add tests for the mathematics module

docs/build/html/_modules/mathematics.html

@@ -45,6 +45,7 @@
 
 <span class="sd">.. moduleauthor:: Daniel Weschke &lt;daniel.weschke@directbox.de&gt;</span>
 <span class="sd">&quot;&quot;&quot;</span>
+<span class="kn">import</span> <span class="nn">math</span>
 <span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">gcd</span>
 
 <div class="viewcode-block" id="lcm"><a class="viewcode-back" href="../mathematics.html#mathematics.lcm">[docs]</a><span class="k">def</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>

docs/build/html/_modules/pylib/mathematics.html

@@ -45,6 +45,7 @@
 
 <span class="sd">.. moduleauthor:: Daniel Weschke &lt;daniel.weschke@directbox.de&gt;</span>
 <span class="sd">&quot;&quot;&quot;</span>
+<span class="kn">import</span> <span class="nn">math</span>
 <span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">gcd</span>
 
 <div class="viewcode-block" id="lcm"><a class="viewcode-back" href="../../pylib.html#pylib.mathematics.lcm">[docs]</a><span class="k">def</span> <span class="nf">lcm</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>

tests/test_mathematics.py

@@ -0,0 +1,397 @@
+"""Test of mathematics module.
+
+:Date: 2019-12-20
+
+.. module:: test_mathematics
+  :platform: *nix, Windows
+  :synopsis: Test of mathematics module.
+
+.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
+"""
+import unittest
+
+import os
+import sys
+sys.path.insert(0, os.path.abspath('../pylib'))
+
+import math
+from mathematics import vector, matrix
+
+class TestGeometry(unittest.TestCase):
+
+  #
+  # vector
+  # NOTE: vector: scalar != 1 element vector
+  #
+
+  def test_vector(self):
+    self.assertEqual(
+        vector(),
+        [])
+    self.assertEqual(
+        vector([1, 0, 0, 1]),
+        [1, 0, 0, 1])
+
+  def test_vector_mul_vs(self):
+    self.assertEqual(
+        vector([1, 2, 3]) * 4,
+        [4, 8, 12])
+    self.assertEqual(
+        vector([-1, -2, -3]) * 4,
+        [-4, -8, -12])
+    self.assertEqual(
+        vector([1, 2, 3]) * -4,
+        [-4, -8, -12])
+    self.assertEqual(
+        vector([-1, -2, -3]) * -4,
+        [4, 8, 12])
+
+  def test_vector_mul_vv(self):
+    self.assertEqual(
+        vector([1, 2, 3]) * vector([1, 2, 3]),
+        14)
+    self.assertEqual(
+        vector([-1, -2, -3]) * vector([1, 2, 3]),
+        -14)
+    self.assertEqual(
+        vector([1, 2, 3]) * vector([-1, -2, -3]),
+        -14)
+    self.assertEqual(
+        vector([-1, -2, -3]) * vector([-1, -2, -3]),
+        14)
+
+  def test_vector_mul_vm(self):
+    r"""
+    .. math::
+      &
+      \begin{bmatrix}
+        1 & 2 & 3
+      \end{bmatrix}
+      \cdot
+      \begin{bmatrix}
+        1 & 2 & 3 \\
+        4 & 5 & 6 \\
+        7 & 8 & 9
+      \end{bmatrix}
+      \\
+      =&
+      \begin{bmatrix}
+        1+8+21 & 2+10+24 & 3+12+27
+      \end{bmatrix}
+      \\
+      =&
+      \begin{bmatrix}
+        30 & 36 & 42
+      \end{bmatrix}
+    """
+    self.assertEqual(
+        vector([1, 2, 3]) * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [30, 36, 42])
+    self.assertEqual(
+        vector([-1, -2, -3]) * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [-30, -36, -42])
+    self.assertEqual(
+        vector([1, 2, 3]) * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [-30, -36, -42])
+    self.assertEqual(
+        vector([-1, -2, -3]) * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [30, 36, 42])
