126 lines
3.2 KiB
Python
126 lines
3.2 KiB
Python
from typing import List
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def matmul(A: List[List[float]], B: List[List[float]]) -> List[List[float]]:
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"""
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Multiplies two matrices A and B (nested Python lists).
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Requirements:
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- A has shape (m x n), B has shape (n x p).
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- All rows in A and B must have equal length.
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- Elements are numeric (float/int).
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Args:
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A: Left matrix, list of rows (m x n).
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B: Right matrix, list of rows (n x p).
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Returns:
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New matrix C = A * B with shape (m x p).
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Raises:
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ValueError: If matrices are empty, ragged,
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or shapes are incompatible.
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"""
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if not A or not B:
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raise ValueError("Empty matrices are not supported.")
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if not A[0] or not B[0]:
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raise ValueError("Matrices must have at least one column.")
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a_cols = len(A[0])
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for row in A:
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if len(row) != a_cols:
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raise ValueError("Left matrix has inconsistent row lengths.")
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b_cols = len(B[0])
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for row in B:
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if len(row) != b_cols:
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raise ValueError("Right matrix has inconsistent row lengths.")
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if a_cols != len(B):
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raise ValueError(
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f"Incompatible shapes: A is {len(A)}x{a_cols}, "
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f"B is {len(B)}x{b_cols}; need cols(A) == rows(B)."
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)
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m, n, p = len(A), a_cols, b_cols
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C: List[List[float]] = [[0 for _ in range(p)] for _ in range(m)]
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for i in range(m):
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for k in range(n):
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a_ik = A[i][k]
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for j in range(p):
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C[i][j] += a_ik * B[k][j]
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return C
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from math import cos, sin
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from typing import List
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def rot_3D(angle: float, axis: str) -> List[List[float]]:
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"""
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Berechnet die 3x3-Rotationsmatrix für eine Rotation im 3D-Raum.
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Die Rotationsmatrizen lauten:
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Rotation um die x-Achse:
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Rx(θ) = [[1, 0, 0],
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[0, cos θ, -sin θ],
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[0, sin θ, cos θ]]
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Rotation um die y-Achse:
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Ry(θ) = [[ cos θ, 0, sin θ],
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[ 0, 1, 0],
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[-sin θ, 0, cos θ]]
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Rotation um die z-Achse:
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Rz(θ) = [[cos θ, -sin θ, 0],
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[sin θ, cos θ, 0],
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[ 0, 0, 1]]
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:param angle: Rotationswinkel in Radiant.
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:param axis: Rotationsachse: 'x', 'y' oder 'z' (Groß-/Kleinschreibung egal).
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:return: 3x3-Rotationsmatrix als verschachtelte Liste.
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:raises ValueError: Wenn axis nicht 'x', 'y' oder 'z' ist.
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"""
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a = axis.lower()
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c = cos(angle)
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s = sin(angle)
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if a == "x":
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return [
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[1.0, 0.0, 0.0],
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[0.0, c, -s ],
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[0.0, s, c ],
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]
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if a == "y":
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return [
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[c, 0.0, s ],
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[0.0, 1.0, 0.0],
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[-s, 0.0, c ],
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]
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if a == "z":
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return [
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[c, -s, 0.0],
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[s, c, 0.0],
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[0.0, 0.0, 1.0],
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]
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raise ValueError("axis must be 'x', 'y' or 'z'")
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if __name__ == "__main__":
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matrix_a = [[3, 4, -1, 4],
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[-2, 2, 5, 1]]
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matrix_b = [[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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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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