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pre-commit-ci[bot] 2024-11-20 09:16:12 +00:00
parent ab246373e6
commit d470987ca8
1 changed files with 15 additions and 13 deletions
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28
linear_algebra/Lanczos-algorithm.py
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@ -1,20 +1,22 @@
import numpy as np import numpy as np
def lanczos(A: np.ndarray) -> ([float], [float]): def lanczos(A: np.ndarray) -> ([float], [float]):
""" """
Implements the Lanczos algorithm for a symmetric matrix. Implements the Lanczos algorithm for a symmetric matrix.
Parameters: Parameters:
----------- -----------
matrix : numpy.ndarray matrix : numpy.ndarray
Symmetric matrix of size (n, n). Symmetric matrix of size (n, n).
Returns: Returns:
-------- --------
alpha : [float] alpha : [float]
List of diagonal elements of the resulting tridiagonal matrix. List of diagonal elements of the resulting tridiagonal matrix.
beta : [float] beta : [float]
List of off-diagonal elements of the resulting tridiagonal matrix. List of off-diagonal elements of the resulting tridiagonal matrix.
""" """
n = A.shape[0] n = A.shape[0]
V = np.zeros((n, n)) V = np.zeros((n, n))
V[:, 0] = np.random.randn(n) V[:, 0] = np.random.randn(n)
@ -31,4 +33,4 @@ def lanczos(A: np.ndarray) -> ([float], [float]):
w -= beta[j - 1] * V[:, j - 1] w -= beta[j - 1] * V[:, j - 1]
beta.append(np.linalg.norm(w)) beta.append(np.linalg.norm(w))
V[:, j + 1] = w / beta[j] V[:, j + 1] = w / beta[j]
return alpha, beta return alpha, beta