From d470987ca8b417e435cc6f4d2f4fd2a2351e2fd5 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 20 Nov 2024 09:16:12 +0000
Subject: [PATCH] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 linear_algebra/Lanczos-algorithm.py | 28 +++++++++++++++-------------
 1 file changed, 15 insertions(+), 13 deletions(-)

diff --git a/linear_algebra/Lanczos-algorithm.py b/linear_algebra/Lanczos-algorithm.py
index 4bdba1bce..d8e9ea291 100644
--- a/linear_algebra/Lanczos-algorithm.py
+++ b/linear_algebra/Lanczos-algorithm.py
@@ -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)
@@ -31,4 +33,4 @@ def lanczos(A: np.ndarray) -> ([float], [float]):
             w -= beta[j - 1] * V[:, j - 1]
         beta.append(np.linalg.norm(w))
         V[:, j + 1] = w / beta[j]
-    return alpha, beta
\ No newline at end of file
+    return alpha, beta