
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      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  bool    ):
			# The first operation in a checkpoint can't be in-place, but it's
			# nice to have in-place addition during inference. Thus...
			if not inplace:
						lowerCAmelCase__ :    List[Any]				      =			ma + ma
			else:
						ma += ma

			return ma



def      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  List[int]    ):
			lowerCAmelCase__ :    List[str]				      =			-1 * len(__UpperCamelCase    )
			lowerCAmelCase__ :    List[str]				      =			list(range(len(tensor.shape[:zero_index]    )    )    )
			return tensor.permute(first_inds + [zero_index + i for i in inds]    )



def      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  int    ):
			return t.reshape(t.shape[:-no_dims] + (-1,)    )



def      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  int	,__UpperCamelCase       :  float = 1e-4    ):
			lowerCAmelCase__ :    List[str]				      =			mask.expand(*value.shape    )
			return torch.sum(mask * value	,dim=__UpperCamelCase    ) / (eps + torch.sum(__UpperCamelCase	,dim=__UpperCamelCase    ))



def      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  torch.types.Number = 2.3_125	,__UpperCamelCase       :  torch.types.Number = 21.6_875	,__UpperCamelCase       :  int = 64    ):
			lowerCAmelCase__ :    Dict				      =			torch.linspace(__UpperCamelCase	,__UpperCamelCase	,no_bins - 1	,device=pts.device    )
			lowerCAmelCase__ :    Optional[Any]				      =			torch.sqrt(torch.sum((pts.unsqueeze(-2    ) - pts.unsqueeze(-3    )) ** 2	,dim=-1    )    )
			return torch.bucketize(__UpperCamelCase	,__UpperCamelCase    )



def      _a     (   __UpperCamelCase       :  Callable[[list], Any]	,__UpperCamelCase       :  List[dict]    ):
			lowerCAmelCase__ :    List[Any]				      =			dicts[0]
			lowerCAmelCase__ :    str				      =			{}
			for k, v in first.items():
						lowerCAmelCase__ :    Union[str, Any]				      =			[d[k] for d in dicts]
						if isinstance(__UpperCamelCase	,__UpperCamelCase    ):
									lowerCAmelCase__ :    Optional[int]				      =			dict_multimap(__UpperCamelCase	,__UpperCamelCase    )
						else:
									lowerCAmelCase__ :    List[str]				      =			fn(__UpperCamelCase    )

			return new_dict



def      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  torch.Tensor    ):
			lowerCAmelCase__ :    Any				      =			v_bins.view(((1,) * len(x.shape    )) + (len(__UpperCamelCase    ),)    )
			lowerCAmelCase__ :    int				      =			x[..., None] - reshaped_bins
			lowerCAmelCase__ :    List[str]				      =			torch.argmin(torch.abs(__UpperCamelCase    )	,dim=-1    )
			return nn.functional.one_hot(__UpperCamelCase	,num_classes=len(__UpperCamelCase    )    ).float()



def      _a     (   __UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  torch.Tensor	,__UpperCamelCase       :  int = 0	,__UpperCamelCase       :  int = 0    ):
			lowerCAmelCase__ :    List[Union[slice, torch.Tensor]]				      =			[]
			for i, s in enumerate(data.shape[:no_batch_dims]    ):
						lowerCAmelCase__ :    Optional[int]				      =			torch.arange(__UpperCamelCase    )
						lowerCAmelCase__ :    Optional[int]				      =			r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape    ) - i - 1)))    )
						ranges.append(__UpperCamelCase    )

			lowerCAmelCase__ :    List[Union[slice, torch.Tensor]]				      =			[slice(__UpperCamelCase    ) for _ in range(len(data.shape    ) - no_batch_dims    )]
			lowerCAmelCase__ :    int				      =			inds
			ranges.extend(__UpperCamelCase    )
			# 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(__UpperCamelCase    )]


