




from __future__ import annotations

from typing import Any




def    lowerCamelCase__			(		*A__			:   list[list[int]]      ):





       '''simple docstring'''



       if all(_check_not_integer(A__      ) for m in matrix_s      ):
              for i in matrix_s[1:]:
                     _verify_matrix_sizes(matrix_s[0]    ,     A__      )
              return [[sum(A__      ) for t in zip(*A__      )] for m in zip(*A__      )]
       raise TypeError("""Expected a matrix, got int/list instead"""      )




def    lowerCamelCase__			(		A__			:   list[list[int]]    ,     A__			:   list[list[int]]      ):





       '''simple docstring'''



       if (
           _check_not_integer(A__      )
           and _check_not_integer(A__      )
           and _verify_matrix_sizes(A__    ,     A__      )
       ):
              return [[i - j for i, j in zip(*A__      )] for m in zip(A__    ,     A__      )]
       raise TypeError("""Expected a matrix, got int/list instead"""      )




def    lowerCamelCase__			(		A__			:   list[list[int]]    ,     A__			:   int | float      ):





       '''simple docstring'''



       return [[x * n for x in row] for row in matrix]




def    lowerCamelCase__			(		A__			:   list[list[int]]    ,     A__			:   list[list[int]]      ):





       '''simple docstring'''



       if _check_not_integer(A__      ) and _check_not_integer(A__      ):
              __lowerCamelCase,  __lowerCamelCase  =		_verify_matrix_sizes(A__    ,     A__      )

       if cols[0] != rows[1]:
              __lowerCamelCase  =		(
                  """Cannot multiply matrix of dimensions """
                  f'({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'
              )
              raise ValueError(A__      )
       return [
           [sum(m * n for m, n in zip(A__    ,     A__      )      ) for j in zip(*A__      )] for i in matrix_a
       ]




def    lowerCamelCase__			(		A__			:   int      ):





       '''simple docstring'''



       __lowerCamelCase  =		int(A__      )
       return [[int(row == column      ) for column in range(A__      )] for row in range(A__      )]




def    lowerCamelCase__			(		A__			:   list[list[int]]    ,     A__			:   bool = True      ):





       '''simple docstring'''



       if _check_not_integer(A__      ):
              if return_map:
                     return map(A__    ,     zip(*A__      )      )
              else:
                     return list(map(A__    ,     zip(*A__      )      )      )
       raise TypeError("""Expected a matrix, got int/list instead"""      )




def    lowerCamelCase__			(		A__			:   list[list[int]]    ,     A__			:   int    ,     A__			:   int      ):





       '''simple docstring'''



       __lowerCamelCase  =		matrix[:row] + matrix[row + 1 :]
       return [row[:column] + row[column + 1 :] for row in minor]




def    lowerCamelCase__			(		A__			:   list[list[int]]      ):





       '''simple docstring'''



       if len(A__      ) == 1:
              return matrix[0][0]

       return sum(
           x * determinant(minor(A__    ,     0    ,     A__      )      ) * (-1) ** i
           for i, x in enumerate(matrix[0]      )      )




def    lowerCamelCase__			(		A__			:   list[list[int]]      ):





       '''simple docstring'''



       __lowerCamelCase  =		determinant(A__      )
       if det == 0:
              return None

       __lowerCamelCase  =		[
           [determinant(minor(A__    ,     A__    ,     A__      )      ) for j in range(len(A__      )      )]
           for i in range(len(A__      )      )
       ]

       __lowerCamelCase  =		[
           [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]      )]
           for row in range(len(A__      )      )
       ]
       __lowerCamelCase  =		list(transpose(A__      )      )
       return scalar_multiply(A__    ,     1 / det      )




def    lowerCamelCase__			(		A__			:   list[list[int]]      ):





       '''simple docstring'''



       return not isinstance(A__    ,     A__      ) and not isinstance(matrix[0]    ,     A__      )




def    lowerCamelCase__			(		A__			:   list[list[int]]      ):





       '''simple docstring'''



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




def    lowerCamelCase__			(		A__			:   list[list[int]]    ,     A__			:   list[list[int]]      ):





       '''simple docstring'''



       __lowerCamelCase  =		_shape(A__      ) + _shape(A__      )
       if shape[0] != shape[3] or shape[1] != shape[2]:
              __lowerCamelCase  =		(
                  """operands could not be broadcast together with shape """
                  f'({shape[0], shape[1]}), ({shape[2], shape[3]})'
              )
              raise ValueError(A__      )
       return (shape[0], shape[2]), (shape[1], shape[3])




def    lowerCamelCase__			(		):





       '''simple docstring'''



       __lowerCamelCase  =		[[12, 10], [3, 9]]
       __lowerCamelCase  =		[[3, 4], [7, 4]]
       __lowerCamelCase  =		[[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
       __lowerCamelCase  =		[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
       print(f'Add Operation, {add(A__    ,     A__      ) = } \n'      )
       print(
           f'Multiply Operation, {multiply(A__    ,     A__      ) = } \n'    ,     )
       print(f'Identity: {identity(5      )}\n'      )
       print(f'Minor of {matrix_c} = {minor(A__    ,     1    ,     2      )} \n'      )
       print(f'Determinant of {matrix_b} = {determinant(A__      )} \n'      )
       print(f'Inverse of {matrix_d} = {inverse(A__      )}\n'      )


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       main()







from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   torch.Tensor    ,     A__			:   bool      ):





