"""simple docstring"""




from __future__ import annotations

import math





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list      ,_lowerCamelCase						:	list     )	->				list:
  if len(_lowerCamelCase     ) != 2 or len(a[0]     ) != 2 or len(_lowerCamelCase     ) != 2 or len(b[0]     ) != 2:
    raise Exception("""Matrices are not 2x2"""     )
  _lowerCAmelCase						:	Union[str, Any]        =					[
      [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 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list      ,_lowerCamelCase						:	list     )	->				List[str]:
  return [
      [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]     )     )]
      for row in range(len(_lowerCamelCase     )     )
  ]





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list      ,_lowerCamelCase						:	list     )	->				Optional[int]:
  return [
      [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]     )     )]
      for row in range(len(_lowerCamelCase     )     )
  ]





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list     )	->				tuple[list, list, list, list]:
  if len(_lowerCamelCase     ) % 2 != 0 or len(a[0]     ) % 2 != 0:
    raise Exception("""Odd matrices are not supported!"""     )

  _lowerCAmelCase						:	Optional[int]        =					len(_lowerCamelCase     )
  _lowerCAmelCase						:	List[Any]        =					matrix_length // 2

  _lowerCAmelCase						:	List[str]        =					[[a[i][j] for j in range(_lowerCamelCase      ,_lowerCamelCase     )] for i in range(_lowerCamelCase     )]
  _lowerCAmelCase						:	List[Any]        =					[
      [a[i][j] for j in range(_lowerCamelCase      ,_lowerCamelCase     )] for i in range(_lowerCamelCase      ,_lowerCamelCase     )
  ]

  _lowerCAmelCase						:	Dict        =					[[a[i][j] for j in range(_lowerCamelCase     )] for i in range(_lowerCamelCase     )]
  _lowerCAmelCase						:	Optional[int]        =					[[a[i][j] for j in range(_lowerCamelCase     )] for i in range(_lowerCamelCase      ,_lowerCamelCase     )]

  return top_left, top_right, bot_left, bot_right





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list     )	->				tuple[int, int]:
  return len(_lowerCamelCase     ), len(matrix[0]     )





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list     )	->				None:
  print("""\n""".join(str(_lowerCamelCase     ) for line in matrix     )     )





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list      ,_lowerCamelCase						:	list     )	->				list:
  if matrix_dimensions(_lowerCamelCase     ) == (2, 2):
    return default_matrix_multiplication(_lowerCamelCase      ,_lowerCamelCase     )

  _lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase						:	Any        =					split_matrix(_lowerCamelCase     )
  _lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase						:	Any        =					split_matrix(_lowerCamelCase     )

  _lowerCAmelCase						:	List[Any]        =					actual_strassen(_lowerCamelCase      ,matrix_subtraction(_lowerCamelCase      ,_lowerCamelCase     )     )
  _lowerCAmelCase						:	List[Any]        =					actual_strassen(matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )      ,_lowerCamelCase     )
  _lowerCAmelCase						:	Any        =					actual_strassen(matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )      ,_lowerCamelCase     )
  _lowerCAmelCase						:	List[str]        =					actual_strassen(_lowerCamelCase      ,matrix_subtraction(_lowerCamelCase      ,_lowerCamelCase     )     )
  _lowerCAmelCase						:	int        =					actual_strassen(matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )      ,matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )     )
  _lowerCAmelCase						:	int        =					actual_strassen(matrix_subtraction(_lowerCamelCase      ,_lowerCamelCase     )      ,matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )     )
  _lowerCAmelCase						:	Any        =					actual_strassen(matrix_subtraction(_lowerCamelCase      ,_lowerCamelCase     )      ,matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )     )

  _lowerCAmelCase						:	Optional[Any]        =					matrix_addition(matrix_subtraction(matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )      ,_lowerCamelCase     )      ,_lowerCamelCase     )
  _lowerCAmelCase						:	Optional[Any]        =					matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )
  _lowerCAmelCase						:	List[Any]        =					matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )
  _lowerCAmelCase						:	List[str]        =					matrix_subtraction(matrix_subtraction(matrix_addition(_lowerCamelCase      ,_lowerCamelCase     )      ,_lowerCamelCase     )      ,_lowerCamelCase     )

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





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	list      ,_lowerCamelCase						:	list     )	->				list:
  if matrix_dimensions(_lowerCamelCase     )[1] != matrix_dimensions(_lowerCamelCase     )[0]:
    _lowerCAmelCase						:	List[str]        =					(
        """Unable to multiply these matrices, please check the dimensions.\n"""
        f"Matrix A: {matrixa}\n"
        f"Matrix B: {matrixa}"
    )
    raise Exception(_lowerCamelCase     )
  _lowerCAmelCase						:	Dict        =					matrix_dimensions(_lowerCamelCase     )
  _lowerCAmelCase						:	int        =					matrix_dimensions(_lowerCamelCase     )

