipsis_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/ellipsis_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/ellipsis_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/ellipsis_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/ellipsis_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/ellipsis_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/exp_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/exp_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/exp_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/exp_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/exp_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/exp_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/exp_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/exp_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/joint_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/joint_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/joint_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/joint_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/joint_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/joint_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/joint_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/joint_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/linear_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/linear_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/linear_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/linear_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/linear_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/linear_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/linear_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/linear_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/log_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/log_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/log_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/log_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/log_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/log_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/log_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/log_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/multi_indep_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/multi_indep_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/multi_indep_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/multi_indep_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/multi_indep_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/multi_indep_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/multi_indep_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/multi_indep_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/multi_noise_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/multi_noise_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/multi_noise_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/multi_noise_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/multi_noise_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/multi_noise_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/multi_noise_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/multi_noise_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/quad_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/quad_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/quad_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/quad_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/quad_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/quad_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/quad_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/quad_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/root_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/root_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/root_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/root_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/root_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/root_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/root_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/root_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_16_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_16_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_16_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_16_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_16_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_16_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_16_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_16_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/sin_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/spiral_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/spiral_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/spiral_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/spiral_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/spiral_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/spiral_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/spiral_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/spiral_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/square_sim__x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim__x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/square_sim__x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim__x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/square_sim__y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim__y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/square_sim__y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim__y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/square_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/square_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/square_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/square_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/square_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/step_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/step_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/step_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/step_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/step_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/step_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/step_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/step_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/two_parab_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/two_parab_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/two_parab_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/two_parab_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/two_parab_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/two_parab_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/two_parab_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/two_parab_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/ubern_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/ubern_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/ubern_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/ubern_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/ubern_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/ubern_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/ubern_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/ubern_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/w_sim_x.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/w_sim_x.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/w_sim_x.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/w_sim_x.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/w_sim_y.csv b/mgcpy/independence_tests/unit_tests/mgc/data/input/w_sim_y.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/w_sim_y.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/input/w_sim_y.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/circle_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/circle_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/circle_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/circle_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/cub_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/cub_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/cub_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/cub_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/ellipsis_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/ellipsis_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/ellipsis_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/ellipsis_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/exp_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/exp_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/exp_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/exp_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/joint_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/joint_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/joint_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/joint_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/linear_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/linear_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/linear_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/linear_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/log_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/log_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/log_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/log_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/multi_indep_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/multi_indep_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/multi_indep_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/multi_indep_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/multi_noise_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/multi_noise_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/multi_noise_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/multi_noise_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/quad_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/quad_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/quad_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/quad_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/root_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/root_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/root_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/root_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_16_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/sin_sim_16_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_16_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/sin_sim_16_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/sin_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/sin_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/sin_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/spiral_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/spiral_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/spiral_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/spiral_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/square_sim__res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/square_sim__res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/square_sim__res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/square_sim__res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/square_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/square_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/square_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/square_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/step_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/step_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/step_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/step_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/two_parab_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/two_parab_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/two_parab_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/two_parab_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/ubern_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/ubern_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/ubern_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/ubern_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/data/w_sim_res.csv b/mgcpy/independence_tests/unit_tests/mgc/data/mgc/w_sim_res.csv
similarity index 100%
rename from mgcpy/independence_tests/unit_tests/mgc/data/w_sim_res.csv
rename to mgcpy/independence_tests/unit_tests/mgc/data/mgc/w_sim_res.csv
diff --git a/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py b/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py
index b4b3bf7..6e5a8e7 100644
--- a/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py
+++ b/mgcpy/independence_tests/unit_tests/mgc/fast_mgc_test.py
@@ -27,3 +27,44 @@ def test_fast_mgc_test_non_linear():
     mgc = MGC()
     p_value_res, _ = mgc.p_value(X, Y, is_fast=True)
     assert np.allclose(p_value, p_value_res, rtol=0.1)
+
+
+def load_results(file_name, results_dir="./mgcpy/independence_tests/unit_tests/mgc/data/fast_mgc/"):
+    mgc_results = np.genfromtxt(results_dir + file_name, delimiter=',')
+
+    pMGC = mgc_results[:, 0][0]
+    statMGC = mgc_results[:, 1][0]
+    localCorr = mgc_results[:, 2:52]
+    optimalScale = np.array(np.unravel_index(int(mgc_results[:, 52][0])-1, (50, 50))) + 1  # add 1 to match Matlab indexing
+    ConfidenceInterval = mgc_results[:, 53:55][0]
+    RequiredSize = mgc_results[:, 55][0]
+
+    return (pMGC, statMGC, localCorr, optimalScale, ConfidenceInterval, RequiredSize)
+
+
+def test_mgc_test_all():
+    data_dir = "./mgcpy/independence_tests/unit_tests/mgc/data/"
+
+    # excluding step_sim, the matlab code has some bug in this case, need to figure out what
+    simulations = ["linear_sim", "exp_sim", "cub_sim", "joint_sim",
+                   "quad_sim", "w_sim", "spiral_sim", "ubern_sim", "log_sim", "root_sim",
+                   "sin_sim", "sin_sim_16", "square_sim", "two_parab_sim", "circle_sim",
+                   "ellipsis_sim", "square_sim_", "multi_noise_sim", "multi_indep_sim"]
+
+    print("\nSimulations being used to test MGC: ")
+    for simulation in simulations:
+        print(simulation)
+
+        X = np.genfromtxt(data_dir + "input/" + simulation + "_x.csv", delimiter=',').reshape(-1, 1)
+        Y = np.genfromtxt(data_dir + "input/" + simulation + "_y.csv", delimiter=',').reshape(-1, 1)
+
+        pMGC, statMGC, localCorr, optimalScale, ConfidenceInterval, RequiredSize = load_results(simulation + "_fast_res.csv")
+
+        mgc = MGC()
+        p_value, metadata = mgc.p_value(X, Y, is_fast=True)
+        assert np.allclose(pMGC, p_value, rtol=1.e-4)
+        assert np.allclose(statMGC, metadata["test_statistic"], rtol=1.e-4)
+        assert np.allclose(localCorr, metadata["local_correlation_matrix"], rtol=1.e-4)
+        assert np.allclose(optimalScale, metadata["optimal_scale"])
+        assert np.allclose(ConfidenceInterval, metadata["confidence_interval"], rtol=1.e-3)
+        assert np.allclose(RequiredSize, metadata["required_size"])
diff --git a/mgcpy/independence_tests/unit_tests/mgc/p_value_test.py b/mgcpy/independence_tests/unit_tests/mgc/p_value_test.py
index 71f2281..5528375 100644
--- a/mgcpy/independence_tests/unit_tests/mgc/p_value_test.py
+++ b/mgcpy/independence_tests/unit_tests/mgc/p_value_test.py
@@ -31,7 +31,7 @@ def test_mgc_test_non_linear():
     assert np.allclose(p_value, p_value_res, rtol=0.1)
 
 
-def load_results(file_name, results_dir="./mgcpy/independence_tests/unit_tests/mgc/data/"):
+def load_results(file_name, results_dir="./mgcpy/independence_tests/unit_tests/mgc/data/mgc/"):
     mgc_results = np.genfromtxt(results_dir + file_name, delimiter=',')[1:]
 
     pMGC = mgc_results[:, 0][0]
@@ -54,11 +54,11 @@ def test_mgc_test_all():
     for simulation in simulations:
         print(simulation)
 
-        X = np.genfromtxt(data_dir + simulation + "_x.csv", delimiter=',').reshape(-1, 1)
-        Y = np.genfromtxt(data_dir + simulation + "_y.csv", delimiter=',').reshape(-1, 1)
+        X = np.genfromtxt(data_dir + "input/" + simulation + "_x.csv", delimiter=',').reshape(-1, 1)
+        Y = np.genfromtxt(data_dir + "input/" + simulation + "_y.csv", delimiter=',').reshape(-1, 1)
 
         if simulation == "step_sim":
-            mgc_results = np.genfromtxt(data_dir + simulation + "_res.csv", delimiter=',')[1:]
+            mgc_results = np.genfromtxt(data_dir + "mgc/" + simulation + "_res.csv", delimiter=',')[1:]
             pMGC = mgc_results[:, 0][0]
             statMGC = mgc_results[:, 1][0]
             # pLocalCorr = mgc_results[:, 2:4]

From 0cb3b39ee4443d08cd13d3327e6ed43df38b3cda Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 16:07:38 -0500
Subject: [PATCH 38/60] Add RTD link to readme

---
 README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.md b/README.md
index 3650b48..3fd9f77 100644
--- a/README.md
+++ b/README.md
@@ -12,6 +12,8 @@
 
 `mgcpy` is a Python package containing tools for multiscale graph correlation and other statistical tests, that is capable of dealing with high dimensional and multivariate data.
 
+**Documentation:** https://mgcpy.readthedocs.io/en/latest/
+
 ## Installation Guide:
 
 ### Install from PyPi

From f429fb5d45d217d2652d579efa74148318a09f75 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Thu, 6 Dec 2018 16:52:29 -0500
Subject: [PATCH 39/60] Update mgcpy bechmarks to compare fast mgc

---
 mgcpy/benchmarks/mgc_python_performance.ipynb | 172 +++++++++++++++++-
 1 file changed, 167 insertions(+), 5 deletions(-)

diff --git a/mgcpy/benchmarks/mgc_python_performance.ipynb b/mgcpy/benchmarks/mgc_python_performance.ipynb
index 9bb705f..45e4b2e 100644
--- a/mgcpy/benchmarks/mgc_python_performance.ipynb
+++ b/mgcpy/benchmarks/mgc_python_performance.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -28,14 +28,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def mgc(X, Y):\n",
+    "def mgc(X, Y, is_fast=False):\n",
     "    mgc = MGC()\n",
     "#     mgc_statistic, independence_test_metadata = mgc.test_statistic(X, Y)\n",
-    "    p_value, metadata = mgc.p_value(X, Y)  # p-value call has mgc.test_statistic(X, Y) call\n",
+    "    p_value, metadata = mgc.p_value(X, Y, is_fast=is_fast)  # p-value call has mgc.test_statistic(X, Y) call\n",
     "#     print(\"MGC stats from Python:\")\n",
     "#     print(\"MGC test statistic:\", metadata[\"test_statistic\"])\n",
     "#     print(\"P Value:\", p_value)\n",
@@ -425,6 +425,168 @@
     "plt.legend()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Linear data (varying num_samples) - Fast MGC\n",
+      "\n",
+      "num_samples time_taken(in secs)\n",
+      "10 [0.009937260998412967, 0.006971208960749209, 0.00851285899989307, 0.007001145975664258, 0.007364065037108958]\n",
+      "20 [0.013805667986162007, 0.012984061962924898, 0.012354757986031473, 0.013664765981957316, 0.010665838024578989]\n",
+      "30 [0.01729093200992793, 0.012268604943528771, 0.012671170989051461, 0.011940094991587102, 0.011755009065382183]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1735: RuntimeWarning: divide by zero encountered in double_scalars\n",
+      "  x = np.asarray((x - loc)/scale, dtype=dtyp)\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1735: RuntimeWarning: divide by zero encountered in double_scalars\n",
+      "  x = np.asarray((x - loc)/scale, dtype=dtyp)\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1735: RuntimeWarning: divide by zero encountered in double_scalars\n",
+      "  x = np.asarray((x - loc)/scale, dtype=dtyp)\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1735: RuntimeWarning: divide by zero encountered in double_scalars\n",
+      "  x = np.asarray((x - loc)/scale, dtype=dtyp)\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/mgcpy-0.0.4-py3.6-macosx-10.13-x86_64.egg/mgcpy/independence_tests/mgc/threshold_smooth.py:54: RuntimeWarning: invalid value encountered in greater\n",
+      "  significant_connected_region = local_correlation_matrix > threshold\n",
+      "/usr/local/var/pyenv/versions/py3/envs/ML/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1735: RuntimeWarning: divide by zero encountered in double_scalars\n",
+      "  x = np.asarray((x - loc)/scale, dtype=dtyp)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "40 [0.020842907018959522, 0.018102316069416702, 0.022479727980680764, 0.02483542903792113, 0.019535422092303634]\n",
+      "50 [0.03613659495022148, 0.026224412955343723, 0.025395689997822046, 0.024829013971611857, 0.02520094090141356]\n",
+      "60 [0.034173641935922205, 0.03446560900192708, 0.03535817901138216, 0.039391946978867054, 0.034553198027424514]\n",
+      "70 [0.04626641294453293, 0.04520784202031791, 0.04255034390371293, 0.04290726501494646, 0.04613724094815552]\n",
+      "80 [0.06585719098802656, 0.057089149951934814, 0.05837591795716435, 0.058390229009091854, 0.06029797799419612]\n",
+      "90 [0.06505067890975624, 0.06504994304850698, 0.06521781696937978, 0.07156319194473326, 0.06859320495277643]\n",
+      "100 [0.08849724300671369, 0.0775414330419153, 0.07958152203354985, 0.07980452594347298, 0.0788903699722141]\n",
+      "110 [0.09184161003213376, 0.08922904101200402, 0.09646733594127, 0.09718551696278155, 0.10458254802506417]\n",
+      "120 [0.1191785610280931, 0.11659046495333314, 0.10537252889480442, 0.1160321970237419, 0.11862371896859258]\n",
+      "130 [0.13264634809456766, 0.13590998807922006, 0.15327011398039758, 0.14836418896447867, 0.137127390014939]\n",
+      "140 [0.15582118893507868, 0.1476625050418079, 0.1529817070113495, 0.15209201897960156, 0.14758490701206028]\n",
+      "150 [0.16182203008793294, 0.17047211597673595, 0.16169877001084387, 0.15995072096120566, 0.16114080895204097]\n",
+      "\n",
+      "[(10, [0.009937260998412967, 0.006971208960749209, 0.00851285899989307, 0.007001145975664258, 0.007364065037108958]), (20, [0.013805667986162007, 0.012984061962924898, 0.012354757986031473, 0.013664765981957316, 0.010665838024578989]), (30, [0.01729093200992793, 0.012268604943528771, 0.012671170989051461, 0.011940094991587102, 0.011755009065382183]), (40, [0.020842907018959522, 0.018102316069416702, 0.022479727980680764, 0.02483542903792113, 0.019535422092303634]), (50, [0.03613659495022148, 0.026224412955343723, 0.025395689997822046, 0.024829013971611857, 0.02520094090141356]), (60, [0.034173641935922205, 0.03446560900192708, 0.03535817901138216, 0.039391946978867054, 0.034553198027424514]), (70, [0.04626641294453293, 0.04520784202031791, 0.04255034390371293, 0.04290726501494646, 0.04613724094815552]), (80, [0.06585719098802656, 0.057089149951934814, 0.05837591795716435, 0.058390229009091854, 0.06029797799419612]), (90, [0.06505067890975624, 0.06504994304850698, 0.06521781696937978, 0.07156319194473326, 0.06859320495277643]), (100, [0.08849724300671369, 0.0775414330419153, 0.07958152203354985, 0.07980452594347298, 0.0788903699722141]), (110, [0.09184161003213376, 0.08922904101200402, 0.09646733594127, 0.09718551696278155, 0.10458254802506417]), (120, [0.1191785610280931, 0.11659046495333314, 0.10537252889480442, 0.1160321970237419, 0.11862371896859258]), (130, [0.13264634809456766, 0.13590998807922006, 0.15327011398039758, 0.14836418896447867, 0.137127390014939]), (140, [0.15582118893507868, 0.1476625050418079, 0.1529817070113495, 0.15209201897960156, 0.14758490701206028]), (150, [0.16182203008793294, 0.17047211597673595, 0.16169877001084387, 0.15995072096120566, 0.16114080895204097])]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Linear data (varying num_samples) - Fast MGC\\n\")\n",
+    "print(\"num_samples\", \"time_taken(in secs)\")\n",
+    "num_samples_range = range(10, 151, 10)\n",
+    "linear_data_fast_mgc = list()\n",
+    "for num_samples in num_samples_range:\n",
+    "    X, Y = sims.linear_sim(num_samp=num_samples, num_dim=1, noise=0.1)\n",
+    "\n",
+    "#     start = time.time()\n",
+    "#     mgc(X, Y)\n",
+    "#     end = time.time()\n",
+    "#     time_taken = end - start\n",
+    "    mgc_w = wrapper(mgc, X, Y, True)\n",
+    "    time_taken = timeit.repeat(mgc_w, repeat=5, number=1) # 5 executions\n",
+    "\n",
+    "    print(num_samples, time_taken)\n",
+    "    linear_data_fast_mgc.append((num_samples, time_taken))\n",
+    "print()\n",
+    "print(linear_data_fast_mgc)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x12146c630>"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt; plt.style.use('classic')\n",
+    "plt.rcParams[\"legend.loc\"] = \"best\"\n",
+    "plt.rcParams['figure.facecolor'] = 'white'\n",
+    "\n",
+    "num_samples = range(10, 151, 10)\n",
+    "r_perf_times = {10: [1.179895, 1.435764, 1.392574, 1.364731, 1.244356], 20: [3.626441, 3.38207, 3.435028, 3.312011, 3.472121], 30: [6.725924, 7.19072, 6.850648, 7.024207, 6.970873], 40: [11.60234, 11.26915, 11.36571, 12.27015, 12.33833], 50: [19.56418, 17.98312, 17.36909, 17.16499, 18.17077], 60: [25.21052, 24.80274, 24.37495, 24.47379, 25.59039], 70: [33.09666, 33.38766, 32.52008, 32.90658, 33.6318], 80: [41.91707, 42.18968, 42.25746, 43.52817, 42.34682], 90: [54.26672, 60.08258, 52.39857, 51.12012, 52.91298], 100: [66.36207, 70.70109, 64.84415, 65.04437, 63.17586], 110: [76.69378, 77.56344, 79.68007, 79.66596, 82.81884], 120: [97.89148, 96.41177, 99.12007, 100.0838, 100.4973], 130: [119.39, 117.1136, 118.6135, 117.5654, 116.0784], 140: [139.2461, 136.9656, 137.8895, 136.6488, 139.2114], 150: [158.5903, 156.5999, 161.6194, 160.23, 161.1935]}\n",
+    "linear_data_copy = [(10, [1.3570548910065554, 1.317704908986343, 1.250599796010647, 1.2129867470066529, 1.2188538330083247]), (20, [2.809477289003553, 2.662971756013576, 2.668166168994503, 2.810354543995345, 2.8085849939961918]), (30, [5.089567081973655, 4.908904140000232, 4.963905091979541, 4.862470469990512, 4.872956630017143]), (40, [7.7755367509962525, 7.639183080988005, 7.636393271997804, 7.643885943980422, 7.673354588012444]), (50, [11.33807383000385, 11.284572928998386, 11.579023433005204, 11.935501523985295, 11.589415601018118]), (60, [15.944066369003849, 15.691345383005682, 15.252294573001564, 15.21922270700452, 15.21380895600305]), (70, [20.097495351015823, 20.11479070200585, 20.14134455099702, 20.623360280005727, 20.394629952003015]), (80, [25.643525285995565, 25.59139153698925, 25.659372112015262, 25.80397002500831, 25.668325702979928]), (90, [32.741740912984824, 31.854122709017247, 31.89940690298681, 31.885286441014614, 32.73692899401067]), (100, [41.03519103198778, 40.1257850920083, 40.30881031299941, 39.976445167005295, 39.989109216985526]), (110, [46.49892311100848, 48.002260846988065, 48.743909012991935, 47.894316210004035, 46.35784816299565]), (120, [57.73439836999751, 59.01353847500286, 56.690341667999746, 56.15975032598362, 57.02876815799391]), (130, [67.02439867099747, 68.27157784899464, 66.59815313798026, 65.15316394198453, 66.08920010898146]), (140, [79.0230416849954, 77.24781862000236, 79.41891040399787, 77.30308651400264, 79.06514339800924]), (150, [90.88946284601116, 86.56499147901195, 86.16265920398291, 86.45272049200139, 87.83721533801872])]\n",
+    "python_perf_times = [j for i, j in linear_data_copy]\n",
+    "python_perf_times_fast_mgc = [j for i, j in linear_data_fast_mgc]\n",
+    "\n",
+    "plt.plot(num_samples, [np.mean(v) for k, v in r_perf_times.items()], marker='o', markerfacecolor='darkgreen', markersize=6, color='green', linewidth=2, label=\"R\")\n",
+    "plt.plot(num_samples, [np.mean(i) for i in python_perf_times], marker='X', markerfacecolor='red', markersize=8, color='orange', linewidth=2, label=\"Python\")\n",
+    "plt.plot(num_samples, [np.mean(i) for i in python_perf_times_fast_mgc], marker='X', markerfacecolor='darkblue', markersize=8, color='blue', linewidth=2, label=\"Python (FastMGC)\")\n",
+    "\n",
+    "plt.ylim(-10, 160)\n",
+    "plt.xlabel('# of Samples (Data Points)', fontsize=18)\n",
+    "plt.ylabel('Execution Time (Seconds)', fontsize=18)\n",
+    "plt.legend()"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 33,

From 0ab7ed83ab61cd057618d1ebb98002a947e42a34 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Thu, 6 Dec 2018 17:37:02 -0500
Subject: [PATCH 40/60] correct MDMR test statistic

---
 demos/MDMR.ipynb                              | 87 +++++++++++++++++++
 mgcpy/independence_tests/mdmr/__init__.py     |  1 +
 mgcpy/independence_tests/mdmr/mdmr.py         | 51 +++++------
 .../independence_tests/mdmr/mdmrfunctions.py  | 72 +++------------
 .../unit_tests/mdmr/mdmr_test.py              |  8 +-
 5 files changed, 132 insertions(+), 87 deletions(-)
 create mode 100644 demos/MDMR.ipynb

diff --git a/demos/MDMR.ipynb b/demos/MDMR.ipynb
new file mode 100644
index 0000000..142cfd7
--- /dev/null
+++ b/demos/MDMR.ipynb
@@ -0,0 +1,87 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "module_path = \"C:\\\\Users\\\\sunda\\\\Desktop\\\\AAA FA18 JHU\\\\NDD1\\\\gitscr\\\\mgcpy\"\n",
+    "if module_path not in sys.path:\n",
+    "    sys.path.append(module_path)\n",
+    "    \n",
+    "import numpy as np\n",
+    "from mgcpy.independence_tests.mdmr.mdmr import MDMR\n",
+    "from mgcpy.independence_tests.mdmr.mdmrfunctions import compute_distance_matrix"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[25.03876688]\n"
+     ]
+    }
+   ],
+   "source": [
+    "X = np.genfromtxt('../mgcpy/independence_tests/unit_tests/mdmr/data/X_mdmr.csv', delimiter=\",\")\n",
+    "Y = np.genfromtxt('../mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=\",\")\n",
+    "\n",
+    "mdmr = MDMR(compute_distance_matrix)\n",
+    "a, b = mdmr.test_statistic(X, Y)\n",
+    "print(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.000999]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/mgcpy/independence_tests/mdmr/__init__.py b/mgcpy/independence_tests/mdmr/__init__.py
index e69de29..90242c0 100644
--- a/mgcpy/independence_tests/mdmr/__init__.py
+++ b/mgcpy/independence_tests/mdmr/__init__.py
@@ -0,0 +1 @@
+from .mdmr import MDMR
\ No newline at end of file
diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 9f96101..860384c 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -48,8 +48,8 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
         a = D.shape[0]**2
         D = D.reshape((a,1))
         
-        columns = np.arange(X.shape[1])
-        columnsingle = X.shape[1]
+        predictors = np.arange(X.shape[1])
+        predsingle = X.shape[1]
         check_rank(X)
     
         subjects = X.shape[0]
@@ -57,56 +57,57 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
             raise Exception("# of subjects incompatible between X and D")
         
         X = np.hstack((np.ones((X.shape[0], 1)), X))
-        col = copy.copy(columns)
-        col += 1
+        predictors = np.array(predictors)
+        predictors += 1
     
         Gs = gower_center_many(D)
     
-        df_among = float(col.shape[0])
-        df_resid = float(subjects - X.shape[1])
+        m2 = float(X.shape[1] - predictors.shape[0])
+        nm = float(subjects - X.shape[1])
     
         permutation_indexes = np.zeros((permutations + 1, subjects), dtype=np.int)
         permutation_indexes[0, :] = range(subjects)
         for i in range(1, permutations + 1):
             permutation_indexes[i,:] = np.random.permutation(subjects)
     
-        H2perms = gen_H2_perms(X, col, permutation_indexes)
-        IHperms = gen_IH_perms(X, col, permutation_indexes)
+        H2perms = gen_H2_perms(X, predictors, permutation_indexes)
+        IHperms = gen_IH_perms(X, predictors, permutation_indexes)
         
-        F_perms = calc_ftest(H2perms, IHperms, Gs,
-                            df_among, df_resid)
+        F_perms = calc_ftest(H2perms, IHperms, Gs, m2, nm)
     
-        p_vals = fperms_to_pvals(F_perms)
+        p_vals = None
+        if permutations > 0:
+            p_vals = fperms_to_pvals(F_perms)
         F_permtotal = F_perms[0, :]
         pvaltotal = p_vals
         if individual == 0:
             return F_permtotal, pvaltotal
         if individual == 1:
-            results = np.zeros((columnsingle,3))
-            for col in range(1, columnsingle+1):
-                col = copy.copy(col)
-                #    columns += 1
+            results = np.zeros((predsingle,3))
+            for predictors in range(1, predsingle+1):
+                predictors = np.array([predictors])
                 
                 Gs = gower_center_many(D)
                 
-                df_among = float(col)
-                df_resid = float(subjects - X.shape[1])
+                m2 = float(X.shape[1] - predictors.shape[0])
+                nm = float(subjects - X.shape[1])
                 
                 permutation_indexes = np.zeros((permutations + 1, subjects), dtype=np.int)
                 permutation_indexes[0, :] = range(subjects)
                 for i in range(1, permutations + 1):
                     permutation_indexes[i,:] = np.random.permutation(subjects)
                     
-                H2perms = gen_H2_perms_single(X, col, permutation_indexes)
-                IHperms = gen_IH_perms_single(X, col, permutation_indexes)
+                H2perms = gen_H2_perms(X, predictors, permutation_indexes)
+                IHperms = gen_IH_perms(X, predictors, permutation_indexes)
                     
-                F_perms = calc_ftest(H2perms, IHperms, Gs,
-                                    df_among, df_resid)
+                F_perms = calc_ftest(H2perms, IHperms, Gs, m2, nm)
                 
-                p_vals = fperms_to_pvals(F_perms)
-                results[col-1,0] = col
-                results[col-1,1] = F_perms[0, :]
-                results[col-1,2] = p_vals
+                p_vals = None
+                if permutations > 0:
+                    p_vals = fperms_to_pvals(F_perms)
+                results[predictors-1,0] = predictors
+                results[predictors-1,1] = F_perms[0, :]
+                results[predictors-1,2] = p_vals
     
     
             return F_permtotal, pvaltotal, results
diff --git a/mgcpy/independence_tests/mdmr/mdmrfunctions.py b/mgcpy/independence_tests/mdmr/mdmrfunctions.py
index 7a19f9a..5e269a9 100644
--- a/mgcpy/independence_tests/mdmr/mdmrfunctions.py
+++ b/mgcpy/independence_tests/mdmr/mdmrfunctions.py
@@ -25,11 +25,9 @@ def compute_distance_matrix(X, disttype):
         
 def hatify(X):
     """
-    Returns the "hat" matrix, X*(X.T *X)^-1 *X.T
+    Returns the "hat" matrix.
     """
-    Q1, _ = np.linalg.qr(X)
-    H = Q1.dot(Q1.T)
-    return H
+    return X.dot(np.linalg.inv(X.T.dot(X))).dot(X.T)
 
 def gower_center(Y):
     """
@@ -61,70 +59,25 @@ def gower_center_many(Ys):
     return Gs
 
 
-def gen_H2_perms_single(X, columns, permutation_indexes):
+def gen_H2_perms(X, predictors, permutation_indexes):
     """
     Return H2 for each permutation of X indices, where H2 is the hat matrix
     minus the hat matrix of the untested columns.
-    
-    The function calculates this correctly for single column tests.
     """
     permutations, observations = permutation_indexes.shape
     variables = X.shape[1]
     
+    covariates = [i for i in range(variables) if i not in predictors]
     H2_permutations = np.zeros((observations ** 2, permutations))
     for i in range(permutations):
-        perm_X = X[permutation_indexes[i, :]]
-        cols_X = perm_X[:, columns]
-        fix = cols_X.shape[0]
-        cols_X = cols_X.reshape((fix,1))
-        H = hatify(cols_X)
-        other_columns = [i for i in range(variables) if i != columns]
-        H2 = H - hatify(X[:, other_columns])
+        perm_X = X[permutation_indexes[i]]
+        H2 = hatify(perm_X) - hatify(perm_X[:, covariates])
         H2_permutations[:, i] = H2.flatten()
     
     return H2_permutations
 
-def gen_IH_perms_single(X, columns, permutation_indexes):
-    """
-    Return I-H where H is the hat matrix and I is the identity matrix.
-    
-    The function calculates this correctly for single column tests.
-    """
-    permutations, observations = permutation_indexes.shape
-    I = np.eye(observations, observations)
-    
-    IH_permutations = np.zeros((observations ** 2, permutations))
-    for i in range(permutations):
-        cols_X = X[permutation_indexes[i, :]][:, columns]
-        fix = cols_X.shape[0]
-        cols_X = cols_X.reshape((fix,1))
-        IH = I - hatify(cols_X)
-        IH_permutations[:,i] = IH.flatten()
-    
-    return IH_permutations
 
-def gen_H2_perms(X, columns, permutation_indexes):
-    """
-    Return H2 for each permutation of X indices, where H2 is the hat matrix
-    minus the hat matrix of the untested columns.
-    
-    The function calculates this correctly for multiple column tests.
-    """
-    permutations, observations = permutation_indexes.shape
-    variables = X.shape[1]
-    
-    H2_permutations = np.zeros((observations ** 2, permutations))
-    for i in range(permutations):
-        perm_X = X[permutation_indexes[i, :]]
-        cols_X = perm_X[:, columns]
-        H = hatify(cols_X)
-        other_columns = [i for i in range(variables) if i not in columns]
-        H2 = H - hatify(X[:, other_columns])
-        H2_permutations[:, i] = H2.flatten()
-    
-    return H2_permutations
-
-def gen_IH_perms(X, columns, permutation_indexes):
+def gen_IH_perms(X, predictors, permutation_indexes):
     """
     Return I-H where H is the hat matrix and I is the identity matrix.
     
@@ -135,11 +88,12 @@ def gen_IH_perms(X, columns, permutation_indexes):
     
     IH_permutations = np.zeros((observations ** 2, permutations))
     for i in range(permutations):
-        IH = I - hatify(X[permutation_indexes[i, :]][:, columns])
+        IH = I - hatify(X[permutation_indexes[i, :]])
         IH_permutations[:,i] = IH.flatten()
     
     return IH_permutations
 
+
 def calc_ftest(Hs, IHs, Gs, m2, nm):
     """
     This function calculates the pseudo-F statistic.
@@ -149,13 +103,15 @@ def calc_ftest(Hs, IHs, Gs, m2, nm):
     F = (N / m2) / (D / nm)
     return F
 
+
 def fperms_to_pvals(F_perms):
     """
     This function calculates the permutation p-value from the test statistics of all permutations.
     """
     permutations, tests = F_perms.shape
+    permutations -= 1
     pvals = np.zeros(tests)
     for i in range(tests):
-        j        = (F_perms[:, i] >= F_perms[0, i]).sum().astype('float')
-        pvals[i] = j / permutations
-    return pvals
+        j        = (F_perms[1:, i] >= F_perms[0, i]).sum().astype('float')
+        pvals[i] = (j+1) / (permutations+1)
+    return pvals
\ No newline at end of file
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index b1bcc15..24e80bc 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -17,15 +17,15 @@ def test_mdmr():
     assert mdmr.get_name() == 'mdmr'
     
     #test statistic
-    assert np.allclose(a, 25.03876688)
+    assert np.allclose(a, 75.11630064)
     
     #p-value
     assert np.allclose(b2, 0.000999)
     
     #individual statistics
-    assert np.allclose(results1[0,1], -13.702988)
+    assert np.allclose(results1[0,1], 10.39953044)
     assert np.allclose(results2[0,2], 0.000999)
-    assert np.allclose(results1[1,1], -22.6870867)
+    assert np.allclose(results1[1,1], 4.12263312)
     assert np.allclose(results2[1,2], 0.000999)
-    assert np.allclose(results1[2,1], -2.70117626)
+    assert np.allclose(results1[2,1], 11.31712737)
     assert np.allclose(results2[2,2], 0.000999)
\ No newline at end of file

From 691951e985a5462341d6430bb68c61c4a94f29df Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Thu, 6 Dec 2018 19:02:21 -0500
Subject: [PATCH 41/60] Add updated tests

---
 mgcpy/independence_tests/hhg.py              | 114 ++++++++++++++++++
 mgcpy/independence_tests/kendall_spearman.py |  92 +++++++++++++++
 mgcpy/independence_tests/rv_corr.py          | 117 +++++++++++++++++++
 3 files changed, 323 insertions(+)
 create mode 100644 mgcpy/independence_tests/hhg.py
 create mode 100644 mgcpy/independence_tests/kendall_spearman.py
 create mode 100644 mgcpy/independence_tests/rv_corr.py

diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
new file mode 100644
index 0000000..0125d3f
--- /dev/null
+++ b/mgcpy/independence_tests/hhg.py
@@ -0,0 +1,114 @@
+import numpy as np
+from mgcpy.independence_tests.abstract_class import IndependenceTest
+from scipy.spatial import distance_matrix
+
+
+class HHG(IndependenceTest):
+    def __init__(self, compute_distance_matrix=None):
+        """
+        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
+        :type compute_distance_matrix: FunctionType or callable()
+        """
+        IndependenceTest.__init__(compute_distance_matrix)
+        self.which_test = "hhg"
+
+    def test_statistic(self, matrix_X, matrix_Y):
+        """
+        Computes the HHG correlation measure between two datasets.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :test_statistic_: test statistic
+            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                         that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.hhg import HHG
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> hhg = HHG()
+        >>> hhg_test_stat = hhg.test_statistic(X, Y)
+        """
+        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
+        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
+
+        # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not
+        if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0:
+            dist_mtx_X = distance_matrix(matrix_X, matrix_X)
+        else:
+            dist_mtx_X = matrix_X
+        if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0:
+            dist_mtx_Y = distance_matrix(matrix_Y, matrix_Y)
+        else:
+            dist_mtx_Y = matrix_Y
+
+        n = dist_mtx_X.shape[0]
+        S = np.zeros((n, n))
+
+        for i in range(n):
+            for j in range(n):
+                if i != j:
+                    tmp1 = dist_mtx_X[i, :] <= dist_mtx_X[i, j]
+                    tmp2 = dist_mtx_Y[i, :] <= dist_mtx_Y[i, j]
+                    t11 = np.sum(tmp1 * tmp2) - 2
+                    t12 = np.sum(tmp1 * (1-tmp2))
+                    t21 = np.sum((1-tmp1) * tmp2)
+                    t22 = np.sum((1-tmp1) * (1-tmp2))
+                    denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22)
+                    if denom > 0:
+                        S[i, j] = (n-2) * \
+                            np.power((t12*t21 - t11*t22), 2) / denom
+        corr = np.sum(S)
+
+        # no metadata for HHG
+        self.test_statistic_metadata_ = {}
+        self.test_statistic_ = corr
+
+        return self.test_statistic_, self.test_statistic_metadata_
+
+    def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
+        """
+        Tests independence between two datasets using HHG and permutation test.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :p_value_: P-value
+            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                 that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.hhg import HHG
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> hhg = HHG()
+        >>> hhg_p_value = hhg.p_value(X, Y)
+        """
+        return super(HHG, self).p_value(matrix_X, matrix_Y)
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
new file mode 100644
index 0000000..24a0670
--- /dev/null
+++ b/mgcpy/independence_tests/kendall_spearman.py
@@ -0,0 +1,92 @@
+from mgcpy.independence_tests.abstract_class import IndependenceTest
+from scipy.stats import kendalltau, spearmanr
+
+
+class KendallSpearman(IndependenceTest):
+    def __init__(self, compute_distance_matrix=None, which_test='kendall'):
+        """
+        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
+        :type compute_distance_matrix: FunctionType or callable()
+
+        :param which_test: specifies which test to use, including 'kendall' or 'spearman'
+        :type which_test: str
+        """
+        IndependenceTest.__init__(self, compute_distance_matrix)
+        self.which_test = which_test
+
+    def test_statistic(self, matrix_X, matrix_Y):
+        """
+        Computes the Spearman's rho or Kendall's tau measure between two datasets.
+        - Implments scipy.stats's implementation for both
+
+        :param matrix_X: a [n*1] data matrix, a square matrix with n samples in 1 dimension
+        :type matrix_X: 1D numpy.array
+
+        :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in 1 dimension
+        :type matrix_Y: 1D numpy.array
+
+        :return: returns a list of two items, that contains:
+            - :test_stat_: test statistic
+            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                         that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> kendall_spearman = KendallSpearman()
+        >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y)
+        """
+        if matrix_X is None:
+            matrix_X = self.matrix_X
+        if matrix_Y is None:
+            matrix_Y = self.matrix_Y
+        assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape"
+        assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape"
+
+        if self.which_test == 'kendall':
+            self.test_statistic_ = kendalltau(matrix_X, matrix_Y)[0]
+        else:
+            self.test_statistic_ = spearmanr(matrix_X, matrix_Y)[0]
+
+        self.test_statistic_metadata_ = {}
+
+        return self.test_statistic_, self.test_statistic_metadata_
+
+    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
+        """
+        Tests independence between two datasets using the independence test.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :p_value_: P-value
+            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                 that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> kendall_spearman = KendallSpearman()
+        >>> kendall_spearman_p_value = kendall_spearman.p_value(X, Y)
+        """
+        return super(KendallSpearman, self).p_value(matrix_X, matrix_Y)
diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py
new file mode 100644
index 0000000..7fec1fa
--- /dev/null
+++ b/mgcpy/independence_tests/rv_corr.py
@@ -0,0 +1,117 @@
+import numpy as np
+from mgcpy.independence_tests.abstract_class import IndependenceTest
+from numpy import matlib as mb
+from scipy.sparse.linalg import svds
+from scipy.stats import pearsonr
+
+
+class RVCorr(IndependenceTest):
+    def __init__(self, compute_distance_matrix=None, which_test='rv'):
+        """
+        :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
+        :type compute_distance_matrix: FunctionType or callable()
+
+        :param which_test: specifies which test to use, including 'rv', 'pearson', and 'cca'.
+        :type which_test: str
+        """
+        IndependenceTest.__init__(self, compute_distance_matrix)
+        self.which_test = which_test
+
+    def test_statistic(self, matrix_X=None, matrix_Y=None):
+        """
+        Computes the Pearson/RV/CCa correlation measure between two datasets.
+        - Default computes linear correlation for RV
+        - Computes pearson's correlation
+        - Calculates local linear correlations for CCa
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :test_statistic_: test statistic
+            - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                         that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.rv_corr import RVCorr
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> rvcorr = RVCorr()
+        >>> rvcorr_test_stat = rvcorr.test_statistic(X, Y)
+        """
+        row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1]
+        row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1]
+
+        mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0),
+                                         matrix_X.shape[0], 1)
+        mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0),
+                                         matrix_Y.shape[0], 1)
+
+        covar = np.dot(mat1.T, mat2)
+        varX = np.dot(mat1.T, mat1)
+        varY = np.dot(mat2.T, mat2)
+
+        if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)):
+            corr, covar = pearsonr(matrix_X, matrix_Y)
+        elif (self.which_test == 'rv'):
+            covar = np.trace(np.dot(covar, covar.T))
+            corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX))
+                                            * np.trace(np.dot(varY, varY))))
+        else:
+            if varX.size == 1 or varY.size == 1 or covar.size == 1:
+                covar = np.sum(np.power(covar, 2))
+                corr = np.divide(covar, np.sqrt(np.sum(np.power(varX, 2))
+                                                * np.sum(np.power(varY, 2))))
+            else:
+                covar = np.sum(np.power(svds(covar, 1)[1], 2))
+                corr = np.divide(covar, np.sqrt(np.sum(np.power(svds(varX, 1)[1], 2))
+                                                * np.sum(np.power(svds(varY, 1)[1], 2))))
+        self.test_statistic_ = corr
+        self.test_statistic_metadata_ = {"covariance": covar}
+
+        return self.test_statistic_, self.test_statistic_metadata_
+
+    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
+        """
+        Tests independence between two datasets using the independence test.
+
+        :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions
+        :type matrix_X: 2D `numpy.array`
+
+        :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions
+        :type matrix_Y: 2D `numpy.array`
+
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to 1000.
+        :type replication_factor: int
+
+        :return: returns a list of two items, that contains:
+            - :p_value_: P-value
+            - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
+                                 that the independence tests computes in the process
+        :rtype: float, dict
+
+        **Example:**
+        >>> import numpy as np
+        >>> from mgcpy.independence_tests.rv_corr import RVCorr
+
+        >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
+                      0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
+        >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
+                      1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
+        >>> rvcorr = RVCorr()
+        >>> rvcorr_p_value = rvcorr.p_value(X, Y)
+        """
+        return super(RVCorr, self).p_value(matrix_X, matrix_Y)

From 53227a28ac8f8e4a1b3360ce9cfb438ad4cacbd0 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Thu, 6 Dec 2018 23:10:06 -0500
Subject: [PATCH 42/60] Add demo and fixed abstract class to include p-value
 for scipy tests

---
 demos/other_tests.ipynb                      | 840 +++++++++++++++++++
 demos/rv_cca_hhg.ipynb                       | 264 ------
 mgcpy/independence_tests/abstract_class.py   |   8 +-
 mgcpy/independence_tests/kendall_spearman.py |   4 -
 4 files changed, 847 insertions(+), 269 deletions(-)
 create mode 100644 demos/other_tests.ipynb
 delete mode 100644 demos/rv_cca_hhg.ipynb

