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Replaced loops in jacobi_iteration_method function with vector operations. That gives a reduction in the time for calculating the algorithm.

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quant12345 2023-08-09 15:39:11 +05:00
parent ae0fc85401
commit cc1455088b
1 changed files with 31 additions and 5 deletions
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36
arithmetic_analysis/jacobi_iteration_method.py
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@ -10,10 +10,10 @@ from numpy.typing import NDArray
# Method to find solution of system of linear equations # Method to find solution of system of linear equations
def jacobi_iteration_method( def jacobi_iteration_method(
coefficient_matrix: NDArray[float64], coefficient_matrix: NDArray[float64],
constant_matrix: NDArray[float64], constant_matrix: NDArray[float64],
init_val: list[int], init_val: list[int],
iterations: int, iterations: int,
) -> list[float]: ) -> list[float]:
""" """
Jacobi Iteration Method: Jacobi Iteration Method:
@ -115,6 +115,17 @@ def jacobi_iteration_method(
strictly_diagonally_dominant(table) strictly_diagonally_dominant(table)
"""
denom - a list of values along the diagonal
val - values of the last column of the table array
masks - boolean mask of all strings without diagonal elements array coefficient_matrix
ttt - coefficient_matrix array values without diagonal elements
ind - column indexes for each row without diagonal elements
arr - list obtained by column indexes from the list init_val
the code below uses vectorized operations based on
the previous algorithm on loopss:
# Iterates the whole matrix for given number of times # Iterates the whole matrix for given number of times
for _ in range(iterations): for _ in range(iterations):
new_val = [] new_val = []
@ -130,8 +141,23 @@ def jacobi_iteration_method(
temp = (temp + val) / denom temp = (temp + val) / denom
new_val.append(temp) new_val.append(temp)
init_val = new_val init_val = new_val
"""
return [float(i) for i in new_val] denom = np.diag(coefficient_matrix)
val = table[:, -1]
masks = ~np.eye(coefficient_matrix.shape[0], dtype=bool)
ttt = coefficient_matrix[masks].reshape(-1, rows - 1)
i_row, i_col = np.where(masks)
ind = i_col.reshape(-1, rows - 1)
# Iterates the whole matrix for given number of times
for _ in range(iterations):
arr = np.take(init_val, ind)
temp = np.sum((-1) * ttt * arr, axis=1)
new_val = (temp + val) / denom
init_val = new_val
return init_val.tolist()
# Checks if the given matrix is strictly diagonally dominant # Checks if the given matrix is strictly diagonally dominant