
'''simple docstring'''
import math

from numpy import inf
from scipy.integrate import quad







def        A_     (						__SCREAMING_SNAKE_CASE						:  float )				->       float:





  """simple docstring"""

  if num <= 0:
    raise ValueError("""math domain error""" )

  return quad(__SCREAMING_SNAKE_CASE			,     0			,     __SCREAMING_SNAKE_CASE			,     args=(__SCREAMING_SNAKE_CASE) )[0]







def        A_     (						__SCREAMING_SNAKE_CASE						:  float			,     __SCREAMING_SNAKE_CASE						:  float )				->       float:





  """simple docstring"""

  return math.pow(__SCREAMING_SNAKE_CASE			,     z - 1 ) * math.exp(-x )


if __name__ == "__main__":
     from doctest import testmod

     testmod()





'''simple docstring'''
import logging
import math
from functools import partial
from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union

import torch

from .tensor_utils import tensor_tree_map, tree_map







def        A_     (						__SCREAMING_SNAKE_CASE						:  Union[dict, list, tuple, torch.Tensor] )				->       List[Tuple[int, ...]]:





  """simple docstring"""

  __A		:     Optional[Any]												=		[]
  if isinstance(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):
    for v in tree.values():
      shapes.extend(_fetch_dims(__SCREAMING_SNAKE_CASE ) )
  elif isinstance(__SCREAMING_SNAKE_CASE			,     (list, tuple) ):
    for t in tree:
      shapes.extend(_fetch_dims(__SCREAMING_SNAKE_CASE ) )
  elif isinstance(__SCREAMING_SNAKE_CASE			,     torch.Tensor ):
    shapes.append(tree.shape )
  else:
    raise ValueError("""Not supported""" )

  return shapes







@torch.jit.ignore
def        A_     (						__SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  Tuple[int, ...] )				->       Tuple[int, ...]:





  """simple docstring"""

  __A		:     List[str]												=		[]
  for d in reversed(__SCREAMING_SNAKE_CASE ):
    idx.append(flat_idx % d )
    __A		:     Any												=		flat_idx // d

  return tuple(reversed(__SCREAMING_SNAKE_CASE ) )







@torch.jit.ignore
def        A_     (						__SCREAMING_SNAKE_CASE						:  Sequence[int]			,     __SCREAMING_SNAKE_CASE						:  Sequence[int]			,     __SCREAMING_SNAKE_CASE						:  Sequence[int]			,     __SCREAMING_SNAKE_CASE						:  Optional[Sequence[bool]] = None			,     __SCREAMING_SNAKE_CASE						:  Optional[Sequence[bool]] = None			,     )				->       List[Tuple[slice, ...]]:





  """simple docstring"""

  def reduce_edge_list(__SCREAMING_SNAKE_CASE						:  List[bool] ) -> None:
    __A		:     Dict												=		True
    for i in range(len(__SCREAMING_SNAKE_CASE ) ):
      __A		:     List[str]												=		-1 * (i + 1)
      l[reversed_idx] &= tally
      __A		:     Optional[Any]												=		l[reversed_idx]

  if start_edges is None:
    __A		:     Any												=		[s == 0 for s in start]
    reduce_edge_list(__SCREAMING_SNAKE_CASE )
  if end_edges is None:
    __A		:     List[str]												=		[e == (d - 1) for e, d in zip(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )]
    reduce_edge_list(__SCREAMING_SNAKE_CASE )

  # Base cases. Either start/end are empty and we're done, or the final,
  # one-dimensional tensor can be simply sliced
  if len(__SCREAMING_SNAKE_CASE ) == 0:
    return [()]
  elif len(__SCREAMING_SNAKE_CASE ) == 1:
    return [(slice(start[0]			,     end[0] + 1 ),)]

  __A		:     List[Tuple[slice, ...]]												=		[]
  __A		:     List[slice]												=		[]

  # Dimensions common to start and end can be selected directly
  for s, e in zip(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):
    if s == e:
      path_list.append(slice(__SCREAMING_SNAKE_CASE			,     s + 1 ) )
    else:
      break