+
+  def test_vector_rmul_sv(self):
+    self.assertEqual(
+        4 * vector([1, 2, 3]),
+        [4, 8, 12])
+    self.assertEqual(
+        -4 * vector([1, 2, 3]),
+        [-4, -8, -12])
+    self.assertEqual(
+        4 * vector([-1, -2, -3]),
+        [-4, -8, -12])
+    self.assertEqual(
+        -4 * vector([-1, -2, -3]),
+        [4, 8, 12])
+
+  def test_vector_rmul_mv(self):
+    # 2d list * vector, matrix * vector see matrix.__mul__
+    self.assertEqual(
+        [[1, 2, 3], [4, 5, 6], [7, 8, 9]] * vector([1, 2, 3]),
+        [14, 32, 50])
+    self.assertEqual(
+        [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]] * vector([1, 2, 3]),
+        [-14, -32, -50])
+    self.assertEqual(
+        [[1, 2, 3], [4, 5, 6], [7, 8, 9]] * vector([-1, -2, -3]),
+        [-14, -32, -50])
+    self.assertEqual(
+        [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]] * vector([-1, -2, -3]),
+        [14, 32, 50])
+
+  def test_vector_abs(self):
+    self.assertEqual(
+        abs(vector([0.6, 0.8])),
+        1)
+    self.assertEqual(
+        abs(vector([3, 4])),
+        5)
+
+  def test_vector_full(self):
+    self.assertEqual(
+        vector.full(3, 7),
+        [7, 7, 7])
+
+  def test_vector_zeros(self):
+    self.assertEqual(
+        vector.zeros(3),
+        [0, 0, 0])
+    self.assertEqual(
+        vector.zeros((3)),
+        [0, 0, 0])
+    self.assertEqual(
+        vector.zeros(-1),
+        [])
+
+  def test_vector_ones(self):
+    self.assertEqual(
+        vector.ones(3),
+        [1, 1, 1])
+    self.assertEqual(
+        vector.ones((3)),
+        [1, 1, 1])
+    self.assertEqual(
+        vector.ones(-1),
+        [])
+
+  def test_vector_random(self):
+    obj = vector.random(3)
+    self.assertEqual(
+        len(obj),
+        3)
+
+  def test_vector_normalize(self):
+    v = vector.normalize(vector([3, 4]))
+    self.assertEqual(
+        v,
+        [0.6, 0.8])
+    self.assertEqual(
+        abs(v),
+        1)
+
+  def test_vector_rotate_x(self):
+    # rotation of vector coordinate system about x axis
+
+    # vector points to x -> vector points to x still
+    self.assertEqual(                             vector([1, 0, 0, 1]).rotate_x(math.pi/2), [1, 0, 0, 1])
+    # vector points to y -> vector points to -z
+    [self.assertAlmostEqual(i, j) for i, j in zip(vector([0, 1, 0, 1]).rotate_x(math.pi/2), [0, 0, 1, 1])]
+    # vector points to z -> vector points to y
+    [self.assertAlmostEqual(i, j) for i, j in zip(vector([0, 0, 1, 1]).rotate_x(math.pi/2), [0, -1, 0, 1])]
+
+  def test_vector_rotate_y(self):
+    # rotation of vector coordinate system about y axis
+
+    # vector points to x ->, vector points to z
+    [self.assertAlmostEqual(i, j) for i, j in zip(vector([1, 0, 0, 1]).rotate_y(math.pi/2), [0, 0, -1, 1])]
+    # vector points to y -> vector points to y still
+    self.assertEqual(                             vector([0, 1, 0, 1]).rotate_y(math.pi/2), [0, 1, 0, 1])
+    # vector points to z -> vector points to -x
+    [self.assertAlmostEqual(i, j) for i, j in zip(vector([0, 0, 1, 1]).rotate_y(math.pi/2), [1, 0, 0, 1])]
+
+  def test_vector_rotate_z(self):
+    # rotation of vector coordinate system about z axis
+
+    # vector points to x ->, vector points to z
+    [self.assertAlmostEqual(i, j) for i, j in zip(vector([1, 0, 0, 1]).rotate_z(math.pi/2), [0, 1, 0, 1])]
+    # vector points to y -> vector points to