diff --git a/demos/other_tests.ipynb b/demos/other_tests.ipynb
new file mode 100644
index 0000000..229220c
--- /dev/null
+++ b/demos/other_tests.ipynb
@@ -0,0 +1,840 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Tutorial for Tests other than MGC"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy.spatial.distance import pdist, squareform\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Simulations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First, import the simultions utilizing the import statement below (for this tutorial only 4 out of 20 were imported):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, w_sim, spiral_sim"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the readme. Visualizations of the 4 simulations imported above are shown below with and without the noise:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 4 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1, 4, num=1, figsize=(20,5))\n",
+    "\n",
+    "x_normal, y_normal = linear_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = linear_sim(1000, 1, noise=0)\n",
+    "ax[0].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
+    "ax[0].plot(x_no_noise, y_no_noise, 'ro')\n",
+    "ax[0].set_xlim([-1, 1])\n",
+    "ax[0].set_ylim([-1, 1])\n",
+    "\n",
+    "x_normal, y_normal = quad_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = quad_sim(1000, 1, noise=0)\n",
+    "ax[1].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
+    "ax[1].plot(x_no_noise, y_no_noise, 'ro')\n",
+    "ax[1].set_xlim([-1, 1])\n",
+    "ax[1].set_ylim([-1, 2])\n",
+    "\n",
+    "x_normal, y_normal = w_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = w_sim(1000, 1, noise=0)\n",
+    "ax[2].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
+    "ax[2].plot(x_no_noise, y_no_noise, 'ro')\n",
+    "ax[2].set_xlim([-1, 1])\n",
+    "ax[2].set_ylim([-1, 2])\n",
+    "\n",
+    "x_normal, y_normal = spiral_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = spiral_sim(1000, 1, noise=0)\n",
+    "ax[3].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
+    "ax[3].plot(x_no_noise, y_no_noise, 'ro')\n",
+    "ax[3].set_xlim([-4, 4])\n",
+    "ax[3].set_ylim([-4, 4])\n",
+    "\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## DCorr, MCorr, Mantel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First, import the `DCorr` class from the mgcpy package:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'mgcpy.independence_tests.mgc.distance_transform'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-4-e329c2ea85bd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdcorr\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/dcorr.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabstract_class\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mIndependenceTest\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistance_transform\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtransform_distance_matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'mgcpy.independence_tests.mgc.distance_transform'"
+     ]
+    }
+   ],
+   "source": [
+    "from mgcpy.independence_tests.dcorr import DCorr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### DCorr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Put description here..."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `DCorr` object with `'dcorr'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Dcorr's test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x, y = quad_sim(100, 1)\n",
+    "\n",
+    "dcorr = DCorr(which_test='dcorr')\n",
+    "test_stat = dcorr.test_statistic(x, y)[0]\n",
+    "print(\"DCorr's test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p_value = dcorr.p_value(x, y)[0]\n",
+    "print(\"DCorr p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### MCorr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Put description here..."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `DCorr` object with `'mcorr'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the MCorr's test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x, y = quad_sim(100, 1)\n",
+    "\n",
+    "mcorr = DCorr(which_test='mcorr')\n",
+    "test_stat = mcorr.test_statistic(x, y)[0]\n",
+    "print(\"MCorr's test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p_value = mcorr.p_value(x, y)[0]\n",
+    "print(\"MCorr p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Mantel"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Put description here..."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `DCorr` object with `'mantel'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Mantel's test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x, y = quad_sim(100, 1)\n",
+    "\n",
+    "mantel = DCorr(which_test='mantel')\n",
+    "test_stat = mantel.test_statistic(x, y)[0]\n",
+    "print(\"Mantel's test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p_value = mantel.p_value(x, y)[0]\n",
+    "print(\"Mantel p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## HHG"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The HHG test statistic was developed as specified in Heller, et. al. (2012). For more information about the test statistic, refer to the documentation specified in the R package here: https://cran.r-project.org/web/packages/HHG/vignettes/HHG.html.\n",
+    "\n",
+    "Essentially, the test takes the distance between two points, $P_{0}$ and $P_{1}$, and calculates how far each of the other data points in the data set are from $P_{0}$ and $P_{1}$ and organizes it in the following table:\n",
+    "<table>\n",
+    "  <tr>\n",
+    "    <th style=\"width:200px\"><center></center></th>\n",
+    "    <th style=\"width:200px\"><center>$d_{y}(P_{0},\\cdot) \\leq d_{y}(P_{0},P_{1})$</center></th> \n",
+    "    <th style=\"width:200px\"><center>$d_{y}(P_{0},\\cdot) > d_{y}(P_{0},P_{1})$</center></th>\n",
+    "    <th style=\"width:200px\"><center></center></th>\n",
+    "  </tr>\n",
+    "  <tr>\n",
+    "    <th style=\"width:200px\"><center>$d_{x}(P_{0},\\cdot) \\leq d_{x}(P_{0},P_{1})$</center></th>\n",
+    "    <td style=\"width:200px\"><center>$A_{11}(P_{0}, P_{1})$</center></td> \n",
+    "    <td style=\"width:200px\"><center>$A_{12}(P_{0}, P_{1})$</center></td>\n",
+    "    <th style=\"width:200px\"><center>$A_{1\\cdot}(P_{0}, P_{1})$</center></th>\n",
+    "  </tr>\n",
+    "  <tr>\n",
+    "    <th style=\"width:200px\"><center>$d_{x}(P_{0},\\cdot) > d_{x}(P_{0},P_{1})$</center></th>\n",
+    "    <td style=\"width:200px\"><center>$A_{21}(P_{0}, P_{1})$</center></td> \n",
+    "    <td style=\"width:200px\"><center>$A_{22}(P_{0}, P_{1})$</center></td>\n",
+    "    <th style=\"width:200px\"><center>$A_{2\\cdot}(P_{0}, P_{1})$</center></th>\n",
+    "  </tr>\n",
+    "  <tr>\n",
+    "    <th style=\"width:200px\"><center></center></th>\n",
+    "    <th style=\"width:200px\"><center>$A_{\\cdot 1}(P_{0}, P_{1})$</center></td> \n",
+    "    <th style=\"width:200px\"><center>$A_{\\cdot 2}(P_{0}, P_{1})$</center></td>\n",
+    "    <th style=\"width:200px\"><center>$N-2$</center></th>\n",
+    "  </tr>\n",
+    "</table>\n",
+    "\n",
+    "A Chi square test statistic is then computed from table and the HHG test statistic is simply the sum of all the test statistics calculated:\n",
+    "\n",
+    "$$S(i, j)=\\frac{(N-2)(A_{12}A_{21}-A_{11}A_{22})}{A_{1\\cdot}A_{2\\cdot}A_{\\cdot 1}A_{\\cdot 2}}$$\n",
+    "\n",
+    "$$T=\\sum_{i=1}^{N}\\sum_{j=1, i \\neq j}^{N}S(i, j)$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First, import the `HHG` class from the mgcpy package:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from mgcpy.independence_tests.hhg import HHG"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `HHG` object and then call the test statistic method. This is done below, by utilizing a simulation and calculating the HHG test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "HHG test statistic: 36.88\n"
+     ]
+    }
+   ],
+   "source": [
+    "x, y = w_sim(10, 1)\n",
+    "\n",
+    "hhg = HHG()\n",
+    "test_stat = hhg.test_statistic(x, y)[0]\n",
+    "print(\"HHG test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "HHG p-value: 0.92\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = hhg.p_value(x, y)[0]\n",
+    "print(\"HHG p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Kendall, Spearman"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First, import the `KendallSpearman` class from the mgcpy package. Note that these tests utilize the `scipy.stats` implementation of the kendall and spearman tests and were included out of convenience:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from mgcpy.independence_tests.kendall_spearman import KendallSpearman"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Kendall"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The Kendall tau coefficient was calculated utilizing the `scipy.stats` implementation. Further explanation this test can be found here: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html. <b>Note: The inputs for this test must be 1 dimensional.</b>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `KendallSpearman` object with `'kendall'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Kendall's test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Kendall's test statistic: -0.05\n"
+     ]
+    }
+   ],
+   "source": [
+    "x, y = quad_sim(100, 1)\n",
+    "\n",
+    "kendall = KendallSpearman(which_test='kendall')\n",
+    "test_stat = kendall.test_statistic(x, y)[0]\n",
+    "print(\"Kendall's test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Pearson's p-value: 0.74\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = kendall.p_value(x, y)[0]\n",
+    "print(\"Pearson's p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Spearman"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The Spearman rho coefficient was calculated utilizing the `scipy.stats` implementation. Further explanation this test can be found here: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.spearmanr.html. <b>Note: The inputs for this test must be 1 dimensional.</b>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `KendallSpearman` object with `'spearman'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Spearman's test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Spearman's test statistic: 0.09\n"
+     ]
+    }
+   ],
+   "source": [
+    "x, y = spiral_sim(100, 1)\n",
+    "\n",
+    "spearman = KendallSpearman(which_test='spearman')\n",
+    "test_stat = spearman.test_statistic(x, y)[0]\n",
+    "print(\"Spearman's test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Pearson's p-value: 0.15\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = spearman.p_value(x, y)[0]\n",
+    "print(\"Pearson's p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Pearson's, RV, and CCA"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First, import the `RVCorr` class from the mgcpy package:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from mgcpy.independence_tests.rv_corr import RVCorr"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Pearson's"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$\\newcommand{\\cov}{\\mathrm{cov}}$The Pearson's correlation was calculated utilizing the `scipy.stats` implementation. Further explanation this test can be found here: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.pearsonr.html.\n",
+    "\n",
+    "This is a test returns a statistic between -1 and 1 and measures the linear correlation between two vectors. <b>Note: The inputs for this test must be 1 dimensional.</b>\n",
+    "\n",
+    "The correlation is calculated via the following formula:\n",
+    "\n",
+    "$$\\rho _{X, Y}=\\frac{\\cov(X, Y)}{\\sigma _{X}\\sigma _{Y}}$$\n",
+    "\n",
+    "where $\\cov$ is the covariance, $\\sigma _{X}$ is the standard deviation of $X$, and $\\sigma _{Y}$ is the standard deviation of $Y$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `RVCorr` object with `'pearson'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Pearson's test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Pearson's test statistic: 0.46\n"
+     ]
+    }
+   ],
+   "source": [
+    "x, y = linear_sim(100, 1)\n",
+    "\n",
+    "pearson = RVCorr(which_test='pearson')\n",
+    "test_stat = pearson.test_statistic(x, y)[0]\n",
+    "print(\"Pearson's test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Pearson's p-value: 0.00\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = pearson.p_value(x, y)[0]\n",
+    "print(\"Pearson's p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### RV"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$\\newcommand{\\COVV}{\\mathrm{COVV}}$$\\newcommand{\\Tr}{\\mathrm{Tr}}$$\\newcommand{\\VAV}{\\mathrm{VAV}}$$\\newcommand{\\RV}{\\mathrm{RV}}$This test is essentially the a multivariate generalization of the square pearson's correlation coefficient. It returns values between 0 and 1. If $X$ and $Y$ are matrices of centered column vectors with covariance:\n",
+    "\n",
+    "$$\\Sigma _{XY}=E(X^{T}Y)$$\n",
+    "\n",
+    "Then the scaled covariance ($\\COVV$) is:\n",
+    "\n",
+    "$$\\COVV(X,Y)=\\Tr(\\Sigma _{XY}\\Sigma _{YX})$$\n",
+    "\n",
+    "Then the scaled-valued variance is defined similarly ($\\COVV$):\n",
+    "\n",
+    "$$\\VAV(X)=\\Tr(\\Sigma _{XX}^{2})$$\n",
+    "\n",
+    "Then, the RV Coefficient is defined as:\n",
+    "\n",
+    "$$\\RV(X,Y)=\\frac{\\COVV(X,Y)}{\\sqrt{\\VAV(X)\\VAV(Y)}}$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `RVCorr` object with `'rv'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the RV test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "RV test statistic: 0.00\n"
+     ]
+    }
+   ],
+   "source": [
+    "x, y = quad_sim(100, 3)\n",
+    "\n",
+    "rv = RVCorr(which_test='rv')\n",
+    "test_stat = rv.test_statistic(x, y)[0]\n",
+    "print(\"RV test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "RV p-value: 0.88\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = rv.p_value(x, y)[0]\n",
+    "print(\"RV p-value: %.2f\" % p_value)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### CCA"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$\\newcommand{\\cov}{\\mathrm{cov}}$This test infers information from the cross-covariance matrices of random variables. It is a generalization of the RV test and can be considered the most general case of almost all statistical tests.\n",
+    "\n",
+    "If $\\Sigma _{XX}=\\cov(X, X)$ and $\\Sigma _{YY}=\\cov(Y, Y)$, then:\n",
+    "\n",
+    "$$\\frac{a^{T}\\Sigma _{XX}b}{\\sqrt{a^{T}\\Sigma _{XX}a}\\sqrt{b^{T}\\Sigma _{YY}b}}$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As with the other tests, simply create an `RVCorr` object with `'cca'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the CCA test statistic from that data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CCA test statistic: 0.28\n"
+     ]
+    }
+   ],
+   "source": [
+    "x, y = spiral_sim(100, 6)\n",
+    "\n",
+    "cca = RVCorr(which_test='cca')\n",
+    "test_stat = cca.test_statistic(x, y)[0]\n",
+    "print(\"CCA test statistic: %.2f\" % test_stat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CCA p-value: 0.00\n"
+     ]
+    }
+   ],
+   "source": [
+    "p_value = cca.p_value(x, y)[0]\n",
+    "print(\"CCA p-value: %.2f\" % p_value)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/demos/rv_cca_hhg.ipynb b/demos/rv_cca_hhg.ipynb
deleted file mode 100644
index 3a064f3..0000000
--- a/demos/rv_cca_hhg.ipynb
+++ /dev/null
@@ -1,264 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 174,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "from scipy.spatial.distance import pdist, squareform\n",
-    "import matplotlib.pyplot as plt"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 175,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from mgcpy import RVCorr, HHG\n",
-    "from mgcpy.benchmarks.power import power\n",
-    "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, ubern_sim, exp_sim, w_sim, joint_sim, spiral_sim"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Test Statistic"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 176,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def test_stats_vs_dimension(corr_type, simulation_type, dim_range):\n",
-    "    test_stats = []\n",
-    "    for d in range(1, dim_range+1):\n",
-    "        x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n",
-    "        if corr_type == 'rv' or corr_type == 'cca':\n",
-    "            corr = RVCorr(which_test=corr_type)\n",
-    "        #else:\n",
-    "            #corr = HHG()\n",
-    "        test_stats.append(corr.test_statistic(x, y)[0])\n",
-    "    return test_stats"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 177,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_test_stats(simulation_type, dim_range, simulation_name):\n",
-    "    rv_test_stats = test_stats_vs_dimension('rv', simulation_type, dim_range)\n",
-    "    cca_test_stats = test_stats_vs_dimension('cca', simulation_type, dim_range)\n",
-    "    #hhg_test_stats = test_stats_vs_dimension('hhg', simulation_type, dim_range) \n",
-    "    plt.plot(rv_test_stats, label='RV')\n",
-    "    plt.plot(cca_test_stats, label='CCA')\n",
-    "    #plt.plot(hhg_test_stats, label='HHG')\n",
-    "    plt.xlabel('Dimensions')\n",
-    "    plt.ylabel('Test Statistics')\n",
-    "    plt.legend()\n",
-    "    plt.gca().set_xlim(1, dim_range+1)\n",
-    "    plt.xticks(np.arange(0, dim_range+1, 5))\n",
-    "    plt.title('Test Statistics \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
-    "    plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 178,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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sF5FfReT4YMVijDH5MjMziYmJqXUJAUBEiImJqdBVUDDrFN7CjXZYnBG40Qg74+bKfTmIsRhjTIHamBDyVfS5BS0pqOosvFnJijEKeFudeUAjEWlR2nHT9+wsbRNjjDHlVJWtj1py5NR9iRQ9NR4icpOILBSRhRGZu8nLs/GajDE1V2hoKAkJCfTs2ZPzzjuPffvcXELt27dnzZo1R2x711138cwzz1RabFWZFIq6xiny215VX1XVfqraL5wc1m3aFOTQjDEmeOrUqcOSJUtYvnw5TZo0YcKECQCMHj2aiRMPTwaXl5fHxx9/zOWXX15psVVlUkjkyPlcW+Hn3LebfrUh1Y0xtcOAAQPYts1NFT1mzJgjksKsWbNo164dbdu2LW73gKvKJqmTgXEiMhE3BWSqqu7wZ8f0zYuAa4IZmzHmGPDolBWs3L4/oMfsHt+AP5/Xw69tc3Nz+fbbb7n++usB6N27NyEhISxdupQ+ffowceJExoyp3Inmgtkk9QPc/KZdRSRRRK4XkVtE5BZvk6m4OVzX4+aqvbWYQx0hJySCBvtWkJWTF5S4jTEm2A4ePEhCQgIxMTHs2bOHM888s2Bd/tVCTk4On3/+OZdeemmlxha0K4XS5lFVN7vPbWU+blhdurGJxb/tpX+HmHLHZ4wx/v6iD7T8OoXU1FTOPfdcJkyYwB133AG4pHDWWWcxdOhQevfuTdOmTSs1tho39lFoZF1aSTKLVm+o6lCMMaZCGjZsyPPPP8+zzz5LdnY2AB07diQmJob777+/0ouOoAYmhZCIugAkr51fxZEYY0zF9e3bt6D+IN+YMWNYvXo1F154YaXHU+OSAuEuKdRJXkZaZnYVB2OMMWV34MCBIx5PmTKFq6++uuDx3XffTWZmJg0bNqzs0GpgUggJ5WD9NvSQTczfWFKHaWOMMWVV85ICENHqeHqFbGbOhuSqDsUYY2qVGpkUQlsm0Fp28eta69lsjDGBVCOTAi0SAIhKWc6u/bVzogxjjKkKNTQp9AGgl2yyIiRjjAmgmpkU6jZBG7Whb/gW5qxPqepojDGm1qiZSQGQFgleUkjGdY42xpiaY+fOnYwePZqOHTvSvXt3Ro4cydq1a1m7di0jR46kU6dOdOvWjcsuu4ykpKSC/e68805atmxJXl5whvqpsUmB+ASaZm8nPTWFjcnpVR2NMcb4TVW58MILGTZsGBs2bGDlypU88cQTJCUlcc455zB27FjWr1/PqlWrGDt2LLt37wbcUNqfffYZrVu3ZtasWUGJreYmBa9eoUfIZuast3oFY0zNMXPmTMLDw7nlllsKliUkJLBu3ToGDBjAeeedV7D81FNPpWfPngX79ezZk7Fjx/LBBx8EJbaqHDq7Ylr0BWBQ3UTmrE/mmgHtqjYeY0zN89X9sHNZYI/ZvBeMeKrETZYvX84JJ5zg9/J8H3zwAWPGjGHUqFE8+OCDZGdnEx4eXuGQfdXcK4XoGGjYmoHRiczdkEKuTdFpjKnFsrKymDp1KhdccAENGjSgf//+zJgxI+DnqblXCgAt+tApcTlpmTks25ZKQutGVR2RMaYmKeUXfbD06NGDjz/+uMjlP/zwQ5H7TJs2jdTUVHr16gVARkYGdevW5ZxzzglobDX3SgGgRQL1DmymHhlWr2CMqTFOO+00Dh06xGuvvVawbMGCBXTq1Im5c+fy5ZdfFiyfNm0ay5Yt44MPPuD1119n8+bNbN68mU2bNjFjxgwyMjICGltQk4KIDBeRNSKyXkTuL2J9WxH5VkR+FZHvRaRVmU4Q73o2j4zdbUnBGFNjiAifffYZX3/9NR07dqRHjx6MHz+e+Ph4vvjiC1544QU6d+5M9+7deeutt2jQoAHTp08/4qogOjqaQYMGMWXKlIDGFrTiIxEJBSYAZwKJwAIRmayqK302exZ4W1X/KyKnAU8CVx99tGJ4LZDObLSD2zbt5WBWLnUiQgP1FIwxJmji4+OZNGlSkeumTZt21LI9e44eFfrTTz8NeFzBvFI4CVivqhtVNQuYCIwqtE134Fvv/swi1pesXlOoH0+v0M1k5eaxcIsNpW2MMRURzKTQEtjq8zjRW+ZrKXCxd/9CoL6IHDXxsojcJCILRWRhfieOAvEJND2wivBQ4UcrQjLGmAoJZlKQIpYVbjf6B2CoiCwGhgLbgJyjdlJ9VVX7qWq/uLi4I1e2SCAkZT0DWkYy18ZBMsb4oTYPjVPR5xbMpJAItPZ53ArY7ruBqm5X1YtUtS/wkLcstUxnadEHUM5rtofl21PZm55VsaiNMbVaVFQUKSkptTIxqCopKSlERUWV+xjB7KewAOgsIu1xVwCjgSt8NxCRWGCPquYBDwBvlPksXgukk+v8hupx/LQxhZG9WlQwdGNMbdWqVSsSExM5qii6loiKiqJVq7I15PQVtKSgqjkiMg6YDoQCb6jqChF5DFioqpOBYcCTIqLALOC2Mp+ofnOo15yWB9dQL7Inc9YnW1IwxhQrPDyc9u3bV3UY1VZQezSr6lRgaqFlj/jc/xg4ultfWbXoQ8jOpfRvf6P1VzDGmAqo2T2a88UnQPJahraPZnNKBlv3BLaHnzHGHCtqR1JokQCax7BGbiKKuTZFpzHGlEvtSApeZXPrg2uIqx9pU3QaY0w51Y6kUL8FRMchO39lYMcY5qxPJs+G0jbGmDKrHUlBxBUhbV/CwE6xpKRnsSYpraqjMsaYGqd2JAVwRUi7VzOwXTSAtUIyxphyqD1JoUUf0FziMzfSIS7akoIxxpRDLUoKrrKZ7YsZ2DGW+Zv2kJWTV7UxGWNMDVN7kkLDVlA3Bna4eoWMrFyWbN1X1VEZY0yNUnuSgogrQtq+lAEdYggRbChtY4wpo9qTFMAVIe1eRcPwXHq1bMhcSwrGGFMmtSspxCdAXg7sWsHATrEs3rqPtMzsqo7KGGNqjNqVFLw5m9m+hEGdYsnNU37eZFN0GmOMv2pXUmjUFqIawY6lHN+2MZFhIVavYIwxZVC7koKIK0LasYSo8FBObNfEpug0xpgyCGpSEJHhIrJGRNaLyP1FrG8jIjNFZLGI/CoiIyt80hYJkLQScg4xsFMsa5LS2JWWWeHDGmPMsSBoSUFEQoEJwAigOzBGRLoX2uxhYJI3R/No4KUKn7hFH8jLhl2rGNQpFsCuFowxxk/BvFI4CVivqhtVNQuYCIwqtI0CDbz7DYHtFT6rN4w2O5bQPb4BjeqGW72CMcb4KZhJoSWw1edxorfM13jgKhFJxE3beXtRBxKRm0RkoYgsLHWy7cbtIbIhbF9CaIgwoEMMc9cno2pDaRtjTGmCmRSkiGWFv5nHAG+paitgJPCOiBwVk6q+qqr9VLVfXFxcKWcVaNEbdiwBYGCnWLanZrIpOb08z8EYY44pwUwKiUBrn8etOLp46HpgEoCq/gREAbEVPnN8AiStgNzsgnoFGzXVGGNKF8yksADoLCLtRSQCV5E8udA2vwGnA4hIN1xSKKV8yA8tEiA3C3atom1MXVo2qmNTdBpjjB+ClhRUNQcYB0wHVuFaGa0QkcdE5Hxvs3uBG0VkKfABcK0GovC/xeHKZhFhYKcY5m5IJtem6DTGmBKFBfPgqjoVV4Hsu+wRn/srgYEBP3GTDhBRH3YsBVy9wqSFiSzflkqf1o0CfjpjjKktaleP5nwhId4w2q6y+ZSOrl7BmqYaY0zJamdSAJcUkpZDbg5x9SM5rnl95m6wpGCMMSWpvUkhPgFyMiF5DeCKkBZs3ktmdm4VB2aMMdVX7U0KBXM2uyKkQZ1iycrJY+HmvVUYlDHGVG+1NynEdIKIegWd2E5q34SwELF6BWOMKUHtTQohIdC8V8GVQnRkGH3bNOLH9RXvBmGMMbVV7U0K4IqQdi6DPFePMLhzHCu27yflwKEqDswYY6qn2p0U4hMg5yAkrwVgSJc4VK1pqjHGFKd2JwWfOZsBerVsSKO64fyw1oqQjDGmKLU7KcR2gfC6BT2bQ0OEQZ1imb3OhtI2xpii1O6kEBLqKpu9FkjgipB2px1i1Y60KgzMGGOqp1KTgoicLCJ1vftjROQZEWld2n7VRos+sOPXgsrmIZ3dfAyz11kRkjHGFObPlcKrwEER6Q08CCQB7wY1qkBqkQDZ6ZCyAYDmDaPo2qw+sywpGGPMUfxJCjnecNajgOdU9e9A/eCGFUA+czbnG9w5lgWb9pKRlVNFQRljTPXkT1JIF5E/AlcBX3rTZYYHN6wAiu0KYVEFLZDA1Stk5eYxf+OeKgzMGGOqH3+SwuW4+ZZvUdUduGk1/+HPwUVkuIisEZH1InJ/Eev/KSJLvNtaEdlXpuj9ERoGzXoecaVwUvsmRIaFWNNUY4wpxJ9JdsKAF1T1oPd4N/BNaTuJSCgwATgTN1/zAhGZ7E2sA4Cq3u2z/e1A3zLE7r/4BFj6IeTlQUgIUeGh9O8QY/UKxhhTiD9XCp8CvuNN5wGf+LHfScB6Vd2oqlnARFy9RHHG4KbkDLwWCZCVBns2Fiwa0jmWjbvTSdybEZRTGmNMTeRPUgjzvtQBUNVDQKQf+7UEtvo8TvSWHUVE2gLtge/8OG7Z5fds9ilCGtolv2mqDXlhjDH5/EkKKSIyMv+BiJwL+FNDK0UsK64b8WjgY1UtcgYcEblJRBaKyMLdu8tR5NO0G4RGHpEUOjWtR4uGUcyyegVjjCngT1IYCzwmIptEZBPwCHCzH/slAr6d3FoB24vZdjQlFB2p6quq2k9V+8XFxflx6kJCw6FZjyNaIIkIgzvH8uP6ZHJy88p+TGOMqYVKTQqqulZV++Eqgfuq6kmqutaPYy8AOotIexGJwH3xTy68kYh0BRoDP5Ut9DLK79nsM+bRkC5xpGXmsDQx8I2ejDGmJiq29ZGIjFHVD0TkjkLLAVDV50s6sKrmiMg4YDoQCryhqitE5DFgoarmJ4gxwEQN9gh18Qmw6E3YuwmadADcFJ0hAj+sTeaEtk2CenpjjKkJSmqS2tj7W1R5jV9f4Ko6FZhaaNkjhR6P9+dYFeY7Z7OXFBrVjaB3q0bMWrube87sUilhGGNMdVZsUlDVl7y7X6rqPN91InJyUKMKhqbdICTcVTb3vKhg8ZAucbz43Tr2ZWTRqG5EFQZojDFVz5+K5peKWDYh0IEEXVikq2xe9gls/KFg8dAuseQpzFmfUoXBGWNM9VBsUhCRk0TkTiBORO7wuT1MTRr7yNfwJyEkBN4+HyZdA/u20qdVI+pHhVnTVGOMoeQrhWggFlfEFOdzywIuDX5oQdD2FLjtZzj1IVg7A148kbDZf2NYezeUts3GZow51pVUpzATmCkib6rqRgBxTY/qqmp6ZQUYcOF1YOh90Gc0zPgTfP8ET9Zpyb1pl7E+6UQ6N29Q1REaY0yV8adOYbyINPBmX1sBbBKRe4IcV/A1agOX/ReumUxk3Xr8O+Kf1Jl0KexeU9WRGWNMlfEnKfRS1f3ABcAMXM/ka4MZVKXqMJTwW+fyQuSNNN67HF4+BaY/BJmpVR2ZMcZUOn+SQoSIhOFGOP2fNzhe7RoXIjSMlB7XcUbOP8jpfQX8NAFe6AeL33PDbRtjzDHCn6TwOvAbrjPbDyLSBjgQ1KiqwNAucezIrsdPPR6BG7+Dxm3h81vhP2fCtkVVHZ4xxlQKf8Y++qeqxqvqWd5QFFuB04IfWuXq36EJEaEhrmlqy+Ph9zPgglcgdSu8djp8Pg4OWLNVY0ztVuaxj3yUOPZRTVM3Iox+7Roza20yD52D68+QMAaOOwdm/Q3mvQwrJ8OoF6B7SXMFGWNMzVXSlYLv2EeFb7FBjqtKDOkSx5qkNHamZh5eGNUAznocbv0JGrV2ldDWn8EYU0sVmxQKjX30J98bhQa5qy2GdHZj/xU5d3NsZxgwzhUnWR2DMaaWOnbGPvJDtxb1iasfWfwUnV1HuEH1VnxWuYEZY0wlKalO4SRgAN7YRz6rGlBTxz4qRf5sbDNX7yI3TwkNKTSjaJ1G0Ol0WPE/OOsvIEXNOGqMMTXXsTX2kR+Gdoljb0Y2y7cV03mtx4WwPxESF1ZuYMYYUwnKNPZRWYnIcOA53Mxrr6vqU0VscxkwHjdxz1JVvaI85wqUQZ1iEYFZa3fTp3XHUDHfAAAgAElEQVSjozfoOgJCI2Dl/6D1iZUfoDHGBJE/dQr7ReRJEZksIjPyb6XtJCKhuLqHEUB3YIyIdC+0TWfgAWCgqvYA7ir7UwismHqR9IxvWHRlM0BUQ+joFSFZb2djTC3jT1J4F9gMdAGeBnYCS/zY7yRgvapu9IbGmIgbKsPXjcAEVd0LoKq7/Iw7qAZ3juWX3/axPzO76A3yi5C2WRGSMaZ28ScpxKnqv4EsVf0W+B3uC780LXG9n/Mlest8dQG6iMgcEZnnFTcdRURuEpGFIrJw9+7g9yoe0iWO3Dzlpw3FzMbWdQSERlorJGNMreNPUsj/ubxTRM4GegKt/divqKY5hXt9hQGdgWHAGOB1ETmqIF9VX1XVfqraLy4uzo9TV8zxbRoTHRFa/GxsUQ1cK6SVn1sRkjGmVvEnKTwhIg2BPwAP44qT/uDHfokcmTxaAduL2OZzVc1W1U3AGlySqFIRYSEM6Bhb8mxsPS6E/dsgcUHlBmeMMUHkT1LYpaqpqvqrqg5W1T7ADj/2WwB0FpH2IhIBjAYmF9rmf8CpACISiytOKldLp0Ab2iWWrXsOsjklo+gNugy3IiRjTK0TtB7NqpoDjAOmA6uASaq6QkQeE5Hzvc2mAykishKYCfxRVYspyK9cQ7p4Q16UWIR0hhUhGWNqlaD2aFbVqRQaJ0lVH/G5r8A93q1aaRsTTduYusxau5vfndKu6I16XAhrvoTEn6HNyZUanzHGBIP1aC7B4M6x/LQxhaycYq4EuloRkjGmdilTj2YRqa+qaZUWXRUb0jmOd+f9xqItexnQMeboDSLrQ+czXRHS2U+6ORiMMaYGK/ZbTEQeEpHjVHWjiER4vZgTRSRJRGrdzGtFGdAxhrAQKb53M7gipLQdsHV+5QVmjDFBUtJP2ytwTUQBrgEigRjcVJxPBjmuaqF+VDjHt21cfGUzQJezISzKipCMMbVCSUkhSw830h8OfKCqOaq6glo6dHZRhnaJY8X2/exOO1T0Br5FSNYKyRhTw5WUFA6JSDcRyb868B0Er25ww6o+8mdj+3F9CVcL3S+AAzth67xKisoYY4KjpKRwL66z2XrgeZ/K5pHAr5UQW7XQI74BTaIjmLW2mNnYwHVksyIkY0wtUNIczXNUtbOqNlbV8T7Lp6rqZZUSXTUQEiIM6hTL7HXJ5OUVM+RFZD3ofJZXhJRbuQEaY0wAWRtKPwzpEkfygUOs2rm/+I16XAgHkuC3nyovMGOMCTBLCn4Y0jkWoJQipLMhrI6bfMcYY2qoUpOCiBzVwa2oZbVZ0wZRHNe8fslNUyOioUuQi5CWfwK7Vgfn2MYYg39XCj/7uaxWG9oljoVb9pB+KKf4jXpcCOm7YMvcwAew5iv4+Pcw5c7AH9sYYzwl9WhuKiJ9gDoi0ktEenu3QRxDTVLzDekSR3auMm9jCYO4dj7LFSGtDHAR0oFd8Pk4CI1wzV6T1wf2+MYY4ynpSuEc4EXc5DgTfG4PAn8KfmjVS792jYkKD+Gr5TuLn3gnItrVLQSyCEkVPr8Nsg7AlR+BhMKS9wJzbGOMKaSkJqlvqupg4HpVHeJNsDNYVUeq6keVGGO1EBkWysXHt+LjRYk88vkKcnKL6b3c40JI3w1b5gTmxAteh3Uz4MzHocMwN4fD0onW9NUYExT+1Ck0FZEGACLyioj8LCKn+3NwERkuImtEZL2I3F/E+mtFZLeILPFuN5Qx/kr1+Kie3Dy0A+/M28J1by0g9WD20Rt1PgvC6wamI9uu1TDjYeh0Jpx0o1vW90pI2w4bZlb8+MYYU4g/SeEmVd0vImfhipLGAs+UtpOIhOKKm0YA3YExItK9iE0/VNUE7/Z6GWKvdCEhwgMjuvH0xb34aUMKF788l98KT9cZUdcVIa2aArklVEqXJucQfHqDK5IaNQFE3PIuI6BOE1jybvmPbYwxxfAnKeQXoI8A3lTVRX7udxKwXlU3qmoWMBEYVb4wq5fLT2zDO9f3Z3faIS54aQ4LNu85coNAFCF99xfYucwlhPrNDi8Pi4Del8HqLyFjT/H7G2NMOfjz5b5URKYC5wFfiUg9DieKkrQEtvo8TvSWFXaxiPwqIh+LSOuiDiQiN4nIQhFZuHt3CX0FKtGAjjH877aBNKwTzpWvzefTXxIPr+x0JoRHl78IaeMPMPcFOOE66Dri6PUJV0Buluu3YIwxAeRPUrgOGA+cpKoZQBRwvR/7SRHLCieTKUA7Ve0NfAP8t6gDqeqrqtpPVfvFxcX5cerK0T42ms9uPYXj2zbinklLeXb6Gjc+UkWKkDL2wGe3QExHOPuvRW/Tog806wWLrQjJGBNYpSYFVc0FOuDqEgDq+LMf7srA95d/K2B7oWOnqGr+RAWvASf4cdxqpVHdCN7+fX8u69eKF2eu5/YPFnMwK9cVIWUkw5Yf/T+YKnxxt+sAd/Hrrj6hOH2vhB1LIGlFxZ+EMcZ4/Bnm4kXgVOAqb1E68Iofx14AdBaR9iISAYzGDcXte+wWPg/PB1b5E3R1ExEWwtMX9+bBkccxdfkORr/6E7uaDy57EdLSD1zHt1MfhPi+JW/b6zIICYfF1mfBGBM4/vziP0VVbwYyAVR1DxBR2k6qmgOMA6bjvuwnqeoKEXlMRM73NrtDRFaIyFLgDuDacjyHakFEuGlIR1656gTWJh3ggn//Qmqb0/0vQtqzCab+EdoOhIF3lb59dAx0HQ6/fgi5RTSNNcaYcvAnKWSLSAhefYA3E5tf8056cy90UdWOqvpXb9kjqjrZu/+AqvZQ1T6qeqqq1vjR3s7u0ZyPbhlAnsKf1nWGjBTYPLvknXJz4NObXG/lC1+BkFD/TpZwlSuiWjej9G2NMcYPJY19lD8S6gTgEyBORB4FfgSeroTYaqyeLRvy+biBbIsdyAGNYvW3bxc/NAbA7L9D4s9w7j+gURv/T9TpDKjXzIqQjDEBU9KVws8Aqvo28DDwLLAXuFRVJ1ZCbDVaswZRvHvLMFbWH0jTbTN4+NMlZBc1NMbWBfDD066OoNclZTtJaBj0vhzWTYcD1aOprjGmZitpXoSCJqWqugKwZi5lVCcilH4jryNk0rf8tmga1+49xB/O6kp2rpKZnUt2Rionf/17iGrGlLg7SJu1kUM5uWRm55GZnUum7/3sPLJy87iyfxvO7tH88En6XgVzn3d1C6eMq7ona4ypFaS4Yg0RSQT+UdyOqlrsumDq16+fLly4sCpOXT7ZmfC3jmxsfjZnb7iE7NzDr/fTYa9ySegPjM76Ewv0uILlIQJR4aHuFhZCVHgokeGhpGZkkZKexeRxg+javP7hc7x2OmRnwNi5h4fDMMYYHyKySFX7lbZdSVcKoUA9iu6EZvwVHgVdR9Jh/dd8Ne7vbNqbRVR4CC22f02nmd+z5/jb+cegsUSGh3hJIJTwUEGK+HLfnXaIEc/NZtz7vzB53CDqRHgV0n2vdP0bti+GlsdX8hM0xtQmJSWFHar6WKVFUpv1uACWTaJT+iI6dT8D9m+HT11fhCbn/JkmoeF+HSaufiT/ujyBq9+Yz6NTVvDUxb3dip4Xw7QH3DwLlhSMMRVQUkWzXSEESsfTIaI+rPgf5OXB/8a6UVAveh38TAj5BnWOZezQjkxcsJXJS70O4lENodt5sOwjV1xljDHlVFJS8GvOBOOH8Cg4bqTryDb3edj4PZz9BMR2Ktfh7j6zCye0bcyDny5jS0q6W5hwBWSmwpovAxe3MeaYU9LMazYucyB1vwAy98E3f4au58AJ15b7UOGhITw3OoEQgds/WExWTh60HwoNWlmfBWNMhfjTo9kEQsfTILKB62x2/vMVbiXUqnFdnrmkD78mpvLMtNWuF3TCGNjwHaRuC1DQxphjjSWFyhIeBZe/C1d9AtGxATnk8J7NuWZAW17/cRPfrU5yRUioG1jPGGPKwZJCZeowFJr3CughHxzZjW4tGnDvpKXsDI13A+otec8Nw22MMWVkSaGGiwoP5cUr+nIoJ487Jy4mr88VsGcj/DavqkMzxtRAlhRqgY5x9XhsVE/mb9rDK7t7uXkcltisbMaYsrOkUEtcckIrLurbkme/T2RXmxGuT0RWelWHZYypYSwp1CKPXdCTtjHR/GlLAmQdgJWfV3VIxpgaJqhJQUSGi8gaEVkvIveXsN0lIqIiUupgTaZ49SLDeGFMX2Ye7EhSWEt0sRUhGWPKJmhJQURCcRP0jAC6A2NEpHsR29XHTcU5P1ixHEt6tmzIgyO78fbBgciWOW6aT2OM8VMwrxROAtar6kZVzQImAqOK2O5x4Bm8OaBNxf3ulHbs7ngheSokzX6zqsMxxtQgwUwKLYGtPo8TvWUFRKQv0FpVvyjpQCJyk4gsFJGFu3fbDGOlEREeHH0GC0L6kLfkfdIOHqrqkJyDe63/hDHVXDCTQlHjOBR8I4hICPBP4N7SDqSqr6pqP1XtFxcXF8AQa69GdSOIHXwdLXQ3/33vnZLniA6mrAxY+iG8dS483Q6++0vVxGGM8Uswk0Ii0NrncStgu8/j+kBP4HsR2QycDEy2yubA6Tj4cg6F1qPllk/5aGFi5Z1YFRIXwZS74O9d4bObIDUR2g6C2X93o8QaY6qlkibZqagFQGcRaQ9sA0YDV+SvVNVUoGAQIBH5HviDqtaguTarufA6hCdcxjmL3uWUyT/Tt00jOjerX/p+5ZWe7OaKXvwu7FoJYXXcBEN9r3LDb2RnwKvD4NObYeycgI0BZYwJnKBdKahqDjAOmA6sAiap6goReUxEzg/Wec2RQvpeRQRZXBA2n3HvLyYzOzewJ8jNgbUz4MOr4O/HwfQHIbwunPsv+MMauPAVaDfIjQobEQ2XvOHqFv43tlLrFzYnp/PolBVMW76D3Dyr16hxFvwHPrnRTVJlgkqqrKy5nPr166cLF9rFhN9U4aWTSc2Los+2+2hUN5wT2zWhf/smnNS+Cd1bNCAstBy/DVI2uIH3lrwPaTugbiz0Ge2uCpp2K3nf+a/CV3+Es5+EAbeW73n5SVX5aFEi4yevICPLJcR2MXW5fnAHLj2hFVHhoUE9vwmA7Yvh9TMgLwcueMUNEW/KTEQWqWqpxfOWFI4Fc56Hr//EvBFT+eS3evy8eQ9bUjIAiI4I5QSfJNG7VUMiw4r5osxKd72kF78LW+aAhEDns1wi6Hw2hEX4F48qTLwC1n0NN3wD8QkBeqJHSs3I5sHPlvHlsh2c3KEJz17q5p/496yNLN26jybREVwzoC3XDGhHk2g/YzeVKzsTXh3qZhWs1xQO7IbbF7qrTlMmlhTMYWlJ8I9ucMo4OPMxAHamZvLz5j38vCmFnzftYW3SAQAiwkLo3yqKs5vu58R6yXQgkfC962D3Wjf6al42NOnoEkGfMdCgRfliytgDLw+E8Dpw8yyIrBeoZwvAvI0p3PPhEnalHeKes7pw85COhIa4BnGqys+b9vDa7I18s2oXUeEhXHJCK24Y1IF2sfZlU63MeBjmvuDmIYmoB2+cDcMehGH/V9WR1TiWFMyR3h8N23+Bu1dCqNe+IGMPJK+F3Ws4uGMVBxKXE75nHY2ydhbslqMhJIW1IL1+RyJaHEeLfqOI7DCwwjPHAbBpNvz3PDc50AUvVfx4QHZuHv/6Zi0vfb+BdjHR/OvyBPq0blTs9ut3pfHarE18tngb2Xl5DO/RnJuGdKBvm8YBicdUwOY58NY50O86OPefbtmk38G6GXD7L+X/QXKMsqRgjrRqiqsMPu5cOLgPktdAuk9HwLAoiO0MsV0hrisHG3ZkWVZzZifX56ctB1iauI/sXKVFwyhuP60zl/ZrRXh56iIK++6vMOsZuOh16H1phQ61OTmdOycuZmliKpf1a8Wfz+tBdKR/Dex27c/krbmbeXfeFvZn5nBSuybcOKQDpx/XlJCQACRAUzaH0tyVpAjcMufwleSeTTDhJOh1GVwwoWpjrGEsKZgj5WS5f6aDe7wv/i4Qd9zh+w3bQEjxX/KZ2bn8tCGF579bx+Lf9tE2pi53ndGZ8/u0LCiWKZfcHPdrMGkF3DILmnQo8yF8K5PDQoSnLu7NyF7l+xWZfiiHDxds5T8/bmLbvoN0jIvmxsEduKBvS6uUrkxT7oRF/4XfT4M2Jx+5bsafXJHSzT9Aiz5VE18NZEnBHC0vz/3yqkDRj6ry3epdPDtjLat27KdLs3rcc2YXzu7RHCnvcff9Bq8McnUVv5/uf4U1R1Ym92/fhH9enkB8ozrli8NHTm4eXy7bwauzNrJi+35i60Vy3cB2XD+ovSWHYFv3Nbx3CQy8s6AO7AgH98ELx0PT7vC7KYEpyjwG+JsUbD6FY0lISIX/gUSE07s148vbB/HiFX3JyVNuefcXzn9xDt+v2VW+4TQatYHzX3B1HjP9HwZj/sYURjw3i+krdnLf8K68f+PJRScEVVj4BvyrN6yZ5texw0JDGJXQki9uH8T7N/SnR3wD/jZ9Dee/+COrd+73O8ZqY/knrv7m4N6qjqRkGXvg83HuC//Uh4repk4jGPYAbJ4Na76q3PiOAXalYCokJzePzxZv47lv15G49yAntmvMH87qSv8OMWU/2JS7YNGbcNWn0On0YjfzrUxu26Quz43uW3xl8r6tMHmcG1ojPNo1o73xW4jrWubwfli7m3snLWV/ZjYPjezGNQPalv/qqDKtnQ4fjAHNhZNugpF/q+qIivfx72HlZLjxO2jRu/jtcnPg5VNc34Vb55Xp6vJYZVcKplKEhYZwab/WfHfvMB4f1YMtKRlc/uo8rv7PfJZu3Ve2g539BMR1g89ugQO7itxkc3I6l7zyExNmbuDSE1rx5R2Di04IqvDL2/DSAEhc6Fqv3DYfwqPcF+TBMsYGDO0Sx7S7BjOwYwx/nryC6/+7kOQD1WQE2uJsmQuTroHmvSDhKljwOuxcXtVRFW35J+427P9KTgjgWtCd9RfYswEW/qdy4jtG2JWCCaiDWbm8M28zL3+/gb0Z2ZzVvRn3ntWVrs39HHMpaSW8dqobK+nKjzmUp+xJzyLlQBaLt+7jqamrCA0RnryoN+f0LqYyOXUbTLkD1n8D7QbDqAnQuK1bt+UnV4zSYRhc8SGElL1+QFX579zNPPHVahpEhfP3y/owtEs1HL135zJ48xzX6ev309xV0gsnuB7n135Zvcri03bCSycfrlcK9aPVmCq8c6Hr8XzHYqjbJPhx1mBW0WyqVFpmNm/8uJnXZ2/kQFYO5/eJ5+4zutCycR32pmeR4n3Rp6QfKvi7Jz2L5ANZ9Nv1KTcfmMDf9GomHBpxxHFLrExWdcNuTHvAdbI78zHod/3RraoWvgFf3A2D7oYzxpf7Oa7euZ87PljM2qQD3DCoPX8c3rX43uCVbc9GeGM4hIS5L9lG3oDFC9+EL+6Ci/8DvS6p2hjzqcL7l7l+K7fMdk2j/ZW0wjVS6H8LDH8yeDHWApYUTLWwLyOLf8/ayFtzNpOZk1vsGHihIUKT6AhioiOIiQ7nvtS/0jP9Jz5JeIOc5n2JqRdB0/qR9G7VqOgmsPt3uGaM66a7q4xRL5bcvDW//uKSN6DnxeV+fpnZuTwxdRVv/7SF7i0a8PyYvnRqGtje2WWWttP1/M3c764QfOtP8nLdlVh1Gi5i0X/dld2IZ6D/zWXff/IdbhyuW+dDbKfAx1dLWFIw1cqutEw+/HkreQpN6kUQGx3hkkC9SGLrRdAgKvzITmIZe+CVwRAa7obBiGpQ9IFV3XDdX93n+mKcMd5VppbQ5wJw2759PmxfAtdPr3B7969XJnHfx0s5mJ3Ln8/rwegTW1dNJfTBva7IaO9m11yz1QlHb/PbfHjjLBh8L5z+SKWHeIS9m10ntZbHw9Wfl/6+FSUtyTVR7TAMRr8X4ABrD0sKpubbMtd1bOt1KVz06tHr05JcUciaqdD6ZDdURkxH/49/YJeb30FC4KbvKzy/Q9L+TO6dtJQf1yczvEdznrq4F43qVmKrmKwMV8a+bRFc+RF0PLX4bT+9GVZ86lrulOU1C6S8PPjvua7uY+zcw0Vc5THrWfjucfjdF9B+cOBirEWs9ZGp+dqeAkP/z10JLPng8HJVWPYxvNQfNnwHZ/0Vrpta9i+3ek3h8nfdcB+Tfge52RUKt1mDKN7+/Uk8OPI4vl2dxPB/zeanDSkVOqbfcrPho9/B1vlw8eslJwSAMx+F0Eg3/0VVmfeSG213+FMVSwgAA26Dhq3d87E5FyokqElBRIaLyBoRWS8i9xex/hYRWSYiS0TkRxHpHsx4TA005I+ujuDLeyF5vSsLn3Q1fHK9a6ly82w3+ms5WhEBrtjivOdhy48B+YIMCRFuGtKRT8cOpG5EKFe8Po9npq0mO9e/L6q8PGVXWiZLt+5j2vIdvPHjJv765Upue/8Xbn5nIcu3pRa1E/zvVjdQ3Ln/dLPdlaZ+cxh6H6yd5iZJqmy7VsO3j0HXc9yAiBUVXscVHe78FX6dWPHjHcOCVnwkIqHAWuBM3HzNC4AxqrrSZ5sGqrrfu38+cKuqDi/puFZ8dAxKTXTlzvWaQkYKHDoApz4Ip9xe/mRQ2PSH4KcX4fwX4firA3LI9EM5PDZlJR8u3Eqf1o147vIEGtQJZ/u+g+xMzWRH6kG2p2ayY5/3N/UgSamHyCqUQCLCQohvGEXqwWz2Z+Zwy9AO3H5aZzfchip89X/w879d/cDge/0PMCfLdQDTXK8DWGRAnnepcrPdpDmpW13lcL0ANedVdcfdvw1uX1Q9KtGrEX+Lj4I5R/NJwHpV3egFNBEYBRQkhfyE4IkGalYFh6kcDVu5+oKJV0D88XDBy9D0uMCe44xHXfPGL+9xAwW2PrHCh4yODOPpS3ozpEscD3z6K8Oe/f6obcJChOYNo4hvWIe+rRvTope736JhFPGN3N8m0RGICPsysnj8i1VMmLmB6SuSeOaS3hy/6TWXEAaMg0H3lC3AsAgY8TS8exH8NAEGl3H/8pr1LOxYApe9E7iEAK7fxdlPuEr0uS/AsKMKJ4wfgnmlcAkwXFVv8B5fDfRX1XGFtrsNuAeIAE5T1XVFHOsm4CaANm3anLBly5agxGyquT0b3Wiu/nRsKo+MPa65Znamq3gO4Hj92/YdZNKCrTSoE058wyhaNKpDfMMoYutFlnlo7plrdvHQp8s4/cAUHg9/k5xeYwi78KXytdwBmHglbJjpmqg2iC/fMfy17Rf3a77XJUU3HgiEj651Q3vcvij4z6cGqQ4VzUV90o/KQKo6QVU7Av8HPFzUgVT1VVXtp6r94uKqYc9RUzmadAheQgDXI3b0B24s/w+vcskhQFo2qsPdZ3bh+kHtGdGrBQmtG9G0QVS55mo4tWtTvj07mUfD3+Lr3BM4c/0lzN20p/zBnf1XN4bQjD+V/xj+yD7ohjCp18z1SQiWM8a75/Od/4MrmsOCmRQSAd8mBa2A7SVsPxHwo4bMmCBq1h0u+jdsW+gqt6tjk+1131Dni1sJaXsKDa56h7yQUK54bT4PfbaMtMxytKBq3M4NU738YzfbWbB8+7ib3OmCCW6k02Bp3A5OHut6t29fErzz1FLBTAoLgM4i0l5EIoDRwGTfDUTEtz/7OcBRRUfGVLpu57mmsEvehZ+DVMRRXlt/dq2v4rrBmA/o37Ul0+4cwg2D2vP+z79x9j9nMXNN0YMJlmjQ3a5J51f3uRFIA0hVWf79R+i8l8g94XroeFpAj1+kwfe6K78ZD1fPxF6NBS0pqGoOMA6YDqwCJqnqChF5zGtpBDBORFaIyBJcvcLvghWPMWUy9H7XXHLaA7BpVlVH4ySthPcudc1Jr/4UohoCUCcilIfP7c4nY0+hbmQY1725gHsmLWFfRpb/x46o60YdTVruhv8IgEM5uXz88ybee+oWus+8kTV5rTh39Vn8sHZ36TtXVFRD10Jt82zXudH4zXo0G1OczP2uUjR9N9w00xVL+CMv1w3fsGsV7F7l/u5a7ZZJiBu6IzTC3cK8vwXLIn3ue3/DvGX5/Qmun15sLIdycnnh2/W8/MMGGteN4C8X9GB4Tz8rzFXd0B87foXbf4HocsyJAexNz+K9+Vv4au4vPJL1D/qHrGZzq1Fs6T+e8dN/Y1NyOiN6Nufhc7vTMgCz5BWrYM6FbNf09Rifc8GGuTAmEFI2uBZJDVvD9TOObPuu6tra71p1+LZ7FexeAzk+ldQN27jhqvN7XOdmebds9zfn0OH7BX99l3nLoxrCJW+6eo9SLN+Wyn0f/8rKHfs5p1cLxp/fg7j6fvRD2LXK9Qk5/mo477kyvVQbdx/gjTmb+HhRIqfkLuS5qFepG5JDyLn/QBLGAC5pvT57Ey98tw5BGHdaJ24Y3D54o8vmT+159pMw4NbgnKOGsKRgTKCs/8YV23QZAe0G+iSANZCVdni7+vGu/0RcN5cEmnZzI5RG+jmXRIBl5+bx6qyNPPfNOupGhnL/8OMY3CWO+IZRJQ/WN+0BmPeyuzqK71viOVSV+Zv28PrsjXy7ehd1Q/J4pfnnDE75yE3sc8lbRY5cmrg3g8e/WMn0FUm0j41m/Pk9gjMnharrh7HtlwrNuaCqNWOWvRJYUjAmkOY8B197I4pGx7kObk27uyTQtLv78q/TuGpjLMa6pDTu++RXFv/mZptrEBVGtxYN6NaiAd29v52b1XM9pAEyU91kPI3bu7kYiuj/kJ2bx9RlO3ht9kaWb9tPk+gIxvUJ4eptjxKetNSNVHvm426muxJ8v2YX4yevYHNKRvCKlPLnXOgyHHpcBDEd3BApRbSAUlV2px1iTVIaa3amsTYpjTVJB1iXlEaP+Aa8ed1J1IsMZp/f4LGkYEygpWxwRTgVHE21KuTmKUu27mPljv2s8m5rdqaRkZULuPksOsRGFySLUw9O57j5D6AXvIz4jE2UejCbiT//xltzN7MjNZMOcdHcMKgDl0TOI6GJW1kAAAtWSURBVGLqPW7YkVEToNu5fsd2KCeX12Zt5MWZ64NXpPTtYzD7H/h2lcqrE0NGvTYkhbdkc15zlmXGMj+1EcsPxpJGXQBi60XQpVl9Wjeuy8e/JDKwUyz/+V0/wkNr3liilhSMMSXKy1O27MkoSBLulsa2fQcR8vgs4s+0Cknhgfg3adeyOVk5eXy8KJH0rFwGdIjhxiHtGdYumpDp98Pid6B1fzejWzlHPC1cpPTo+T0YEoAipX0ZWWxKTmfjjhSSt67h4M51hOzdQOyhRNrJTtqF7CRejuz8lx3ZBGI6Eh7X2XWajOnAlOTm3D5tH6NPbM2TF/WqccVJlhSMMeWSmpHNqp372b16Duf9fDWfRl3E/QcuIy9POb9PPL8f1J6eLRu6JrIfXQvJa924ScMecK2kKqg8RUoZWTlsSk5nU3I6m5PT2ehzf2/G4Q59kWEhdG5Wjy7N6tO1WX26NHd/W9TNQ/ZugT0b3BXhng2QstH9TdtRsP/O6G68tu94Wg26gutGDKrwc61MlhSMMRX3+W2wdCI5N8/hUKNOREeGucrbRW/BtPshsoHrAR7gDmn/396dx1hVnnEc//4cQGBQVBjrArIoaHGpCNIqLqDUYNuIO9qSWG1ibTUt2sQQaWpjYrXaWou1UmtFY1GjAmqta62CcamgIpuyBK2yQ6osyjo8/eMcruP1Mgwzc++ZA79PMrn3nnPPOc+8OXOfue857/OW6lK65MTuLFu9If3wX8cHqz5PHz9j+ZqNX9r+gL3b0qNzNT1qqunRqZoenavpWVNNt07Vpadzrc+mz5K6WwtfJmY+hpYmo6RXdepH529eDH3Obt7CfmXipGBmTbduZXLRuUs/GDERNq5J5sKePQl6Dk6K2nXYv2yHr9ulVGy/6jZ079SeHp070LOmmu7ph3/3zu1p36Z8F4M3rZjP4w/cQd81/6KXFoOqoOepyVzfR3yvvCU8msBJwcyaxxt3Jd8KBo+Gd/6ezG9x2i9h4MjGV2bdSVPmreTtjz6hW6f2hQ//ik51WmT1+s1cMPY1qj+dxz3H/ZdOH/4jGZxY1QYOG5IkiMPPbFFzOjgpmFnzqN0MY09OBuZ17Arn3wtdB2QdVeYWf7qec+58lao9xKSfnMgBn82BWROTn7VLoHX75DbYo85LEsUObs8tNycFM2s+S2fAzEeTC8otdDxGFmYvWc2FY1/nkE7VPHrFCckYhq1b4aPXYdYEmPN4MlvgnntD3xEw9KbMYnVSMDOrgMnzVnLZfVNLj2Go3QIfTE4SRLt9k7krMtISJtkxM9vlndq7ht+ccxRT5q1k9KSZfOkf7apWcNjpyXSyGSaEnZHP8dpmZi3I8OMPYfEn6xnz7wV02bc9Pzu91443aqGcFMzMmsHV3+7Nok/Wc9sL8zhon3ac369L1iE1ipOCmVkzkMTN5x3D8rUbGDVhBgd2bMvAw/JXJ6us1xQkDZU0V9ICSaNKrL9G0hxJMyS9KKlbOeMxMyunNq324K4R/Ti0pgNXPPAW7y9bk3VIO61sSUFSFXAncCbQB7hYUvHsIO8A/SPiGOAx4JZyxWNmVgl7t23NuEuPp/2eVVw6bipLV6/POqSdUs5vCgOABRGxMCI2AQ8Dw+q+ISJeiojP05dvAPnshDMzq+Ogfdox7ocDWLthC5eOm8raDZt3vFELUc6kcDDwcZ3Xi9Jl2/Mj4JlSKyRdLmmapGkrV1Zg0m8zsybqc9De/PkHxzF/xTp+Ov5tNtduzTqkBilnUihVirDkSDlJI4D+wK2l1kfE3RHRPyL619S0/GqEZmYAp/Su4aZzj+aV+au4bmLRGIYWqpx3Hy0C6s620QVYUvwmSUOA0cCpEbGxeL2ZWZ5d2L8rSz5d37wzyZVROZPCVKCXpB7AYuAi4Pt13yCpL/AXYGhErChjLGZmmRk5pHfWITRY2bqPImILcBXwHPAe8EhEzJZ0g6Sz0rfdCnQAHpU0XdKT5YrHzMx2rKyD1yLiaeDpomW/qvN8SDmPb2ZmO8cF8czMrMBJwczMCpwUzMyswEnBzMwKnBTMzKzAScHMzApyN0ezpLXA3KzjyLHOwKqsg8gxt1/jue2apqnt1y0idlgnKI+T7MxtyOTTVpqkaW6/xnP7NZ7brmkq1X7uPjIzswInBTMzK8hjUrg76wByzu3XNG6/xnPbNU1F2i93F5rNzKx88vhNwczMysRJwczMCnKVFCQNlTRX0gJJo7KOJ08kfShpZjpvxbSs42npJN0raYWkWXWW7SfpBUnz08d9s4yxJdtO+/1a0uL0HJwu6TtZxthSSeoq6SVJ70maLenn6fKKnH+5SQqSqoA7gTOBPsDFkvpkG1XuDI6IY32veIPcBwwtWjYKeDEiegEvpq+ttPv4avsB/CE9B49N51uxr9oC/CIivg58C7gy/ayryPmXm6QADAAWRMTCiNgEPAwMyzgm20VFxBTgf0WLhwH3p8/vB86uaFA5sp32swaIiKUR8Xb6fC3JzJUHU6HzL09J4WDg4zqvF6XLrGECeF7SW5IuzzqYnPpaRCyF5A8X2D/jePLoKkkz0u4ld7/tgKTuQF/gP1To/MtTUlCJZb6ftuEGRsRxJN1vV0o6JeuAbLdzF3AocCywFPh9tuG0bJI6ABOAkRGxplLHzVNSWAR0rfO6C7Ako1hyJyKWpI8rgEkk3XG2c5ZLOhAgfVyRcTy5EhHLI6I2IrYCf8Xn4HZJak2SEMZHxMR0cUXOvzwlhalAL0k9JLUBLgKezDimXJBULWmvbc+BM4BZ9W9lJTwJXJI+vwR4IsNYcmfbB1rqHHwOliRJwN+A9yLitjqrKnL+5WpEc3oL2+1AFXBvRNyYcUi5IKknybcDSCrjPui2q5+kh4BBJOWKlwPXA48DjwCHAB8BF0SEL6aWsJ32G0TSdRTAh8CPt/WR2xcknQS8AswEtqaLryO5rlD28y9XScHMzMorT91HZmZWZk4KZmZW4KRgZmYFTgpmZlbgpGBmZgVOCrbLklSbVuOcLeldSddI2iNd11/SmIziei2L45o1hG9JtV2WpHUR0SF9vj/wIPBqRFyfbWRmLZe/KdhuIS3vcTlJQTZJGiTpKSjU+b9f0vPpvBPnSrolnX/i2bTkAJL6SZqcFhV8rk7JgZcl/VbSm5LmSTo5XX5kumx6WgSuV7p8XfooSbdKmpUea3i6fFC6z8ckvS9pfDrKFUk3S5qT7u93lW5H2/W1yjoAs0qJiIVp91Gp6pKHAoNJ5up4HTgvIq6VNAn4rqR/AncAwyJiZfoBfiNwWbp9q4gYkI66vx4YAlwB/DEixqelWaqKjnkuyQjfb5CM/J0qaUq6ri9wJEl9r1eBgZLmkJSHOCIiQtI+TW4UsyJOCra7KVVtF+CZiNgsaSbJh/ez6fKZQHfgcOAo4IX0n/Yqkkqf22wrWvZW+n5IkstoSV2AiRExv+iYJwEPRUQtSbGzycDxwBrgzYhYBCBperrPN4ANwD1pknpqp35zswZw95HtNtIaULWUri65ESCt4Lk5vrjYtpXknycBs+vMGnZ0RJxRvH26/1bpvh4EzgLWA89JOq04pHrC3VjneS3JN5EtJJVFJ5BMsPJsqQ3NmsJJwXYLkmqAscCfonF3V8wFaiSdkO6vtaQjd3DMnsDCiBhDUuHymKK3TAGGS6pK4zsFeLOe/XUAOqbTWI4k6Xoya1buPrJdWbu066U1yby3DwC31b9JaRGxSdL5wBhJHUn+dm4HZtez2XBghKTNwDLghqL1k4ATgHdJKodeGxHLJB2xnf3tBTwhqS3Jt4yrG/O7mNXHt6SamVmBu4/MzKzAScHMzAqcFMzMrMBJwczMCpwUzMyswEnBzMwKnBTMzKzg/+vbpHju4xWeAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_test_stats(linear_sim, 20, 'Linear')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 179,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_test_stats(spiral_sim, 20, 'Spiral')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 180,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_test_stats(quad_sim, 20, 'Quadratic')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## P-value"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 184,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def pvalue_vs_dimension(corr_type, simulation_type, dim_range):\n",
-    "    p_value = []\n",
-    "    for d in range(1, dim_range+1):\n",
-    "        x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n",
-    "        if corr_type == 'rv' or corr_type == 'cca':\n",
-    "            corr = RVCorr(which_test=corr_type)\n",
-    "        #else:\n",
-    "            #corr = HHG()\n",
-    "        p_value.append(corr.p_value(x, y)[0])\n",
-    "    return p_value"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 185,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_p_value(simulation_type, dim_range, simulation_name):\n",
-    "    rv_pvalue = pvalue_vs_dimension('rv', simulation_type, dim_range)\n",
-    "    cca_pvalue = pvalue_vs_dimension('cca', simulation_type, dim_range)\n",
-    "    #hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\n",
-    "    plt.plot(rv_pvalue, label='RV')\n",
-    "    plt.plot(cca_pvalue, label='CCA')\n",
-    "    #plt.plot(hhg_pvalue, label='HHG')\n",
-    "    plt.xlabel('Dimensions')\n",
-    "    plt.ylabel('pvalue')\n",
-    "    plt.legend()\n",
-    "    plt.gca().set_xlim(1, dim_range+1)\n",
-    "    plt.xticks(np.arange(0, dim_range+1, 5))\n",
-    "    plt.title('P-value \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
-    "    plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 186,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "TypeError",
-     "evalue": "float() argument must be a string or a number, not 'dict'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-186-0052d0a51dfd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_p_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlinear_sim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Linear'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-185-5ab204793fab>\u001b[0m in \u001b[0;36mplot_p_value\u001b[0;34m(simulation_type, dim_range, simulation_name)\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mcca_pvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpvalue_vs_dimension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'cca'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msimulation_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0;31m#hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'RV'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcca_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'CCA'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0;31m#plt.plot(hhg_pvalue, label='HHG')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2747\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2748\u001b[0m     return gca().plot(\n\u001b[0;32m-> 2749\u001b[0;31m         *args, scalex=scalex, scaley=scaley, data=data, **kwargs)\n\u001b[0m\u001b[1;32m   2750\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2751\u001b[0m \u001b[0;31m# Autogenerated by boilerplate.py.  Do not edit as changes will be lost.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1783\u001b[0m                         \u001b[0;34m\"the Matplotlib list!)\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1784\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1785\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1786\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1787\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1603\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1604\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1605\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1606\u001b[0m             \u001b[0mlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1607\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36madd_line\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m   1883\u001b[0m             \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_clip_path\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpatch\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1884\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1885\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_update_line_limits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1886\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_label\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1887\u001b[0m             \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_label\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'_line%d'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlines\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_update_line_limits\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m   1905\u001b[0m         \u001b[0mFigures\u001b[0m \u001b[0mout\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mdata\u001b[0m \u001b[0mlimit\u001b[0m \u001b[0mof\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mgiven\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mupdating\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdataLim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1906\u001b[0m         \"\"\"\n\u001b[0;32m-> 1907\u001b[0;31m         \u001b[0mpath\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_path\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1908\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvertices\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1909\u001b[0m             \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/lines.py\u001b[0m in \u001b[0;36mget_path\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    943\u001b[0m         \"\"\"\n\u001b[1;32m    944\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_invalidy\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_invalidx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 945\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecache\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    946\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    947\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/lines.py\u001b[0m in \u001b[0;36mrecache\u001b[0;34m(self, always)\u001b[0m\n\u001b[1;32m    643\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0malways\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_invalidy\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    644\u001b[0m             \u001b[0myconv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconvert_yunits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_yorig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 645\u001b[0;31m             \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_to_unmasked_float_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0myconv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mravel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    646\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    647\u001b[0m             \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_y\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/cbook/__init__.py\u001b[0m in \u001b[0;36m_to_unmasked_float_array\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m   1363\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfilled\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnan\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1364\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1365\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1366\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1367\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m    499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    500\u001b[0m     \"\"\"\n\u001b[0;32m--> 501\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    503\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mTypeError\u001b[0m: float() argument must be a string or a number, not 'dict'"
-     ]
-    },
-    {
-     "data": {
-      "image/png": "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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_p_value(linear_sim, 20, 'Linear')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.6"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/mgcpy/independence_tests/abstract_class.py b/mgcpy/independence_tests/abstract_class.py
index 3174d3f..c3a68a4 100644
--- a/mgcpy/independence_tests/abstract_class.py
+++ b/mgcpy/independence_tests/abstract_class.py
@@ -7,7 +7,7 @@
 
 import numpy as np
 from scipy.spatial.distance import pdist, squareform
-from scipy.stats import t
+from scipy.stats import kendalltau, pearsonr, spearmanr, t
 
 
 def EUCLIDEAN_DISTANCE(x): return squareform(pdist(x, metric='euclidean'))
@@ -129,6 +129,12 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
                                 "p_local_correlation_matrix": p_local_correlation_matrix,
                                 "local_correlation_matrix": local_correlation_matrix,
                                 "optimal_scale": independence_test_metadata["optimal_scale"]}
+        elif self.get_name() == "kendall":
+            p_value = kendalltau(matrix_X, matrix_Y)[1]
+        elif self.get_name() == "spearman":
+            p_value = spearmanr(matrix_X, matrix_Y)[1]
+        elif self.get_name() == "pearson":
+            p_value = pearsonr(matrix_X, matrix_Y)[1]
         else:
             # estimate the null by a permutation test
             test_stats_null = np.zeros(replication_factor)
diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py
index 24a0670..96d7cac 100644
--- a/mgcpy/independence_tests/kendall_spearman.py
+++ b/mgcpy/independence_tests/kendall_spearman.py
@@ -42,10 +42,6 @@ def test_statistic(self, matrix_X, matrix_Y):
         >>> kendall_spearman = KendallSpearman()
         >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y)
         """
-        if matrix_X is None:
-            matrix_X = self.matrix_X
-        if matrix_Y is None:
-            matrix_Y = self.matrix_Y
         assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape"
         assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape"
 

From 2decdcb25a6117af8e1f80ffe7e8fb5c5d0f0337 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Thu, 6 Dec 2018 23:44:52 -0500
Subject: [PATCH 43/60] Fix unit tests

---
 mgcpy/independence_tests/unit_tests/hhg_test.py              | 2 +-
 mgcpy/independence_tests/unit_tests/kendall_spearman_test.py | 2 +-
 mgcpy/independence_tests/unit_tests/rv_corr_test.py          | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
index 9c65b9b..75acd6e 100644
--- a/mgcpy/independence_tests/unit_tests/hhg_test.py
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
 import pytest
-from mgcpy import HHG
+from mgcpy.independence_tests.hhg import HHG
 
 
 def test_hhg():
diff --git a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
index 1937704..b5a3a13 100644
--- a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
+++ b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
 import pytest
-from mgcpy import KendallSpearman
+from mgcpy.independence_tests.kendall_spearman import KendallSpearman
 
 
 def test_kendall_spearman():
diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
index 4aee659..59d97f4 100644
--- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py
+++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py
@@ -1,7 +1,7 @@
 import mgcpy.benchmarks.simulations as sims
 import numpy as np
 import pytest
-from mgcpy import RVCorr
+from mgcpy.independence_tests.rv_corr import RVCorr
 
 
 def test_local_corr():

From a2b880b94024a83230bbf2b22cdd6f2581e9751e Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Fri, 7 Dec 2018 00:48:53 -0500
Subject: [PATCH 44/60] update p_value function in class

---
 mgcpy/independence_tests/mdmr/mdmr.py         | 118 +++++++++++++-----
 .../unit_tests/mdmr/mdmr_test.py              |  10 +-
 2 files changed, 91 insertions(+), 37 deletions(-)

diff --git a/mgcpy/independence_tests/mdmr/mdmr.py b/mgcpy/independence_tests/mdmr/mdmr.py
index 860384c..abaca7e 100644
--- a/mgcpy/independence_tests/mdmr/mdmr.py
+++ b/mgcpy/independence_tests/mdmr/mdmr.py
@@ -1,3 +1,6 @@
+"""
+    **Main MDMR Independence Test Module**
+"""
 from mgcpy.independence_tests.abstract_class import IndependenceTest
 
 import copy
@@ -7,42 +10,50 @@
 class MDMR(IndependenceTest):
     def __init__(self, compute_distance_matrix):
         '''
-        :param data_matrix_X: is interpreted as:
-            - a [n*d] data matrix, a square matrix with n samples in d dimensions
-        :type data_matrix_X: 2D numpy.array
-        :param data_matrix_Y: is interpreted as either:
-            - a [n*d] data matrix, a square matrix with n samples in d dimensions
-        :type data_matrix_Y: 2D numpy.array
         :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
-        :type compute_distance_matrix: FunctionType or callable()
+        :type compute_distance_matrix: ``FunctionType`` or ``callable()``
         '''
         IndependenceTest.__init__(self, compute_distance_matrix)
+        self.which_test = "mdmr"
     
     def get_name(self):
-        return "mdmr"
+        return self.which_test
     
-    def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individual = 0, disttype = 'cityblock'):
+    def test_statistic(self, matrix_X, matrix_Y, permutations = 0, individual = 0, disttype = 'cityblock'):
         """
-        Computes MDMR between two datasets.
+        Computes MDMR Pseudo-F statistic between two datasets.
+        
         - It first takes the distance matrix of Y (by )
-        - Next it regresses X into a portion due to Y and a portion due to residual for each variable of X
+        - Next it regresses X into a portion due to Y and a portion due to residual
         - The p-value is for the null hypothesis that the variable of X is not correlated with Y's distance matrix
+        
         :param data_matrix_X: (optional, default picked from class attr) is interpreted as:
-            - a [n*d] data matrix, a square matrix with n samples in d dimensions
-        :type data_matrix_X: 2D numpy.array
+            
+            - a ``[n*d]`` data matrix, a square matrix with n samples in d dimensions
+        :type data_matrix_X: 2D `numpy.array`
+        
         :param data_matrix_Y: (optional, default picked from class attr) is interpreted as:
-            - a [n*d] data matrix, a square matrix with n samples in d dimensions
-        :type data_matrix_Y: 2D numpy.array
+            
+            - a ``[n*d]`` data matrix, a square matrix with n samples in d dimensions
+        :type data_matrix_Y: 2D `numpy.array`
+        
         :parameter 'individual':
-            with value 0 tests the entire X matrix by (default), returns 2 values
-            with value 1 it tests the entire X matrix and then each column (variable) individually, returns 3 values
-        :return: with individual = 0, returns the test statistic of the entire X matrix and the associated p-value
-        with individual = 1, returns the above as well as an array with the 
-        variable of X in the first column, the test statistic in the 2nd, and the permutation p-value in the 3rd
+            
+            -integer, `0` or `1`
+            with value `0` tests the entire X matrix (default)
+            with value `1` tests the entire X matrix and then each predictor variable individually
+            
+        :return: with individual = `0`, returns 1 values, with individual = `1` returns 2 values, containing:
+            
+            -the test statistic of the entire X matrix
+            -for individual = 1, an array with the variable of X in the first column, 
+                the test statistic in the second, and the permutation p-value in the third (which here will always be 1)
+        :rtype: list
         """
-        X = data_matrix_X
-        Y = data_matrix_Y
+        X = matrix_X
+        Y = matrix_Y
         
+        #calculate distance matrix of Y
         D = self.compute_distance_matrix(Y, disttype)
         D = scp.distance.squareform(D)
         a = D.shape[0]**2
@@ -51,7 +62,8 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
         predictors = np.arange(X.shape[1])
         predsingle = X.shape[1]
         check_rank(X)
-    
+        
+        #check number of subjects compatible
         subjects = X.shape[0]
         if subjects != np.sqrt(D.shape[0]):
             raise Exception("# of subjects incompatible between X and D")
@@ -60,11 +72,13 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
         predictors = np.array(predictors)
         predictors += 1
     
+        # Gower Center the distance matrix of Y
         Gs = gower_center_many(D)
     
         m2 = float(X.shape[1] - predictors.shape[0])
         nm = float(subjects - X.shape[1])
     
+        #form permutation indexes
         permutation_indexes = np.zeros((permutations + 1, subjects), dtype=np.int)
         permutation_indexes[0, :] = range(subjects)
         for i in range(1, permutations + 1):
@@ -73,15 +87,20 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
         H2perms = gen_H2_perms(X, predictors, permutation_indexes)
         IHperms = gen_IH_perms(X, predictors, permutation_indexes)
         
+        #Calculate test statistic
         F_perms = calc_ftest(H2perms, IHperms, Gs, m2, nm)
     
+        #Calculate p-value
         p_vals = None
         if permutations > 0:
             p_vals = fperms_to_pvals(F_perms)
         F_permtotal = F_perms[0, :]
         pvaltotal = p_vals
+        self.test_statistic_ = F_permtotal
         if individual == 0:
-            return F_permtotal, pvaltotal
+            return self.test_statistic_, self.test_statistic_metadata_
+        
+        #code for individual test
         if individual == 1:
             results = np.zeros((predsingle,3))
             for predictors in range(1, predsingle+1):
@@ -110,16 +129,47 @@ def test_statistic(self, data_matrix_X, data_matrix_Y, permutations = 0, individ
                 results[predictors-1,2] = p_vals
     
     
-            return F_permtotal, pvaltotal, results
+            return F_permtotal, results
 
-    def p_value(self, data_matrix_X, data_matrix_Y, permutations = 1000, individual = 0, disttype = 'cityblock'):
+    def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
+        """
+        Tests independence between two datasets using MGC and permutation test.
+        
+        :param matrix_X: is interpreted as:
+            
+            - a ``[n*d]`` data matrix, a square matrix with ``n`` samples in ``d`` dimensions
+        :type matrix_X: 2D `numpy.array`
+        
+        :param matrix_Y: is interpreted as:
+            
+            - a ``[n*d]`` data matrix, a square matrix with ``n`` samples in ``d`` dimensions
+        :type matrix_Y: 2D `numpy.array`
+        
+        :param replication_factor: specifies the number of replications to use for
+                                   the permutation test. Defaults to ``1000``.
+        :type replication_factor: integer
+        
+        :return: returns a list of two items,that contains:
+            
+            - :p_value: P-value of MGC
+            - :p_value_metadata:
+        :rtype: list
         """
-        Computes the permutation p-value of the pseudo-F test statistic.
+        return super(MDMR, self).p_value(matrix_X, matrix_Y)
+    
+    def ind_p_value(self, matrix_X, matrix_Y, permutations = 1000, individual = 1, disttype = 'cityblock'):
         """
-        if individual == 0:
-            p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations)[1]
-            return p_value
-        if individual == 1:
-            p_value = self.test_statistic(data_matrix_X, data_matrix_Y, permutations, individual)[1]
-            results = self.test_statistic(data_matrix_X, data_matrix_Y, permutations, individual)[2]
-            return p_value, results
+        Individual predictor variable p-values calculation
+        
+        :param matrix_X: is interpreted as:
+            
+            - a ``[n*d]`` data matrix, a square matrix with ``n`` samples in ``d`` dimensions
+        :type matrix_X: 2D `numpy.array`
+        
+        :param matrix_Y: is interpreted as:
+            
+            - a ``[n*d]`` data matrix, a square matrix with ``n`` samples in ``d`` dimensions
+        :type matrix_Y: 2D `numpy.array`
+        """
+        results = self.test_statistic(matrix_X, matrix_Y, permutations, individual)[1]
+        return results
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index 24e80bc..e7cf54f 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -10,8 +10,9 @@ def test_mdmr():
     Y = np.genfromtxt('./mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=",")
 
     mdmr = MDMR(compute_distance_matrix)
-    a, b1, results1 = mdmr.test_statistic(X, Y, individual=1)
-    b2, results2 = mdmr.p_value(X, Y, individual = 1)
+    a, results1 = mdmr.test_statistic(X, Y, individual=1)
+    b, c = mdmr.p_value(X, Y, individual = 1)
+    results2 = mdmr.ind_p_value(X, Y)
     
     #test get_name
     assert mdmr.get_name() == 'mdmr'
@@ -20,12 +21,15 @@ def test_mdmr():
     assert np.allclose(a, 75.11630064)
     
     #p-value
-    assert np.allclose(b2, 0.000999)
+    assert np.allclose(b, 0.0) #0.000999
     
     #individual statistics
     assert np.allclose(results1[0,1], 10.39953044)
+    assert np.allclose(results2[0,1], 10.39953044)
     assert np.allclose(results2[0,2], 0.000999)
     assert np.allclose(results1[1,1], 4.12263312)
+    assert np.allclose(results2[1,1], 4.12263312)
     assert np.allclose(results2[1,2], 0.000999)
     assert np.allclose(results1[2,1], 11.31712737)
+    assert np.allclose(results2[2,1], 11.31712737)
     assert np.allclose(results2[2,2], 0.000999)
\ No newline at end of file

From 659c0688b1cf349c94d96ffe7e290c8020025f53 Mon Sep 17 00:00:00 2001
From: sundaysundya <s.ramachandran8@gmail.com>
Date: Fri, 7 Dec 2018 01:16:23 -0500
Subject: [PATCH 45/60] remove individual from mdmr unit test p_value

---
 demos/MDMR.ipynb                              | 23 +++----------------
 .../unit_tests/mdmr/mdmr_test.py              |  2 +-
 2 files changed, 4 insertions(+), 21 deletions(-)

diff --git a/demos/MDMR.ipynb b/demos/MDMR.ipynb
index 142cfd7..26c1992 100644
--- a/demos/MDMR.ipynb
+++ b/demos/MDMR.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -34,27 +34,10 @@
     "Y = np.genfromtxt('../mgcpy/independence_tests/unit_tests/mdmr/data/Y_mdmr.csv', delimiter=\",\")\n",
     "\n",
     "mdmr = MDMR(compute_distance_matrix)\n",
-    "a, b = mdmr.test_statistic(X, Y)\n",
+    "a, _ = mdmr.test_statistic(X, Y)\n",
     "print(a)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[0.000999]\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(b)"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
diff --git a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
index e7cf54f..15380d5 100644
--- a/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
+++ b/mgcpy/independence_tests/unit_tests/mdmr/mdmr_test.py
@@ -11,7 +11,7 @@ def test_mdmr():
 
     mdmr = MDMR(compute_distance_matrix)
     a, results1 = mdmr.test_statistic(X, Y, individual=1)
-    b, c = mdmr.p_value(X, Y, individual = 1)
+    b, c = mdmr.p_value(X, Y)
     results2 = mdmr.ind_p_value(X, Y)
     
     #test get_name

From 5c94dbffd02b2fab52da5fda15ac2708d9e77fcb Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 07:28:24 -0500
Subject: [PATCH 46/60] Fixed issues with hhg

---
 .../benchmarks/unit_tests/simulations_test.py | 95 ++++++++++---------
 mgcpy/independence_tests/hhg.py               |  2 +-
 2 files changed, 49 insertions(+), 48 deletions(-)

diff --git a/mgcpy/benchmarks/unit_tests/simulations_test.py b/mgcpy/benchmarks/unit_tests/simulations_test.py
index ac8861a..a143847 100644
--- a/mgcpy/benchmarks/unit_tests/simulations_test.py
+++ b/mgcpy/benchmarks/unit_tests/simulations_test.py
@@ -1,6 +1,6 @@
+import matplotlib.pyplot as plt
 import numpy as np
 from mgcpy.benchmarks import simulations as sims
-import matplotlib.pyplot as plt
 from mpl_toolkits.mplot3d import Axes3D
 
 
@@ -11,24 +11,24 @@ def test_simulations():
     independent = True
 
     np.random.seed(0)
-    fig1 = plt.figure(figsize = (50, 80))
+    fig1 = plt.figure(figsize=(50, 80))
     plt.axis('off')
-    fig2 = plt.figure(figsize = (50, 80))
+    fig2 = plt.figure(figsize=(50, 80))
 
     # Linear Simulation
     returns_low_dim = sims.linear_sim(num_samps, num_dim1)
     returns_high_dim = sims.linear_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.linear_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 1)
     ax1.scatter(x1, y1)
     ax1.set_title('Linear', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.linear_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 1, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 1, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Linear', fontweight='bold')
     ax2.axis('off')
@@ -38,15 +38,15 @@ def test_simulations():
     returns_high_dim = sims.exp_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.exp_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 2)
     ax1.scatter(x1, y1)
     ax1.set_title('Exponential', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.exp_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 2, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 2, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Exponential', fontweight='bold')
     ax2.axis('off')
@@ -56,15 +56,15 @@ def test_simulations():
     returns_high_dim = sims.cub_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-     
+
     x1, y1 = sims.cub_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 3)
     ax1.scatter(x1, y1)
     ax1.set_title('Cubic', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.cub_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 3, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 3, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Cubic', fontweight='bold')
     ax2.axis('off')
@@ -74,15 +74,15 @@ def test_simulations():
     returns_high_dim = sims.joint_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.joint_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 4)
     ax1.scatter(x1, y1)
     ax1.set_title('Joint Normal', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.joint_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 4, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 4, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Joint Normal', fontweight='bold')
     ax2.axis('off')
@@ -92,15 +92,15 @@ def test_simulations():
     returns_high_dim = sims.step_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.step_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 5)
     ax1.scatter(x1, y1)
     ax1.set_title('Step', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.step_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 5, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 5, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Step', fontweight='bold')
     ax2.axis('off')
@@ -110,15 +110,15 @@ def test_simulations():
     returns_high_dim = sims.quad_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.quad_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 6)
     ax1.scatter(x1, y1)
     ax1.set_title('Quadratic', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.quad_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 6, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 6, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Quadratic', fontweight='bold')
     ax2.axis('off')
@@ -128,15 +128,15 @@ def test_simulations():
     returns_high_dim = sims.w_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.w_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 7)
     ax1.scatter(x1, y1)
     ax1.set_title('W-Shaped', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.w_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 7, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 7, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('W-Shaped', fontweight='bold')
     ax2.axis('off')
@@ -146,15 +146,15 @@ def test_simulations():
     returns_high_dim = sims.spiral_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.spiral_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 8)
     ax1.scatter(x1, y1)
     ax1.set_title('Spiral', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.spiral_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 8, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 8, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Spiral', fontweight='bold')
     ax2.axis('off')
@@ -162,15 +162,15 @@ def test_simulations():
     # Uncorrelated Bernoulli Simulation
     returns = sims.ubern_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.ubern_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 9)
     ax1.scatter(x1, y1)
     ax1.set_title('Uncorrelated Bernoulli', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.ubern_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 9, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 9, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Uncorrelated Bernoulli', fontweight='bold')
     ax2.axis('off')
@@ -180,16 +180,16 @@ def test_simulations():
     returns_high_dim = sims.log_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.log_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 10)
     ax1.scatter(x1, y1)
     ax1.set_title('Logarithmic', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.log_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 10, projection = '3d');
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
+    ax2 = fig2.add_subplot(4, 5, 10, projection='3d')
+    ax2.scatter(x2[:, 0], x2[:, 1], y2[:, 0]*y2[:, 1])
     ax2.set_title('Logarithmic', fontweight='bold')
     ax2.axis('off')
 
@@ -198,15 +198,15 @@ def test_simulations():
     returns_high_dim = sims.root_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.root_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 11)
     ax1.scatter(x1, y1)
     ax1.set_title('Fourth Root', fontweight='bold')
     ax1.axis('off')
-    
+
     x2, y2 = sims.root_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 11, projection = '3d');
+    ax2 = fig2.add_subplot(4, 5, 11, projection='3d')
     ax2.scatter(x2[:, 0], x2[:, 1], y2)
     ax2.set_title('Fourth Root', fontweight='bold')
     ax2.axis('off')
@@ -216,7 +216,7 @@ def test_simulations():
     returns_high_dim = sims.sin_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.sin_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 12)
     ax1.scatter(x1, y1)
@@ -229,7 +229,7 @@ def test_simulations():
         num_samps, num_dim2, period=16*np.pi, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi)
     ax1 = fig1.add_subplot(4, 5, 13)
     ax1.scatter(x1, y1)
@@ -239,7 +239,7 @@ def test_simulations():
     # Square Simulation
     returns = sims.square_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.square_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 14)
     ax1.scatter(x1, y1)
@@ -251,7 +251,7 @@ def test_simulations():
     returns_high_dim = sims.two_parab_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 15)
     ax1.scatter(x1, y1)
@@ -261,7 +261,7 @@ def test_simulations():
     # Circle Simulation
     returns = sims.circle_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.circle_sim(num_samps, 1, noise=0)
     ax1 = fig1.add_subplot(4, 5, 16)
     ax1.scatter(x1, y1)
@@ -271,7 +271,7 @@ def test_simulations():
     # Ellipse Simulation
     returns = sims.circle_sim(num_samps, num_dim2, radius=5)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5)
     ax1 = fig1.add_subplot(4, 5, 17)
     ax1.scatter(x1, y1)
@@ -282,7 +282,7 @@ def test_simulations():
     returns = sims.square_sim(
         num_samps, num_dim2, period=-np.pi/4, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4)
     ax1 = fig1.add_subplot(4, 5, 18)
     ax1.scatter(x1, y1)
@@ -292,7 +292,7 @@ def test_simulations():
     # Multiplicative Noise Simulation
     returns = sims.multi_noise_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.multi_noise_sim(num_samps, 1)
     ax1 = fig1.add_subplot(4, 5, 19)
     ax1.scatter(x1, y1)
@@ -302,11 +302,12 @@ def test_simulations():
     # Multimodal Independence Simulation
     returns = sims.multi_indep_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-    
+
     x1, y1 = sims.multi_indep_sim(num_samps, 1)
     ax1 = fig1.add_subplot(4, 5, 20)
     ax1.scatter(x1, y1)
     ax1.set_title('Multimodal Independence', fontweight='bold')
     ax1.axis('off')
 
