
'''simple docstring'''



from __future__ import annotations

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


def A (__lowerCamelCase :NDArray[floataa]					,      __lowerCamelCase :NDArray[floataa]					,      __lowerCamelCase :list[int]					,      __lowerCamelCase :int					,      ):
						_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(__lowerCamelCase						)

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

						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(__lowerCamelCase						)

						if len(__lowerCamelCase						) != rowsa:
												_lowerCAmelCase    		=					(
												    """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"""						)

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

						_lowerCAmelCase		,       _lowerCAmelCase    		=					table.shape

						strictly_diagonally_dominant(__lowerCamelCase						)

						# Iterates the whole matrix for given number of times
						for _ in range(__lowerCamelCase						):
												_lowerCAmelCase    		=					[]
												for row in range(__lowerCamelCase						):
																		_lowerCAmelCase    		=					0
																		for col in range(__lowerCamelCase						):
																								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(__lowerCamelCase						)
												_lowerCAmelCase    		=					new_val

						return [float(__lowerCamelCase						) for i in new_val]


def A (__lowerCamelCase :NDArray[floataa]						):
						_lowerCAmelCase		,       _lowerCAmelCase    		=					table.shape

						_lowerCAmelCase    		=					True

						for i in range(0					,      __lowerCamelCase						):
												_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()







import sys

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

__A							:			List[Any]         =			"python tqdm regex requests packaging filelock numpy tokenizers".split()
if sys.version_info < (3, 7):
 pkgs_to_check_at_runtime.append("dataclasses")
if sys.version_info < (3, 8):
 pkgs_to_check_at_runtime.append("importlib_metadata")

for pkg in pkgs_to_check_at_runtime:
 if pkg in deps:
  if pkg == "tokenizers":
   # must be loaded here, or else tqdm check may fail
   from .utils import is_tokenizers_available

   if not is_tokenizers_available():
    continue  # not required, check version only if installed

  require_version_core(deps[pkg])
 else:
  raise ValueError(f"can't find {pkg} in {deps.keys()}, check dependency_versions_table.py")





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE=None				)							-> Union[str, Any]:




    """simple docstring"""




    require_version(deps[pkg]							,     _SCREAMING_SNAKE_CASE				)





