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26
linear_algebra/Lanczos-algorithm.py
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@ -1,20 +1,22 @@
import numpy as np
def lanczos(A: np.ndarray) -> ([float], [float]):
"""
Implements the Lanczos algorithm for a symmetric matrix.
Implements the Lanczos algorithm for a symmetric matrix.
Parameters:
-----------
matrix : numpy.ndarray
Symmetric matrix of size (n, n).
Parameters:
-----------
matrix : numpy.ndarray
Symmetric matrix of size (n, n).
Returns:
--------
alpha : [float]
List of diagonal elements of the resulting tridiagonal matrix.
beta : [float]
List of off-diagonal elements of the resulting tridiagonal matrix.
"""
Returns:
--------
alpha : [float]
List of diagonal elements of the resulting tridiagonal matrix.
beta : [float]
List of off-diagonal elements of the resulting tridiagonal matrix.
"""
n = A.shape[0]
V = np.zeros((n, n))
V[:, 0] = np.random.randn(n)