From 3c14e6ae3aa6506ca8e5baa73321f3a04caf83d0 Mon Sep 17 00:00:00 2001
From: Kamil <32775019+quant12345@users.noreply.github.com>
Date: Mon, 16 Oct 2023 12:29:46 +0500
Subject: [PATCH] Refactoring and optimization of the lu_decomposition
 algorithm (#9231)

* Replacing the generator with numpy vector operations from lu_decomposition.

* Revert "Replacing the generator with numpy vector operations from lu_decomposition."

This reverts commit ad217c66165898d62b76cc89ba09c2d7049b6448.

* Replacing the generator with numpy vector operations from lu_decomposition.
---
 arithmetic_analysis/lu_decomposition.py | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/arithmetic_analysis/lu_decomposition.py b/arithmetic_analysis/lu_decomposition.py
index eaabce544..094b20abf 100644
--- a/arithmetic_analysis/lu_decomposition.py
+++ b/arithmetic_analysis/lu_decomposition.py
@@ -88,15 +88,19 @@ def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray
 
     lower = np.zeros((rows, columns))
     upper = np.zeros((rows, columns))
+
+    # in 'total', the necessary data is extracted through slices
+    # and the sum of the products is obtained.
+
     for i in range(columns):
         for j in range(i):
-            total = sum(lower[i][k] * upper[k][j] for k in range(j))
+            total = np.sum(lower[i, :i] * upper[:i, j])
             if upper[j][j] == 0:
                 raise ArithmeticError("No LU decomposition exists")
             lower[i][j] = (table[i][j] - total) / upper[j][j]
         lower[i][i] = 1
         for j in range(i, columns):
-            total = sum(lower[i][k] * upper[k][j] for k in range(j))
+            total = np.sum(lower[i, :i] * upper[:i, j])
             upper[i][j] = table[i][j] - total
     return lower, upper