Replacing the generator with numpy vector operations from lu_decompos…

…ition.

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