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updates to contour plots (#7)
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* wip for contour plots

* adding notebook

* adding updated scripts
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@mathematicalmichael
mathematicalmichael authored Feb 7, 2021
1 parent 3fbbcbd commit 1075f99
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332 changes: 332 additions & 0 deletions notebooks/Contours.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"presentation = False\n",
"save = True"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import ipywidgets as wd\n",
"from mud_examples.plotting import plot_2d_contour_example as plot_full\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import matplotlib\n",
"if not presentation:\n",
" matplotlib.rcParams['mathtext.fontset'] = 'stix'\n",
" matplotlib.rcParams['font.family'] = 'STIXGeneral'\n",
" fdir = 'contours'\n",
"else:\n",
" fdir = '../presentation/figures'\n",
"\n",
"matplotlib.rcParams['font.size'] = 24\n",
"matplotlib.backend = 'Agg'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"plt.rcParams['figure.figsize'] = 10,10"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"lam_true = np.array([0.7, 0.3])\n",
"initial_mean = np.array([0.25, 0.25])\n",
"A = np.array([[1, 1]])\n",
"b = np.zeros((1,1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Projection is to the nullspace of $A\\Sigma_{in}$, not $A$. If $\\Sigma_{in}$ is non-diagonal, then performing $\\Sigma_{in} = U \\Sigma W^T$ yields a transformation matrix $U$ that \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Slider objects"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "63f3e6e6ef95429dacf80e99c531278f",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"VBox(children=(interactive(children=(FloatSlider(value=0.5, continuous_update=False, description='$\\\\sigma_{11…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"out = wd.Output()\n",
"cov_11_slider = wd.FloatSlider(value=1, min=0.05, max=1, step=0.05, description='$\\sigma_{11}$', continuous_update=False)\n",
"cov_01_slider = wd.FloatSlider(value=0, min=-0.95-1E-4, max=0.95+1E-4, step=0.01, description='$\\sigma_{01}=\\sigma_{10}$', continuous_update=False)\n",
"\n",
"def mv_slider(val):\n",
" pr_slide.max = tk_slide.value + 1E-4\n",
"\n",
"def ensure_positive_determinant(val):\n",
" \"\"\"\n",
" Bound limits of covariance to ensure det(C)>0\n",
" \"\"\"\n",
" rt = np.sqrt(cov_11_slider.value)\n",
" # need to account for slider numerical rounding\n",
" cov_01_slider.max = rt-1E-4\n",
" cov_01_slider.min = -rt+1E-4\n",
"\n",
"cov_11_slider.observe(ensure_positive_determinant)\n",
"\n",
"tk_slide = wd.FloatSlider(value=1, min=0, max=1, step=0.02, description='Tikonov', continuous_update=False)\n",
"pr_slide = wd.FloatSlider(value=1, min=0, max=1, step=0.02, description='Unreg', continuous_update=False)\n",
"tk_slide.observe(mv_slider)\n",
"full_check = wd.Checkbox(value=True, description='Show Full')\n",
"data_check = wd.Checkbox(value=True, description='Show Data')\n",
"numr_check = wd.Checkbox(value=False, description='Numerical')\n",
"comparison = wd.Checkbox(value=False, description='Compare MAP')\n",
"\n",
"fig_title = wd.Text(value='latest_figure.png')\n",
"obs_std_slider = wd.FloatSlider(value=1, min=0.01, max=1, step=0.01, description='Obs. Std', continuous_update=False)\n",
"# pr_slide.observe(mv_slider)\n",
"cov_11_slider.value = 0.5\n",
"cov_01_slider.value = -0.25\n",
"obs_std_slider.value = 0.5\n",
"\n",
"I = wd.interactive(plot_full, A=wd.fixed(A), b=wd.fixed(b), save=wd.fixed(save),\n",
" param_ref=wd.fixed(lam_true), compare=comparison,\n",
" cov_01=cov_01_slider, cov_11=cov_11_slider, \n",
" initial_mean=wd.fixed(initial_mean),\n",
" alpha=tk_slide,\n",
" omega=pr_slide,\n",
" show_full=full_check,\n",
" show_data=data_check,\n",
" show_est=numr_check,\n",
" obs_std = obs_std_slider,\n",
" figname=fig_title)\n",
"\n",
"display(wd.VBox([I, out]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Figures\n",
"---\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"assert save is True, \"No saving requested. Stopping notebook.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data Mismatch"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"fig_title.value = f'{fdir}/data_mismatch_contour.png'\n",
"data_check.value = True\n",
"full_check.value = False\n",
"tk_slide.value = 0\n",
"pr_slide.value = 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Tikonov Regularization"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"fig_title.value = f'{fdir}/tikonov_contour.png'\n",
"tk_slide.value = 1\n",
"pr_slide.value = 0\n",
"data_check.value = False\n",
"full_check.value = False"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Modified Regularization"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"fig_title.value = f'{fdir}/consistent_contour.png'\n",
"tk_slide.value = 1\n",
"pr_slide.value = 1\n",
"data_check.value = False\n",
"full_check.value = False"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Classical Solution"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"fig_title.value = f'{fdir}/classical_solution.png'\n",
"tk_slide.value = 1\n",
"pr_slide.value = 0\n",
"data_check.value = True\n",
"full_check.value = True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Consistent Solution"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"fig_title.value = f'{fdir}/consistent_solution.png'\n",
"tk_slide.value = 1\n",
"pr_slide.value = 1\n",
"data_check.value = True\n",
"full_check.value = True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Comparison"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"fig_title.value = f'{fdir}/map_compare_contour.png'\n",
"data_check.value = True\n",
"full_check.value = True\n",
"tk_slide.value = 1\n",
"pr_slide.value = 0\n",
"comparison.value = True\n",
"cov_01_slider.value = -0.5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cleanup"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"!rm latest_figure.png"
]
},
{
"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": "3.8.6"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
8 changes: 8 additions & 0 deletions src/mud_examples/helpers.py
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import os

import numpy as np
from mud.funs import mud_sol, map_sol


def check_dir(directory):
if not os.path.exists(directory):
os.makedirs(directory)


def fit_log_linear_regression(input_values, output_values):
x, y = np.log10(input_values), np.log10(output_values)
X, Y = np.vander(x, 2), np.array(y).reshape(-1, 1)
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