Erster Stand: compute.py

compute.py

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+import math
+
+
+def matmul(a: list[list[float]], b: list[list[float]]) -> list[list[float]]:
+    """Multiplicates two matrices.
+
+    Parameters
+    ----------
+    a : list[list[float]]
+        Left matrix in row‑major order.
+    b : list[list[float]]
+        Right matrix in row‑major order.
+
+    Returns
+    -------
+    list[list[float]]
+        Product matrix `c = a × b`.
+
+    Raises
+    ------
+    ValueError
+        If matrices are not rectangular or if the number of columns in ``a``
+        does not equal the number of rows in ``b``.
+
+    Notes
+    -----
+    * Empty matrices (``[]``) yield an empty result.
+    * The implementation uses pure Python lists and does not depend on
+      external libraries such as NumPy.
+    """
+    # Validate input matrices are non‑empty lists of lists
+    if not isinstance(a, list) or not isinstance(b, list):
+        raise ValueError("Both arguments must be lists of lists.")
+
+    # Handle empty matrices early – return empty list for any empty input
+    if not a or not b:
+        return []
+
+    # Determine dimensions of left matrix ``a``
+    a_rows = len(a)
+    a_cols = None
+    for row in a:
+        if not isinstance(row, list):
+            raise ValueError("Matrix a must be a list of lists.")
+        if a_cols is None:
+            a_cols = len(row)
+        elif len(row) != a_cols:
+            raise ValueError("All rows in matrix a must have the same length.")
+
+    # Determine dimensions of right matrix ``b``
+    b_rows = len(b)
+    b_cols = None
+    for row in b:
+        if not isinstance(row, list):
+            raise ValueError("Matrix b must be a list of lists.")
+        if b_cols is None:
+            b_cols = len(row)
+        elif len(row) != b_cols:
+            raise ValueError("All rows in matrix b must have the same length.")
+
+    # Check for dimensional compatibility between ``a`` and ``b``
+    if a_cols != b_rows:
+        raise ValueError(
+            f"Matrix dimensions do not align: a.columns={a_cols} != b.rows={b_rows}"
+        )
+
+    # Initialize result matrix with zeros – dimensions a_rows × b_cols
+    result = [[0.0 for _ in range(b_cols)] for _ in range(a_rows)]
+
+    # Perform multiplication: iterate over rows of ``a`` and columns of ``b``
+    for i in range(a_rows):
+        for j in range(b_cols):
+            s = 0.0
+            for k in range(a_cols):
+                s += a[i][k] * b[k][j]
+            result[i][j] = s
+
+    return result
+
+
+def transpose(a: list[list[float]]) -> list[list[float]]:
+    """Transposes a matrix.
+
+    Parameters
+    ----------
+    a : list[list[float]]
+        Matrix in row‑major order.
+
+    Returns
+    -------
+    list[list[float]]
+        Transposed matrix where rows and columns are swapped.
+
+    Raises
+    ------
+    ValueError
+        If the matrix is not rectangular.
+
+    Notes
+    -----
+    * Empty matrices (``[]``) yield an empty result.
+    * The implementation uses pure Python lists and does not depend on
+      external libraries such as NumPy.
+    """
+    # Validate input is a list
+    if not isinstance(a, list):
+        raise ValueError("Argument must be a list of lists.")
+
+    # Handle empty matrix early – return empty list
+    if not a:
+        return []
+
+    # Determine dimensions and check rectangularity
+    rows = len(a)
+    cols = None
+    for row in a:
+        if not isinstance(row, list):
+            raise ValueError("Matrix must be a list of lists.")
+        if cols is None:
+            cols = len(row)
+        elif len(row) != cols:
+            raise ValueError("All rows in the matrix must have the same length.")
+
+    # Build transposed matrix with dimensions cols × rows
+    result = [[a[i][j] for i in range(rows)] for j in range(cols)]
+
+    return result
+
+
+def rot_2D(angle: float) -> list[list[float]]:
+    """Creates a 2×2 rotation matrix.
+
+    Parameters
+    ----------
+    angle : float
+        Rotation angle in radians (counter‑clockwise).
+
+    Returns
+    -------
+    list[list[float]]
+        Matrix ``[[cos(angle), -sin(angle)], [sin(angle), cos(angle)]]``.
+
+    Raises
+    ------
+    ValueError
+        If ``angle`` is not a real number.
+
+    Notes
+    -----
+    * The implementation uses pure Python lists and does not depend on
+      external libraries such as NumPy.
+    """
+    # Validate input is a real number
+    if not isinstance(angle, (int, float)) or isinstance(angle, bool):
+        raise ValueError("Angle must be a real number (radians).")
+
+    c = math.cos(angle)
+    s = math.sin(angle)
+
+    return [[c, -s], [s, c]]
+
+
+if __name__ == "__main__":
+    # Beispiel 1: 2x3 × 3x2
+    a = [[1, 2, 3], [4, 5, 6]]
+    b = [[7, 8], [9, 10], [11, 12]]
+    print("Beispiel 1 Ergebnis:")
+    for row in matmul(a, b):
+        print(row)
+
+    # Beispiel 2: 2x2 × 2x2
+    a2 = [[1, 0], [0, 1]]
+    b2 = [[5, 6], [7, 8]]
+    print("\nBeispiel 2 Ergebnis:")
+    for row in matmul(a2, b2):
+        print(row)
+
+    # Beispiel 3: Transponieren einer 2x3-Matrix -> 3x2
+    m = [[1, 2, 3], [4, 5, 6]]
+    print("\nBeispiel 3 Original:")
+    for row in m:
+        print(row)
+    print("Beispiel 3 Transponiert:")
+    for row in transpose(m):
+        print(row)
+
+    # Beispiel 4: Rotationsmatrix (90°) und Probe durch Drehen von (1, 0)
+    r = rot_2D(math.pi / 2)
+    print("\nBeispiel 4 Rotationsmatrix (90°):")
+    for row in r:
+        print(row)
+    print("Beispiel 4 Vektor (1, 0) nach 90°:")
+    for row in matmul(r, [[1.0], [0.0]]):
+        print([round(v, 10) for v in row])
+
+# Docstring und Type Hints sind vorhanden und stimmen mit dem Code überein.
+# Fehlerfälle werden behandelt
+# Namen sind Aussagekräftig