



"""simple docstring"""






from __future__ import annotations

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


def      _lowercase							(    __snake_case   ,__snake_case   ,__snake_case   ,__snake_case   ,)		->  list[float]:
			__lowerCAmelCase		,      __lowerCAmelCase :    int				=			coefficient_matrix.shape
			__lowerCAmelCase		,      __lowerCAmelCase :    Tuple				=			constant_matrix.shape

			if rowsa != colsa:
						__lowerCAmelCase :    Tuple				=			F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
						raise ValueError(__snake_case      )

			if colsa != 1:
						__lowerCAmelCase :    str				=			F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
						raise ValueError(__snake_case      )

			if rowsa != rowsa:
						__lowerCAmelCase :    str				=			(
						    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
						    F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
						)
						raise ValueError(__snake_case      )

			if len(__snake_case      ) != rowsa:
						__lowerCAmelCase :    str				=			(
						    "Number of initial values must be equal to number of rows in coefficient "
						    F"""matrix but received {len(__snake_case      )} and {rowsa}"""
						)
						raise ValueError(__snake_case      )

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

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

			__lowerCAmelCase		,      __lowerCAmelCase :    List[str]				=			table.shape

			strictly_diagonally_dominant(__snake_case      )

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

			return [float(__snake_case      ) for i in new_val]


def      _lowercase							(    __snake_case      )		->  bool:
			__lowerCAmelCase		,      __lowerCAmelCase :    Tuple				=			table.shape

			__lowerCAmelCase :    Dict				=			True

			for i in range(0   ,__snake_case      ):
						__lowerCAmelCase :    Optional[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()




"""simple docstring"""






from ..utils import DummyObject, requires_backends



class      A__  (    metaclass=__SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE        =      ['torch', 'transformers', 'onnx']

	def __init__(	self:						Union[str, Any]			,     *_SCREAMING_SNAKE_CASE:						Any			,     **_SCREAMING_SNAKE_CASE:						int)							->			List[Any]:

				"""simple docstring"""

				requires_backends(self			,     ["torch", "transformers", "onnx"])

	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Union[str, Any]			,     *_SCREAMING_SNAKE_CASE:						List[Any]			,     **_SCREAMING_SNAKE_CASE:						Union[str, Any])							->			Union[str, Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])







	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						int			,     *_SCREAMING_SNAKE_CASE:						Any			,     **_SCREAMING_SNAKE_CASE:						str)							->			Union[str, Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])






class      A__  (    metaclass=__SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE        =      ['torch', 'transformers', 'onnx']

	def __init__(	self:						Tuple			,     *_SCREAMING_SNAKE_CASE:						Optional[Any]			,     **_SCREAMING_SNAKE_CASE:						List[str])							->			Optional[int]:

				"""simple docstring"""

				requires_backends(self			,     ["torch", "transformers", "onnx"])

	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Dict			,     *_SCREAMING_SNAKE_CASE:						Optional[Any]			,     **_SCREAMING_SNAKE_CASE:						int)							->			List[Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])







	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Optional[Any]			,     *_SCREAMING_SNAKE_CASE:						Dict			,     **_SCREAMING_SNAKE_CASE:						Optional[Any])							->			Union[str, Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])






class      A__  (    metaclass=__SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE        =      ['torch', 'transformers', 'onnx']

	def __init__(	self:						int			,     *_SCREAMING_SNAKE_CASE:						List[Any]			,     **_SCREAMING_SNAKE_CASE:						int)							->			List[str]:

				"""simple docstring"""

				requires_backends(self			,     ["torch", "transformers", "onnx"])

	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Dict			,     *_SCREAMING_SNAKE_CASE:						Any			,     **_SCREAMING_SNAKE_CASE:						Any)							->			str:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])







	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						List[Any]			,     *_SCREAMING_SNAKE_CASE:						List[str]			,     **_SCREAMING_SNAKE_CASE:						int)							->			int:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])






class      A__  (    metaclass=__SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE        =      ['torch', 'transformers', 'onnx']

	def __init__(	self:						Tuple			,     *_SCREAMING_SNAKE_CASE:						List[str]			,     **_SCREAMING_SNAKE_CASE:						List[str])							->			Optional[Any]:

				"""simple docstring"""

				requires_backends(self			,     ["torch", "transformers", "onnx"])

	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						List[str]			,     *_SCREAMING_SNAKE_CASE:						Tuple			,     **_SCREAMING_SNAKE_CASE:						int)							->			int:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])







	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Optional[int]			,     *_SCREAMING_SNAKE_CASE:						str			,     **_SCREAMING_SNAKE_CASE:						Any)							->			int:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])






class      A__  (    metaclass=__SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE        =      ['torch', 'transformers', 'onnx']

	def __init__(	self:						Optional[Any]			,     *_SCREAMING_SNAKE_CASE:						Union[str, Any]			,     **_SCREAMING_SNAKE_CASE:						Optional[int])							->			str:

				"""simple docstring"""

				requires_backends(self			,     ["torch", "transformers", "onnx"])

	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Optional[int]			,     *_SCREAMING_SNAKE_CASE:						List[Any]			,     **_SCREAMING_SNAKE_CASE:						Tuple)							->			Union[str, Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])







	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						int			,     *_SCREAMING_SNAKE_CASE:						str			,     **_SCREAMING_SNAKE_CASE:						Any)							->			Optional[Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])






class      A__  (    metaclass=__SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE        =      ['torch', 'transformers', 'onnx']

	def __init__(	self:						List[Any]			,     *_SCREAMING_SNAKE_CASE:						List[str]			,     **_SCREAMING_SNAKE_CASE:						List[str])							->			int:

				"""simple docstring"""

				requires_backends(self			,     ["torch", "transformers", "onnx"])

	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						Union[str, Any]			,     *_SCREAMING_SNAKE_CASE:						Optional[int]			,     **_SCREAMING_SNAKE_CASE:						Optional[Any])							->			List[Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])







	@classmethod
	def 				_SCREAMING_SNAKE_CASE  (	cls:						str			,     *_SCREAMING_SNAKE_CASE:						Optional[int]			,     **_SCREAMING_SNAKE_CASE:						Dict)							->			Optional[Any]:

				"""simple docstring"""

				requires_backends(cls			,     ["torch", "transformers", "onnx"])