Start of matrixmania

.gitignore

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+.venv/
+__pycache__/
+.env

AGENTS.md

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+# AGENTS.md 
+## Code-Konventionen 
+- PEP 8 einhalten, Zeilenlänge max. 88 Zeichen 
+- Jede Funktion braucht Type Hints und einen Docstring 
+- Nach Erstellung mit "ruff check" und "ruff format" prüfen

compute.py

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+"""Matrix operations module.
+
+This module provides utilities for basic matrix arithmetic:
+* :func:`matmul` – standard matrix multiplication
+* :func:`transpose` – matrix transposition
+* :func:`rot_2D` – 2‑D rotation matrix generator
+
+All functions validate inputs and raise ``ValueError`` where
+appropriate.  Type hints use the built‑in ``list`` and ``int | float`` union.
+"""
+
+from __future__ import annotations
+import math
+
+# Public type alias for a matrix of numeric values.
+Matrix = list[list[int | float]]
+
+# ---------------------------------------------------------------------------
+# matmul
+# ---------------------------------------------------------------------------
+
+def matmul(a: Matrix, b: Matrix) -> Matrix:
+    """Multiply two matrices.
+
+    Parameters
+    ----------
+    a: Matrix
+        Left‑hand operand. Must be a non‑empty, rectangular matrix.
+    b: Matrix
+        Right‑hand operand. Must be a non‑empty, rectangular matrix
+        whose column count equals ``a``'s row count.
+
+    Returns
+    -------
+    Matrix
+        Result of the matrix product ``a @ b``.
+
+    Raises
+    ------
+    ValueError
+        If either matrix is empty, not rectangular, or the inner
+        dimensions do not agree.
+    """
+    if not a or not a[0] or not b or not b[0]:
+        raise ValueError("Both matrices must be non‑empty")
+
+    a_rows, a_cols = len(a), len(a[0])
+    b_rows, b_cols = len(b), len(b[0])
+
+    if any(len(row) != a_cols for row in a):
+        raise ValueError("Matrix 'a' is not rectangular")
+    if any(len(row) != b_cols for row in b):
+        raise ValueError("Matrix 'b' is not rectangular")
+    if a_cols != b_rows:
+        raise ValueError(
+            f"Inner matrix dimensions must agree: a_cols={a_cols} != b_rows={b_rows}"
+        )
+
+    result: Matrix = [[0 for _ in range(b_cols)] for _ in range(a_rows)]
+
+    for i in range(a_rows):
+        for j in range(b_cols):
+            s = 0
+            for k in range(a_cols):
+                s += a[i][k] * b[k][j]
+            result[i][j] = s
+    return result
+
+# ---------------------------------------------------------------------------
+# Transpose
+# ---------------------------------------------------------------------------
+
+def transpose(mat: Matrix) -> Matrix:
+    """Return the transpose of a matrix.
+
+    Parameters
+    ----------
+    mat: Matrix
+        Input matrix to transpose. Must be a non‑empty, rectangular matrix.
+
+    Returns
+    -------
+    Matrix
+        Transposed matrix: columns become rows and vice versa.
+
+    Raises
+    ------
+    ValueError
+        If ``mat`` is empty or the rows have differing lengths.
+    """
+    if not mat or not mat[0]:
+        raise ValueError("Matrix must be non‑empty")
+
+    row_len = len(mat[0])
+    if any(len(row) != row_len for row in mat):
+        raise ValueError("Matrix must be rectangular – rows have varying lengths")
+
+    transposed: Matrix = [[mat[row][col] for row in range(len(mat))] for col in range(row_len)]
+    return transposed
+
+# ---------------------------------------------------------------------------
+# Rotation matrix generator
+# ---------------------------------------------------------------------------
+
+def rot_2D(theta: float) -> Matrix:
+    """Return a 2‑D rotation matrix for an angle ``theta``.
+
+    The matrix corresponds to a rotation about the origin by ``theta``
+    radians (counter‑clockwise).  For a vector ``(x, y)`` the rotated
+    coordinates are obtained via ``matmul(rot_2D(theta), [x, y])``.
+
+    Parameters
+    ----------
+    theta: float
+        Rotation angle in radians.
+
+    Returns
+    -------
+    Matrix
+        2×2 rotation matrix.
+
+    Raises
+    ------
+    ValueError
+        Never raised – the function accepts any floating‑point value.
+    """
+    c = math.cos(theta)
+    s = math.sin(theta)
+    return [[c, -s], [s, c]]
+
+# ---------------------------------------------------------------------------
+# Example usage / tests
+# ---------------------------------------------------------------------------
+if __name__ == "__main__":
+    # Example multiply
+
+    matrix_a = [
+        [3, 4, -1, 4],
+        [-2, 2, 5, 1]
+    ]
+
+    matrix_b = [
+        [1, 3, -2],
+        [2, 5, 1],
+        [-1, 4, -4],
+        [2, 3, 6]
+    ]
+
+    matrix_c = matmul(matrix_a, matrix_b)
+    print("Ergebnis C = A * B:")
+    for row in matrix_c:
+        print(row)
+
+    # Example transpose
+    matrix_d = [[1, 2, 3], [4, 5, 6]]
+    print("Transpose of", matrix_d, "=", transpose(matrix_d))
+
+    # Demonstrate rot_2D
+    angle = math.radians(45)
+    rot = rot_2D(angle)
+    vec = [[1], [0]]
+    print("Rotation matrix for 45°:", rot)
+    print("Rotated vec:", matmul(rot, vec))

pyproject.toml

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+[project] 
+name = "matrixmania" 
+version = "0.1.0"
+dependencies = ["tabulate", "ruff"]