-test_simulations()
\ No newline at end of file
+
+test_simulations()
diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py
index 0125d3f..47890a6 100644
--- a/mgcpy/independence_tests/hhg.py
+++ b/mgcpy/independence_tests/hhg.py
@@ -9,7 +9,7 @@ def __init__(self, compute_distance_matrix=None):
         :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
         :type compute_distance_matrix: FunctionType or callable()
         """
-        IndependenceTest.__init__(compute_distance_matrix)
+        IndependenceTest.__init__(self, compute_distance_matrix)
         self.which_test = "hhg"
 
     def test_statistic(self, matrix_X, matrix_Y):

From 30ccbde32881fd077d7b56341907d3c9f8b78d7d Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 07:40:51 -0500
Subject: [PATCH 47/60] Fix hhg and sims test

---
 mgcpy/benchmarks/unit_tests/simulations_test.py | 3 ---
 mgcpy/independence_tests/unit_tests/hhg_test.py | 8 +++-----
 2 files changed, 3 insertions(+), 8 deletions(-)

diff --git a/mgcpy/benchmarks/unit_tests/simulations_test.py b/mgcpy/benchmarks/unit_tests/simulations_test.py
index a143847..555f7d5 100644
--- a/mgcpy/benchmarks/unit_tests/simulations_test.py
+++ b/mgcpy/benchmarks/unit_tests/simulations_test.py
@@ -308,6 +308,3 @@ def test_simulations():
     ax1.scatter(x1, y1)
     ax1.set_title('Multimodal Independence', fontweight='bold')
     ax1.axis('off')
-
-
-test_simulations()
diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
index 75acd6e..f185bc7 100644
--- a/mgcpy/independence_tests/unit_tests/hhg_test.py
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -11,21 +11,19 @@ def test_hhg():
     Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917,
                   7.1748, 6.5792, 2.4012])[:, np.newaxis]
     hhg = HHG()
-    test_stat = hhg.test_statistic(X, Y)
+    test_stat = hhg.test_statistic(X, Y)[0]
 
     assert np.round(test_stat, decimals=2) == 411.88
 
     # Against linear simulations
     np.random.seed(0)
     X, Y = sims.linear_sim(100, 1)
-    hhg = HHG()
-    test_stat = hhg.test_statistic(X, Y)
+    test_stat = hhg.test_statistic(X, Y)[0]
 
     assert np.round(test_stat, decimals=2) == 28986.52
 
     X, Y = sims.linear_sim(100, 1, noise=0)
-    hhg = HHG()
-    test_stat = hhg.test_statistic(X, Y)
+    test_stat = hhg.test_statistic(X, Y)[0]
 
     assert np.round(test_stat, decimals=2) == 950600.00
 

From 246eabf432505a5113da286f6546a2cdb987fbba Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 07:58:05 -0500
Subject: [PATCH 48/60] Update hhg_test.py

---
 mgcpy/independence_tests/unit_tests/hhg_test.py | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py
index f185bc7..f887d66 100644
--- a/mgcpy/independence_tests/unit_tests/hhg_test.py
+++ b/mgcpy/independence_tests/unit_tests/hhg_test.py
@@ -26,6 +26,3 @@ def test_hhg():
     test_stat = hhg.test_statistic(X, Y)[0]
 
     assert np.round(test_stat, decimals=2) == 950600.00
-
-
-test_hhg()

From 99cff38f7b4917e9e4970fd0a070149e2708eb7b Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 08:25:49 -0500
Subject: [PATCH 49/60] Fix p-value for class

---
 mgcpy/independence_tests/abstract_class.py | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/mgcpy/independence_tests/abstract_class.py b/mgcpy/independence_tests/abstract_class.py
index c3a68a4..8c619d1 100644
--- a/mgcpy/independence_tests/abstract_class.py
+++ b/mgcpy/independence_tests/abstract_class.py
@@ -131,10 +131,13 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000):
                                 "optimal_scale": independence_test_metadata["optimal_scale"]}
         elif self.get_name() == "kendall":
             p_value = kendalltau(matrix_X, matrix_Y)[1]
+            p_value_metadata = {}
         elif self.get_name() == "spearman":
             p_value = spearmanr(matrix_X, matrix_Y)[1]
+            p_value_metadata = {}
         elif self.get_name() == "pearson":
             p_value = pearsonr(matrix_X, matrix_Y)[1]
+            p_value_metadata = {}
         else:
             # estimate the null by a permutation test
             test_stats_null = np.zeros(replication_factor)

From 2e163708aba16e50a36a7ef0c5f0b517e7d31d86 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 10:06:14 -0500
Subject: [PATCH 50/60] Remove matplotlib

---
 .../benchmarks/unit_tests/simulations_test.py | 194 +-----------------
 1 file changed, 1 insertion(+), 193 deletions(-)

diff --git a/mgcpy/benchmarks/unit_tests/simulations_test.py b/mgcpy/benchmarks/unit_tests/simulations_test.py
index 555f7d5..fd5bee5 100644
--- a/mgcpy/benchmarks/unit_tests/simulations_test.py
+++ b/mgcpy/benchmarks/unit_tests/simulations_test.py
@@ -1,7 +1,6 @@
-import matplotlib.pyplot as plt
 import numpy as np
+import pytest
 from mgcpy.benchmarks import simulations as sims
-from mpl_toolkits.mplot3d import Axes3D
 
 
 def test_simulations():
@@ -10,219 +9,76 @@ def test_simulations():
     num_dim2 = 300
     independent = True
 
-    np.random.seed(0)
-    fig1 = plt.figure(figsize=(50, 80))
-    plt.axis('off')
-    fig2 = plt.figure(figsize=(50, 80))
-
     # Linear Simulation
     returns_low_dim = sims.linear_sim(num_samps, num_dim1)
     returns_high_dim = sims.linear_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.linear_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 1)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Linear', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.linear_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 1, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Linear', fontweight='bold')
-    ax2.axis('off')
-
     # Exponential Simulation
     returns_low_dim = sims.exp_sim(num_samps, num_dim1)
     returns_high_dim = sims.exp_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.exp_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 2)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Exponential', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.exp_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 2, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Exponential', fontweight='bold')
-    ax2.axis('off')
-
     # Cubic Simulation
     returns_low_dim = sims.cub_sim(num_samps, num_dim1)
     returns_high_dim = sims.cub_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.cub_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 3)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Cubic', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.cub_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 3, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Cubic', fontweight='bold')
-    ax2.axis('off')
-
     # Joint-Normal Simulation
     returns_low_dim = sims.joint_sim(num_samps, num_dim1)
     returns_high_dim = sims.joint_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.joint_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 4)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Joint Normal', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.joint_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 4, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Joint Normal', fontweight='bold')
-    ax2.axis('off')
-
     # Step Simulation
     returns_low_dim = sims.step_sim(num_samps, num_dim1)
     returns_high_dim = sims.step_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.step_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 5)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Step', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.step_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 5, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Step', fontweight='bold')
-    ax2.axis('off')
-
     # Quadratic Simulation
     returns_low_dim = sims.quad_sim(num_samps, num_dim1)
     returns_high_dim = sims.quad_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.quad_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 6)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Quadratic', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.quad_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 6, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Quadratic', fontweight='bold')
-    ax2.axis('off')
-
     # W Simulation
     returns_low_dim = sims.w_sim(num_samps, num_dim1)
     returns_high_dim = sims.w_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.w_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 7)
-    ax1.scatter(x1, y1)
-    ax1.set_title('W-Shaped', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.w_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 7, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('W-Shaped', fontweight='bold')
-    ax2.axis('off')
-
     # Spiral Simulation
     returns_low_dim = sims.spiral_sim(num_samps, num_dim1)
     returns_high_dim = sims.spiral_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.spiral_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 8)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Spiral', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.spiral_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 8, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Spiral', fontweight='bold')
-    ax2.axis('off')
-
     # Uncorrelated Bernoulli Simulation
     returns = sims.ubern_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.ubern_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 9)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Uncorrelated Bernoulli', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.ubern_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 9, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Uncorrelated Bernoulli', fontweight='bold')
-    ax2.axis('off')
-
     # Logarithmic Simulation
     returns_low_dim = sims.log_sim(num_samps, num_dim1)
     returns_high_dim = sims.log_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.log_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 10)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Logarithmic', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.log_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 10, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2[:, 0]*y2[:, 1])
-    ax2.set_title('Logarithmic', fontweight='bold')
-    ax2.axis('off')
-
     # Nth Root Simulation
     returns_low_dim = sims.root_sim(num_samps, num_dim1)
     returns_high_dim = sims.root_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.root_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 11)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Fourth Root', fontweight='bold')
-    ax1.axis('off')
-
-    x2, y2 = sims.root_sim(num_samps, 2, noise=0)
-    ax2 = fig2.add_subplot(4, 5, 11, projection='3d')
-    ax2.scatter(x2[:, 0], x2[:, 1], y2)
-    ax2.set_title('Fourth Root', fontweight='bold')
-    ax2.axis('off')
-
     # Sinusoidal Simulation (4*pi)
     returns_low_dim = sims.sin_sim(num_samps, num_dim1)
     returns_high_dim = sims.sin_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.sin_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 12)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Sinusoidal (4\u03C0)', fontweight='bold')
-    ax1.axis('off')
-
     # Sinusoidal Simulation (16*pi)
     returns_low_dim = sims.sin_sim(num_samps, num_dim1, period=16*np.pi)
     returns_high_dim = sims.sin_sim(
@@ -230,81 +86,33 @@ def test_simulations():
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi)
-    ax1 = fig1.add_subplot(4, 5, 13)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Sinusoidal (16\u03C0)', fontweight='bold')
-    ax1.axis('off')
-
     # Square Simulation
     returns = sims.square_sim(num_samps, num_dim2, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.square_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 14)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Square', fontweight='bold')
-    ax1.axis('off')
-
     # Two Parabolas Simulation
     returns_low_dim = sims.two_parab_sim(num_samps, num_dim1)
     returns_high_dim = sims.two_parab_sim(num_samps, num_dim2)
     assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1))
     assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 15)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Two Parabolas', fontweight='bold')
-    ax1.axis('off')
-
     # Circle Simulation
     returns = sims.circle_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.circle_sim(num_samps, 1, noise=0)
-    ax1 = fig1.add_subplot(4, 5, 16)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Circle', fontweight='bold')
-    ax1.axis('off')
-
     # Ellipse Simulation
     returns = sims.circle_sim(num_samps, num_dim2, radius=5)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5)
-    ax1 = fig1.add_subplot(4, 5, 17)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Ellipse', fontweight='bold')
-    ax1.axis('off')
-
     # Diamond Simulation
     returns = sims.square_sim(
         num_samps, num_dim2, period=-np.pi/4, indep=independent)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4)
-    ax1 = fig1.add_subplot(4, 5, 18)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Diamond', fontweight='bold')
-    ax1.axis('off')
-
     # Multiplicative Noise Simulation
     returns = sims.multi_noise_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
 
-    x1, y1 = sims.multi_noise_sim(num_samps, 1)
-    ax1 = fig1.add_subplot(4, 5, 19)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Multiplicative Noise', fontweight='bold')
-    ax1.axis('off')
-
     # Multimodal Independence Simulation
     returns = sims.multi_indep_sim(num_samps, num_dim2)
     assert np.all(returns[0].shape == (num_samps, num_dim2))
-
-    x1, y1 = sims.multi_indep_sim(num_samps, 1)
-    ax1 = fig1.add_subplot(4, 5, 20)
-    ax1.scatter(x1, y1)
-    ax1.set_title('Multimodal Independence', fontweight='bold')
-    ax1.axis('off')

From 61c2caaee562c90dec1e1468a26e56229f1f60ed Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 11:08:56 -0500
Subject: [PATCH 51/60] Remove simulations from other_tests.ipynb and added new
 simulations demo

---
 demos/other_tests.ipynb |  218 +++++----
 demos/simulations.ipynb | 1012 +++++++++++++++++++++++++++++++++++++++
 2 files changed, 1128 insertions(+), 102 deletions(-)
 create mode 100644 demos/simulations.ipynb

