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Praktikumsaufgaben/compute.py

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+# Prog3B/compute.py
+
+"""Matrix transpose implementation.
+
+The function `transpose` accepts a 2‑D list `matrix` and returns a new
+2‑D list where rows and columns are swapped.  The implementation uses
+simple for‑loops and basic list operations to stay within the beginner
+Python skill level.
+
+Example
+-------
+>>> transpose([[1, 2, 3], [4, 5, 6]])
+[[1, 4], [2, 5], [3, 6]]
+
+"""
+
+from typing import List, Any
+import math
+
+
+def transpose(matrix: List[List[Any]]) -> List[List[Any]]:
+    """Return the transpose of a rectangular matrix.
+
+    Parameters
+    ----------
+    matrix: list of list
+        A non‑empty 2‑D list where each sub‑list represents a row.  All
+        rows are assumed to be the same length.
+
+    Returns
+    -------
+    list of list
+        A new matrix where the i‑th row of the result contains the i‑th
+        column of the input.
+    """
+    if not matrix:
+        return []
+
+    rows = len(matrix)
+    cols = len(matrix[0])
+
+    # initialise result with correct dimensions
+    result: List[List[Any]] = [[0] * rows for _ in range(cols)]
+
+    for i in range(rows):
+        for j in range(cols):
+            result[j][i] = matrix[i][j]
+
+    return result
+
+
+def rotate(matrix: List[List[Any]]) -> List[List[Any]]:
+    """Return a new matrix rotated 90 degrees clockwise.
+
+    The original matrix is not modified.
+
+    Parameters
+    ----------
+    matrix: list of list
+        A rectangular matrix.
+
+    Returns
+    -------
+    list of list
+        Rotated matrix.
+    """
+    if not matrix:
+        return []
+    inter = transpose(matrix)
+    rows = len(inter); cols = len(inter[0])
+    result: List[List[Any]] = [[0] * rows for _ in range(cols)]
+    for i in range(cols):
+        for j in range(rows):
+            result[i][j] = inter[rows - 1 - j][i]
+    return result
+
+def rot_2D(theta):
+    """Erzeugt eine Rotationsmatrix für einen Winkel."""
+
+    return [
+        [math.cos(theta), -math.sin(theta)],
+        [math.sin(theta), math.cos(theta)]
+    ]
+
+def matmul(A, B):
+    """Multipliziert zwei Matrizen."""
+
+    rows_A = len(A)
+    cols_A = len(A[0])
+    cols_B = len(B[0])
+
+    if cols_A != len(B):
+        raise ValueError("Matrizen können nicht multipliziert werden")
+
+    result = [[0] * cols_B for _ in range(rows_A)]
+
+    for i in range(rows_A):
+        for j in range(cols_B):
+            for k in range(cols_A):
+                result[i][j] += A[i][k] * B[k][j]
+
+    return result
+
+
+if __name__ == "__main__":
+    # simple demonstration / sanity check
+    sample = [[1, 2, 3], [4, 5, 6]]
+    print("Input:")
+    print(sample)
+    print("\nTransposed:")
+    print(transpose(sample))
+    print("\nRotated:")
+    print(rotate(sample))
+