'''simple docstring'''

from __future__ import annotations



class 			UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self	,   __lowerCAmelCase )  ->  Tuple:
        lowercase__				:    Any  =					TypeError(
            '''Matrices must be formed from a list of zero or more lists containing at '''
            '''least one and the same number of values, each of which must be of type '''
            '''int or float.''' )
        if len(__lowerCAmelCase ) != 0:
         lowercase__				:    List[str]  =					len(rows[0] )
         if cols == 0:
          raise error
         for row in rows:
          if len(__lowerCAmelCase ) != cols:
           raise error
          for value in row:
           if not isinstance(__lowerCAmelCase	,   (int, float) ):
            raise error
         lowercase__				:    Optional[int]  =					rows
        else:
         lowercase__				:    List[str]  =					[]

       def _lowerCAmelCase(						self )  ->  List[Any]:
        return [[row[i] for row in self.rows] for i in range(len(self.rows[0] ) )]

       @property
       def _lowerCAmelCase(						self )  ->  List[Any]:
        return len(self.rows )

       @property
       def _lowerCAmelCase(						self )  ->  Dict:
        return len(self.rows[0] )

       @property
       def _lowerCAmelCase(						self )  ->  Union[str, Any]:
        return (self.num_rows, self.num_columns)

       @property
       def _lowerCAmelCase(						self )  ->  List[Any]:
        return self.order[0] == self.order[1]

       def _lowerCAmelCase(						self )  ->  Optional[Any]:
        lowercase__				:    Any  =					[
            [0 if column_num != row_num else 1 for column_num in range(self.num_rows )]
            for row_num in range(self.num_rows )
        ]
        return Matrix(__lowerCAmelCase )

       def _lowerCAmelCase(						self )  ->  int:
        if not self.is_square:
         return 0
        if self.order == (0, 0):
         return 1
        if self.order == (1, 1):
         return int(self.rows[0][0] )
        if self.order == (2, 2):
         return int(
             (self.rows[0][0] * self.rows[1][1])
             - (self.rows[0][1] * self.rows[1][0]) )
        else:
         return sum(
             self.rows[0][column] * self.cofactors().rows[0][column]
             for column in range(self.num_columns ) )

       def _lowerCAmelCase(						self )  ->  Tuple:
        return bool(self.determinant() )

       def _lowerCAmelCase(						self	,   __lowerCAmelCase	,   __lowerCAmelCase )  ->  Optional[int]:
        lowercase__				:    int  =					[
            [
                self.rows[other_row][other_column]
                for other_column in range(self.num_columns )
                if other_column != column
            ]
            for other_row in range(self.num_rows )
            if other_row != row
        ]
        return Matrix(__lowerCAmelCase ).determinant()

       def _lowerCAmelCase(						self	,   __lowerCAmelCase	,   __lowerCAmelCase )  ->  Union[str, Any]:
        if (row + column) % 2 == 0:
         return self.get_minor(__lowerCAmelCase	,   __lowerCAmelCase )
        return -1 * self.get_minor(__lowerCAmelCase	,   __lowerCAmelCase )

       def _lowerCAmelCase(						self )  ->  List[Any]:
        return Matrix(
            [
                [self.get_minor(__lowerCAmelCase	,   __lowerCAmelCase ) for column in range(self.num_columns )]
                for row in range(self.num_rows )
            ] )

       def _lowerCAmelCase(						self )  ->  Optional[Any]:
        return Matrix(
            [
                [
                    self.minors().rows[row][column]
                    if (row + column) % 2 == 0
                    else self.minors().rows[row][column] * -1
                    for column in range(self.minors().num_columns )
                ]
                for row in range(self.minors().num_rows )
            ] )

       def _lowerCAmelCase(						self )  ->  List[Any]:
        lowercase__				:    Optional[Any]  =					[
            [self.cofactors().rows[column][row] for column in range(self.num_columns )]
            for row in range(self.num_rows )
        ]
        return Matrix(__lowerCAmelCase )

