erster_Stand_compute.py

compute.py

@@ -0,0 +1,143 @@
+"""
+Mathematical operations on matrices.
+
+``matmul`` multiplies two matrices in the usual way.  The matrices are
+represented as nested ``list`` objects.  All rows must be of the same
+length; all columns are assumed to contain numeric values that can be
+multiplied and added.
+
+If the inner dimension does not match (number of columns in ``matrix_a``
+must equal the number of rows in ``matrix_b``) a ``ValueError`` with the
+error message "diese matriezen können nicht multiplieziert werden."
+is raised.
+"""
+
+import math
+from typing import List, Iterable
+
+
+def _is_rectangular(matrix: Iterable[Iterable]) -> bool:
+    """Return ``True`` if the matrix contains rows of equal length."""
+    try:
+        rows: List[List] = [list(row) for row in matrix]
+    except TypeError:
+        return False
+    if not rows:
+        return True
+    first_len = len(rows[0])
+    return all(len(r) == first_len for r in rows)
+
+
+def transpose(matrix: List[List[float]]) -> List[List[float]]:
+    """Return the transpose of ``matrix``.
+
+    Parameters
+    ----------
+    matrix: list[list[float]]
+        The source rectangular matrix.
+
+    Returns
+    -------
+    list[list[float]]
+        Transposed matrix.
+
+    Raises
+    ------
+    ValueError
+        If the input is not a rectangular matrix.
+    """
+    if not _is_rectangular(matrix):
+        raise ValueError("Input is not a rectangular matrix.")
+    rows = [list(row) for row in matrix]
+    n_rows = len(rows)
+    n_cols = len(rows[0]) if rows else 0
+    return [[rows[i][j] for i in range(n_rows)] for j in range(n_cols)]
+
+def rot_2D(x: float, y: float, theta: float) -> List[float]:
+    """Rotate the point ``(x, y)`` around the origin by ``theta`` radians.
+
+    Uses the rotation matrix
+    R = [[cos(theta), -sin(theta)],
+         [sin(theta),  cos(theta)]].
+    """
+    rotation_matrix = [
+        [math.cos(theta), -math.sin(theta)],
+        [math.sin(theta), math.cos(theta)],
+    ]
+    return [
+        rotation_matrix[0][0] * x + rotation_matrix[0][1] * y,
+        rotation_matrix[1][0] * x + rotation_matrix[1][1] * y,
+    ]
+
+
+
+def matmul(matrix_a: List[List[float]], matrix_b: List[List[float]]) -> List[List[float]]:
+    """Return the product of two matrices.
+
+    Parameters
+    ----------
+    matrix_a, matrix_b
+        Nested lists representing the matrices.
+
+    Returns
+    -------
+    list[list[float]]
+        The resulting matrix.
+
+    Raises
+    ------
+    ValueError
+        If the inner dimension is incompatible or the input is not
+        rectangular.
+    """
+    if not (_is_rectangular(matrix_a) and _is_rectangular(matrix_b)):
+        raise ValueError("diese matriezen können nicht multiplieziert werden.")
+    a = [list(row) for row in matrix_a]
+    b = [list(row) for row in matrix_b]
+    rows_a, cols_a = len(a), len(a[0]) if a else 0
+    rows_b, cols_b = len(b), len(b[0]) if b else 0
+    if cols_a != rows_b:
+        raise ValueError("diese matriezen können nicht multiplieziert werden.")
+    result: List[List[float]] = [[0.0 for _ in range(cols_b)] for _ in range(rows_a)]
+    for i in range(rows_a):
+        for k in range(cols_a):
+            aik = a[i][k]
+            for j in range(cols_b):
+                result[i][j] += aik * b[k][j]
+    return result
+
+
+my_matrix = [
+    [1.0, 2.0, 3.0],
+    [4.0, 5.0, 6.0]
+]
+
+# Alle öffentlichen Funktionen korrekt exportieren
+#exportieren
+__all__ = ["transpose", "matmul","rot_2D" ]
+
+
+if __name__ == "__main__":
+    a = [[1, 2, 3],
+         [4, 5, 6]]
+    b = [[7, 8],
+         [9, 10],
+         [11, 12]]
+
+    print("multiplication (matmul):")
+    print(matmul(a, b))
+
+    print("\nOriginal Matrix:")
+    print(my_matrix)
+
+    print("\ntranspose Matrix:")
+    trsp = transpose(my_matrix)
+    print(trsp)
+
+    print("\nrot_2D:")
+    # Punkt (1, 0) um 90 Grad (pi / 2) drehen
+    x_neu, y_neu = rot_2D(1.0, 0.0, math.pi / 2)
+
+    print(f"Gedrehter Punkt: x = {x_neu:.2f}, y = {y_neu:.2f}")
+
+