diff --git a/demos/other_tests.ipynb b/demos/other_tests.ipynb
index 229220c..d508d36 100644
--- a/demos/other_tests.ipynb
+++ b/demos/other_tests.ipynb
@@ -9,9 +9,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 20,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(None, <pyximport.pyximport.PyxImporter at 0x1a23c2b358>)"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "import numpy as np\n",
     "from scipy.spatial.distance import pdist, squareform\n",
@@ -19,13 +30,6 @@
     "%matplotlib inline"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Simulations"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -35,72 +39,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, w_sim, spiral_sim"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the readme. Visualizations of the 4 simulations imported above are shown below with and without the noise:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1440x360 with 4 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "fig, ax = plt.subplots(1, 4, num=1, figsize=(20,5))\n",
-    "\n",
-    "x_normal, y_normal = linear_sim(100, 1)\n",
-    "x_no_noise, y_no_noise = linear_sim(1000, 1, noise=0)\n",
-    "ax[0].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
-    "ax[0].plot(x_no_noise, y_no_noise, 'ro')\n",
-    "ax[0].set_xlim([-1, 1])\n",
-    "ax[0].set_ylim([-1, 1])\n",
-    "\n",
-    "x_normal, y_normal = quad_sim(100, 1)\n",
-    "x_no_noise, y_no_noise = quad_sim(1000, 1, noise=0)\n",
-    "ax[1].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
-    "ax[1].plot(x_no_noise, y_no_noise, 'ro')\n",
-    "ax[1].set_xlim([-1, 1])\n",
-    "ax[1].set_ylim([-1, 2])\n",
-    "\n",
-    "x_normal, y_normal = w_sim(100, 1)\n",
-    "x_no_noise, y_no_noise = w_sim(1000, 1, noise=0)\n",
-    "ax[2].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
-    "ax[2].plot(x_no_noise, y_no_noise, 'ro')\n",
-    "ax[2].set_xlim([-1, 1])\n",
-    "ax[2].set_ylim([-1, 2])\n",
-    "\n",
-    "x_normal, y_normal = spiral_sim(100, 1)\n",
-    "x_no_noise, y_no_noise = spiral_sim(1000, 1, noise=0)\n",
-    "ax[3].plot(x_normal, y_normal, 'bo', alpha=0.5)\n",
-    "ax[3].plot(x_no_noise, y_no_noise, 'ro')\n",
-    "ax[3].set_xlim([-4, 4])\n",
-    "ax[3].set_ylim([-4, 4])\n",
-    "\n",
-    "plt.show()"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -117,19 +62,61 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
-     "ename": "ModuleNotFoundError",
-     "evalue": "No module named 'mgcpy.independence_tests.mgc.distance_transform'",
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/anaconda3/lib/python3.6/site-packages/Cython/Compiler/Main.py:367: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/mgc/distance_transform.pyx\n",
+      "  tree = Parsing.p_module(s, pxd, full_module_name)\n"
+     ]
+    },
+    {
+     "ename": "ImportError",
+     "evalue": "Building module mgcpy.independence_tests.mgc.distance_transform failed: [\"distutils.errors.CompileError: command 'gcc' failed with exit status 1\\n\"]",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-4-e329c2ea85bd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdcorr\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mDistutilsExecError\u001b[0m                        Traceback (most recent call last)",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m    117\u001b[0m             self.spawn(compiler_so + cc_args + [src, '-o', obj] +\n\u001b[0;32m--> 118\u001b[0;31m                        extra_postargs)\n\u001b[0m\u001b[1;32m    119\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mspawn\u001b[0;34m(self, cmd)\u001b[0m\n\u001b[1;32m    908\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mspawn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 909\u001b[0;31m         \u001b[0mspawn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdry_run\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdry_run\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    910\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/spawn.py\u001b[0m in \u001b[0;36mspawn\u001b[0;34m(cmd, search_path, verbose, dry_run)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'posix'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m         \u001b[0m_spawn_posix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msearch_path\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdry_run\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdry_run\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     37\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'nt'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/spawn.py\u001b[0m in \u001b[0;36m_spawn_posix\u001b[0;34m(cmd, search_path, verbose, dry_run)\u001b[0m\n\u001b[1;32m    158\u001b[0m                           \u001b[0;34m\"command %r failed with exit status %d\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 159\u001b[0;31m                           % (cmd, exit_status))\n\u001b[0m\u001b[1;32m    160\u001b[0m             \u001b[0;32melif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mWIFSTOPPED\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mDistutilsExecError\u001b[0m: command 'gcc' failed with exit status 1",
+      "\nDuring handling of the above exception, another exception occurred:\n",
+      "\u001b[0;31mCompileError\u001b[0m                              Traceback (most recent call last)",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m    214\u001b[0m             so_path = build_module(module_name, pyxfilename, pyxbuild_dir,\n\u001b[0;32m--> 215\u001b[0;31m                                    inplace=build_inplace, language_level=language_level)\n\u001b[0m\u001b[1;32m    216\u001b[0m         \u001b[0mmod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mimp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_dynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mbuild_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, inplace, language_level)\u001b[0m\n\u001b[1;32m    190\u001b[0m                                   \u001b[0minplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 191\u001b[0;31m                                   reload_support=pyxargs.reload_support)\n\u001b[0m\u001b[1;32m    192\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Cannot find: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyxbuild.py\u001b[0m in \u001b[0;36mpyx_to_dll\u001b[0;34m(filename, ext, force_rebuild, build_in_temp, pyxbuild_dir, setup_args, reload_support, inplace)\u001b[0m\n\u001b[1;32m    101\u001b[0m         \u001b[0mobj_build_ext\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_command_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"build_ext\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m         \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_commands\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m         \u001b[0mso_path\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mobj_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_outputs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_commands\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    954\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mcmd\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommands\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 955\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_command\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    956\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_command\u001b[0;34m(self, command)\u001b[0m\n\u001b[1;32m    973\u001b[0m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mensure_finalized\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 974\u001b[0;31m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    975\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhave_run\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcommand\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    185\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 186\u001b[0;31m         \u001b[0m_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    187\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    338\u001b[0m         \u001b[0;31m# Now actually compile and link everything.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 339\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    340\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mbuild_extensions\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    193\u001b[0m             \u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 194\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    195\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mbuild_extension\u001b[0;34m(self, ext)\u001b[0m\n\u001b[1;32m    532\u001b[0m                                          \u001b[0mextra_postargs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextra_args\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 533\u001b[0;31m                                          depends=ext.depends)\n\u001b[0m\u001b[1;32m    534\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sources, output_dir, macros, include_dirs, debug, extra_preargs, extra_postargs, depends)\u001b[0m\n\u001b[1;32m    573\u001b[0m                 \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 574\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcc_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_postargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpp_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    575\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m    119\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mCompileError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mCompileError\u001b[0m: command 'gcc' failed with exit status 1",
+      "\nDuring handling of the above exception, another exception occurred:\n",
+      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-23-e329c2ea85bd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdcorr\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/dcorr.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabstract_class\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mIndependenceTest\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistance_transform\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtransform_distance_matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'mgcpy.independence_tests.mgc.distance_transform'"
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(self, fullname)\u001b[0m\n\u001b[1;32m    460\u001b[0m                                  \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyxbuild_dir\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    461\u001b[0m                                  \u001b[0mbuild_inplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 462\u001b[0;31m                                  language_level=self.language_level)\n\u001b[0m\u001b[1;32m    463\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mmodule\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    464\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m    229\u001b[0m                 name, traceback.format_exception_only(*sys.exc_info()[:2])))\n\u001b[1;32m    230\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mversion_info\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 231\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mexc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    232\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    233\u001b[0m                 \u001b[0mexec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"raise exc, None, tb\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m'exc'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mexc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'tb'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtb\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m    213\u001b[0m                 \u001b[0mmodule_name\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    214\u001b[0m             so_path = build_module(module_name, pyxfilename, pyxbuild_dir,\n\u001b[0;32m--> 215\u001b[0;31m                                    inplace=build_inplace, language_level=language_level)\n\u001b[0m\u001b[1;32m    216\u001b[0m         \u001b[0mmod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mimp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_dynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    217\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_package\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'__path__'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mbuild_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, inplace, language_level)\u001b[0m\n\u001b[1;32m    189\u001b[0m                                   \u001b[0msetup_args\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    190\u001b[0m                                   \u001b[0minplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 191\u001b[0;31m                                   reload_support=pyxargs.reload_support)\n\u001b[0m\u001b[1;32m    192\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Cannot find: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    193\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyxbuild.py\u001b[0m in \u001b[0;36mpyx_to_dll\u001b[0;34m(filename, ext, force_rebuild, build_in_temp, pyxbuild_dir, setup_args, reload_support, inplace)\u001b[0m\n\u001b[1;32m    100\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m         \u001b[0mobj_build_ext\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_command_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"build_ext\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m         \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_commands\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m         \u001b[0mso_path\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mobj_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_outputs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mobj_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_commands\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    953\u001b[0m         \"\"\"\n\u001b[1;32m    954\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mcmd\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommands\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 955\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_command\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    956\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    957\u001b[0m     \u001b[0;31m# -- Methods that operate on its Commands --------------------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_command\u001b[0;34m(self, command)\u001b[0m\n\u001b[1;32m    972\u001b[0m         \u001b[0mcmd_obj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_command_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcommand\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    973\u001b[0m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mensure_finalized\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 974\u001b[0;31m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    975\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhave_run\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcommand\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    976\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    184\u001b[0m             \u001b[0moptimization\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisable_optimization\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    185\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 186\u001b[0;31m         \u001b[0m_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    187\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    188\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    337\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    338\u001b[0m         \u001b[0;31m# Now actually compile and link everything.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 339\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    340\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    341\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcheck_extensions_list\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextensions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mbuild_extensions\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    192\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mext\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mextensions\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    193\u001b[0m             \u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 194\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    195\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    196\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextension\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mbuild_extension\u001b[0;34m(self, ext)\u001b[0m\n\u001b[1;32m    531\u001b[0m                                          \u001b[0mdebug\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdebug\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    532\u001b[0m                                          \u001b[0mextra_postargs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextra_args\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 533\u001b[0;31m                                          depends=ext.depends)\n\u001b[0m\u001b[1;32m    534\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    535\u001b[0m         \u001b[0;31m# XXX outdated variable, kept here in case third-part code\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sources, output_dir, macros, include_dirs, debug, extra_preargs, extra_postargs, depends)\u001b[0m\n\u001b[1;32m    572\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    573\u001b[0m                 \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 574\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcc_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_postargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpp_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    575\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    576\u001b[0m         \u001b[0;31m# Return *all* object filenames, not just the ones we just built.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m    118\u001b[0m                        extra_postargs)\n\u001b[1;32m    119\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mCompileError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    122\u001b[0m     def create_static_lib(self, objects, output_libname,\n",
+      "\u001b[0;31mImportError\u001b[0m: Building module mgcpy.independence_tests.mgc.distance_transform failed: [\"distutils.errors.CompileError: command 'gcc' failed with exit status 1\\n\"]"
      ]
     }
    ],
@@ -160,9 +147,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'DCorr' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-24-f67b9d90e903>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad_sim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mdcorr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwhich_test\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'dcorr'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mtest_stat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdcorr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_statistic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"DCorr's test statistic: %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mtest_stat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'DCorr' is not defined"
+     ]
+    }
+   ],
    "source": [
     "x, y = quad_sim(100, 1)\n",
     "\n",
@@ -298,7 +297,6 @@
    ]
   },
   {
-   "attachments": {},
    "cell_type": "markdown",
    "metadata": {},
    "source": [
@@ -348,7 +346,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -364,14 +362,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "HHG test statistic: 36.88\n"
+      "HHG test statistic: 56.76\n"
      ]
     }
    ],
@@ -392,14 +390,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "HHG p-value: 0.92\n"
+      "HHG p-value: 0.51\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/abstract_class.py:154: UserWarning: The p-value is greater than 0.05, implying that the results are not statistically significant.\n",
+      "Use results such as test_statistic and optimal_scale, with caution!\n",
+      "  \"Use results such as test_statistic and optimal_scale, with caution!\")\n"
      ]
     }
    ],
@@ -424,7 +431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -454,14 +461,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Kendall's test statistic: -0.05\n"
+      "Kendall's test statistic: 0.05\n"
      ]
     }
    ],
@@ -482,14 +489,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Pearson's p-value: 0.74\n"
+      "Pearson's p-value: 0.49\n"
      ]
     }
    ],
@@ -521,14 +528,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Spearman's test statistic: 0.09\n"
+      "Spearman's test statistic: -0.04\n"
      ]
     }
    ],
@@ -549,14 +556,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Pearson's p-value: 0.15\n"
+      "Pearson's p-value: 0.72\n"
      ]
     }
    ],
@@ -581,7 +588,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -619,14 +626,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Pearson's test statistic: 0.46\n"
+      "Pearson's test statistic: 0.53\n"
      ]
     }
    ],
@@ -647,7 +654,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -700,14 +707,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "RV test statistic: 0.00\n"
+      "RV test statistic: 0.02\n"
      ]
     }
    ],
@@ -728,14 +735,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "RV p-value: 0.88\n"
+      "RV p-value: 0.43\n"
      ]
     }
    ],
@@ -771,7 +778,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -799,7 +806,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -814,6 +821,13 @@
     "p_value = cca.p_value(x, y)[0]\n",
     "print(\"CCA p-value: %.2f\" % p_value)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/demos/simulations.ipynb b/demos/simulations.ipynb
new file mode 100644
index 0000000..9a576e7
--- /dev/null
+++ b/demos/simulations.ipynb
@@ -0,0 +1,1012 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Tutorial for Simulations"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First, import the simultions utilizing the import statement below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from mgcpy.benchmarks import simulations as sims"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the documentation. Visualizations of the 4 simulations imported above are shown below with and without the noise. Each simulation is also shown in 2D."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Linear Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.linear_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.linear_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Linear', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exponential Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.exp_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.exp_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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/Bm3y4eeAb1OTam1tx/PU1hZnOx4Hm6xFWsH88Ic/bA+7Kif69u3LzJkzozYj8QQVFpgNP7vj06fDzJmQGq+tqnK2gwyVMiGtYI466ihGjRoVtRm+c/7559O9uwWklEqYgzZ+dsebm2HxYmhrc7bb2pztILNFmZAahpGVMAdt/BzwtVF7wzBiQ5iDNn4O+NqovWEkgDgnGPaTsOe3T58Or78Oe/c6j8X6NKMYtY9MSEWkl4g8LSLPi8gaEfmeu3+YiPxZRF4TkXtEpEdUNpZKFNmfis2YZHgjzAGYqIn9/PYcRJHgJMoW6cfA51T1M8Bo4AQRGQ/8F/AjVT0EeAe4IEIbS6LU7E/FUGzGJKMz2VqecU8w7Dd+tRLDJIo/gMiE1A3T2u5uVrtFgc8Bqak5i4GpoRgUQH+tmOxP6YSZMcnoSK6W54YN2euXYRRZogn9D8BLsGlQBagCVgPbcVqiA4D1accPAl7K8do5QAvQUldX1ymQtqDAaz8jeNMoJvtTOmFnTKoEvN4XuQLEq6r8Cxw3CiOsyQHpkISAfFVtU9XRwFDgSODQbNVyvHaRqo5V1bGpLEZFE2B/LT37UzpPPvkk55xzDuBkf1q1alXW16cyJg0YMCBrxqTevXu3Z0xKZ9y4cdxxxx0sWLCAF198kT59+vDUU0+1Z0waPXo0ixcvZkOuJlaFk6uF2dYW7wTD5UrcfdOxGLVX1XeBlcB4oK+IpKKphwKbAjcg4HiJQrM/pRNmxiRjH7lGeFP+tqQNwCSduPumoxy1Hygifd3nNcAUYB3wKHCGW20m8EDgxgQcL+F39qegMiYlkdZWeOEFaGlxHltb/TlvVyO/SRyASTq2+F1uDgQeFZEXgL8AK1T1N8C3gUtEZD3QHwi+yRRCvISf2Z+CyJiURFpbnS7erl3O9q5dzrYfYprU0J9yJe6L34mXbmLcGTt2rLa0tHTYt27dOg49NJvLNQep2JY33nC+nVTTw4gtL7ywT0TT6dEDcqUQKPi+MGJBZtZ7cNo6Qf+5icgzqjo2Xz3L7JBi+nQTzoSRTUS72m8kl9RPM65tHRNSI7H06JG7RWqUH3Fu68Ri1D4oysFtYeRmyBBn/kQ63bo5+7Nh94N3KiWfgF+UbYu0V69etLa20r9//5yhRUay6d/feXzzTadl2qOHI6Kp/emoKq2trfTq1StcIxNIFKtwJp2yHWzavXs3GzduzLuaplE59OrVi6FDh1JdXR21Ke3EcYyzoSH7VNj6eifcq1ji+FnzUfGDTdXV1QwbNixqMwwjJ3Ft+QURsxnXz+oXZdsiNYy4E1TLr1SCsCuunzUfXlukZT3YZBhxJq6zdYKYnxLXz+oXJqSGERFxna0TxKyuuH5WvzAhNYyIiCKTu1f8zicQ58/qByakhhERlTSfv9w/qw02GYZh5MAGmwzDMELChNQwDKNETEgNwzBKxITUMAyjRExIDcMwSsSE1EgEltat8kjSd162SUuM8qHcE14YnUnad25xpEbsSWrCC6N44vKdWxypUTaUe8KLMEhSNxmS952bkBqxp9wTXgTN3Llw7rlOC091XzfZLzENQqST9p2bkBqxp9wTXgRJczPccosjoOns2OFkq/fj/HPmFCfSXQlw4r5zVU18GTNmjBrlTVOTan29qojz2NQUtUXJoL5e1ZG4zkUkuPNXVXX9XTU1qdbWdnxNbW3HunH4zoEW9aBBNthkGGVMt26dW6Mp/Bi46er8KWprO2d6CnIwyc+1oWywyTCMnD5FEX+6yV58ltncCEENJpXiaigFE1LDKGOy+RpF4Ktf9SceM9v5s5EpkEENJs2bty/2NIVf/uCuMCE1jDImW0Llu+6Cm24K5vxVVdnr9evXcWDppJOCGUyKKmwqMiEVkYNE5FERWScia0TkInd/PxFZISKvuY8HRGWjYZQDfi8b0tX5Fy/uLJDV1fDBBx2724sXw8yZ/mfMT7Vo36OWvUh7aVOBKVNKO3kXRNki3QNcqqqHAuOBr4nIcOBy4BFVPQR4xN02DCMBZGsB778/7NrVsd6OHbB8uf8Cf+WV0IbQh48Q6FB45JHAxDQ2o/Yi8gBwo1uOVdXNInIgsFJV/6Wr19qovWHEl1wj+yKOiPqKCIornLkoQPMSNWovIg3A4cCfgU+q6mYA93FQjtfMEZEWEWnZunVrWKZWLEmbYmjEh1BmKTU3O8pMHhENiMiFVER6A78GLlbV972+TlUXqepYVR07cODA4Aw0IgspMcqDwGcpNTfDjBk+naw4IhVSEanGEdFmVV3q7t7idulxH9+Kyj7DIaqQEqM8CHQp5trawkR08mQf3rQzkflIRUSAxcDbqnpx2v5rgFZVvUpELgf6qeplXZ3LfKTBEqqPyzC8IgV24idPhocfLvAtvPlIo0zsPBE4F3hRRFa7+74LXAXcKyIXAG8AZ0Zkn+FSV5d9Ol9cM/EYFUCPHoXVD7jBGFnXXlVXqaqo6ihVHe2W5araqqqTVfUQ9/HtqGw0HBKXiaeMsUE/HBHdvdtbXS/JAHwg8sEmI/4E6uMyspJNMCt+0C81Ml+IiLa1BWuTS2ziSEvBfKRGOZG5XhE4PYCaGmht7Vy/IpZcqa2Fjz7yXr+6uvMsgCJIVBypYRj7yBUlkU1EIZzlN8J2KaS/3x4RtBARHTzYFxEtBBNSw4gZhQpj0IN+YbsUUu/3zQ1z2aNCFQUE2Tc2wptvBmNYF1jX3jBiRq6kx/37O73bzC5/0P7qsFf0bGiAn26YwvE84l1AferKZ2Jde8NIKLmiJH784+IH/XJ1zb102UNNTdfczN82SGEiWlMTele+E17WI4l7sTWbjHLDz/WKcq2P1NiYf90k1dzrMtXXF29TVqqrcy8wlasMHuyzER3B1mwyDANyd82rqrJHB2V22XNFEfjqUqiqKnyaXGOjfxmqc2Bde8MwgNxd8Fwhlpn1A40jnju38LnGffs67dGARbQQTEgNo8zJNaqfa1mQbPVLzbKf1RdbWws331zQeXZV19DwiXdiN7PLhNQwypxcg1dz5mRfGG/DBn9FKjN86i8bDuCcGQXGhgLb+w7mgOodsZzZZUJqGGVOrq75TTft2w/OsdSQiZ8ilT7BYCdVDODdfct/eEWVEZ94M7bpHE1IQ8KSTRhRkqtrntpfX985t4dfIvXGG3ADc9mL0IO9hQloyh9KdCuEesGENASSmGzChL+yCFKktukBfI2bC2+FNjbCO++0b4ayZEmRmJCGQNIyzCdR+I3S8CJSBf+5TpkCIhzgduU9M3ly1lH5WKdz9BJsGvcSVUC+16BpkeyxxCJhWuud0AKwjdiQK2g/dU/nO96BxsbCA+vBCcj3YKdfExW8gMeA/MhF0I8ShZAWcmMlTZiSJvyGP3QlUp7v4b59ixPR4cND+5yF4FVIrWtfJIV012PdJclCnH1Rhj9k66Z3FSua14c6ZIgz7P/uu4Ub09QEa9YU/roYYUJaJIU455OWYT5pwm/kxq9M+7n+RO+odWcmbdpUuHGDBzsGxPWHUAhdNVeBKuAaL03bKEsUXfukddcLJWxflOE/udxP/fsXfu9mnusGGnUv6N5iuvEiibmh8MtHCvwBN29pXEvcfaRRY6JYmeT6s+9K37KRun9A9cZSBBScgagE4VVIvSzH/BzwgIj8CvgwrSW71PfmcYJI9UbmzXO683V1Ttc3br2UzMw9qW4cxM9Ww1/8yLSffv+8zhDq2FRYKFOKmprOgwplRN40eiJyR5bdqqqzgzGpcCyNXm7Czm5uxAc/Mu2nZ6uHAgPqUwwfntjBJN/S6Knq+VlKbETU6Jo4T6szgqXkTPtTpvD3tGz1hYioAjupppsoDR+uCXQyRyxm4eXr+wNDgfuAt4AtwK+BoV78BmEVy5Cfm3IfFCs3/PZnF3W+YmNB3fJxdU1o4wdBj1Xg42DTCuB8oLtbZgErvJw8rGJCmpskDYpVOpF/V8OHlySgqcGkMP+8g34vP4V0tZd9URYT0q6xUftkEFnvoampdAFNu6nCnBkX9Ht5FVIvAfnbRGSGiFS5ZQbQ6p9zwQiaUrObB00sfFwxIOzVOunTx3GSzphR/HmyBNWHOTMuLrPwvAjpbOAs4P8Bm4EzcLr6JSMit4vIWyLyUtq+fiKyQkRecx8P8OO9jHiSbZbNjBkwYEDlCWooopBaI2nGDNi+vfjzNDY6X9ibb3Y6FObMuNjMwsvXZAUmetlXTAEmAUcAL6Xtuxq43H1+OfBf+c5jXfvk0lXQeKX5cgP1kfrh/8zowuf7LGG5k4J8L3z0kT7rZV+xBWjIENJXgAPd5wcCr+Q7hwlpcsnl46rU6ALfRcEvAZ082YdPlzy8CmnOrr2ITBCRS4GBInJJWlmAMwc/KD6pqpsB3MdBOeybIyItItKydevWAM0pT+Lil8zXbS33eNfM7wF88GfPneucUATWri3NwFSS5YcfLu08ZU5XU0R7AL3dOn3S9r+P4yeNFFVdBCwCZ2ZTxOYkijhNG73yyo62ZFLOqft8/x6GDCkuC1M2EjwbKRLyNVmBei9N22IL1rUPnbgF6Tc1Zc9IVO4+Ul++h8bG/P4RryWmyZWjBB/Dn24Vkb6pDRE5QER+76+cd2AZMNN9PhN4IMD3aicuXd0wiNu00enTYds2J79vUnK2+kHR30NzsxPWIAI33+zIYJGoWxbv10jzd60FWjT5lBZ4zsu+YgrwS5yQqt3ARuACoD/wCPCa+9gv33lKbZFGPqMkZOLWIs1GJUwiKPh7KHYtpCxlL+jHVOnZNFXEPV8s+Dhq/wxQl7Zdj4+j9n6UUoU0CcLiJ3H/44i7fX7h6XNOnuybeKaXO/drrKh7vlj8FNITgDeAu9yyAfiCl5OHVUoV0kpc7C3OLb5K+mPL+j342PLsUNJCmCrxni8G34TUORcDgFOALwIDvLwmzGIt0vIiaT9yX/6UmppUq6r8F89u3bJmpbd73htehTTvYJOIiNsqPUJV/xuoFZEjS/HLxo3YTDMzgPjMn/ZCMQvJtZNaeTM1ZbOtzT/Dhg93DGprg5tu6nTY7nmfyae0wM3AT4B17vYBwF+8qHRYxY/wpzh3dSuNJPlIC27Z+TXTKFeTvYCLZPd8fvB7iihpI/XA815OHlaxONLyIyk/8rxuiKD8neklrhenDPAqpF4Wv9stIlWAAojIQGCvv+1iw9hHc3P8FxVMUVfXcV2ks2nmDmbSQ9uKXODII5Mn27TNGOElIH8hzlIjg0TkSmAV8H8DtcrIS7lOICjJ5xgBV14JGxjCXoS9CM3MoCdtwWloU5NzYUxE44WXZivwaeBrwNeBQ728JsxSaV37JPkQCyURo8kZsZ1Fr/HeRemwdnyM1oJPisvFLyjVRwr8FpgO7OflRFGWShPSRIhNkcQy9CnIAaIM4UyV3zHZ059j2Hk/y/UPPBd+COmpOFM4twL3AFOBHl5OGnapNCGNpdj4RCz+JGpqAhfOzLK2anjBnztsYYvFdxMyXoU0p49UVR9Q1bOBOmApTgKRN9zlQT4fiJ/B8ESS4iwLJfT4xtTSG+nlo48CerMMUrk+VTlsb/aEIV0lMJk3r3P6wR07nP1BELdkN3Ei72CTqn6kqveo6mnA8cDhwO8Ct8zISTkHU0+f7mR9CiQLVHMz9OzZUTRvvtmHExdAaq0j1Q4DRsX8OYYtbMXYWOigaGIHUfM1WYFPAt8A/gj8DfgvYLSX5m5YpdK69qrxd/pHbl8Y8Zteisccn8V008PuahdqY9D1wwAffKQXAn8A3gRuwKcF74IolSikcSbfD8J3ke3bN3rBTJUS1jYq9LpEITyF2Fio0MfRB+uHkN6B05Xv5uVEURYT0s5E2SLs6gdR0o8/hNHzgkvE3YHIW/5dUOigaBwHUb0KaVeDTeer6kOqarOYEkbUQe1d+e48DZBMmdJ5AMiPhdz8oHv3fUHxqiWsUFcc+RbLg/j4GAv1qSZ6ENWL2sa9RNEijXNLIOouUlfvn2p17KRbp9jJyFuXmaVXr1h9sV5cJnHyMZqPVBVgOdDg5SRRl7CFNI5feDpRd5FS1+cGGrWNzsHmsRXOHLk740K+P8io/0CzUYzfN04NFK9CKk7dzojIWcAPgMXA1arUE3t5AAAPVElEQVS6O6RGcsGMHTtWW1paQnu/hoaOiSpS1Nfv615FSSj2NTfDV78K27dnPZy6q4LM21ESCVxuuFs3RxozEXG69vmOG4UjIs+o6th89brykd6LEzO6P9AiIt8UkUtSxUdbE0fcA5PzxZnmjdXL5aNMLzNm5BRRcAQ0NiLav39Hv6Zq4kQU8vsQ4+5jTGyMqAfyBeTvBj4EegJ9MkrFUsgNG8XNkzOonWZ21/ThnBnC3zcIbeo8njND0HSRfOSR4I0MisGDO/dut22Lbx6+Asj3Bxn0RI1S7uWoB0ADJ1efH2d5kbXAVUCtFz9BVCWuPtJQfKmDB0fvW4yieAx0Lzfy+RCD8jGWei/H0X/rBXwYbHoCOMzLSaIucRi1b2zsfAPHahmKmJecA1GNjbEbgKhEShXCqAdAi6VkIU1SiTogP/Vv/RZ9c45Qx37EOkIBbQM9m6b23XEO6alUShXCcm+ResmQX754GVTxUM6ZIWzfIQzg3fZBlnylHNEuSnqmo/QyrF6pQvkl+3yY6QH6YWc4MrJT6kBWOSfaAW9LjZQnU6b4NqhS0QKZYvhwhtUr3ehchtVrzqUx8kVAxD1ColIoVQgDzeoVAypXSJM8Mh0ym2RwboFMtS7XrClK9OIW0lPOITql4IcQTp/ecTpruYgoUME+0hj4B6P2TT7WY7KnARyv/rFi/GBxmvYYpT/WBtTiCUkfbMIJv3oFWA9c3lVdE1K3BJT70qtAFitEUYX0ZBLVgEi5DaiV059CooUUqAL+ChwM9ACeB4bnql+UkPboEaiolTQyX1UV6N1XqGAU8kNP8o8oqhCdpI5oZ6Pc/hSSLqQTgN+nbX8H+E6u+kUJaVOTb4KZWT6muz7RGN87pxjBSLJAesWLoAVxHZIaY5mNcvpTUE2+kJ4B3Jq2fS5wY0adOUAL0FJXV1fcVfLpV5E0kSm3m90vovLXltP3UU5/CqrJF9IzswjpDbnqRx2QnzTKrfvlJ139KQYleOX0fZTTn4KqdyGNa/jTRuCgtO2hwKaIbCk7yj2mrxS6CtEJKqa1nL6Pcg+8z4kXtQ27AN1xViwdxr7Bppzz/uPQIk1a994onHJrbQVFOf0WSHKLVFX3AF8Hfg+sA+5V1dgmkCz7FGEGUMGtrQIp68D7HHSP2oBcqOpynOVOYk+u+eAzZzrPK+FGqgRS3+O8eU53vq7OEVH7fo1YtkiTRi4fWVtbcS1Tm6YYXyqxtWXkx4TUB7qa911opiJzExhG8jAh9YFsvrN0ChnVtbRxhpE8TEh9IBW+UlWV/XhdnffuuqWNM4zkYULqE9Onw+LF2Ud1TzrJe3c9LitBmp/WMLxjQuojuQKrly/33l2PQ4iN+WkNozDEiTlNNmPHjtWWlpaozchJt26OIGUi4oz+ZtLcHG2ITUODI56Z1Nc7I9WGUSmIyDOqOjZfvdjGkZYTdXXZhSlXd3369GjDasxPaxiFYV37EMjWXRdxxDWO/sco/LTmkzWSjAlpCKT7TsER0VRXP47+x7D9tOaTNZKO+UhDJin+xzD9tEm5Jkbl4dVHakIaMoUOPFUCdk2MuOJVSK1rHzJxiRONE3ZNjKRjQhoycYgTjRt2TYykY0IaMuWUDd0vvFwTG9U34oz5SI3YkxrVT58dVltrf0BG8JiP1CgbLCOWEXdMSAPCuqL+YTOtjLhjQhoAFmDuLzaqb8QdE9IA8KMrai3afdiovhF3TEgDoNSuaJxbtFEIvEU6GHHHRu0DoNQpj3GdMmmj50alYaP2EVJqVzSugys2em4Y2TEhDYBSu6JxHVyJq8AbRtSYkAZEKeufx3VwJa4CbxhRY0IaQ+I6uBJXgTeMqLGlRmJK1MuNZCNlT5TrSRlGHDEhNQoijgJvGFETSddeRM4UkTUisldExmYc+46IrBeRV0TkC1HYZxiGUQhR+UhfAk4HHk/fKSLDgWnAYcAJwE0iUhW+ecFjM5cMo3yIpGuvqusARCTz0KnA3ar6MfB3EVkPHAk8Ga6FwZIZ2J6auQTWbTaMJBK3UfshwD/Stje6+zohInNEpEVEWrZu3RqKcX5hge2GUV4EJqQi8rCIvJSlnNrVy7LsyzqHVVUXqepYVR07cOBAf4wOCQtsN8qRSnZXBda1V9UpRbxsI3BQ2vZQYJM/FsWHurrsc+ktsN1IKpXuropb134ZME1EeorIMOAQ4OmIbfIdC2w3yo1Kd1dFFf50mohsBCYAvxWR3wOo6hrgXmAt8Dvga6raFoWNQRLXmUuV3DUzSqPS3VWWRs8ALEWeURpxTf1YKpZGzyiISu+aGaVR6e4qE1IDsK6ZURpxdVeFhQlpEYThSwzbX2kp8oxSKSV1ZNIxIS2QMNZTimLNpkrvmhlGKdhgU4GE4VSPynHf3Gwp8gwjHa+DTSakBdKtm9NKzETE6dIk5T0Mw8iPjdoHRBi+RPNXGkayMCEtkDB8ieavNIxkYUJaIGGEeVR6KIlhJA3zkRqGYeTAfKRG4rC5/kZSscXvjFhQ6WnYjGRjLVIjFthcfyPJmJAascDm+htJxoQ0oSTZn5jNdoudNZKMCWkCiWIuvl/ksv2kkyx21kguJqQJJMn+xFy2L19usbNGcrE40gSS5Ln4SbbdqDwsjrSMSbI/Mcm2G0YuTEgTSJLn4ifZdsPIhQlpAknyXPwk224YuTAfacyxZMuGER1efaQ2RTTG2LRJw0gG1rWPMVGGOSU54N8wwsZapDEmqmmT1hI2jMKwFmmMiSpUKMkB/4YRBSakMSaqUCFLIGIYhWFCGmOiChWyoHnDKIxIhFRErhGRl0XkBRG5T0T6ph37joisF5FXROQLUdgXJ6ZPd9ay37vXeQzDR2lB84ZRGFG1SFcAI1R1FPAq8B0AERkOTAMOA04AbhKRqohsrFgsaN4wCiOSUXtVfSht8yngDPf5qcDdqvox8HcRWQ8cCTwZsokVz/TpJpyG4ZU4+EhnAw+6z4cA/0g7ttHdZxiGEVsCa5GKyMPAP2U5NE9VH3DrzAP2AKlwb8lSP+scVhGZA8wBqLNREMMwIiQwIVXVKV0dF5GZwCnAZN034X8jcFBataHAphznXwQsAmeufckGG4ZhFElUo/YnAN8GvqSq6aHfy4BpItJTRIYBhwBPR2GjYRiGV6KaInoj0BNYISIAT6nqV1V1jYjcC6zF6fJ/TVXbIrLRMAzDE2WRRk9EtgIbSjjFAGCbT+YEhdnoH0mw02z0j1LsrFfVgfkqlYWQloqItHjJORglZqN/JMFOs9E/wrAzDuFPhmEYicaE1DAMo0RMSB0WRW2AB8xG/0iCnWajfwRup/lIDcMwSsRapIZhGCViQmoYhlEiFSOkInKCm+N0vYhcnuV4TxG5xz3+ZxFpCN9KT3bOEpGtIrLaLV+JwMbbReQtEXkpx3ERkYXuZ3hBRI6IoY3Hish7adfxighsPEhEHhWRdSKyRkQuylIn0mvp0cY4XMteIvK0iDzv2vm9LHWC+42ratkXoAr4K3Aw0AN4HhieUWcucIv7fBpwT0ztnAXcGPH1nAQcAbyU4/hJOBm9BBgP/DmGNh4L/Cbi63ggcIT7vA9Obt7M7zvSa+nRxjhcSwF6u8+rgT8D4zPqBPYbr5QW6ZHAelX9m6ruAu7GyX2azqnAYvf5EmCyuPNXQ8SLnZGjqo8Db3dR5VTg5+rwFNBXRA4MxzoHDzZGjqpuVtVn3ecfAOvonDYy0mvp0cbIca/Pdnez2i2ZI+mB/cYrRUi95Dltr6Oqe4D3gP6hWJfFBpdc+Vi/7HbzlojIQVmOR01S8spOcLuCD4rIYVEa4nYzD8dpSaUTm2vZhY0Qg2spIlUishp4C1ihqjmvpd+/8UoRUi95Tj3nQg0QLzb8N9CgzjItD7PvHzZOxOFa5uNZnHnUnwFuAO6PyhAR6Q38GrhYVd/PPJzlJaFfyzw2xuJaqmqbqo7GSb95pIiMyKgS2LWsFCH1kue0vY6IdAc+Qfhdw7x2qmqrOkuxAPwMGBOSbYXgOa9sVKjq+6muoKouB6pFZEDYdohINY5ANavq0ixVIr+W+WyMy7VMs+ddYCXOum/pBPYbrxQh/QtwiIgME5EeOI7mZRl1lgEz3ednAH9Q1ysdInntzPCPfQnHZxU3lgHnuSPO44H3VHVz1EalIyL/lPKPiciROL+F1pBtEOA2YJ2qXpejWqTX0ouNMbmWA8VdjVhEaoApwMsZ1QL7jUeVjzRUVHWPiHwd+D3OyPjt6uQ+/T7QoqrLcG6Wu8RZcO9tHBGLo53/LiJfwsnX+jbOKH6oiMgvcUZqB4jIRmA+jnMfVb0FWI4z2rwe2AGcH0MbzwAaRWQP8BEwLYI/zonAucCLrm8P4LtAXZqdUV9LLzbG4VoeCCwWZ9XhbsC9qvqbsH7jNkXUMAyjRCqla28YhhEYJqSGYRglYkJqGIZRIiakhmEYJWJCahiGUSImpEZscTMP/V1E+rnbB7jb9Rn1VorIFzL2XSwiNxXxnlNFZHhplhuVhgmpEVtU9R/AzcBV7q6rgEWqmrn09i/pHBM4zd1fKFOBgoTUnSVjVDAWR2rEGnd64jPA7cCFwOFuZqz0Ov1xZrEMVdWP3eQaj+PM/1YR+RZwFtATuE9V57uvOw/4Js586xdwRPs3OMks3gO+jJM67hagFifF4WxVfUdEVgJ/wglYX6aqPwzqGhjxx/5JjVijqrtdIfwdcHymiLp1WkXkaZy51Q+wL9ekisjxwCE4KQoFWCYik3CmMM4DJqrqNhHpp6pvi8gynNyaSwBE5AXgG6r6mDtLZj5wsfvWfVX1X4P8/EYysK69kQROBDYDmdl80knv3qd36493y3M4WYo+jSOsnwOWqOo2AFXtlLxCRD6BI5aPubsW4ySMTnFPMR/GKD9MSI1YIyKjgc/jZIf/X10kNb4fJ1HvEUBNKhkxTiv0P1V1tFs+paq3uftL9Wt9WOLrjTLBhNSILW5GoZtxcmC+AVwDXJutrpvGbSWOLzV9kOn3wGw3nyYiMkREBgGPAGe5/lVSkQHABzh+UVT1PeAdETnGPXYu8BiGkYEJqRFnLgTeUNUV7vZNwKdFJJdf8pfAZ3CWaAFAVR8CfgE8KSIv4iwx0UdV1wBXAo+JyPNAKkXc3cC3ROQ5EflnnLRr17i+0tHA9339hEZZYKP2hmEYJWItUsMwjBIxITUMwygRE1LDMIwSMSE1DMMoERNSwzCMEjEhNQzDKBETUsMwjBL5/25gjxz4bEW6AAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Exponential Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Cubic Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.cub_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.cub_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Cubic Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Joint-Normal Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.joint_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.joint_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Joint-Normal Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Step Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.step_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.step_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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tz0A9e/ast2cgoK5noMKvH44cOZIzzzyTzZs3c/zxxzNs2DAeeuihup6BADZt2sTBBx/covUzs64Ymnn2DUfSy9GIESMavei6oTsltrRnoHvuuYcJEyZwwQUXsPPOO3P00Udzyy23ZF8JM2tQ19s9z7lvuNbu5SivnoHMrHm6Xmjm3TccSS9HhWfRp0+fzowZMxg6dCi/+c1v+MlPflLyvAp7Bho1alSDPQMNGzaM4cOH87vf/Y5vfvObW/UMNHToUEaPHs3y5ctbbR3Nuqqu2cvRrFn59g1n7YJ7ObIsSu3lqOsd04QkIB2SZtYMXW/33MysBTpNaHa0wwyWL/8+WF46RWj26tWLdevW+Q/FgCQw161bR69evcpdinVCneKY5sCBA6mpqWHNmjXlLsXaiV69ejFw4MByl2GdUKcIzR49erD33nuXuwwz6wI6xe65mVlbcWiamWXg0DQzy8ChaWaWgUPTzCwDh6aZWQYOTTOzDByaZmYZ5BqaksZJel7SCkkX1fP+npIekPS0pGclfSbPeszMWiq30JTUDbgGGA8MAk6RNKio2XeA2yJiOHAy8PO86jEzaw15bmkeBKyIiJcjYhNwK3BcUZsAdkpffwhYlWM9ZmYtlud3z3cHXisYrgFGFbWZBtwn6RvAjsBROdZjZtZieW5p1nfLxeK+204BZkbEQOAzwG8kbVOTpCmSqiVVuycjMyunPEOzBtijYHgg2+5+TwJuA4iIx4BeQP/iGUXEtRFRFRFVFRUVOZVrZta0PENzIbCfpL0lbU9yomdOUZtXgSMBJO1PEprelDSzdiu30IyILcDZwFxgGclZ8iWSLpF0bNrsfGCypEXALcDEcPfrZtaO5doJcUTcC9xbNO7igtdLgUPzrMHMrDX5G0FmZhk4NM3MMnBompll4NA0M8vAoWlmloFD08wsA4emmVkGDk0zswwcmmZmGTg0zcwycGiamWXg0DQzy8ChaWaWgUPTzCwDh6aZWQYOTTOzDByaZmYZODTNzDJwaJqZZeDQNDPLwKFpZpaBQ9PMLAOHpplZBg5NM7MMHJpmZhk4NM3MMnBompll4NA0M8vAoWlmloFD08wsg1xDU9I4Sc9LWiHpogbanCRpqaQlkm7Osx4zs5bqnteMJXUDrgGOBmqAhZLmRMTSgjb7Af8bODQi3pQ0IK96zMxaQ55bmgcBKyLi5YjYBNwKHFfUZjJwTUS8CRARb+RYj5lZizUampK6Sbq8mfPeHXitYLgmHVfoo8BHJT0qaYGkcQ3UMUVStaTqNWvWNLMcM7OWazQ0I+J94EBJasa865smioa7A/sBRwCnAL+W1K+eOq6NiKqIqKqoqGhGKWZmraOUY5pPA3dJuh1YXzsyIu5oYroaYI+C4YHAqnraLIiIzcBfJT1PEqILS6jLzKzNlXJMcxdgHfAp4N/Sx+dKmG4hsJ+kvSVtD5wMzClqcycwFkBSf5Ld9ZdLK93MrO01uaUZEWc0Z8YRsUXS2cBcoBtwQ0QskXQJUB0Rc9L3jpG0FHgfuCAi1jVneWZmbUERxYcZixpIA4GfAoeSHJOcD3wzImryL29bVVVVUV1dXY5Fm1knJunJiKhqql0pu+czSHarP0Jy9vsP6Tgzsy6nlNCsiIgZEbElfcwEfArbzLqkUkJzraRT02s2u0k6leTEkJlZl1NKaJ4JnAT8DXgd+CLQrJNDZmYdXSnXae4REccWjpB0KPBqPiWZmbVfpWxp/rTEcWZmnV6DW5qSDgYOASoknVfw1k4k112amXU5je2ebw/0Sdv0LRj/3yTHNc3MupwGQzMiHgIekjQzIla2YU1mZu1WKcc0t+p5SNLOkubmWJOZWbtVSmj2j4h/1A6kHQa7h3Uz65JKCc1/StqzdkDSXmzbL6aZWZdQynWaU4H5kh5Kh8cAU/Irycys/Sqla7g/SRoBjCbpjf0/ImJt7pWZmbVDTe6ep7e6GAeMiIg/ADtIOij3yszM2qFSjmn+HDiY5B4+AG+T3JrXzKzLKeWY5qiIGCHpaUjOnqe3rzAz63JK2dLcLKkb6RlzSRXAP3OtysysnSolNKcDvwcGSPo+ye0u/m+uVZmZtVOlnD2fJelJ4EiSs+fHR8Sy3CszM2uHGuvl6B7gZuDOiFgOLG+zqszM2qnGds+vJbm/+SuSfivpeJ8AMrOursHQjIi7IuIUYE/gDuB04FVJN0g6uq0KNDNrT5o8ERQR70bEbyPiBOAYYDjwp9wrMzNrh0r5RtCHJX1D0qPAncB9wIG5V2Zm1g41diJoMsm3gD5Gsnt+YUQ82laFmZm1R41dcnQI8ENgXkT4YnYzMxq/3YXvbW5mVqSUbwSZmVmqwdCUdK+kypbMXNI4Sc9LWiHpokbafVFSSKpqyfLMzPLW2JbmTOA+SVMl9cg647STj2uA8cAg4BRJg+pp1xc4B3g86zLMzNpaYxe330ZyTeZOQLWkb0k6r/ZRwrwPAlZExMsRsQm4FTiunnb/CVwGbMxevplZ22rqmOZmYD3QE+hb9GjK7sBrBcM16bg6koYDe0TE3Y3NSNIUSdWSqtesWVPCos3M8tHYdZrjgCuBOSS3utiQcd6qZ1zdXSwlbQdcBUxsakYRcS3Jd+GpqqrynTDNrGwau05zKnBiRCxp5rxrgD0KhgcCqwqG+wKDgQeT2xDxL8AcScdGRHUzl2lmlqvGrtM8vIXzXgjsJ2lv4P8DJwNfKpj/W0D/2mFJDwLfcmCaWXuW23WaEbEFOBuYCywDbouIJZIukXRsXss1M8tTKTdWa7aIuBe4t2jcxQ20PSLPWszMWoO/EWRmloFD08wsA4emmVkGDk0zswwcmmZmGTg0zcwycGiamWXg0DQzy8ChaWaWgUPTzCwDh6aZWQYOTTOzDByaZmYZODTNzDJwaJqZZeDQNDPLwKFpZpaBQ9PMLAOHpplZBg5NM7MMHJpmZhk4NM3MMnBompll4NA0M8vAoWlmloFD08wsA4emmVkGDk0zswwcmmZmGeQampLGSXpe0gpJF9Xz/nmSlkp6VtJ/Sdorz3rMzFoqt9CU1A24BhgPDAJOkTSoqNnTQFVEDAVmA5flVY+ZWWvIc0vzIGBFRLwcEZuAW4HjChtExAMRsSEdXAAMzLEeM7MWyzM0dwdeKxiuScc1ZBLwxxzrMTNrse45zlv1jIt6G0qnAlXAJxt4fwowBWDPPfdsrfrMzDLLc0uzBtijYHggsKq4kaSjgKnAsRHxXn0ziohrI6IqIqoqKipyKdbMrBR5huZCYD9Je0vaHjgZmFPYQNJw4FckgflGjrWYmbWK3EIzIrYAZwNzgWXAbRGxRNIlko5Nm10O9AFul/SMpDkNzM7MrF3I85gmEXEvcG/RuIsLXh+V5/LNzFqbvxFkZpaBQ9PMLAOHpplZBg5NM7MMHJpmZhk4NM3MMnBompll4NA0M8vAoWlmloFD08wsA4emmVkGDk0zswwcmmZmGTg0zcwycGiamWXg0DQzy8ChaWaWgUPTzCwDh6aZWQYOTTOzDByaZmYZODTNzDJwaJqZZeDQNDPLwKFpZpaBQ9PMLAOHpplZBg5NM7MMHJpmZhk4NM3MMuie58wljQN+AnQDfh0RPyx6vydwE3AgsA7494h4JZdidtiBePfdbWsEoolJlT431S4PeSy7lHVuC2q6CdDyWjVoECxZ0sK5mCVy29KU1A24BhgPDAJOkTSoqNkk4M2I2Be4CvhRLsWkgSnY5kE94+prU0q7PB55LLtc69LQujWlpcuJpUvhE5/IsESzhuW5e34QsCIiXo6ITcCtwHFFbY4DbkxfzwaOlJTl76k0aWBa1ySApUvLXYZ1EnmG5u7AawXDNem4ettExBbgLWDX4hlJmiKpWlL1mjVrcirXzKxpeYZmfRt3xYenSmlDRFwbEVURUVVRUdEqxZmZNUeeoVkD7FEwPBBY1VAbSd2BDwF/b/VKevduFyc+rDwCYFDx4XSz5skzNBcC+0naW9L2wMnAnKI2c4DT09dfBO6PiNbPtw0bUBqcxQ/qGVdfm1La5fHIY9nlWpeG1q0pLV2Oz55ba8rtkqOI2CLpbGAuySVHN0TEEkmXANURMQe4HviNpBUkW5gn51UPGzY0eDKo1JNE5TyZ1NrL7kgnxjpSrdb55XqdZkTcC9xbNO7igtcbgRPzrMHMrDX5G0FmZhk4NM3MMnBompll4NA0M8vAoWlmloFD08wsA4emmVkGyuMLOHmStAZY2YJZ9AfWtlI5HYnXu2vxeme3V0Q02blFhwvNlpJUHRFV5a6jrXm9uxavd368e25mloFD08wsg64YmteWu4Ay8Xp3LV7vnHS5Y5pmZi3RFbc0zcyazaFpZpZBpw9NSSdKWiLpn5IavBRB0jhJz0taIemitqwxD5J2kfRnSS+mzzs30O59Sc+kj+Ke9TuEpn52knpK+m36/uOSKtu+ytZXwnpPlLSm4Od7VjnqbG2SbpD0hqTnGnhfkqann8uzkka0agER0akfwP7Ax4AHgaoG2nQDXgL2AbYHFgGDyl17C9f7MuCi9PVFwI8aaPdOuWtt4Xo2+bMDvgb8Mn19MvDbctfdRus9EfhZuWvNYd3HACOA5xp4/zPAH0k6/R8NPN6ay+/0W5oRsSwinm+iWSn3aO9oCu8pfyNwfBlryVMpP7vCz2I2cKSkjn4Xjc74O1uSiHiYxm/AeBxwUyQWAP0k7dZay+/0oVmiUu7R3tF8OCJeB0ifBzTQrld6T/kFkjpisJbys6trExFbgLeAXdukuvyU+jv7hXQXdbakPep5vzPK9e8513sEtRVJ84B/qeetqRFxVymzqGdcu78Wq7H1zjCbPSNilaR9gPslLY6Il1qnwjZRys+uQ/58m1DKOv0BuCUi3pP0FZKt7U/lXln55frz7hShGRFHtXAWpdyjvd1pbL0lrZa0W0S8nu6avNHAPFalzy9LehAYTnKsrKMo5WdX26ZGUnfgQzS+e9cRNLneEbGuYPA64EdtUFd7kOvfs3fPE6Xco72jKbyn/OnANlvcknaW1DN93R84FFjaZhW2jlJ+doWfxReB+yM9Y9CBNbneRcfxjgWWtWF95TQHOC09iz4aeKv2UFWrKPeZsDY403YCyX+e94DVwNx0/EeAe4vOuL1AspU1tdx1t8J67wr8F/Bi+rxLOr4K+HX6+hBgMcmZ18XApHLX3cx13eZnB1wCHJu+7gXcDqwAngD2KXfNbbTePwCWpD/fB4CPl7vmVlrvW4DXgc3p3/Yk4CvAV9L3BVyTfi6LaeCqmeY+/DVKM7MMvHtuZpaBQ9PMLAOHpplZBg5NM7MMHJpmZhk4NK1dkLSHpL9K2iUd3jkd3quo3YOSPl007lxJP2/GMo+XNKhllVtX49C0diEiXgN+AfwwHfVD4NqIKL5d8y0kF3IXOjkdn9XxQKbQTL9RZF2Yr9O0dkNSD+BJ4AZgMjA8kh58CtvsCiwHBkbynepK4GGSe1aHpAuAk4CewO8j4rvpdKcB3yL5DvKzJAF9N0nnHW8BXwD6Ar8EdiC5MPrMiHgz/XrpX0i+MTUnIq7I6zOw9s//Na3diIjNaej9CTimODDTNuskPQGMI/lqaG3/mCHpGGA/km7TBMyRNAZYR9KJyaERsVbSLhHx97TT5bsjYjaApGeBb0TEQ5IuAb4LnJsuul9EfDLP9beOwbvn1t6MJ/mK3OBG2hTuohfumh+TPp4GngI+ThKinwJmR8RagIjYprMOSR8iCcaH0lE3knR2W+u3zVkZ63wcmtZuSBoGHE3S2/Z/NNJx7J0kHQmPAHpHxFO1swB+EBHD0se+EXF9Or6lx6HWt3B66yQcmtYupD2p/wI4NyJeBS4Hflxf24h4h+T2JTew9QmgucCZkvqk89xd0gCSDktOSo+HUnuGHnib5DgmEfEW8Kakw9P3JgAPYVbEoWntxWTg1Yj4czr8c+Djkho6jngLcADJbR4AiIj7gJuBxyQtJrm1Rd+IWAJ8H3hI0iLgynSSW4ELJD0t6V9Juo+7PD22OYykxyCzrfjsuZlZBt7SNDPLwKFpZpaBQ9PMLAOHpplZBg5NM7MMHJpmZhk4NM3MMvgf6XhTgix1iiEAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Step Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Quadratic Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.quad_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.quad_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Quadratic Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## W-Shaped Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.w_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.w_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('W-Shaped Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Spiral Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.spiral_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.spiral_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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jTCmF9vbyjh2Pww03sPnj17NDEowCI8Qo2bIfVEq5TGaio6mlBfr7g9m3pWKsYFpKY2Cg9F5kMfJ7d/G4CWHw2+ubORMWLIDFi8eXRML0Xostu3ZBMknvT5MkdDstKFMYIUmKP9M5UTjb2kzbRMyr83ciARddNDlmLQhGR00vdOpU2/OsA6wNMwBEhEsvvXRsiuOXv/xl9uzZE2rGouOPP77spBW+ybVHtrXBW95SfviOGyKmR5mPI0hVIt8n9l2SfJckIiU8D044AVatKuzIqpShoXHbJ5jvZu1a64WvMraHGQCVZisqh6qI5cDAeE9yaCh4sZwyxXiNqyiMbgQyCyyZND3WVMr0OsEMqXNfgyJ36G7tnlWj+QQzhPxu5WQryqWaGX5cyWSMLdIJ+XnhhcqH2rHYRFvklCnw9rePD5sXLaoLsYSAZ4Elk8b7r2pMFrmvfX2l22eLkcmYwHsrmqFTc8EUkRYReVxEvNPuBEFY+d0oL1tRLtXK8FOQTMbc4JUKpIMjjEceaZY6FMh8qpZtaN064x3P7YUG4TByhuw2zjNUai6YwCrgmaocKcT8brnZinJ56KGH+OhHPwqYbEWbN28u+Hknw8+MGTMKZvjp6uoay/CTy9FHH83GjRu54oorePLJJ5k+fToPP/zwWIafRYsWccMNNzDgTPtz+M1vJvYmK5nx5fSY2tqMUNaxMHrhdAxHR81rqObB3F7o6Kh5TaWg0qz2AwOwbJkNkg+JmgqmiBwKnAn8v6ocMOQ6AqVmK8qlahl+Mhl49FEoJ6lGLGY80o732hFIpxe5cOEkocyNQNq2LRx/SMOQTJrfJZWq7IHjXDe5c+GteAZCrXuYVwGXAa5jQRFZKSJbRGTLq5U6HULO7xZ0tiK/GX5aWg7hmGMu5NRTP85ddz3GX/1VgQw/zz037sgppzfZ1maGkImEEUYXgcylkN9oYMCKZlEc51Fu+FNfX2X7dMTTOogqomaCKSJnAa+o6qNe26nqBlVdrKqLnUS4ZVOFOgJBZivyk+Hn9tvv44QTFnHuuUdw770/5NxzV7F370zWrv02S5cuZeH8+Ry7aBHP/tu/lefImTnTlzgWotCU8NHRyRN7LD5Yty4Yu2cmY4bsNhi+LGqWrUhE/hlYBuwH2oEDgFtUtdftM4FkK0qnjc2yQTLKbNtWeOp1WxssnO0v648rM2eO36BlkPdTTWBx0bwwldE0WazyC6KXgo3lHMNvtqKaBa6r6ueAzwGIyMnAZ73EMjAarI5AvlgeTIbZvEjb0BC8UOLOpk+H//pfA2tbW5u7mFsCwrmWV68ez+fpl0zGiG3ufiye1NqGaamQXPE5mAwJBpjKECUP2MoUSy+nTqEp4bFY4Yk9lgrI9bh3d5f22cFBG45UAnUhmKp6n6qeVcHng2xOpMgVpdm8SIu7/2wyjpd78eKyxdLLqZM/JdzxG4UdcdTM1wObNpUXHJ/rUZ8yxdo4XagLwayE9vZ2MplM094kuaLUho88krHYuEiW4cjJxY9TJx737VQPBFUlk8nQXm72okagUHB8KThp56xoTiLyJSqGh4fZuXNn0eqJDUMmA7nTHLu6xlVo587xRLWFaGmBgw6CvGqV5eJlMqvAV1Qx7e3tHHroobS2ttauEfVGOs2rvauYQca/uaalpfyUfRHDr9MHVY3MctRRR2nT0tfnnqSsr89sk0qpdnRMfK+jw6wPgUSicHMSiVAOZ6mQREJ1KSl9gYSO+kt+Z5aWlvFrrEEBtqgPDaq5CJayNK1geomlc0E7pFLmzhAxryGJpXOoKuqzpUJyf6+lpHQPHd7XlduDuQGxgtkopFL+LuYaNq9K+mwJgNzf6+J4SnfHE/4FM/fB3GD4FczI2zAblv5+uO46f0HnTWRrsoREf79Jz+RlAwdjnG6QSR+52DK7ESSdhk/PSDMoU9H16/3P0HGCjy2Wclm3bjxnp1ey49zUiE04xdIKZp2QTsOmj6X5SuYCOvwGnouYmDtbptUSJH4fwKpNF35kBbNOWL0avji8ilaKDIkc+vpMD9SKpSVo1q0z15ff8hrXXts0s4SsYNYJO3bADHzkPevoMAHJVigtYbJuHekb9jM3ocRG97OzxSOwVjWQJNxRwApmrcnWGNqvPn6Kzs6Q6iZYLBPJr+Zy2cgaRr0MRQMD47XU58933WfA5bSqjx9Xer0sDRVWlEqpxuP+Qzq6u2vdYksTUWhSwjX0+Q94P/DACfur95hdfIYV2R5mLejvNx5Gv6nH+/pMUgWLpUoUqtpyMetYR5+/5MV/+hNMmzbWjQyxnFZVsYJZJmUNL9JpUyJg/friZSKc0oXWXmmpAW5VW76UWAc33eQvWcC+fWPlf0Mup1U9/HRD62WplyF5WcOL7m7/w287GdtSY3xd427JBApcz/WedwA7JA+PkocX/f1wzz3+dh5wjSGLpRx81Wn3e50ODJB6fzrsclpVwU6NLINYrPCIWsRlck5LS9FZOwqIrbFiiRrptEk8