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







  """simple docstring"""





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

  return shapes



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







  """simple docstring"""





  SCREAMING_SNAKE_CASE__										=      []
  for d in reversed(__UpperCamelCase	):
    idx.append(flat_idx % d	)
    SCREAMING_SNAKE_CASE__										=      flat_idx // d

  return tuple(reversed(__UpperCamelCase	)	)



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







  """simple docstring"""





  def reduce_edge_list(__UpperCamelCase    :       List[bool]	) -> None:
    SCREAMING_SNAKE_CASE__										=      True
    for i in range(len(__UpperCamelCase	)	):
      SCREAMING_SNAKE_CASE__										=      -1 * (i + 1)
      l[reversed_idx] &= tally
      SCREAMING_SNAKE_CASE__										=      l[reversed_idx]

  if start_edges is None:
    SCREAMING_SNAKE_CASE__										=      [s == 0 for s in start]
    reduce_edge_list(__UpperCamelCase	)
  if end_edges is None:
    SCREAMING_SNAKE_CASE__										=      [e == (d - 1) for e, d in zip(__UpperCamelCase ,     __UpperCamelCase	)]
    reduce_edge_list(__UpperCamelCase	)

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

  SCREAMING_SNAKE_CASE__										=      []
  SCREAMING_SNAKE_CASE__										=      []

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

  SCREAMING_SNAKE_CASE__										=      tuple(__UpperCamelCase	)
  SCREAMING_SNAKE_CASE__										=      len(__UpperCamelCase	)

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

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

    SCREAMING_SNAKE_CASE__										=      start[divergence_idx]
    return tuple(
        path + (slice(__UpperCamelCase ,     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

    SCREAMING_SNAKE_CASE__										=      end[divergence_idx]
    return tuple(
        path + (slice(__UpperCamelCase ,     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()	)
    SCREAMING_SNAKE_CASE__										=      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 	__SCREAMING_SNAKE_CASE  (					__UpperCamelCase    :       torch.Tensor ,     __UpperCamelCase    :       int ,     __UpperCamelCase    :       int ,     __UpperCamelCase    :       int	)							->					torch.Tensor:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__										=      t.shape[:no_batch_dims]
  SCREAMING_SNAKE_CASE__										=      list(_flat_idx_to_idx(__UpperCamelCase ,     __UpperCamelCase	)	)
  # _get_minimal_slice_set is inclusive
  SCREAMING_SNAKE_CASE__										=      list(_flat_idx_to_idx(flat_end - 1 ,     __UpperCamelCase	)	)

  # Get an ordered list of slices to perform
  SCREAMING_SNAKE_CASE__										=      _get_minimal_slice_set(
      __UpperCamelCase ,     __UpperCamelCase ,     __UpperCamelCase ,     )

  SCREAMING_SNAKE_CASE__										=      [t[s] for s in slices]

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



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







  """simple docstring"""





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

  SCREAMING_SNAKE_CASE__										=      [shape[:no_batch_dims] for shape in _fetch_dims(__UpperCamelCase	)]
  SCREAMING_SNAKE_CASE__										=      tuple([max(__UpperCamelCase	) for s in zip(*__UpperCamelCase	)]	)

  def _prep_inputs(__UpperCamelCase    :       torch.Tensor	) -> torch.Tensor:
    if not low_mem:
      if not sum(t.shape[:no_batch_dims]	) == no_batch_dims:
        SCREAMING_SNAKE_CASE__										=      t.expand(orig_batch_dims + t.shape[no_batch_dims:]	)
      SCREAMING_SNAKE_CASE__										=      t.reshape(-1 ,     *t.shape[no_batch_dims:]	)
    else:
      SCREAMING_SNAKE_CASE__										=      t.expand(orig_batch_dims + t.shape[no_batch_dims:]	)
    return t

  SCREAMING_SNAKE_CASE__										=      tensor_tree_map(_prep_inputs ,     __UpperCamelCase	)
  SCREAMING_SNAKE_CASE__										=      None
  if _out is not None:
    SCREAMING_SNAKE_CASE__										=      tensor_tree_map(lambda __UpperCamelCase	: t.view([-1] + list(t.shape[no_batch_dims:]	)	) ,     _out	)

  SCREAMING_SNAKE_CASE__										=      1
  for d in orig_batch_dims:
    flat_batch_dim *= d

  SCREAMING_SNAKE_CASE__										=      flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