A__       :   int   						=					TypeVar("""T""")



def      _a     (   __UpperCamelCase       :  Callable[[T], Any]	,__UpperCamelCase       :  Dict[Any, Union[dict, list, tuple, T]]	,__UpperCamelCase       :  Type[T]    ):
			lowerCAmelCase__ :    Dict[Any, Union[dict, list, tuple, Any]]				      =			{}
			for k, v in dic.items():
						if isinstance(__UpperCamelCase	,__UpperCamelCase    ):
									lowerCAmelCase__ :    Union[str, Any]				      =			dict_map(__UpperCamelCase	,__UpperCamelCase	,__UpperCamelCase    )
						else:
									lowerCAmelCase__ :    str				      =			tree_map(__UpperCamelCase	,__UpperCamelCase	,__UpperCamelCase    )

			return new_dict



@overload
def      _a     (   __UpperCamelCase       :  Callable[[T], Any]	,__UpperCamelCase       :  T	,__UpperCamelCase       :  Type[T]    ):
			...



@overload
def      _a     (   __UpperCamelCase       :  Callable[[T], Any]	,__UpperCamelCase       :  dict	,__UpperCamelCase       :  Type[T]    ):
			...



@overload
def      _a     (   __UpperCamelCase       :  Callable[[T], Any]	,__UpperCamelCase       :  list	,__UpperCamelCase       :  Type[T]    ):
			...



@overload
def      _a     (   __UpperCamelCase       :  Callable[[T], Any]	,__UpperCamelCase       :  tuple	,__UpperCamelCase       :  Type[T]    ):
			...



def      _a     (   __UpperCamelCase       :  str	,__UpperCamelCase       :  Union[str, Any]	,__UpperCamelCase       :  Union[str, Any]    ):
			if isinstance(__UpperCamelCase	,__UpperCamelCase    ):
						return dict_map(__UpperCamelCase	,__UpperCamelCase	,__UpperCamelCase    )
			elif isinstance(__UpperCamelCase	,__UpperCamelCase    ):
						return [tree_map(__UpperCamelCase	,__UpperCamelCase	,__UpperCamelCase    ) for x in tree]
			elif isinstance(__UpperCamelCase	,__UpperCamelCase    ):
						return tuple(tree_map(__UpperCamelCase	,__UpperCamelCase	,__UpperCamelCase    ) for x in tree    )
			elif isinstance(__UpperCamelCase	,__UpperCamelCase    ):
						return fn(__UpperCamelCase    )
			else:
						print(type(__UpperCamelCase    )    )
						raise ValueError('''Not supported'''    )


A__       :   Optional[Any]   						=					partial(tree_map, leaf_type=torch.Tensor)





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



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    Any				      =			np.shape(__UpperCamelCase    )

			lowerCAmelCase__ :    NDArray[floataa]				      =			np.zeros((rows, 1)	,dtype=__UpperCamelCase    )
			for row in reversed(range(__UpperCamelCase    )    ):
						lowerCAmelCase__ :    List[str]				      =			0
						for col in range(row + 1	,__UpperCamelCase    ):
									total += coefficients[row, col] * x[col]

						lowerCAmelCase__ :    int				      =			(vector[row] - total) / coefficients[row, row]

			return x



def      _a     (   __UpperCamelCase       :  NDArray[floataa]	,__UpperCamelCase       :  NDArray[floataa]    ):
			lowerCAmelCase__      ,				lowerCAmelCase__ :    str				      =			np.shape(__UpperCamelCase    )
			if rows != columns:
						return np.array(()	,dtype=__UpperCamelCase    )

			# augmented matrix
			lowerCAmelCase__ :    NDArray[floataa]				      =			np.concatenate((coefficients, vector)	,axis=1    )
			lowerCAmelCase__ :    List[str]				      =			augmented_mat.astype('''float64'''    )

			# scale the matrix leaving it triangular
			for row in range(rows - 1    ):
						lowerCAmelCase__ :    str				      =			augmented_mat[row, row]
						for col in range(row + 1	,__UpperCamelCase    ):
									lowerCAmelCase__ :    Optional[int]				      =			augmented_mat[col, row] / pivot
									augmented_mat[col, :] -= factor * augmented_mat[row, :]

			lowerCAmelCase__ :    int				      =			retroactive_resolution(
			    augmented_mat[:, 0:columns]	,augmented_mat[:, columns : columns + 1]    )

			return x


if __name__ == "__main__":
							import doctest

							doctest.testmod()



