


"""simple docstring"""



from __future__ import annotations

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






def       lowerCamelCase					(a_						:NDArray[floataa]				,				a_						:NDArray[floataa]				,				a_						:list[int]				,				a_						:int				,				)     ->							list[float]:
       lowercase							,  lowercase		:Optional[int]       							=				coefficient_matrix.shape
       lowercase							,  lowercase		:List[str]       							=				constant_matrix.shape

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

       if colsa != 1:
              lowercase		:Optional[int]       							=				F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
              raise ValueError(a_)

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

       if len(a_) != rowsa:
              lowercase		:Optional[int]       							=				(
                  '''Number of initial values must be equal to number of rows in coefficient '''
                  F"""matrix but received {len(a_)} and {rowsa}"""
              )
              raise ValueError(a_)

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

       lowercase		:NDArray[floataa]       							=				np.concatenate(
           (coefficient_matrix, constant_matrix)				,				axis=1)

       lowercase							,  lowercase		:Any       							=				table.shape

       strictly_diagonally_dominant(a_)

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

       return [float(a_) for i in new_val]






def       lowerCamelCase					(a_						:NDArray[floataa])     ->							bool:
       lowercase							,  lowercase		:List[Any]       							=				table.shape

       lowercase		:Optional[int]       							=				True

       for i in range(0				,				a_):
              lowercase		:Tuple       							=				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()





"""simple docstring"""



from __future__ import annotations

from decimal import Decimal

from numpy import array






def       lowerCamelCase					(a_						:list[list[float]])     ->							list[list[float]]:
       lowercase		:List[str]       							=				Decimal

       # Check if the provided matrix has 2 rows and 2 columns
       # since this implementation only works for 2x2 matrices
       if len(a_) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
              # Calculate the determinant of the matrix
              lowercase		:List[str]       							=				float(
                  d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1]))
              if determinant == 0:
                     raise ValueError('''This matrix has no inverse.''')

              # Creates a copy of the matrix with swapped positions of the elements
              lowercase		:Optional[Any]       							=				[[0.0, 0.0], [0.0, 0.0]]
              lowercase							,  lowercase		:List[Any]       							=				matrix[1][1], matrix[0][0]
              lowercase							,  lowercase		:Union[str, Any]       							=				-matrix[1][0], -matrix[0][1]

              # Calculate the inverse of the matrix
              return [
                  [(float(d(a_)) / determinant) or 0.0 for n in row] for row in swapped_matrix
              ]
       elif (
           len(a_) == 3
           and len(matrix[0]) == 3
           and len(matrix[1]) == 3
           and len(matrix[2]) == 3
       ):
              # Calculate the determinant of the matrix using Sarrus rule
              lowercase		:Any       							=				float(
                  (
                      (d(matrix[0][0]) * d(matrix[1][1]) * d(matrix[2][2]))
                      + (d(matrix[0][1]) * d(matrix[1][2]) * d(matrix[2][0]))
                      + (d(matrix[0][2]) * d(matrix[1][0]) * d(matrix[2][1]))
                  )
                  - (
                      (d(matrix[0][2]) * d(matrix[1][1]) * d(matrix[2][0]))
                      + (d(matrix[0][1]) * d(matrix[1][0]) * d(matrix[2][2]))
                      + (d(matrix[0][0]) * d(matrix[1][2]) * d(matrix[2][1]))
                  ))
              if determinant == 0:
                     raise ValueError('''This matrix has no inverse.''')

              # Creating cofactor matrix
              lowercase		:Optional[Any]       							=				[
                  [d(0.0), d(0.0), d(0.0)],
                  [d(0.0), d(0.0), d(0.0)],
                  [d(0.0), d(0.0), d(0.0)],
              ]
              lowercase		:Optional[int]       							=				(d(matrix[1][1]) * d(matrix[2][2])) - (
                  d(matrix[1][2]) * d(matrix[2][1])
              )
              lowercase		:str       							=				-(
                  (d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[1][0]) * d(matrix[2][1])) - (
                  d(matrix[1][1]) * d(matrix[2][0])
              )
              lowercase		:Union[str, Any]       							=				-(
                  (d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[0][0]) * d(matrix[2][2])) - (
                  d(matrix[0][2]) * d(matrix[2][0])
              )
              lowercase		:List[str]       							=				-(
                  (d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
              )
              lowercase		:Union[str, Any]       							=				(d(matrix[0][1]) * d(matrix[1][2])) - (
                  d(matrix[0][2]) * d(matrix[1][1])
              )
              lowercase		:Union[str, Any]       							=				-(
                  (d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
              )
              lowercase		:Any       							=				(d(matrix[0][0]) * d(matrix[1][1])) - (
                  d(matrix[0][1]) * d(matrix[1][0])
              )

              # Transpose the cofactor matrix (Adjoint matrix)
              lowercase		:Union[str, Any]       							=				array(a_)
              for i in range(3):
                     for j in range(3):
                            lowercase		:Any       							=				cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
              lowercase		:str       							=				array(a_)
              for i in range(3):
                     for j in range(3):
                            inverse_matrix[i][j] /= d(a_)

        # Calculate the inverse of the matrix
              return [[float(d(a_)) or 0.0 for n in row] for row in inverse_matrix]
       raise ValueError('''Please provide a matrix of size 2x2 or 3x3.''')