+    [self.assertAlmostEqual(i, j) for i, j in zip(vector([0, 1, 0, 1]).rotate_z(math.pi/2), [-1, 0, 0, 1])]
+    # vector points to z -> vector points to z still
+    self.assertEqual(                             vector([0, 0, 1, 1]).rotate_z(math.pi/2), [0, 0, 1, 1])
+
+  #
+  # matrix
+  # NOTE: matrix: scalar != 1x1 matrix
+  #
+
+  def test_matrix_mul_ms(self):
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * 4,
+        [[4, 8, 12], [16, 20, 24], [28, 32, 36]])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * 4,
+        [[-4, -8, -12], [-16, -20, -24], [-28, -32, -36]])
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * -4,
+        [[-4, -8, -12], [-16, -20, -24], [-28, -32, -36]])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * -4,
+        [[4, 8, 12], [16, 20, 24], [28, 32, 36]])
+
+  def test_matrix_mul_mv(self):
+    r"""
+    .. math::
+      \begin{bmatrix}
+        1 & 2 & 3 \\
+        4 & 5 & 6 \\
+        7 & 8 & 9
+      \end{bmatrix}
+      \cdot
+      \begin{bmatrix}
+        1 \\
+        2 \\
+        3
+      \end{bmatrix}
+      =
+      \begin{bmatrix}
+        1+4+9   \\
+        4+10+18 \\
+        7+16+27
+      \end{bmatrix}
+      =
+      \begin{bmatrix}
+        14 \\
+        32 \\
+        50
+      \end{bmatrix}
+    """
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * vector([1, 2, 3]),
+        [14, 32, 50])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * vector([1, 2, 3]),
+        [-14, -32, -50])
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * vector([-1, -2, -3]),
+        [-14, -32, -50])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * vector([-1, -2, -3]),
+        [14, 32, 50])
+
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[1], [2], [3]]),
+        [[14], [32], [50]])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * matrix([[1], [2], [3]]),
+        [[-14], [-32], [-50]])
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[-1], [-2], [-3]]),
+        [[-14], [-32], [-50]])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * matrix([[-1], [-2], [-3]]),
+        [[14], [32], [50]])
+
+  def test_matrix_mul_vm(self):
+    # matrix-vector * matrix, vector * matrix see vector.__mul__
+    self.assertEqual(
+        matrix([[1, 2, 3]]) * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [[30, 36, 42]])
+    self.assertEqual(
+        matrix([[-1, -2, -3]]) * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [[-30, -36, -42]])
+    self.assertEqual(
+        matrix([[1, 2, 3]]) * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [[-30, -36, -42]])
+    self.assertEqual(
+        matrix([[-1, -2, -3]]) * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [[30, 36, 42]])
+
+  def test_matrix_mul_mm(self):
+    r"""
+    .. math::
+      &
+      \begin{bmatrix}
+        1 & 2 & 3 \\
+        4 & 5 & 6 \\
+        7 & 8 & 9
+      \end{bmatrix}
+      \cdot
+      \begin{bmatrix}
+        11 & 12 & 13 \\
+        14 & 15 & 16 \\
+        17 & 18 & 19
+      \end{bmatrix}
+      \\
+      =&
+      \begin{bmatrix}
+        11+28+51   & 12+30+54   & 13+32+57   \\
+        44+70+102  & 48+75+108  & 52+80+114  \\
+        77+112+153 & 84+120+162 & 91+128+171
+      \end{bmatrix}
+      \\
+      =&
+      \begin{bmatrix}
+        90  & 96  & 102 \\
+        216 & 231 & 246 \\
+        342 & 366 & 390
+      \end{bmatrix}
+
+    interesting
+
+    .. math::