XIyODjZfsIHenybrcmalnRoZIr6r9TqGziJiOYoYY/quXfVzBVksfkgmTe+hWGmMwUFO/Olqtm83t8P27dG81K1gloGvar09PebJ65FlV4FXidPLTcaYbrFElU2bjIPSK6X+wECEAzANVjDLoKh9x6fN8g3aOIRd3NqRjJwtx2KZRDJpRkleHnSndtCMGZEUTiuYZeIU6is4vNiwoejnh4lxIdcXNqZbLFGm0BAsn0xmLOQoSljBDAMfOQVbUzeS1mRkbTkWiyu5QzAvhoZg1arqtCkgrGCGgVd2l1QquhZvi8UvzhCsmGhmMmO9zCjMNbeCGQTODB4n+YCbYHZ3N6VQRuFGsISEn+H5ypVs7k9PSPbh5CcWqbNrxk90e70s9TLTZwKplGpb2+QpDCKqsZiO1UJp4AJSXlQ16UJ+gaG+vvH/43HVzs7xRnR1Tfzf+a1sYaLgSaXGv1+XZT8xXUrKdZOwE3Vgi6BVCa/pYfUy76uGhDIlrq/PiKCzs/b2ieIX1CJi9msrvFVOKqXa2ur5fQ/R4imaYd5OfgXTDskrIZ32jLOMXmaB4HH7CgYGfA7R880d7e2Tk5fs2wd79wbZbIOq2a/qeDiM046enuCP18gkk7Bxo6d9v5URruXvXN+vh9vJCma5OBlWvXCbEtREeH0Fjg4tWwZPz+4BETR/6e2dmAbvzTfDb7Qf7rkHenp4tqef/TIFFWG/TOHZnuapb1MyySTccIPnJtPZyzUU/g7r4nby0w2tl6VuhuSplLFLeg3nWlvtEE4L2zBzl6WkdBjxn5i2jpbR7FJwnR3Cu1MkcfYo6J10WxtmpUtdCGYxBQBzQTTZzZLvb8k9/dz3HJF8hXhBwYnSUrTt9ZRSvJ5IpXx9t9/u7Kua+dgKZlgUywHYZI4et0obE7Ri3rwJN0JVRDIeL81LHoZgwuSRyJQpVkRVzW9T7LuLxarWHCuYYVDsydhkPYpine1vd/q4KcpZcj3kYLzk8Xj53mynC1zoOB6ml5FKz6NJQ83G8COaVbqfrGAGTTF1aGlpKrFU9e5sb2dWYD3JCfuphbmj0I3d3a3PdJdQFMxt6exsuutmAkVE8wUSdkhe7lIzwSzm5GmynqVDfkdvKSndS1vFw+7RnGVEYnXdE8vMmheciaGOzzNUPMq3jCBVucWsYAaFHydPE4ql6ngP8xr6dKRCkRxbYvUtkAXp65v8QPVb76ZAz7UpcbEnv0BiwlcaFlYwg8I6eVzZOa87GCdOo0YV5Di7Slo6O/WBvpRr1EFDUqBjsoeOCTN/RMI7fN0LJvA24F7gGeApYFWxz1RdMIs4eYbbmnMo7isO1Q4/DWWK5ijoXqaOCUZTWH2yzrcRRF8hroO0jz2Q9yPGiRgSURDMtwJHZv+eDjwHzPP6TFUFs8hQfJgWvTje6FdwAUopF5y/zJpV69ZXHccBfyfdZfXER0HvyAZxN8tg5oG+lA4xpeB3EdaDtu4Fc1JD4FbgVK9tqiqYHkNxZ6gQ5hChLqlELJvQNpf/zF1KSgckUbJwjoJeQ1/zXG9eZrCWllAOGSnBBOYCO4ADCry3EtgCbJkzZ04Y39VkPIRhFMaGSc3yxNdUqvwg7yYUSgfPTE2plOrUqSWJ5jBNkiYwP/wifwmByAgm0AU8Cny42LZV6WEW6UU5XrumsCmp+krLlXtTj4KZRdMUX443bvf9hJ6in+Dt/KUE0fSaslq3FHO0zpsX+CEjIZhAK3AncKmf7asimB4/1F7p0I+Sis6FVykl3MyjoFuZ1zy9bh/4zgVaYm/Tr2hWNXlzkKRSOhKbbMMs96Hhh7oXTECAG4Gr/H6m1oJZ/1daQOQn6C0ilLne3JBGTJGkZMEq1UacJxr5vUm3pEBReKhdHE9523oDNuhGQTBPBBTYBmzNLu/3+kzNBbPRKdFWmevBdZaQbPKRpeQhcan24qxo+plfEZLWhIKIGpttlTowdS+Y5SxVEcz29sI/Tnt7+McOGc+b1602kYdYXkNfUz5XqoZfk0hfX0kTi6LQw0wkzAwyz15mW1tgx7OCWSpuGWvATNeL+HC86PDQ5xBcQTUe14vjhWuvROFmjBQ+RfOjHrVwXH/zOsa5Xt8sEI9ZqIddKVYwS6GQzc75v0E8PG7PgovjJc7a8RgCRuVmjBw+RHOvdBQsIBaPR9BLniWV8mHLDMgGZAXTL6mUe++qgbpLhU5xKSndh/9heDEnQ5RuxsjhQzRfJd6YD7BiNt0AsILpFy/jTxSs4z4pdJqv4F1bJehhj8Wbog+gIqI5CpqJxRsv9M0rp4PtYVZZML2EooF6mIWG0L6m6DXMXVff+DZx+LFptrU13u/mFnIV0EwyK5h+8HpyiTTcRef0YK6hT4dpKS6YTZgso1b4DnJXk5yi6G/XiPFdhUQzILuDFUw/eJX7bNRhaJ/PsgohTD+zuONrGqWO90R9mVMa7Td0e6rE4xXv2q9gxiqrah5xMhn399atq147qkU6DevXI17btLZCKgVPPVWtVlmAOXP8rV+9GgYHYRVr2UuH906fftr85piXuXMhFjOv2dXRYseOwuszmeqdkJeaAi3Al/wobzWWQHuYxWxBjUaR6Y6joLvjiYYzQ0QFvzbM3J9wKSndT5H42a6uxgkB83LQVtjLJKghOfDvgPjZWdhLYILpFUoUUBe/rihWHhh0JNaANq+I4SdMK18zllLcnvntzsIzsiLn0yx2HVeAX8EUs607IvIV4J3AvwJ7c3qmt4TT53Vn8eLFumXLlsp3NHcuDAy4v59KQTJZ+XHqhenTYc8e7236+hrTDNFgpNOwcqUZljtsYz4LeNrV1DIKtDD5PheB0dFQmhke4mFQquC+FZFHVXVxse382DAPBjLA3wAfyC5nldWqesHNFgIQjzeWWM6f7ymWCpESy4awxVVAMgkbNkAiYbQjkYBtqaeQefNcPyPAUiZ/UW5207omHnd/b9Wq8I/vpxtaL0tgQ3I373ijhRIVSRc2ipmDHBUaxhYXFh6/9et0Nsb3FtKwnKC85CJyqIj8SEReEZGXReSHInJo+FIeEuk07N5d+L2LLmqs3uU993i+vZtOHkxE53wdD3Eug4NmvQXo6nJ9azp7J/QyN2yI6KVerNH9/aEe3s+QfCNwGzALmA38W3ZdNLnoIhgamrw+Ho/MsNQXPT2eb48Cq1qvY82a6jQnCNwsKV4Wlqbi2mtd3xJgLWbI2mhWpwls2BDq7v0I5kxV3aiq+7PLt4GZobYqLPr73e15r71W3baEjUfvUoGbOvvo2ZiM1I3jN1axaUkmobPT9e0ZmLjjP/854rZfLzvmyEioh/YjmLtEpFdEWrJLL+AR8V3HeD19GumuKzIskXnzuGDPukiJJcCaNdCRF6vd2mqegc3qBJrEddcV8IePs53ZDA9H3Iyxdm3tjl3MyAnMwQzJXwVeAX4MzPFjIA16qdjp42UsjqQFvAB+kjNEmNxYxXh8cpL4yDozAmSovcvT0beUVPQTcXld32VMaybAOMwTVPXBYuuqQUVxmP39sH594fciGZDmglecGkB3N2zaVJ22hIxbOG0iAdu3V7s1dUQ6jfb2usZlvkqcoxO7ov0deV3nZdzPQcZoNrOzAAAcnklEQVRhXuNzXX1z3XXu7110UfXaESbFxqMNJJbg7uwZGGjuWE2SSc98ATPIRMrZVxAvO2aRTmAluAqmiBwnIp8BZorIpTnLFZg55tHC64nTKN7xYoapBhJLcDc7ixjRVDWvK1c2n2i+Nmuepy0z+WC44TehUyM7plcPsw3oAqYA03OWPwP/LfymWUqmyeJrCjmBRCZ3MPzGaubOIpoxwyxR7aUe2eqebUrAMwQpEtTKY1nMyAkk/BhDq7GU7fTxmh3Q2VnePuuAXAfIxfGUSaDRgOfpRX7CitxTvoNuHc06OjwTVMybV7Sud9ScSSI+MupHnS4X51ZXV8m7IsBsRXcDB+b8fxBwp5+dB72ULZheiYKjdBfkkHuDLyWle/C42xttyqcb3RMF0lei5Bzv8QjutdYhWtl9EonxB0bDCmaA5xakYD7uZ101lrIFswEvmtze1Ask3M8vHm98sfRZu9uvcI6C7qNlUtnaKIXiOA/URhbMEYkVPK8RiZW8L7+COcXHqH1UROao6g4AEUmApz3ZUgVyzZUJPFLV7doVfmNqxezZ8NJLge7S8S5PZYQ0vVzOP7EIYw+M0tyGMRNfb02bESqihR25buuDwE9Y0Wpgs4jcJCI3AfcDnwutRRZfODfvNXh4O1uiF8zgi3TaeHcCFst8BFjI04xkZfT97w/1cIGTTOJdjiTkRBU1JSQvXdHAdQARmQEci/n+H1LVmnRbygpc9wpYj8cj2wNzEsm+PjiFKXjMn/Xx+0aK+fNNrZoqotnlsIRGL9g74ADvekJF3B8IJd7bfgPXiw7JRUSA04HDVPVKEZkjIu9V1Ud8t6aWeIVP1HJOaoU4Q66WXg+xTCSq05hq0dEBb7xR1kcLPTaKzImatN3PB2YDL5Z1/JrR1eWacEZVfX8HkcOrwGEF+BmSrwOOA5Zm/98NfCOU1oSBVw8ratkn8ig65Ir8dI4c2trKFkuAB9q6iaFjyy4OHOs5+umDCzCHcE0AoXDttQ3rcBCv2T4h4Ucwj1HVTwL7AFT1j5igdkuNSaeL3OwRfyCM0dEBw8Olfaa7e4Lv9OThibOcDuGPY+L5Dfp8CydtEbv0G+UaKMDmj6yt+sPAj2AOi0gL2etJRGZi8s/WP16G32JJKuqcdBr2nN/ARnvMOb4mB6Gl9CxTKSOSedNAvTzcF7OOGMo2vKcTCpQu3JbQOOcHSd5w67t55AWtBD+CeTXwI+AQEVkDbAb+KZTWBI1XUaSIO0NWr4YLR6/1NnpHmHQa/qK3h4P4kz8727Rp5jd16VGtWePeOWxrM1/XIp4qKpqW+iGTgb1ML/xme3soxyzq9FHVtIg8CnRjHrLnqOozobQmaLwMvxF3iOzYAeJ1a0fYoQXmgfAC9/gTy1mz4EVvZ4yjo6tWTbws4vHxr2r5cli0/ylG8PC+Ro102vVcGuEc47hUSgipgoJXtqKfiEhSRDpV9VlV/Yaqfj0yYlmMiDtEPnVwkTiziNuu7h+Y7W9D1aJi6ZBMmkiT3GkhTuTJ6tWwfz98nf6GEJIxqlF6tkbE45Dh4MJvhjTLwGtIvgFTf3y7iHxfRM4RkUAt3iJyuoj8RkSeF5G/D3LfgPuwtKsr8oLyxTdXNdaNnUs6zdt4qfj5dXcHcShWroTPDvQzitDP+sb6XkMKr6kHfvyRNAcV6GGOtLSG1yEqNncSmAb8d4wd8z+B64FT/cy7LLLfFuC3wGEYr/sTwDyvz5Q8lzyVmlzDoK2tMeZWe80RLiNFf10hUnS+t3Z3B3KoREL1GvpKStQRKRrpXPLp7Cx8Tm1tJe+KoOqSq+obqvp9Vf0QcBpwBHBHAFr9XuB5Vf2dqg4B3wM+GMB+x0km4frrjb1SxLxef33ke5dFiXpCZA+HnAIbu1OBJUPesQMuYoP/XuW8eYEcty7o66t1Cypj797C6wuV0Q4IPzN9/gL4CHAe8FbgX4GPBXDs2cDvc/7fCRxT4PgrgZUAc8qxSySTjS+QDYbi7pAYRVixKbjfc84caBkoXpp1rE1PuSfmrTvSadfvUgGJ+oO1Bng5fS4UkX8HHgP+CrhMVQ9T1ctVdWsAx3b7HSeuUN2gqotVdfHMmdEsh27xz2uz53u+35K6KdDjrVkDI0UqrowFtUctFG1VA9u5a4TXkPx44F+At6nqxRp8lcidwNty/j8Uojj3zBIkB730tPdNHvBoIZmE57tXugZoOWJ5SFwjV6bCy+Gzi2jH6dYKV8FU1Y+p6l2qoSWX+xXwThF5e9b7fh6m/rnFUlXetWkd0tc3YW65s+ziQFpQMhn42MeiV9unEApcwtqGOJdq42emTyio6n7gU8CdwDPAD1Q1QgaiGuM2tTPiUz7dUAjXSbFuHaI6tsyMm3nmh/DHsU2GhyMU1lgk1+V3SPoqDFe31EjtXfNhishPgX5V3V7VFnlQVj7MRsVLGKNma8vBLcehAlLF84r81+txAgrE0Ginw5w719RQdqPEH8lvPkyvHua3gbtEZLWItJZ0dIvFUrc4Tq4oldyYhFdJ6ZASb4C3DfMHmJjLA4AtIvJZEbnUWUJrkcXiQjVHYW6TxCKR02S+e6SBAteyko6OiM8OPthlSiTAddeFdthiNsxhYC8wFZiet1hqSZPZMIGq2tzWrp2c3aitLQI5TdLpoiU8LmlZx4YNEQ9Pdgtab28P9cS84jBPB7YCHcCRqvoPqvoFZwmtRRZ/XHRRaesbgM8OVC//Z2Qnif3d37m+pcA25jE6GoHz8CKdhn37Cr/ntj4gvJw+DwAX1ZPn2jp98ujpgXvuGf+/uzuwKYO1wquw1QhCS4glVCNPOg297nV1HWdPhGv/GQJ2+EAATh9VPamexNKSRzoNDz00cd1DD0U+UNDLoBBDicXM/RLx0wwHD7EE3LOTRw0vsQzZyFyzOExLhaxeDYODE9cNDlbX0FcDVM39snKlFc0JzPbOH6rAJ7geCC23bn0QspHZCmZE0YHCYRVu6yNDdsaNG3fQAzTFs8E//f3wkvusYgW+QR/fxRguIx1OVCQgP2zjrKsNsx6xNsxxdk6Zy6Ejk4cme+ikSwvXoY4MPoKunc0iG3gdFEXsljDxO+voINoecq8okEQCtm8vc7eVB65b6pjLR9YwXCDLTid7iz+FI852zPAz0j2lIEinYdkyz00UU5Pd8fRHWiyLXddVCCy1PcyIMncu/HaghZZCFY9bWkyBmqjS3w/r17u+rcCGWB9dN66L7s0fBFOneibLVSDDgdyZ+mNjfE+xmLsHPBaDkeJ5Td2wPcwGZ80aiLmVh6/gwqkLiiS2FWDl6PrGEIFymT/fV2bxmfyxcWy9Xp07j/jTILGCGVGSSdCYS+LbRpjtU6QUhEDDmx5cmT276Gwex9ED3tOuI0OxkIgqZY+3ghlhnjulcOJbVY2+mDz1lKe3HDDD9qifZ6n09Hh6xMGI5V10czFGRBrC1lsn3WQrmBHm9OfXFRQVAbj22iq3JljSafg186xoOqTTMGPGxJldBXDE8nTMjK/IJ9lw8ApWr2IxNyuYEWbHDo+ZMRFy5hVi9WpYyFO8Qas/0ezoqEazakNPjwkdKlJjPF8sReCCC6LhFU+njSOz4EyudNrdzNTVVdUqqVYwI0xDDLVccOxunQwx4qeU1xtvNJ5optPGE16kVwnjiTUcsQTzzPzpT0NsX0Ck02bm1sDA+EyuZcuMRs6dC0Mr/q5wB0Ck6iMpK5gRpiGGWi7kPgzO56aCMaeTeOMNcxM1wpzJ+fNNr9Jnje3fM4tFTE79EAWHT6FZvo4+fnagn9Yhl1RuqlXvPlvBjDBRGGqVy5o14x3G75LkAm5g1G/R2N7e6No1e3qM6Bfxgk+gu5sliRcLvhWFUYiXqPdxnfuvnkiE0RxPrGBGHIl5/IQ9PdVrSMAkk2ZWipOP8heJJL/ou6m4PdNh/Xpj34pSb3P+fF/D7zHicUilYNOmCQ8Yh6g4fNxE/Rr63WONoTYnp6qRWY466ii15NHXp2oGJ4WX7u5atzBQ7qRbR73ON2rfwbx5pZ2Ls7S1TdpVKqWaSKiKmNdUqupnUxaplGpHx8TTW0rK+3eOxQJtA7BFfWhQzUWwlMUKpgseojkKtW5doCQSqneUI5r1KJyxWHliKRIdNfSJI/bO6b1Ol/d30NcX6PH9CqYdkjcCRcIqNvdHaFhahDVr4MMdm0iSYj/4H6KDGe6KgAjP9vS7h7GEhWOfdJZyUi11dsJNNzWcATuZNImGVOH+i9JMp0jGrSqGEk3Aj6rWy2J7mB54PI0zsXitWxcouUPP3Uwrq7c5CjoC+gIJXUpKOzpC6LR1d5fXgyy0tLc3XK/Slc5O7+8iHvz1jO1hWhwOGvUOeI4aTm9kdBRuTQ2yIdbHKFJSb1MwHs+5DJCmlz2Dwkd7c3p/5XQ702njaHL2UYoDx4tUyoRMNVivsiD9/e4VIR1qWbrTj6rWy2J7mB50u9v1RrM2n6g6Bbxw7F6geg195dk2K1m6u80XGY8Hv+/Ozsb4kfySSvn7TkIA6/RpPvZLi+uFNoro8tbUhNWhDEOrjMjEU11KSveZ2pLVE838RlS6dHVF/4cph9ynn9sS0vfiVzDtkLyBaLnpBtdhqaD8w/DEjC+NUBcnP4bvuyRpZz83dlYvIQPq9q2XyKxZZl+7dzfH8DuXdNo7wQaYJBs1/l6sYDYSySTiUWZ0DpOnVERh6pwXbgHbU65bN94vmTWrNo3zgxN8rgovFp6t0/Ck07B8ufc2nZ2184znYAWz0Vi71jWzyw4mT6mIwtQ5L/JnBBWsW/Pii0aQ+vpM+Y5aEouZdjhivmuXZ6/JM4tPo7B8uXdJlZYWuO66qjXHEz/j9npZrA3TJ319k+xqo9llP6LX0NcwNsyKKDZLKggbZgWOm0IzYBruN/MTelWFE8Y6fZocD8/tKOjP27ob68YLklLiJx0veQjhB24+kEQikN3XB8W+3yqdrF/BnFLrHq4lJJJJ49EpkHRWgCVD9wBpoMmcC37YtKn4NvmE4Ixwsy9H3e48hh/7Qp1lD7E2zEam2J3l4iJvCrtZBHCzL0fd7gyMZw32og684vlYwWxkitxZOjDAp2ekJwhioezXK1da0awFUU7Z5kk6bWpn5GcNzmXevLrwiudTE8EUkS+JyLMisk1EfiQiB9aiHQ1PkTtLgLWZXvac3z8miIWyXzdCvGYU8RUBEDX6+02C55ER9226u+Gpydnj6wEx9s4qH1TkNODfVXW/iPxfAFW9vNjnFi9erFu2bAm9fQ1Ff79JpuuBAqviKa7elSQWKxyHXW5yHYtljHTaiKUXiYRJFFBlRORRVV1cbLua9DBV9S5VdQKvHgYOrUU7moJ160xgtEdAuwD/J7MKaHC7maV2OD1LLyJgb6gHG+YK4Gdub4rIShHZIiJbXn311So2q4FIJk2AtAczMN70hrWbWWrH/PlFRzlAJOwNoQmmiGwSkV8XWD6Ys81qYD8mvqUgqrpBVRer6uKZM2eG1VwLwIwZJEk3nt0sIGz0QBnMn++voFs8HomLLLQ4TFX1rMAlIhcAZwHdWgtDajPS3e2ao1HAxGz29pLs3khyexmxiA2MEz3gOMSc6AGIxH1eG2bPhpdeKr5dLFbbHJclUCsv+enA5cDZquoRW2AJlE2bTLhGMe65J7plakPCRg+UyPz5/sQyHocbb4zMU6dWNsyvA9OBu0Vkq4hcW6N2NB9PPWWcQMXYsCH8tkSIhp91EyQ9Pf6G4X19RZOP1Bu18pK/Q1XfpqqLsstFtWhH05JMGuOkFyMj1kiXg40e8El/f9HSHAp1G5hejHrwkltqwZo10NrqvU1vL8yYYYUTGz3gC58xv08yr24D04thBbNZSSZh40Zoa/PeLpOxcyNp0Fk3QeJTLHcwi7MT0RRLsILZ3CST8OabxpbkxeCgmftrRXOsWuX27bUXy7oIc3JqrfsQy23MY17Hi5HulVvBtBhbkh+bph2i1w11kSRl9mxfpYQVuJtuPph4KvK9ciuYFkMhI10h7BC9Lqh5mFN/v7+wIUD6+jhNN9VFr7xSrGBaDI6RzmPO+Rh2iF5zah7m5DfsrK8vkt5wN6xgWsZx5pynUsWLhTlD9GnTrHDWgJqEOeUaTb3Ss4G5fhpMLMEKpqUQySTccIO/Ifq+fUY4ezxnwloCpqphTv39RgB7e8eNpl50d5sqkA0mlmAF0+JGKUN0MMb/9nbb26wSQYU5FfW09/QYD7jfZKizZpVXEykq+KmUVi+LrRpZI1Ip1ZYWf1UUW1oarA5s41K0jG8q5b96ZkuLKVscUbBVIy2B4XRbiiWAhXHb5oMPNuSQrJEo5Gn/4GCa05etgt7J1UYLUqMM6bXCDskt/kgmjW3KL+vXw9Spdohex+R71K+hnxS9xNWnWDbh3FArmBb/bNpUfFZQLkNDprfZ1WWFsw7J9agvJU0/1/oXhM7OppwbagXTUhpOjaBS2LvXCKd1CtUVuZ72f2I1MXzm8e7uhj17mk4swQqmpRySSSOanZ2lfe7NN41w2uTEtSHPJZ5bjmQOPiLeEwnzuzeyF7wIVjAt5ZFMml5GVjhLqjGyfr2JhZk+3fY4q0U6DStWTJx8vmIFSdJs3w6xhEfEe1ub+Z0bYW5jhVjBtFRGVjgfaOsuTTTBCG5vrxFPm9QjXFatMjblXIaGzHpwzyXQ2QnXX9/0QulgBdMSCL+/fhMrWlP8mRJ7mw7ZAmxWPAMiPyI94+L5dtYXioRPpZrWVumGaIQKNi5evFi3bNlS62ZYXEinTWzf8QNpvsUnaGefqUZZCd3dTW0zKwnnBxgYMKLn996OkAaEhYg8qqqLi21ne5iWwEgmzcju1o4kHbzBN+hjFMrrcTrcc4+5+UXsfHU30mnTK3fmeoN/EfQ79dUCWMG0BEzu7JGLWUcLSpIUe6Sr8p3fc48ZYjb7cD13uD1jhnHmuA25vWhtjUw98HrBCqYlUArlY/wuSQ5gtwl6lwoH6arjtk5nicUaN1TJyRTknOvUqRO93ZnMZGeOG/H4RBvlxo3WPlkiVjAtgeKZp3HdOpP1RrW8OE43VE2oUtTDlJz6OLlLfqagoSH/AplLR4fpTdZTUaIIYgXTEii+8zTmxnEGZUfbs2di+Yy6qBLmQn7b5s/3VR+nFEYRRsGWuAwSPymN6mWx6d2iQSqlmkioipjXkrK9zZrlP6WY2+IcND93WbElFgsmRVkqpRqPux+nvV21tbXy83RZRkFfIa5LSWkiUfnpNAP4TO9WcxEsZbGC2ST09fnPv1locZS63M93dxcWvXjctG3KlMmf6ew0n0mlQhXDgktrq77RFdcRRF8goUtJKeTltrR4YgXT0hj09ZmeX6k9TJHKRKjUY4IRea+eZVCLiDlOXhe+op59k+NXMK0N01LfrFtnkhKrGntnsfrpjsG00mpgfksy5DIyUl54TylMnQo33WSK1eU5b5JJ69MJGyuYlujgKEJuf8sR0fzCNn7rrNcLHR0wb97EdS0txiGWO1Vx3z6rhDXElqiwRJtksrCAOOtWrQq/15dLPA5//jMMD3tvF4vBQQfBa6+Z3vCaNVYII4DtYVoal9w668WG8rm0tRlBK5WWFhPruHGjd6hUVxfceGPBYbWlvrGCaWl8Cg3lvYb1119vBC1f9OJxM1tpSoGBWWenqeXu9Hh37XI/3u7dViAjis1WZLFYmh6brchisVgCxgqmJdLU8+xHS+NRU8EUkc+KiIrIjFq2w1I/lCKA6bSZOp5bpiZ3KrnFEjQ1E0wReRtwKvgpV2dpBkoVwNzcmw6Dg2a9xRIGtexhfg24DCpLyG1pHEoVwEK5N73WWyyVUhPBFJGzgRdV9YlaHN9Sn5QqgJ65Ny2WEAhNMEVkk4j8usDyQWA18Hmf+1kpIltEZMurr74aVnMtdUCpAug796bFEhChCaaq9qjqgvwF+B3wduAJEdkOHAo8JiL/xWU/G1R1saounjlzZljNtdQBpQpgocqwNk+uJUxqHrieFc3Fqrqr2LY2cL3xcSrF7thhp1hbqoffwHWbfMNSV7jl0rBY6oGaC6aqzq11GywWi8UPdqaPxWKx+MQKpsVisfjECqbFYrH4xAqmxWKx+KTmYUWlICKvAgO1bodPZgBFQ6Uiij23aGLPzZ2EqhYN9I6UYEYJEdniJ64rithziyb23CrHDsktFovFJ1YwLRaLxSdWMMNjQ60bECL23KKJPbcKsTZMi8Vi8YntYVosFotPrGBaLBaLT6xghkwjFnoTkS+JyLMisk1EfiQiB9a6TZUiIqeLyG9E5HkR+ftatydIRORtInKviDwjIk+JyKpatyloRKRFRB4XkdvDPI4VzBBp4EJvdwMLVHUh8BzwuRq3pyJEpAX4BnAGMA9YKiLzatuqQNkPfEZV3w0cC3yywc4PYBXwTNgHsYIZLg1Z6E1V71LV/dl/H8ZkzY8y7wWeV9XfqeoQ8D3ggzVuU2Co6h9U9bHs37sxwjK7tq0KDhE5FDgT+H9hH8sKZkg0UaG3FcDPat2ICpkN/D7n/500kKDkIiJzgSOAX9a2JYFyFaZjMhr2gWqeQDjKiMgmoFAtotXA/wJOq26LgsPr3FT11uw2qzHDPZfK4ZFBCqxrqFEBgIh0AT8ELlHVP9e6PUEgImcBr6jqoyJyctjHs4JZAaraU2i9iBzOeKE3GC/09l5V/c8qNrFs3M7NQUQuAM4CujX6wbw7gbfl/H8o8FKN2hIKItKKEcu0qt5S6/YEyAnA2SLyfqAdOEBEUqraG8bBbOB6FSil0FsUEJHTga8Cf62qka99LCJTMM6rbuBF4FfAR1X1qZo2LCDEPLVvAF5T1Utq3Z6wyPYwP6uqZ4V1DGvDtJTD14HpwN0islVErq11gyoh68D6FHAnxiHyg0YRyywnAMuAv8n+XluzPTJLidgepsVisfjE9jAtFovFJ1YwLRaLxSdWMC0Wi8UnVjAtFovFJ1YwLRaLxSdWMC01J5tN5wUROTj7/0HZ/xN5290nIu/LW3eJiKwr45jnNGACCkvIWMG01BxV/T2wHviX7Kp/ATaoan5J5e8C5+WtOy+7vlTOwWQm8k02wN3SxNg4TEtdkJ269yhwPXAhcEQ2c1DuNnHgWeBQVX0zm0jifkxNaRWR/wl8BJgK/EhV/yH7ufOBz2Lmh2/DiPPtwOvZ5W8xgfjXAh3Ab4EVqvpHEbkP+AUm+Ps2Vf1KWN+Bpf6xT0xLXaCqw1nBuwM4LV8ss9tkROQR4HTgVkzv8vtZsTwNeCcmVZsAt4nIEiCDSYZygqruEpGDVfU1EbkNuF1VbwYQkW3Axar6cxG5EvgHwJlGeKCq/nWY52+JBnZIbqknzgD+ACzw2CZ3WJ47HD8tuzwOPAa8CyOgfwPc7MzjV9XX8ncoIm/BiOLPs6tuAJbkbPL9ck7G0nhYwbTUBSKyCJOd/ljgf4jIW102/THQLSJHAtOcxLiYXuU/q+qi7PIOVf1Wdn2ldqe9FX7e0iBYwbTUnGw2nfWYPI07gC8BXy60raruAe7D2DpznT13AiuyOR8RkdkicghwD/CRrP0TxxMP7MbYLVHV14E/ishJ2feWAT/HYsnDCqalHrgQ2KGqd2f/Xwe8S0Tc7IbfBd6DKSUBmLIZwHeAh0TkSeBmYHo269Aa4Oci8gQmLR3Zz/7PbOGsvwQuAL6UtWUuAq4M9AwtDYH1klssFotPbA/TYrFYfGIF02KxWHxiBdNisVh8YgXTYrFYfGIF02KxWHxiBdNisVh8YgXTYrFYfPL/A8zs1GOPVeBNAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Spiral Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Uncorrelated Bernoulli Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.ubern_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.ubern_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Uncorrelated Bernoulli Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Logarithmic Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.log_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.log_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Logarithmic Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Fourth-Root Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.root_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.root_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Fourth-Root Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Sinusoidal (4$\\pi$) Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.sin_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.sin_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Sinusoidal (4$\\pi$) Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Sinusoidal (16$\\pi$) Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.sin_sim(100, 1, period=16*np.pi)\n",
+    "x_no_noise, y_no_noise = sims.sin_sim(1000, 1, noise=0, period=16*np.pi)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Sinusoidal (16$\\pi$) Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Square Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.square_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.square_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Square Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Diamond Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.square_sim(100, 1, period=-np.pi/4)\n",
+    "x_no_noise, y_no_noise = sims.square_sim(1000, 1, noise=0, period=-np.pi/4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Diamond Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Two Parabolas Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.two_parab_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.two_parab_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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WfnxTFkY2SGLzKZVHUh5MtUS5GbUS8bDr7HR/qHXrCtertLQPqtpGXYDzgO/4li8A/j2rThMw0Pt+CfBIseOGChAI6JnfDbqWCYk2sNcTaTVjJJVyX+VLfeuO/PebMCHwfzmMfYKU2FinAQ/4lr8AfKFA/QbgnWLHDSVYm5pKEq7doI82tpbejmHCMMFEYbcO+vtGOnDa0aE6cGBwoVoFG2ucgrU/8CJwOL2DVxOz6hzi+/4R4Ilixw0lWDs6gv8oPgGrEyaU3lYdU00vBP8fvKnJFRPmhanm4FNkbbW3lxYT3hB+QDoVgtX1kw8Cz+O8AxZ5664BPux9/wrwtCd0fwEcXeyYoXMFdHTkz3oSpJiQLUq1/rjFkiabKSc31XzwReLVUcqrf6aUcTKpEayVKGUnYenoUB06NLyArWYWk5RRLRepfAK80lpYLdDR0dcyVqnsUqEfsoMHh/9vlqn8lCJYLaQ1m7Y22L4d2tvD7b9sGcycGW2fqkylQkWrNWocZMA3SfHoSQvN/etfe793dVVmzqmSvToyo/3+zpVCays8/XS4fcMQVAKnpUSaNrBc80AKtddKvg5W61UzTRprHNFvhQaYojDXlDKAVbReR4dqY2Mi/oOYKSBi2tvD/7AiqTLoVdoOWg2vgDTZWKsdrVRMkJdrron0QdHaGrsw9WOCtVKUI2BTosHWSqhoWrwCqn29iwnycgV92Q+Kcsc4KjiIbIK1knR0lJ7yP0UCNpHx3jVMta93MUFersYZ+kFRqttUrtJaWd9yE6zVoFzttQo3QhiSkPGqnqj29Q4iyMsx14R6UIwYUd7/qEqKignWalKucT2BGqxFRxUm6utTzetdaUFe8vHD+KKC+89V+cY0wRoHUWiwMdwsRmnUgkZfaUFe8Pjl2lBjVERKEazi6tcOU6dO1TVr1sTXgZkz4eGHyztGe7ubl8VIHJk5yrLJTIBn5CGK/8Whh8Jrr0XTnxCIyG9VdWqQuhYgEDUrV7rn6oQJ4Y+xbJlzhvbywCbNgbyeSVTO0TSwcKG7l8sVqq2tsQrVUjHBWimefho6OqCxMfwxli1DRfjkHOHbG2aiWnqOTCNaEpFzNA10dsKwYU5JCMvQoe4/pOoUlhRhgrWStLXB7t3uxggZIiteOYOH2YdwPp1VnaLa6Isl2C7CwoXu1WrOHNixI9wx+vd3AnX79tRmfjfBWi2WLnU3y9ChoXYXXELaTubQjfCHDcNMbY2BKGZ+qDnTTkaYijgNNcy4TXt77/DU3r2pFag9BB3lSkuJzSugVKLwIjBPgkQRZLS9FrwKeggbcppdEujPnQvM3SpFRHVzgnNjSeU/NP0EFZipjmzr6FAdNCi6+7VSOQkrRCmC1UwBcZPxImhtLf9YO3Y429YwMxNUm0WLgk0Gmkqvgs5OZ/ecMwd27SrvWP4BqTffTP8rfx5MsCaFjIDt6HCGu3LICFgRE7JlEtQeGlRgpsqrYObM3imk9+8v71gZG2qKB6RKIqhqm5aSOlNAIaI0E4Az/iUsfDbJlGIPDfqKn3gba1S2/xo0T2E21hojbDx1DQwYxEkp9tBSBGbicjF0dKgOGxbdvTVsWAJOKnoiE6w4D58bgh4sCaUmBaufqDUKKGvmylqm1BR4iROYxYj6Xjr00LjPqKKUIlgL2lhVdT9wgohIxW0SRjCWLnW3cdg5uXKxf3+vTdYXSlvvBLGHdnbCqFG9psjt2+F733N5AxJnSsyEl2ZKOVFR2bS3pyrktOIUk7zA14AVwAXARzMlqOSudql5jTWbKBIEFyp1PK13sdf7jg7VAQMOvGSJcy2OIjl7rlJn9noidrcaCXQB7wc+5JVzKiHkjRAsXQrd3e5W7+iAgQOjPf66db0aTkNDXWmzxaKsFi1yQULZ7NkTU8ixX33OlEx4qVOSymfw4F7RahnY8mJpA2uRzk645BL3XlpJmprgG99I4DtvdejXL7+8EnHPu4ozdixs2lTZNlpbU5cEpRJEmjZQRMaJyL0i8oaIbBaRn4jIuPK7aVSMtjbYtq1Xi21qqkw7XV19bbN14jOb8W0tpJNUxC+1sxOGD++rkVZSqE6Y4E7ShGrJBDEF3IGzsR4KjAX+01tnpIG2NhfhEvWAVy78gQmZMmhQTQnbzk6XtjFXsusMjY2Fs10FCjrI9VqfGR2rFP6oKFWX+tIIRzEjLLA2yLqklLobvApL1L6LpZSUxYj7yefbGvTUcg2IzRvQoXsGxfRb1OEgVFiIePDqTRGZIyINXpmDG8wy0ozfXJApldZoM2SbEPxl4sTq9CEk+UJXRdwlLBb+ftj8mWzfKXTTW27fO4cBuypsD8/2mGxttUGoChJEsM4HPgH8GXgd+DjwqUp2yoiJjI9sR4ezl8aB3wshu/TvH7tZoahvaya+Pk+ZvufhnuTl/lIxRNwDM+M5kilmN60oQQTrYar6YVUdrapjVHUWcFgUjYvImSLynIisF5GrcmwfKCI/9Lb/j4i0RNGuUYRsbTaKzFtRkB3IELQMH16aQM4YQXMc66UNfbXNTHlpgwSa26lqkTaNje4B2d1tGmkMBBGs/x5wXUmISAPwTeAsYAJwvohkz8B3EfCWqh4J3AR8tdx2jRBkMm9ltNmQsyDExvbtpQnkOXPyjk7l0jYrrnUGxZ+Ff/fuunWDSwL9820QkWnAqcBoEbnct+kgXA6BcjkJWK+qL3rt3Q2cC6zz1TkXWOx9Xw7cIuIitSNo3whDW9uBf9iFC6MNjzSCYf6liaWQxtoIDMMJ3+G+8hecnbVcxgKv+pY3euty1lHVfcA7QIWcMo3QZGyzfq22Ur6z9YhIXzcos5Mmnrwaq6o+CjwqIneqagGvvdDkenvK1kSD1EFEFgALAMYnMmNwnZHRahcudDGg5SZJrmeGDoVvf9te61NGEBvrd0RkRGZBRA4WkQciaHsjfQfBxgHZYSQ9dUSkP/AuYGv2gVT1VlWdqqpTR48eHUHXjJJZuNCN2mdnTzKhWh65gi4sA1niCSJYR6nq25kFVX0LGBNB2/8LHCUih4tIIzAbF+HlZwUw1/v+ceARs68mhM5Ol/DFhGg8LFvWe+1HjYrdDc3oSxDB2i0iPe/XItJMjtfxUvFspp8BHgCeAX6kqk+LyDUi8mGv2m1Ak4isBy4HDnDJMqpAvvDKPXvi7pkBuQMuTKONlaLZrUTkTOBW4FFv1QxggapGYQ6IHMtuFRFJt49OmJCMWPbOTrj0Uifckkp7u/myRkCk2a1U9b+B44EfAj8CTkiqUDXKIFd2+TiFaq5RcH9JglCFvkluCpU8s+9Wxa7lNxsUmmrWiIwgaQMFOBM4XlX/ExgiIidVvGdG5fEL0zj8UJua8gvQWhsFb2tz87VkneddQ9vpxglYf6kYGzb0mg3MNlsxgthYlwLTgPO95W24iCkjjfhH76slTDPhldnCs1jGkjqg/7eXMnyI0o/eMn9AB7uGVcEP2G+bHTDAhGyEBBGsJ6vqPwO7oMcroLGivTKixZ8gudKv+P6wSguvLEqu6V9m3tHGoG1vHmhKqGRinH37TJONkCCCda8X168AIjIaqMakE0Y5dHa6+YkqkSA5k4KuublHE+3sUFqalX7fWmpmvBLJWAm6uwvM7porzWMl5jiDXk02AdnEUkuxhK1AG86fdCNwLfAccF7QhK/VLnWf6Lq1tdgwSrhSYLbWYrOZGlWgo0N16NDK/PaWEFtVNdpE16raCVwJfAWXj3WWqv64UoLeCIHfz7RI2rpQtLcXHIVftAh27uy7bufOmGYqrVfa2txbiV+bbYzYYpfxLujXz/xki5DXj1VE/gv4PvBTVd1R1V6VQd34sS5c6GLIKzUVaAm+j/lmK63aTKVGcXz+tkrEaQ7rJMtWVH6stwLnAC97yaZneaGnRpxkXKSWLYtWamWP3JfgUF40q74RPz5/22cbJkTr2vXww+6eNHtsD3kFq6rep6rnA+OBe3Ax+6+IyO0i8oFqddCgMv6mmSk7Ihi5v/ZaGDKk77ohQwrPVGrEx8Tup3tcu9roYAtN0QjZjFeBjV4WH7zyF2Ay8Dtgfyn7VbPU1OBVR4dqQ0N0gw+DBlVsRKmjw81gKuI+beAqueSbafbRxogHPmtssIsoB69E5G9E5LMi8ivgp8CDwAmVFPZ1z8SJvW5SUficZjTTv/61Yv6kgVyGjESQ7w3j1dt9U/BMyJ4lKQSZwa5S5xyrAfIKVhG5WEQeAZ4E3g1cqapHqOrnVXVt1XpYb4wd62YqLYf+/UPbS43aJ1dQwq23Zj0Mn36617ug3Nkg/HOO1UmEVyGN9VTgOtwsrZ9V1V9VqU/1RWeni6jJ2FA3Zef6LpHWVti711RGow+ZiWf79XOfEPANw59kJgohm4nwGjSopgVs0bSBaSM17lZRTsBn03cYBejshAUL+voaDxmSQ0sthYkTy3+zAjj0UHjttfKPUwUiTRtoRIzfXaoc/BPMbd9uQtXIS0UCODKmgvb23hDnMGzaVJPJuQvZWO8XkZbqdaXGiUqggruZu7tNmBqBeOWV0taXxNKl7l6MwkyQGeyaODGCjsVLIY31TuBBEVkkIgOq1J/aY+bMaARqa6sNRsVIto0yTebBqgRw+G2x5Wqx69a5C52mi5xFoQCBHwHHAQcBa0TkX0Xk8kypWg/TSmenuznKid0fOrT3db8OQgaTSsZGuWGD+yk2bHDLafnfhw3gCP0wyWixqjBiRPH6uVB1g1wNDak0ERSzse4FdgADgeFZxchFZ2evD2qIgcGePdrbzXaaENKeZCaQe1UWkT1M3nqrPA22u9u97aVNg80XOYCbjmUdzuVqSNCIg7hLbJFXZURJdXvlHYbqZ5ssZClpiOT+6UTi7lnlyBed1dxc5oEnTEhtRBcRRV4twuVdvUpVdxaoZyxcGDpKSoEHaaUfyrvYzi1bTUNNGvWYZKZiA14Zb4JyIruWLUt8oEEhG+t0VU3IVJgJZeFCZwMKMTClwG4aaKODM+m1n9bynzWt1GOSmYo/TDICtrU13P779sG8eYkVrubHGoZyU/e1tvL9DmXkkH38gF4Ntdb/rGkljI0y7VTtYbJyZXgNNhPFlUQ3jaA2g7SUittYy5n6ZOjQPmmfLCOUkWSqfn9mGgz7/xKpqP2VEmysFtIalM5O+Kd/gh0hJlMYMcKNjhqGEYxyQmb794c774z8lcJCWqMkkyRlzpzShWpDg/NDTaFQTbNDvFED+ENmSyVjIogxgssEaz4yEVNhBGpTkxOo+/ZVxBBXaaGXdod4o4ZYupTODuW7Q9vZj5Q208G6de4/PHNmBTuYh6A2g7SUsm2sHR2qjY2Js+/4u1fpqaYr5sNoGCWS636fN6BD9zYOKf0/WuafBLOxhrSxhk3lV8VZKltanAaZTXOzy6sZBTbrqpEU8t3vn23qZMnuS1x0YimU8V9NvI1VREaKyEMi8oL3eXCeevtFZK1XVlS0U2GFant7VeP4K5qpyCOJDvFm861P8t3Xt2xtg23bSnfTyswoW+n8A0FV2ygLcD1wlff9KuCreeptL/XYoUwBHR354xbzlWHDYvGPqsZrejXMDWnuj1GcqFy1At3vYcNkSzTdUYIpIC7B+hxwiPf9EOC5PPWqI1hL8Z2r4EynQaiWkEmSj22cNt8kXYe0EOQeDXpdA9/v7e2lC9aGhpLOKw2C9e2s5bfy1NsHrAGeAGYVON4Cr96a8ePHl3SxVDW4ttraWvqxK0C9/dnjSoJimnI4ij0IS72uJd3vpQbwlEAiBCuwEvhjjnJuCYL1UO/zCOBl4G+LtVsRjbWpyf5NMRKFxhrmYZQG74gkPmSLPQircl0PPbS4UK1BjTWQKSBrnzuBjxerF9rGmv0IhQNCUI14KFdzDLt/uZpypYVeUjXqYoKzqm8ghTTYGrSx3pA1eHV9jjoHAwO976OAF4AJxY4d2o81iY9+o4ewP0+hNLnFNKRyNKt69jcudu5V73dHhxts9kvwED7naRCsTcDDnrB8GBjprZ8KfMf7firwFPB77/OiIMeOLdG1kTjyvYgE1ZDKEY7VEB5JTsBd6EGYVE27GIkXrJUsJliNDMVM50E1zzCacjWEXlI11iCk8QWxFMFquQKMmqU/TnZyAAAW50lEQVRQ0ETQyfQWLXLHGT/e1Q+a+qEaQRZpTsDd1uYiBbu73Wet5bY1wWrULPmEWEND5SfTq4bQq8cE3GnBcgUYNUtGOPpnWB0yJJjwiSInQzkar5E8Ep8rwDCqQTkaXRQ5GdLyumt5GKKnf9wdMIxK0tYWTqCNH59bY621yR6ztfqMyQOS+yBIA6axGkYO0jwwVAqLFvU1lYBbXrQonv7UCiZYU4a9tlWHehkYqkYaynrETAEpwl7bqktYM0KaqBeTR7UxjTVF1PJrm2ni8VAvJo9qY4I1RdTqa1vUkxdGKaRrXeDXi8mj6gQN0UpLqeWQ1lJDGNMSNhhlaGaUcehpjWk3KgOWKyAekpQmLk1CoVCe8VKJUkinORbfiB4TrDGQtClT0iQU8vVVpPTrF2XykyRnjzKqTymC1UJaI6Ia01KXQpqmsO7shAsuyN3fUq9flL9D0n5TI14spDUGkjawlMQprPPR1pZbqELp1y/KUW4bMTfCYoI1IpImyNImFJqbc68v9fpFOcptI+ZGaILaDNJSat3GWmqfkuQVUItZ5Y36ARu8ioekCbIkEeVc84YRB6UIVhu8MqqCDQSlB8sjmxsbvDISR9IG98JS65FYUUfB1SsmWOuEuMM8kza4F4Z6EDq1nI+iqgS1GaSl1HJIa1iSEOZZC4NTaQq6CIsFReQHs7GajdVPUpzm0267S1PQRVjMFp4fs7HGRFLtb1HaN8s5VlrmgMpHLZgzipE2/+ekYoI1IpJsf4tSINSDcMlHPQgdC4qIiKA2g7SUuGysSba/JcHGWiuYr239Qgk2VtNYIyJJ7kTZJgmwMM+oSLs5w09STVe1gA1eRURSjP7Z82KBe12tJ+FnFMfuk9KxwasYiMr+Vq4WYX6IRi6y76tLL7X7pJLYLK0RkXnKl+NOFMUsrEkySRjJINd9lQ+7T6IhFo1VRM4TkadFpFtE8qrWInKmiDwnIutF5Kpq9jEM5drfotA262XU3uyDwcl1X+UjqvukGr9P0DZiuVeCjnJFWYBjgPcAq4Cpeeo0AH8CjgAagd8DE4odO82RV1FEvdTDqH09nGOUFJpTrBLXsBq/T9A2ouwLaYm8EpFVwL+q6gGjTSIyDVisqv/gLX8BQFW/UuiYaYy8ykQk5XtFK3UArFiE0969e9m4cSO7du0qq99xsXEj7N9/4PqGBhg3rvr9STr5rle/fs6zY+9eeO21QQwfPo7ZsweU3V41BnKDthFlX0oZvEqyjXUs8KpveSNwcq6KIrIAWAAwPmXvvLlGZ/2EGQBrazvQDOEXtt/+9kZmzhzO0Ue3ICLhOh4jO3bk33bMMdXrR7Xp6oLXXoM9e6CxEcaOhaam4vuNGeOEiz/stl8/J1yamtxba1dXF9u2bQQOL7uf1bDzB20jrjGHitlYRWSliPwxRzk36CFyrMupXqvqrao6VVWnjh49OnynY6CQ/SsqH9HsqLCxY3exdWsTW7emT6iCEyqlrE87XV2wdi289JITquA+N2xw24rR1OTupcz1aWzsFaoAIkJTU1NkbzDVsPMHbSOuMYeKaayqOrPMQ2wEDvMtjwM2lXnMxJHvySkS3WtTtvB2yUSE114LpvEkjbFjc2tgY8fG16dK0dV14Llm6O4m8G/Y1FS4XpRvLtdem9tHNsrQ36BtVKMvuUiyH+v/AkeJyOEi0gjMBlbE3KfIqcYTNZ/wzmg/aaOYBlZLvPZa4cxZSfwNqxGdF7SNuCIF43K3+oiIbASmAf8lIg946w8VkfsBVHUf8BngAeAZ4Eeq+nQc/a0k1UjskU9Ix/nqLCJcccUVPcs33ngjixcvDrx/UxNMngxTp7rPMEJ13rx5LF++POe2yy67jMceeyzQcb74xS+ycuVKAG6++WZ2+tSjYcOGld4xH/kE5/z5pwKl/4azZ8/mhRdeKKtPQahG6G/QNuIIQ45FsKrqvao6TlUHqurfZEb+VXWTqn7QV+9+VX23qv6tqtZQDqFeqvFEzSW8S3l1roQf4MCBA7nnnnt48803Q+2/b9++8juRh61bt/LEE08wY8aMQPWvueYaZs50lq9swVou+QTn7bf/OpT5o729neuvv778jnmYP3FukmwKqBsq/UTNFt4NDcFfnSuVDrF///4sWLCAm2666YBtGzZsoLW1lcmTJ9Pa2sorni1j3rx5XH755Zx++ul8/vOfZ/HixcydO5czzjiDlpYW7rnnHq688kqOPfZYzjzzTPbu3Qs4wXfiiScyadIkFixYQDEXw+XLl3PmmWcC8Jvf/IaPfvSjANx3330MHjyYPXv2sGvXLo444oiefi1fvpwlS5awadMmTj/9dE4//fSe4y1atIi/+7u/45RTTmHz5s0HtLd48WLmz5/P+973Po444giWLFnSs+2++77O7NmT+Md/nMT3v39zz/oZM4bR3Ax79rzOjBkzmDJlCpMmTeKXv/wlAA8++CDTpk3j+OOP57zzzmP79u0ATJ8+nZUrV0byYEpyqszYCerwmpaS5gCBarFu3brAdSuVDnHo0KH6zjvvaHNzs7799tt6ww036NVXX62qquecc47eeeedqqp622236bnnnquqqnPnztWzzz5b9+3bp6qqV199tZ522mm6Z88eXbt2rQ4ePFjvv/9+VVWdNWuW3nvvvaqq2tXV1dPunDlzdMWKFT3H+/GPf3xA3y688MKeOnv37tWWlhZVVb3iiit06tSpunr1al21apXOnj37gOM0Nzfrli1beo4F9Bzrc5/7nP7bv/3bAe1dffXVOm3aNN21a5du2bJFR44cqXv27NE1a9bopEmTdMOG7fr449v08MMn6N13P6lvvumun6rqjTfeqF/+8pdVVXXfvn36l7/8Rbds2aLTp0/X7du3q6rqddddp1/60pd62ps5c6auWbPmgH6Ucl+4c63MvZFUKCFAIMl+rEYCqKQf4EEHHcSFF17IkiVLGDx4cM/6xx9/nHvuuQeACy64gCuvvLJn23nnnUdDQ0PP8llnncWAAQM49thj2b9/f4+meeyxx/Ky51bxi1/8guuvv56dO3eydetWJk6cyIc+9KG8/Xr99dfJuO3179+fI488kmeeeYbf/OY3XH755Tz22GPs37+f6dOnFz3HxsZGzjnnHABOOOEEHnrooZz1zj77bAYOHMjAgQMZM2YMmzdvZvXq1XzkIx9h/PihjB8PbW0fZfPmX9LUdFzPfieeeCLz589n7969zJo1iylTpvDoo4+ybt06TjvtNAD27NnDtGnTevYZM2YMmzZt4oQTTija/0JYXor8mCnAKEilvRYuu+wybrvtNnYU8Pr3uwINHTq0z7aBAwcC0K9fPwYMGNBTt1+/fuzbt49du3axcOFCli9fzlNPPcXFF19c1F9z8ODBfepMnz6dn//85wwYMICZM2eyevVqVq9eHcgG6+9TQ0ND3lfwzHn462mAqMgZM2bw2GOPMXbsWC644ALuuusuVJUPfOADrF27lrVr17Ju3Tpuu+22nn127drV50EWlnrJSxEGE6xGQSrttTBy5Eg+8YlP9Pnjn3rqqdx9990AdHZ28t73vjf08TMCctSoUWzfvj2vF4CfY445hvXr1/csz5gxg5tvvplp06YxevRourq6ePbZZ5k4ceIB+w4fPpxt27aF7q+fGTNm8NOf/pSdO3eyY8cO7r333gO05A0bNjBmzBguvvhiLrroIp588klOOeUUfvWrX/Wcw86dO3n++ed79nn++edz9r1U6mGqmrCYYDUKUg2vhSuuuKKPd8CSJUu44447mDx5Mt/73vf4xje+EfrYI0aM4OKLL+bYY49l1qxZnHjiiUX3Ofvss1m1alXP8sknn8zmzZt7NNTJkyczefLknE71CxYs4KyzzuozeBWW448/nnnz5nHSSSdx8skn8+lPf5rjjjuuT51Vq1YxZcoUjjvuOH7yk59w6aWXMnr0aO68807OP/98Jk+ezCmnnMKzzz4LwObNmxk8eDCHHHJI2f2r99kkCmEzCNQhzzzzDMfUclB9BLz3ve/lZz/7GSNGjIi7K5Fy0003cdBBB3HRRRcdsM3ui8LYDAIJwPz70s3Xvva1HjevWmLEiBHMnTs37m7UPCZYK4D596Wfk08+mcmTJ8fdjcj51Kc+Rf/+1XEGqmflwgRrmeS6eWzeKaPeqXflwgRrGeS7efIlrK7BN0vDyEm9KxcmWMsg383j81/vg/n3GfVCvQcPmGAtg3w3yf795t9n1Df1HjxggjUPQQzv+W6SjD+f+fflp9y0gWE49dRTK3p8o5d6Dx4wwZqDoIb3QjdPHDkgK0YFhnfLTRsYhl//+tdVa6veqffgAROsOQhqeK+Lm6dCw7th0gb6KZRq7+tf/zqTJk1i0qRJ3Hxzb6q9TNLp118vLdWeEY6aUi5KJWgarLSUKNIG5puHXaTsQyeCktLDVSg3XJi0gX6Kpdrbvn27btu2TSdMmKBPPvlkT5uq4VLt1QOlpg2sNyghbaBprDmod8N7Hyo4vOtPG+jn8ccf55Of/CTg0gauXr065/6ZVHujRo06INXe0KFDGTZsGB/96Ed7NNIMJ554InfccQeLFy/mqaeeYvjw4TzxxBM9qfamTJnCd7/7XTbk85szKk7agwtMsOag3g3vfajwU6bUtIF+qplqz6getRBcYII1B3VhOw1KhZ8yUacNrFSqPaN61EJwgc0gkIe2tjoVpNlkLsKiRe71f/z4XreHiLjiiiu45ZZbepaXLFnC/PnzueGGGxg9ejR33HFH4GP5U+0BeVPt3XDDDQwYMIBhw4Zx11139Um1t3v3bgC+/OUv8+53vzuCMzRKoRaCCyxtYB1i6eGMXCTlvmhpyR0W3tzsvAviwtIGGoaRWmphjMMEq2EYiaIWxjjMxlqnqGre0Xaj/kiaSTDtYxymsdYhgwYNoqurK3F/JiMeVJWuri4GDRoUd1dqBtNY65Bx48axceNGtmzZEndXjIQwaNAgxo0bF3c3agYTrHXIgAEDOPzww+PuhmHULGYKMAzDiBgTrIZhGBFjgtUwDCNiai7ySkS2AGHTEo0Cqpd5OTltx92+tW1tp6HtZlUdHaRizQnWchCRNUFD1mqp7bjbt7at7Vpr20wBhmEYEWOC1TAMI2JMsPbl1jptO+72rW1ru6baNhurYRhGxJjGahiGETEmWA3DMCKm7gSriJwnIk+LSLeI5HW7EJEzReQ5EVkvIlf51h8uIv8jIi+IyA9FpLGEtkeKyEPevg+JyME56pwuImt9ZZeIzPK23SkiL/m2TYmyba/eft/xV1TxvKeIyOPeb/MHEflH37aSzzvf7+fbPtA7j/XeebX4tn3BW/+ciPxD0PMsoe3LRWSdd54Pi0izb1vO6x9h2/NEZIuvjU/7ts31fqMXRGRuBdq+ydfu8yLytm9bued9u4i8ISJ/zLNdRGSJ17c/iMjxvm1lnXdOgs6TXSsFOAZ4D7AKmJqnTgPwJ+AIoBH4PTDB2/YjYLb3/VtAewltXw9c5X2/Cvhqkfojga3AEG/5TuDjIc87UNvA9jzrK3rewLuBo7zvhwKvAyPCnHeh389XZyHwLe/7bOCH3vcJXv2BwOHecRoibvt032/anmm70PWPsO15wC157rUXvc+Dve8HR9l2Vv3PArdHcd7e/jOA44E/5tn+QeDngACnAP8TxXnnK3WnsarqM6r6XJFqJwHrVfVFVd0D3A2cKyICvB9Y7tX7LjCrhObP9fYJuu/HgZ+r6s4i9SrRdg/VOG9VfV5VX/C+bwLeAAJFueQg5+9XoE/LgVbvPM8F7lbV3ar6ErDeO15kbavqL3y/6RNAVPn6gpx3Pv4BeEhVt6rqW8BDwJkVbPt84AclHL8gqvoYTgnJx7nAXep4AhghIodQ/nnnpO4Ea0DGAq/6ljd665qAt1V1X9b6oPyNqr4O4H2OKVJ/NgfefNd6rzI3icjACrQ9SETWiMgTGRMEVT5vETkJp/X8ybe6lPPO9/vlrOOd1zu48wyyb7lt+7kIp0llyHX9o277Y961XC4ih4Xsd9i28UwfhwOP+FaXc97l9K/c885JTeZjFZGVwP/JsWmRqt4X5BA51mmB9YHaDtCu/ziHAMcCD/hWfwH4M07o3Ap8Hrgm4rbHq+omETkCeEREngL+kqNeJc/7e8BcVe32Vhc871yHKdbfAnWC7FuIwPuLyBxgKvD3vtUHXH9V/VOu/UO2/Z/AD1R1t4hcgtPa319Kv8toO8NsYLmq7vetK+e8y+lfueedk5oUrKo6s8xDbAQO8y2PAzbhkjeMEJH+npaTWR+obRHZLCKHqOrrngB5o0AfPgHcq6p7fcd+3fu6W0TuAP416ra913BU9UURWQUcB/yEKpy3iBwE/Bfwf73XtUDnnYN8v1+uOhtFpD/wLtyrZJB9y20bEZmJe+j8varuzqzPc/2DCpiibatql2/xP4Cv+vZ9X9a+qwK2G6htH7OBf87qVznnXU7/yj3vnJgpIDf/CxwlbiS8EXcjrFBn7f4FzvYJMBcIogFnWOHtE2TfA2xQnlDK2DxnATlHQMO2LSIHZ16zRWQUcBqwrhrn7V3ne3F2sB9nbSv1vHP+fgX69HHgEe88VwCzxXkNHA4cBfwm0FkGbFtEjgO+DXxYVd/wrc95/SNu+xDf4oeBZ7zvDwBneH04GDiDvm9LZbfttf8e3CDR47515Z53EFYAF3reAacA73gP7HLPOzfljn6lrQAfwT2ldgObgQe89YcC9/vqfRB4HvfUXORbfwTuj7Ye+DEwsIS2m4CHgRe8z5He+qnAd3z1WoDXgH5Z+z8CPIUTLB3AsCjbBk71jv977/Oiap03MAfYC6z1lSlhzzvX74czH3zY+z7IO4/13nkd4dt3kbffc8BZIe6xYm2v9O69zHmuKHb9I2z7K8DTXhu/AI727Tvfux7rgU9F3ba3vBi4Lmu/KM77BzhPkr24//dFwCXAJd52Ab7p9e0pfB5B5Z53rmIhrYZhGBFjpgDDMIyIMcFqGIYRMSZYDcMwIsYEq2EYRsSYYDUMw4gYE6xGahCRw8RluRrpLR/sLTdn1VslWVmpROQyEVkaos1ZIjKhvJ4b9YYJViM1qOqrwDLgOm/VdcCtqpo93fkPcA7qfnLlXQjCLFzGq8B4kVxGHWN+rEaqEJEBwG+B24GLgePUZVPy12kCngXGqYuJbwEew80LryLyOVzI8EBc2PDV3n4X4sJlFfgDToj/DJeg5R3gY8BwXNrEIThn8/mq+pYXhvlrXNTQClX9WqWugZF87MlqpApV3esJxv8GzsgWql6dLhH5DS7923305ltVETkDF6Z6Ei4aZ4WIzAC6cBFXp6nqmyIyUlW3iku6/DNVXQ4gIn8APquqj4rINcDVwGVe0yNU1Z9QxahTzBRgpJGzcOGLkwrU8ZsD/GaAM7zyO+BJ4GicoH0/LuPSmwCqekBuTxF5F054Puqt+i4uwXKGH4Y5GaP2MMFqpApx07J8AJcF/l+ykor4+SkuefXxwGBVfTJzCOArqjrFK0eq6m3e+nLtYjvK3N+oEUywGqnBy261DLhMVV8BbgBuzFVXVbfj0r/dTt9BqweA+SIyzDvmWBEZg0sO8wnPPkvG8wDYhrOroqrvAG+JyHRv2wXAoxhGFiZYjTRxMfCKqj7kLS8FjhaRfHbNHwB/h5smBABVfRD4PvC4l8R7OTBcVZ8GrgUeFZHfA1/3drkb+JyI/E5E/haXavAGz9Y6hcIJt406xbwCDMMwIsY0VsMwjIgxwWoYhhExJlgNwzAixgSrYRhGxJhgNQzDiBgTrIZhGBFjgtUwDCNi/n93HMWU6dP/GAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Two Parabolas Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Circle Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.circle_sim(100, 1)\n",
+    "x_no_noise, y_no_noise = sims.circle_sim(1000, 1, noise=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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zymduegXmcWX3+t//buPMU0eQYi1BJ4Q0SsKEtRpob/ecDFCBK2jt9lYBdu4s/xxbRggESZGzWV4jx0ZeVQMjR0JnZ97dCtTQ93tQIWVXqw+f/zeQe5ie4YmNvDI+oL3d90e2idzNx8RlNBjBuPRS/2MszhMpJqyVzuzZvofc1bYp+RkNRnCCdGTZJISRYsJaycyfD7t3ex/T1paOjAajMILktk6fHr0dVUqswioiM0TkJRF5VUS+n2P/HBFZLyLL3eW0OOxMLUGGMrrqmeiMBqM4Wn2GJQeYRyvOwkJpJjZhFZFa4ArgaKAJOElEmnIc+mtVneQuV5XVyDQT5BcQZCikkV5KnEIn7sJCaSZOj/Ug4FVV/Yuq7gB+BRwboz2Vhd8omzFjgjUXjXTj9/D0yG+Ou7BQmolTWMcCf8taX+tu680/i8izIrJURPbOdSIRmSsiy0Rk2fr166OwNX34pdPEXGfVmphlwu/huWpV3rzWJBQWSitxCmuuGsu91eD3QKOqTgQ6gOtynUhVF6vqVFWdOmrUqJDNTCEJVylrYpaZplwRtiyuvDLn5tQUFkogcQrrWiDbA90L6DHeTlU7VfV9d/WXwJQy2ZZuTvPp4/Pr1IgYa2KWmZUrvffnad2korBQQolTWJ8CPioi+4hIHXAicFv2ASKyZ9bqMcALZbQvvWzf7r2/xE6NUrEmZgz4PUxzpF5ZGl7xxCasqroL+CZwD45g/kZVV4rID0XkGPewM0RkpYisAM4A5sRjbYrwa0/H7K2CNTFjwe9hmif1ytLwisNqBVQaQ4d6FrJOwhjxTIw1OxwweLB5Q5FTW+td/KGtzf4BHlitgGrGS1RLJKyefGtixoTfBJKnnFIeO6qAfnEbYIRIhGGA3l5mpicfihPElhYT0rKzcCHcemv+mqw7dpTXngrGQgGVhF+5uBL+142Njpj2pqHBib0ZKUJyZTq6WDggLxYKqEb8ygMOGVLS6dPSk28DD0rEct5CwYS1Ujj1VO/9v/hFSadPQ09+roEHs2ZZwfyCyNUsMQrGhLVSeP/9/PtaW0tu3qUhWTzXwANVZ2CRea5ZJCDlrtIxYa0E/FQjhAEBaejJzxeWULUWbg/8vg9Wp7VkrPOqEkhB7mo5yNfBBjZ/Vx+8bhZUzXemEKzzqtqIMHc1TZx/fv4O7yTFghOBXwzHYiclYcKadvx+APX15bEjAbS0wLx5fcU1abHgROAXw/n2t8tjR4Viwpp2/CYLDDJjZwWxcCHccEOyY8GpwG/6bMMTE9a04zFZoALtVJ+iWOGQgFh2QGSYsFY4VkDayItfdoB9cYrGhDXNeHzxFbiXZisgbRSPX9EWIy8mrGlm5kzP3TNw5jtK2rBTIyVYtknRmLBWAZZqVNkEqY+Q9xibAj0SrGxghfIedYClGlU6Qco55jvmscfgzlc7+CuSc2ZPo3jMY61AFDidqy3VqAoIMjFjvmOuvDJAzRXrwCoKG9KaZrzqalbY/9XITU1N/n91Q4PTWpk1y/vrsItaaskz3nfIENiypXRDKwAb0loN+HgSVpe0OvCKn2ea/CNGeJ9jEV8nr+5aB1ZRmLCmFY/5ibqkpk9dUstnrUxylXPMJhMC6H1MdmPnW8Q7HXo5KLejYcKaVjzmJ7ph8Nd9425GZZBdzjEfGzf2Lfk4b563IFcSuQqgR+5oqGpFLVOmTNFKoa1NtaFBVcR5bWvL2ul8R3IuIrl3icT0QYyy0NCQ+//e0JD7+OzvV5fH96nnFy99FHpf8gEs04A65OmxikitiPw0Ql038lDKUzYN06gY4VPoLA/ZNRU8063KOAIriiZ7LPO1+Skv8Afc7IE0LJXisfo+ZT08jLY21cGDe24ePDj1jocRAM9WjhdeHitEaPEHRPW9jcNjDSKsFwG3AbOAL2eWoBco91IpwurZnG9t9f0RFP0DM6qT+vrYhTUsAexNWIJdiLD65rGKyDW5HV3N3y0dI5WSx5pv5oyGBli9xqPhFiDvcOfOnaxdu5bt27cHtmfrVti0yalSWFsLw4eXPKO2kSAGdnay1zHH0H/TptwH+OhEGOTLyQ1jWp32dqfz9vXXnZDY+ecXPnCmkDxW3yGtqvq1wi5vhMH55/cchghZ8TKv2isBprleu3Yte+yxB42NjYjXIAOXzk5H5IcP/2BbTQ2MHl1VExRULKpKZ2cna885h31inDlg3LjczkQYfQMtLeUdgeibbiUie4nILSLytoi8JSK/FZG9ymFcNVP0rKgBvj3bt2+nvr4+kKgCvPFGX4+hq8vZbhRGZyc8+ywsW+a8JqFQv4hQX1/P9v32i9WONEyxHpQgRViuAW4ETnDXZ7rbjorKKMMhyqdsUFGF/CmzHqm0Rg4ynn/mIbVjxwceWi7Pv7PTeXjt2AF1dTB2bHQtBBFxmiExkvmul9pkTwJBhHWUqmbHWa8VkTOjMshIHnV1uUW0rq78tqQZL8+/t2AWKsKVQrmb7FER5BG1QURmujmttSIyE0hAA8YoF2PH9nVmamqc7cUiInznO9/pXr/wwgs555xzij9hEcyZM4elS5fm3HfmmWfy8MMPBzrPD37wAzo6nKLil1xyCduyAuNDhw7t/rsQz98v/HLYYYcFsq03J554Iq+88krhbxw/vqjrVStBhPUU4CvA/wBvAv8CWIdWFXH33XDssXDQQfClL8F99zkx31I8pwEDBnDzzTezYcOGot6/a9eu4i/uw8aNG3n88ceZNm1aoON/+MMfMn36dKCvsGaTz8PPtd1PhP/4xz8Gsq03ra2t/OQnPyn8jatWFXW9aiWIsO6tqseo6ihVHa2qxwF7R22YkQwyI8DWrnVSYf7nf+C88xyxLYV+/foxd+5cfvazn/XZt2bNGpqbm5k4cSLNzc287g6RmTNnDmeddRZHHnkk//7v/84555zD7Nmz+exnP0tjYyM333wz3/ve99h///2ZMWMGO3fuBBzhO/DAA5kwYQJz587FL8Vw6dKlzJgxA4Ann3ySL3/5ywDceuutDBo0iB07drB9+3b23XffbruWLl3KZZddxrp16zjyyCM58sgju8+3YMECPvnJT3LKKYewadNbPa5VUwNtbedwyimn8OlPf5p9992Xyy67rFts29sv5qtfncBXvzqBG2+8pHt7xhN+8803mTZtGpMmTWLChAk88sgjANx7770ceuihTJ48mRNOOIEtbgreEUccQUdHR6QPJiOYsF4ecJtRgQQppFws3/jGN2hvb2fz5s09tn/zm9/k5JNP5tlnn6WlpYUzzjije9/LL79MR0cHF110EQCvvfYad9xxB7feeiszZ87kyCOP5LnnnmPQoEHccccd3ed76qmneP7553nvvfe4/fbbPe167LHHmDJlCgCTJ0/mmWeeAeCRRx5hwoQJPPXUUzzxxBMcfPDBPd53xhlnMGbMGB544AEeeOABALZu3cohhxzCihUr+MxnpvHAA7/sFse6OsfzHzwYXnzxRe655x6efPJJzj33XEaP3slLL/2Z3//+Gq699gmuueZxbr31l3R2PtPjmjfeeCOf+9znWL58OStWrGDSpEls2LCB8847j46ODp5++mmmTp3KxRdfDEBNTQ377bcfK1as6PvB+/f3vC9GcPJ2XonIocBhwCgROStr14eA2qgNM5JBlOOsP/ShD3HyySdz2WWXMWjQoO7tf/rTn7j55psBmDVrFt/73ve6951wwgnU1n7w9Tv66KPp378/+++/P7t37+72NPfff39Wr14NwAMPPMBPfvITtm3bxsaNGxk/fjxf+tKX8tr15ptvMmrUKMDxrPfbbz9eeOEFnnzySc466ywefvhhdu/ezRFHHOH7Gevq6vjiF78IwJQpU7jvvvuYOLHvcV/4whcYMGAAAwYMYPTo0eza9RZr1jxKc/PxDBo0hLo6OP74L/Pcc49w5JEHdL/vwAMP5JRTTmHnzp0cd9xxTJo0iYceeohVq1Zx+OGHA7Bjxw4OPfTQ7veMHj2adevWdT88uhkzxvfzGMHwygqoA4a6x+yRtf3vOHFWowooNmk7aKrQmWeeyeTJk/na1/KH7bNTw4b0Gu41YMAAwPHE+vfv331sTU0Nu3btYvv27cyfP59ly5ax9957c8455/iOOBs0aFCPY4444gjuuusu+vfvz/Tp05kzZw67d+/mwgsv9L4J0MOm2travE3wzOfIPm7wYOXDH4apUzN29X3ftGnTePjhh7njjjuYNWsW3/3udxk+fDhHHXUUN910U85rbd++vceDLAiKT6EWowd5QwGq+pCqngscoqrnZi0Xq2oR3YpGGikmaTuTKpTpaMmkCuVKhh8xYgRf+cpXWLJkSfe2ww47jF/96lcAtLe386lPfapo+zMCOXLkSLZs2ZI3CyCbT3ziE7z66qvd69OmTeOSSy7h0EMPZdSoUXR2dvLiiy8yPkdP+R577MG7775btL3ZTJs2jd/97nds27aNrVu3csstt/TxktesWcPo0aM5/fTTOfXUU3n66ac55JBDeOyxx7o/w7Zt23j55Ze73/Pyyy/ntN2L3VRGofRyFbwOEmO9SkSGZVZEZLiI3BONOUbSKGYEWKEjtb7zne/0yA647LLLuOaaa5g4cSI33HADl156adH2Dxs2jNNPP53999+f4447jgMPPND3PV/4whd48MEHu9cPPvhg3nrrre4sgYkTJzJx4sScgyzmzp3L0Ucf3aPzqlgmT57MnDlzOOiggzj44IM57bTTOOCAA3oc8+CDDzJp0iQOOOAAfvvb3/Ltb3+bUaNGce2113LSSScxceJEDjnkEF588UUA3nrrLQYNGsSee+5ZkC21pL9QelkLXvtVaQGeCbKtmAWYAbwEvAp8P8f+AcCv3f1PAI1+5yy0ulXqqkC1tZVchWjVqlWRmvjUU/mXtHD44Yfrpk2b4jYjdC6++GK96qqrcu5btWpV3u9Vl1tAPc2UWj2LsApdu3SJSHdETUQaIP/cY0ERkVrgCuBooAk4SUSaeh12KrBJVfcDfgb8uNTrZhPLlA2l4lUko7W1fHZ4UEi+ZlK56KKLutO8Kolhw4Yxe/bsot6b9kLp5Sx4HURYFwCPisgNInID8DDwHyFc+yDgVVX9i6ruAH4FHNvrmGOB69y/lwLNUsggdx+iTCWKDI+qHe2HL0zEzKxRjNQqNwcffDATc3Xfp5yvfe1r9OsXZCR7X9JYDCWbcs6sEaRs4N0iMhk4BKdj8N9UtbjhMj0ZC/wta30tcHC+Y1R1l4hsBuqBHtcXkbnAXIBxBdylWKZsiAilZ5nBjPcN5R97nen9L1cBEaMnURVvSfsYfs9SnCETpGyg4MRCJ6vq74HBInJQCNfO5Xn2DjEEOQZVXayqU1V1aib/MAiVNjfUj7fN77Eep/ddXw8TJzqpQhMnmqiWi0IyMgqhElKtii7FWQRBQgELgUOBk9z1d3Fio6Wylp5DY/cC1uU7RkT6Af8AbAzh2kBl1X8UYD5X9tmeRu/bKB6rnetN9gSKq1dH54UHEdaDVfUbwHYAVd2EM3igVJ4CPioi+4hIHXAiztxa2dwGZCLt/wL8we2dC4VyPsFCw2M+FMnRp5hU7zuO6lbFVoRKE1Y7NxkEEdadbg++AojIKKDEGWicmCnwTeAe4AXgN6q6UkR+KCLHuIctAepF5FXgLOD7pV63N+V6goVGgKlXMiTZ+y61ulUxFFsRKk1UQkZGJRBEWC8DbgFGi8j5wKPAj8K4uKreqar/pKofUdXz3W0/UNXb3L+3q+oJqrqfqh6kqn8J47pJouCRID7KH4n3HcFwlWKqW2Vzzjl9K0JluPjii5kwYQITJkzgkksu6d5ebEWoNFEJGRkVQZBkV+DjwDdwPMxPBE2SjWNJ0/TXRU/LW84BAhFN9j5kyBDdvHmzNjQ06DvvvKM//elP9eyzz1ZV1S9+8Yt67bXXqqrqkiVL9Nhjj+3z/rPPPlsPPfRQ3b59u65fv15HjBihO3bs0GXLlumECRN0y5Yt+u6772pTU5M+/fTT3ddUVb3wwgv1vPPOU1XVXbt26d///nddv369HnHEEbplyxZVVb3gggv03HPPLekzxsWGDaorVjgDMlascNaD4DVAoFxTYCcZChhH/54hAAAWEklEQVQg4FXd6g6cua5+p6ovAi+WQeerCq882sSEJCI0spjqVtn0rgj11ltv8eijj3L88cd3F2v58pe/zCOPPNJjKGgxFaHSRH29ZWHEjVcoYDHwRWC1iPxaRI5zO5mMkEhFHm3ERp555pksWbKErVu35j0m35iQXBWhNEDfZqYi1NixY5k1axbXX389qspRRx3F8uXLWb58OatWrepRGKYq8PgfGIXhVd3qVlU9CRgH3IzTO/+6iFwtIjZDawikIo82YiPDrm4VVUWoqsAr2dUjG8Xoi2/nlaq+p6q/VtXjgc8CBwAlTsxhQEryaMtgZJjVraKoCFU1eHn7BWSjGASqbvVh4FvAY8BfcAqhTAoaxC33kqbOK9Uiq2uVu7pV6kqAGcWw6q67rOPKA0LqvDodZ7TVx3BCAd9T1ceiFvpqIxXzqKfCSMNIDl5FWA4DLgA6VLXkAQGGYRjVQl5hVdX8kxAZyaW9PfHeZVTVlwwjKQQZeWWkCa9C2FlogLSkKIiq+pJRGqrat3qLUTR5hVVE7hSRxvKZYoRCAIUaOHAgnZ2dsYirVV9KHqpKZ2cnA7MmUDRKwyvGei1wr4hcB/xEVXeWxyQjavbaay/Wrl3L+vXry37tdb0LQ2bRv3/57DB6MvCVV9gr4upi1YRXjPU37rDWHwDL3GlZurL2X1wG+4xctLbCokVFv71///7ss88+IRoUnKOPdpr+vWlocKqLGTExYYKFAkLEL8a6E9iKM1vqHr0WIy4WLozbgqJJxaCIasRLVN2qYEZwvPJYZwAX4xSbnqyq2/IdaxhBySQsLFjglBsYN84R1YQnMlQ3V/admcLwRvJ1YIjII8A8VV1ZXpNKY+rUqbps2bK4zYiempr8QxCbmmBlqv5tRtz06we7d/fdXlsLu3aV354EIiJ/VtWpQY71irEekW+fkQC8evRXrSqfHUb6aW/PLaoAAweW15YKwfJY00pDQ9wWGJWCV+6zlRIsChPWtGK9PUZY2OiM0DFhTSt+vT3z55fHDqOsRDD9mDc21rgoTFgrFevJrTja22HuXCcPWNV5nTu3RHH1e3MBtXCND8ibFZBWqiYrAJzpWL2osP9ttdPYGMHginwnzWDfoW4KyQowjzXNWAdWVRHJ9GNeomoUjQlrmvHrwLI4a0WRijnSDMCENd34dGDtWrS4PB0cRlkIfTiw3xejqanIExsmrBVMLbvD6eAwEkFLCyxe7ESARJzXxYtLGA48b573fhu9VzTWeZV2Ro7Mm4eoQA3O/9eqRxl9sM7PgrDOq2oiYDpMSR0cRvVh+aslYcJaJiJL7PZpB56EcyHr4DB6YPmrkWLCWgYiSezOJo93IcASTrN6p0ZfvOoD1NVZHccSMWEtAwsWwLZe1Wy3bXO2F0pOz9fDuxjIdu6Z3W6/E6MnXvUBrr66fHZUKCasZSCsxO68ni/5VVOAT/0m2MytRpUwfbr3fnsKl4wJaxkIK7Hb0/P16uG16kVGNvffn3eXUuYiLxWKCWsZCCux29Pz9ctJtFFYRkAi6wuoIkxYy0BYid2enq/PBINdixbl9ELKXobOSDTvMaDHerF9AdVO3qlZjHBpaSk9dHX++Y4HkR0OCOr5CnCZzudbaxYyd+4H27PPl/FQMvYaFcjYsXl3KXAaS/pstxzoIlDVilqmTJmilUxbm2pDg6qI89rWlrWzqUnVacXlXHZR073a0OAsuQ5taIjjkxmR09zs+f24dkirfR88AJZpQB2yIa2VhkcnVvYQ18xhuf79It7TzBspxWcIa3ub5mwRlVSPoIKwIa3VzNChnrsvx+nEGjfOytAZPQm9yEsVE4vHKiIjgF8DjcBq4CuquinHcbuB59zV11X1GL9zV73H2t4OM2fm3d0F7DFYWbzYWTcPpYrw8liHDIEtW8pnSwpJg8f6feB+Vf0ocL+7nov3VHWSu/iKqoGjiEOG5N0twMuN07s708xDqRL8BgX84hflsaNKiMtjfQn4tKq+KSJ7Ag+q6sdyHLdFVb3btr2oeo8VfL1WwErCVRN+34cBA2D79vLZk1LS4LF+WFXfBHBfR+c5bqCILBORx0XkuHwnE5G57nHL1q9fH4W96cJcTiOb2bO99y/pm2JllEZkwioiHSLyfI7l2AJOM859QvwrcImIfCTXQaq6WFWnqurUUaNGhWJ/6mlt9d5vI7ESTWgDN9rbYffu/PtrauxBHAGJDgX0es+1wO2qutTrOAsFZFFTk7/JbzlViSVTbCeUTsVBg7yb+a2tvqP2DIc0hAJuAzLtk9nArb0PEJHhIjLA/XskcDiwqmwWVgI33JB/nyoMH14+W4zAhFZmcvp0/9hpBYhqEodlxyWsFwBHicgrwFHuOiIyVUSuco/5BLBMRFYADwAXqKoJayG0tDjftny88w6MH18+e4xAhFVm0quKFQDNzQWeMHlEXkS+SGIRVlXtVNVmVf2o+7rR3b5MVU9z//6jqu6vqp90Xy3CXgxf/7r3/lX2rEoaoQzc8IuhNzVBR0cBJ/QnDs8xzCLyYWIjryqdIE0968hKFKGUmfTLSw15auu4PMfQvPuQMWGtBvwyBBYtKo8dRiBKHrgxfbp3x+TAgaHYmU1cnmNSh2WbsFYD5rV2k8SOjly0tMDq1Y4+rl5dgKjOn+8fW73qKu/9RRCX5xhWEfnQCVoGKy1LpZcNLBqfkoIqEreFkdPWpjp4cM+PPXhwr9KLacfrfwxO6cAIiLMEpWcpzRChgLKB5rFWC34xNVX/8eQpJ6kdHaERpNURcodVhjg9x6K9+wgxYU0RJTdj/dJr7r8/uW3jEEhqR0do+HVY1ddHdmkr6NMTE9aUEEqva0cHjBnjfYxfelaKSWpHRyjMn+8/ku7SSyM1IYmeY1yYsKaE0Jqxb7zhvX/r1or1WhPb0VEq8+f7Z3Y0NVW30pUZE9aYKLRZH2oz1i/9qmKCjj2p2Oaqn6iKhJ63anhjwhoDxTTrQ23GLlzoncu4Zk3Feq0V11z1q/dQU+NdM8KIBBPWGCimWR96M9Yvl3HWrKrJbU0t06c79R68uP76Cnh6pA8T1hgoplkfejO2pcUJCeSbB0nVaWKauEZGSVkeQQYCgIlqXARNeE3LkoYBAvX1uZOp6+tjMKatzT+pvLU1BsPKT7kSzTPXKnqwQpD/WYSDAaoVChggEEuh6yhJQ6HrkSOhs7Pv9vp62LCh/PbQ2OjEVb1obo4suTwJhFpcOgD5bnlDgxP79aRfP+9ZAcApcN073mSURBoKXVc1GzcWtj1yggRq77+/okdmlXtUVtFZHsOH+4sqmKjGjAlrDCQuUd1nyuxuKnhkVrlHZRX1HQjSWQX+6XRG5JiwxkAiE9WDzit/6qnR2hET5X7YFfwdaG8P1lnV3FzQdCu5OtDSUgEs0QQNxqZlSUPnlWp5O0oC09patZ0icVS+Kug7MHBg6J2MuT5zXZ1q//7lvQ9pgQI6r2IXwrCXtAhrYmluDiauY8bEbWlOSnlgJfJh19amOnSo//+jiLKP+Ur9xVX+L+mYsBol8UJzq3YF+bU1NcVtag8qrt5q0BYEFPUhRYKfvgrK9fpSiLBajNXoQXs7TPnTQq6gFd9EvFWrYOzYcpgViIqqt9reDldeGezYtraicsIKiR9XRAWwMmLCavQgI07fYiH30uwvruvWQV1dOUzzpWLqrU6fDjNnOs6iH62tRSfa5upAq6uD/v17bou9YzWFmLAaPcgWoRl0BBPXnTudLuSYu48Tl8ZWDMOHB+v9h4IzAHqTa5j01VfDNddUYAWwMmMjr4we5BoRtJqxjGMdeaoK9KS1taQfeymUe/RU6Iwd67QAghDjfa5WbOSVUTS5modNg99g05imYCeIsXBLauuttrfDgAHBRHXIECemaqKaaPrFbYCRLDIitGCBExYYN84R2xEtK4N7VJnCyzH8+FtaUiCk2UyfHrzpLwJbtkRrjxEKFgowCqOuzompBmHMGP+pYKqZ8eOdzIqgWPM/ViwUYETHjh3+ExJmWLfO8bISlJKVCNrbnftiolqxWCjAKJw33nDEYd68YE3TTErWjh3R25Z0CuigUmDrsDEM3WRef9owj9UojpYWePfd4JWUdu50vLQKLj3oyfz5zucvQFTvpZkP73gj7iw2owhMWI3SWLiwsDJ199/vPwFeJZERVL+ZVLPIiOoMOtI7cqzKMWE1SmfhwuBxV3BqioqUxYONtQTe9OkFC2oXcAWtzOCD2RqKGTlmpf9iJmhRgbQsVoQlRoYNC17VI3sZNCjwJQqpQBVbUZagFcJ6LZ0MC6WyVMUVo0kIWHWryiWRpe2yKVJUuhePmqKFCka+sniRlcALOslfrmXYsNAEseyfu0owYa1QUuOJtLUFK8xcoMAWKhj5yuIVUgLP90FWSGm/AJ81jAdnGJ/b6IsJa4WSSk+k2PBADuEpVDBKvV+eD7KQBTVMUvk9SQEmrBVKWj2RtU3N2gXBimd7LF2gd9McWDBK9fB7C9TltIbyOaIU1TA+t5EbE9YKJa2eSMbuuyldYDPv3w36Vxr0JNq0vj6/aJTStP5X2nQzQ7qvWbKglnGusMTH4lOICWuFUognUo4fVtBr9Pa0l9MUmueXLXq7i/UEm5rynrNkz7QMHqpRHhIvrMAJwEqctL2pHsfNAF4CXgW+H+TclSysqsHErBxNwUKukc/TXlXblHtHiGKbTyD99odlw0N1zX3uiXmT6SQNwvoJ4GPAg/mEFagFXgP2BeqAFUCT37krXViDUI6QQSHX8BThtjbVfv0iEdg4loygvp2Vk5r9wLH4Z3pJvLB2X9xbWA8F7sla/w/gP/zOacJank6uQq8RyEsLo6c9zqWpyfeBk9Y4uVGYsCZ5SOtY4G9Z62vdbX0QkbkiskxElq1fv74sxiWZcsz9VOg1Wlpg9Wro6nJecxajXrjQ0ZnmZgA0a0k0TU2O3StX+k5oWDETHhqeRCasItIhIs/nWI4Neooc23L+xlR1sapOVdWpo0aNKt7oCiHX9Cphz7QZ6TU6OkCVG9uUoYOVFtpYT32sItvjujU1TuGZjMO5cmX3Lr8HTkVMeGj4E9S1jWLBQgGRkaSsgDCv8Uhrm2pdXSRN+a6s156LBP5wfjFUi7GmFyokxtoP+AuwDx90Xo33O6cJa5WSVaOgmKyAnf0GhKZufg8cywpIJ4UIayxzXonI8cDlwCjgHWC5qn5ORMYAV6nq593jPg9cgpMhcLWq+jY0bc4rwzCioJA5r2KZmkVVbwFuybF9HfD5rPU7gTvLaJphGEbJJDkrwDAMI5WYsBqGYYSMCathGEbImLAahmGEjAmrYRhGyJiwGoZhhIwJq2EYRsjEMkAgSkRkPbAmglOPBDZEcN5SSKJNYHYVitlVGHHZ1aCqgYqRVJywRoWILAs66qJcJNEmMLsKxewqjKTalY2FAgzDMELGhNUwDCNkTFiDszhuA3KQRJvA7CoUs6swkmpXNxZjNQzDCBnzWA3DMELGhNUwDCNkTFjzICIniMhKEekSkbypHSKyWkSeE5HlIhJphe0CbJohIi+JyKsi8v0obXKvN0JE7hORV9zX4XmO2+3ep+UicluE9nh+fhEZICK/dvc/ISKNUdlSoF1zRGR91j06rQw2XS0ib4vI83n2i4hc5tr8rIhMjtqmgHZ9WkQ2Z92rH5TDrsAEnWqg2hbgE8DH8Jg+xj1uNTAyKTbhzLbwGrAvH0xp0xSxXT8Bvu/+/X3gx3mO21KGe+T7+YH5wJXu3ycCv06IXXOAn5fju5R1zWnAZOD5PPs/D9yFM7nnIcATCbHr08Dt5bxXhSzmseZBVV9Q1ZfitiObgDYdBLyqqn9R1R3Ar4CgM+MWy7HAde7f1wHHRXw9L4J8/mx7lwLNIpJrVuBy21V2VPVhYKPHIccC16vD48AwEdkzAXYlGhPW0lHgXhH5s4jMjdsYYCzwt6z1te62KPmwqr4J4L6OznPcQBFZJiKPi0hU4hvk83cfo6q7gM1AfUT2FGIXwD+7Te6lIrJ3xDYFIY7vU1AOFZEVInKXiIyP25hsYpnzKimISAfwjzl2LVDVWwOe5nBVXScio4H7RORF92kbl025PK+Sc+q87CrgNOPce7Uv8AcReU5VXyvVtl4E+fyR3CMfglzz98BNqvq+iMzD8ao/E7FdfsRxr4LwNM7Y/S3upKO/Az4as03dVLWwqur0EM6xzn19W0RuwWnyFS2sIdi0Fsj2dPYC1pV4Tk+7ROQtEdlTVd90m4lv5zlH5l79RUQeBA7AiTuGSZDPnzlmrYj0A/6B6JudvnapamfW6i+BH0dsUxAi+T6Viqr+PevvO0VkoYiMVNVEFI2xUEAJiMgQEdkj8zfwWSBnL2YZeQr4qIjsIyJ1OJ0zkfXAu9wGzHb/ng308axFZLiIDHD/HgkcDqyKwJYgnz/b3n8B/qBuj0iE+NrVK3Z5DPBCxDYF4TbgZDc74BBgcybsEyci8o+ZuLiIHISjZZ3e7yojcfeeJXUBjsd5Wr8PvAXc424fA9zp/r0vTu/uCmAlTnM9Vpvc9c8DL+N4g5Ha5F6vHrgfeMV9HeFunwpc5f59GPCce6+eA06N0J4+nx/4IXCM+/dA4L+BV4EngX3L9J3ys+u/3O/RCuAB4ONlsOkm4E1gp/vdOhWYB8xz9wtwhWvzc3hkyJTZrm9m3avHgcPKYVfQxYa0GoZhhIyFAgzDMELGhNUwDCNkTFgNwzBCxoTVMAwjZExYDcMwQsaE1UgNIrK3iPxVREa468Pd9YZexz0oIp/rte1MEVlYxDWPE5Gm0iw3qg0TViM1qOrfgEXABe6mC4DFqtp7uvObcBLwsznR3V4oxwEFCas7msuoYiyP1UgVItIf+DNwNXA6cIA61aKyj6kHXgT2UmfcfSPOMOMGVVUR+S7wFWAAcIuqnu2+72Tgf+OMhX8WR8RvxynSshn4Z2AP4EpgME7S/CmquskdovtHnBFlt6nqRVHdAyP52JPVSBWqutMVxruBz/YWVfeYThF5EpiBM7w2U3NVReSzOMU6DsIZVXSbiEzDGQ65AKeozgYRGaGqG92C3Ler6lIAEXkW+JaqPiQiPwTOBs50Lz1MVf9XlJ/fSAcWCjDSyNE4wx0neByTHQ7IDgN81l2ewamQ9HEcof0MsFTdIh6q2qcoi4j8A454PuRuug6nIHOGXxfzYYzKw4TVSBUiMgk4Cqea/b95FF3+HU4B68nAIFV9OnMK4L9UdZK77KeqS9ztpcbFtpb4fqNCMGE1UoNbzWgRcKaqvg78FLgw17GqugVnCpur6dlpdQ9wiogMdc851q2lez/wFTc+SybzAHgXJ66Kqm4GNonIEe6+WcBDGEYvTFiNNHE68Lqq3ueuLwQ+LiL54po3AZ/EmQYFAFW9F7gR+JOIPIczNcseqroSOB94SERWABe7b/kV8F0ReUZEPoJTbvCnbqx1Ek51KsPogWUFGIZhhIx5rIZhGCFjwmoYhhEyJqyGYRghY8JqGIYRMiashmEYIWPCahiGETImrIZhGCHz/wHTbH2TFlV5PQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Circle Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Ellipse Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x_normal, y_normal = sims.circle_sim(100, 1, radius=5)\n",
+    "x_no_noise, y_no_noise = sims.circle_sim(1000, 1, noise=0, radius=5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Note change in X axis compared to circle simulation\n",
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n",
+    "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n",
+    "ax1.set_title('Ellipse Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Multiplicative Noise Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Note that this simulation has no noise parameter\n",
+    "x_normal, y_normal = sims.multi_noise_sim(1000, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal')\n",
+    "ax1.set_title('Multiplicative Noise Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Multimodal Independence Simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Note that this simulation has no noise parameter\n",
+    "x_normal, y_normal = sims.multi_indep_sim(1000, 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 4))\n",
+    "ax1 = fig.add_subplot(1, 1, 1)\n",
+    "ax1.scatter(x_normal, y_normal, c='b', label='Normal')\n",
+    "ax1.set_title('Multimodal Independence Simulation', fontweight='bold')\n",
+    "ax1.set_xlabel('X Vector')\n",
+    "ax1.set_ylabel('Y Vector')\n",
+    "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

