





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


UpperCAmelCase_							=				{
    """configuration_transfo_xl""": ["""TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP""", """TransfoXLConfig"""],
    """tokenization_transfo_xl""": ["""TransfoXLCorpus""", """TransfoXLTokenizer"""],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase_							=				[
							    """TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """AdaptiveEmbedding""",
							    """TransfoXLForSequenceClassification""",
							    """TransfoXLLMHeadModel""",
							    """TransfoXLModel""",
							    """TransfoXLPreTrainedModel""",
							    """load_tf_weights_in_transfo_xl""",
							]

try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase_							=				[
							    """TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """TFAdaptiveEmbedding""",
							    """TFTransfoXLForSequenceClassification""",
							    """TFTransfoXLLMHeadModel""",
							    """TFTransfoXLMainLayer""",
							    """TFTransfoXLModel""",
							    """TFTransfoXLPreTrainedModel""",
							]


if TYPE_CHECKING:
							from .configuration_transfo_xl import TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP, TransfoXLConfig
							from .tokenization_transfo_xl import TransfoXLCorpus, TransfoXLTokenizer

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_transfo_xl import (
														    TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
														    AdaptiveEmbedding,
														    TransfoXLForSequenceClassification,
														    TransfoXLLMHeadModel,
														    TransfoXLModel,
														    TransfoXLPreTrainedModel,
														    load_tf_weights_in_transfo_xl,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_transfo_xl import (
														    TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
														    TFAdaptiveEmbedding,
														    TFTransfoXLForSequenceClassification,
														    TFTransfoXLLMHeadModel,
														    TFTransfoXLMainLayer,
														    TFTransfoXLModel,
														    TFTransfoXLPreTrainedModel,
														)

else:
							import sys

							UpperCAmelCase_							=				_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)






from __future__ import annotations

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





def  __magic_name__  (				lowercase				,       lowercase				,       lowercase				,       lowercase				,       )				-> list[float]:

							"""simple docstring"""



							lowercase_				,		lowercase_	:   List[str]  				=     coefficient_matrix.shape
							lowercase_				,		lowercase_	:   Any  				=     constant_matrix.shape

							if rowsa != colsa:
														lowercase_	:   List[Any]  				=     f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
														raise ValueError(lowercase				)

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

							if rowsa != rowsa:
														lowercase_	:   Tuple  				=     (
														    """Coefficient and constant matrices dimensions must be nxn and nx1 but """
														    f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
														)
														raise ValueError(lowercase				)

							if len(lowercase				) != rowsa:
														lowercase_	:   int  				=     (
														    """Number of initial values must be equal to number of rows in coefficient """
														    f"""matrix but received {len(lowercase				)} and {rowsa}"""
														)
														raise ValueError(lowercase				)

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

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

							lowercase_				,		lowercase_	:   Dict  				=     table.shape

							strictly_diagonally_dominant(lowercase				)

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

							return [float(lowercase				) for i in new_val]





def  __magic_name__  (				lowercase				)				-> bool:

							"""simple docstring"""



							lowercase_				,		lowercase_	:   str  				=     table.shape

							lowercase_	:   str  				=     True

							for i in range(0				,       lowercase				):
														lowercase_	:   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()