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Modified file name to be lowercase and replaced - for _

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Changed argument name A to a
Changed variable name V to v
Added specifications for beta and alpha
Changed np.random.randn
This commit is contained in:
Pablito 2024-11-20 10:36:33 +01:00
parent f38f1a7c83
commit 03a37ebaca
1 changed files with 13 additions and 12 deletions
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25
linear_algebra/Lanczos-algorithm.py → linear_algebra/lanczos_algorithm.py
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@ -1,5 +1,5 @@
import numpy as np import numpy as np
def lanczos(A: np.ndarray) -> ([float], [float]): def lanczos(a: np.ndarray) -> tuple[list[float], list[float]]:
""" """
Implements the Lanczos algorithm for a symmetric matrix. Implements the Lanczos algorithm for a symmetric matrix.
@ -15,20 +15,21 @@ def lanczos(A: np.ndarray) -> ([float], [float]):
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) rng = np.random.default_rng()
V[:, 0] /= np.linalg.norm(V[:, 0]) v[:, 0] = rng.standard_normal(n)
alpha = [] v[:, 0] /= np.linalg.norm(v[:, 0])
beta = [] alpha : list[float] = []
beta : list[float] = []
for j in range(n): for j in range(n):
w = np.dot(A, V[:, j]) w = np.dot(a, v[:, j])
alpha.append(np.dot(w, V[:, j])) alpha.append(np.dot(w, v[:, j]))
if j == n - 1: if j == n - 1:
break break
w -= alpha[j] * V[:, j] w -= alpha[j] * v[:, j]
if j > 0: if j > 0:
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