From 9588020a1c5ee05f28dd3173691c28fb5a98ca55 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 13:24:24 -0500
Subject: [PATCH 52/60] Added equations for each sim

---
 demos/simulations.ipynb | 268 ++++++++++++++++++++++++++++++++++++----
 1 file changed, 244 insertions(+), 24 deletions(-)

diff --git a/demos/simulations.ipynb b/demos/simulations.ipynb
index 9a576e7..4b136b1 100644
--- a/demos/simulations.ipynb
+++ b/demos/simulations.ipynb
@@ -38,7 +38,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the documentation. Visualizations of the 4 simulations imported above are shown below with and without the noise. Each simulation is also shown in 2D."
+    "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the documentation. Visualizations of the 4 simulations imported above are shown below with and without the noise. Each simulation is also shown in 2D.\n",
+    "\n",
+    "For all the below simulations, $(X, Y) \\overset{i.i.d}{\\sim} F_{XY}=F_{Y|X}F_{X}$ where $X$ and $Y$ are independently identically distributed."
    ]
   },
   {
@@ -48,9 +50,20 @@
     "## Linear Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Linear $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=w^{T}X+\\kappa \\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -60,12 +73,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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ev8pBRMmJ1/TqZmBL9N51dVYtuL3d+suBcOQXP0f5jgfwZQDrROQ1e9u/qOrTPpaJiGIoL4/e9Brur3RzVDdHjFM28HOU719UVVT1E6p6vp0YTIkMMX1faB5O1tHe3t4ufheCgsP+PbTHej4Qo3yJyCw3JjwIVH+lN9bv2bPndAZVAqxgumfPntMBrI+1j++jfFPBUb5EyYk3MjbTUbe5KNoo31WrVvUvKCh4EMC5YOWDrJrp+ra2tpuqq6t3R9uB66ES5aDATHiQxeyT5hV+l4OyB6+6KGcEYpL0gAjMhAdEeYQBldIStOAVmEnSAyIPBxAR+Y4BlVIWxODl5lyy2SgPBxAR+Y4BlVIWxODFPsPOvJ7wIGitFkReY0CllAUxeLHP0F9BbLUg8hoDKqUsiMGLfYb+CmKrBZHXGFApZUEMXuwz9FcQWy2IvMaASikLavDiJOn+CWKrBZHXGFApLQxe5BTEVgsirzGgZjmOrEwfPztzgtpqQeQlBtQsxpGV6cuVzy5IFwVstaB8x4CaxZIZWRmkE26Q5MKo1EwvCvjbIDKLq81ksVDIOpFGErFqCeETrjNwlJayKQ5I/Nllg0xWlOFvo6Noq80QpYo11CyWaGRlLtTC3JILo1IzuVWFvw0i8xhQs1iikZW8NzC2XBiVmslFAX8bROYxoGaxRCMrc6EW5pZcGJWayUUBfxtE5jGgZrl4IytzoRbmpmwflZrJRQF/G0TmMaDmsFyohVF86V4U8LdBZB5H+RIloanJGrCzbZvVLDp7NoNPLuEoXzLB1xqqiDwkIrtFZL2f5SCKJ1cmgcg5l1xiVa+dafp0v0tFeczvJt9fAbjM5zIQxcVbTAIiMoA+/3znfebMYVAl3/gaUFV1BYAP/SwDUSK8xcS8pGdpGjkyfgCNZv58Q6UkSk2B3wVIRESmApgKAOUc008+KC+PPiMRf47piZylKdyEDgB13xsMvP9+ZhmcOJHZ64nS5HeTb0KqOl9Va1S1pl+/fn4Xh/IQbzExK9yEfj+m4wQE7RAcahVcN0UyD6YA0KVL5u9BlIbAB1Qiv/EWE0OamoCCArzdYgXRb2AOQgDEkYwIV3eJPBb4Jl+iIKirYwBNS69ewL59HTYZC5zR1NcDDzzgZg5EMfl928wiAC8BGC4i74rI1/wsDxFlKHIkbkQwdU1trXVPE4Mp+cjXGqqqXutn/kSUoenTrVtV/MDaKAUMm3yJKHlNTcCNNwIff+x6VuE53E42ETOAUsAxoBJRbCNHAhs3epJV5CSoB9EVPaU1axZ8J+Io3ziSvvmcKFc4J1IQ8TSYvo4qhKAn0+lo5b2+lFUYUGPg/K2UFwYP9iWAAjg1kEgVCxsVF5Vu6PA07/WlbMOAGgPnb81ded3y0NQE9O17KoCamEghGSJWH6gdQKEKLFly8mne60u5gAE1Brfnb83rk7qP8q7lIbIJd8oUYO9eb/IuKzsVPNvb0TT+gbi/+Wxf8J2IATWGWH03Jvp08u6kHiC50PIQ92LMzybcqqqONdD33utQZv7mKddxgfEYIifwBqw+HRPNUJWV0Sdbr6iwrszJPaGQdUKPJIKsGE0a+bu8H9MxHXPMTt2XitraDk23sQT9N88FxskE1lBjcLNPh8uBZS7dJnM3Wx688Mq3m7CntRjt6Dwfruscg4ii9YPGw9885QMG1Djc6tPJ9pO63zJpPsy6lWMipvL7r71TUIqPzU8oH02XLkBjY8rBMxr+5ikfMKD6ICgn9WwdGJVJP2jgR5NGzoUbsai2qwG0oKBjAG1rM/bBBOU3T+QqVc2aVF1drbmisVG1okJVxPrb2Oh9/qWlHdvvSku9L0c6RCLbHa0k4nfJ0tDYqFpUFP2AvEgefuGp/ua9/D8CYKUG4BzHlN3J9wKkknIpoPqtokKjnl8rKvwuWWKmy+7pxU1VVfTCu50KCrLjasnm9QUfAyqTicQm3zzl9SARk83LJpsPPbmdo6jIs9tYFBFz4oYnUzh+PEDt2onlwu1NlH8YUPOUl4NETActk/2grpy4I+8FPX48gzeLTx2pHcAvUI8zKxwVuyxdnSXaLTYARwVTsDGg5ikvB4m4EbRMjcA2UlN31kA9nM5PAcwP1Z+cTL4LFN8vfSDrB/o0NVkfYzQcFUxBxoAaRbaOfk2Fl6Ndg3wPYlo19cjp/FysgXbimI1IVNH9kQeCO2I5TQ0NsSffyPaLBcpxfnfippK8GJSUyWAIv0fuBlWQB0Al9X17OJCo3ZFUJC9/RLFGcQPu5QkOSmIykFhDjZBu8yTnKo0tyPcgRtbUb+nThP3HilE3xbv5cMN9oB+jAHVoRAiK7qWKpgXt2V/dTEOs1oGKCm/LQZQyvyN6KsmLGmq69zgGuRYWBF7X3pPOr74++hfnRSoqUm1s5G8ngh/3SIM1VCYDyfcCpJK8CKh9+mhaJzcvJxtg03J8CU/IhYXRvywvUn19p/Lm1EQVhnj9G2dAZTKR2OTr0NQEHDzYeXthYefmyciBS717R39P06MS2bScWGSz/f2YjoOtguum+DuICKpRb2Pxc57boA7A49qolJX8jOYALgPwBoAtAH6QaH+3a6ixmt769Om4X7QaUFFR54qPG81UbB5MrAVlHQb3tHtV+6yqSqu8fk0DmWy+btYWg9LaAtZQmQwk/zIGugDYCuAsAEUA1gKoivcatwNqsk1v8QKv2yeHIDQPBuUkeFJEP6hnATRGE246/PhMk7k4czPYB2k+aQZUJhPJv4yBcQCedTy+A8Ad8V7jVw01svaXKKi5eXJMtYaaTlnivSYQJ8GysugfghfJ96sHc5K5OHOzRSRIrS0MqEwmkn8ZA1cDeNDx+MsAfh7vNW4H1GSDRbwTgdsBJ5X3T6csiV7jy0mwtjZ6pl6k2loXD8xfyXyXbraIBKG1JYwBlclE8i9j4JooAfX+KPtNBbASwMry8nJ1WzI1unhBx4uAk2ytM52yJHqNJyfBxkbVkpLoGbmd0uwHzfRw/WhCT+aCizVUJqbkU/wnrX7Oe1zJOIBNvqmIdRIM0lV3OmVJ9BpXToJ+3sZSVpZBwTPndxN6omDOPlQmpuRT4h2AFwCI8YyBAgBvATjTMShpZLzXmAyobtUKgnTV7UYN1chJ0K8mXBFjg4hMifV5hz/zIHTZBm2UrxvlYUBlMpES7wD8B4DFdpPsVeFkJHPgcwCa7dG+DYn2NxVQ3bwyrq/vXMvz66rbjT7U8D7RTmgxT3QeB84Oo3x79nTls40nlRN+vHlr/fztuCWZGrEfNWYGVCYTKfEOwMNR0kN+FNZUQHWrFhntP7vflSKvagDOY/8jaj29BzTyntNfdfPvA0/1hB+vhmrqdxkUiT4bP/t0GVCZTCTfC5BKMhVQ3ernDFJzb6oyakarqvJlIoV2QE8Aei0aM/oeTTYhpnNbU2QQMf27DIpEn42fo44ZUJlMpMQ7AEMA/A7AbgC7APwWwBA/Chv0GmqQBiSlIuVmNA+XM+uUHIOITHyPppsQ0/kNxBsdni0XZMlI9Nn4eV8sAyqTiZR4B+A5AF+1BxEVALgBwHN+FDbofajZWkNNWG4/J1KIcx+oie/R9HeW7vs1NkZfmCGX+lBN1FDZh8oU5JR4B+C1ZLZ5kYI+yjdItwFEk+ytPteiUQ+jyNsp/JzVkRQ+MOcx9eljpVS+U9OtCqYGggHWsQTlt2OCiT7U8H4c5csUxJR4B2AJgCn2Pald7H8/70dh/bgPNdX/vJn+Z3frFoV4J6tb+jTqbvTxfjJ5wNhECulezLjRqpDqd5itLRvpyHSUr1sYUJlMpMQ7AOX2bTN77H7U3wMo96OwXgdUr2ucbuYXedK+Fo16FF28D6CAK8OeM2lq9btVIVv73nMJAyqTiZR4B2B8Mtu8SF4HVK9rDpnkF/fKPsooXM+CqEdz4WYSlPyqFYVlw+QOuY4BlclEElVFPCKyWlXHJNrmhZqaGl25cqVn+YVC1mktkoi18HFQ8gsvOh5eVPt+TMd0zIEAEPPF7CRcZAGsBbU3bPAg144qK63F1iNVVFgLVAdZ5PcXqbQUmD+fi2y7SURWqWqN3+Wg7BaK9YSIjBOR2wD0E5EZjvQjWH2pOa+8PLXtfuX3yrebsKO1B9ohaIfgG5iDENwLphqRfoF6nFlhV6riBNOmJivwhULW36Ymc2WaPdsKPE6lpdb2oKurswJmRUX051tbgYYGb8tERKmLGVBhza/bHdatMj0c6QCspdeyTqondK9P0knn19QEFBdbVVcR/NfeKTgNh07WSE0HUmfwbEUx6tCIEPRk+n7pAwk/k3AtrKXFirstLdbjdINq5HcJnApKItbfbKrV1dVZNWmJ8eVt2+ZpcYgoHYnahAFU+N0uHU6Z9KGmO/jE6/61qPnV12vMTjYP0qba+g5lqq9P/TMx2R8dhIFE4XKY/m3k04jfIAH7UJkMpMQ7WBM79HQ87gXHsmtepkwCaqwTVZcuwRv00dioegSF/tzGAriyJqjJkaxBCDpuBfWgXCzkGwZUJhMpXpNvWF9V3eeo0X4EoL/pmrLbYjWZnTiRWdOjMXbzrYrguimCYhx3rQm3g27dgMZGNDUqKisUIVFUHt5g/PMw2R8d67v0slm0oaHzICITfZ3O/lTTTddu9mETEZKqoa6C475TABUAVvsR/d2oofrWpNbYqFpUFL9QbqWIRbW9qBWZzCMINdRsu3eUNd/4wBoqk4GUeAfgMgDbACywUwuAz/pRWNN9qJ6eCAM6H66qdwHKVJ9jEIJDEIJ6KrKtvF5jQGUykZLbCegL4PMALofVBOxLYTOd2KGx0eozTefEknIwqK2NnpHbKcW5cFVTq235PQlCUMoRhKCeimyrUXuNAZXJREq8g9WFNwXATPtxOYCxfhTWxExJpiYv7/QavwIooFpYmNFnkmztxWQQ8TsgmihDEI4hWayhxseAymQiJd4BmAPgFwA22Y97AfibH4U1uXxbppOX/xG1ni6kffJxSYnxM3eygdLUSTkItbsglMFL+Xa8qWJAZTKREu9gD0ACsMaxba0fhfVjtRlVK/C+gzJ/5sJ1IYBGk8xFhqlmwyDUloJQBq9lU43aawyoTCZSMnP5vgLgIrtWOkZE+gH4k6qOTndkcbo8nct3+nRgzhwA6DhXrQs08r1ra4ElS1zKLX2m5sv1eo7koJaBgoNz+ZIJydyH+t8Afgegv4jMBvAXAHe5Wio/DB588l5QiJwMpoD5e0HVkVpRjBsLrftAoXaKEUz9vo/Q1FSMXs+RHNQyEFGOSaYaC2AEgG8A+CaAc/yqThtt8vVwOr/IpuLd6JlyU2NQ+sBMNBsG4ViCUAYKDrDJl8lAiv0E8AcAdQC6+V3IcMoooHo8CjccPA+jWK9F48mTdbr9kLnW5xeE/rwglIGCgQGVyUSK1+Q7H9a9p++IyG9E5EoRKTJRKxaRa0Rkg4i0i4j7/Ra9egHPP+96Nid164YX6xtxZoWiuxzFXyvqTk4fl25TYxCm2zMpvLpKe7v1149VYeKVwe/mdSLKPjEDqqo+qarXwrrv9AkA1wPYJiIPichnMsx3PYCrAKzI8H0Su+QSYN++xPulq7gYaGzsWHE8dAgXP1AX9WSdbj8k+/xOcTvYmV5qjojyRCrVWQCfALAGwAkT1WMAywDUJLt/Wk2+bjTppjEbkVM6TY1u9PllY5OnF32fuda8TomBTb5MBlLiHYABAG4B8CKAtwD8FMD5RjJPIqACmApgJYCV5eXlmjITAbS+PvV8I5gazGMqAGbroBwvgh2n6cs/DKhMJlLM+1BF5GYA1wIYDqvJ91FVfTHZmq+ILAEwMMpTDar6pL3PMgDfVdWkbi5N6z5USeOGl6Ii4KGHjHXshZsQnct9lZaaW5YrHabuKfWaF/ePZutnQ+njfahkQrxBSRcBuBvAGap6SyrBFABU9RJVPTdKejKjEqeqtja5/Zz9oMeOGY10bq2dmYlsHeTkRV+yqfttiSi/xBuU9FVV/ZOqZve8MUuWdA6qRUWdBxK5WFUMYvDK1kFOXgQ7Nxf5JqLclcxMScaJyD+JyLsAxgH4g4g862qGS5Z0DJ6Ga6CJBDF4ZWstzKtgF4Tbeogou8QMqCLytIjtT1QIAAAPZklEQVRUupGpqv5OVYeoarGqDlDVz7qRj0mZ3KoRxOCVzbUwBjsiCqJ4NdRfAfiTiDSISKFH5QmkTO9LTDZ4eT2ZAANTZ5zQgYjSFXe1GRHpBmAmgMsALABwsj9VVe91vXQRPF1txsGLUZ9BHAmcb/gd5C+O8iUTEvWhHgdwGEAxgB4RKW94MagoiCOB8w2/AyLKREGsJ0TkMgD3AlgMYIyqtsbaN9eVl0evoZocVBTEkcD5ht8BEWUiXg21AcA1qvqDfA6mgDeDioI4Ejjf8DsgokzEuw/1k6q6wcvCBJUXI2KDOBI43/A7IKJM+HIfajZye0RsNt/Gkiu8+g44kpgoN8Ud5Rs0fo3yJcpUU5M1uKmlxQrWzv92HEnsP47yJRNYQyVymfM+ZqDz5P4cSUyUGxhQiVwW7XacSBxJTJT9GFCJXJZMsORIYqLsx4AaQBy0klsSBUuOJCbKDQyoAZPpvMEUPNFuxwmve8/R3ES5gwE1YDj9Xe6JdjvOggXWBRMXJSDKHbxtJmBCoc6jQAHrRNye3Uu9EwUWb5shE1hDDZhsmv4uH/p68+EYicgMBtSAyZbp7/KhrzcfjpGIzGFANSzTGk22TEGYD329+XCMRGQOA6pBpmo0bs8bbIKppc6C3KTK5dyIKBUMqAblU43GRF9v0JtUs6k/m4j8x4BqUD7VaEz09Qb9AiRb+rOJKBgYUA3KpxqNib7eoF+AZEt/NhEFgy8BVUTuEZHNIvK6iPxORHr6UQ7T3K7RBK2/MdO+3my4AMmG/mwiCga/aqjPAThXVT8BoBnAHT6Vwyg3azRB729MR7QLkKIi4NCh4Fw0EBEly5eAqqp/UtU2++HLAIb4UQ43pFujSVT7DHp/YzoiL0D69LEuFvbuzZ2LBiLKH75PPSgiTwH4jao2xnh+KoCpAFBeXl7dEl6lOYeEa5/OgFla2rF2mw9TElZWnlqE26miwro4IXILpx4kE1wLqCKyBMDAKE81qOqT9j4NAGoAXKVJFCRX5/JNJpDkQ7DJh4sGCiYGVDKhwK03VtVL4j0vItcD+DyA2mSCaS5LZrTr7NnRa7G5dAtHeXn0i4YgDVIiIorFr1G+lwH4PoArVLU10f65LpnRrvlwCwfv+ySibObXKN+fA+gB4DkReU1E5vpUjkBINpDk+i0c+XDRQES5y7Um33hU9Ww/8g2qcMBoaLCaecvLrWCaj4Gkri4/j5uIsp8vAZU6YyAhIspunHqQiIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUImIiAxgQKW0BW3BcyIiP3FiB0pL5JJz4bVLAU5QQUT5iTVUSksuLnhORJQJBtQ05XtzZzJLzhER5RMG1DSEmztbWqwFscPNnfkUVJNZco6IKJ8woKaBzZ1cu5SIKBIDahrY3Mm1S4mIInGUbxrKy61m3mjb8wmXnCMiOoU11DSwuZOIiCIxoKaBzZ1ERBSJTb5pYnMnERE5sYZKRERkAAMqERGRAQyoREREBjCgEhERGeBLQBWRH4vI6yLymoj8SUTK/CgHERGRKX7VUO9R1U+o6vkA/g/ATJ/KQUREZIQvAVVVDzgedgOgfpSDiIjIFN/uQxWR2QC+AmA/gE/H2W8qgKkAUJ5vc/sREVHWEFV3KocisgTAwChPNajqk4797gBQoqr/mug9a2pqdOXKlQZLSUQEiMgqVa3xuxyU3VyroarqJUnuuhDAHwAkDKhERERB5dco36GOh1cA2OxHOYiIiEzxqw/1bhEZDqAdQAuAaT6Vg4iIyAhfAqqqftGPfImIiNzCmZKIiIgMYEAlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUImIiAxgQCUiIjKAAZWIiMgABlQiIiIDGFCJiIgMYEAlIiIygAGViIjIAAZUFzQ1AZWVQChk/W1q8rtERETkNl8WGM9lTU3A1KlAa6v1uKXFegwAdXX+lYuIiNzFGqphDQ2ngmlYa6u1nYiIchcDqmHbtqW2nYiIcgMDqmHl5altJyKi3MCAatjs2UBpacdtpaXWdiIiyl0MqIbV1QHz5wMVFYCI9Xf+fA5IIiLKdb4GVBH5roioiPT1sxym1dUB77wDtLdbfxlMiYhyn28BVUTOAPAZAByuQ0REWc/PGup9AL4HQH0sAxERkRG+BFQRuQLAe6q6Nol9p4rIShFZuWfPHg9KR0RElDrXZkoSkSUABkZ5qgHAvwC4NJn3UdX5AOYDQE1NDWuzREQUSK4FVFW9JNp2ETkPwJkA1ooIAAwBsFpExqrqTrfKQ0RE5CbP5/JV1XUA+ocfi8g7AGpU9QOvy0JERGSKqPrbippKQBWRPQBa0syqLwC/gjbzZt7MO9j5V6hqP5OFofzje0D1ioisVNUa5s28mXfu5R2E/Ik4UxIREZEBDKhEREQG5FNAnc+8mTfzztm8g5A/5bm86UMlIiJyUz7VUImIiFzDgEpERGRATgVUEblGRDaISLuIxBw+LyKXicgbIrJFRH7g2H6miLwiIm+KyG9EpCiFvHuLyHP2a58TkV5R9vm0iLzmSEdF5Er7uV+JyNuO5843mbe93wnH+y/28LjPF5GX7O/mdRH5kuO5lI871vfneL7YPo4t9nFVOp67w97+hoh8NtnjTCHvGSKy0T7O50WkwvFc1M/fYN43iMgeRx43OZ673v6O3hSR613I+z5Hvs0iss/xXKbH/ZCI7BaR9TGeFxH5b7tsr4vIGMdzGR03UUpUNWcSgHMADAewDNZkEdH26QJgK4CzABQBWAugyn7uMQCT7X/PBVCfQt7/DuAH9r9/AOCnCfbvDeBDAKX2418BuDrN404qbwCHYmx39bgBDAMw1P53GYAdAHqmc9zxvj/HPtMBzLX/PRnAb+x/V9n7F8Oa/nIrgC6G8/604zutD+cd7/M3mPcNAH4e47f2lv23l/3vXibzjtj/FgAPmThu+/X/AGAMgPUxnv8cgGcACIALAbxi4riZmFJNOVVDVdVNqvpGgt3GAtiiqm+p6scAHgXwBRERABMBPG7v92sAV6aQ/Rfs1yT72qsBPKOqrSnkYSrvk7w4blVtVtU37X+/D2A3gHRnpYn6/cUp0+MAau3j/AKAR1X1mKq+DWCL/X7G8lbVpY7v9GVYc1WbkMxxx/JZAM+p6oeq+hGA5wBc5mLe1wJYlML7x6WqK2BdfMbyBQCPqOVlAD1FZBAyP26ilORUQE3SYADbHY/ftbf1AbBPVdsitidrgKruAAD7b/8E+09G55PObLvJ6j4RKXYh7xKxlsJ7OdzUDI+PW0TGwqrlbHVsTuW4Y31/Ufexj2s/rONM5rWZ5u30NVg1p7Bon7/pvL9of5aPi8gZaZY73bxhN3GfCeAFx+ZMjjuT8mV63EQp8Xxy/ExJnGXhVPXJZN4iyjaNsz2pvJPI1/k+gwCcB+BZx+Y7AOyEFWzmA/g+gFmG8y5X1fdF5CwAL4jIOgAHouzn5nEvAHC9qrbbm+Med7S3SVTeOPsk89p4kn69iEwBUAPgU47NnT5/Vd0a7fVp5v0UgEWqekxEpsGqpU9MpdwZ5B02GcDjqnrCsS2T486kfJkeN1FKsi6gaoxl4VLwLoAzHI+HAHgf1qTaPUWkwK7VhLcnlbeI7BKRQaq6ww4cu+OU4Z8B/E5Vjzvee4f9z2Mi8jCA75rO225uhaq+JSLLAIwG8Ft4cNwichqAPwD4od0sl9RxRxHr+4u2z7siUgDgdFhNhsm8NtO8ISKXwLrY+JSqHgtvj/H5JxtYEuatqnsdD38J4KeO106IeO2yJPNNKm+HyQC+EVGuTI47k/JletxEKcnHJt+/ARgq1sjWIlgngMWqqgCWwurbBIDrASRT4w1bbL8mmdd26mOyg1G4T/NKAFFHNKabt4j0CjenikhfAOMBbPTiuO3P+Xew+rn+N+K5VI876vcXp0xXA3jBPs7FACaLNQr4TABDAbya1FEmmbeIjAYwD8AVqrrbsT3q528470GOh1cA2GT/+1kAl9pl6AXgUnRsHck4bzv/4bAG/7zk2JbpcSdjMYCv2KN9LwSw375Qy/S4iVLj96gokwnAP8G6Kj0GYBeAZ+3tZQCeduz3OQDNsK6SGxzbz4J1gt0C4H8BFKeQdx8AzwN40/7b295eA+BBx36VAN4DEIp4/QsA1sEKKI0AupvMG8BF9vuvtf9+zavjBjAFwHEArznS+eked7TvD1Yz8RX2v0vs49hiH9dZjtc22K97A8CkNH5jifJeYv/2wse5ONHnbzDvfwOwwc5jKYARjtfeaH8eWwB81XTe9uMfAbg74nUmjnsRrJHhx2H9//4agGkAptnPC4Bf2GVbB8cI/0yPm4kplcSpB4mIiAzIxyZfIiIi4xhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUMl3InKGWCvO9LYf97IfV0Tst0wiVogRke+IyANp5HmliFRlVnIiolMYUMl3qrodwBwAd9ub7gYwX1VbInZdBGtSAadocyIn40pYq88kzZ51iYgoKt6HSoEgIoUAVgF4CMDNAEartbKJc58+ADYDGKLWfLWVAFYAqFBVFZHbYU3rWAxrasd/tV/3FVhTGiqA12EF7/+DNWn+fgBfBNAD1tJ1pbAmCLhRVT+yp8r7K6wZfhar6n+49RkQUXbjFTcFgqoetwPiHwFcGhlM7X32isirsJbgehKn1jpVEbkU1lSCY2HNnLNYRP4BwF5YsyONV9UPRKS3qn4o1kLX/6eqjwOAiLwO4BZVXS4iswD8K4Dv2Fn3VFXnJPdERJ2wyZeCZBKsKebOjbOPs9nX2dx7qZ3WAFgNYASsADsR1uonHwCAqnZaV1NETocVNJfbm34Na1HrsN+kczBElF8YUCkQROR8AJ8BcCGAWyMmenf6PawFw8cA6Kqqq8NvAeDfVPV8O52tqv9jb8+0X+Nwhq8nojzAgEq+s1eamQPgO6q6DcA9AH4WbV9VPQRrCa6H0HEw0rMAbhSR7vZ7DhaR/rAm7P9nu/8V4ZHEAA7C6jeFqu4H8JGIfNJ+7ssAloOIKAUMqBQENwPYpqrP2Y8fADBCRGL1Wy4CMArAo+ENqvonAAsBvGQvnP44gB6qugHAbADLRWQtgHvtlzwK4HYRWSMifwdrubd77L7U8xF/kXMiok44ypeIiMgA1lCJiIgMYEAlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyID/B1FWtwXytR3YAAAAAElFTkSuQmCC\n",
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UIqLI2tvb28XrSpB/2J+H9mj3M6ASEUW2bvfu3WczqBJgBdPdu3efDWBdtH2YlEREFEFbW9stO3bseHTHjh0Xgo0Pslqm69ra2m6JtgMDKhFRBNXV1bsAXOV1PSg4+KuLiIjIAAZUIiIiAxhQiSgwmpqAykogL8/6t6nJ6xoRncYxVCIKhKYmYMYM4OhR63Zrq3UbAOrqvKsXUQhbqEQUCA0Np4NpyNGj1nYiP2BAJaJA+OCD5LYTZRoDKhEFQnl5ctuJMo0BlYgC4b77gOLiztuKi63tRH7AgEpEgVBXByxcCFRUACLWvwsXMiGJ/INZvkQUGHV1DKDkX561UEXkHBFZLiIbRWS9iHzLq7oQERGly8sWahuAO1V1jYj0BLBaRF5U1Q0e1omIiCglnrVQVXW7qq6x/z4EYCOAQV7Vh4iIKB2+SEoSkUoAowH82duaEBERpcbzgCoiPQD8GsDtqnowwv0zRKRZRJp3796d+QoSERElwNOAKiKFsIJpk6o+HWkfVV2oqjWqWlNaWprZChIRESXIyyxfAfDfADaq6o+9qgcREZEJXrZQxwO4EcBEEfmrXa7wsD5EREQp8zLL94+qKqr6KVUdZZfnvaoPmcV1K4ko13ielETZJ7RuZWsroHp63UoG1WDx048iP9WFKBpRVa/rkLCamhptbm72uhoUR2WlFUTDVVQAW7dmujaUivDFvAFrInov5s7NRF1EZLWq1ph5NspVDKhkXF6e1TINJwK0t2e+PpQ8P/0oykRdGFDJBHb5knFctzL4/LSYt5/qQhQLAyoZx3Urg89PP4r8VBeiWBhQyTiuWxl8fvpR5Ke6EMXCgErGNTUBDQ1Wl1x5ufXFx2AaLH76UeSnuhDFwgXGyajwjMzQJTMAvwCDxi+LefMHGgUFW6hkVEND58sbAOt2Q4M39aFg4zXNFCQMqGQUMzLJJP5AoyBhQCWjmJEZGWf6iS/Sa8QfaBQkDKhklB8zMr0OZuy2jC/aa1RSEnn/XP+BRv7EgEpG+S0j0w/BjN2W8UV7jQD//UAjioZTD1JW88MUepyKMb5Yr9GiRe5n+XLqQTKBl81QVvPDGFx5eeSgzm7L02K9Rn65fIcoHnb5UlbzQ5KUH8eV/SbSayRiBVkmcVFQMKBSVvNDMPPbuLIfOV8jwHqdQl3Akca9vU40I4qEY6iU9TjTTrDEG/d2Y31UjqGSCWyhUtarq7O+iNvbrX/TCaZsGbkv3rg3s6bJrxhQiRLkh0twckG8cW8/JJoRRcKASpQgtowyI964tx8SzYgiYUAlShBbRpkRL4nLD4lmRJEwoBIliC2jzIk17s2safIrBlSiBLFl5B8mE82ITMmZgMrsTEoXW0ZEFEtOBFRmZwaX334I+all5LfXJllBrz/RGVQ1MKW6ulpTUVGhaoXSzqWiIqWnowxpbFQtLu78nhUXW9tzXdBfm1Tr39ho/b8Vsf41db4AmtUH33EswS6ezpQkIo8B+AKAXap6Ybz9U50piat9BJMfVorxq6C/NqnUP3yGpOvRhEWYhjwAEtqpW7czr21KAGdKIhO87vL9OYDL3T4IszMtQeti42Uq0QX9tUml/g0NwA+PzkI7BO0QNGEa8uEIpgBw7NiZmWNEGeJpQFXVVQA+dvs4zM4M5jgyfwhFF/TXJuH6z5pldSWJ4P1WwdcxDwJ0lIiOHTNWT6JkeN1CjUtEZohIs4g07969O6XnYHZmMGf54Q+h6IL+2sSs/6RJHUEU8+Z13B8ziBL5gOerzYhIJYDfuTmGSsEdR+ZKMdEF/bVx1n8bBqFM/2YuYCb5vcYxVDLB9y1UMiMoXYTh47yAfy5T8Rs/XcITksw4fcWrTdjY2hWnVMwG027dTD0TUVIYUHNEELoIZ80CbrwxWOO8IUFK+HKrrjHH6ZuagIKCjq5cFcH4edPQDZ+Y78pNIcuXyAgvr9kBsBjAdgAnAXwI4Kux9k/1OlSyuHUNnwmNjVa9gni9cJCuCXWzruHXe/8VVdoOaHukN9WNUlWVct3B61BZDBTPx1CTkUtjqEEfH0tWtOsSAf+P8wbpmlA36/qwzMIsOws3xNUkohSvOY2EY6hkQswuXxHJF5EHM1UZsgTxEpd0xbr+0G/jvOGCdE2o8bo6MnK/jnkdkyy4kpFbVta5TcquXfKZmAFVVU8BqBYRZqtnUBAvcUlXtKAp4q9x3kj8nPAVPl5aUhJ5v4Tr6rykRQR46aWOu1z7kmhstALoRx+5dQQiIxJJSloL4BkRuVFErgkVtyuWy4LU4jElUtKUCDBzpv+7uv2a8BWpp+PQIaCwsPN+cevqDKKOAGqKOgoAoLa2c0vU7x8AIlsiAbUEwF4AEwFcaZcvuFmpXOfnFo9bIk2+sWgR8Mgj7h3TVLZrqO59+pze5ocrNyL1dHzyCXDWWXEmOXHMTuRGEO0UPAFIVRXESuiwAuiyZUaPR5QpBfF2UNV/yURF6LT77us8CTjgjxaP2+rqMtcYCZ9oPTROHapHKpwz3u3dm/7zpStaj8bHHwN79oRtHDEC2LDBtbo4A+gfUIspsszXiWZEqYjbQhWRwSLyGxHZJSI7ReTXIjI4E5XLVZwq8Uymr500PU7tx3HvmD0dTU3WixlqhboUTEOt0Q9Qhjwo8qC4HMuyureFclciXb6PA3gWQBmAQQCes7eRi/w4C45X3Mh6Nj1O7cdx7/Cx3evRhDbk4f1WAaZNS3p6vqTV1+OJRkWPYkUlTicU5UJvC+WmRAJqqao+rqptdvk5gFKX60XUwY3WX7LZrvFayH4c966rA/Zq77DlztSdbNzu3U9n44bKI4+wt4VySiIBdY+ITLOvSc0XkWmwkpTIBUGawi5TTLf+mpqsbNdwhYWRW06JtJB9k+kbdllL0bH97l0XCpzOyD18OGqUZG8L5Yx4UykBKIfV5bsbwC4AvwVQ7sW0Ttk+9WCQprDLpPAp7dKdkjDa8/Xpk97xPZnasbFRtaAgcgXdKLW1GTipzAOnHmQxUOJOPSgi41X11XjbMiHbpx4M0hR2mRSekQtYrb9Uuw6TXcrOd0vfTZrkyvWgURUWWtfbZDFOPUgmJNLl+5MEt1Ga/JjY4gemx+GSHe/0fHzU5etCz1BV1bldmuXBlMiUqAFVRMaJyJ0ASkVktqPcAyA/YzX0gFfjmJ5/cfuYyXG4ZMc7PRkf7d37dACdN8/FA9nq608H0PXr3T8eURaK1ULtAqAHrMkfejrKQQDXul81b3g5MX2mv7hzNQEq2RZvRjJVw9YLxf79Bp88CmcQdXNKKqJcEW+QFUCF1wO9oZKJpCTTCTDJylRiCxOgfKC+PvKHza1SVpZQtfy8bq5bwKQkFgMlkaSkFwFcp6r77du9ASxR1c+7HezDZSIpyXcJKC5hApQHZs3KTPdtSFVV0t23phPAgoJJSWRCIklJfUPBFABUdR+Afu5VyVu5Mo7JBKgMGTEis2OhzoSiFMZC/TiFIlFQJBJQ20WkI5yISAU6z3WdVXxzgb7LcuWHgyeckyu4OOE8gDOXOkszoYg/tIhSl0hAbQDwRxFZJCKLAKwCcLe71fJOrkyV5tUPh0QToQKVMBVj0W1XOFuhhpc64w8tojQkMtAKoC+sNVCvhNUF7MmAb7bPlJRpmU4+STQRyvcJU5lOJqqqMlr9WO97sq99tiQwgUlJLAZK/B2sKUCnAZhj3y4HMNaLyvohoGbiCyRbvqTCJZpB7XWmdURlZZEr5Ubp0cO1Nz2RgJno58/3P3ySwIDKYqLE3wGYB+CnADbat3sD+IsXlfU6oGbiCySbvqTCiWjE+CGS2n6uq6qKXBE3ikhG3mSTP1Z8+cMnRQyoLCZKImOoF6vq1wEct7uI98Ga9CHnZCIDMpuzLGONzznHTPOifCpdH8fL0KLbHQoLT8eh9vaMDNSbTDpiAhNRZ4kE1JMikg9Ymb0iUgogi67ITFwmvkCy+UsqUiKUCHD++Z1npzp16szHupIw1dTUOZnI7UW3y8o6N+Y8mCM30aSjRJLCmMBE1FkiAfW/APwGQD8RuQ/AHwHc72qtfCoTXyDZ/CVVVwdMn27FrhBV4OWXz2yVA0B+fvRM65SzgIuLOwdQtzmD6EcfuX+8OBLJ7k50+s1cucSMKGGJ9AsDGA7g6wC+AeACr/qngz6GmkiyRzaPoapGH3dLZsw0qdeosVG1e/fED5puCcB6ofE+h8mMjWZLAh04hspioES/A/hfAHUAurt2cOByAO8A2Azgu/H29zqgqqb+BZJMEMiWLymn0DklE5uiJbfE/cJvbFQtKkruYC4F0SC+l75JCssgBlQWEyX6HcAXASwGsBvArwBcDaCLsQNbS8BtAXAerCSnNwFUxXqMHwJqqrIpIzJZkX5MRPqyTrRVHr7v9WjUI+iq7ZkKoL16pXzeQehtyMXPKgMqi4kSdQxVVZ9R1ethXXf6NIDpAD4QkcdE5HMGepvHAtisqu+p6icAlthBPCv5OdnI7VmJImUuOxUXAzNnJj47VXk5sAu90Q5BOwRNmIZinIBE3t0M5xR/+/Yl9JCgZmxzbJQoRclEXwCfArAWwKl0IzmsNVUfddy+EcDDsR7DFqp5mWhFRetCDJ1/QsdyzE7UbhfXW6Jpvggmu06dXcd9+liFk4uYA7ZQWQyU+DsA/QHcBuBVAO8B+CGAUWkfGLguQkD9SYT9ZgBoBtBcXl6uQeXX7r9MJKCk/GOitjbyA90qEcZC0wkspn5Exesy98PnKOgYUFlMlOh3ALcCeBnARwB+AmC80QMD4wAsddy+G8DdsR4T5Baqqj9/9SfaikrnB0HCj21sjFyZDAdRE+ds4vEhiSRzed3TEXQMqCwmSvQ7gMcBTAaQ58qBgQK7xXsuTicljYj1mKAHVD/K1Py6UX9MNDbG7hM2XVx4bVI67yQk8vJ4mYEb7xz9+EMyHAMqi4ni7cGBKwC0wMr2bYi3PwOqeYm2ooxeStGrV+Qnc6N06ZLyN3gi55yJYOHnFmq8z49fhzrCMaCymCieVyCZwoDqjkQSXtJqrdmTzLcjQwlFCV7WEk+8c85UsPDbGKrz85KfH/s18msyXjgGVBYTJfodwPMAKr2uoLMwoLorVoBIenYix45uBNBOz1lfn/HXQzWzwSLTWb6x6hHvmmJnKz4ok0QwoLKYKNHvAP7Z7o5tAFDodUVVGVDdFi1A5OefDqoxuzddXng71Lo9BejG2tSDaDLdtLH2DUqwMCnR2a7YQmXJxRL7TqC7fZnMmwC+DWB2qHhRWQZUd8VKfomaldujR/QHGQykpwC9AY1pt8hMdtMGJViYlEiCFMdQWXK1xFtt5iSAIwC6AugZVsgQt2cqSlSsFW2OHgXavjbr9BIwodVaDh92r0L27ESiijxVNGkdtm5Nb9lQk7MX5eKMQtE+I841bLt1O/13XZ0161Wis2ARBVq0SAtr4voNAB4AUOx15FfNzhaqn37BR6rLLvRyNZnI+dynIK6fuOlu2iBcEmJSpM9Ily6qhYX++AynCmyhshgo0e8AXkGc60IzXYIUUBP9ovVbt+HG2vpOQc50EHU+70F0N9KNmwy/vd5BFP7Z7tMn+K8pAyqLieJ5BZIpQQmoybQ6fZHYYl/W4lZxBtEN+VWuXFaSTJKRX3oEsoUvPsNpYkBlMVHijaFSCpIZp4s2JhVrPDNtI0acHgcVATZscPFggNTXQ9QaC72gbb3R8bOmJmDGDKC11foab221bkcbh+aYnnmefIaJfIgB1QXJLNWWkcSWpiYrayRDARRlZZ0bK4884tqhUkkyqqsDtm4F2tuRdpIT5WZyFlEkDKiGODN186K8qpF+sbvWYpo1q3M2rmqaTxhHr16nA+hHH7l7LAc/rzObKr9kfSeKrX4im9d9zskUv46hJjJ7jOvjdJmeZD7J2Ynq609PU5efb25yo2xLMuIYrzfAMVQWA8XzCiRT/BpQY80w5OrlFI2Nqt27Rz64G6WqKqVqRptAyURQzbYAlG0/EIKCAZXFRBFVl7sCDaqpqdHm5mavq3GGvLzIPaoi1jidMbNmAfPnu99961RbCyxbltZTFBQAp06duT0/H2hrS+upAVhdog0NVjdvebk1dhfU7saMfZaoExFZrao/UZCAAAAPhElEQVQ1XteDgo1jqAa4muXozMidN8/9YFpf37lxlGYwBSIH01jbk+VmklGmxzOZMUsUXAyoBhjNcmxqspp0mcrIBToH0SQychMNNvn5yW1PhRuBL9lLckxgxixRgHnd55xM8esYqmrsyQXC76uv73z7w6pajTl26XFCUbTzTXTs0s0x1GTrkgyvxjNzbTpDPwDHUFkMFM8rkEzJREA1/WUWLQPY7TlyO5XaWhMvTSfJBhu3snxTqUuismEGIEoMAyqLicKkJIdQF59zooDi4vSuqaustLoKf49JmIyXOt0nqVc1vvp6VydU8FPyjFt1Cb134SoqrLFayh5MSiITOIbqYHJpLwDAiBF4v1XQDsFkvAQBOhXj7OXOoMmNhabCT8kzbtWF45lElAwGVIe0Z91pagJ69uyUUORqAA2f4s9ARm6i/BRs3KoLZwAiomQwoDok3dKZNavzHLluL7gNdG6FZnCKv3B+CjZu1oXz/vpD0KZjpBzl9SBuMsXtpKSEskVrM5yR60JCUbKYdUpeysRsWGBSEouBwhaqQ6SWztLpTaib7rgu9KWX4j9RuhobPenGjcSLazGJnIznNhC5hFm+kUyalJnAGVJVBaxfn7njJYGZruS1TGSUM8uXTGALNcQ5xZ/bwbSoqHMr1KfBFMjO5dEoWPyUUU4US+4G1EmTTgfQTEzx55ze79ixtLNbMpWkwS8z8pqfMsqJYsmtgOoMopno0nXputBMjmvyy4y85qeMcqJYPBlDFZHrANwD4AIAY1U1oYHRlMdQMzUm6vLsRCGZHtfMpuXRiCLhGCqZUODRcdcBuAbAAteP5GYwzVAADZfpcc26OgZQIqJ4POnyVdWNqvpORg5mIJiqXQBYGbkudOMmI9lxTV4UT0TkPt+PoYrIDBFpFpHm3bt3Z+SYGlb+gFrki38ycpMZ1zQ13sqgTEQUm2sBVUSWici6COWLyTyPqi5U1RpVrSktLXWruh2Ooyvq0Ig8aEe5HMt8ldWaTJKGiYviObkDEVF8nk7sICIrAHzb1aSkRMdQGxuBujpXlnDzkomL4jm5A2U7JiWRCb7v8k3bsmXW5StO4RMrqHZEy2xL0TdxHSkndwgmdtMTZZYnAVVE/klEPgQwDsD/ishSVw+4bFmn4Nn06DFUNtRF/aLJphVGTFxHyskdgofd9ESZ51WW729UdbCqdlXV/qr6+UwdO9e+aEy0uDm5Q/BwQnmizMu5yfE5HpgaTu4QLJmYUD6bcAyVTMj+MdQwHA9MTaRucI7R+Re76YkyL+cCKr9ozMi1rvOgYTc9UeblXEDlF40ZHKPzt2zLVicKgpwbQwU4HmgCx+gom3AMlUzwanJ8T3Gy9/SVl0dO7mLXORHlqpzr8iUzvOo6ZyIUEfkVAyqlxIsxOiZCEZGf5eQYKgUTryEmt3AMlUxgC5UCg9cQE5GfMaBSYPAaYiLyMwbULJELyTq8hpiI/IwBNQvkSrIOJysgIj9jUlIWYLIOUXqYlEQm5FQLNVu7RZmsQ0TkvZwJqNncLcpkHSIi7+VMQM3mydyZrENE5L2cCajZ3C0ahGSdbO1up/j43lOuyJnJ8bN9Mnc/T/gf6m4P9RCEutsB/9aZzOB7T7kkZ1qo7Bb1TjZ3t1NsfO8pl+RMQA1Ct2i2yubudoqN7z3lkpzp8gX83S2azbK9u52i43tPuSRnWqjkHXa35y6+95RLGFAdmI3oDna35y6+95RLOPWgLTwbEbB+SfM/P1H249SDZAJbqDZmIxIRUTo8Cagi8qCIbBKRt0TkNyLSy4t6ODEbkYiI0uFVC/VFABeq6qcAtAC426N6dOB8uERElA5PAqqq/kFV2+ybrwMY7EU9nJiNSERE6fDDGOrNAF7wuhLMRiQionS4luUrIssADIhwV4OqPmPv0wCgBsA1GqUiIjIDwAwAKC8vr26NdJU4EVEamOVLJrg2U5KqTop1v4hMB/AFALXRgqn9PAsBLASsy2aMVpKIiMgQT6YeFJHLAXwHwGdU9Wi8/YmIiPzOqzHUhwH0BPCiiPxVROZ7VA8iIiIjvMryPV9Vz1HVUXaZ6UU9TOB0hUREBOTYajOmcfFkIiIK8cNlM4HF6QqJiCiEATUNnK6QiIhCGFDTwOkKiYgohAE1DZyukIiIQhhQ08DpComIKIQBNU11dcDWrUB7u/Vv0IMpLwMiIkoNL5uhDrwMiIgodWyhUgdeBuQ/7DEgCg62UKkDLwPyF/YYEAULW6jUgZcB+Qt7DIiChQGVOvAyIH9hjwFRsDCgUgdeBuQv7DEgChYGVOok2y4DCjL2GBAFCwMqkU+xx4AoWJjlS+RjdXUMoERBwRYqERGRAQyoREREBjCgEhERGcCASkREZAADKhERkQEMqERERAaIqnpdh4SJyG4ArSk+vC+APQarw2Pz2H49Po+dvApVLTVZGco9gQqo6RCRZlWt4bF57Gw/Po9N5A12+RIRERnAgEpERGRALgXUhTw2j50jx+exiTyQM2OoREREbsqlFioREZFrGFCJiIgMyKqAKiLXich6EWkXkajp8yJyuYi8IyKbReS7ju3nisifReRdEfmViHRJ4tglIvKi/dgXRaR3hH0+KyJ/dZTjInK1fd/PReR9x32jTB7b3u+U4/mfzeB5jxKR1+z35i0R+bLjvqTPO9r757i/q30em+3zqnTcd7e9/R0R+Xyi55nEsWeLyAb7PF8SkQrHfRFff4PHvklEdjuOcYvjvun2e/SuiEx34dgPOY7bIiL7Hfele96PicguEVkX5X4Rkf+y6/aWiIxx3JfWeRMlRVWzpgC4AMAwACsA1ETZJx/AFgDnAegC4E0AVfZ9TwKYav89H0B9Esf+DwDftf/+LoAfxtm/BMDHAIrt2z8HcG2K553QsQEcjrLd1fMGMBTAEPvvMgDbAfRK5bxjvX+OfWYBmG//PRXAr+y/q+z9uwI4136efMPH/qzjPa0PHTvW62/w2DcBeDjKZ+09+9/e9t+9TR47bP/bADxm4rztx/8DgDEA1kW5/woALwAQAJcA+LOJ82ZhSbZkVQtVVTeq6jtxdhsLYLOqvqeqnwBYAuCLIiIAJgJ4yt7vFwCuTuLwX7Qfk+hjrwXwgqoeTeIYpo7dIRPnraotqvqu/fffAOwCkOqsNBHfvxh1egpArX2eXwSwRFVPqOr7ADbbz2fs2Kq63PGevg5gcBLPn9axY/g8gBdV9WNV3QfgRQCXu3js6wEsTuL5Y1LVVbB+fEbzRQC/VMvrAHqJyECkf95EScmqgJqgQQC2OW5/aG/rA2C/qraFbU9Uf1XdDgD2v/3i7D8VZ37p3Gd3WT0kIl1dOHaRiDSLyOuhrmZk+LxFZCysVs4Wx+Zkzjva+xdxH/u8DsA6z0Qem+6xnb4Kq+UUEun1N33sL9mv5VMick6K9U712LC7uM8F8LJjczrnnU790j1voqQUeF2BZInIMgADItzVoKrPJPIUEbZpjO0JHTuB4zqfZyCAiwAsdWy+G8AOWMFmIYDvAJhr+Njlqvo3ETkPwMsi8jaAgxH2c/O8FwGYrqrt9uaY5x3paeLVN8Y+iTw2loQfLyLTANQA+Ixj8xmvv6puifT4FI/9HIDFqnpCRGbCaqVPTKbeaRw7ZCqAp1T1lGNbOuedTv3SPW+ipAQuoKrqpDSf4kMA5zhuDwbwN1iTavcSkQK7VRPantCxRWSniAxU1e124NgVow7/DOA3qnrS8dzb7T9PiMjjAL5t+th2dytU9T0RWQFgNIBfIwPnLSJnAfhfAN+zu+USOu8Ior1/kfb5UEQKAJwNq8swkceme2yIyCRYPzY+o6onQtujvP6JBpa4x1bVvY6bPwPwQ8djJ4Q9dkWCx03o2A5TAXw9rF7pnHc69Uv3vImSkotdvn8BMESszNYusL4AnlVVBbAc1tgmAEwHkEiLN+RZ+zGJPPaMMSY7GIXGNK8GEDGjMdVji0jvUHeqiPQFMB7Ahkyct/06/wbWONf/hN2X7HlHfP9i1OlaAC/b5/ksgKliZQGfC2AIgDcSOssEjy0iowEsAHCVqu5ybI/4+hs+9kDHzasAbLT/Xgpgsl2H3gAmo3PvSNrHto8/DFbyz2uObemedyKeBfAVO9v3EgAH7B9q6Z43UXK8zooyWQD8E6xfpScA7ASw1N5eBuB5x35XAGiB9Su5wbH9PFhfsJsB/A+Arkkcuw+AlwC8a/9bYm+vAfCoY79KAB8ByAt7/MsA3oYVUBoB9DB5bACX2s//pv3vVzN13gCmATgJ4K+OMirV8470/sHqJr7K/rvIPo/N9nmd53hsg/24dwBMSeEzFu/Yy+zPXug8n433+hs89r8DWG8fYzmA4Y7H3my/HpsB/IvpY9u37wHwQNjjTJz3YliZ4Sdh/f/+KoCZAGba9wuAn9p1exuODP90z5uFJZnCqQeJiIgMyMUuXyIiIuMYUImIiAxgQCUiIjKAAZWIiMgABlQiIiIDGFDJcyJyjlgrzpTYt3vbtyvC9lshYSvEiMjtIvJICse8WkSq0qs5EdFpDKjkOVXdBmAegAfsTQ8AWKiqrWG7LoY1qYBTpDmRE3E1rNVnEmbPukREFBGvQyVfEJFCAKsBPAbgVgCj1VrZxLlPHwCbAAxWa77aSgCrAFSoqorIXbCmdewKa2rHf7Mf9xVYUxoqgLdgBe/fwZo0/wCALwHoCWvpumJYEwTcrKr77Kny/gRrhp9nVfX/uvUaEFGw8Rc3+YKqnrQD4u8BTA4PpvY+e0XkDVhLcD2D02udqohMhjWV4FhYM+c8KyL/AGAvrNmRxqvqHhEpUdWPxVro+neq+hQAiMhbAG5T1ZUiMhfAvwG43T50L1V1TnJPRHQGdvmSn0yBNcXchTH2cXb7Ort7J9tlLYA1AIbDCrATYa1+sgcAVPWMdTVF5GxYQXOlvekXsBa1DvlVKidDRLmFAZV8QURGAfgcgEsA3BE20bvTb2EtGD4GQDdVXRN6CgD/rqqj7HK+qv63vT3dcY0jaT6eiHIAAyp5zl5pZh6A21X1AwAPAvhRpH1V9TCsJbgeQ+dkpKUAbhaRHvZzDhKRfrAm7P9ne/wVoUxiAIdgjZtCVQ8A2Ccin7bvuxHAShARJYEBlfzgVgAfqOqL9u1HAAwXkWjjlosBjASwJLRBVf8A4AkAr9kLpz8FoKeqrgdwH4CVIvImgB/bD1kC4C4RWSsifwdrubcH7bHUUYi9yDkR0RmY5UtERGQAW6hEREQGMKASEREZwIBKRERkAAMqERGRAQyoREREBjCgEhERGcCASkREZMD/B1WOn8OTpEXpAAAAAElFTkSuQmCC\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -95,6 +108,17 @@
     "## Exponential Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Exponential $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(0,3)^{p}$$\n",
+    "\n",
+    "$$Y=\\exp(w^{T}X)+10\\kappa \\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 5,
@@ -112,7 +136,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -142,6 +166,17 @@
     "## Cubic Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Cubic $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=128\\left(w^{T}X-\\frac{1}{3}\\right)^{3}+48\\left(w^{T}X-\\frac{1}{3}\\right)^{2}-12\\left(w^{T}X-\\frac{1}{3}\\right)+80\\kappa \\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 7,
@@ -159,7 +194,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -189,6 +224,18 @@
     "## Joint-Normal Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Joint normal $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Let $\\rho=1/2p$, $I_{p}$ be the identity matrix of size $p\\times p$, $J_{p}$ be the matrix of ones of size $p\\times p$, and $\\Sigma =\\begin{bmatrix}\n",
+    "    I_{p} & \\rho J_{p} \\\\\n",
+    "    \\rho J_{p} & (1+0.5\\kappa)I_{p}\\\\\n",
+    "\\end{bmatrix}$. Then\n",
+    "\n",
+    "$$(X,Y) \\sim \\mathcal{N}(0,\\Sigma)$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 9,
@@ -206,7 +253,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -233,7 +280,20 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Step Simulation"
+    "## Step Function Simulation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Step Function $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=\\textbf{I}(w^{T}X>0)+\\epsilon$$\n",
+    "\n",
+    "where $\\textbf{I}$ is the indicator function, that is $\\textbf{I}(z)$ is unity whenever $z$ is true, and $0$ otherwise."
    ]
   },
   {
@@ -253,7 +313,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -283,6 +343,17 @@
     "## Quadratic Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Quadratic $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=(w^{T}X)^{2}+0.5\\kappa \\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 13,
@@ -300,7 +371,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -330,6 +401,17 @@
     "## W-Shaped Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "W-Shape $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U \\sim \\mathcal{U}(-1,1)^{p}$,\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=4\\left[\\left((w^{T}X)^{2}-\\frac{1}{2}\\right)^{2}+w^{T}U/500\\right]+0.5\\kappa\\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 15,
@@ -347,7 +429,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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4cGHZfffdtynV9x4wYEB7fX39jurq6tMmTZr08TPPPPNAsm0uvvjiPUuWLOkdeT5+/Pj9O3fuLB4/fvx+AKiurj44cuTIg5Gap9PUqVM/nDRp0nBnp6RUjRs3rvWqq67aefbZZ59aU1Nz6tVXX73D2dwLAM8880zv6urq00499dTqP/7xj/2+//3vb6uoqGibN2/ee5MnTz5lxIgR1TU1NaPefPPN7gCwadOmom7dumllZaWnXklZNX1bbW2tcizf7BV9XRMASkuB+fPTfw01nXlR9hORZapa61z2+uuvv3fmmWd+GFSZskFNTc3IZ555Zt2AAQPagy6LSbfffvuJffr06bj55puP+/5ff/31AWeeeWZVrO1YQ6WMqa+3AlplJSBiPaYrwGUyL6J89aMf/Wjz+vXrfXe8Cpu+ffu2f/vb3/Z8MsUaKhHlPdZQya1Q1lBFpLuI/ENEXheRVSJye1BlISIi8ivI+1APA7hAVfeLSDGAv4nIU6r6aoBlIiIiSklgAVWttuZIN+9iO2VP+zMREZFDoJ2SRKRQRP4FYDuAZ1X1tRjrTBORZhFp3rFjR+YLSUQUkCBmm0l1hhYKOKCqaruqngVgKIAxInLcTOiqOl9Va1W1trw85vCOREQ5ye9sM6lIdYYWCsltM6q6G8CLAC4MuChERKmZO7c/KirOQEFBDSoqzsDcub6nb0tlthmnTM7QQsH28i0Xkb723z0ATADAMyMiyj5z5/bHzTdXYsuWEljzt5Xg5psrTQTVVGabccrUDC0UbA11MIDFIvIGgH/Cuob65wDLQ0SUmtmzhyB6MPlDhwowe7bv6ducs804l69YsaLntGnTPgKs2WaWLVvWK9b2kRlaBg8eHHOGlhNOOKEjMkOLc7tzzz33wMKFCwfMmDGj4h//+EePfv36dbz44os9IzO0jBo1qvrRRx8t27hxY84N7JCqIHv5vgFgdFD5ExEZs3Vr7KASb7lHt95667azzz67evLkyZ4HmvA7Q8vvfve7E6655pqTv/Od72zr379/27hx4/b+6U9/etdrOfIB276JiPwaNCj2NG3xlntkeraZdM3Qku8YUImI/Jo1631079517szu3Tswa5aR6dsAs7PNpGOGFuJYvkREZsbynTu3P2bPHoKtW0swaNARzJr1PqZPNzZ9G4VDorF8gxx6kIgod0yf/hEDaH5jky8REZEBDKhEREQGMKASEcXW0dHRIUEXgsLD/j10xHudAZWIKLaVO3bsOIFBlQArmO7YseMEACvjrcNOSUREMbS1tV23devWB7Zu3Xo6WPkgq2a6sq2t7bp4KzCgEhHFUFNTsx3AxUGXg7IHz7qIiIgMYEAlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUImIiAxgQCUiIjKAAZWIiMgABlQiIiIDGFDJuKYmoKoKKCiwHpuagi4REVH6cbYZMqqpCZg2DWhttZ5v2GA9B4D6+uDKRUSUbqyhklEzZ3YG04jWVms5EVEuY0AlozZu9LaciChXMKCSUcOGeVtORJQrGFDJqDlzgNLSrstKS63lRES5jAGVjKqvB+bPByorARHrcf58dkgiotzHXr5kXH09AygR5Z/AaqgicpKILBaRNSKySkRuDKosREREfgVZQ20DcIuqLheR3gCWicizqro6wDIRERGlJLAaqqpuUdXl9t/7AKwBMCSo8hAREfkRik5JIlIFYDSA12K8Nk1EmkWkeceOHZkuGhERkSuBB1QR6QXgdwBuUtW90a+r6nxVrVXV2vLy8swXkIiIyIVAA6qIFMMKpk2q+kSQZaHsEabB98NUFiIKVmCdkkREAPwvgDWq+pOgykHZJUyD74epLEQUPFHVYDIWGQfgJQBvAuiwF/9fVV0Ub5va2lptbm7ORPEopKqqrMAVrbISeO+9/C0L+SMiy1S1NuhyUHYLspfv31RVVPUTqnqWneIGU8pNXptMwzT4fpjKQkTBC7xTEuWvSJPphg2AameTaaKgGqbB98NUFiIKHgMq+ZZqx5xU5k4N0+D7YSoLEQWPAZV8SaWWGZFKk2mYBt93lgUACgs7TwjY25co/zCgkmuxaqKp1DIjUm0yra+3Ov10dFiPQfaora/vrKm2t1vLvJxUEFHuYEAlV+LVRGP1cgXcdczJlSbTG29M/aSCiHIHAyq5Eq8mWlgYe303HXPC1HybqqYmYOfO2K+xty9RfuF8qORKvODQ3m7VKp3B1kstM9vnTk1UC2VvX6L8whoquRIvOERqldlcy/QjUS3Ub9N1Kr2nc3koxFzeN8oRqpo1qaamRikYjY2qpaWq1hVUK5WWWssTbVNZqSpiPSZaN1tVVnb9TCKprMzf+6b6eXvdJluke98ANGsIjnFM2Z0CL4CXxIAaLC8BMpcP7k7p2s9EgTredxBvm8pKf2UJg3TvGwMqk4kU2Fi+qeBYvuEVuYVm40areXj//tiddXJxnNvofZ8zx3+Td0GBFTKSKS3tbGKPt42IdYtRNkv3vnEsXzKB11DJt1i31GRrz9dUrtOl477Y/v3dree8PcfNfb3Zeh2SwzxSNmBAJd9i3VITT5gP7n5GfQpS5CQl2X292bp/QO7cs0w5Lug2Zy+J11DDSURjXt+KTs5ri2G8xhqma5BuP9Po8iW6zh2m/UtFOju5gddQmQwkXkMl3+LNC1pWBvTqFfvaYhjnEg3TNch4n49I1zI6r6EmE6b9CxteQyUT2ORLvsVrjrvnnvjXFuNdS92wIX7zb7qbiMN0nS7eZzp9eur3/IZp/4hyUtBVZC+JTb7h5bU5Ll7zY7zm30w0EYetGdp0E2fY9i9MwCZfJgMp8AJ4SQyouSPWwT3Rtb1MXf8L82AUJsoW5v0LEgMqk4nEa6gUmMj9m/FmrHFe28uV63+p3rMa6aEbPWZyPg3zmE68hkom8BoqBSZy/2Zkgu5ozmt7uXD9z89tK37mnSWizGBApUA1NVmjKkWLvscwF+5D9BMU43XiCvtAGUT5hAGVAhOpsUWPqlRWdnxTZi7MneonKOZCDZ0o1zGgUmBuvDH2CEu9esUOlOkY4i+T/ATFXKihE+U6BlQKRFNT9o73myo/QTFba+hhG16SKJ3Yy5cCEW8kICA3Z6SJSMfMNGGVTT2T2cuXTGBApUAkmp6ssTF8B1zyLozDS8bDgEomJGzyFZFCEflRpgqTbdiclbp41w3LyhhMcwV7JlO+SRhQVbUdQI2ISIbKkzWyeSqsMEg0/i/lBlM9k3niStnCTaekFQD+KCJXi8hlkZTugoVdttxob+JglI4DWrZ2siH3TPRM5okrZZVkYxMCeChGejCIcRLTPZavl3FO481XKZLWInpiYjB0DqiePtkwrq7fMvrdPlNjOINj+TIZSMFmDjwIYDuAlW7WTymguvyP9ho4smGyZhNlDOV+1tXFLpTXJKLa0BDILmTDiUoYypj0xNXQWQkDKpOJlHwFYCiA39uBbxuA3wEYaiRz4NMAzk5bQI03pUld3XGreg0cYTjYxCtX5PiSKI64FYqaeEND/J0xnQoKMhJkQ3miEiUMZUxYhsZG1ZKSri+UlKT0T8iAymQiJV8BeBbA1wEU2ekaAM8aKwBQlbaAmmjSzaiDZiqBI2xNdm6mRMuaGmpxcfIdSXcqK0vblxqKE5UkwlDGhCeuvXrF/948YkBlMpGSrwD8y82ylAuQJKACmAagGUDzsGHD1JNE1TSgy6phOBv3K9mk3V0ORi5lrCbe2Jj8+woy9epldKez4fcWljLGPHFtbHT9v+0GAyqTiZR8BeA5AFMAFNppCoDnjRUgqBoq0KWWmo7AkekabLJm3lBOSl1dnfg7Cmvy2Swc1ksGTqEuY8+eib8fjxhQmUyk5CsAwwA8CWCHfR31DwCGGStAOgNqsrPYgoLjVjcVOII4GIWlRpFUY6NqYWHi7ybkqQPQdkDX1KUeWMN2ySCW0JYx2Xfk+e0YUJn8p+QrAGPdLEu5AOkMqGrvosF/PLfcBrdsD+KeJDvBycLUYSetrg76080vib4XXkNlCii5GdjhXpfLPBORhQBeATBSRDaLyDdMvG8XDQ2JXzd0h3j04AfxBn53Drtm+qb1UA+WcP31wJQp6c+nrMwaDFjtw2uy798nsRNWr7Y+9NNOS2t+5AKH26KgxIu0AM4DcAuATQBmONJtAF4PIvqnPLBDoubFoqLU3tMhVs0w3vVMZw01a5poU5Wupl1TbY+R5oF01F4DqrGGtonWkMZG1RvKGq1WgXgpBWANlclASlRDLQHQC9atMr0daS+Ay9MU39Pj4Yfjv9bW5rtWEWsYQlWrwuIUPexazg4e3tQEFBVZNdL2dv/vV1LStdZpanbxyIzl6jgc19X5f1+gs8Y6YYKZ93Mh14fpa2oCnvt6E364cxriDi6e5hYJooSSRVwAlUFH/UjyNfRgWZkmrFH4kKh3baLaQiZrqBmpuZi8RhqGa5INDVbHNRP7E4LBIrK99lpZqXoA3dLyGYM1VCYDKfkK1sAOfR3P+wF4JojC+gqohu9bc0o1MGaqE1FG8jExHGCMEaxCw96/hE2NyVLfvmktYqKBGELfYc2FZ1AX//P3OdoEAyqTiZR8BWCFm2WZSL4Hx09TDcLPwaqhofMyY2Fheioyaa0JmxpXN6AxdT0zMQBFmqJYou85F67XJzyZ8bkjDKhMJlLyFYBlcNx3CqASwPIgCpvWgGogqHptTstUrSFtQ8j16JH8M42X0jisX8b4GR6xosJ4cRL9nsIwjKAvDQ1xA2qHgZMUBlQmEyn5CsCFADYCWGCnDQA+H0RhfQfUeGN/BnR0yVStwXg+fkY3SnOzZ8Y1Nia/Pp8oGW7mjndil/U11GSfo++3Z0Bl8p+S3oeqqk/DmhHmNwAeA1Cjqs/47w4VgLlzrd6n8ahmriyIf69qvOWpMjHRMwCrm6WI1YM1FQ0NwK5dqW0bVvX1wIcfWr+dvn29b//889ZnaqgrbqTjckdH187Qxn4DQbj++sSvm+qZTeRXsogL6771KQBm2c+HARgTRPQ3MsF4ss5JaWiKiyfeLZqFhebz8tvDc2dFdUodckw0x2UVP7X3NHfKytpevmmunVpZsIbK5D+5GSnpPliDPFxpP98H4BfGI3umJLt/8YMPkp8RGxLvFs1Ubt2MHqkpusITr+biqpxSiH4frI5/718MCuAwCnFtcSOaEIahmjJk1SrrntnCQu/bGq6tRvPzG8gk5295v5Qis+1GRD4ki7iwOyDB0bMX2TZSUjQ3E1Zn4PTd1HWttHVuSuFWkQ5A2yB6JRqz7zpdOqR6H2tUbTVra5ceOX/L9yJ+RyTTtXqwhspkICVfAXgN1rRtkcBajmy9bcYp2T9qz57m8orDVCA03uEkxSED24EugTSSsqYnabq4OYGLlezLD7lwD6lbzt9yu8vPxwQGVCYTKfkKQD2s6ds2A5gD4C0AVwRRWKMB1c21rgwcsUzUPIzeEpHqwb+6Ovt7kqZbRUVKn+1mqcibzzXyW74SScbrBYzmy4DKZCKJqiZtFhaRUQDqYHVQel5V1xhrc/agtrZWm5ubzb1hQYH1rxmPiHXBKeTizW5TWWldK3OlqQmYOtXTBVwFINXV1nVDdI4l6xzXuLQ0RDPehEVhoafflQI4ggJ0R9fvJkt+np5EfstHUYQiJPgtGt55EVmmqrXG3pDyUtxOSSLyFxGpF5GeqrpWVX+hqj8PKpimxYIFiV9XzYrpuGLdEiECXHSRyzc47TRPA9mrnaSh4VgwBUI+fVyYtLcDPXq4Xl0AlKAD7RDci84Oc8OGpaFsAZszB3gWE1CYKJgCyf93iYIQr+oK4BIACwHsgHUP6qUASoKsThtt8o3o2VOTNrtlgYaG45t+XV1nS/U2D/Ivheb1DkCfRt2x79Z5yaCszErZ3nEpaVNvGvo3gE2+TAZS3Bqqqv5RVa+Edd/pEwCmAtgoIg+KyOfSHegzZt685OsMGZL+cvi0aNHxrdetrdbUcjE1NQHdunkfpKG6OnEzObl3333WZ1ld7XoTATARz2N/q6Dy5aYu07Xt3Gkl1WCmbkt265YrEyYkvz3Lzf8sURC8RF8AnwCwAkC0q/3mAAAV6klEQVR7ENE/LTVUVXcDvId88HbXHZNSnfS7uDiQ/cobKXwvHYD+C9UJV8tUxyUjPZHd/B+mafALsIbKZCAlHdhBRAaKyA0i8jKAPwD4K4CadAb5jHvuueTr3H9/+svhQ7zraV2WX399apN+FxQAR46kXDZyob7emuzewwTZAuATWI0DKIm7jsnJ6hPVQGfO7NoZDUjSQhL1nn+VCdDnn0+8ckWFu/9VoqDEi7QAvgngBQDvA7gXwNigo7/pGqrz+tNmqUh+7aZHD6P5m5S0hpDq7TAhr5nnJI/fVYed3sPxt9eYqqEm+32lcuuW8z1dDR6SRmANlclAiv8C8BCAiQAKgi5kJJkMqLEOEAdQHPg/th8x72lNYb7SDkB3oG9Wd2zJeinMu9oBa3CNe9GQWpNrAvEm1IkE7FTuQY5sswc9MjYiUjwMqEwmUuAF8JJMBtR4BwBXATUbriemGEgPoKTLaEe5OiJP1kixJ/BRiL7UYOaLSzSfRKQGmso1VBHVp1GX9H+uIwMnsQyoTCZS4AXwkkwG1Hgn/z+HywNYms+Yfenb190+RKV8GpEn66TwfXYASYfnczNSV7yTz+jfhtdRv24oSz4aUgegz6Iu7Sd1DKhMJlL8F4BFAKqCLqAzZaKGWlmp7u/NDGPVLcVgqnV1ZocwJPNSaHVIdALotlaZqOU50b9AwgBbnXw6QOd14XSf1DGgMplI8V8AvgKgBcBMAMVBF1TVXEBtbIx9TajLwaRHj+NXCHNNNdVAWl197C04Fm+WcPvbjE5Rnercft/x1isri1/EhMG6uDhpWTsA3Y6+GTupY0BlMpESDezwGIDRAPoAaBaR74rIjEgy3t04QyLjze7c2XV5WVnUMHnR9wDE8/zzwQ78UFpqjfO3e7f3baOGDow1hGFpqbWcQqS1Fair877dwYPWb8X+vca7pSZ6ebzfxT33xM8q1m00l7Q24copAhw9mrSoCuBE7Dr2PBeHWaTck+w+1KMADgDoBqB3VMpKsf7RAaBXrxhjzjY2unvTDz4AJkzwXTZPhgyxDo4HD6a2fWOjNVKPramp87OJzI3NsXhD7Lnnjv0+1eu2H3wAiOCh0utjvhwdvFIZozk6KD+NCWjClOQ3vgNog2AKOv/3eFJHWSNe1RXAhQBWA7gLQGnQVWlVM02+nq8Teh3rNt1NwKk27QLWtjHk03ybOamh4di9qF5+D5Ftnkad0e89etCn7ejrqWwvNTRmfDJ1sMmXyUCK/wLwEoDTgi6gM5kIqCldJ/QaxETMHwVSvW4WSQl6e/LaabBMzImrqimfbEUC65IS/71po0/OXN1j6kyOa/qZxIDKZCIFXgAvyURATbk2lkJA21lRnfqBsrFRtajIc54xU5LRjti7NzjGWwdSnT0oOnXvnlIhKis77y31XGsO8P5uBlQmEynwAnhJJnv5phToPB6sIgeUyGAJrg6Ufpp0UzzbZw01OGn57Bsb3U1L6DYVFLjLN8WmZwUCH9aTAZXJRBJVDebiLQARuRDAPQAKATygqnclWr+2tlabm5szUra4mpqAq6+2DgMeONdOOj1ViiJ5dAB4paER4+5z15so0vPZ2VmrtJQdkjKhoCD2T0kE6OgwkEG/fqn1AM+kurrAB70XkWWqWhtoISjruel0lxYiUgjgFwAmAagGcKWIuJ8YMij19cCCBZ1dYV0SR0oHBbARFSiAogiKzz9c73o+ylR6cZIZrmYJ8mPXLitiFxcbekODevSwysYZZChHBBZQAYwBsE5V31HVIwAeBXBJgOVxLzLVVir3AqZBB4BfoAFVeP/YMjdTZznV1wPvvWfVit57L7VgamSC6TyTsXt/jxwJze8VgDUVm9t7vYmyRJABdQiATY7nm+1lXYjINBFpFpHmHTt2ZKxwrjz3nHWGXVERTP4iQGMjikRxA+477mWTc2EmE2k23rDB+kg2bLCeM6gmltHWgcjvtbHRyiwAHQAe7tmAgi3v86SLck6QATXWf/RxV5NUdb6q1qpqbXl5eQaK5U6X2ljx+1hb535iaN/q6qwDY0cHUF+f/mbDJJqagKlTU5tgmsy0DnjOsMPuOmTXWhUx/vkMW1vXgN6limsO3MeTLspJQQbUzQBOcjwfCuCDgMriSazaWM0r96Gp0T7779bNfKY9e1rvHeOaU5BDBkY+i/b22K9nspZMKbBrrSdXKn6BhmOB1WiAtU8AL1x3H0+6KLcF1b0YQBGAdwCcDKAEwOtIMpCEydlm/HB9q4Of2UEAa/Rxl/f0GBscwKNEU3vx1pvsEet+2CvRqG2Q1G6FifEjDPP9zuBtM0wGUrCZAxfBmtFmPYCZydYPS0D1fWAIKvqlQaKpvTh8YXaJ/CyBzqEDu/w8k66QWJjvd2ZAZTKRAr0P1atQ3IcK69rphg3HL6+stK6B5ZN4n0VhIfDww7z1hjqF+X5n3odKJgR5DTVrcZqzTvE+CwZTisb7nSnXMaCmgAeGTvwsyIuM92gmyiA2+RJR3mOTL5nAGioREZEBDKhElBIONUnUVVHQBSCi7BPdYzcy6hHA66KUv1hDJaJj3NY6Z87kUJNE0RhQMygXmshyYR8oNi8THMQbUpJDTVI+Y0DNkFyYjSUX9oHi81LrDHpCBqIwYkDNkFxoIsuFfchVJloOvNQ6ObgJ0fEYUDMkF5rIcmEfcpGplgMvtU4O6EF0PAbUDMmFJrJc2IdcZKrlwGutk6MeEXXFgJohudBElgv7kItMtRyw1knkDwNqhuTCwSoX9iEXmWw5YK2TKHUMqBmUCwerXNiHVIX1liG2HBCFAwOqAWE90JI5Qd8ylOg3xpYDonDgbDM+hXnSZDInyEnl+RtLP842QyYwoPoU5IGWMqegwKqZRhOxmr/Tib+x9GNAJRPY5OsT783MD0HeMsTfGFF2YED1KQz3ZvIabvoF2fHH72+Mvw+izMj7gOr3YBN0D8ugO8vkiyA7/vj5jfH3QZRBqpo1qaamRk1qbFQtLVW1DjVWKi21lnt9n8pKVRHr0ev2flRWdi1/JFVWun+PIMtP7qT6HZn4feQDAM0agmMcU3anvO6UlAudPfx2lmEP0tzS1GQNObhxo9UkHOv3DWSmM1U2YackMiGvm3xNd/YI4lqV3+trnEEmd8Rq3hWJvS7HXyYyL68DqskORUFdq/J7DZc9SHNHrJMj1eODaqLfBzswEaUurwOqiQ5FkQPQlCnB1PT8dpYJQy9lMiPeSZCqu98HOzAR+RT0RVwvyXSnJFV/HXJidWqKTiLBlM1LHiY6ZlHw/HZAyucOTGCnJCYDKfACeEnpCKh+xDsAmTgYZTLQsZdvuKT6ffj9zYjE/g37OSnMFgyoTCZSXvfy9SteD9sIP71lc6EHMnnnt9d1dC/fOXPc//7y+TfHXr5kQl5fQ/Ur0XVGvzf+s7NQfvLb69rN9HrxOh4FPUgJUbYLJKCKyBUiskpEOkQka88K4x2AGhv9zxXKzkL5Kd0nUok6HnEaOCJ/gqqhrgRwGYClAeVvRDoPQKwt5Kd0n0glqwHn8wTyRH4FElBVdY2qvhVE3qal6wDE2kJ+SveJlNcaMO9LJXKvKOgCJCMi0wBMA4BhedbeWV/PAJpvIt93qh2Lkok3HGGsf63oDlKR5mFnOYmoU9pqqCLynIisjJEu8fI+qjpfVWtVtba8vDxdxTWGZ/TkVzqbXb3UgDksJZE3aauhquqEdL13WPGMnsLOSw2YPc2JvOFtMwbxjJ6ygdsaMHuaE3kT1G0z/yYimwGcB+AvIvJMEOUwjWf0lEvY05zIm6B6+f5eVYeqajdVHaiqnw+iHKbxjJ5yCXuaE3nDJl+DeEZPuYb3pRK5x4BqEM/oiYjyV+jvQ802vHeUiCg/sYaaB3hvLBFR+rGGmuN4bywRUWawhppjomujN96Yv/fGsmZORJnEGmoOiVUbjSfX741lzZyIMo011BwSa6SmeHL93liOWkVEmcaAmkPc1jrz4d5YjlpFRJnGgJpD4tU6y8ry795YjlpFRJnGgJpD4o3UdM89+TfaDUetIqJMY0DNIRypqRM/CyLKNFHVoMvgWm1trTY3NwddDCLKMSKyTFVrgy4HZTfWUImIiAxgQCUiIjKAAZWIiMgABlQiIiIDGFCJiIgMYEAlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABNQSamoCqKqCgwHpsagq6RERE5FVR0AXId01NwLRpnZNhb9hgPQc4kDsRUTZhDTVgM2d2BtOI1lZrORERZQ8G1IBt3OhtORERhRMDasCGDfO2nIiIwokBNWBz5gClpV2XlZZay4mIKHswoAasvh6YPx+orARErMf589khiYgo2wTSy1dEfgTgSwCOAFgP4OuqujuIsoRBfT0DKBFRtguqhvosgNNV9RMAWgDcGlA5iIiIjAgkoKrqX1W1zX76KoChQZSDiIjIlDBcQ70WwFNBF4KIiMiPtF1DFZHnAAyK8dJMVf2jvc5MAG0A4g62JyLTAEwDgGG8l4SIiEIqbQFVVSckel1EpgL4IoA6VdUE7zMfwHwAqK2tjbseERFRkILq5XshgH8H8BlVbU22PhERUdhJgsph+jIVWQegG4Cd9qJXVXW6i+12ANiQYrYDAHyY4rZ+MW/mzbzDnXelqpabKgzlp0ACahBEpFlVa5k382bezJsoHcLQy5eIiCjrMaASEREZkE8BdT7zZt7Mm3kTpUveXEMlIiJKp3yqoRIREaUNAyoREZEBORVQReQKEVklIh0iErcLvYhcKCJvicg6EfkPx/KTReQ1EXlbRH4jIiUe8u4vIs/a2z4rIv1irPNZEfmXIx0SkUvt134lIu86XjvLZN72eu2O938yg/t9loi8Yn83b4jIVx2ved7veN+f4/Vu9n6ss/eryvHarfbyt0Tk827300PeM0Rktb2fz4tIpeO1mJ+/wbyvEZEdjjyuc7w21f6O3rZHKTOd992OfFtEZLfjNb/7/aCIbBeRlXFeFxH5mV22N0TkbMdrvvabyBNVzZkE4FQAIwG8CKA2zjqFsOZgPQVACYDXAVTbrz0GYLL991wADR7y/n8A/sP++z8A/HeS9fsD+AhAqf38VwAuT3G/XeUNYH+c5WndbwAjAAy3/64AsAVA31T2O9H351jnegBz7b8nA/iN/Xe1vX43ACfb71NoOO/POr7ThkjeiT5/g3lfA+DncX5r79iP/ey/+5nMO2r9GwA8aGK/7e0/DeBsACvjvH4RrAk2BMC5AF4zsd9MTF5TTtVQVXWNqr6VZLUxANap6juqegTAowAuEREBcAGAx+31HgZwqYfsL7G3cbvt5QCeUjNDL3rN+5hM7Leqtqjq2/bfHwDYDiDVUWlifn8JyvQ4gDp7Py8B8KiqHlbVdwGss9/PWN6qutjxnZqcmtDNfsfzeQDPqupHqroL1nzEF6Yx7ysBLPTw/gmp6lJYJ5/xXALg12p5FUBfERkM//tN5ElOBVSXhgDY5Hi+2V5WBmC3ds7TGlnu1kBV3QIA9uOJSdafjOMPOnPsJqu7RaRbGvLuLiLNIvJqpKkZGd5vERkDq5az3rHYy37H+/5irmPv1x5Y++lmW795O30DXacmjPX5m877y/Zn+biInJRiuVPNG3YT98kAXnAs9rPffsrnd7+JPAlkcHw/xMW0cMneIsYyTbDcVd4u8nW+z2AAZwB4xrH4VgBbYQWb+bAmD5htOO9hqvqBiJwC4AUReRPA3hjrpXO/FwCYqqod9uKE+x3rbZKVN8E6brZNxPX2IjIFQC2AzzgWH/f5q+r6WNunmPefACxU1cMiMh1WLf0CL+X2kXfEZACPq2q7Y5mf/fZTPr/7TeRJ1gVUTTItnAubAZzkeD4UwAewBtbuKyJFdq0mstxV3iKyTUQGq+oWO3BsT1CGrwD4vaoedbz3FvvPwyLyEIDvms7bbm6Fqr4jIi8CGA3gd8jAfotIHwB/AfADu1nO1X7HEO/7i7XOZhEpAnACrCZDN9v6zRsiMgHWycZnVPVwZHmcz99tYEmat6rudDz9JYD/dmw7PmrbF13m6ypvh8kA/k9Uufzst5/y+d1vIk/yscn3nwCGi9WztQTWAeBJVVUAi2Fd2wSAqQDc1HgjnrS3cbPtcdeY7GAUuaZ5KYCYPRpTzVtE+kWaU0VkAICxAFZnYr/tz/n3sK5z/TbqNa/7HfP7S1CmywG8YO/nkwAmi9UL+GQAwwH8w9VeusxbREYDmAfgYlXd7lge8/M3nPdgx9OLAayx/34GwES7DP0ATETX1hHfedv5j4TV+ecVxzK/++3GkwC+Zvf2PRfAHvtEze9+E3kTdK8okwnAv8E6Kz0MYBuAZ+zlFQAWOda7CEALrLPkmY7lp8A6wK4D8FsA3TzkXQbgeQBv24/97eW1AB5wrFcF4H0ABVHbvwDgTVgBpRFAL5N5Azjffv/X7cdvZGq/AUwBcBTAvxzprFT3O9b3B6uZ+GL77+72fqyz9+sUx7Yz7e3eAjAphd9Ysryfs397kf18MtnnbzDvHwJYZeexGMAox7bX2p/HOgBfN523/fw2AHdFbWdivxfC6hl+FNb/9zcATAcw3X5dAPzCLtubcPTw97vfTExeEoceJCIiMiAfm3yJiIiMY0AlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBApcCJyElizTjT337ez35eGbXeixI1Q4yI3CQi96WQ56UiUu2v5EREnRhQKXCqugnA/QDushfdBWC+qm6IWnUhrEEFnGKNiezGpbBmn3HNHnWJiCgm3odKoSAixQCWAXgQwDcBjFZrZhPnOmUA1gIYqtZ4tVUAlgKoVFUVke/BGtaxG6yhHf/T3u5rsIY0VABvwAref4Y1aP4eAF8G0BvW1HWlsAYIuFZVd9lD5f0d1gg/T6rq/6TrMyCi7MYzbgoFVT1qB8SnAUyMDqb2OjtF5B+wpuD6IzrnOlURmQhrKMExsEbOeVJEPg1gJ6zRkcaq6oci0l9VPxJrous/q+rjACAibwC4QVWXiMhsAP8J4CY7676q6hzknojoOGzypTCZBGuIudMTrONs9nU290600woAywGMghVgL4A1+8mHAKCqx82rKSInwAqaS+xFD8Oa1DriN6nsDBHlFwZUCgUROQvA5wCcC+DmqIHenf4Aa8LwswH0UNXlkbcA8ENVPctOH1fV/7WX+72uccDn9kSUBxhQKXD2TDP3A7hJVTcC+BGAH8daV1X3w5qC60F07Yz0DIBrRaSX/Z5DROREWAP2f8W+/opIT2IA+2BdN4Wq7gGwS0Q+Zb92NYAlICLygAGVwuCbADaq6rP28/sAjBKReNctFwI4E8CjkQWq+lcAjwB4xZ44/XEAvVV1FYA5AJaIyOsAfmJv8iiA74nIChH5GKzp3n5kX0s9C4knOSciOg57+RIRERnAGioREZEBDKhEREQGMKASEREZwIBKRERkAAMqERGRAQyoREREBjCgEhERGfD/ATkeUR3S1XMrAAAAAElFTkSuQmCC\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -377,6 +459,20 @@
     "## Spiral Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Spiral $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U \\sim \\mathcal{U}(0,5)$, $\\epsilon\\sim\\mathcal{N}(0,1)$,\n",
+    "<br></br>\n",
+    "<br></br>\n",
+    "<center>$X_{|d|}=U\\sin(\\pi U)\\cos^{d}(\\pi U)$ for $d=1,...,p-1$</center>\n",
+    "\n",
+    "$$X_{|p|}=U\\cos^{p}(\\pi U)$$\n",
+    "\n",
+    "$$Y=U\\sin(\\pi U)+0.4p\\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 17,
@@ -394,7 +490,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -424,6 +520,17 @@
     "## Uncorrelated Bernoulli Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Uncorrelated Bernoulli $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U \\sim \\mathcal{B}(0.5)$, $\\epsilon_{1}\\sim \\mathcal{N}(0,I_{p})$, $\\epsilon_{2}\\sim \\mathcal{N}(0,1)$,\n",
+    "\n",
+    "$$X \\sim \\mathcal{B}(0.5)^{p}+0.5\\epsilon_{1}$$\n",
+    "\n",
+    "$$Y=(2U-1)w^{T}X+0.5\\epsilon_{2}$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 19,
