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Fix Gaussian elimination pivoting #11393

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39 changes: 16 additions & 23 deletions linear_algebra/src/gaussian_elimination_pivoting.py
Original file line number Diff line number Diff line change
Expand Up @@ -22,40 +22,33 @@ def solve_linear_system(matrix: np.ndarray) -> np.ndarray:
>>> solution = solve_linear_system(np.column_stack((A, B)))
>>> np.allclose(solution, np.array([2., 3., -1.]))
True
>>> solve_linear_system(np.array([[0, 0], [0, 0]], dtype=float))
array([nan, nan])
>>> solve_linear_system(np.array([[0, 0, 0]], dtype=float))
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)
num_of_rows = ab.shape[0]
num_of_columns = ab.shape[1] - 1
x_lst: list[float] = []

# Lead element search
for column_num in range(num_of_rows):
for i in range(column_num, num_of_columns):
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:
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, :]
)
if num_of_rows != num_of_columns:
raise ValueError("Matrix is not square")

# Upper triangular matrix
for column_num in range(num_of_rows):
# Lead element search
for i in range(column_num, num_of_columns):
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

# Upper triangular matrix
if abs(ab[column_num, column_num]) < 1e-8:
raise ValueError("Matrix is singular")

if column_num != 0:
for i in range(column_num, num_of_rows):
ab[i, :] -= (
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