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Fix Gaussian elimination pivoting (#11393)

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* updating DIRECTORY.md

* Fix Gaussian elimination pivoting

* Fix review issues

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Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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Maxim Smolskiy 2024-12-28 11:43:25 +03:00 committed by GitHub
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1 changed files with 16 additions and 23 deletions
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37
linear_algebra/src/gaussian_elimination_pivoting.py
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@ -22,40 +22,33 @@ def solve_linear_system(matrix: np.ndarray) -> np.ndarray:
>>> solution = solve_linear_system(np.column_stack((A, B))) >>> solution = solve_linear_system(np.column_stack((A, B)))
>>> np.allclose(solution, np.array([2., 3., -1.])) >>> np.allclose(solution, np.array([2., 3., -1.]))
True True
>>> solve_linear_system(np.array([[0, 0], [0, 0]], dtype=float)) >>> solve_linear_system(np.array([[0, 0, 0]], dtype=float))
array([nan, nan]) Traceback (most recent call last):
...
ValueError: Matrix is not square
>>> solve_linear_system(np.array([[0, 0, 0], [0, 0, 0]], dtype=float))
Traceback (most recent call last):
...
ValueError: Matrix is singular
""" """
ab = np.copy(matrix) ab = np.copy(matrix)
num_of_rows = ab.shape[0] num_of_rows = ab.shape[0]
num_of_columns = ab.shape[1] - 1 num_of_columns = ab.shape[1] - 1
x_lst: list[float] = [] x_lst: list[float] = []
# Lead element search if num_of_rows != num_of_columns:
raise ValueError("Matrix is not square")
for column_num in range(num_of_rows): for column_num in range(num_of_rows):
# Lead element search
for i in range(column_num, num_of_columns): for i in range(column_num, num_of_columns):
if abs(ab[i][column_num]) > abs(ab[column_num][column_num]): if abs(ab[i][column_num]) > abs(ab[column_num][column_num]):
ab[[column_num, i]] = ab[[i, column_num]] ab[[column_num, i]] = ab[[i, column_num]]
if ab[column_num, column_num] == 0.0:
raise ValueError("Matrix is not correct")
else:
pass
if column_num != 0:
for i in range(column_num, num_of_rows):
ab[i, :] -= (
ab[i, column_num - 1]
/ ab[column_num - 1, column_num - 1]
* ab[column_num - 1, :]
)
# Upper triangular matrix # Upper triangular matrix
for column_num in range(num_of_rows): if abs(ab[column_num, column_num]) < 1e-8:
for i in range(column_num, num_of_columns): raise ValueError("Matrix is singular")
if abs(ab[i][column_num]) > abs(ab[column_num][column_num]):
ab[[column_num, i]] = ab[[i, column_num]]
if ab[column_num, column_num] == 0.0:
raise ValueError("Matrix is not correct")
else:
pass
if column_num != 0: if column_num != 0:
for i in range(column_num, num_of_rows): for i in range(column_num, num_of_rows):
ab[i, :] -= ( ab[i, :] -= (