


"""simple docstring"""







from __future__ import annotations

import math


def      lowercase			(				A_  ,   A_       )->      list:
  '''simple docstring'''







  if len(A_       ) != 2 or len(a[0]       ) != 2 or len(A_       ) != 2 or len(b[0]       ) != 2:
    raise Exception("Matrices are not 2x2"       )
  a						:		Dict      							=			[
      [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
      [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
  ]
  return new_matrix


def      lowercase			(				A_  ,   A_       )->      Optional[int]:
  '''simple docstring'''







  return [
      [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]       )       )]
      for row in range(len(A_       )       )
  ]


def      lowercase			(				A_  ,   A_       )->      Tuple:
  '''simple docstring'''







  return [
      [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]       )       )]
      for row in range(len(A_       )       )
  ]


def      lowercase			(				A_       )->      tuple[list, list, list, list]:
  '''simple docstring'''







  if len(A_       ) % 2 != 0 or len(a[0]       ) % 2 != 0:
    raise Exception("Odd matrices are not supported!"       )

  a						:		Optional[int]      							=			len(A_       )
  a						:		str      							=			matrix_length // 2

  a						:		Dict      							=			[[a[i][j] for j in range(A_  ,   A_       )] for i in range(A_       )]
  a						:		Optional[Any]      							=			[
      [a[i][j] for j in range(A_  ,   A_       )] for i in range(A_  ,   A_       )
  ]

  a						:		Dict      							=			[[a[i][j] for j in range(A_       )] for i in range(A_       )]
  a						:		Optional[Any]      							=			[[a[i][j] for j in range(A_       )] for i in range(A_  ,   A_       )]

  return top_left, top_right, bot_left, bot_right


def      lowercase			(				A_       )->      tuple[int, int]:
  '''simple docstring'''







  return len(A_       ), len(matrix[0]       )


def      lowercase			(				A_       )->      None:
  '''simple docstring'''







  print("\n".join(str(A_       ) for line in matrix       )       )


def      lowercase			(				A_  ,   A_       )->      list:
  '''simple docstring'''







  if matrix_dimensions(A_       ) == (2, 2):
    return default_matrix_multiplication(A_  ,   A_       )

  a							,		a							,		a							,		a						:		List[str]      							=			split_matrix(A_       )
  a							,		a							,		a							,		a						:		Any      							=			split_matrix(A_       )

  a						:		List[str]      							=			actual_strassen(A_  ,   matrix_subtraction(A_  ,   A_       )       )
  a						:		Optional[Any]      							=			actual_strassen(matrix_addition(A_  ,   A_       )  ,   A_       )
  a						:		int      							=			actual_strassen(matrix_addition(A_  ,   A_       )  ,   A_       )
  a						:		List[Any]      							=			actual_strassen(A_  ,   matrix_subtraction(A_  ,   A_       )       )
  a						:		List[str]      							=			actual_strassen(matrix_addition(A_  ,   A_       )  ,   matrix_addition(A_  ,   A_       )       )
  a						:		Dict      							=			actual_strassen(matrix_subtraction(A_  ,   A_       )  ,   matrix_addition(A_  ,   A_       )       )
  a						:		str      							=			actual_strassen(matrix_subtraction(A_  ,   A_       )  ,   matrix_addition(A_  ,   A_       )       )

  a						:		Optional[Any]      							=			matrix_addition(matrix_subtraction(matrix_addition(A_  ,   A_       )  ,   A_       )  ,   A_       )
  a						:		Union[str, Any]      							=			matrix_addition(A_  ,   A_       )
  a						:		Optional[Any]      							=			matrix_addition(A_  ,   A_       )
  a						:		Any      							=			matrix_subtraction(matrix_subtraction(matrix_addition(A_  ,   A_       )  ,   A_       )  ,   A_       )

