Create Transformations2D.py (#2310)

* Create Transformations2D.py

* Update Transformations2D.py

* Drop numpy and add type hints and doctests

* Rename Transformations2D.py to transformations_2d.py

Co-authored-by: Christian Clauss <cclauss@me.com>

linear_algebra/src/transformations_2d.py

@@ -0,0 +1,62 @@
+"""
+2D Transformations are regularly used in Linear Algebra.
+
+I have added the codes for reflection, projection, scaling and rotation 2D matrices.
+
+    scaling(5) = [[5.0, 0.0], [0.0, 5.0]]
+  rotation(45) = [[0.5253219888177297, -0.8509035245341184],
+                  [0.8509035245341184, 0.5253219888177297]]
+projection(45) = [[0.27596319193541496, 0.446998331800279],
+                  [0.446998331800279, 0.7240368080645851]]
+reflection(45) = [[0.05064397763545947, 0.893996663600558],
+                  [0.893996663600558, 0.7018070490682369]]
+"""
+from math import cos, sin
+from typing import List
+
+
+def scaling(scaling_factor: float) -> List[List[float]]:
+    """
+    >>> scaling(5)
+    [[5.0, 0.0], [0.0, 5.0]]
+    """
+    scaling_factor = float(scaling_factor)
+    return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]
+
+
+def rotation(angle: float) -> List[List[float]]:
+    """
+    >>> rotation(45)  # doctest: +NORMALIZE_WHITESPACE
+    [[0.5253219888177297, -0.8509035245341184],
+     [0.8509035245341184, 0.5253219888177297]]
+    """
+    c, s = cos(angle), sin(angle)
+    return [[c, -s], [s, c]]
+
+
+def projection(angle: float) -> List[List[float]]:
+    """
+    >>> projection(45)  # doctest: +NORMALIZE_WHITESPACE
+    [[0.27596319193541496, 0.446998331800279],
+     [0.446998331800279, 0.7240368080645851]]
+    """
+    c, s = cos(angle), sin(angle)
+    cs = c * s
+    return [[c * c, cs], [cs, s * s]]
+
+
+def reflection(angle: float) -> List[List[float]]:
+    """
+    >>> reflection(45)  # doctest: +NORMALIZE_WHITESPACE
+    [[0.05064397763545947, 0.893996663600558],
+     [0.893996663600558, 0.7018070490682369]]
+    """
+    c, s = cos(angle), sin(angle)
+    cs = c * s
+    return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]
+
+
+print(f"    {scaling(5) = }")
+print(f"  {rotation(45) = }")
+print(f"{projection(45) = }")
+print(f"{reflection(45) = }")