       '''simple docstring'''



       if not inplace:
              __lowerCamelCase  =		ma + ma
       else:
              ma += ma

       return ma




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   List[int]      ):





       '''simple docstring'''



       __lowerCamelCase  =		-1 * len(A__      )
       __lowerCamelCase  =		list(range(len(tensor.shape[:zero_index]      )      )      )
       return tensor.permute(first_inds + [zero_index + i for i in inds]      )




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   int      ):





       '''simple docstring'''



       return t.reshape(t.shape[:-no_dims] + (-1,)      )




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   torch.Tensor    ,     A__			:   int    ,     A__			:   float = 1E-4      ):





       '''simple docstring'''



       __lowerCamelCase  =		mask.expand(*value.shape      )
       return torch.sum(mask * value    ,     dim=A__      ) / (eps + torch.sum(A__    ,     dim=A__      ))




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   torch.types.Number = 2.3_125    ,     A__			:   torch.types.Number = 21.6_875    ,     A__			:   int = 64      ):





       '''simple docstring'''



       __lowerCamelCase  =		torch.linspace(A__    ,     A__    ,     no_bins - 1    ,     device=pts.device      )
       __lowerCamelCase  =		torch.sqrt(torch.sum((pts.unsqueeze(-2      ) - pts.unsqueeze(-3      )) ** 2    ,     dim=-1      )      )
       return torch.bucketize(A__    ,     A__      )




def    lowerCamelCase__			(		A__			:   Callable[[list], Any]    ,     A__			:   List[dict]      ):





       '''simple docstring'''



       __lowerCamelCase  =		dicts[0]
       __lowerCamelCase  =		{}
       for k, v in first.items():
              __lowerCamelCase  =		[d[k] for d in dicts]
              if isinstance(A__    ,     A__      ):
                     __lowerCamelCase  =		dict_multimap(A__    ,     A__      )
              else:
                     __lowerCamelCase  =		fn(A__      )

       return new_dict




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   torch.Tensor      ):





       '''simple docstring'''



       __lowerCamelCase  =		v_bins.view(((1,) * len(x.shape      )) + (len(A__      ),)      )
       __lowerCamelCase  =		x[..., None] - reshaped_bins
       __lowerCamelCase  =		torch.argmin(torch.abs(A__      )    ,     dim=-1      )
       return nn.functional.one_hot(A__    ,     num_classes=len(A__      )      ).float()




def    lowerCamelCase__			(		A__			:   torch.Tensor    ,     A__			:   torch.Tensor    ,     A__			:   int = 0    ,     A__			:   int = 0      ):





       '''simple docstring'''



       __lowerCamelCase  =		[]
       for i, s in enumerate(data.shape[:no_batch_dims]      ):
              __lowerCamelCase  =		torch.arange(A__      )
              __lowerCamelCase  =		r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape      ) - i - 1)))      )
              ranges.append(A__      )

       __lowerCamelCase  =		[slice(A__      ) for _ in range(len(data.shape      ) - no_batch_dims      )]
       __lowerCamelCase  =		inds
       ranges.extend(A__      )
       # Matt note: Editing this to get around the behaviour of using a list as an array index changing
       # in recent Numpy versions
       return data[tuple(A__      )]


UpperCAmelCase_   							=      TypeVar('T')




def    lowerCamelCase__			(		A__			:   Callable[[T], Any]    ,     A__			:   Dict[Any, Union[dict, list, tuple, T]]    ,     A__			:   Type[T]      ):





       '''simple docstring'''



       __lowerCamelCase  =		{}
       for k, v in dic.items():
              if isinstance(A__    ,     A__      ):
                     __lowerCamelCase  =		dict_map(A__    ,     A__    ,     A__      )
              else:
                     __lowerCamelCase  =		tree_map(A__    ,     A__    ,     A__      )

       return new_dict




@overload
def    lowerCamelCase__			(		A__			:   Callable[[T], Any]    ,     A__			:   T    ,     A__			:   Type[T]      ):





       '''simple docstring'''



       ...




@overload
def    lowerCamelCase__			(		A__			:   Callable[[T], Any]    ,     A__			:   dict    ,     A__			:   Type[T]      ):





       '''simple docstring'''



       ...




@overload
def    lowerCamelCase__			(		A__			:   Callable[[T], Any]    ,     A__			:   list    ,     A__			:   Type[T]      ):





       '''simple docstring'''



       ...




@overload
def    lowerCamelCase__			(		A__			:   Callable[[T], Any]    ,     A__			:   tuple    ,     A__			:   Type[T]      ):





       '''simple docstring'''



       ...




def    lowerCamelCase__			(		A__			:   Dict    ,     A__			:   List[str]    ,     A__			:   List[str]      ):





       '''simple docstring'''



       if isinstance(A__    ,     A__      ):
              return dict_map(A__    ,     A__    ,     A__      )
       elif isinstance(A__    ,     A__      ):
              return [tree_map(A__    ,     A__    ,     A__      ) for x in tree]
       elif isinstance(A__    ,     A__      ):
              return tuple(tree_map(A__    ,     A__    ,     A__      ) for x in tree      )
       elif isinstance(A__    ,     A__      ):
              return fn(A__      )
       else:
              print(type(A__      )      )
              raise ValueError("""Not supported"""      )




UpperCAmelCase_   							=      partial(tree_map, leaf_type=torch.Tensor)