  # construct the new matrix from our 4 quadrants
  a						:		Optional[Any]      							=			[]
  for i in range(len(A_       )       ):
    new_matrix.append(top_left[i] + top_right[i]       )
  for i in range(len(A_       )       ):
    new_matrix.append(bot_left[i] + bot_right[i]       )
  return new_matrix


def      lowercase			(				A_  ,   A_       )->      list:
  '''simple docstring'''







  if matrix_dimensions(A_       )[1] != matrix_dimensions(A_       )[0]:
    a						:		str      							=			(
        "Unable to multiply these matrices, please check the dimensions.\n"
        F'''Matrix A: {matrixa}\n'''
        F'''Matrix B: {matrixa}'''
    )
    raise Exception(A_       )
  a						:		Any      							=			matrix_dimensions(A_       )
  a						:		Optional[Any]      							=			matrix_dimensions(A_       )

  if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
    return [matrixa, matrixa]

  a						:		Optional[Any]      							=			max(*A_  ,   *A_       )
  a						:		Optional[Any]      							=			int(math.pow(2  ,   math.ceil(math.loga(A_       )       )       )       )
  a						:		Union[str, Any]      							=			matrixa
  a						:		Optional[int]      							=			matrixa

  # Adding zeros to the matrices so that the arrays dimensions are the same and also
  # power of 2
  for i in range(0  ,   A_       ):
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]  ,   A_       ):
        new_matrixa[i].append(0       )
    else:
      new_matrixa.append([0] * maxim       )
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]  ,   A_       ):
        new_matrixa[i].append(0       )
    else:
      new_matrixa.append([0] * maxim       )

  a						:		Dict      							=			actual_strassen(A_  ,   A_       )

  # Removing the additional zeros
  for i in range(0  ,   A_       ):
    if i < dimensiona[0]:
      for _ in range(dimensiona[1]  ,   A_       ):
        final_matrix[i].pop()
    else:
      final_matrix.pop()
  return final_matrix


if __name__ == "__main__":
 __lowercase    					=      [
     [2, 3, 4, 5],
     [6, 4, 3, 1],
     [2, 3, 6, 7],
     [3, 1, 2, 4],
     [2, 3, 4, 5],
     [6, 4, 3, 1],
     [2, 3, 6, 7],
     [3, 1, 2, 4],
     [2, 3, 4, 5],
     [6, 2, 3, 1],
 ]
 __lowercase    					=      [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
 print(strassen(matrixa, matrixa))










"""simple docstring"""







from ...configuration_utils import PretrainedConfig
from ...utils import logging


__lowercase    					=      logging.get_logger(__name__)

__lowercase    					=      {
    """facebook/dpr-ctx_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-ctx_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-multiset-base""": (
        """https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/config.json"""
    ),
}






class 						_A  (  _a  ):







    """simple docstring"""




    UpperCAmelCase       :							int	=       """dpr"""






    def __init__(					self				:    List[Any]				, __UpperCAmelCase				:    int=30522				, __UpperCAmelCase				:    Union[str, Any]=768				, __UpperCAmelCase				:    Dict=12				, __UpperCAmelCase				:    List[str]=12				, __UpperCAmelCase				:    Any=3072				, __UpperCAmelCase				:    Optional[int]="gelu"				, __UpperCAmelCase				:    Any=0.1				, __UpperCAmelCase				:    Union[str, Any]=0.1				, __UpperCAmelCase				:    str=512				, __UpperCAmelCase				:    List[str]=2				, __UpperCAmelCase				:    Tuple=0.02				, __UpperCAmelCase				:    List[str]=1e-12				, __UpperCAmelCase				:    List[str]=0				, __UpperCAmelCase				:    str="absolute"				, __UpperCAmelCase				:    int = 0				, **__UpperCAmelCase				:    Tuple				, ):
      super().__init__(pad_token_id=__UpperCAmelCase				, **__UpperCAmelCase)

      a						:		List[Any]      							=			vocab_size
      a						:		Optional[Any]      							=			hidden_size
      a						:		Union[str, Any]      							=			num_hidden_layers
      a						:		Dict      							=			num_attention_heads
      a						:		int      							=			hidden_act
      a						:		Any      							=			intermediate_size
      a						:		Any      							=			hidden_dropout_prob
      a						:		Dict      							=			attention_probs_dropout_prob
      a						:		Any      							=			max_position_embeddings
      a						:		Union[str, Any]      							=			type_vocab_size
      a						:		Optional[Any]      							=			initializer_range
      a						:		Dict      							=			layer_norm_eps
      a						:		int      							=			projection_dim
      a						:		str      							=			position_embedding_type






