Erster Stand: compute.py

To_the_moon/compute.py

@@ -0,0 +1,106 @@
+"""
+Mathematical matrix multiplication, transposition, and rotation without external libraries.
+
+The ``matmul`` function implements a straightforward algorithm that
+multiplies two 2‑D matrices where each element is a ``float``.
+
+The functions perform validity checks on the dimensions:
+- Matrices must be non-empty lists of lists and rectangular.
+
+"""
+
+from __future__ import annotations
+import math
+
+
+def matmul(a: list[list[float]], b: list[list[float]]) -> list[list[float]]:
+    """Multiply two 2‑D matrices."""
+    if not a or not a[0]:
+        raise ValueError("Matrix 'a' must not be empty")
+    if not b or not b[0]:
+        raise ValueError("Matrix 'b' must not be empty")
+
+    a_rows = len(a)
+    a_cols = len(a[0])
+    for row in a:
+        if len(row) != a_cols:
+            raise ValueError("Matrix 'a' rows must all have the same length")
+
+    b_rows = len(b)
+    b_cols = len(b[0])
+    for row in b:
+        if len(row) != b_cols:
+            raise ValueError("Matrix 'b' rows must all have the same length")
+
+    if a_cols != b_rows:
+        raise ValueError(
+            f"Cannot multiply: number of columns in 'a' ({a_cols}) "
+            f"does not equal number of rows in 'b' ({b_rows})"
+        )
+
+    result: list[list[float]] = []
+    for i in range(a_rows):
+        result_row: list[float] = []
+        for j in range(b_cols):
+            element = 0.0
+            for k in range(a_cols):
+                element += a[i][k] * b[k][j]
+            result_row.append(element)
+        result.append(result_row)
+
+    return result
+
+
+def transpose(a: list[list[float]]) -> list[list[float]]:
+    """Transposes a 2‑D matrix."""
+    if not a or not a[0]:
+        raise ValueError("Matrix must not be empty")
+
+    a_rows = len(a)
+    a_cols = len(a[0])
+    for row in a:
+        if len(row) != a_cols:
+            raise ValueError("Matrix rows must all have the same length")
+
+    result: list[list[float]] = []
+    for j in range(a_cols):
+        result_row: list[float] = []
+        for i in range(a_rows):
+            result_row.append(a[i][j])
+        result.append(result_row)
+
+    return result
+
+
+def rot_2D(theta: float) -> list[list[float]]:
+    """Erzeugt eine 2D-Rotationsmatrix für den Winkel theta (im Bogenmaß)."""
+    cos_t = math.cos(theta)
+    sin_t = math.sin(theta)
+    return [
+        [cos_t, -sin_t],
+        [sin_t, cos_t]
+    ]
+
+
+if __name__ == "__main__":
+    # Valid example: multiplication
+    matrix_a = [[1, 2, 3], [4, 5, 6]]
+    matrix_b = [[7, 8], [9, 10], [11, 12]]
+    print("Valid multiplication result:")
+    print(matmul(matrix_a, matrix_b))
+
+    # Valid example: transposition
+    print("\nTransposed matrix_a result:")
+    print(transpose(matrix_a))
+
+    # Valid example: rotation (2D)
+    print("\nRotated 2D matrix (theta = 0.5) result:")
+    print(rot_2D(0.5))
+
+    # Example that raises ValueError
+    try:
+        invalid_b = [[1, 2], [3, 4]]
+        print("\nThis should raise an error:")
+        print(matmul(matrix_a, invalid_b))
+    except ValueError as e:
+        print("Caught ValueError as expected:", e)