  __A		:     Tuple[slice, ...]												=		tuple(__SCREAMING_SNAKE_CASE )
  __A		:     Dict												=		len(__SCREAMING_SNAKE_CASE )

  # start == end, and we're done
  if divergence_idx == len(__SCREAMING_SNAKE_CASE ):
    return [path]

  def upper() -> Tuple[Tuple[slice, ...], ...]:
    assert start_edges is not None
    assert end_edges is not None

    __A		:     List[Any]												=		start[divergence_idx]
    return tuple(
        path + (slice(__SCREAMING_SNAKE_CASE			,     sdi + 1 ),) + s
        for s in _get_minimal_slice_set(
            start[divergence_idx + 1 :]			,     [d - 1 for d in dims[divergence_idx + 1 :]]			,     dims[divergence_idx + 1 :]			,     start_edges=start_edges[divergence_idx + 1 :]			,     end_edges=[True for _ in end_edges[divergence_idx + 1 :]]			,     ) )

  def lower() -> Tuple[Tuple[slice, ...], ...]:
    assert start_edges is not None
    assert end_edges is not None

    __A		:     Optional[int]												=		end[divergence_idx]
    return tuple(
        path + (slice(__SCREAMING_SNAKE_CASE			,     edi + 1 ),) + s
        for s in _get_minimal_slice_set(
            [0 for _ in start[divergence_idx + 1 :]]			,     end[divergence_idx + 1 :]			,     dims[divergence_idx + 1 :]			,     start_edges=[True for _ in start_edges[divergence_idx + 1 :]]			,     end_edges=end_edges[divergence_idx + 1 :]			,     ) )

  # If both start and end are at the edges of the subtree rooted at
  # divergence_idx, we can just select the whole subtree at once
  if start_edges[divergence_idx] and end_edges[divergence_idx]:
    slices.append(path + (slice(start[divergence_idx]			,     end[divergence_idx] + 1 ),) )
  # If just start is at the edge, we can grab almost all of the subtree,
  # treating only the ragged bottom edge as an edge case
  elif start_edges[divergence_idx]:
    slices.append(path + (slice(start[divergence_idx]			,     end[divergence_idx] ),) )
    slices.extend(lower() )
  # Analogous to the previous case, but the top is ragged this time
  elif end_edges[divergence_idx]:
    slices.extend(upper() )
    slices.append(path + (slice(start[divergence_idx] + 1			,     end[divergence_idx] + 1 ),) )
  # If both sides of the range are ragged, we need to handle both sides
  # separately. If there's contiguous meat in between them, we can index it
  # in one big chunk
  else:
    slices.extend(upper() )
    __A		:     List[Any]												=		end[divergence_idx] - start[divergence_idx]
    if middle_ground > 1:
      slices.append(path + (slice(start[divergence_idx] + 1			,     end[divergence_idx] ),) )
    slices.extend(lower() )

  return slices







@torch.jit.ignore
def        A_     (						__SCREAMING_SNAKE_CASE						:  torch.Tensor			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int )				->       torch.Tensor:





  """simple docstring"""

  __A		:     List[Any]												=		t.shape[:no_batch_dims]
  __A		:     Dict												=		list(_flat_idx_to_idx(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ) )
  # _get_minimal_slice_set is inclusive
  __A		:     List[str]												=		list(_flat_idx_to_idx(flat_end - 1			,     __SCREAMING_SNAKE_CASE ) )

  # Get an ordered list of slices to perform
  __A		:     Optional[Any]												=		_get_minimal_slice_set(
      __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE			,     )

  __A		:     int												=		[t[s] for s in slices]

  return torch.cat([s.view((-1,) + t.shape[no_batch_dims:] ) for s in sliced_tensors] )







def        A_     (						__SCREAMING_SNAKE_CASE						:  Callable			,     __SCREAMING_SNAKE_CASE						:  Dict[str, Any]			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  int			,     __SCREAMING_SNAKE_CASE						:  bool = False			,     __SCREAMING_SNAKE_CASE						:  Any = None			,     __SCREAMING_SNAKE_CASE						:  bool = False			,     )				->       Any:





  """simple docstring"""

  if not (len(__SCREAMING_SNAKE_CASE ) > 0):
    raise ValueError("""Must provide at least one input""" )

  __A		:     str												=		[shape[:no_batch_dims] for shape in _fetch_dims(__SCREAMING_SNAKE_CASE )]
  __A		:     Any												=		tuple([max(__SCREAMING_SNAKE_CASE ) for s in zip(*__SCREAMING_SNAKE_CASE )] )

  def _prep_inputs(__SCREAMING_SNAKE_CASE						:  torch.Tensor ) -> torch.Tensor:
    if not low_mem:
      if not sum(t.shape[:no_batch_dims] ) == no_batch_dims:
        __A		:     Optional[Any]												=		t.expand(orig_batch_dims + t.shape[no_batch_dims:] )
      __A		:     Dict												=		t.reshape(-1			,     *t.shape[no_batch_dims:] )
    else:
      __A		:     str												=		t.expand(orig_batch_dims + t.shape[no_batch_dims:] )
    return t

  __A		:     Dict[str, Any]												=		tensor_tree_map(_prep_inputs			,     __SCREAMING_SNAKE_CASE )
  __A		:     List[str]												=		None
  if _out is not None:
    __A		:     Dict												=		tensor_tree_map(lambda __SCREAMING_SNAKE_CASE : t.view([-1] + list(t.shape[no_batch_dims:] ) )			,     _out )

  __A		:     Any												=		1
  for d in orig_batch_dims:
    flat_batch_dim *= d

  __A		:     Union[str, Any]												=		flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

  def _select_chunk(__SCREAMING_SNAKE_CASE						:  torch.Tensor ) -> torch.Tensor:
    return t[i : i + chunk_size] if t.shape[0] != 1 else t

  __A		:     str												=		0
  __A		:     str												=		prepped_outputs
  for _ in range(__SCREAMING_SNAKE_CASE ):
    # Chunk the input
    if not low_mem:
      __A		:     List[str]												=		_select_chunk
    else:
      __A		:     Optional[int]												=		partial(
          _chunk_slice			,     flat_start=__SCREAMING_SNAKE_CASE			,     flat_end=min(__SCREAMING_SNAKE_CASE			,     i + chunk_size )			,     no_batch_dims=len(__SCREAMING_SNAKE_CASE )			,     )

    __A		:     Dict[str, Any]												=		tensor_tree_map(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )

    # Run the layer on the chunk
    __A		:     List[Any]												=		layer(**__SCREAMING_SNAKE_CASE )

    # Allocate space for the output
    if out is None:
      __A		:     str												=		tensor_tree_map(lambda __SCREAMING_SNAKE_CASE : t.new_zeros((flat_batch_dim,) + t.shape[1:] )			,     __SCREAMING_SNAKE_CASE )

    # Put the chunk in its pre-allocated space
    if isinstance(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):

      def assign(__SCREAMING_SNAKE_CASE						:  dict			,     __SCREAMING_SNAKE_CASE						:  dict ) -> None:
        for k, v in da.items():
          if isinstance(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):
            assign(__SCREAMING_SNAKE_CASE			,     da[k] )
          else:
            if _add_into_out:
              v[i : i + chunk_size] += da[k]
            else:
              __A		:     int												=		da[k]

      assign(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE )
    elif isinstance(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):
      for xa, xa in zip(__SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE ):
        if _add_into_out:
          xa[i : i + chunk_size] += xa
        else:
          __A		:     int												=		xa
    elif isinstance(__SCREAMING_SNAKE_CASE			,     torch.Tensor ):
      if _add_into_out:
        out[i : i + chunk_size] += output_chunk
      else:
        __A		:     int												=		output_chunk
    else:
      raise ValueError("""Not supported""" )

    i += chunk_size

  __A		:     Optional[Any]												=		tensor_tree_map(lambda __SCREAMING_SNAKE_CASE : t.view(orig_batch_dims + t.shape[1:] )			,     __SCREAMING_SNAKE_CASE )

  return out







class  __A				:
 def __init__(   self			:    Any				,   lowerCamelCase			:    int = 5_12				,   ):



