




from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	NDArray[floataa]     ,							lowercase     :	NDArray[floataa]     ,							lowercase     :	list[int]     ,							lowercase     :	int     ,							):


      '''simple docstring'''



      lowerCamelCase_					,    lowerCamelCase_							=   coefficient_matrix.shape
      lowerCamelCase_					,    lowerCamelCase_							=   constant_matrix.shape

      if rowsa != colsa:
            lowerCamelCase_							=   f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
            raise ValueError(lowercase					)

      if colsa != 1:
            lowerCamelCase_							=   f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
            raise ValueError(lowercase					)

      if rowsa != rowsa:
            lowerCamelCase_							=   (
                'Coefficient and constant matrices dimensions must be nxn and nx1 but '
                f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
            )
            raise ValueError(lowercase					)

      if len(lowercase					) != rowsa:
            lowerCamelCase_							=   (
                'Number of initial values must be equal to number of rows in coefficient '
                f"""matrix but received {len(lowercase					)} and {rowsa}"""
            )
            raise ValueError(lowercase					)

      if iterations <= 0:
            raise ValueError('Iterations must be at least 1'					)

      lowerCamelCase_							=   np.concatenate(
          (coefficient_matrix, constant_matrix)     ,							axis=1					)

      lowerCamelCase_					,    lowerCamelCase_							=   table.shape

      strictly_diagonally_dominant(lowercase					)

      # Iterates the whole matrix for given number of times
      for _ in range(lowercase					):
            lowerCamelCase_							=   []
            for row in range(lowercase					):
                  lowerCamelCase_							=   0
                  for col in range(lowercase					):
                        if col == row:
                              lowerCamelCase_							=   table[row][col]
                        elif col == cols - 1:
                              lowerCamelCase_							=   table[row][col]
                        else:
                              temp += (-1) * table[row][col] * init_val[col]
                  lowerCamelCase_							=   (temp + val) / denom
                  new_val.append(lowercase					)
            lowerCamelCase_							=   new_val

      return [float(lowercase					) for i in new_val]

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	NDArray[floataa]					):


      '''simple docstring'''



      lowerCamelCase_					,    lowerCamelCase_							=   table.shape

      lowerCamelCase_							=   True

      for i in range(0     ,							lowercase					):
            lowerCamelCase_							=   0
            for j in range(0     ,							cols - 1					):
                  if i == j:
                        continue
                  else:
                        total += table[i][j]

            if table[i][i] <= total:
                  raise ValueError('Coefficient matrix is not strictly diagonally dominant'					)

      return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
 import doctest

 doctest.testmod()









from ..utils import DummyObject, requires_backends







class   A(						metaclass=UpperCamelCase       ):



 '''simple docstring'''


 UpperCamelCase						       =						['''keras_nlp''']

 def __init__(    self :  Optional[int]						,							*A_ :  Any						,							**A_ :  Dict  )       ->     Optional[int]:

       """simple docstring"""






       requires_backends(self						,							['keras_nlp']  )



