Brian's Homework

README.md

@@ -41,9 +41,9 @@ After completing this assignment, you should be able to:
 
 Implement two object types, `Matrix` and `Vector`. These objects should implement:
 
-* shape
-* addition and subtraction
-* multiplication by a scalar
+<!-- * shape -->
+<!-- * addition and subtraction -->
+<!-- * multiplication by a scalar -->
 * matrix multiplication by a vector
 * matrix multiplication by a matrix
 * vector dot product

classy_matrix_math.py

@@ -0,0 +1,58 @@
+class ShapeException(Exception):
+    pass
+
+class Vector:
+
+    def __init__(self, alist):
+        self.alist = alist
+
+    def __eq__(self, other):
+        return self.alist == other.alist
+
+    def shape(self):
+        return (len(self.alist), )
+
+    def __repr__(self):
+        return "Vector({})".format(self.alist)
+
+    def __add__(self, other):
+        if self.shape() != other.shape():
+            raise ShapeException
+        return Vector([self.alist[idx] + other.alist[idx] for idx \
+                                in range(len(self.alist))])
+
+    def __sub__(self, other):
+        if self.shape() != other.shape():
+            raise ShapeException
+        return Vector([self.alist[idx] - other.alist[idx] for idx \
+                                in range(len(self.alist))])
+
+    def __mul__(self, other):
+        if self.shape() != other.shape():
+            raise ShapeException
+        return Vector([self.alist[idx] * other.alist[idx] for idx \
+                                in range(len(self.alist))])
+
+    def dot(self, other):
+        if self.shape() != other.shape():
+            raise ShapeException
+        return sum([num for num in (self * other).alist])
+
+    def vector_multiply(self, other):
+        return [num * other for num in self.alist]
+
+class Matrix:
+
+    def __init__(self, alist):
+        self.alist = alist
+
+    def __eq__(self, other):
+        return self.alist == other.alist
+
+    def matrix_shape(self):
+        for vec in self.alist:
+            if len(vec) == len(self.alist[0]):
+                return (len(self.alist), len(self.alist[len(self.alist)-1]))
+
+    def matrix_row(self, row_number):
+        return self.alist[row_number]

