'''simple docstring'''




class 		__A       :






       def __init__(      self				,     UpperCamelCase_      ):
              __UpperCAmelCase  :				Any       				=		set_counts
              __UpperCAmelCase  :				int       				=		max(UpperCamelCase_      )
              __UpperCAmelCase  :				List[str]       				=		len(UpperCamelCase_      )
              __UpperCAmelCase  :				Any       				=		[1] * num_sets
              __UpperCAmelCase  :				Any       				=		list(range(UpperCamelCase_      )      )






       def 			_snake_case						(      self				,     UpperCamelCase_				,     UpperCamelCase_      ):
              __UpperCAmelCase  :				Optional[int]       				=		self.get_parent(UpperCamelCase_      )
              __UpperCAmelCase  :				List[Any]       				=		self.get_parent(UpperCamelCase_      )

              if src_parent == dst_parent:
                     return False

              if self.ranks[dst_parent] >= self.ranks[src_parent]:
                     self.set_counts[dst_parent] += self.set_counts[src_parent]
                     __UpperCAmelCase  :				Optional[Any]       				=		0
                     __UpperCAmelCase  :				List[Any]       				=		dst_parent
                     if self.ranks[dst_parent] == self.ranks[src_parent]:
                            self.ranks[dst_parent] += 1
                     __UpperCAmelCase  :				Union[str, Any]       				=		self.set_counts[dst_parent]
              else:
                     self.set_counts[src_parent] += self.set_counts[dst_parent]
                     __UpperCAmelCase  :				Union[str, Any]       				=		0
                     __UpperCAmelCase  :				Dict       				=		src_parent
                     __UpperCAmelCase  :				Dict       				=		self.set_counts[src_parent]

              __UpperCAmelCase  :				Dict       				=		max(self.max_set				,     UpperCamelCase_      )
              return True







       def 			_snake_case						(      self				,     UpperCamelCase_      ):
              if self.parents[disj_set] == disj_set:
                     return disj_set
              __UpperCAmelCase  :				str       				=		self.get_parent(self.parents[disj_set]      )
              return self.parents[disj_set]







'''simple docstring'''




from __future__ import annotations

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

def _lowercase	(      lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    lowerCamelCase__							,    )					->       list[float]:





       """simple docstring"""


       __UpperCAmelCase				, __UpperCAmelCase  :				Union[str, Any]       				=		coefficient_matrix.shape
       __UpperCAmelCase				, __UpperCAmelCase  :				Any       				=		constant_matrix.shape

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

       if colsa != 1:
              __UpperCAmelCase  :				Optional[Any]       				=		f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
              raise ValueError(lowerCamelCase__						)

       if rowsa != rowsa:
              __UpperCAmelCase  :				Optional[int]       				=		(
                  "Coefficient and constant matrices dimensions must be nxn and nx1 but "
                  f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
              )
              raise ValueError(lowerCamelCase__						)

       if len(lowerCamelCase__						) != rowsa:
              __UpperCAmelCase  :				List[str]       				=		(
                  "Number of initial values must be equal to number of rows in coefficient "
                  f"""matrix but received {len(lowerCamelCase__						)} and {rowsa}"""
              )
              raise ValueError(lowerCamelCase__						)

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

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

       __UpperCAmelCase				, __UpperCAmelCase  :				Tuple       				=		table.shape

       strictly_diagonally_dominant(lowerCamelCase__						)

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

       return [float(lowerCamelCase__						) for i in new_val]

def _lowercase	(      lowerCamelCase__						)					->       bool:





       """simple docstring"""


       __UpperCAmelCase				, __UpperCAmelCase  :				Optional[int]       				=		table.shape

       __UpperCAmelCase  :				str       				=		True

       for i in range(0							,    lowerCamelCase__						):
              __UpperCAmelCase  :				Union[str, Any]       				=		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()






