comprehensive testing for the speed and accuracy of the determinant a…

…nd inverse implementation of 2x2 matrices

src/doptics/triangle_mesh.py

@@ -38,9 +38,12 @@ def inv_2x2(a: NDArray([2, 2])):
     :param a:
     :return:
     """
-    a_inv = np.array([[a[1, 1], -a[0, 1]],
-                      [-a[1, 0], a[0, 0]]]
-                     ) / det_2x2(a)
+    det_a = det_2x2(a)
+    if det_a == 0:
+        raise ValueError(f"det(A) = 0 => Matrix {a} is not invertible")
+    return np.array([[a[1, 1], -a[0, 1]],
+                     [-a[1, 0], a[0, 0]]]
+                    ) / det_2x2(a)
 
 
 def transform(triangle: Triangle, target: Triangle = {'a': (0, 0), 'b': (1, 0), 'c': (0, 1)}):

tests/test_triangle_mesh.py

@@ -4,13 +4,44 @@
 import numpy as np
 from typing import Callable
 from icecream import ic
+import pytest
+from time import perf_counter
 
 
 def test_det_2x2():
+    """
+    asserting that the direct implementation of the 2x2 determinant is close to the np.linalg.det() and that it is faster
+    :return:
+    """
     a = [np.random.rand(2, 2) for x in range(100)]
+    start_dir = perf_counter()
     det_dir = [tm.det_2x2(x) for x in a]
+    end_dir = perf_counter()
     det_np = [np.linalg.det(x) for x in a]
+    end_np = perf_counter()
     np.testing.assert_allclose(det_dir, det_np)
+    assert end_np - end_dir > end_dir - start_dir
+
+
+def test_inv_2x2():
+    """
+    asserting that the direct implementation of the 2x2 inverse is close to the np.linalg.inv() and that it is faster.
+    Also asserts that an exception is raised appropriately if det(A) = 0 <=> the determinant cannot be calculated.
+    :return:
+    """
+    a = [np.random.rand(2, 2) for x in range(100)]
+    start_dir = perf_counter()
+    inv_dir = [tm.inv_2x2(x) for x in a]
+    end_dir = perf_counter()
+    inv_np = [np.linalg.inv(x) for x in a]
+    end_np = perf_counter()
+    np.testing.assert_allclose(inv_dir, inv_np)
+    assert end_np - end_dir > end_dir - start_dir
+    # non-invertible
+    with pytest.raises(ValueError) as e:
+        x = tm.inv_2x2(np.zeros([2,2]))
+    assert str(e.value.args[0]) == "det(A) = 0 => Matrix [[0. 0.]\n [0. 0.]] is not invertible"
+    assert e.type is ValueError
 
 
 def test_Triangles():