@@ -441,7 +548,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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ZYYcd1lBUVHRg06ZNXZ599tme55577keHH354EwB8/vOf/3Dp0qW9xo0bt8d/3mmnnbbrm9/8ZumBAwfyLrroog9PP/30PYsWLer15ptvdh8zZsxwADhw4ABHjx59sK59+/Zt2LhxY0GiugdlLOh6+T/jZmE3l3fwW+HUSESyWWXloYDr273bbe8IQbd/f+zfvLllgO3fH/tTsf8f/OAHW0eNGlU2adKkbcmU79mzZ7O+4W7duhngWnBdunSxvDzXKM/Ly0NDQwN3797N73znOyUvvPDCq8cdd9yBmTNnDty7d2/c3tLu3bs37dmz52CZ008/fefixYuPKCgosC9+8YsfX3rppaWNjY289dZbN8bbD4BmderSpQsaGhqixg//dfivpaGhIakUthMnTty5fPny1//4xz8eccUVVxzz7W9/e2tRUVHDGWec8fGjjz76drTn7Nu3L6+wsDB+H3uEjE+kEhFJxrvvtm57tpk1C//u3h3NvqC7d0fTrFn4dyr2f9RRRzV+8Ytf/PC+++7r628bOXLkrrvuuqs3ANx5551F5eXlSU1oimb37t15ANC/f/+G7du35z366KNRZysHHX/88XvXr19/cIbv+PHjd9555539/uM//mPnwIEDGz788MMub731VvfRo0fvjXxujx49Gv3x0/aaMGHCziVLlhy5Y8eOvI8//jhvyZIlvT/72c/uCJZZv35910GDBh34zne+s23y5MnbVq5cWTh+/PhdNTU1PdesWdMNAHbs2JH3yiuvHHw9b7/9dreRI0e2qHs8Croi0iEMGdK67dlm2jR88ItfoHbAAOwngQEDsP8Xv0DttGn4IFXHqKys3PLRRx8d7MGcO3fuuwsWLOg7bNiwskWLFvWZM2dOwhZlLH379m2sqKioKysrO3HixInHjRgxYlei55x33nnbly1b1su/P378+J319fUF48eP3wkAZWVle44//vg9fgs26PLLL982ceLEocGJVG11xhln7L700kvrR40adcLo0aNPuOyyy+qCXcsA8MQTT/QqKys78YQTTih75JFHen//+9/fOnDgwIY777zznUmTJh07bNiwstGjRw9fvXp1dwDYuHFjl27dullJSUmrZlIl1ezuaMrLy01rL4t0LpFjugBQWAjMnx9e9zLJFWZW7t9ftWrVOyNGjEiqOzdXjR49+vgnnnhiQ9++fRszXZdUuummm/odfvjhTddff33Uz3/VqlV9R4wYURq5XS1dEckKiWYmV1S4AFtSApDuOsyAK23zs5/9bNObb77Z7sli2ebII49svPrqq1v9g6tTZhkSkY4l2ZnJFRUKsh3NhAkTEnZDd0TXXnttfVuep5auiGRcvJnJIp2Jgq6IZFxHn5kskiwFXRHJuI4+M1kkWQq6IpJxVVVuJnJQYaHbLvFlIstQWzPziIKuiGQBzUxuu/ZmGWqLtmbmEQVdEUmzZJMUVFQA77wDNDW5604ZcOfNK8LAgScjL280Bg48GfPmtTu1X1uyDAWFmZlHFHRFJI38U4FqawGzQ6cCdaTsQCkzb14Rrr++BJs3d4XL7dcV119fkorA25YsQ0FhZeYRBV0RSQO/dTt5sk4FOmj27EGITBCwd28eZs9ud2q/YJah4PaXXnqpx9SpUz8AXJahFStW9Iz2fD8zz4ABA6Jm5jniiCOa/Mw8weeddtppuxYtWtR35syZA//1r38d1rt376Znn322h5+ZZ/jw4WX3339/n3fffbfTLY7RVlocQ0RSasYMYN4817KNJSdPBdqyJXrgibW9lVqbZSgozMw8uU4tXRFJmRkzgLlz4wdcIEdPBerfP3oKv1jbWynVWYbSlZkn12U06JK8m+T7JNfEeHw8ye0kX/Yus8Kuo4gkp7ratXATydlTgWbN+je6d2+ee7V79ybMmpWS1H5AarMMpSMzj2Q4yxDJTwPYCeD3ZnZSlMfHA/iumX2hNftVliGR8JWWuolS8ZSUuIDbUWcmtzvL0Lx5RZg9exC2bOmK/v33Y9asf2PatJSl9pPsESvLUEbHdM1sOcnSTNZBRFIj3jgtCSxY0HGDbcpMm/aBgmxu6whjumNJriL5GMkTM10ZEYku3jjttGkKuCJA9gfdlQBKzGwEgF8D+HOsgiSnkqwhWVNXVxdaBUXEibaUIwlMnw7MmZOZOolkm6wOumb2sZnt9G4vAVBAsm+MsvPNrNzMyouLi0Otp0guaEuS+QULOn3AbWpqamKmKyHZxfubaIr2WFafp0uyP4CtZmYkx8D9SGhT4mARaTslmY9pTV1dXVlxcfH2vLy8zM1KlazR1NTEurq6IwBEPSsno0GX5CIA4wH0JbkJwA8BFACAmc0DcBGA6SQbAOwBMMkyOd1aJEfFSzKfY0G2mYaGhqu2bNly15YtW05ClvccSmiaAKxpaGi4KtqDGT1lKF10ypBIauXlRV/wgnQJCnJF5ClDIq2lX2YikpCSzIukhoKuiCSkJPMiqaGgKyIA4s9OVpJ5kdTI6tnLIhKOZGYn5+DMZJGUU0tXROLOThaR1FHQFZGY6ybnZN5bkTRS0BURzU4WCYmCrkiOqK4G+vZ1E6FId9ufLKXZySLh0EQqkRxQXQ1MmQLs339oW309cOWV7rY/Qaqy0nUpDxnSsfPeimQrrUgl0slVVwOXXw40NkZ/vKQEeOedUKvUYWlFKmkvdS+LdGIzZgCXXRY74AKaLCUSJgVdkU6quhqYNy/6mslBmiwlEh4FXZFOxl9ZavLkxAG3oECTpUTCpIlUIp1I5MpS8fTpA9x2myZLiYRJQVekE4m2slQkEliwQMFWJBPUvSzSiSSaFEUC06Yp4IpkSkaDLsm7Sb5Pck2Mx0nyVyQ3kHyF5Kiw6yiStfxVLgKXeJOiSkpcC3fOnPCqKCLNZbql+zsA58R5fCKAod5lKoC5IdRJJOs1kYg2R+qtWkZdWWrhQncurlq4IpmV0aBrZssBfBCnyPkAfm/O8wCOJDkgnNqJZKcZMwDCXSLlQXlvRbJZplu6iQwCsDFwf5O3rQWSU0nWkKypq6sLpXIiYfPPvY2nosK1apua1LoVyTbZHnSj/ZiPeuahmc03s3IzKy8uLk5ztUQyo7Iy8bm3IpK9sj3obgJwdOD+YADvZaguIhnnz042tPz1qVgskv2yPeguBvA1bxbzaQC2m9nmTFdKJCz+6lJ5ee66qMhtz4cdDLzBi5rBItkt06cMLQLwTwDHk9xE8uskp5Gc5hVZAuAtABsA/AbAjAxVVSR0/upStbUultbWAjt2uKUbARd482DIp+Fb0w15CrgiWS+jK1KZ2SUJHjcA3wqpOiJZJdrqUvv3u+Ube/ZU3luRjijbu5clSTNmAF26uNNEunRx96Vji7W61AcfaHaySEeloNsJzJgBzJ17KGdqY6O7r8DbscVaXUqp+EQ6LgXdTmD+/NZtl46hqgpRV5dSKj6RjktBtxPwW7jJbpeOoaJCq0uJdDZK7dcJ5OdHD7D5+eHXRVKrokJBVqQzUUu3E5g6NfH2yPM9q6vDqJmIiASppdsJ+Kna5s93Ld78fBdw/e3++Z7+6Se1tYcCslpRIiLhoXXCE+rLy8utpqYm09XIGqWlLtBGKilxp5yISHJIrjCz8kzXQzoudS/ngFjne8baLiIi6aGgmwN0vqeISHZQ0M0Bic731CQrEZFwKOjmgHjne0ZbVH/qVAVeEZF00ESqHBdrkhXgFta/7TbNcBbxaSKVtJdaujku3mSq+nrgyivV6hURSRUF3RyXaDLVgQPA5Mka6xURSYVMJ7E/h+TrJDeQvCHK41eQrCP5sne5KhP17MyiTbKKRmO9LWkCmoi0VsaCLsl8AHcAmAigDMAlJMuiFH3AzE7xLneFWskc4E+ySmad5t27XWJ10QQ0EWmbTLZ0xwDYYGZvmdl+APcDOD+D9clZFRXAvfcCXbsmLpurC2pEtmqvvfbQspo+/SgRkUQyGXQHAdgYuL/J2xbpyyRfIfkQyaPDqVruqagA7r7bzViOJxcX1KiuBqZMad6qra+PXjZXf5SISHIyGXQZZVvk+UuPAig1s08CeBrAvTF3Rk4lWUOypq6uLoXVzB0VFcC2bS6wLFyoBOq+b34T2L8/ubK5+KNERJKXyaC7CUCw5ToYwHvBAmZWb2b7vLu/ATA61s7MbL6ZlZtZeXFxccorm2uUQN2prgZ27UqubK7+KBGR5GUy6L4IYCjJY0h2BTAJwOJgAZIDAnfPA7AuxPrlvIoKl4Woqcld51rABRKP0eb6jxIRaZ2M5dM1swaSVwN4AkA+gLvNbC3J2QBqzGwxgG+TPA9AA4APAFyRqfpKboo3Rtunj1IjikjrZPQ8XTNbYmbDzOwTZlblbZvlBVyY2Q/M7EQzG2FmnzWz1zJZX+m8qquBvn1dq5V0t6ur44/R3nZbePUTkc5BK1JJzvNnJwdnJPtLYJ57bssJZSQwfbq6kkWk9RR0JedVVkafnXzgALBkScsJZQsWAHPmhF9PEen4lGVIcl5enjtNKhrSTSQTAZRlSNpPLV1Ju2xfozjeuK3OuxWRVFLQlbTKpjWKYwX/qqroS2AWFOi8WxFJLQVdSavKyuxYozjaUo5Tprjt0ZbA7NMHuOceTZYSkdSKO6brZQK6xcy+F16V2k9jutkj1nhp2GOlfftGXy+5Tx+39KVIMjSmK+0Vt6VrZo0ARpOMtk6ySEKxxkSLisIZ5/W7lGMlKIi1XUQkHZJZkeolAI+Q/AOAg6vQmtnDaauVdBpVVW4MN9jFXFAA7NhxKOD547xAartz/fHkyO5tEZFMSSboFgGoBzAhsM0AKOhKQn4Qrax0SyoOGQLs3Nmyhbl7N3D55c2f017RxpMjJUplKCKSSgmDrpldGUZFpPOqqGgeSPNiDGo0Nqa2xZsot21BgZZyFJFwJZy9THIwyT+RfJ/kVpJ/JDk4jMpJ5xTv3NdUzmyOd5ySEs1OFpHwJXPK0D1wKfcGAhgEl1j+nnRWSjq3qqqW6xkH1da2bpJVvPNvI49TWAgsXJi7qQpFJLOSGdMtNrNgkP0dyevSVSHp/Pxgd/nlrks5EukCL5B4klXkZKlo5YPjyVVVCrYikjkJ114m+TSA3wFY5G26BMCVZnZmeqvWdjpPt2OINruYjH5eb0lJ9Ny1paWHAnQy5UXaQ+fpSnsl0708BcBXAGwBsBnARQA0uUraraKiZQafWL8BY02Kau12EZFMSiboHm1m55lZsZn1M7MLABydioOTPIfk6yQ3kLwhyuPdSD7gPf4CydJUHFeyR0WFa5E2NbnrkpLo5YYMAUDCApcmEkVFccqLiGSZZILur5Pc1ireEpN3AJgIoAzAJSTLIop9HcCHZnYcgF8A+Gl7jyvZLdbkp7dqCQPAiMv79WyRrKCwUIkKRCQ7xZxIRXIsgNMBFJOcGXjocAD5KTj2GAAbzOwt73j3AzgfwKuBMucDuNG7/RCA20nSOmMSYAHQcvJTURGwb9+hIBvk3y8oAAYM0GQpEcl+8Vq6XQH0hAvMvQKXj+HGddtrEICNgfubvG1Ry5hZA4DtAKKuIURyKskakjV1dXUpqJ5kit/lvGCBWy5y58745XftcmUWLNCpQCKS3WK2dM1sGYBlJH9nZlHmh7ZbtCQKkS3YZMq4jWbzAcwH3Ozl9lVNMqm62rV0o81KjqW+HrjsMuC554A5c9JXNxGR9khmTPcukkf6d0j2JvlECo69Cc0nZA0G8F6sMiS7ADgCwAcpOLZkqWDS+yBDy19bkdvMgLlzXRq/dGUtEhFpj2SCbl8z+8i/Y2YfAuiXgmO/CGAoyWNIdgUwCW7lq6DFALxl8HERgGc0ntt5VVe7BTOiJSnIhx0MssFLfpSOj/p6F7gVeEUk2yQTdJtIHjwBg2QJYnTxtoY3Rns1gCcArAPwoJmtJTmb5Hlesd8C6ENyA4CZAFqcViSdg9/CjbZClS8fhrzAJVrA9aVyDWcRkVRJZhnISgB/J7nMu/9pAFNTcXAzWwJgScS2WYHbewFcnIpjSXZq7fhtnz7AV74CPPhg4gT0WiBDRLJNwpaumT0OYBSABwA8CGC0maViTFdyWHW1G3udPDlxwPWTFJgB27a5iVLbtgHTp7sMt9MLAAAUh0lEQVSVrGLRAhkikm2SSe1HAOcAGGVmjwIoJDkm7TWTTsvvSk7UUgWA/Hy3VGS004DmzHGnCUVLRB9cICNWFiIRkbAlM6Y7B8BYuEQHALADbiUpkVaLN1kqUmEhcO+98c+7rahwrd6FC5uv4ewH6uBsaLNDWYgUeEUkE5LJMrTSzEaRfMnMRnrbVpnZiFBq2AbKMpR9qquBa69NrnULuMCZipWllIVIUklZhqS9kplIdcBbJ9kAgGQxgKa01ko6lRkzgHnzYmcQCiosjN2d3BbKQiQi2SSZ7uVfAfgTgH4kqwD8HcDNaa2VdBrV1ckH3D59UhtwgdiTqTTJSkQyIZnZy9UAvg/gJ3D5dC8wsz+ku2LSOVRWJg64+fluTHbbttSvmxwra1FV1aEZ1KS7aCUrEUm3mEGX5F9IVpDsYWavmdkdZna7ma0Ls4LS8QRnCydzOlCiyVLtUVHhWs+Rk6wA4Morm48x19cDU6Yo8IpI+sQb050PtzTjL0k+A2ARgCVmtj+UmkmHU10NfPObLutPMvr0AW67Lf1ZgSoqWh6jtBQ4cKBl2f373exq/3kiIqkUs6VrZo+Y2SUAhgB4GG4N5HdJ3k3yc2FVUDqG6mrXSkwm4JJuYYt0dCcnK95EqsZGl7Foxozw6iMiuSGZMd09ZvaAmX0JwNkARgJ4PO01kw5hxgw3Jjt5smslxuN37y5YkPn0e4kmUvkZi/LzFXxFJHUSnjJE8igAX4Hrah4A4A8ArkxzvaQDOOss4K9/Ta5stp0XW1XlxnSjdTEHNTW54Atk/oeCiHR88SZSfcMby10JYBiA75vZsWb2X2b2cmg1lKw0Y0byAZc8tCRjtqioAO65J/oSktEoT6+IpEK87uXTAdwC4Ggzu8bMngupTpLl/HNvkzVtWnZOSgouIRkvcYKvvt51oyv4ikhbxZtIdaWZPWlmWn1Kmp0GdPnlyS92sXBh9nfLVlS4HwbJBF5ApxaJSNslsyKV5LjIpAHxEs0D6V3sIl38jEU9eiRXfv9+t5a0iEhrxBvTXUKyNB0HJVlE8imSb3jXvWOUayT5sndZnI66SHytyQoEAF27pnexi3SqqAB27nSnMyUj2eQNIiK+eC3d3wF4kmQlyYIUH/cGAH81s6EA/urdj2aPmZ3iXc5LcR0kAb+Fm6hlCxw693bfvo4ZcIPmzHEt9YIk/uqVo1dEWiPemO6DcOfkHg6ghuR3Sc70L+087vkA7vVu3wvggnbuT1LIH7+dPDl+Czc/P7vOvU2lZGc3+zl6NcFKRJKRaEz3AIBdALoB6BVxaY+jzGwzAHjX/WKU606yhuTzJOMGZpJTvbI1dXV17axe7gqO38bjr5nc1OTOv+3ordtogrObk2n11te7906BV0RiiZnEnuQ5AG4FsBjAbDNLclTv4POfBtA/ykOVAO41syMDZT80sxbjuiQHmtl7JI8F8AyAM83szUTHVhL7touV9D0oP7/jjtu2VXW1y5j07ruJZ25n20IgkjpKYi/tFa+lWwngYjO7obUBFwDM7CwzOynK5REAW0kOAADv+v0Y+3jPu34LwLNw3d2SYtmUFShbVVS4QNrU5IJqPPHWdRaR3BZvTPdTZrY2TcddDJdAAd71I5EFSPYm2c273RfAOACvpqk+OSvydKB4/LR4uRZwI0XL0RtUVHToR4wmWYlIUKbO070FwOdIvgHgc959kCwneZdX5gS4CVyrACwFcIuZKeimWGVl4tOBCgvduGZnHbttLT9Hb7RJVgUFwI4dh37E1NZqnFdEDok5ptuRaUw3eXl5sVu4pMvGU1WlYBtLcKx3yBB3nm+s83dLSvRednQa05X2SphlSDq3IUOij+NqMlByKiqaB9G8OH1HfqvXf56I5B4tA5njoo1PFhZmX1agjiJRnt7du13LWERyk4JujvPHJ0tKDi10oclSbZdokhWg2c0iuUzdy9Kii1Tazn8fKytjn36VqDUsIp2XWroiKeaf07twobruRaQ5BV2RNFHXvYhEUtDtZIKrS2lhhswLrmQV7zxnfW4iuUFjup2Iv7qUv9iFTlHpGPS5ieQOtXQ7kWirS+kUlewX63ObPFmtXpHORkG3E4l1KopOUclu8T4fLSMp0rko6HYisU5F0Skq2U0LaojkDgXdTkSrS3VMySyoUVurSVYinYGCbieiU1Q6puDnFo+ftWjyZCA/H5gxI5z6iUjqKMuQSBaJnMmcyPTpwJw56a2THKIsQ9JeaumKZJHI3opE5s9Pf51EJHUyEnRJXkxyLckmkjF/NZI8h+TrJDeQvCHMOopkSnBBjXhdzo0gDjTSRWf/IiJZLVMt3TUALgSwPFYBkvkA7gAwEUAZgEtIloVTPZHsEGuSVSMIAmgRZhV4RbJaRoKuma0zs9cTFBsDYIOZvWVm+wHcD+D89Ncus7QcoAT53c09ejTfHjXgikjWy+Yx3UEANgbub/K2RUVyKskakjV1dXVpr1w6+JNoamsPzVTVwghSUQHs3OkmTeXnxy9r0A82kWyWtqBL8mmSa6Jckm2tRvshH3OqtZnNN7NyMysvLi5uW6UzTMs4Sjxz5gANDe4HWbxWrv+D7bLLdFqRSLZJW8IDMzurnbvYBODowP3BAN5r5z6zmpZxlPYwNP9VagbMmweMG6dztUWyRTZ3L78IYCjJY0h2BTAJwOIM1ymttIyjJC3i/Ho/4OZHdAaZucU0unRRq1ckG2TqlKEvkdwEYCyAv5B8wts+kOQSADCzBgBXA3gCwDoAD5rZ2kzUNyxaxlFaxezg5ZgSaxFwgxobgblzgZ49NdYrkkmZmr38JzMbbGbdzOwoM/tPb/t7ZnZuoNwSMxtmZp8ws04ferSMo7RVVVVyZwvt2qWxXpFM0jKQIp3EjBluDDeZf2kSWLBAP+haS8tASntl85iuiLTCnDkukCZKnAC4wKxZ8SLhU9AV6UT8JSSnT09cVrPiRcKXtlOGRCRz/MxDd97p1nCORrPiRcKnlq5IJzVnjpu1PH16y0lWmhUvkhkKuiKdXHCsN96seK37LZJ+mr0sIgfX/Q4uQ0oC06Yd6qoWzV6W9lNLV0SirvvtLyOpFq9I6ijoikjMmcz+MpLqbhZJDQVdEUk4k1lpJkVSQ0FXRJJaRlJpJkXaT0FXRFBR4SZNJQq8tbXqahZpDwVdEQGQ/DKS6moWaTsFXRE5yF9GcuHClmkmg3bv1gQrkbZQ0BWRFoJpJuOprXWpAkkFYJFkKOiKSFR+qzdR4PXX11G3s0hiGQm6JC8muZZkE8mYq7uQfIfkapIvk9QSUyIZUFUVv6s5SDOcReLLVEt3DYALASxPouxnzewULb0mkhnJdjX7lDJQJLaMBF0zW2dmr2fi2CLSeslOsAJcwgQlTRCJLtvHdA3AkyRXkJwaryDJqSRrSNbU1dUlfQBlVhFJXmSrN9p5vY2NbpxXY7wiLaUt6JJ8muSaKJfzW7GbcWY2CsBEAN8i+elYBc1svpmVm1l5cXFxUjv3M6vU1upLQiRZfqvXrHnKwPz8lmU1xivSXEZT+5F8FsB3zSzhJCmSNwLYaWY/T1Q22dR+paUu0EYqKXFfKiKSvLy8QzOZg0igqSn8+qSDUvtJe2Vt9zLJHiR7+bcBnA03AStlYk340EQQkdaLlTQhUTIFkVySqVOGvkRyE4CxAP5C8glv+0CSS7xiRwH4O8lVAP4F4C9m9ngq66EvCZHUiXZqUWGh2y4iTpdMHNTM/gTgT1G2vwfgXO/2WwBGpLMeVVVuDDeYvFtfEiJtU1HhrisrXW/RkCHuf8nfLiIZCrrZQl8SIqlVUaH/H5F4cjroAvqSEBGR8GTtRCoREZHORkFXREQkJAq6IiIiIVHQFRERCYmCroiISEgUdEVEREKioCsiIhISBV0REZGQKOiKiIiEREFXREQkJAq6IiIiIVHQFRERCYmCroiISEgylcT+ZyRfI/kKyT+RPDJGuXNIvk5yA8kbwq6niIhIKmWqpfsUgJPM7JMA1gP4QWQBkvkA7gAwEUAZgEtIloVaSxERkRTKSNA1syfNrMG7+zyAwVGKjQGwwczeMrP9AO4HcH5YdRQREUm1bBjTnQLgsSjbBwHYGLi/ydsWFcmpJGtI1tTV1aW4iiIiIu3XJV07Jvk0gP5RHqo0s0e8MpUAGgBUR9tFlG0W63hmNh/AfAAoLy+PWU5ERCRT0hZ0zeyseI+TvBzAFwCcaWbRguQmAEcH7g8G8F7qaigiIhKuTM1ePgfAfwE4z8x2xyj2IoChJI8h2RXAJACLw6qjiHQ+1dVAaSmQl+euq6P1sYmkUabGdG8H0AvAUyRfJjkPAEgOJLkEALyJVlcDeALAOgAPmtnaDNVXRDq46mpg6lSgthYwc9dTpyrwSrgYvWe3YysvL7eamppMV0NEskhpqQu0kUpKgHfeSW4fJFeYWXkq6yW5JRtmL4uIpN2777Zuu0g6KOiKSE4YMqR120XSQUFXRHJCVRVQWNh8W2Gh2y4SFgVdEckJFRXA/PluDJd01/Pnu+0iYUnbeboiItmmokJBVjJLLV0REZGQKOiKiIiEREFXREQkJAq6IiIiIVHQFRERCYmCroiISEg65drLJOsARFlltVX6AtiWguq0V7bUA8ieuqgezWVLPYDsqUu66lFiZsVp2K/kiE4ZdFOBZE02LGyeLfUAsqcuqkd21gPInrpkSz1EIql7WUREJCQKuiIiIiFR0I1tfqYr4MmWegDZUxfVo7lsqQeQPXXJlnqINKMxXRERkZCopSsiIhISBV0REZGQKOh6SF5Mci3JJpIxTzUg+Q7J1SRfJlmTwXqcQ/J1khtI3pDqenjHKCL5FMk3vOveMco1eu/HyyQXp/D4cV8jyW4kH/Aef4FkaaqO3cp6XEGyLvAeXJWmetxN8n2Sa2I8TpK/8ur5CslRGarHeJLbA+/HrDTV42iSS0mu8/5nro1SJpT3RCRpZqaLG9c+AcDxAJ4FUB6n3DsA+mayHgDyAbwJ4FgAXQGsAlCWhrr8/wBu8G7fAOCnMcrtTMOxE75GADMAzPNuTwLwQIbqcQWA29P1NxE4zqcBjAKwJsbj5wJ4DAABnAbghQzVYzyA/wvh/RgAYJR3uxeA9VE+m1DeE110Sfailq7HzNaZ2esdpB5jAGwws7fMbD+A+wGcn4bqnA/gXu/2vQAuSMMxYknmNQbr9xCAM0kyA/UIhZktB/BBnCLnA/i9Oc8DOJLkgAzUIxRmttnMVnq3dwBYB2BQRLFQ3hORZCnotp4BeJLkCpJTM1SHQQA2Bu5vQssvm1Q4ysw2A+4LDkC/GOW6k6wh+TzJVAXmZF7jwTJm1gBgO4A+KTp+a+oBAF/2ui8fInl0iuuQrLD+LpIxluQqko+RPDHdB/OGFkYCeCHioWx6T0TQJdMVCBPJpwH0j/JQpZk9kuRuxpnZeyT7AXiK5GveL/8w6xGtNdemc7/i1aUVuxnivSfHAniG5Goze7Mt9QlWLcq2yNeYsvehnfV4FMAiM9tHchpc63tCiuuRjDDej2SshFujeCfJcwH8GcDQdB2MZE8AfwRwnZl9HPlwlKfoPEnJmJwKumZ2Vgr28Z53/T7JP8F1P7Yq6KagHpsABFtTgwG815YdxasLya0kB5jZZq9L7v0Y+/Dfk7dIPgvX4mhv0E3mNfplNpHsAuAIpL7bM2E9zKw+cPc3AH6a4jokK2V/F+0RDHxmtoTkHJJ9zSzlCQhIFsAF3GozezhKkax4T0R86l5uBZI9SPbybwM4G0DUGZxp9iKAoSSPIdkVbhJRymYNBywGcLl3+3IALVrhJHuT7Obd7gtgHIBXU3DsZF5jsH4XAXjGzFLdiklYj4gxwvPgxhYzYTGAr3kzdk8DsN0fHggTyf7+2DrJMXDfM/Xxn9Wm4xDAbwGsM7NbYxTLivdE5KBMz+TKlguAL8H9Kt4HYCuAJ7ztAwEs8W4fCzd7dRWAtXDdwaHXw7t/LtxszTfTUQ/vGH0A/BXAG951kbe9HMBd3u3TAaz23pPVAL6ewuO3eI0AZgM4z7vdHcAfAGwA8C8Ax6bpfUhUj594fw+rACwFMDxN9VgEYDOAA97fyNcBTAMwzXucAO7w6rkacWbhp7keVwfej+cBnJ6mepwB11X8CoCXvcu5mXhPdNEl2YuWgRQREQmJupdFRERCoqArIiISEgVdERGRkCjoioiIhERBV0REJCQKutJheFll3iZZ5N3v7d0viSj3LMn/jNh2Hck5bTjmBSTL2ldzERFHQVc6DDPbCGAugFu8TbcAmG9mtRFFF8EtYhE0ydveWhcAaFXQ9VbHEhFpQefpSofiLfu3AsDdAL4BYKS57D/BMn0AvAZgsLn1kEvhluosMTMj+T0AXwHQDcCfzOyH3vO+BuC7OLTgwlwA/weXSGE7gC/DpZCbB6AQbsGFKWb2obf85T/gVuRabGb/m673QEQ6Lv0ilw7FzA54QfNxAGdHBlyvTD3JfwE4B27pSj/XrpE8G27x/TFwqxUtJvlpuGUKK+ESWmwjWWRmH5BcDJcb9iEAIPkKgGvMbBnJ2QB+COA679BHmtln0vn6RaRjU/eydEQT4ZYhPClOmWAXc7Br+Wzv8hJcNpzhcEF4AoCHzFuU38xaJE4geQRcYF3mbboXLqG774G2vBgRyR0KutKhkDwFwOcAnAbg+jgJyf8Ml9R+FIDDzEt2Dte6/YmZneJdjjOz33rb2zvWsqudzxeRTk5BVzoML6vMXLi8qe8C+BmAn0cra2Y7ATwLN/YbnED1BIApXg5WkBzk5Ub+K4CveOPB8GdIA9gBN44LM9sO4EOSn/IeuwzAMoiIJElBVzqSbwB418ye8u7PATCcZKxx1EUARgC4399gZk8CuA/AP0muBvAQgF5mthZAFYBlJFcB8FPF3Q/geyRfIvkJuFSCP/PGdk+ByzYkIpIUzV4WEREJiVq6IiIiIVHQFRERCYmCroiISEgUdEVEREKioCsiIhISBV0REZGQKOiKiIiE5P8B7di91fT20YEAAAAASUVORK5CYII=\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -471,6 +578,17 @@
     "## Logarithmic Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Logarithmic $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $\\epsilon\\sim\\mathcal{N}(0,I_{p})$,\n",
+    "\n",
+    "$$X \\sim \\mathcal{N}(0,I_{p})$$\n",
+    "<br></br>\n",
+    "<center>$Y_{|d|}=2\\log _{2}{(|X_{|d|}|)}+3\\kappa\\epsilon_{|d|}$ for $d=1,...,p$</center>"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 21,
@@ -488,7 +606,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -518,6 +636,17 @@
     "## Fourth-Root Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Fourth-Root $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=|w^{T}X|^{\\frac{1}{4}}+\\frac{\\kappa}{4}\\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 23,
@@ -535,7 +664,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -565,6 +694,18 @@
     "## Sinusoidal (4$\\pi$) Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Sine Period 4$\\pi$ $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $U\\sim\\mathcal{U}(-1,1)$, $V\\sim\\mathcal{N}(0,1)^{p}$, $\\theta=4\\pi$,\n",
+    "<br></br>\n",
+    "<br></br>\n",
+    "<center>$X_{|d|}=U+0.02pV_{|d|}$ for $d=1,...,p$</center>\n",
+    "\n",
+    "$$Y=\\sin(\\theta X)+\\kappa \\epsilon$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 25,
@@ -582,7 +723,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -612,6 +753,13 @@
     "## Sinusoidal (16$\\pi$) Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Sine Period 16$\\pi$ $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Same as above except $\\theta=16\\pi$ and the noise on $Y$ is changed to $0.5\\kappa \\epsilon$."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 27,
@@ -629,7 +777,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -659,6 +807,17 @@
     "## Square Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Square $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $U\\sim\\mathcal{U}(-1,1)$, $V\\sim\\mathcal{U}(-1,1)$, $\\epsilon\\sim\\mathcal{N}(0,1)^{p}$, $\\theta=-\\frac{\\pi}{8}$,\n",
+    "\n",
+    "$$X_{|d|}=U\\cos(\\theta)+V\\sin(\\theta)+0.05p\\epsilon_{|d|}$$\n",
+    "\n",
+    "$$Y_{|d|}=-U\\sin(\\theta)+V\\cos(\\theta)$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 29,
@@ -676,7 +835,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -706,6 +865,13 @@
     "## Diamond Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Diamond $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Same as above except $\\theta=-\\frac{\\pi}{4}$."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 31,
@@ -723,7 +889,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -753,6 +919,17 @@
     "## Two Parabolas Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Two Parabolas $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $\\epsilon\\sim\\mathcal{U}(0,1)$, $U\\sim\\mathcal{B}(0.5)$,\n",
+    "\n",
+    "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n",
+    "\n",
+    "$$Y=\\left((w^{T}X)^{2}+2\\kappa\\epsilon\\right)\\cdot\\left(U-\\frac{1}{2}\\right)$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 33,
@@ -770,7 +947,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -800,6 +977,20 @@
     "## Circle Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Circle $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U\\sim\\mathcal{U}(-1,1)^{p}$, $\\epsilon\\sim\\mathcal{N}(0,I_{p})$, $r=1$,\n",
+    "<br></br>\n",
+    "<br></br>\n",
+    "<center>$X_{|d|}=r\\left(\\sin(\\pi U_{|d+1|})\\prod\\limits_{j=1}^d \\cos(\\pi U_{|j|})+0.4\\epsilon_{|d|}\\right)$ for $d=1,...,p-1$</center>\n",
+    "\n",
+    "$$X_{|d|}=r\\left(\\prod\\limits_{j=1}^p \\cos(\\pi U_{|j|})+0.4\\epsilon_{|p|}\\right)$$\n",
+    "\n",
+    "$$Y_{|d|}=\\sin(\\pi U_{|1|})$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 35,
@@ -817,7 +1008,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -847,6 +1038,13 @@
     "## Ellipse Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ellipse $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Same as above except $r=5$."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 37,
@@ -864,7 +1062,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -895,6 +1093,17 @@
     "## Multiplicative Noise Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Multiplicative Noise $(x,y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $u\\sim\\mathcal{N}(0,I_{p})$,\n",
+    "\n",
+    "$$x \\sim \\mathcal{N}(0,I_{p})$$\n",
+    "<br></br>\n",
+    "<center>$y_{|d|}=u_{|d|}x_{|d|}$ for $d=1,...,p$</center>"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 39,
@@ -912,7 +1121,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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RkRlbo8QwjCqpTDBF5LXAfaq6KW0/Vd2gqpOqOrls2bI+lc4wDGM+VVqYLwaOEpEtwCXAH4jIxgrLYxiNpsxZ/Q1HZYKpqn+pqstVdQJ4E3Ctqh5XVXmagD0QRhI2u1B/qNqHaXhiD4SRhs1h0B9s1ciG0KYV+oziGRpyFWknIm6kjpGOrRrZMmxSDyMNm8OgP5hgNoQqHwjzndYfm8OgP5hgNoSqHgjznTYDm8OgP5gPs0FMTzsn/tatzrJcv778B8J8p8Yg4OvDNME0UrFggjEIWNDHKAQLJhi+DIKv2wTTSMWCCYYPg+LrNsFsMUXU+BZMMHwYlI7z5sNsKZ3L/YKzDE3sjDJouq/bfJgDzqDU+EY9GBRftwlmS7GRQUbZRF0+Dz8MIyNzv2+jr9sEs6UMSo1vdEev/u3OIM/Ona75PTbWbl+3CWZLseh2c+h3d5wiItpxLp/HHoMlS1q+LK+qNiYdcsghavizcaPq+LiqiHvduLGaPIxkNm5UXbRI1UmXS4sWlXuex8fn/l6Yxsf98xCJz0OkrFKXCzCjHhpUuQjmSSaY/SXrYTYx7Z0ixCsvRYhdFeXOopf70QTT6Jm0h6IKy6iNlGWppYlHEWJXt+vfa3lMMI2eSXuY62hhNBHf8xgKIKgOD8+tuDrxaRkUIXZ1amH0ej+aYDaIOt14UdJuwrb5sKrCR7zi9kkTOh/xqOs91y293o8mmA2hm9q+rJu9M9+pqeSymYVZHFnXM+lcJ53zQazMzMIcEMHMe6HL8h0l5Ts1Ff8wx+0v4vY3iiVJAJOEcBArM/NhDohg5rUGynoYusl3amp++S3wUzx5Lcy6BWT6hUXJB0Aw8wpVmrXRSzM9TbiTbsRBtGSqIK8PMzzGN0hURPma7g81wWwIea2BJJHKa+l13uRjY/H5Dg2pjozE551lHbfhQaoL3QhgPyzNtliztRdMYF/gOmAzcDvw7qxj2iiYqvmEJcl32KsfdHR0vjBmNQOtn2a9ybo+RVRmeVoZda5AmyCYvw4cHLzfE7gL2D/tmLYKZl46b7wkUcvrBx0bm7VeslLYVLcoerF0Kypxx2UFi6JpZKQ7AfP1wde9Aq29YM4rCFwOvCptHxPMeLLEKfowJTW9w5vc9yGLyzv6gA9i15Ze6XYoatJxadc6qcLMi2/F2G0F2i+rtFGCCUwAW4G90vYzwYwn7UFLCxjE3bxZEdlQ9ML9k7odmYWZn25dHGktBt9rH6a8+FqO3VSg/bRKGyOYwBJgE/D6hO/XADPAzIoVK4o/Uy0hbyQ76QGL66yeJ0WFenR07nejo/VpgtWRboeiplVs0fuiDMFU9bMCu6lA+1npNkIwgRHgq8AZPvubhZmfPH6sUPCmplQXL+5eNMfG4puD3frJBoVuhqKGwugjLFmV59BQeU3fbqzFfrp1ai+YgACfBT7me4wJZn7yWJjRB62b43zzNuLpptmdFKQLrcus/NMqzjJEM48/0izMuYL5EkCBW4CbgnRk2jEmmPnZuDG/qOW1SvPmbSSTN7CTdq7T8o+KbZLoVl25mQ+zx2SC2R15m9djY+WJZtUPYZOJmxwlbx/cOOrco6FuUXJb02cAWLjQf99wHSDV/L8zPu4WwUrL29YUmkt0PZ+lS11KWttn9Wq3Vk64Zs7VV8dfJxH/8zw97X4vjjosmNf5n6teJ8gEcwC4//7070Xca7jSX9b+SWzb5lYPjGPx4nauIpiXToE8+eS5Ky/u3One+yxMlrRksm9lFy6Gtnv3/O+scountYLZ75X46kyapTA+Dhdf7B6ysAbPsixCge0k7sELeewx+Pa3B/uaxC1N+/jjyfvv2uVWZ+zMIzyHSZYhOCHOOr9xKz8CDA9b5ZaIT7u9LsnXh1n3YVj9Ju/5SIumhv4u3yGUaWlQrklalDtPkCxPlNvHj1ln32W/YZCDPjbKZD55nee9POR5A0x1nZChWzqHonZ24O82SJb3emQJnz0nswy0YLa95uxX5DCvRVNEaqrVOTVVjNWddi7y9lzwGadddEuszjMSpTHQgtnmmrPMJSo6b/R+WJhNvU7R89XLqKi0c9B5TfNcj6xRVUnzaybNDeBzPuJGd/nem1UL7UALZpt9mGVUBt10ig5T2KSOPnh5Z8npTHVvCZRteUcnNwnH5YfnOG6i6Kmpued8bCx+lE/UTRA3KXTaone9nI8qLN28DLRgqlZfY5VFmrsh2iwcHp67IFna+UgS4aGh9Ad7dHS2k3tnnnEPwcjI3P2ThLXuFmY/Le/h4fniFt4D4Zj9rHu8V4HPmgw4yxXRBF9qIYIJDANn+WTUj2QjfZJvrqRm4dRUdg3ezaieJUviBTVq3WRVWnWwLLqhX2KZluKmbks6d70KvM9kwHkFN0odYg6FWZjAtYD4ZFZ2MsFMFpkka3B4OLsG7+aBShNZn0lvo/+n15ZAP1sTeWcyr0JIO89Fr+XtnFg4z/3iUwG2xsJ0+fAR4ArgeOD1YfLJvOhkgumIE4huxC26WFnRPrmsSW/j/lOWHy7pXPTTSq0qENZt6mbm9SzB9BXgul7DOIoUzAtj0gU+mRedBlEwfa2nJD+Sj4UZ9ztFBG7SxCX6X6am0vNK+9/9tk7qYl1m+Zc7hStu0Tvfa9zZNM6qNHyFMkrVMYeBD/q0gaya16dry6pV3XX3SLM6fR7WMoUl/P2s9YmKvhZNsy6jKa0bUVbrorPy2bgxfYVR38qqapGMUqSFuRz4V+A+4GfAF4HlPpkXnQZFMLMezqTm7tDQrJgMDzuxjHsY8jSVerU0q0rdWphxD3EVHfiLTMPDs/8trgIO+16C//r2vVZWdWiGRylSML8OnAwsCNJJwNd9Mi86DYJg+jycWWu8hBTRXG2qVRXtUtXLuS/CB1iH5Hs/+Fp9aS0In/urDoGeKEUK5k0+2/qRBkEwfQQqvKHjvovW7kV016iLzy5vGh7Ob600tXLwuV+yrmVe0s6VTwumDl2JovgKps/0bjtE5DgRGQ7ScUDCrIdGryTNcRgSzlOYNAVbdLvPPlnT4CXlkTTFW13YvRuOO87NOek7jVzWuW8Cw8NzP0fntdxnn+Tj8k61t3797GTTnezcmT2Xp8+9WUuyFBVYgetWtB3nx/wSsMJHjYtOg25hRptIPj4gn6BRt3lE/V51T76+sab8n7Q0Opo82ivNtZDVLE/b5pNnJ232Yb7YZ1s/0iAIZt6+i1n+ps59opMrZC1+lRRZjet8Xnc/n49vLKs/ax1Snu5EnfdOlnslaZz56Gj82POsfLOa122Nkv/AZ1s/0iAIpmp5N5JvtDdcojXLsuwU0ToLp2/ktupy+qS808j1MqKrl3zrPidAlJ4FE/h94EzgXuCMSFoH3OyTedFpUASzLHwfmPHx5H2TrIk4K6RuKSkQVGehLyJFR3T1MplxWr51al53g69gpgV9RoEluK5Ee0bS/wJvKMSBavSN6Wm3lkwWixbBkUcm76sav/2xx9LXp6kDYSBoZASe/3wXuBJx25IWb2sDYSBl9Wq44AJYsqT4fDdscOtDicwuptfKNYGyFBUY91HefiSzMLsjqyk+PDzXx9nkTtqW5qbQvRIlb9M8boq5plmQWVBgt6JPi8je4QcRebqIfLUIsRaRI0TkThG5W0T+oog8jfkkrQ4IzqK86KK5a10n7Vv3rkRtp5vzf+qp8y29vN2n9t4bLrywNwuyNau4ZikqcKPPtrwJN9fmj4Bn45r/NwP7px1jFmY6SVHtNOuhc0RM1r5mfTYjdc7aHqWb4E+v92XdfZwUGCXfRKTfJTBOAVFyXFDpq5HPfwn8ZdoxJpjJdDveubNfZtJ+0fHIbeiv2NY0NJTcfO722nU26/P24mhCFL1IwTwC2ApcHKR7gFf7ZJ6R7xuAT0c+Hw/8Y8x+a4AZYGbFihUlnrLmsnFjbysW+nY7iWKi2awUN8VbN/dIN9Zi3YZBxuErmJk+TFX9CnAw8HngC8AhqlqEDzPOI6Mxv79BVSdVdXLZsmUF/Gy7mJ52w9B27+4+j9CnlebbGh+f+9kn4m7Uh507k33TPoT3Rpw/fNcutz2Jxg6DjCFTMEVEcFbmwar6ZWCRiLywgN/eBuwb+bwc+O8C8h0o0gI6vgwNzaY4RGbHI4MTaQsAVcfixTA2Nn/7okXx233pHIceJRS3pEo1rbKNG3ceHePeJHyi5Ofh/I1vDj4/BHyigN++AXiOiOwnIqPAm3Bj1o0cFDFhxO7drpGUZKV23uxr17r9jWrYtQt27ICpqVmRGx6GE0+Ec86Zf718K7eLLoKNG9PFrRtrsVX9NLPa7AQBHiKRcQoa6QMcCdyFi5avzdrfgj7zKcOXGDdeOeqnqtofV0Taf//spTHqnJLWFo+bKMM3T5+F63wnbKnLGHFfKDDo8z1cF6BQOJdRQLeibtIgC2bSTdjP2cCLWoWwyhSu3x49r70EzOqYOv9fnuvby72YdD/WrQtRHEUK5mpcU3kbsB64E3ijT+ZFp0EVzDxr+5QtNk2Ojneufth5jqsuX5FpyZLZa5bn+vZKE7oQxeErmOL2TUdEnguswkW2/11VNxfhDsjL5OSkzszMVPHTlTIxER+VHh93o3N89i2C8fHmRsdHR9046jS/2dKl7R5TnkXc/ZSXoSEnkZ2IuNFkdUVENqnqZNZ+iUEfEblKRFaLyGJVvUNVP6Gq/1iVWA4yeSKTcRFJERcg6AWRYsRyaKi4yR/ykCWW4AImg0pRUes2dSGKIy1KvgF4LbBFRD4vIscE0WwjB0WMoc1zE8ZFJC++GM47b35fypDx8eTvQjwaIl6IuJmN+o1PRHb16t665TSNxYuLj1onLV3x8MMNHj8eJavNDjwN+BPcUrs/BS4AXuXT3i86Nc2HWZQDPC6ftLHC3ZSn6UvJpqU8/rM2n4cwDQ3NDwwVGdVOml+0zsEfigr6zNkZDgRuBHbnOa6o1DTBLNIBHh0H7Lt2dFo+cQ/H1FRzI+ALFsRPDtJtBdW2yHmYxsay11wvQtiaFvwpTDCBXwXeCXwb+DHwYeAgn8yLTk0TzDLG0JZ1IzZZJJYsmRWCsbH5otDt+UibnXyPPar/33lTXEUbRtPjhDWt61CWRdqE8eNRehZM4BTgWuAnwMepaOGzaGqaYJYhbmkPRLc0tRkaPqxl9fuLa1pGm7NNtsjzpjTXTdz5HjgLE7gQOBwY8smoH6lpglnEw+w7aiOu5vb1Tfn0rQyFoU4CkXZO+vFgNqVPalHXLG2tp87z3bQO7KX4MKtOTRNM1d4c6nktv6xjk27YrAdqbCx9tcheFxAbGurOHZDWWb8fTb8ihGjx4t7zyDq3ReUlku98N2mIpAlmC8hrwfgcG2d5Je0brrK4ceP8ccsjI/7rXZfxYIfi33QLs9d5KtNSkStEhue0aU1tX4pokl8NTPhk0q/UVsGcmpq1sIaHZ31keYUoWoPntQTSrNG6LUE7NpY+lr5fTb+ifL9FWZmLF8+16Iq8bnl9mE2jCME8FjeT0FpgxCezslMbBTNpxpxoE9g3RWv5vJZAWvOpanHMatZV2fSL/nYYnS/7fGQJYVjpZpUlzarvNUreNAppkgOLg25ENwPvAc4Ik0/mRac2CmaS7y5sDsfV5kk3edR6LNISqEosm2i5lN3jII8od2u5djMooun4CmbWBMKPA78A9gD27EhGj0xPJ0/au3v33GGO4CaJ3bUreWbs6FDJIidtrWq4YLj0QZOG1IXnvSzuv99/XPYjj8QPU0yaWR/cvaLq3t9zDxx/vNvW6KVxiyRJSXHLUvwQ+BCwyEd9y05tsjCzLJFwlUaffcu0xoqIgg+ipVlWl6OkvqdJKa753K3boInXwRcK8GH+B/B8n0z6ldokmHnWC0+LYpfpR+pHh/a4mcOThKJJpI3/L6Li8PFRhm6dTsHsRcybdh186Vkw65jaJJhpN3tULNP2LbuvYdkdsxctcv/Vp/tLXYfUpdEpVnFj3X3T0NDcSrHbaxOe8zj/tk9LoonXwQcTzJqTx2qsqu9bmWIZRnJ9H/y2WDZxIhr9nFR5LF48N59erNWopZk1EUdbr0MnJpg1J49fsqiId1J/z6RuImVPxuFrbbXZd9ZJ2nmIklTR+Ay5aaEaAAAOB0lEQVQA6OxNESfg4X6Dch1MMBtA9GZNEqewRu+171tSf89nPjP5wehVEEdG3LRrafukdatqUz8/X3wFM270lW9KG9KatFZU26+DCWbDKNtPmddaTBsGl5RGR+PnW8zKp40jR/IQFaYkC7FzAbeNG7Mro6RzneVLbWuzOw0TzIZRtp8y74Ml4uc28LUE0/7fIFkynfic49FR/+nT0lI4pDTr2LYGdtKotWACZwF3ALfglr7Y2+e4Ngtm2WN0u7Eww3IlHRuKah3+X1PxCf51Boa66UsZ7XmRdaxZmPUTzMOBBcH7DwMf9jmuzYKpWq6lleTD9BHCpD6Fnd2fsv7LIFuSSWS5YpIqGt8uQHHnOc3CHNRKrNaCOacA8Dpg2mfftgtm2ey/v99DFieEecQu6SGPs5QGnSThC32WSeI2Npbef3XJkuTfTHIDRGeBGjSaJJhfBo5L+X4NMAPMrFixooRTNRgkWYmrVhUvYkkP+SB1U/ElSzDTLNC0pnlnkKgTs/bn4iuY4vYtHhG5Bvi1mK/WqurlwT5rgUng9epRkMnJSZ2ZmSm2oAPCxISbTKGT8XHYsiX5uOlpNwHG1q1u0of167Mn8Bgaco+tD1m/33aSzpUIPPlk9nXLOt7wQ0Q2qepk1n5ZsxV1jaq+UlUPiEmhWJ4IvBZY7SOWRm9s3Zq+fXraPZxDQ7Mz00xPw5o17oFVda9r1syftabz2H326b1cg0LSzEPh9vXr5884tGiR2w7J5zrPNTBy4GOGFp2YnQlpWZ7jzIfZPVndevIEFqJR1LhjR0fnd6pOajoOYkQ2ik/vgbTmc9I16hx7bqRDnX2YwN3AvcBNQfqUz3EmmN37ntIezLx9+qL99NKCElkTT5gP09HNNfUdEGC9E/yotWB2mwZdMHvty5j04OTt0xe1Ctu6imBV+JyjPNPuxS2yZhXVfHwFs7SgTxkMetCn28BNFkuXws6d87cvXuwesV27ZrctWjQ7o/jatfHlKaJMg0joM44739FAW9L1yoNdn7lUHvQxiicrcFM0CxfGL3MBs8GgOKJBCcOftWvniiXMLtMRMj3du1iCBdu6xSzMBlGWhZm3a0pSOcJjTj0Vzjuv+/IMKj7XIe3c58EszLmYhVlT4rrv+JLVxaRbsrq2dJJmnajC1Vf3Vp5Bxec6pJ37xYvjt4vM/WwtgB7wcXTWJdUt6JM3iFHEBBRlBE7ylstmuykHn+uQ1ishLXgXXTu9cwo+wz/oU7kI5kl1EsxuxK/fS03kHf/dy1hx61tZDFnXoZvuYdGZpyxiHo8JZsl0I355JwnuxZos++HwmbHbKIek+yLrmle1NlQTMMEsmW5mSM9zw/YqeP16OKxvZb1Iux5VrT7aBHwF06LkXdJNxNq3n123+UexSRmMTsrqZdEGLEpeMt1ErFevju/XGDf7T699LvNGvo32c+SR+bYb8zHB7JI84td53JYtzsrbsiV5/14Fr6wuSEZzSeruZd3A/DHB7AFf8euGXgWvW0E32kuvrZZe+hC3hQVVF8CIJxS2vJP3duZhAmmErFgR78P0abV0+t/DuVFhsO4xC/oYxoCQJ+jYSdsDRhb0MQxjDnncNJ3N76Tx64M2iYc1yQ1jgPBx08Q1v0Xiu6kNWq8LszBrRlizi8CCBe61bg52c/63m7hp5lRtEg8wwawV0UXHAHbvdq9Ji49Vge/CaEZzSWpmq1qvCwv61IisuQ7r4GBvu/PfGMxrbEGfBpLlQK+Dg73fs74b/ccGPSRjglkjshzodXCw25DL9mODHpIxwawRcTV7SF1qeLM+BoMyR7E1GRPMGhGt2QGGh92rbw3fj+i1WR/GIFNp0EdE3gOcBSxT1R1Z+7c96NMLvYziMIxBp/ZBHxHZF3gVYOGCAvBZotUwjN6oskn+UeC9QHP6NdUYi14bRvlUIpgichTwE1W92WPfNSIyIyIz27dv70PpmolFr9uPjbCqntIEU0SuEZHbYtLRwFrgr33yUdUNqjqpqpPLli0rq7iJNOUmteh1u7ERVjXBZ+GfIhOwErgP2BKkJ3B+zF/LOrbfi6A1bVlSW5CsvdiKj+VCUxZBE5EtwKTWMEo+iEPEjHpii9qVS+2j5E3AAilGXTAfdT2oXDBVdcLHuqwCu0mNumA+6npQuWDWGbtJjbpgI6zqgc24nkIRC5EZRlHYonbVY4KZgd2khmGEWJPcMAzDExNMwzAMT0wwDcMwPDHBNAzD8MQE0zCM0mjKXAy+WJTcMIxS6JzUOpwwBJrb88QsTMMwSqGNk1qbYBqGUQptnIvBBNMwjFJo41wMJpiGYZRCG+diMME0DKMU2jhhiEXJDcMojbbNxWAWpmEYhicmmIZhGJ6YYBqGYXhigmkYhuGJCaZhGIYnJpiGYRiemGAahmF4YoJpGIbhSWWCKSLvFJE7ReR2Efn7qsphGIbhSyWCKSKHAUcDB6rq84GzqyhHL7RtYlTDMLKpamjkFPAhVf0lgKreV1E5uqKNE6MahpFNVU3y3wJeKiLfE5FviMihFZWjK9o4MaphGNmUJpgico2I3BaTjsZZtk8Hfg/4c+ALIiIJ+awRkRkRmdm+fXtZxc1FGydGNQxfBtkdVVqTXFVfmfSdiEwBl6mqAt8XkSeBpcA8RVTVDcAGgMnJSS2puLlYscI1w+O2G0abGXR3VFVN8i8BfwAgIr8FjAI7KipLbto4Maph+DDo7qiqBPMC4NkichtwCXBiYG02gjZOjGoYPgy6O6qSKLmqPgYcV8VvF0XbJkY1DB8G3R1lI30Mw/Bm0N1RJpiGYXgz6O4oW9PHMIxcDLI7yixMwzAMT0wwDcMwPDHBNAzD8MQE0zAMwxMTTMMwDE+kQQNsEJHtQEy32b6wlPoO37Sy5aeu5QIrW7f0UrZxVV2WtVOjBLNKRGRGVSerLkccVrb81LVcYGXrln6UzZrkhmEYnphgGoZheGKC6c+GqguQgpUtP3UtF1jZuqX0spkP0zAMwxOzMA3DMDwxwTQMw/DEBDMHIvI3InKLiNwkIl8TkWdWXSYAETlLRO4IyvavIrJ31WUKEZE3isjtIvKkiNSiO4qIHCEid4rI3SLyF1WXJ0RELhCR+4KVCGqDiOwrIteJyObgWr676jKFiMhCEfm+iNwclO0Dpf6e+TD9EZG9VPV/g/fvAvZX1VMrLhYicjhwrao+ISIfBlDV91VcLABE5HnAk8A/Ae9R1ZmKyzMM3AW8CtgG3AC8WVV/WGW5AETkZcDDwGdV9YCqyxMiIr8O/Lqq/kBE9gQ2AcfU5JwJsFhVHxaREeBbwLtV9btl/J5ZmDkIxTJgMVCL2kZVv6aqTwQfvwssr7I8UVR1s6reWXU5IrwQuFtVfxwslXIJcHTFZQJAVb8J3F91OTpR1f9R1R8E7x8CNgPPqrZUDnU8HHwcCVJpz6UJZk5EZL2I3AusBv666vLE8Fbg36ouRI15FnBv5PM2avLwNwERmQBeAHyv2pLMIiLDInITcB/wdVUtrWwmmB2IyDUicltMOhpAVdeq6r7ANHBaXcoV7LMWeCIoW9/wKVuNkJhttWgp1B0RWQJ8ETi9o7VVKaq6W1UPwrWsXigipbkzbImKDlT1lZ67/gtwFfD+EovzFFnlEpETgdcCq/q9ZHGOc1YHtgH7Rj4vB/67orI0hsA/+EVgWlUvq7o8cajqAyJyPXAEUErgzCzMHIjIcyIfjwLuqKosUUTkCOB9wFGquqvq8tScG4DniMh+IjIKvAm4ouIy1ZogsHI+sFlV/6Hq8kQRkWVhrxAReRrwSkp8Li1KngMR+SLw27io7z3Aqar6k2pLBSJyN7AHsDPY9N06RO8BROR1wMeBZcADwE2q+uqKy3Qk8DFgGLhAVWuxSKyIfA54BW6asp8B71fV8ystFCAiLwH+A7gVd+8D/JWqXl1dqRwiciBwEe5aDgFfUNUPlvZ7JpiGYRh+WJPcMAzDExNMwzAMT0wwDcMwPDHBNAzD8MQE0zAMwxMTTKNygtlw/ktE9gk+Pz34PN6x3/Ui8uqObaeLyHld/OYxIrJ/byU3Bg0TTKNyVPVe4JPAh4JNHwI2qGrnksqfw3U0j/KmYHtejgFyCaaI2Mi4Acf6YRq1IBh6twm4ADgFeEEwm1B0nzHcKI7lqvrLYCKIb+LWlFYR+XPgWFwn/n9V1fcHx50AvAc3ZvwWnDhfCTwYpD8G9gQ+BSwCfgS8VVV/Hgy1+0/gxcAVqvqRss6BUX+sxjRqgao+HgjeV4DDO8Uy2GeniHwfN1b4cpx1+flALA8HnoObvk2AK4L5JXcCa4EXq+oOEdlHVe8XkSuAK1X1UgARuQV4p6p+Q0Q+iJsj4PTgp/dW1ZeX+f+NZmBNcqNOvAb4HyBttploszzaHD88SDcCPwCeixPQPwAuVdUdAKo6b75JEfkVnCh+I9h0EfCyyC6f7+bPGO3DBNOoBSJyEG4W9N8D/k8wy3ccXwJWicjBwNPCiW1xVuXfqepBQfrNYBy20Pv0bb/o8XijJZhgGpUTzIbzSdw8i1uBs4Cz4/YNZte+HufrjAZ7vgq8NZizERF5log8A/h34NjA/0kYiQcewvktUdUHgZ+LyEuD744HvoFhdGCCadSBU4Ctqvr14PN5wHNFJMlv+Dngd3DLSwBumQ7cHKXfEZFbgUuBPVX1dmA98A0RuRkIpye7BPhzEblRRH4DOBE4K/BlHgSUNuON0VwsSm4YhuGJWZiGYRiemGAahmF4YoJpGIbhiQmmYRiGJyaYhmEYnphgGoZheGKCaRiG4cn/By5fWr1x2kcwAAAAAElFTkSuQmCC\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]
@@ -941,6 +1150,17 @@
     "## Multimodal Independence Simulation"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Multimodal Independence $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U\\sim\\mathcal{N}(0,I_{p})$, $V\\sim\\mathcal{N}(0,I_{p})$, $U'\\sim\\mathcal{B}(0.5)^{p}$, $V'\\sim\\mathcal{B}(0.5)^{p}$\n",
+    "\n",
+    "$$X=U/3+2U'-1$$\n",
+    "\n",
+    "$$Y=V/3+2V'-1$$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 41,
@@ -958,7 +1178,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n"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GsmsYtSIia1R1cdv5aJu1a9duOPzww+9xDV/H6OWus3bt2gWHH374ePR4a1OGVPU/ie+zDYdR4H82kyMjjiS38cqVXt8teP23IyMwezaEp76NjsKKFc3ltWomJ73rDyoWK1bAxETbuTKM/mPpUu6d6SLrSusDqYzmKDK6OMk9HHWQPP44PPWpXstWxPs855z+FSkbGGYYRh3MyF2GjOlE3cSBiEC6MC5a5IV14d574R5nh1O3SRsY1q8VCcMw2sdaugNC0dHFK1Z4buIwktApsGhR8fx1DRsY1hw2v7sv2blz587U7sFBxr83O+POmegOCC4iElf4TUx4buKw23jp0ulCnNV/228Fa1IFYiZVLLqAufH7lhu2bNmyhwnvdPz9dPcAbog7b+7lASHJTRyISJb7OepSPfro6YOMwBPU6MCjoq7tNlmxIn7Udj8PDOsi5sbvT7Zv3/7OO++889w777zzuVjjLcpO4Ibt27e/M/asqs44O/LII9XYlVWrVEdHVb32hGejo95xVdWxsV3PBTY2Vj7+snG3RZB3Ee8zuFf9RtnrqPM+iMS/GyLVpVElwGrtQBln1r/WegbqMBPdeNIKz7KFX5qw9lvBOpPIqmyl/S54ptHn5/J7V/qtQmaia1bWWlsco05scYz8jI/Hu59dF7cYGpo+jQi8fuAk17YtnFE/RZ5r3IIoeX6fh6TFV7o63cwWxzDKYr54A4gfpZynD3N+wiZdQd+uS9z9NtiqHygyCjuunzXP7+NIerYTE97qZsP+xmzDw973LgquYVRC203tOszcy8Uo2ne3apXqyIhOcxHOnj0VR1bcRd2gRjpF3LdJ3QF53L/h593ree9C3LPtt+eOuZfNSlrrGajD+lF0+3nQTlLBPjTkfh391rfXLxQRtaRn4fr7uDSTnm2/PXcTXbOy1noG6rB+E91+q+1HSWsZuV6HDbaqj7wVurj3MXg+Lr/PEu1wnHU/96orsya6ZmWt9QzUYf0mul2u7bsUWlmFrMt1dPkeDCJlxMrFPQ2qw8Oe67mu515HZdZE16ystZ6BOqzfRLerrTzXQsvFnVhVWkZ7uAqxa0sXvL7e6HiAqp57HRU5E12zstZ6BuqwfhPdrrby8uRr1Sqv5ZJUeXApRPu5X7sOunQ/8lSK4sKOjCRXLnu9eq6zjsqsia5ZWWs9A3VYv4lu3gKtqYI4b6G1alXyb/KsbNUVoWmTpHdi2bKpylBQyWniPuWtGMY9x6Y9OtbSNeuitZs4nAfcDdyQcP4lwAPAdb6d4RJvv4muqpvYpIlz9PdB4SyiOneuN5I4KKiXLXPLQ5H+tiQ3okvBai7mKZIEI0m46r5PLoKZ9Q437dGxPl2zLlq7icOLgedniO738sbbj6LrQlKh1eu5TdEIW1R4k1yCSfMr8+bRBlPlw3UwUpX3KU0009694Ldx70+vt2tFsOlKlY1eNuuatZ8BGDfRdaNIQZxkQ0O7xp1WqOYptJYti48nqXXtcn1tDyhrgzyDkcrep1Wr4r0aYUFctWp6BSwQ1rRNLaLxhT0wWe9TF7saTHTNylr7GcgW3a3AWuD7wHNS4lkCrAZWL1q0SGciRQriNKtyw4OsPFpLNx9pc2WrbOlmjTwPx5nW3eBaIaxi16o2MdE1K2vtZyBddJ8KzPP/Pg64xSXOmdrSTSqIkgrDLJs7d6rATBp5HBSUroVdlnintV66WtC2RVw/fdr9LXKfsipy4UpXWtp5FsQok6+2K2AmumZlrf0MpIhuTNgNwIKscDNVdFXjRct12b0yFhW/ZcumhDo8OCutsHQR1TwuxS66H+smTnhF3Nz3cbius5y1L3KepR/L5KvtrgYTXbOy1n4G0lu6+8CT2w8eBWwKvqfZTBbdJKICdMwx6a3XtJZIVoGZ1m+bJqxVtl76rVVcZQWhyrhcW6hBf2zaPXfd5MDlOrIGbrWFia5ZWWs3cfgGcAfwBLAZeAewFFjqn383cKPfp3sN8CKXeAdRdMPU1fINXJhJ54eHp9KPK0zTBD0vXXU/xtHVCkLSAKok6/Wq80S4zEOOs/DOVW1gomtW1lrPQB026KJb9YCrwObOjR/B6iqeaXNP45aWTCvcu+p+jKOLFYSiFbMkwcsS2Oi5vPOQo5W7toTXRNesrLWegTps0EW3yqlFeSxo6SbhumKVS8uwi0KWRBcrCEUH3yUtAZrUak2ailT2XWvLU2Cia1bWhtI2uDf6k0WL2kl3yRLvc3ISxsdBBGbN8j7Hx71zqvG/3bRp6u/ly2Hbtl3Pb9vmHQ9YsQJGR3cNMzrqHa+C4BqGhrzPycnicSU9D9fnVDQv4d8tWODZ0BDsvjts3eoWR5SNG6fnJel5rVwZn862bTA8XCz9cBzB+1DlszKM2mlb9euwfm3pVjVAponRzFELRs+mpZ02vSncgnJtGdY1ernqPtg8y3fGudmL5KWpd6BMGnnnIce9D033l2MtXbOS1noG6rB+FN06Cvoio5eLWpDPrP7kuCUru+Y6riN916leVd2Luvr146zIexbu201bJjIrjqTrrKvf10TXrKy1noE6rB9Ft46Cvqq+XddC1aWfMGid1NG6q4qm+mBdnnnRvDTdr59HLNOepeuI6iCOtOssMwc8CRNds7LWegbqsH4U3TIFfVJhUra1E15FqqpCPDpgKs+I16ZoqqXt8syL5qXoQKmiNm+ee5ppC3m4uMXzvOPBfaqqImeia1bWWs9AHdZvortq1dTWe1HLWgwgboWicH9hmT63sIuuioI5vOuMy+IJZe9pUdFuqqXtIqhJzzCYM5uU/5GRap5ZHsv7rsU9lzQRDYt1eNpRWoUwqMBUVZEy0TUra61noA7rJ9HNEsY00c2aghN11fV6+VtAWatJVW1ZhaCLmFYhmk20tF3zmeRyTbqmpGcVVOySKnhtWPQaXN6NPJXJ4DdVdRmY6JqVtdYzUIf1k+jmWXA+72/Ljg4NF1xNjohO6+uNtuCCreVc7ksX5/C6inuea8rq52xbaKPmWhnIarUmeXzy3r80THTNylrrGajD+kl0y2zXlvbbJkcu12XRVlBSK31oaNdwXVyMoix5riltRG/bz7SMZbVagzB17mBlomtW1mxxjJZJWyBhdBSOO85b1EDEswULpib/J/1WBHbsqD6vTRNdECNpQYedO72FObLuS1uLhlRBnmuKWzhkZCT9nRgbg1WrPOsi4YVPku7F2Bhs2OC9Dxs2wMTE1LmJCTjnHC+MiPd5zjm7hjGMRmhb9euwfmrpJrlt01xtgUs17rfBNm9Nj14tYsPD3nrOaWHCLbms+IL+77anHFWByxzW8AYBweC08EC1tEFrcS3IJvvui7Z005aWbOL5Yi1ds5LWegbqsH4SXdVdC9hez23kabSgjC660KXBMmmC6hImKExdKhJB2KT9fvuBrB14XBeTcBkEV3akexfes7SR3FVjomtW1oK9amcUixcv1tWrV7edjUIsWOC2Lq6I50aLMjnpuVqja+H2M6OjnisQ4G1vgyeeSA47Nua5IaP3IIijH9yJ4+PeGsdRAvdpVrjobzZt8uQpjl4P7r3XW7e4aJfErFmwfXux31ZB9L7UiYisUdXFzaRmzESsT7dDTE66L0Sf1K8Vt/h8lF4Pli0rv+h8UwR9uxMT8NWvevlPYuNGOO207A0Tukx484e040nhwmzcCPPnJ5/futUT5DJjAPbYwxPeNHq9qb7UefOKpxWHy30wjK5gotshXEVhZCR5N52slg/Ao4/C0UfD+ee7561tgoJ1YgLOOstrmSWRVHHpl8I5qUI1f/6uu+mkiWmY++6rKmfxbN2aLdqPPgoXXOC1SFeujN8hKhjIFT2XRT8PkDMGkDZ928B5wN3ADQnnBfgssB74LfB8l3j7rU83wKWPM+hDS5rHmqcfrMuDZqJWZGGEpDi6TtwqY7Nnx89RThsg1TUL3/9on/sxx0z1V8+d695XHAwcbAqsT9espLWbOLwYeH6K6B4HfN8X3xcAv3SJt19FN0kEg4EiadvD9cNoZRfbbbf440HBWrSi0C+jl/NWKoLKU9MbHJSxrNHUXX62JrpmZa39DMB4iuh+CXhz6PvNwL5Zcfar6KYJa5ogd3GVoSIWjMqNOzc8XE5Y+mX0cpFKRZnfzhRryothomtW1rrep7s/cFvo+2b/2DREZImIrBaR1Vu2bGkkc1WTNoE/qT9y69aZM1JZNblPescO73xRLrqo+G+rZnJy177ZYFEPyN/vHB4Mt2KF198/iGzcOP1eGkYX6broSsyx2KJXVc9R1cWqunjhwoU1Z6s+JibiV9WpYrCISPrI35mM66jwugmmdG3cOFXJcFlNK4kdO6bEG+C88wb3GUfvpWF0ka6L7mbgwND3A4DbW8pLq8Qt7Tc6mq+AdR3tWhdpI44HhbgpXdu2wamnevfn4Yfzt1bD4g1wzz3FRgHPBIKpYWneBMNok64Xg5cCbxGPFwAPqOodbWeqDZJcz2ed5V64bt3abovvKU/JF14keS5x3jnGXWn9JbmPA/d5MG+2SH7Dc5GD96XqObH9QFABSfImGEabtCq6IvIN4BfAs0Rks4i8Q0SWishSP8hlwB/wpgx9Gfj7lrLaKJOT8ZscxLmeo2LcFXGJ45FH3MOOjXnXef758S38vIs5nHVWvvB14eI+fuIJTyzHxvLHHxb1iYluvw8uFOmjHh7u78VRjBlO2yO56rB+Hb2sGr9nLHhTLKJr7+bde7VfbGhoarH+YI3h6JrDeUYyBxshdIE8U4LyzLsObHh46r0o8vs6LVg/Os96zcGzD64NvO9F1nyuYmtHbPSyWUlrPQN1WD+Lbtp827RNusMsW5YcB6jOm7eriB16aHr4ti262H/avrCzZrndozYJb1KRdB3Dw17YpPchbapYcL/KTCWreu/dcCUxT4UpaSpQ1m/S8uBScU3CRNesrLWegTqsX0W3SMskrlByaem67lQTFJBZW/B1xcoWqk2Tdi2q2YuiJIljWdGscrGNqKchjycmqXWaJaxJuzSV3fLRRNesrLWegTqsX0W3iFs4KJRcWk9FC9exsf5Y8SrPAgldEec08QhI2qawqPvYZevIqitZ0e4ClzykPdOsPZPjnq/Lvc7CRNesrLWegTqsX0W3SOsiqWY/aJanxdKlTe5dxMO11ZbnfcmqRNW5T+7IiFv8IyO7inXQug/vPR09n0bS/1eevl4TXbOy1noG6rB+Fd0iLd2sTcpnsgVLQ+ZtqVbR4qmStFZ3Ul6LimJ4w/euDbSKXl90fea4DR7yVJaspWvWBbNN7DtE3Ab0o6Pe/Na4+bVDQ1NFx6BRZlP64L5FEfGmKXWJpLyWQcSLc2zMW4wj7t0aHs43LWvuXNhtt3bmgbtuYp/0/5XnPbJN7I2ydH1xjIEi7wIYO3eWL5BF4NBDvc+uE6xoFV6TughJc2W7uC9rHXkK3pmNG+P32h0d9cQp+s6lzZkVgQcfrC6PeXBdrzptbXPDaIy2m9p1WL+6l9MIuyCrns4RnZJT9dZreSzod+v1vKlNcXkt2/fapT7dLJp2AYf3p41ze1eRRtY+wKOj+QbuNdktgLmXzUpa6xmow2ai6IapY+/UaMFVdDR0nr7GrMEwRfrgXEcld2X0sgtNjxxPu79FKnzRCl1wPUFcSceiI5zL9ulWgYmuWVlrPQN12EwX3ToGTiWN4Fy1Kr/wuoyqdWmd5B1t2k8t2DzEXVednoi0+1tGwLPmHMddY9ro5TYqSya6ZmWt9QzUYTNddOuYItTrxS+3l7eVFcwjTWsRibgVlklzRYMRuOG8hVtLRQS+68TN1U17DmVEOe5+FXnnAld1IJJJXpCxse6NKE/CRNesrLWegTpspouuarV9fbNnuy9W4GJBH3FamDLXNzKSP7/94kqOI6kVmCRiwfrLRTwiSZ6Bot4VF6EWSfemdOl5meialbXWM1CHDYLoqmYXhEHrNdp3Gu1HraPPcGwsuaXq0nqp0oXuumZ1V8lzL7IW1ki7R2kVkjRRTHp/XPt/01q6ZZ5XHa5oE12zstZ6BuqwQRHdtEI1raCKFkZVC25gSbsluRR+VQ0WS4qna27LNFzvRXSHoWh3QZIIlqkEBS7kuL5a12ca2+QyAAAgAElEQVS0bFl2xS/v86qrf99E16ystZ6BOqyLolvXAJC4wjVr1G6VruQ0AYg77rrNXlplIG2EdLh1nxZHFdu8NUWeipFqtQv+u7ipk3bvccn33LnuLugq7lnZypaJrllZaz0DdVjXRLdLo2qLuJKzWlp5WjmuhWdS5WBoKHnB/LhWdL8M0EnCZZ3ksIX3n80Sx6y1i13d02mjnauaj5v1vFy9N2UrWya6ZmWt3cThWOBmYD1wesz5twJbgOt8e6dLvF0T3S4V/GkFW1wLctas9L65YFH64Huvlz6IKhh57DqXNhp32H2adC4aR1cqPHlJEr20HYCC9aizBGfZsuy+btcWdtp7nNbf6zodzaU1Hr1PdXUrmOialbX2EoZh4FbgIGAEWAscGgnzVuDzeePumuhWsbuJK1mC5lKIhoUsb8s4q/US504Mz9XM4yp3vQ95d6PpCmmVtSwRTHqeLr8NqEIQs979pPzk2cwirb85T15dMNE1K2vtJQwvBC4Pff8w8OFImBkhuk21dF22icsjoEVWpCpqvV6xQWFF7kPXyeoPTVsKNGhBxk0xcunLD1cE6xTE4N2v4lmlvaM2etmsa9ZewnAicG7o+ylRgfVF9w7gt8DFwIEp8S0BVgOrFy1apF2iKRHIKuCKjFSuc1/VvBWAqu5Dl3HpRx0bS3bhJ62b7OqxiI6Adnlv07wrSa7fIJ9Zv3ehyedtomtW1tpLGE6KEd3PRcL0gDn+30uBq1zi7lpLV7WZ5euyXHlNtVqTLNr/m8fyuOKbdOdXTVbFKCx6catUhSm6fnbUO5L23roI8zHHpKdRliY9Gya6ZmWtvYQd3MuR8MPAAy5xd1F0m6COlm6VlrTGrsso1kFp6Wa5Sl2FpOxSoa73KssFnfZcq3weTa3JbKJrVtbaSxhmAX8Anh4aSPWcSJh9Q3+/DrjGJe5BFd20+ZlB4ZhWqBdpCUcXpXdZ/ziugEwbyeq6VnPWfeiHPt2qKgwuFays5+0iXmW8J/3geYhiomtW1tpNHI4D1vmjmJf7x84EXuP//XHgRl+Qfww82yXeQRVd1emCFrcgQnjP2ujSkK6FZVKhXEbw0tIsex/6QXBVq6swZFWuXBewEPHcw0n3soz3xHWhlC5homtW1lrPQB02yKIbxaXllOWKDPpiXQXMdQ5tkbwOAlVUGFzvZRE3dNH1nU10zcxMdDtP2QI4rcUTkNZaKZJm0dZaP7uFu0aee+m6ZGNapS14R/Nscm/uZbNBtPST3uClT7edybw2U0S3ChFKWzggiMfVFVk2TZcWa7+6hbtI3nuZR3jTln50bfn2owfDRNesrGUHgKsAaTujeWymiG4V7ta0AUp5RjXnEft+nrIzyLguy5j1DrqMK+hXD4aJrllZGyKba4F/E5FTROT1gTn8zijJpk35jscxMeEVc2nxrFgBo6Pp8WzbBsuXu6W5aFG+40Y3mJiApUtBJD3c6CgcdxyMj8PQkPc5OblrPBs2wM6d3ufZZ8M558DYmBf32Jj3fWKivmsxjK7iIrrzga3AS4FX+/aqOjNleFQlXmNj6fFMTOxaKCbhKvZxIj466h03us3RR8P8+cnnez049VQ4/3zYuNGr0G3cCEuW7Cq8UaJCbIJrDCxtN7XrsJniXq5qYFHeeKpya1vfbH/hugRlW6PMu/BOYe5ls5KWHQAOAL4D3A3cBXwbOKDtjKfZTBFd1eoKmjzx2CjiwcR1QY02+uy78k6a6JqVNVFN6PDzEZErgQuBC/xDJwMTqvryetre5Vm8eLGuXr267Wz0NZOTXh/upk2eG3rFCnMJznSGhpL7/wN6Pbj/ftixY/q5sTHPdVwH4+OeG7vJNOMQkTWquri5FI2ZhovoXqeqz8s61iVMdA0jP0nCFjB7ttfn//jj08+NjtY7OCqpQiDi9RM3hYmuURaXgVT3iMjJIjLs28l4A6sMw5hBxA2ACwbWjY3BU58aL7jDw/WPRrYR8cZMwUV03w68AbgTb2/bE4G31ZkpY2YzOZk83cRoj+go9rExuOACr4W5YQPce2/873burL/rwUbEGzMFF9E9UFVfo6oLVfVpqvpa4MC6M2bMTCYnvekleaabGM2Q1Y/fZmszrkJgc32NfsSlT/c3qvr8rGNdwvp0u0tXBsQYuxJUhrZtmzoW7ad1CTPTsT5doyyJLV0ReaGIfABYKCLvD9lH8dZkNgaIqlzCVayyZVTP8uW7iilMX4XMWpuGUZ409/IIMA9vs/ndQ/YgXr+uMSAUdQnHCXVeF6X1/zaDa2XIVpYyjJJkTeQFxtqeTJzXZtLiGF2gyApESYsZ5Fn8visLIgwCSc+412t/FagugS2OYVbSXAZSnSsiewZfRGQvEbm8CsEXkWNF5GYRWS8ip8ecnyMi3/LP/1JExqtI18hHEZdwkrvyssvcXZQuLk+jGuJGB8+eDQ89ZIPeDKNKXAZSXauqR2Qdy52wyDCwDng5sBn4NfBmVf1dKMzfA4ep6lIReRPwOlV9Y1bcNpCqWooMfqpiMYOuLIgwKERHLz/8MGyNmZE/yIPebCCVURaXlu5OEXmyx01ExoCMxeKcOApYr6p/UNXHgW8Cx0fCHA+c7/99MXCMSNbGYzOPtvs1i8yRrGJ6iS2I0CzR/tqkebk26M0wiuMiusuB/xSRC0TkAuCnwIcrSHt/4LbQ983+sdgwqrodeADoxUUmIktEZLWIrN6yZUsF2esGXZjXWmTUahWLGdiCCO1ilR7DqAGXjl9gAd4euq8GFlTRmQycBJwb+n4K8LlImBsJ7WgE3Ar0suKeSQOp2tpGrQqq2CGpC9u5DSo2kG062EAqs5I2K0uUfXfuscBBqnqmiCwSkaNU9Vcl9X4zu65sdQBwe0KYzSIyC9gDSHB6zUz6eV7rxET5KSVVxGEUI7jvttuUYVSHi3v5bOCFwJv97w8BX6gg7V8DB4vI00VkBHgTcGkkzKXAqf7fJwJXqWoV/cl9g7n4jDaxebmGUS0uovuXqvo/gccAVPU+vIUzSqFeH+27gcuBm4CLVPVGETlTRF7jB/sK0BOR9cD7gWnTimY61q9pGIYxc8h0LwNP+NN7FEBEFgKVTNhQ1cuAyyLHzgj9/Rhe3+/AYi4+wzCMmYOL6H4W+A7wNBFZgefm/V+15srYBevXNAzDmBlkiq6qTorIGuAYQIDXqupNtefMMAzDMGYYabsM/buITIjIXFX9vap+QVU/b4JrGEa/0vZCM4aRNpDqHLy5uRv89Y9f648yNgzD6Du6sNCMYSSKrqr+m6q+GVgEXII3dWeTiJwnIi9vKoNG/2CtCKPL2AYaRhfInDKkqo+q6rdU9XXAK4AjgB/UnjOjr6ijFWEiblRJPy80Y8wcMkVXRPYWkfeIyM+AfwWuAI6sPWdGX+HainAVUnMFGlVjC80YXSBtINW7ROQq4DfAIcD/q6oHqeo/qOp1jeXQ6AtcWhF5hNRcgeUxT8Gu2EIzRhdIa+m+CPgEcKCqvkdVf9ZQnowOkLfAdmlF5BFScwWWwzwF0ymyW5ZhVE3aQKq3qeoVqmrbhQ8YcQX2ySfDggXJhbZLKyKPkJorsByD6inIqizaWtJG27isvWwMGHEFNsDWrcmtJZdWRB4hNVdgOQbRU2Cte6MfSOvTvUxExpvLitEV0grmtNZSVisij5CaK7Acg+gpGNTWvdFfpLV0vwZcISLLRWR2Q/kxKiZP32wQNmvzxKKtpSwhjeYVzBVYlDY8BUUHblU14GsQW/dGH5K2wz0wF/gksBb4IN72eu8H3p/2u7btyCOPVEN11SrV0VFVT0Y9Gx31jruETbKxsXbzarixapX3rES8zzrvZdHnV+VzHxur/30FVmsHyjiz/rX0k96+uWcAvwf+CfhIYG1nPM1MdD3yFEJJYaNWlxA2UWAa1RAn5kWfX5XPvYmKm4muWVkT1XhfoogcC3wGuBQ4U1VjhtZ0k8WLF+vq1avbzkbrDA0lu4qjx9PCjo3Vv5dvUvoinnvZ6AbBYKVw3+noaPzAO8h+flU/98nJeveeFpE1qrq4uhiNQSOtT3c5cJKqnl614IrIfBG5UkRu8T/3Sgi3Q0Su8+3SKvMwU0jrD0saNCMyvd8sKezYWP5+1SJ9dIM48KcfSRqsNDwcHz54fknvxPz56b/Li00JMjpPG81r4FPA6f7fpwOfTAj3cJH4B8W9nOVOW7XKcwG6uO+qcs11oW/PqI+k9yl4XuHvQdheT3VkJP5cnI2MdPe5Y+5ls5LWTqJwM7Cv//e+wM0J4Ux0U0jqD+v1psIkFWwi0+PLGngTdz56rNeLT8+lj67JgT8ziSrvW7h/dnh46tkFcab1wYZ/myaqWRZ+f8teR9XvkomuWVlrJ1G4P/L9voRw24HVwDXAazPiXOKHXb1o0SIdBNIKNpdCMg95Rje7irxRnrjnErwXecUm7RkHXodly6a/d1GPhOugvLrelTq9Jia6ZmWtvojhh8ANMXZ8DtHdz/88CNgAPMMl7UFv6YZFtaoCqGxB2utZK7YOsp5LnmedFdfQkOrs2bseE/GEOEyZVi54Lewy70edI+FNdM3KWjuJOrqXI7/5GnCiS/yDIrqrVmlmi2FszCsUywpemYJ09uwpV2X4mAlveVyei6vYFH3Gw8O7vmPRZ13EopWFPO7ipOuowttiomtW1tpJFD4dGUj1qZgwewFz/L8XALcAh7rEPyiiq5rch1q2ZRuQNgfTtVU7d25y2KKVAOv/9XB5Nq5i4/IuFbWhIc/y/Kaot8ZaumZdtnYShR7wI19IfwTM948vBs71/34RcD3ealjXA+9wjX+QRNe1r3V4OL9AFenHjSsMs34zMuIV+K75s5HOU7g8o7iR6nED4vKKYp5KWNLo5bRKQ1BZyCui1qdr1mVrPQN1WNui23QrLJxeUWGMI28LN+la8xbSWfnr99Wrqn4/0kYNx7lp4wQpzRtRxsbGsp9X1vki7mIbvWzWVWs9A3VYm6LbdivMVShdBCpPH1+UIm5p1/zlyUfXqOP9CAtMr5fuNSg7IK6IZYnmMcfEnw8GaHWpkmWia1bWWs9AHdam6LZVQOQVOZd+Ptf4oq7rstOLsvKXNFBneLiim1kjVb8fLiKe1xOSZcuW5Quf1IoO3pekfAXvVZx7uq3uBBNds7LWegbqsDZFt86Rk0kUETmXBQiKxFtkwExeEUr7ncs1tTkAq2pXaZKIByOKXQdHuTyz8PSgvM8zOtUoeAdd8zd7dr5+/7ow0TUra61noA4btJZuEZdh0pSdaAGfp+Cuyurq023b9a9a/aCgKlqvs2erzps3/fisWclCV2REe9n3qAt99ia6ZmWt9QzUYYPWp1u04HVZui8YWVy30OZZRanoPe5C32DSClLRBSZc81ymjzbJdRuIZHjubbSveNmyfF6Q4Hdl35G2MdE1K2utZ6AO69ro5SoWp0ijTGFWtu+1CityT4q4idtw/cfhspSiavriJ0Gei/afZ4l2r5ce7+hovr7dQLDLvidtY6JrVtZaz0Adlkd06+7jq6vlGx2xGtda6bp13bXbZj6yxDQaNs8qUFW5p8fGmut6yPOu1Pk/baJrVtZaz0Ad5iq6TbiCswrYIgVEXEtp9uz6Fjeo0sJu5Lo9AFG60Ker6tbiTvNeRLdvTOseiNrQULWbE8T1BVf9roAn7i7Pqe5nbKJrVtZaz0Ad5iq6VbZ8ksQzrYAtUkCkTbFwXeCgbXEO7k/ctdctxG2PXlZ1e+/SBDQQoKT+4SBM0nMOV3ii4gbd9ZqU6bcvu4lCgImuWVlrPQN1mKvoVtXHlyaeaQVsHtEvu9hEHVamcE5yh7r0dXYZF1HPqmy5uItHR9P3Ll61Kp/rN+yBaHK0etxUojTLqhCnVVaqeJdMdM3KWusZqMOabummxZNWwLqKfhWLTbRdWJaxMq74JsnjuUi6lqqedZHnE9znpp5r0PrM06+cVSHOqpiW7b830TUra61noA5ruk83SzyTClhX0Xdp4QYDqpooLIeG6u3Li7u2JDFy7etrgioqcW17M/KuNlU2LdV8FY25c9PvX1ZcZUeqm+ialbXWM1CHNT16ue7FGrJaAsE8zy62iKuwNFd8cM+aHpQVRxXdFXlafVnTerps0XnJq1a5jzVwmced5J63lq5Z29Z6Buqwpufplmkxu4h+muBEf5M2tzMsAm0XuoEF6+tmFbJ58zwy0rzwNt3SDSpabT/DvJa0EMiqVW7jBFzuZ12jmE10zcpa6xmow9pYHKPO/sY8BUiWe7Bt92VSAZy2SEPa+TRzWV+6Sqoo6PN4K4KlPF3vTXh0+267tfvc4yqLrtfh6jmo43/SRNesrLWegTqs7RWp6sB1VKxLizDPQgpNFb5x/dHREb1FXKlNU0VBn2exi6BPO+u5z53bPVd08HzzPts2V6Yy0TUra+0kCicBNwI7gcUp4Y4FbgbWA6e7xj8TRdeFpjcmqLLwTRKTMHmnwRQR3a6MkM4jRKrxC6aE72+Zd6POebtZ/fVRS9qooylMdM3KWjuJwl8AzwKuThJdYBi4FTgIGAHWAoe6xD+IotvkqNMmLLorTTDIJm4lq6pEtysrVoXzE1ynyzXGVUpcW8Jpz8F1gJNL/3ycuf6mCyPVTXTNytoQLaCqN6nqzRnBjgLWq+ofVPVx4JvA8fXnrv+YnISVK9vORbVs3epZwM6d3ufGjXD++bBihXdswwbo9eLjCB+fnITxcRga8j4nJ6eHX74ctm3b9di2bd7xNpiY8K5v5870awyu7eSTd71nAA895H0uWpQ/fREvvuDeZ7Fzp3vYcBrz52eHW7YM7rnHuyeG0c+0IrqO7A/cFvq+2T8Wi4gsEZHVIrJ6y5YttWeuSyxf7rUFBoWoEJ51FoyM7BpmZMQ7Dp4oLVniCbaq97lkyXTh3bQpPr2k402SdI1veMPUtcXx+ONw2mleJWV01D09kfzvVCCeSRWEOII0svJ2zjnpFSbD6BvqakIDPwRuiLHjQ2GuJtm9fBJwbuj7KcDnXNIeNPdyl6YANWVxq3YlrfDkOmezzV2IXAfKRcO49odGf590T3q94iPcZ8/2XP+ua4CHn2Weaynq8q+ivx5zL5uVtHYTTxfdFwKXh75/GPiwS7yDJrouhdXcuf070KqoEOZdnaitPt0y6bpWuPJsxNF0JS7cZ+yadt6KUFXP1kTXrKy1m3i66M4C/gA8namBVM9xiXfQRNdlpGswyKXX69aUoSLmWlgWWYe3jdHLZVrYeVulwb1LqoCVaek2aXmXc6zKi2Gia1bW2kkUXofXR/tn4K6gRQvsB1wWCnccsA5vFPNy1/gHTXRVu7kLUR2WRwjr2nGmamEus3xkXUt/NtHaTRsVHVQSq1rOsaodxUx0zcpa6xmow2aK6LoW7oMkuHmoY2/VvG7KMst8ZuUz/NwDcQqmWnWxn3/evF3vQ1oew5uFVOEWtpauWVes9QzUYTNhGci0wiacVq/X3U3Hq7Yq9zkuSt49kF3SX7UqeSu+tK0Bs96Ptp9XnB1zTPa9jN7Pqlb5sj5dsy5Y6xmow/ppw4Mk0tYibnIv2y5ZkX1123QFuwp01kL/cYKe9n50bbnHqIW39Js1a/r5tFWnyjxPG71s1gVrPQN1WNOiW8dUky66B+OEJu2860pGLpa2Tm+Tq0bledZpAu0yfScc3jXufrDhYe8aklr4YVEOi+SyZe2vGGaia1bWWs9AHda06FY1SCNMV92DQUHnMv1o7tzsVrmreAQFa5tzaVXziX5VrdG4lnG/j0BPc4EHrVDXe9TkBggmumZlrfUM1GEzoaWbVLi3XViWXcs3bK7CEb6PdVRwijwb1wFu0WeW975FBb2O0crBSOEqPRMu15V0zmVN7baevYmuWVlrPQN12Ezo0w3ijRbubS9wEQhg2ZZ4cH9c4gnfx7ZbunkJX2NewY1b4L/IfR8ZyX5vVJvfNCNtOlDee9XUnGoTXbOy1noG6rCZMHo5LZ2kQTdBQVWn6zHojywr/r2eV8i7xBO9/rb79YrgIpZBizPt/SniYchyzQfPo40KXdKzLFK5iO6/XMf/o4muWVlrPQN12EyZp5tE3PzMJgfWNJlWr5d8/W3veZuHrHvmUnEo0pcbrDAVTC+r4xkFLengebiuvRy05MP5Co6ldWGk3YOk/uCqKmYmumZlrfUM1GEzXXQD8rYI+m395ejiEP0otgFZc1JdBDepH3R01Jv/GhWp2bPrn8Mdl3fXStnISPqI5GXLpscVnEvr26+zC8JE16ystZ6BOqwrolunSBxzjBYqJLswGMvVwq3cfnUrB+TJf9x747JqVfR3dVew8o7aTsp/mkAm/Q+lCWudg+1MdM3KWusZqMO6ILp1ikTZAS9NTzcpml64kEwTnX5p+bpUwvKOWk8Tkia6AeJaj1UMyMoSyLT/L2vpmnXZWs9AHdYF0a3zH7+f5mgGBf+8ecV+77JOb7TQ7WfyDiBKe5/S5glX1QqO2x4xz4ppZTY0SKrEWJ+uWZet9QzUYV0Q3XpdXOkWFGRJ8y67JNouA8FcF+NwKay73i+cp3WaJSRZ4pNnVSzX+51WaYjrn61rlSkbvWzWVWs9A3VYF0S3rpbuqlXx8QYWXkIvbhCN6wIIZacf5UnHZQqS68YOaZWafugXdm3puu6U5Co+RV3R0bnEWfEktUzrqghVHbeJrllZaz0DdVgXRLeOAt5lNaIy8xzbmH5UdXpF3K1dWljDdcWpqldhKrPYSfi9zmrpNlnBqeN/0ETXrKy1noE6rAuiq1p9Ldu1YCyyok8TC2vUbVkFaheWkHTBxe1bdUUhb19s1IL5wC7vZlPUUcky0TUra0O0gIicJCI3ishOEVmcEm6DiFwvIteJyOom81gFExOwYQPs3Ol9TkyUi2/TJvdwixbli1vV+9yxI9/vuoAIjI3BOeek3+Oke5L3XtVN8N5ccAHsuef086OjsGJF+XQmJ2F8HIaGYPlyeOc7odcrFtfWrbBxY3Y413e4CpLSajIPhhGlFdEFbgBeD/zUIezfqurzVDVRnAcFV3FYtMgrlEdH681PnQwPu4UbG3Ov1MTdk6oErGomJ2HJEk/MwvR62ZWLPPFv3OhVuDZuhK98Zeq8SLn4k2iygtMvlSxjsGhFdFX1JlW9uY20+xkXIR0ZgYcfhlNOgac8pXjLJczs2V68TTE6Cuef7wlqVrg8gjkx4QnW2Jh767gtli+HbdumH583r5r8xsX/+ONTIq86Jby9XjXPf/Zs790cGvJa2JOT5eNMo58qWcYA0aZvG7gaWJxy/o/Ab4A1wJKMuJYAq4HVixYt0plK3Mbe4bV1o/1yWYNykkYNRxedqHsP16C/NWu+ZVy4mUjd/c+uff5B/+eyZbtORQvWV06LJ2s+sMuUp7JjImz0slnXrL6I4Yd4buSoHR8KkyW6+/mfTwPWAi92SbsrA6maJm3VpqQCNc8Iz6y5tOHvIyPu04bitrAL6Pq82rqoe6S166C8YMRx3DuSJahxc3Dj3s08K3O1/fxNdM3KWruJZ4huJOxHgQ+6hB1U0c0jikW2QUsTgqLr/sbtImTULzquU5PGxopNJ8ozbS3uuro6vctE16ystZt4iugCc4HdQ3//HDjWJd5BFd08oljUVVdFqzhqRjxxWzhW2drPWpQka0efLLHOGz5MV6d3meialbV2EoXXAZuBPwN3AZf7x/cDLvP/Psh3Ka8FbgSWu8Y/qKLbhEuubKs4rhBt22XYZepaZCVrHnDY7Zu2hnPWZgyuohsVU2vpms1Uaz0Dddigiq5qd/pAXd2XXShIu0zV4lNkxas04c9yI+cdsOWSZpuY6JqVtdYzUIcNsuh2iWgFwLWVY0xRtZs1z6pmYbIqc2niGh1tX2Zf4bYx0TUra6KqxecbdZTFixfr6tV9t4DVjGd8PH7VorExb3ELYzpV37OhIU/q0hgdzT9/ecGC6Qt5QHw+Jye9ecLBymkrVnRzrnQcIrJGbaEeowRtrUhlDCC2WEF+qr5nLqsx5RXcyUl48MHpx0dG4vNZ9fKohtFPmOgajdFPK0J1harvWdaqZmNj+eNevhyeeGL68d13t2drGFFMdI1GsVZOfqq8Z4GIxy0PWrQFnbSBwL33xh8Pb7QQLAcZd8z1t4bRT1ifrmEMKFX1rebpdw42Wgiv+zwy4vUzh1vLcf3Kcb8t0v9cBuvTNcpiomsYRiEC0d640XN9h4uSJDFMEug4oqLdhYF4JrpGWcy9bBhGbsJbA4InuMGuRGn9znn2so2Gtf1xjZnArLYzYBhG/xG3NaBqdqtz0SL3lm50pHXSb21/XKOfsJauYRi5KdrqjBs9PTLi7bUbJm5Ql005M2YCJrqGYeQmqXWZ1eqMmwJ13nnw1a9mT4uyKWfGTMAGUhmGkZs6RxJ3ecUqG0hllMVauoZh5KauVmd4gJaq97lkic3HNWYO1tI1DKMzdGFaUBrW0jXKYi1dwzA6g00LMmY6JrqG0SK2rOGuFB2gZRj9QiuiKyKfFpHfi8hvReQ7IrJnQrhjReRmEVkvIqc3nU/DqBPrv5yOTQsyZjpttXSvBJ6rqocB64APRwOIyDDwBeCVwKHAm0Xk0EZzaRg1ErfAxLZt3vFBxaYFGTOdVlakUtUrQl+vAU6MCXYUsF5V/wAgIt8Ejgd+V38ODaN+rP8ynokJE1lj5tKFPt23A9+POb4/cFvo+2b/WCwiskREVovI6i1btlScRcOoHuu/NIzBozbRFZEfisgNMXZ8KMxyYDsQ14slMccS5zep6jmqulhVFy9cuLD8BRhGzVj/pWEMHrW5l1X1ZWnnReRU4FXAMRo/WXgzcGDo+wHA7dXl0DDaJXChdnX1JcMwqqeVPl0RORb4B+BvVHVbQrBfAweLyNOBPwFvAv6uoSwaRiNY/6VhDBZt9el+HtgduFJErhORlQAisgsEKNUAAAfaSURBVJ+IXAagqtuBdwOXAzcBF6nqjS3l1zAMwzBK09bo5WcmHL8dOC70/TLgsqbyZRiGYRh10oXRy4ZhGIYxEJjoGoZhGEZDmOgahmEYRkOY6BqGYRhGQ8zI/XRFZAsQsytnLSwA7mkora6lP6hpt53+oKbddvoLgLmqaqvvGIWZkaLbJCKyus1NrdtMf1DTbjv9QU277fTbvnZjZmDuZcMwDMNoCBNdwzAMw2gIE93ynDPA6Q9q2m2nP6hpt51+29duzACsT9cwDMMwGsJauoZhGIbRECa6hmEYhtEQJro5EZFPi8jvReS3IvIdEdkzIdyxInKziKwXkdMrTP8kEblRRHaKSOL0BRHZICLX+7s4rW447cqvXUTmi8iVInKL/7lXQrgd/jVfJyKXlkwz9TpEZI6IfMs//0sRGS+TXoH03yoiW0LX+86K0j1PRO4WkRsSzouIfNbP129F5PlVpJsj/ZeIyAOh6z6jwrQPFJEfi8hN/rt+WkyYWq/fmOGoqlkOA14BzPL//iTwyZgww8CtwEHACLAWOLSi9P8CeBZwNbA4JdwGYEHF156Zdl3XDnwKON3/+/S4++6fe7iia828DuDvgZX+328CvlXhvXZJ/63A56t8xn68LwaeD9yQcP444PuAAC8Aftlw+i8Bvlf1dftx7ws83/97d2BdzH2v9frNZrZZSzcnqnqFenv9AlwDHBAT7Chgvar+QVUfB74JHF9R+jep6s1VxFVT2nVd+/HA+f7f5wOvrSDONFyuI5yni4FjREQaTL8WVPWnwL0pQY4Hvq4e1wB7isi+DaZfG6p6h6r+xv/7Iby9vPePBKv1+o2ZjYluOd6OV+ONsj9wW+j7Zqb/49aNAleIyBoRWdJgunVd+96qegd4BSPwtIRwu4nIahG5RkTKCLPLdTwZxq+IPQD0SqSZN32AE3wX58UicmBFaWfRhff7hSKyVkS+LyLPqSMBv7vgCOCXkVNduH6jT2llE/uuIyI/BPaJObVcVf/ND7Mc2A5MxkURc8x5bpZL+g4craq3i8jTgCtF5Pd+C6LutAtfe1raLr/3WeRf90HAVSJyvaremuP3T2Yn5lj0Oko95wrS/y7wDVX9s4gsxWt1v7Si9NOo87pd+A0wpqoPi8hxwL8CB1eZgIjMA74NvFdVH4yejvmJzb00nDDRjUFVX5Z2XkROBV4FHKOqcf9sm4Fwq+MA4Paq0neM43b/824R+Q6euzJTdCtIu/C1p6UtIneJyL6qeofvyrs7IY7guv8gIlfjtVSKiK7LdQRhNovILGAPqnOLZqavqltDX7+MN8agCUq932UJi6CqXiYiZ4vIAlWtZCMEEZmNJ7iTqnpJTJBWr9/ob8y9nBMRORb4B+A1qrotIdivgYNF5OkiMoI3yKbUSNqceZwrIrsHf+MN/oodCVoDdV37pcCp/t+nAtNa3SKyl4jM8f9eABwN/K5gei7XEc7TicBVCZWwWtKP9CO+Bq//sQkuBd7ij+J9AfBA4PpvAhHZJ+g7F5Gj8Mqxrem/co5bgK8AN6nqZxKCtXr9Rp/T9kiufjNgPV5/znW+BaNX9wMuC4U7Dm/k4614rtmq0n8dXk37z8BdwOXR9PFGvK717caq0ndJu65rx+sr/RFwi/853z++GDjX//tFwPX+dV8PvKNkmtOuAzgTr8IFsBvwf/134lfAQRW/a1npf9x/vmuBHwPPrijdbwB3AE/4z/sdwFJgqX9egC/4+bqelFH0NaX/7tB1XwO8qMK0/wrPVfzb0P/4cU1ev9nMNlsG0jAMwzAawtzLhmEYhtEQJrqGYRiG0RAmuoZhGIbRECa6hmEYhtEQJrqGYRiG0RAmukbf4O8A80cRme9/38v/PhYJd7WI/LfIsfeKyNkF0nytiBxaLueGYRgeJrpG36CqtwFfBD7hH/oEcI6qbowE/QbeYhJh3uQfz8trgVyi669OZRiGMQ2bp2v0Ff4SfWuA84B3AUeotwtPOEwP+D1wgHrrEo/jLYE5pqoqIh8C3gDMAb6jqh/xf/cW4INMLY7wReB7eBsZPACcgLfd20pgFG9xhLer6n3+kpM/x1sF61JV/ee67oFhGP2L1ciNvkJVn/BF8wfAK6KC64fZKiK/Ao7FWy4y2OtWReQVeIvjH4W3stClIvJivGUEl+NtFHGPiMxX1XtF5FK8vVsvBhCR3wLvUdWfiMiZwEeA9/pJ76mqf1Pn9RuG0d+Ye9noR16Jt0zgc1PChF3MYdfyK3y7Fm+3mmfjifBLgYvVXzRfVadtXCAie+AJ60/8Q+fjbbge8K0iF2MYxuBgomv0FSLyPODlwAuA96VsHv6veJvKPx94ivobk+O1bj+uqs/z7Zmq+hX/eNm+lkdK/t4wjBmOia7RN/g7wHwRb4/TTcCngf8TF1ZVHwauxuv7DQ+guhx4u79fKiKyv7/n8I+AN/j9wQQjpIGH8PpxUdUHgPtE5K/9c6cAP8EwDMMRE12jn3gXsElVr/S/nw08W0SS+lG/ARwOfDM4oKpXABcCvxCR64GLgd1V9UZgBfATEVkLBNu6fRP4kIhcKyLPwNvK79N+3+7z8Hb9MQzDcMJGLxuGYRhGQ1hL1zAMwzAawkTXMAzDMBrCRNcwDMMwGsJE1zAMwzAawkTXMAzDMBrCRNcwDMMwGsJE1zAMwzAa4v8Hqa8GxYSYIT4AAAAASUVORK5CYII=\n",
       "text/plain": [
        "<Figure size 360x288 with 1 Axes>"
       ]

