165 lines
4.0 KiB
Python
165 lines
4.0 KiB
Python
# Matrixberechnungen fuer das Projekt MatrixMania
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import math
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def matmul(
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matrix_a: list[list[float]], matrix_b: list[list[float]]
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) -> list[list[float]]:
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# Basic dimensionality checks
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if not matrix_a:
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raise ValueError("matrix_a cannot be empty")
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if not matrix_b:
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raise ValueError("matrix_b cannot be empty")
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rows_a = len(matrix_a)
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cols_a = len(matrix_a[0])
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rows_b = len(matrix_b)
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cols_b = len(matrix_b[0])
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if cols_a != rows_b:
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raise ValueError(
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f"Cannot multiply: matrix_a has {cols_a} columns "
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f"but matrix_b has {rows_b} rows."
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)
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# Ensure all rows are rectangular
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for r in matrix_a:
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if len(r) != cols_a:
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raise ValueError("matrix_a is not rectangular")
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for r in matrix_b:
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if len(r) != cols_b:
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raise ValueError("matrix_b is not rectangular")
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# Perform multiplication
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result: list[list[float]] = [[0.0 for _ in range(cols_b)] for _ in range(rows_a)]
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for i in range(rows_a):
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for j in range(cols_b):
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total = 0.0
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for k in range(cols_a):
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total += matrix_a[i][k] * matrix_b[k][j]
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result[i][j] = total
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return result
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def transpose(matrix: list[list[float]]) -> list[list[float]]:
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"""
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Transpose a 2D matrix.
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Parameters
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----------
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matrix : list[list[float]]
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A 2D matrix represented as a list of rows, each containing
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floating‑point numbers.
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Returns
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-------
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list[list[float]]
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The transposed matrix, where rows become columns.
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Raises
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------
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ValueError
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If the input matrix is empty or has non‑rectangular rows.
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"""
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# Check for empty matrix
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if not matrix:
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raise ValueError("matrix cannot be empty")
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rows = len(matrix)
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cols = len(matrix[0])
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# Verify rectangular shape
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for r in matrix:
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if len(r) != cols:
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raise ValueError("matrix is not rectangular")
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# Transpose by column index
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return [[matrix[r][c] for r in range(rows)] for c in range(cols)]
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def rot_2D(theta: float) -> list[list[float]]:
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"""
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Return a 2D rotation matrix for angle ``theta`` in radians.
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Parameters
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----------
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theta : float
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Rotation angle in radians.
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Returns
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-------
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list[list[float]]
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2 × 2 rotation matrix
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``[[cos(theta), -sin(theta)],
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[sin(theta), cos(theta)]]``
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Notes
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-----
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Uses :func:`math.sin` and :func:`math.cos` from the standard library.
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"""
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c = math.cos(theta)
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s = math.sin(theta)
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return [[c, -s], [s, c]]
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if __name__ == "__main__":
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# Test Matmul
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matrix_a = [
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[3, 4, -1, 4],
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[-2, 2, 5, 1],
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]
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matrix_b = [
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[1, 3, -2],
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[2, 5, 1],
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[-1, 4, -4],
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[2, 3, 6],
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]
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matrix_c = matmul(matrix_a, matrix_b)
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print("Ergebnis C = A * B:")
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for row in matrix_c:
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print(row)
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# Test Transpose
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matrix = [[1, 2, 3], [4, 5, 6]]
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print("Original matrix:", matrix)
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print("Transposed matrix:", transpose(matrix))
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# Test Rotate
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angle = math.pi / 2 # 90 degrees
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rotation_matrix = rot_2D(angle)
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print("Rotation matrix (90 degrees):")
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for row in rotation_matrix:
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print(row)
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# Test rotation of a point using matmul
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point = [[1], [0]]
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rotated_point = matmul(rotation_matrix, point)
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print("Original point:", point)
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print("Rotated point:", rotated_point)
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# Test invalid matrices
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print("\nTest invalid matrices:")
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# Test Empty matrix
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try:
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transpose([])
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except ValueError as error:
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print("Empty matrix:", error)
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# Test Matrix with different row lengths
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try:
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transpose([[1, 2, 3], [4, 5]])
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except ValueError as error:
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print("Non-rectangular matrix:", error)
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# Test 3 Invalid matrix multiplication
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try:
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matmul([[1, 2, 3]], [[1, 2], [3, 4]])
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except ValueError as error:
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print("Invalid dimensions:", error)
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