test_classy_matrix_math.py

@@ -0,0 +1,216 @@
+from classy_matrix_math import Vector, ShapeException, Matrix
+from nose.tools import raises
+
+
+
+def is_equal(x, y, tolerance=0.001):
+    """Helper function to compare floats, which are often not quite equal
+    even when they should be."""
+    return abs(x - y) <= tolerance
+
+
+m = Vector([3, 4])
+n = Vector([5, 0])
+
+v = Vector([1, 3, 0])
+w = Vector([0, 2, 4])
+u = Vector([1, 1, 1])
+y = Vector([10, 20, 30])
+z = Vector([0, 0, 0])
+
+a = Matrix([[1,0],
+            [2,1],
+            [1,1]])
+
+b = Matrix([[2,1,2],
+            [1,1,1],
+            [1,1,2]])
+
+def test_shape_vectors():
+    """shape should take a vector or matrix and return a tuple with the
+    number of rows (for a vector) or the number of rows and columns
+    (for a matrix.)"""
+    assert m.shape() == (2,)
+    assert v.shape() == (3,)
+    assert Vector([1]).shape() == (1,)
+
+
+def test_vector_can_be_added_with_std_operator():
+    """
+    [a b]  + [c d]  = [a+c b+d]
+
+    Matrix + Matrix = Matrix
+    """
+    assert v + w == Vector([1, 5, 4])
+    assert u + y == Vector([11, 21, 31])
+    assert u + z == u
+
+
+def test_vector_add_is_communicative():
+    assert w + y == y + w
+
+
+@raises(ShapeException)
+def test_vector_add_checks_shapes():
+    """Shape rule: the vectors must be the same size."""
+    m + v
+
+
+def test_vector_sub():
+    """
+    [a b]  - [c d]  = [a-c b-d]
+
+    Matrix + Matrix = Matrix
+    """
+    assert v - w == Vector([1, 1, -4])
+    assert w - v == Vector([-1, -1, 4])
+    assert y - z == y
+    assert w - u == z - (u - w)
+
+
+@raises(ShapeException)
+def test_vector_sub_checks_shapes():
+    """Shape rule: the vectors must be the same size."""
+    m - w
+
+def test_vector_times():
+
+    assert v * w == Vector([0, 6, 0])
+    assert w * v == Vector([0, 6, 0])
+    assert y * z == z
+
+@raises(ShapeException)
+def test_vector_times_checks_shapes():
+    """Shape rule: the vectors must be the same size."""
+    m * w
+
+
+
+def test_dot():
+    """
+    dot([a b], [c d])   = a * c + b * d
+
+    dot(Vector, Vector) = Scalar
+    """
+    assert w.dot(y) == 160
+    assert m.dot(n) == 15
+    assert u.dot(z) == 0
+
+
+@raises(ShapeException)
+def test_dot_checks_shapes():
+    """Shape rule: the vectors must be the same size."""
+    v.dot(m)
+
+
+def test_vector_multiply():
+    """
+    [a b]  *  Z     = [a*Z b*Z]
+
+    Vector * Scalar = Vector
+    """
+    assert v.vector_multiply(0.5) == [0.5, 1.5, 0]
+    assert m.vector_multiply(2) == [6, 8]
+
+
+A = Matrix([[1, 0, 0],
+            [0, 1, 0],
+            [0, 0, 1]])
+B = Matrix([[1, 2, 3],
+            [4, 5, 6],
+            [7, 8, 9]])
+C = Matrix([[1, 2],
+            [2, 1],
+            [1, 2]])
+D = Matrix([[1, 2, 3],
+            [3, 2, 1]])
+
+def test_matrix_shape():
+
+    assert A.matrix_shape() == (3, 3)
+    assert C.matrix_shape() == (3, 2)
+    assert D.matrix_shape() == (2, 3)
+
+
+def test_matrix_row():
+    """
+           0 1  <- rows
+       0 [[a b]]
+       1 [[c d]]
+       ^
+     columns
+    """
+    assert A.matrix_row(0) == [1, 0, 0]
+    assert B.matrix_row(1) == [4, 5, 6]
+    assert C.matrix_row(2) == [1, 2]
+
+
+def test_matrix_col():
+    """
+           0 1  <- rows
+       0 [[a b]]
+       1 [[c d]]
+       ^
+     columns
+    """
+    assert matrix_col(A, 0) == [1, 0, 0]
+    assert matrix_col(B, 1) == [2, 5, 8]
+    assert matrix_col(D, 2) == [3, 1]
+
+
+# def test_matrix_scalar_multiply():
+#     """
+#     [[a b]   *  Z   =   [[a*Z b*Z]
+#      [c d]]              [c*Z d*Z]]
+#
+#     Matrix * Scalar = Matrix
+#     """
+#     assert matrix_scalar_multiply(C, 3) == [[3, 6],
+#                                             [6, 3],
+#                                             [3, 6]]
+#
+#
+# def test_matrix_vector_multiply():
+#     """
+#     [[a b]   *  [x   =   [a*x+b*y
+#      [c d]       y]       c*x+d*y
+#      [e f]                e*x+f*y]
+#
+#     Matrix * Vector = Vector
+#     """
+#     assert matrix_vector_multiply(A, [2, 5, 4]) == [2, 5, 4]
+#     assert matrix_vector_multiply(B, [1, 2, 3]) == [14, 32, 50]
+#     assert matrix_vector_multiply(C, [3, 4]) == [11, 10, 11]
+#     assert matrix_vector_multiply(D, [0, 1, 2]) == [8, 4]
+#
+#
+# @raises(ShapeException)
+# def test_matrix_vector_multiply_checks_shapes():
+#     """Shape Rule: The number of rows of the vector must equal the number of
+#     columns of the matrix."""
+#     matrix_vector_multiply(C, [1, 2, 3])
+#
+#
+# def test_matrix_matrix_multiply():
+#     """
+#     [[a b]   *  [[w x]   =   [[a*w+b*y a*x+b*z]
+#      [c d]       [y z]]       [c*w+d*y c*x+d*z]
+#      [e f]                    [e*w+f*y e*x+f*z]]
+#
+#     Matrix * Matrix = Matrix
+#     """
+#     assert matrix_matrix_multiply(A, B) == A
+#     assert matrix_matrix_multiply(B, C) == [[8, 10],
+#                                             [20, 25],
+#                                             [32, 40]]
+#     assert matrix_matrix_multiply(C, D) == [[7, 6, 5],
+#                                             [5, 6, 7],
+#                                             [7, 6, 5]]
+#     assert matrix_matrix_multiply(D, C) == [[8, 10], [8, 10]]
+#
+#
+# @raises(ShapeException)
+# 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)