       def _lowerCAmelCase(						self )  ->  Optional[int]:
        lowercase__				:    Dict  =					self.determinant()
        if not determinant:
         raise TypeError('''Only matrices with a non-zero determinant have an inverse''' )
        return self.adjugate() * (1 / determinant)

       def __repr__(						self )  ->  Any:
        return str(self.rows )

       def __str__(						self )  ->  int:
        if self.num_rows == 0:
         return "[]"
        if self.num_rows == 1:
         return "[[" + ". ".join(str(self.rows[0] ) ) + "]]"
        return (
            "["
            + "\n ".join(
                [
                    '''[''' + '''. '''.join([str(__lowerCAmelCase ) for value in row] ) + '''.]'''
                    for row in self.rows
                ] )
            + "]"
        )

       def _lowerCAmelCase(						self	,   __lowerCAmelCase	,   __lowerCAmelCase = None )  ->  Union[str, Any]:
        lowercase__				:    Optional[int]  =					TypeError('''Row must be a list containing all ints and/or floats''' )
        if not isinstance(__lowerCAmelCase	,   __lowerCAmelCase ):
         raise type_error
        for value in row:
         if not isinstance(__lowerCAmelCase	,   (int, float) ):
          raise type_error
        if len(__lowerCAmelCase ) != self.num_columns:
         raise ValueError(
             '''Row must be equal in length to the other rows in the matrix''' )
        if position is None:
         self.rows.append(__lowerCAmelCase )
        else:
         lowercase__				:    Union[str, Any]  =					self.rows[0:position] + [row] + self.rows[position:]

       def _lowerCAmelCase(						self	,   __lowerCAmelCase	,   __lowerCAmelCase = None )  ->  Optional[Any]:
        lowercase__				:    int  =					TypeError(
            '''Column must be a list containing all ints and/or floats''' )
        if not isinstance(__lowerCAmelCase	,   __lowerCAmelCase ):
         raise type_error
        for value in column:
         if not isinstance(__lowerCAmelCase	,   (int, float) ):
          raise type_error
        if len(__lowerCAmelCase ) != self.num_rows:
         raise ValueError(
             '''Column must be equal in length to the other columns in the matrix''' )
        if position is None:
         lowercase__				:    Optional[Any]  =					[self.rows[i] + [column[i]] for i in range(self.num_rows )]
        else:
         lowercase__				:    Union[str, Any]  =					[
             self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
             for i in range(self.num_rows )
         ]

       def __eq__(						self	,   __lowerCAmelCase )  ->  List[str]:
        if not isinstance(__lowerCAmelCase	,   __lowerCAmelCase ):
         return NotImplemented
        return self.rows == other.rows

       def __ne__(						self	,   __lowerCAmelCase )  ->  Optional[Any]:
        return not self == other

       def __neg__(						self )  ->  Any:
        return self * -1

       def __add__(						self	,   __lowerCAmelCase )  ->  Union[str, Any]:
        if self.order != other.order:
         raise ValueError('''Addition requires matrices of the same order''' )
        return Matrix(
            [
                [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns )]
                for i in range(self.num_rows )
            ] )

       def __sub__(						self	,   __lowerCAmelCase )  ->  Union[str, Any]:
        if self.order != other.order:
         raise ValueError('''Subtraction requires matrices of the same order''' )
        return Matrix(
            [
                [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns )]
                for i in range(self.num_rows )
            ] )

       def __mul__(						self	,   __lowerCAmelCase )  ->  Union[str, Any]:
        if isinstance(__lowerCAmelCase	,   (int, float) ):
         return Matrix(
             [[int(element * other ) for element in row] for row in self.rows] )
        elif isinstance(__lowerCAmelCase	,   __lowerCAmelCase ):
         if self.num_columns != other.num_rows:
          raise ValueError(
              '''The number of columns in the first matrix must '''
              '''be equal to the number of rows in the second''' )
         return Matrix(
             [
                 [Matrix.dot_product(__lowerCAmelCase	,   __lowerCAmelCase ) for column in other.columns()]
                 for row in self.rows
             ] )
        else:
         raise TypeError(
             '''A Matrix can only be multiplied by an int, float, or another matrix''' )

