102 lines
2.7 KiB
Python
102 lines
2.7 KiB
Python
import math
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def matmul(a: list[list[float]], b: list[list[float]]) -> list[list[float]]:
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"""Multiply two non-empty rectangular matrices.
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Args:
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a: The left matrix.
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b: The right matrix.
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Returns:
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The matrix product a * b.
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Raises:
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ValueError: If either matrix is empty or ragged, or if their
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dimensions are incompatible.
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"""
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_validate_matrix(a, "a")
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_validate_matrix(b, "b")
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if len(a[0]) != len(b):
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raise ValueError(
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"Matrix dimensions are incompatible: the number of columns in a "
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"must equal the number of rows in b."
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)
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return [
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[
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sum(a_row[index] * b[index][column] for index in range(len(b)))
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for column in range(len(b[0]))
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]
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for a_row in a
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]
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def transpose(matrix: list[list[float]]) -> list[list[float]]:
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"""Return the transpose of a non-empty rectangular matrix.
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Args:
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matrix: A matrix represented as rows of numbers.
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Returns:
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A new matrix whose rows are the columns of matrix.
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Raises:
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ValueError: If the matrix is empty or its rows have different lengths.
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"""
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_validate_matrix(matrix, "matrix")
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return [list(column) for column in zip(*matrix)]
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def rot_2D(angle: float) -> list[list[float]]:
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"""Return the 2D rotation matrix for a given angle in radians.
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Args:
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angle: The rotation angle in radians.
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Returns:
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The rotation matrix for rotating points counterclockwise.
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"""
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return [
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[math.cos(angle), -math.sin(angle)],
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[math.sin(angle), math.cos(angle)]
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]
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def _validate_matrix(matrix: list[list[float]], name: str) -> None:
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"""Raise ValueError unless matrix is non-empty and rectangular."""
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if not matrix:
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raise ValueError(f"Matrix {name} must be non-empty.")
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column_count = len(matrix[0])
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if column_count == 0:
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raise ValueError(f"Matrix {name} must have at least one column.")
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if any(len(row) != column_count for row in matrix):
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raise ValueError(f"Matrix {name} must have rows of equal length.")
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if __name__ == "__main__":
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first = [[1, 2, 3], [4, 5, 6]]
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second = [[7, 8], [9, 10], [11.0, 12.0]]
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assert matmul(first, second) == [
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[58.0, 64.0],
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[139.0, 154.0]
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]
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print("Matrix product:", matmul(first, second))
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try:
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matmul([[1, 2]], [[1, 2]])
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except ValueError as error:
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print("Expected error:", error)
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else:
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raise AssertionError(
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"Expected a ValueError for incompatible dimensions."
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)
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assert transpose(first) == [
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[1, 4],
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[2, 5],
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[3, 6]
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]
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print("Transpose:", transpose(first))
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