+      90  \xrightarrow{+6}  96  \xrightarrow{+6}  102 \quad &\Big| \sum\{1, 2, 3\} = 6  \\
+      216 \xrightarrow{+15} 231 \xrightarrow{+15} 246 \quad &\Big| \sum\{4, 5, 6\} = 15 \\
+      342 \xrightarrow{+24} 366 \xrightarrow{+24} 390 \quad &\Big| \sum\{7, 8, 9\} = 24
+
+    .. math::
+      90  \xrightarrow{+126} 216 \xrightarrow{+126} 342 \quad &\Big| \sum\{11, 14, 17\} = 42 = 126/3 \\
+      96  \xrightarrow{+135} 231 \xrightarrow{+135} 366 \quad &\Big| \sum\{12, 15, 18\} = 45 = 135/3 \\
+      102 \xrightarrow{+144} 246 \xrightarrow{+144} 390 \quad &\Big| \sum\{13, 16, 19\} = 48 = 144/3
+    """
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[11, 12, 13], [14, 15, 16], [17, 18, 19]]),
+        [[90, 96, 102], [216, 231, 246], [342, 366, 390]])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * matrix([[11, 12, 13], [14, 15, 16], [17, 18, 19]]),
+        [[-90, -96, -102], [-216, -231, -246], [-342, -366, -390]])
+    self.assertEqual(
+        matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) * matrix([[-11, -12, -13], [-14, -15, -16], [-17, -18, -19]]),
+        [[-90, -96, -102], [-216, -231, -246], [-342, -366, -390]])
+    self.assertEqual(
+        matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]) * matrix([[-11, -12, -13], [-14, -15, -16], [-17, -18, -19]]),
+        [[90, 96, 102], [216, 231, 246], [342, 366, 390]])
+
+  def test_matrix_rmul_sm(self):
+    self.assertEqual(
+        4 * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [[4, 8, 12], [16, 20, 24], [28, 32, 36]])
+    self.assertEqual(
+        -4 * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [[-4, -8, -12], [-16, -20, -24], [-28, -32, -36]])
+    self.assertEqual(
+        4 * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [[-4, -8, -12], [-16, -20, -24], [-28, -32, -36]])
+    self.assertEqual(
+        -4 * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [[4, 8, 12], [16, 20, 24], [28, 32, 36]])
+
+  def test_matrix_rmul_vm(self):
+    # 1d list * matrix, vector * matrix see vector.__mul__
+    self.assertEqual(
+        [1, 2, 3] * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [30, 36, 42])
+    self.assertEqual(
+        [-1, -2, -3] * matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+        [-30, -36, -42])
+    self.assertEqual(
+        [1, 2, 3] * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [-30, -36, -42])
+    self.assertEqual(
+        [-1, -2, -3] * matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]),
+        [30, 36, 42])
+
+  def test_matrix_rmul_mm(self):
+    # 2d list * matrix, matrix * matrix see matrix.__mul__
+    self.assertEqual(
+        [[1, 2, 3], [4, 5, 6], [7, 8, 9]] * matrix([[11, 12, 13], [14, 15, 16], [17, 18, 19]]),
+        [[90, 96, 102], [216, 231, 246], [342, 366, 390]])
+    self.assertEqual(
+        [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]] * matrix([[11, 12, 13], [14, 15, 16], [17, 18, 19]]),
+        [[-90, -96, -102], [-216, -231, -246], [-342, -366, -390]])
+    self.assertEqual(
+        [[1, 2, 3], [4, 5, 6], [7, 8, 9]] * matrix([[-11, -12, -13], [-14, -15, -16], [-17, -18, -19]]),
+        [[-90, -96, -102], [-216, -231, -246], [-342, -366, -390]])
+    self.assertEqual(
+        [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]] * matrix([[-11, -12, -13], [-14, -15, -16], [-17, -18, -19]]),
+        [[90, 96, 102], [216, 231, 246], [342, 366, 390]])
+
+
+if __name__ == '__main__':
+  unittest.main(verbosity=2)