From 13013b23a195a75da848344da622c00af379f1d0 Mon Sep 17 00:00:00 2001
From: Sambit Panda <spanda3@jhu.edu>
Date: Fri, 7 Dec 2018 18:05:44 -0500
Subject: [PATCH 53/60] Update simulations and delete extraneous demos

---
 demos/mcorr_dcorr_mantel.ipynb | 443 ---------------------------------
 demos/other_tests.ipynb        | 339 ++++++++-----------------
 2 files changed, 109 insertions(+), 673 deletions(-)
 delete mode 100644 demos/mcorr_dcorr_mantel.ipynb

diff --git a/demos/mcorr_dcorr_mantel.ipynb b/demos/mcorr_dcorr_mantel.ipynb
deleted file mode 100644
index 04fff1d..0000000
--- a/demos/mcorr_dcorr_mantel.ipynb
+++ /dev/null
@@ -1,443 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "from scipy.spatial.distance import pdist, squareform\n",
-    "import matplotlib.pyplot as plt"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import sys\n",
-    "module_path = '/Users/junhaoxiong 1/Documents/Projects/mgcpy'\n",
-    "if module_path not in sys.path:\n",
-    "    sys.path.append(module_path)\n",
-    "from mgcpy.independence_tests.dcorr import DCorr\n",
-    "from mgcpy.benchmarks.power import power\n",
-    "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, ubern_sim, exp_sim, w_sim, joint_sim, spiral_sim"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def compute_distance_matrix(data_matrix_X, data_matrix_Y):\n",
-    "    # obtain the pairwise distance matrix for X and Y\n",
-    "    dist_mtx_X = squareform(pdist(data_matrix_X, metric='euclidean'))\n",
-    "    dist_mtx_Y = squareform(pdist(data_matrix_Y, metric='euclidean'))\n",
-    "    return (dist_mtx_X, dist_mtx_Y)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Test Statistic"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def test_stats_vs_dimension(corr_type, simulation_type, dim_range):\n",
-    "    test_stats = []\n",
-    "    for d in range(1, dim_range+1):\n",
-    "        x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n",
-    "        corr = DCorr(data_matrix_X=x, data_matrix_Y=y, compute_distance_matrix=compute_distance_matrix, corr_type=corr_type)\n",
-    "        test_stats.append(corr.test_statistic())\n",
-    "    return test_stats"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_test_stats(simulation_type, dim_range, simulation_name):\n",
-    "    mcorr_test_stats = test_stats_vs_dimension('mcorr', simulation_type, dim_range)\n",
-    "    dcorr_test_stats = test_stats_vs_dimension('dcorr', simulation_type, dim_range)\n",
-    "    mantel_test_stats = test_stats_vs_dimension('mantel', simulation_type, dim_range)    \n",
-    "    plt.plot(mcorr_test_stats, label='MCorr')\n",
-    "    plt.plot(dcorr_test_stats, label='DCorr')\n",
-    "    plt.plot(mantel_test_stats, label='Mantel')\n",
-    "    plt.xlabel('Dimensions')\n",
-    "    plt.ylabel('Test Statistics')\n",
-    "    plt.legend()\n",
-    "    plt.gca().set_xlim(1, dim_range+1)\n",
-    "    plt.xticks(np.arange(0, dim_range+1, 5))\n",
-    "    plt.title('Test Statistics \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
-    "    plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1037981d0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_test_stats(linear_sim, 20, 'Linear')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a073990f0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_test_stats(spiral_sim, 20, 'Spiral')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a101518d0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_test_stats(quad_sim, 20, 'Quadratic')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## P-value"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def pvalue_vs_dimension(corr_type, simulation_type, dim_range):\n",
-    "    p_value = []\n",
-    "    for d in range(1, dim_range+1):\n",
-    "        x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n",
-    "        corr = DCorr(data_matrix_X=x, data_matrix_Y=y, compute_distance_matrix=compute_distance_matrix, corr_type=corr_type)\n",
-    "        p_value.append(corr.p_value())\n",
-    "    return p_value"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_p_value(simulation_type, dim_range, simulation_name):\n",
-    "    mcorr_pvalue = pvalue_vs_dimension('mcorr', simulation_type, dim_range)\n",
-    "    dcorr_pvalue = pvalue_vs_dimension('dcorr', simulation_type, dim_range)\n",
-    "    mantel_pvalue = pvalue_vs_dimension('mantel', simulation_type, dim_range)    \n",
-    "    plt.plot(mcorr_pvalue, label='MCorr')\n",
-    "    plt.plot(dcorr_pvalue, label='DCorr')\n",
-    "    plt.plot(mantel_pvalue, label='Mantel')\n",
-    "    plt.xlabel('Dimensions')\n",
-    "    plt.ylabel('pvalue')\n",
-    "    plt.legend()\n",
-    "    plt.gca().set_xlim(1, dim_range+1)\n",
-    "    plt.xticks(np.arange(0, dim_range+1, 5))\n",
-    "    plt.title('P-value \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
-    "    plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a100cc550>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_p_value(linear_sim, 20, 'Linear')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a102b7b00>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_p_value(exp_sim, 20, 'Exponential')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a1035a7f0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_p_value(spiral_sim, 20, 'Spiral')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a10185208>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_p_value(w_sim, 20, 'W-Shape')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a073996d8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_p_value(quad_sim, 20, 'Quadratic')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Power"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def power_vs_dimension(corr_type, simulation_type, dim_range):\n",
-    "    '''\n",
-    "    Generate power of an independence test given a simulation for a range of dimensions\n",
-    "    \n",
-    "    :param simulation_type: a simulation function from mgcpy.benchmarks.simulations\n",
-    "    :param dim_range: the upper end of the range of dimension\n",
-    "    :return: power for each dimension\n",
-    "    '''\n",
-    "    estimated_power = []\n",
-    "    for d in range(1, dim_range+1):\n",
-    "        corr = DCorr(data_matrix_X=np.nan, data_matrix_Y=np.nan, \n",
-    "                        compute_distance_matrix=compute_distance_matrix, corr_type=corr_type)\n",
-    "        estimated_power.append(power(corr, simulation_type, num_samples=100, num_dimensions=d))\n",
-    "    return estimated_power"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_power_curve(simulation_type, dim_range, simulation_name):\n",
-    "    mcorr_power = power_vs_dimension('mcorr', simulation_type, dim_range)\n",
-    "    dcorr_power = power_vs_dimension('dcorr', simulation_type, dim_range)\n",
-    "    mantel_power = power_vs_dimension('mantel', simulation_type, dim_range)    \n",
-    "    plt.plot(mcorr_power, label='MCorr')\n",
-    "    plt.plot(dcorr_power, label='DCorr')\n",
-    "    plt.plot(mantel_power, label='Mantel')\n",
-    "    plt.xlabel('Dimensions')\n",
-    "    plt.ylabel('Power')\n",
-    "    plt.legend()\n",
-    "    plt.gca().set_xlim(1, dim_range+1)\n",
-    "    plt.xticks(np.arange(1, len(mcorr_power)+1))\n",
-    "    plt.title('Power \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n",
-    "    plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a101591d0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_power_curve(quad_sim, 20, 'Quadratic')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a101896a0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_power_curve(w_sim, 20, 'W-Shape')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a10449940>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_power_curve(joint_sim, 10, 'Joint Normal')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1a10643e10>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_power_curve(spiral_sim, 20, 'Spiral')"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.6"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/demos/other_tests.ipynb b/demos/other_tests.ipynb
index d508d36..fd1c2a3 100644
--- a/demos/other_tests.ipynb
+++ b/demos/other_tests.ipynb
@@ -9,20 +9,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 1,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(None, <pyximport.pyximport.PyxImporter at 0x1a23c2b358>)"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "from scipy.spatial.distance import pdist, squareform\n",
@@ -34,16 +23,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "First, import the simultions utilizing the import statement below (for this tutorial only 4 out of 20 were imported):"
+    "First, import the simultions utilizing the import statement below (for this only linear was utilized in this case). Refer to the simulations jupyter notebook for more information about the simulations:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
-    "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, w_sim, spiral_sim"
+    "from mgcpy.benchmarks.simulations import linear_sim"
    ]
   },
   {
@@ -62,64 +51,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/anaconda3/lib/python3.6/site-packages/Cython/Compiler/Main.py:367: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/mgc/distance_transform.pyx\n",
-      "  tree = Parsing.p_module(s, pxd, full_module_name)\n"
-     ]
-    },
-    {
-     "ename": "ImportError",
-     "evalue": "Building module mgcpy.independence_tests.mgc.distance_transform failed: [\"distutils.errors.CompileError: command 'gcc' failed with exit status 1\\n\"]",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mDistutilsExecError\u001b[0m                        Traceback (most recent call last)",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m    117\u001b[0m             self.spawn(compiler_so + cc_args + [src, '-o', obj] +\n\u001b[0;32m--> 118\u001b[0;31m                        extra_postargs)\n\u001b[0m\u001b[1;32m    119\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mspawn\u001b[0;34m(self, cmd)\u001b[0m\n\u001b[1;32m    908\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mspawn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 909\u001b[0;31m         \u001b[0mspawn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdry_run\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdry_run\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    910\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/spawn.py\u001b[0m in \u001b[0;36mspawn\u001b[0;34m(cmd, search_path, verbose, dry_run)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'posix'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m         \u001b[0m_spawn_posix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msearch_path\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdry_run\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdry_run\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     37\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'nt'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/spawn.py\u001b[0m in \u001b[0;36m_spawn_posix\u001b[0;34m(cmd, search_path, verbose, dry_run)\u001b[0m\n\u001b[1;32m    158\u001b[0m                           \u001b[0;34m\"command %r failed with exit status %d\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 159\u001b[0;31m                           % (cmd, exit_status))\n\u001b[0m\u001b[1;32m    160\u001b[0m             \u001b[0;32melif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mWIFSTOPPED\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mDistutilsExecError\u001b[0m: command 'gcc' failed with exit status 1",
-      "\nDuring handling of the above exception, another exception occurred:\n",
-      "\u001b[0;31mCompileError\u001b[0m                              Traceback (most recent call last)",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m    214\u001b[0m             so_path = build_module(module_name, pyxfilename, pyxbuild_dir,\n\u001b[0;32m--> 215\u001b[0;31m                                    inplace=build_inplace, language_level=language_level)\n\u001b[0m\u001b[1;32m    216\u001b[0m         \u001b[0mmod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mimp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_dynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mbuild_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, inplace, language_level)\u001b[0m\n\u001b[1;32m    190\u001b[0m                                   \u001b[0minplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 191\u001b[0;31m                                   reload_support=pyxargs.reload_support)\n\u001b[0m\u001b[1;32m    192\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Cannot find: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyxbuild.py\u001b[0m in \u001b[0;36mpyx_to_dll\u001b[0;34m(filename, ext, force_rebuild, build_in_temp, pyxbuild_dir, setup_args, reload_support, inplace)\u001b[0m\n\u001b[1;32m    101\u001b[0m         \u001b[0mobj_build_ext\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_command_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"build_ext\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m         \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_commands\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m         \u001b[0mso_path\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mobj_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_outputs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_commands\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    954\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mcmd\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommands\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 955\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_command\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    956\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_command\u001b[0;34m(self, command)\u001b[0m\n\u001b[1;32m    973\u001b[0m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mensure_finalized\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 974\u001b[0;31m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    975\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhave_run\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcommand\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    185\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 186\u001b[0;31m         \u001b[0m_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    187\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    338\u001b[0m         \u001b[0;31m# Now actually compile and link everything.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 339\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    340\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mbuild_extensions\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    193\u001b[0m             \u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 194\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    195\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mbuild_extension\u001b[0;34m(self, ext)\u001b[0m\n\u001b[1;32m    532\u001b[0m                                          \u001b[0mextra_postargs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextra_args\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 533\u001b[0;31m                                          depends=ext.depends)\n\u001b[0m\u001b[1;32m    534\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sources, output_dir, macros, include_dirs, debug, extra_preargs, extra_postargs, depends)\u001b[0m\n\u001b[1;32m    573\u001b[0m                 \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 574\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcc_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_postargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpp_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    575\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m    119\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mCompileError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mCompileError\u001b[0m: command 'gcc' failed with exit status 1",
-      "\nDuring handling of the above exception, another exception occurred:\n",
-      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-23-e329c2ea85bd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdcorr\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/dcorr.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabstract_class\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mIndependenceTest\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistance_transform\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtransform_distance_matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(self, fullname)\u001b[0m\n\u001b[1;32m    460\u001b[0m                                  \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyxbuild_dir\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    461\u001b[0m                                  \u001b[0mbuild_inplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 462\u001b[0;31m                                  language_level=self.language_level)\n\u001b[0m\u001b[1;32m    463\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mmodule\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    464\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m    229\u001b[0m                 name, traceback.format_exception_only(*sys.exc_info()[:2])))\n\u001b[1;32m    230\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mversion_info\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 231\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mexc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    232\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    233\u001b[0m                 \u001b[0mexec\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"raise exc, None, tb\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m'exc'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mexc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'tb'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtb\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m    213\u001b[0m                 \u001b[0mmodule_name\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    214\u001b[0m             so_path = build_module(module_name, pyxfilename, pyxbuild_dir,\n\u001b[0;32m--> 215\u001b[0;31m                                    inplace=build_inplace, language_level=language_level)\n\u001b[0m\u001b[1;32m    216\u001b[0m         \u001b[0mmod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mimp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_dynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    217\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_package\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'__path__'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mbuild_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, inplace, language_level)\u001b[0m\n\u001b[1;32m    189\u001b[0m                                   \u001b[0msetup_args\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    190\u001b[0m                                   \u001b[0minplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 191\u001b[0;31m                                   reload_support=pyxargs.reload_support)\n\u001b[0m\u001b[1;32m    192\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Cannot find: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    193\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyxbuild.py\u001b[0m in \u001b[0;36mpyx_to_dll\u001b[0;34m(filename, ext, force_rebuild, build_in_temp, pyxbuild_dir, setup_args, reload_support, inplace)\u001b[0m\n\u001b[1;32m    100\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m         \u001b[0mobj_build_ext\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_command_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"build_ext\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m         \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_commands\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m         \u001b[0mso_path\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mobj_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_outputs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mobj_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_commands\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    953\u001b[0m         \"\"\"\n\u001b[1;32m    954\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mcmd\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommands\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 955\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_command\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    956\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    957\u001b[0m     \u001b[0;31m# -- Methods that operate on its Commands --------------------------\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/dist.py\u001b[0m in \u001b[0;36mrun_command\u001b[0;34m(self, command)\u001b[0m\n\u001b[1;32m    972\u001b[0m         \u001b[0mcmd_obj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_command_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcommand\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    973\u001b[0m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mensure_finalized\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 974\u001b[0;31m         \u001b[0mcmd_obj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    975\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhave_run\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcommand\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    976\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    184\u001b[0m             \u001b[0moptimization\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisable_optimization\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    185\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 186\u001b[0;31m         \u001b[0m_build_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    187\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    188\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    337\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    338\u001b[0m         \u001b[0;31m# Now actually compile and link everything.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 339\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    340\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    341\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcheck_extensions_list\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextensions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mbuild_extensions\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    192\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mext\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mextensions\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    193\u001b[0m             \u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 194\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    195\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    196\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextension\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/command/build_ext.py\u001b[0m in \u001b[0;36mbuild_extension\u001b[0;34m(self, ext)\u001b[0m\n\u001b[1;32m    531\u001b[0m                                          \u001b[0mdebug\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdebug\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    532\u001b[0m                                          \u001b[0mextra_postargs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextra_args\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 533\u001b[0;31m                                          depends=ext.depends)\n\u001b[0m\u001b[1;32m    534\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    535\u001b[0m         \u001b[0;31m# XXX outdated variable, kept here in case third-part code\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sources, output_dir, macros, include_dirs, debug, extra_preargs, extra_postargs, depends)\u001b[0m\n\u001b[1;32m    572\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    573\u001b[0m                 \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 574\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcc_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_postargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpp_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    575\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    576\u001b[0m         \u001b[0;31m# Return *all* object filenames, not just the ones we just built.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m    118\u001b[0m                        extra_postargs)\n\u001b[1;32m    119\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mCompileError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    122\u001b[0m     def create_static_lib(self, objects, output_libname,\n",
-      "\u001b[0;31mImportError\u001b[0m: Building module mgcpy.independence_tests.mgc.distance_transform failed: [\"distutils.errors.CompileError: command 'gcc' failed with exit status 1\\n\"]"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from mgcpy.independence_tests.dcorr import DCorr"
    ]
@@ -147,25 +81,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
-     "ename": "NameError",
-     "evalue": "name 'DCorr' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-24-f67b9d90e903>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad_sim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mdcorr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwhich_test\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'dcorr'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mtest_stat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdcorr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_statistic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"DCorr's test statistic: %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mtest_stat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'DCorr' is not defined"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "DCorr's test statistic: 1.00\n"
      ]
     }
    ],
    "source": [
-    "x, y = quad_sim(100, 1)\n",
+    "x, y = linear_sim(100, 1, noise=0)\n",
     "\n",
-    "dcorr = DCorr(which_test='dcorr')\n",
+    "dcorr = DCorr(which_test='biased')\n",
     "test_stat = dcorr.test_statistic(x, y)[0]\n",
     "print(\"DCorr's test statistic: %.2f\" % test_stat)"
    ]
@@ -179,9 +109,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "DCorr p-value: 0.00\n"
+     ]
+    }
+   ],
    "source": [
     "p_value = dcorr.p_value(x, y)[0]\n",
     "print(\"DCorr p-value: %.2f\" % p_value)"
@@ -210,13 +148,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "MCorr's test statistic: 1.00\n"
+     ]
+    }
+   ],
    "source": [
-    "x, y = quad_sim(100, 1)\n",
+    "x, y = linear_sim(100, 1, noise=0)\n",
     "\n",
-    "mcorr = DCorr(which_test='mcorr')\n",
+    "mcorr = DCorr(which_test='unbiased')\n",
     "test_stat = mcorr.test_statistic(x, y)[0]\n",
     "print(\"MCorr's test statistic: %.2f\" % test_stat)"
    ]
@@ -230,9 +176,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "MCorr p-value: 0.00\n"
+     ]
+    }
+   ],
    "source": [
     "p_value = mcorr.p_value(x, y)[0]\n",
     "print(\"MCorr p-value: %.2f\" % p_value)"
@@ -261,11 +215,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Mantel's test statistic: 0.26\n"
+     ]
+    }
+   ],
    "source": [
-    "x, y = quad_sim(100, 1)\n",
+    "x, y = linear_sim(100, 1)\n",
     "\n",
     "mantel = DCorr(which_test='mantel')\n",
     "test_stat = mantel.test_statistic(x, y)[0]\n",
@@ -281,9 +243,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Mantel p-value: 0.00\n"
+     ]
+    }
+   ],
    "source": [
     "p_value = mantel.p_value(x, y)[0]\n",
     "print(\"Mantel p-value: %.2f\" % p_value)"
@@ -346,7 +316,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -362,19 +332,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "HHG test statistic: 56.76\n"
+     "ename": "AttributeError",
+     "evalue": "'NoneType' object has no attribute 'test_statistic_'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-11-3204f2eb6b1e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlinear_sim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mhhg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mHHG\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mtest_stat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhhg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_statistic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"HHG test statistic: %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mtest_stat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/code/mgcpy/independence_tests/hhg.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, compute_distance_matrix)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0;34m:\u001b[0m\u001b[0mtype\u001b[0m \u001b[0mcompute_distance_matrix\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mFunctionType\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \"\"\"\n\u001b[0;32m---> 12\u001b[0;31m         \u001b[0mIndependenceTest\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcompute_distance_matrix\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwhich_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"hhg\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/code/mgcpy/independence_tests/abstract_class.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, compute_distance_matrix)\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcompute_distance_matrix\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 28\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_statistic_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     29\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_statistic_metadata_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     30\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mp_value_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mAttributeError\u001b[0m: 'NoneType' object has no attribute 'test_statistic_'"
      ]
     }
    ],
    "source": [
-    "x, y = w_sim(10, 1)\n",
+    "x, y = linear_sim(10, 1)\n",
     "\n",
     "hhg = HHG()\n",
     "test_stat = hhg.test_statistic(x, y)[0]\n",
@@ -390,26 +366,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "HHG p-value: 0.51\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/abstract_class.py:154: UserWarning: The p-value is greater than 0.05, implying that the results are not statistically significant.\n",
-      "Use results such as test_statistic and optimal_scale, with caution!\n",
-      "  \"Use results such as test_statistic and optimal_scale, with caution!\")\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "p_value = hhg.p_value(x, y)[0]\n",
     "print(\"HHG p-value: %.2f\" % p_value)"
@@ -431,7 +390,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -461,19 +420,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Kendall's test statistic: 0.05\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "x, y = quad_sim(100, 1)\n",
+    "x, y = linear_sim(100, 1)\n",
     "\n",
     "kendall = KendallSpearman(which_test='kendall')\n",
     "test_stat = kendall.test_statistic(x, y)[0]\n",
@@ -489,17 +440,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Pearson's p-value: 0.49\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "p_value = kendall.p_value(x, y)[0]\n",
     "print(\"Pearson's p-value: %.2f\" % p_value)"
@@ -528,19 +471,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Spearman's test statistic: -0.04\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "x, y = spiral_sim(100, 1)\n",
+    "x, y = linear_sim(100, 1)\n",
     "\n",
     "spearman = KendallSpearman(which_test='spearman')\n",
     "test_stat = spearman.test_statistic(x, y)[0]\n",
@@ -556,17 +491,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Pearson's p-value: 0.72\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "p_value = spearman.p_value(x, y)[0]\n",
     "print(\"Pearson's p-value: %.2f\" % p_value)"
@@ -588,7 +515,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -626,17 +553,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Pearson's test statistic: 0.53\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "x, y = linear_sim(100, 1)\n",
     "\n",
@@ -654,17 +573,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Pearson's p-value: 0.00\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "p_value = pearson.p_value(x, y)[0]\n",
     "print(\"Pearson's p-value: %.2f\" % p_value)"
@@ -707,19 +618,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RV test statistic: 0.02\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "x, y = quad_sim(100, 3)\n",
+    "x, y = linear_sim(100, 3)\n",
     "\n",
     "rv = RVCorr(which_test='rv')\n",
     "test_stat = rv.test_statistic(x, y)[0]\n",
@@ -735,17 +638,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RV p-value: 0.43\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "p_value = rv.p_value(x, y)[0]\n",
     "print(\"RV p-value: %.2f\" % p_value)"
@@ -778,19 +673,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CCA test statistic: 0.28\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "x, y = spiral_sim(100, 6)\n",
+    "x, y = linear_sim(100, 6)\n",
     "\n",
     "cca = RVCorr(which_test='cca')\n",
     "test_stat = cca.test_statistic(x, y)[0]\n",
@@ -806,17 +693,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CCA p-value: 0.00\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "p_value = cca.p_value(x, y)[0]\n",
     "print(\"CCA p-value: %.2f\" % p_value)"
@@ -846,7 +725,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.6"
+   "version": "3.6.7"
   }
  },
  "nbformat": 4,

From d8f2d5601ffe33f8ba414295c7f9e8227f2c4803 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 18:11:54 -0500
Subject: [PATCH 54/60] Make Docker build's branch specific

---
 Dockerfile                                          | 3 ++-
 mgcpy/independence_tests/unit_tests/mgc/__init__.py | 0
 2 files changed, 2 insertions(+), 1 deletion(-)
 mode change 100644 => 100755 mgcpy/independence_tests/unit_tests/mgc/__init__.py

diff --git a/Dockerfile b/Dockerfile
index fd65d2b..c5a1760 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -82,7 +82,8 @@ RUN mkdir /root/code/
 WORKDIR /root/code/
 
 # clone the mgcpy code into the container
-RUN git clone https://github.com/NeuroDataDesign/mgcpy.git .
+ARG SOURCE_BRANCH=master
+RUN git clone -b ${SOURCE_BRANCH} https://github.com/NeuroDataDesign/mgcpy.git .
 
 # install python requirements
 RUN pip install -r requirements.txt
diff --git a/mgcpy/independence_tests/unit_tests/mgc/__init__.py b/mgcpy/independence_tests/unit_tests/mgc/__init__.py
old mode 100644
new mode 100755

From c63d0108a596987d4da6fca31af45470f9a56bd8 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 18:22:04 -0500
Subject: [PATCH 55/60] Remove pytest call from Dockerfile, Travis CI does that
 Replace with simple import check

---
 Dockerfile | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Dockerfile b/Dockerfile
index c5a1760..056b5cb 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -100,9 +100,9 @@ RUN python setup.py build_ext --inplace
 # add mgcpy to PYTHONPATH for dev purposes
 RUN echo "export PYTHONPATH='${PYTHONPATH}:/root/code'" >> ~/.bashrc
 
-# test if mgcpy is correctly installed
+# clean dir and test if mgcpy is correctly installed
 RUN py3clean .
-RUN pytest
+RUN python -c "import mgcpy"
 
 # launch terminal
 CMD ["/bin/bash"]

From 857f3f46e21347ce5d6d0f85d7205d64ce4744d7 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 19:09:28 -0500
Subject: [PATCH 56/60] Move git-hooks into hooks

---
 {git-hooks => hooks}/pre-commit | 0
 install-hooks.sh                | 2 +-
 2 files changed, 1 insertion(+), 1 deletion(-)
 rename {git-hooks => hooks}/pre-commit (100%)

diff --git a/git-hooks/pre-commit b/hooks/pre-commit
similarity index 100%
rename from git-hooks/pre-commit
rename to hooks/pre-commit
diff --git a/install-hooks.sh b/install-hooks.sh
index 83c8b1b..3ac90f0 100755
--- a/install-hooks.sh
+++ b/install-hooks.sh
@@ -2,7 +2,7 @@
 
 basedir=$(git rev-parse --show-toplevel)
 repohookspath="$basedir/.git/hooks"
-localhook="$basedir/git-hooks/pre-commit"
+localhook="$basedir/hooks/pre-commit"
 
 repohook="$repohookspath/pre-commit"
 

From 3dfea197e921f470978fc71faa7b771b3d72b728 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 19:13:12 -0500
Subject: [PATCH 57/60] Add DockerHub build and env hooks

---
 hooks/build | 12 ++++++++++++
 hooks/env   | 10 ++++++++++
 2 files changed, 22 insertions(+)
 create mode 100644 hooks/build
 create mode 100644 hooks/env

diff --git a/hooks/build b/hooks/build
new file mode 100644
index 0000000..e6e7f92
--- /dev/null
+++ b/hooks/build
@@ -0,0 +1,12 @@
+#!/bin/bash -xe
+
+. ./hooks/env
+
+docker build \
+	--build-arg BUILD_DATE=`date -u +"%Y-%m-%dT%H:%M:%SZ"` \
+	--build-arg "SOURCE_COMMIT=$GIT_SHA1" \
+  --build-arg "SOURCE_BRANCH=$SOURCE_BRANCH" \
+	--build-arg "DOCKERFILE_PATH=$DOCKERFILE_PATH" \
+	--build-arg "SOURCE_TYPE=$SOURCE_TYPE" \
+	${VERSION:+--build-arg "VERSION=$VERSION"} \
+	-t $IMAGE_NAME .
diff --git a/hooks/env b/hooks/env
new file mode 100644
index 0000000..a6f477b
--- /dev/null
+++ b/hooks/env
@@ -0,0 +1,10 @@
+[ -n "$SOURCE_BRANCH" ]  || SOURCE_BRANCH=$(git symbolic-ref -q --short HEAD)
+[ -n "$GIT_SHA1" ]       || GIT_SHA1=$(git rev-parse -q HEAD)
+
+if [[ "${SOURCE_BRANCH/-*/}" =~ ^[0-9][0-9.]*$ ]]; then
+	VERSION=${SOURCE_BRANCH/-*/}
+fi
+
+[ -n "$SOURCE_TYPE" ]        || SOURCE_TYPE=git
+[ -n "$DOCKERFILE_PATH" ]    || DOCKERFILE_PATH=.
+[ -n "$IMAGE_NAME" ]         || IMAGE_NAME=tpsatish95/mgcpy:${SOURCE_BRANCH}

From 97e5c845d80fa4a748e6dcf91470d35b58626dad Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 19:14:43 -0500
Subject: [PATCH 58/60] Update Readme to have all automated docker images

---
 README.md | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/README.md b/README.md
index 3fd9f77..83e8a98 100644
--- a/README.md
+++ b/README.md
@@ -33,12 +33,12 @@ python3 setup.py install
 ## Setting up the development environment:
 - To build image and run from scratch:
   - Install [docker](https://docs.docker.com/install/)
-  - Build the docker image, `docker build -t mgcpy-dev:latest .`
+  - Build the docker image, `docker build -t mgcpy:latest .`
     - This takes 20-30 mins to build
-  - Launch the container to go into mgcpy's dev env, `docker run -it --rm --name mgcpy-dev-env mgcpy-dev`
-- Pull master branch image from Dockerhub and run:
-  - `docker pull tpsatish95/mgcpy-dev:latest`
-  - `docker run -it --rm -p 8888:8888 --name mgcpy-dev-env tpsatish95/mgcpy-dev`
+  - Launch the container to go into mgcpy's dev env, `docker run -it --rm --name mgcpy-env mgcpy:latest`
+- Pull image from Dockerhub and run:
+  - `docker pull tpsatish95/mgcpy:latest` or `docker pull tpsatish95/mgcpy:development`
+  - `docker run -it --rm -p 8888:8888 --name mgcpy-env tpsatish95/mgcpy:latest`
 
 
 - To run demo notebooks (from within Docker):
@@ -49,7 +49,7 @@ python3 setup.py install
   - Then open `mgc.ipynb`
 
 - To mount/load local files into docker container:
-  - Do `docker run -it --rm -v <local_dir_path>:/root/workspace/ -p 8888:8888 --name mgcpy-dev-env tpsatish95/mgcpy-dev`, replace `<local_dir_path>` with your local dir path.
+  - Do `docker run -it --rm -v <local_dir_path>:/root/workspace/ -p 8888:8888 --name mgcpy-env tpsatish95/mgcpy:latest`, replace `<local_dir_path>` with your local dir path.
   - Do `cd ../workspace` when you are inside the container to view the mounted files. The **mgcpy** package code will be in `/root/code` directory.
 
 

From a9779dd2764729aafa72d92850f51614d5d86530 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 19:28:53 -0500
Subject: [PATCH 59/60] Remove mgcpy sys path addition

---
 docs/source/conf.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/docs/source/conf.py b/docs/source/conf.py
index d193053..a65d5ac 100644
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -12,9 +12,9 @@
 # add these directories to sys.path here. If the directory is relative to the
 # documentation root, use os.path.abspath to make it absolute, like shown here.
 #
-import os
-import sys
-sys.path.insert(0, os.path.abspath('../../'))
+# import os
+# import sys
+# sys.path.insert(0, os.path.abspath('../../'))
 
 
 # -- Project information -----------------------------------------------------

From 6b9c5cd0f8c382269ff5fea92f7a2abdfe2713f4 Mon Sep 17 00:00:00 2001
From: tpsatish95 <tpsatish95@gmail.com>
Date: Sat, 8 Dec 2018 19:35:33 -0500
Subject: [PATCH 60/60] Update Sphinx docs

---
 docs/source/mgcpy.independence_tests.mdmr.rst | 30 +++++++++++++++
 docs/source/mgcpy.independence_tests.mgc.rst  |  8 ----
 docs/source/mgcpy.independence_tests.rst      |  1 +
 docs/source/mgcpy.rst                         |  1 -
 docs/source/mgcpy.utils.rst                   | 38 -------------------
 5 files changed, 31 insertions(+), 47 deletions(-)
 create mode 100644 docs/source/mgcpy.independence_tests.mdmr.rst
 delete mode 100644 docs/source/mgcpy.utils.rst

diff --git a/docs/source/mgcpy.independence_tests.mdmr.rst b/docs/source/mgcpy.independence_tests.mdmr.rst
new file mode 100644
index 0000000..31f27ce
--- /dev/null
+++ b/docs/source/mgcpy.independence_tests.mdmr.rst
@@ -0,0 +1,30 @@
+mgcpy.independence\_tests.mdmr package
+======================================
+
+Submodules
+----------
+
+mgcpy.independence\_tests.mdmr.mdmr module
+------------------------------------------
+
+.. automodule:: mgcpy.independence_tests.mdmr.mdmr
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+mgcpy.independence\_tests.mdmr.mdmrfunctions module
+---------------------------------------------------
+
+.. automodule:: mgcpy.independence_tests.mdmr.mdmrfunctions
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+Module contents
+---------------
+
+.. automodule:: mgcpy.independence_tests.mdmr
+    :members:
+    :undoc-members:
+    :show-inheritance:
diff --git a/docs/source/mgcpy.independence_tests.mgc.rst b/docs/source/mgcpy.independence_tests.mgc.rst
index 811fb3d..0a3f357 100644
--- a/docs/source/mgcpy.independence_tests.mgc.rst
+++ b/docs/source/mgcpy.independence_tests.mgc.rst
@@ -12,14 +12,6 @@ mgcpy.independence\_tests.mgc.distance\_transform module
     :undoc-members:
     :show-inheritance:
 
-mgcpy.independence\_tests.mgc.fast\_mgc module
-----------------------------------------------
-
-.. automodule:: mgcpy.independence_tests.mgc.fast_mgc
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
 mgcpy.independence\_tests.mgc.local\_correlation module
 -------------------------------------------------------
 
diff --git a/docs/source/mgcpy.independence_tests.rst b/docs/source/mgcpy.independence_tests.rst
index fbe9f87..c226f3e 100644
--- a/docs/source/mgcpy.independence_tests.rst
+++ b/docs/source/mgcpy.independence_tests.rst
@@ -6,6 +6,7 @@ Subpackages
 
 .. toctree::
 
+    mgcpy.independence_tests.mdmr
     mgcpy.independence_tests.mgc
     mgcpy.independence_tests.unit_tests
 
diff --git a/docs/source/mgcpy.rst b/docs/source/mgcpy.rst
index 83a90e7..8e01ba7 100644
--- a/docs/source/mgcpy.rst
+++ b/docs/source/mgcpy.rst
@@ -8,7 +8,6 @@ Subpackages
 
     mgcpy.benchmarks
     mgcpy.independence_tests
-    mgcpy.utils
 
 Module contents
 ---------------
diff --git a/docs/source/mgcpy.utils.rst b/docs/source/mgcpy.utils.rst
deleted file mode 100644
index f676b31..0000000
--- a/docs/source/mgcpy.utils.rst
+++ /dev/null
@@ -1,38 +0,0 @@
-mgcpy.utils package
-===================
-
-Submodules
-----------
-
-mgcpy.utils.dist\_transform module
-----------------------------------
-
-.. automodule:: mgcpy.utils.dist_transform
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-mgcpy.utils.permutation\_test module
-------------------------------------
-
-.. automodule:: mgcpy.utils.permutation_test
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-mgcpy.utils.power module
-------------------------
-
-.. automodule:: mgcpy.utils.power
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-
-Module contents
----------------
-
-.. automodule:: mgcpy.utils
-    :members:
-    :undoc-members:
-    :show-inheritance: