Jeremy's homework.

matrix_math.py

@@ -1,2 +1,142 @@
+import math
+
+
 class ShapeException(Exception):
     pass
+
+
+def shape(vector):
+    """
+    with no regard for poorly made lists
+    returns the shape of the list
+    """
+    if isinstance(vector[0], list):
+        return (len(vector), len(vector[0]))
+    return (len(vector), )
+
+
+def compare(vect1, vect2):
+    """
+    Checks if the shapes of the two entries
+    are the same
+    """
+    return shape(vect1) == shape(vect2)
+
+
+def vector_add(vect1, vect2):
+    """
+    Returns the sum of two vectors
+    if they are the same shape
+    """
+    if compare(vect1, vect2):
+        return [coeff1 + coeff2 for (coeff1, coeff2)
+                in list(zip(vect1, vect2))]
+
+    raise ShapeException
+
+
+def vector_sub(vect1, vect2):
+    """
+    Returns the difference of two vectors
+    if their shapes are the same
+    """
+    return vector_add(vect1, [-num for num in vect2])
+
+
+def vector_sum(*vectors):
+    """
+    Returns the sum of any number of vectors
+    if their shapes are the same
+    """
+    vectors = list(vectors)
+    if len(vectors) > 1:
+        return vector_add(vectors.pop(), vector_sum(*vectors))
+    else:
+        return vectors[0]
+
+
+def dot(vect1, vect2):
+    """
+    Returns the dot product of two vectors
+    if their shape is the same
+    """
+    if compare(vect1, vect2):
+        return sum([coeff1 * coeff2 for (coeff1, coeff2)
+                    in list(zip(vect1, vect2))])
+
+    raise ShapeException
+
+
+def vector_multiply(vector, scalar):
+    """
+    Returns the result of multiplying a vector
+    by a scalar
+    """
+    return [entry * scalar for entry in vector]
+
+
+def vector_mean(*vectors):
+    """
+    Returns the mean of any set of vectors
+    if their shape is the same
+    """
+    return vector_multiply(vector_sum(*vectors), 1/len(vectors))
+
+
+def magnitude(vector):
+    """
+    Returns the magnitude of a vector
+    in the Euclidean metric
+    """
+    return math.sqrt(sum([entry**2 for entry in vector]))
+
+
+def matrix_row(matrix, row):
+    """
+    returns a specified row of a matrix
+    """
+    return matrix[row]
+
+
+def transpose(matrix):
+    """
+    returns the transpose of a matrix
+    """
+    return [[row[i] for row in matrix] for i in range(len(matrix[0]))]
+
+
+def matrix_col(matrix, col):
+    """
+    returns a specified column of a matrix
+    """
+    return matrix_row(transpose(matrix), col)
+
+
+def matrix_scalar_multiply(matrix, scalar):
+    """
+    Returns the matrix multiplied by a scalar
+    """
+    return [vector_multiply(vect, scalar) for vect in matrix]
+
+
+def matrix_vector_multiply(matrix, vector):
+    """
+    Returns the result of multiplying
+    a given matrix by a given vector
+    if their shapes are appropriate
+    """
+    if compare(matrix[0], vector):
+        return [dot(row, vector) for row in matrix]
+    raise ShapeException
+
+
+def matrix_matrix_multiply(mat1, mat2):
+    """
+    Returns the result of multiplying
+    a given two matrices
+    if their shapes are appropriate
+    """
+    if shape(mat1)[1] == shape(mat2)[0]:
+        return [[dot(row, col) for col in transpose(mat2)] for row in mat1]
+
+    raise ShapeException

test_matrix_math.py

@@ -1,5 +1,6 @@
 from matrix_math import *
 from nose.tools import raises
+import nose
 
 
 def is_equal(x, y, tolerance=0.001):
@@ -218,7 +219,7 @@ def test_matrix_matrix_multiply():
 
     Matrix * Matrix = Matrix
     """
-    assert matrix_matrix_multiply(A, B) == A
+    assert matrix_matrix_multiply(A, B) == B
     assert matrix_matrix_multiply(B, C) == [[8, 10],
                                             [20, 25],
                                             [32, 40]]
@@ -233,3 +234,7 @@ def test_matrix_matrix_multiply_checks_shapes():
     """Shape Rule: The number of columns of the first matrix must equal the
     number of rows of the second matrix."""
     matrix_matrix_multiply(A, D)
+
+
+if __name__ == '__main__':
+    nose.main()