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# Copyright (c) 2020-2024, Manfred Moitzi
# License: MIT License
from typing import Iterable
import pytest
import math
import numpy as np
from ezdxf.math.linalg import (
Matrix,
detect_banded_matrix,
compact_banded_matrix,
BandedMatrixLU,
banded_matrix,
)
from ezdxf.math.legacy import gauss_vector_solver
BANDED_MATRIX = Matrix(
matrix=[
[3, 1, 0, 0, 0, 0, 0],
[4, 1, 5, 0, 0, 0, 0],
[9, 2, 6, 5, 0, 0, 0],
[0, 3, 5, 8, 9, 0, 0],
[0, 0, 7, 9, 3, 2, 0],
[0, 0, 0, 3, 8, 4, 6],
[0, 0, 0, 0, 2, 4, 4],
]
)
TRICKY = Matrix(
matrix=[
[3, 1, 0, 0, 0, 0, 1],
[4, 1, 5, 0, 0, 0, 0],
[9, 2, 6, 5, 0, 0, 0],
[0, 3, 5, 8, 9, 0, 0],
[0, 0, 7, 9, 3, 2, 0],
[0, 0, 0, 3, 8, 4, 6],
[0, 1, 0, 0, 2, 4, 4],
]
)
def are_close_vectors(
v1: Iterable[float], v2: Iterable[float], abs_tol: float = 1e-12
):
for i, j in zip(v1, v2):
assert math.isclose(i, j, abs_tol=abs_tol)
def test_detect_banded_matrix():
m1, m2 = detect_banded_matrix(BANDED_MATRIX)
assert (m1, m2) == (2, 1)
m1, m2 = detect_banded_matrix(TRICKY, check_all=False)
assert (m1, m2) == (2, 1)
m1, m2 = detect_banded_matrix(TRICKY, check_all=True)
assert (m1, m2) == (5, 6)
assert detect_banded_matrix(Matrix(shape=(10, 10))) == (0, 0)
identity = Matrix.identity(shape=(10, 10))
assert detect_banded_matrix(identity) == (0, 0)
def test_compact_banded_matrix():
m1, m2 = detect_banded_matrix(BANDED_MATRIX)
m = compact_banded_matrix(BANDED_MATRIX, m1, m2)
assert m.ncols == 4
assert m.nrows == 7
assert m.col(0) == [0, 0, 9, 3, 7, 3, 2]
assert m.col(1) == [0, 4, 2, 5, 9, 8, 4]
assert m.col(2) == [3, 1, 6, 8, 3, 4, 4]
assert m.col(3) == [1, 5, 5, 9, 2, 6, 0]
B1 = [5, 3, 2, 6, 8, 2, 1]
B2 = [9, 1, 7, 6, 4, 5, 0]
B3 = [0, 9, 3, 7, 1, 9, 9]
CHK1 = gauss_vector_solver(BANDED_MATRIX.matrix, B1)
CHK2 = gauss_vector_solver(BANDED_MATRIX.matrix, B2)
CHK3 = gauss_vector_solver(BANDED_MATRIX.matrix, B3)
def test_solve_banded_matrix_vector():
m, m1, m2 = banded_matrix(BANDED_MATRIX)
lu = BandedMatrixLU(m, m1, m2)
are_close_vectors(lu.solve_vector(B1), CHK1)
are_close_vectors(lu.solve_vector(B2), CHK2)
are_close_vectors(lu.solve_vector(B3), CHK3)
def test_solve_banded_matrix_matrix():
m, m1, m2 = banded_matrix(BANDED_MATRIX)
lu = BandedMatrixLU(m, m1, m2)
mat_B = np.array(list(zip(B1, B2, B3)))
r = lu.solve_matrix(mat_B)
are_close_vectors(r.col(0), CHK1)
are_close_vectors(r.col(1), CHK2)
are_close_vectors(r.col(2), CHK3)
if __name__ == "__main__":
pytest.main([__file__])
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