[docs]def lcm(a, b):
diff --git a/docs/build/html/_modules/pylib/mathematics.html b/docs/build/html/_modules/pylib/mathematics.html
index 4a419ac..aa57d66 100644
--- a/docs/build/html/_modules/pylib/mathematics.html
+++ b/docs/build/html/_modules/pylib/mathematics.html
@@ -45,6 +45,7 @@
.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
"""
+
import math
from math import gcd
[docs]def lcm(a, b):
diff --git a/tests/test_mathematics.py b/tests/test_mathematics.py
new file mode 100644
index 0000000..3769a3c
--- /dev/null
+++ b/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
+"""
+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)