       def __pow__(						self	,   __lowerCAmelCase )  ->  Union[str, Any]:
        if not isinstance(__lowerCAmelCase	,   __lowerCAmelCase ):
         raise TypeError('''A Matrix can only be raised to the power of an int''' )
        if not self.is_square:
         raise ValueError('''Only square matrices can be raised to a power''' )
        if other == 0:
         return self.identity()
        if other < 0:
         if self.is_invertable():
          return self.inverse() ** (-other)
         raise ValueError(
             '''Only invertable matrices can be raised to a negative power''' )
        lowercase__				:    Optional[Any]  =					self
        for _ in range(other - 1 ):
         result *= self
        return result


       @classmethod
       def _lowerCAmelCase(						cls	,   __lowerCAmelCase	,   __lowerCAmelCase )  ->  Dict:
        return sum(row[i] * column[i] for i in range(len(__lowerCAmelCase ) ) )


if __name__ == "__main__":
  import doctest

  doctest.testmod()



from . import __version__

# Backward compatibility imports, to make sure all those objects can be found in file_utils
from .utils import (
    CLOUDFRONT_DISTRIB_PREFIX,
    CONFIG_NAME,
    DISABLE_TELEMETRY,
    DUMMY_INPUTS,
    DUMMY_MASK,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    FEATURE_EXTRACTOR_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_PREFIX,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    MODEL_CARD_NAME,
    MULTIPLE_CHOICE_DUMMY_INPUTS,
    PYTORCH_PRETRAINED_BERT_CACHE,
    PYTORCH_TRANSFORMERS_CACHE,
    S3_BUCKET_PREFIX,
    SENTENCEPIECE_UNDERLINE,
    SPIECE_UNDERLINE,
    TF2_WEIGHTS_NAME,
    TF_WEIGHTS_NAME,
    TORCH_FX_REQUIRED_VERSION,
    TRANSFORMERS_CACHE,
    TRANSFORMERS_DYNAMIC_MODULE_NAME,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
    ContextManagers,
    DummyObject,
    EntryNotFoundError,
    ExplicitEnum,
    ModelOutput,
    PaddingStrategy,
    PushToHubMixin,
    RepositoryNotFoundError,
    RevisionNotFoundError,
    TensorType,
    _LazyModule,
    add_code_sample_docstrings,
    add_end_docstrings,
    add_start_docstrings,
    add_start_docstrings_to_model_forward,
    cached_property,
    copy_func,
    default_cache_path,
    define_sagemaker_information,
    get_cached_models,
    get_file_from_repo,
    get_full_repo_name,
    get_torch_version,
    has_file,
    http_user_agent,
    is_apex_available,
    is_bsa_available,
    is_coloredlogs_available,
    is_datasets_available,
    is_detectrona_available,
    is_faiss_available,
    is_flax_available,
    is_ftfy_available,
    is_in_notebook,
    is_ipex_available,
    is_librosa_available,
    is_offline_mode,
    is_onnx_available,
    is_pandas_available,
    is_phonemizer_available,
    is_protobuf_available,
    is_psutil_available,
    is_pyanvml_available,
    is_pyctcdecode_available,
    is_pytesseract_available,
    is_pytorch_quantization_available,
    is_rjieba_available,
    is_sagemaker_dp_enabled,
    is_sagemaker_mp_enabled,
    is_scipy_available,
    is_sentencepiece_available,
    is_seqio_available,
    is_sklearn_available,
    is_soundfile_availble,
    is_spacy_available,
    is_speech_available,
    is_tensor,
    is_tensorflow_probability_available,
    is_tfaonnx_available,
    is_tf_available,
    is_timm_available,
    is_tokenizers_available,
    is_torch_available,
    is_torch_bfaa_available,
    is_torch_cuda_available,
    is_torch_fx_available,
    is_torch_fx_proxy,
    is_torch_mps_available,
    is_torch_tfaa_available,
    is_torch_tpu_available,
    is_torchaudio_available,
    is_training_run_on_sagemaker,
    is_vision_available,
    replace_return_docstrings,
    requires_backends,
    to_numpy,
    to_py_obj,
    torch_only_method,
)




