






from __future__ import annotations

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





def 		_UpperCAmelCase   (							__A							:   NDArray[floataa]						,		__A							:   NDArray[floataa]						,		__A							:   list[int]						,		__A							:   int						,		):
				a_		:  int											=      coefficient_matrix.shape
				a_		:  Optional[Any]											=      constant_matrix.shape

				if rowsa != colsa:
								a_		:  Dict											=      f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
								raise ValueError(__A      )

				if colsa != 1:
								a_		:  Tuple											=      f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
								raise ValueError(__A      )

				if rowsa != rowsa:
								a_		:  List[Any]											=      (
								    '''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:
								a_		:  Tuple											=      (
								    '''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'''      )

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

				a_		:  Optional[Any]											=      table.shape

				strictly_diagonally_dominant(__A      )

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

				return [float(__A      ) for i in new_val]





def 		_UpperCAmelCase   (							__A							:   NDArray[floataa]      ):
				a_		:  Dict											=      table.shape

				a_		:  int											=      True

				for i in range(0						,		__A      ):
								a_		:  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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCAmelCase       		=      {
    'configuration_git': ['GIT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'GitConfig', 'GitVisionConfig'],
    'processing_git': ['GitProcessor'],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__lowerCAmelCase       		=      [
		    'GIT_PRETRAINED_MODEL_ARCHIVE_LIST',
		    'GitForCausalLM',
		    'GitModel',
		    'GitPreTrainedModel',
		    'GitVisionModel',
		]

if TYPE_CHECKING:
		from .configuration_git import GIT_PRETRAINED_CONFIG_ARCHIVE_MAP, GitConfig, GitVisionConfig
		from .processing_git import GitProcessor

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_git import (
				    GIT_PRETRAINED_MODEL_ARCHIVE_LIST,
				    GitForCausalLM,
				    GitModel,
				    GitPreTrainedModel,
				    GitVisionModel,
				)

else:
		import sys

		__lowerCAmelCase       		=      _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