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

  _lowerCAmelCase						:	Optional[int]        =					max(*_lowerCamelCase      ,*_lowerCamelCase     )
  _lowerCAmelCase						:	List[Any]        =					int(math.pow(2      ,math.ceil(math.loga(_lowerCamelCase     )     )     )     )
  _lowerCAmelCase						:	List[Any]        =					matrixa
  _lowerCAmelCase						:	List[str]        =					matrixa

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

  _lowerCAmelCase						:	Optional[Any]        =					actual_strassen(_lowerCamelCase      ,_lowerCamelCase     )

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


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





"""simple docstring"""




import contextlib
from multiprocessing import Pool, RLock

from tqdm.auto import tqdm

from ..utils import experimental, logging


_a				:		List[Any]	   =       logging.get_logger(__name__)
class 						__A							:
     _UpperCamelCase							:      str		 =		None







@experimental
def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	Optional[int]      ,_lowerCamelCase						:	Any      ,_lowerCamelCase						:	Optional[int]      ,_lowerCamelCase						:	List[str]      ,_lowerCamelCase						:	List[Any]      ,_lowerCamelCase						:	Tuple      ,_lowerCamelCase						:	Optional[int]     )	->				List[Any]:
  if ParallelBackendConfig.backend_name is None:
    return _map_with_multiprocessing_pool(
        _lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase     )

  return _map_with_joblib(_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase      ,_lowerCamelCase     )





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	List[str]      ,_lowerCamelCase						:	Optional[Any]      ,_lowerCamelCase						:	str      ,_lowerCamelCase						:	Tuple      ,_lowerCamelCase						:	Any      ,_lowerCamelCase						:	Optional[int]      ,_lowerCamelCase						:	Tuple     )	->				Union[str, Any]:
  _lowerCAmelCase						:	int        =					num_proc if num_proc <= len(_lowerCamelCase     ) else len(_lowerCamelCase     )
  _lowerCAmelCase						:	Union[str, Any]        =					[]  # We organize the splits ourselve (contiguous splits)
  for index in range(_lowerCamelCase     ):
    _lowerCAmelCase						:	List[str]        =					len(_lowerCamelCase     ) // num_proc
    _lowerCAmelCase						:	str        =					len(_lowerCamelCase     ) % num_proc
    _lowerCAmelCase						:	Tuple        =					div * index + min(_lowerCamelCase      ,_lowerCamelCase     )
    _lowerCAmelCase						:	int        =					start + div + (1 if index < mod else 0)
    split_kwds.append((function, iterable[start:end], types, index, disable_tqdm, desc)     )

  if len(_lowerCamelCase     ) != sum(len(i[1]     ) for i in split_kwds     ):
    raise ValueError(
        f"Error dividing inputs iterable among processes. "
        f"Total number of objects {len(_lowerCamelCase     )}, "
        f"length: {sum(len(i[1]     ) for i in split_kwds     )}"     )

  logger.info(
      f"Spawning {num_proc} processes for {len(_lowerCamelCase     )} objects in slices of {[len(i[1]     ) for i in split_kwds]}"     )
  _lowerCAmelCase      ,     _lowerCAmelCase						:	List[str]        =					None, None
  if not disable_tqdm:
    _lowerCAmelCase      ,     _lowerCAmelCase						:	Optional[Any]        =					(RLock(),), tqdm.set_lock
  with Pool(_lowerCamelCase      ,initargs=_lowerCamelCase      ,initializer=_lowerCamelCase     ) as pool:
    _lowerCAmelCase						:	str        =					pool.map(_lowerCamelCase      ,_lowerCamelCase     )
  logger.info(f"Finished {num_proc} processes"     )
  _lowerCAmelCase						:	int        =					[obj for proc_res in mapped for obj in proc_res]
  logger.info(f"Unpacked {len(_lowerCamelCase     )} objects"     )

  return mapped





def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	List[str]      ,_lowerCamelCase						:	Union[str, Any]      ,_lowerCamelCase						:	int      ,_lowerCamelCase						:	Dict      ,_lowerCamelCase						:	Tuple      ,_lowerCamelCase						:	Any      ,_lowerCamelCase						:	str     )	->				Optional[Any]:
  # progress bar is not yet supported for _map_with_joblib, because tqdm couldn't accurately be applied to joblib,
  # and it requires monkey-patching joblib internal classes which is subject to change
  import joblib

  with joblib.parallel_backend(ParallelBackendConfig.backend_name      ,n_jobs=_lowerCamelCase     ):
    return joblib.Parallel()(
        joblib.delayed(_lowerCamelCase     )((function, obj, types, None, True, None)     ) for obj in iterable     )






@experimental
@contextlib.contextmanager
def 							SCREAMING_SNAKE_CASE					(      _lowerCamelCase						:	str     )	->				Any:
  _lowerCAmelCase						:	List[Any]        =					backend_name

  if backend_name == "spark":
    from joblibspark import register_spark

    register_spark()

    # TODO: call create_cache_and_write_probe if "download" in steps
    # TODO: raise NotImplementedError when Dataset.map etc is called

  try:
    yield
  finally:
    _lowerCAmelCase						:	Optional[Any]        =					None




