Homework.Ben()

matrix_math.py

@@ -1,2 +1,193 @@
+import math
+import operator
+
+
 class ShapeException(Exception):
     pass
+
+
+def shape(a_list):
+    """Takes a list and returns a tuple of form
+    (length_of_list, length_of_each_element). The length of each element is
+    only used if each element is also a list.
+    """
+    if type(a_list[0]) == list:
+        is_shape = len(a_list), len(a_list[0])
+    else:
+        is_shape = len(a_list),
+    return is_shape
+
+###############################################################################
+
+
+def list_operator(list1, list2, operation):
+    """Takes two lists and an operation. Checks that the lists have the same
+    "shape" as defined by the shape() function. Creates a list where each
+    element is the result of performing the given operation with each
+    pair of corresponding elements from the two given lists.
+    """
+    if shape(list1) != shape(list2):
+        raise ShapeException()
+
+    new_list = [operation(list1[index], list2[index])
+                for index in range(len(list1))]
+
+    return new_list
+###############################################################################
+
+
+def vector_add(vector1, vector2):
+    """Adds the given vectors. Returns a vector"""
+    new_vector = list_operator(vector1, vector2, operator.add)
+
+    return new_vector
+
+###############################################################################
+
+
+def vector_sub(vector1, vector2):
+    """Subtracts the given vectors. Returns a vector."""
+    new_vector = list_operator(vector1, vector2, operator.sub)
+
+    return new_vector
+
+###############################################################################
+
+
+def vector_sum(*args):
+    """Takes the sum of any number of vectors.  Returns a vector."""
+    vector_list = list(args)
+    shape_check = [vector
+                   for vector in vector_list
+                   if len(vector) == len(vector_list[0])]
+
+    if vector_list != shape_check:
+        raise ShapeException()
+
+    new_vector = [sum([vector[i]
+                  for vector in vector_list])
+                  for i in range(len(vector_list[0]))]
+
+    return new_vector
+
+###############################################################################
+
+
+def dot(vector1, vector2):
+    """Takes the dot product of two vectors. Returns a scalar."""
+    new_scalar = sum(list_operator(vector1, vector2, operator.mul))
+
+    return new_scalar
+
+###############################################################################
+
+
+def vector_multiply(vector, factor):
+    """Multiplies two vectors. Returns a vector."""
+    new_vector = [coefficient * factor for coefficient in vector]
+
+    return new_vector
+
+###############################################################################
+
+
+def find_mean(a_list):
+    """Finds the mean of the elements of a given list."""
+    mean = sum(a_list)/len(a_list)
+
+    return mean
+
+###############################################################################
+
+
+def vector_mean(*args):
+    """Finds the mean of some number of vectors. Returns a vector."""
+    vector_list = list(args)
+    shape_check = [vector
+                   for vector in vector_list
+                   if len(vector) == len(vector_list[0])]
+
+    if vector_list != shape_check:
+        raise ShapeException()
+
+    new_vector = [find_mean([vector[i]
+                  for vector in vector_list])
+                  for i in range(len(vector_list[0]))]
+
+    return new_vector
+
+###############################################################################
+
+
+def magnitude(vector):
+    """Finds the magnitude of a vector. Returns a scalar."""
+    new_scalar = math.sqrt(sum([coefficient**2 for coefficient in vector]))
+
+    return new_scalar
+
+###############################################################################
+
+
+def matrix_row(matrix, row):
+    """Takes a matrix and row number and returns that row"""
+    return matrix[row]
+
+###############################################################################
+
+
+def transform_matrix(matrix):
+    """Transposes the rows and columns of a matrix"""
+    columns = [[row[i]
+               for row in matrix]
+               for i in range(len(matrix[0]))]
+
+    return columns
+
+###############################################################################
+
+
+def matrix_col(matrix, column):
+    """Takes a matrix and a column number and returns the column"""
+    get_column = transform_matrix(matrix)
+
+    return get_column[column]
+
+###############################################################################
+
+
+def matrix_scalar_multiply(matrix, factor):
+    """Multiplies a matrix by a scalar. Returns a matrix."""
+    new_matrix = [[value * factor
+                  for value in row]
+                  for row in matrix]
+
+    return new_matrix
+
+###############################################################################
+
+
+def matrix_vector_multiply(matrix, vector):
+    """Multiplies a matrix and a vector (dot product). Returns a vector."""
+    if shape(matrix[0]) != shape(vector):
+        raise ShapeException()
+
+    new_vector = [dot(row, vector) for row in matrix]
+
+    return new_vector
+
+###############################################################################
+
+
+def matrix_matrix_multiply(matrix1, matrix2):
+    """Multiplies two matrices. Returns a matrix of the same
+    shape as matrix1
+    """
+    if shape(matrix1)[1] != shape(matrix2)[0]:
+        raise ShapeException()
+
+    transformed_matrix2 = transform_matrix(matrix2)
+
+    new_matrix = [matrix_vector_multiply(transformed_matrix2, row)
+                  for row in matrix1]
+
+    return new_matrix

test_matrix_math.py

@@ -218,7 +218,7 @@ 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]]