   """simple docstring"""





   __A		:     Optional[Any]												=		max_chunk_size
   __A		:     Optional[int]												=		None
   __A		:     Optional[tuple]												=		None
 def 		lowercase_(   self			:    Union[str, Any]				,   lowerCamelCase			:    Callable				,   lowerCamelCase			:    tuple				,   lowerCamelCase			:    int       ):



   """simple docstring"""





   logging.info("""Tuning chunk size..."""       )

   if min_chunk_size >= self.max_chunk_size:
     return min_chunk_size

   __A		:     List[int]												=		[2**l for l in range(int(math.log(self.max_chunk_size				,   2       )       ) + 1       )]
   __A		:     List[str]												=		[c for c in candidates if c > min_chunk_size]
   __A		:     List[str]												=		[min_chunk_size] + candidates
   candidates[-1] += 4

   def test_chunk_size(lowerCamelCase			:    int       ) -> bool:
     try:
       with torch.no_grad():
         fn(*lowerCamelCase				,   chunk_size=lowerCamelCase       )
       return True
     except RuntimeError:
       return False

   __A		:     str												=		0
   __A		:     List[str]												=		len(lowerCamelCase       ) - 1
   while i > min_viable_chunk_size_index:
     __A		:     Optional[Any]												=		test_chunk_size(candidates[i]       )
     if not viable:
       __A		:     Optional[int]												=		(min_viable_chunk_size_index + i) // 2
     else:
       __A		:     Optional[Any]												=		i
       __A		:     Optional[Any]												=		(i + len(lowerCamelCase       ) - 1) // 2

   return candidates[min_viable_chunk_size_index]
 def 		lowercase_(   self			:    Dict				,   lowerCamelCase			:    Iterable				,   lowerCamelCase			:    Iterable       ):



   """simple docstring"""





   __A		:     Optional[int]												=		True
   for aa, aa in zip(lowerCamelCase				,   lowerCamelCase       ):
     assert type(lowerCamelCase       ) == type(lowerCamelCase       )
     if isinstance(lowerCamelCase				,   (list, tuple)       ):
       consistent &= self._compare_arg_caches(lowerCamelCase				,   lowerCamelCase       )
     elif isinstance(lowerCamelCase				,   lowerCamelCase       ):
       __A		:     Dict												=		[v for _, v in sorted(aa.items()				,   key=lambda lowerCamelCase       : x[0]       )]
       __A		:     Any												=		[v for _, v in sorted(aa.items()				,   key=lambda lowerCamelCase       : x[0]       )]
       consistent &= self._compare_arg_caches(lowerCamelCase				,   lowerCamelCase       )
     else:
       consistent &= aa == aa

   return consistent






 def 		lowercase_(   self			:    Optional[int]				,   lowerCamelCase			:    Callable				,   lowerCamelCase			:    tuple				,   lowerCamelCase			:    int				,   ):



   """simple docstring"""





   __A		:     str												=		True
   __A		:     tuple												=		tree_map(lambda lowerCamelCase       : a.shape if isinstance(lowerCamelCase				,   torch.Tensor       ) else a				,   lowerCamelCase				,   lowerCamelCase       )
   if self.cached_arg_data is not None:
     # If args have changed shape/value, we need to re-tune
     assert len(self.cached_arg_data       ) == len(lowerCamelCase       )
     __A		:     Optional[Any]												=		self._compare_arg_caches(self.cached_arg_data				,   lowerCamelCase       )
   else:
     # Otherwise, we can reuse the precomputed value
     __A		:     List[str]												=		False

   if not consistent:
     __A		:     List[Any]												=		self._determine_favorable_chunk_size(
         lowerCamelCase				,   lowerCamelCase				,   lowerCamelCase				,   )
     __A		:     Optional[int]												=		arg_data

   assert self.cached_chunk_size is not None

   return self.cached_chunk_size