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

  SCREAMING_SNAKE_CASE__										=      0
  SCREAMING_SNAKE_CASE__										=      prepped_outputs
  for _ in range(__UpperCamelCase	):
    # Chunk the input
    if not low_mem:
      SCREAMING_SNAKE_CASE__										=      _select_chunk
    else:
      SCREAMING_SNAKE_CASE__										=      partial(
          _chunk_slice ,     flat_start=__UpperCamelCase ,     flat_end=min(__UpperCamelCase ,     i + chunk_size	) ,     no_batch_dims=len(__UpperCamelCase	) ,     )

    SCREAMING_SNAKE_CASE__										=      tensor_tree_map(__UpperCamelCase ,     __UpperCamelCase	)

    # Run the layer on the chunk
    SCREAMING_SNAKE_CASE__										=      layer(**__UpperCamelCase	)

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

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

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

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

    i += chunk_size

  SCREAMING_SNAKE_CASE__										=      tensor_tree_map(lambda __UpperCamelCase	: t.view(orig_batch_dims + t.shape[1:]	) ,     __UpperCamelCase	)

  return out







class __snake_case				:




   def __init__(    self			:				Optional[Any]       ,	_lowercase			:				int = 5_12       ,	):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      max_chunk_size
     SCREAMING_SNAKE_CASE__										=      None
     SCREAMING_SNAKE_CASE__										=      None




   def 	__a						(    self			:				Tuple       ,	_lowercase			:				Callable       ,	_lowercase			:				tuple       ,	_lowercase			:				int      ):



     """simple docstring"""






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

     if min_chunk_size >= self.max_chunk_size:
       return min_chunk_size

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

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

     SCREAMING_SNAKE_CASE__										=      0
     SCREAMING_SNAKE_CASE__										=      len(_lowercase      ) - 1
     while i > min_viable_chunk_size_index:
       SCREAMING_SNAKE_CASE__										=      test_chunk_size(candidates[i]      )
       if not viable:
         SCREAMING_SNAKE_CASE__										=      (min_viable_chunk_size_index + i) // 2
       else:
         SCREAMING_SNAKE_CASE__										=      i
         SCREAMING_SNAKE_CASE__										=      (i + len(_lowercase      ) - 1) // 2

     return candidates[min_viable_chunk_size_index]




   def 	__a						(    self			:				Dict       ,	_lowercase			:				Iterable       ,	_lowercase			:				Iterable      ):



     """simple docstring"""






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

     return consistent




   def 	__a						(    self			:				Dict       ,	_lowercase			:				Callable       ,	_lowercase			:				tuple       ,	_lowercase			:				int       ,	):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      True
     SCREAMING_SNAKE_CASE__										=      tree_map(lambda _lowercase      : a.shape if isinstance(_lowercase       ,	torch.Tensor      ) else a       ,	_lowercase       ,	_lowercase      )
     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(_lowercase      )
       SCREAMING_SNAKE_CASE__										=      self._compare_arg_caches(self.cached_arg_data       ,	_lowercase      )
     else:
       # Otherwise, we can reuse the precomputed value
       SCREAMING_SNAKE_CASE__										=      False

     if not consistent:
       SCREAMING_SNAKE_CASE__										=      self._determine_favorable_chunk_size(
           _lowercase       ,	_lowercase       ,	_lowercase       ,	)
       SCREAMING_SNAKE_CASE__										=      arg_data

     assert self.cached_chunk_size is not None

     return self.cached_chunk_size

import doctest
from collections import deque

import numpy as np







class __snake_case				:




   def __init__(    self			:				Dict      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      [2, 1, 2, -1]
     SCREAMING_SNAKE_CASE__										=      [1, 2, 3, 4]




   def 	__a						(    self			:				int      ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__										=      len(self.first_signal      )
     SCREAMING_SNAKE_CASE__										=      len(self.second_signal      )

     SCREAMING_SNAKE_CASE__										=      max(_lowercase       ,	_lowercase      )

     # create a zero matrix of max_length x max_length
     SCREAMING_SNAKE_CASE__										=      [[0] * max_length for i in range(_lowercase      )]

     # fills the smaller signal with zeros to make both signals of same length
     if length_first_signal < length_second_signal:
       self.first_signal += [0] * (max_length - length_first_signal)
     elif length_first_signal > length_second_signal:
       self.second_signal += [0] * (max_length - length_second_signal)
     for i in range(_lowercase      ):
       SCREAMING_SNAKE_CASE__										=      deque(self.second_signal      )
       rotated_signal.rotate(_lowercase      )
       for j, item in enumerate(_lowercase      ):
         matrix[i][j] += item

        # multiply the matrix with the first signal
     SCREAMING_SNAKE_CASE__										=      np.matmul(np.transpose(_lowercase      )       ,	np.transpose(self.first_signal      )      )

     # rounding-off to two decimal places
     return [round(_lowercase       ,	2      ) for i in final_signal]


if __name__ == "__main__":
   doctest.testmod()
