





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     lowerCamelCase_	(      lowerCAmelCase:	Union[dict, list, tuple, torch.Tensor]				)->		List[Tuple[int, ...]]:
  _snake_case   :				Dict														=	[]
  if isinstance(lowerCAmelCase    ,							lowerCAmelCase				):
    for v in tree.values():
      shapes.extend(_fetch_dims(lowerCAmelCase				)				)
  elif isinstance(lowerCAmelCase    ,							(list, tuple)				):
    for t in tree:
      shapes.extend(_fetch_dims(lowerCAmelCase				)				)
  elif isinstance(lowerCAmelCase    ,							torch.Tensor				):
    shapes.append(tree.shape				)
  else:
    raise ValueError('Not supported'				)

  return shapes


@torch.jit.ignore
def     lowerCamelCase_	(      lowerCAmelCase:	int    ,							lowerCAmelCase:	Tuple[int, ...]				)->		Tuple[int, ...]:
  _snake_case   :				Any														=	[]
  for d in reversed(lowerCAmelCase				):
    idx.append(flat_idx % d				)
    _snake_case   :				Optional[Any]														=	flat_idx // d

  return tuple(reversed(lowerCAmelCase				)				)


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

  # start_edges and end_edges both indicate whether, starting from any given
  # dimension, the start/end index is at the top/bottom edge of the
  # corresponding tensor, modeled as a tree
  def reduce_edge_list(lowerCAmelCase:	List[bool]				) -> None:
    _snake_case   :				List[str]														=	True
    for i in range(len(lowerCAmelCase				)				):
      _snake_case   :				List[Any]														=	-1 * (i + 1)
      l[reversed_idx] &= tally
      _snake_case   :				Tuple														=	l[reversed_idx]

  if start_edges is None:
    _snake_case   :				Union[str, Any]														=	[s == 0 for s in start]
    reduce_edge_list(lowerCAmelCase				)
  if end_edges is None:
    _snake_case   :				int														=	[e == (d - 1) for e, d in zip(lowerCAmelCase    ,							lowerCAmelCase				)]
    reduce_edge_list(lowerCAmelCase				)

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

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

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

  _snake_case   :				Tuple[slice, ...]														=	tuple(lowerCAmelCase				)
  _snake_case   :				Union[str, Any]														=	len(lowerCAmelCase				)

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

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

    _snake_case   :				Tuple														=	start[divergence_idx]
    return tuple(
        path + (slice(lowerCAmelCase    ,							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

    _snake_case   :				List[str]														=	end[divergence_idx]
    return tuple(
        path + (slice(lowerCAmelCase    ,							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()				)
    _snake_case   :				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     lowerCamelCase_	(      lowerCAmelCase:	torch.Tensor    ,							lowerCAmelCase:	int    ,							lowerCAmelCase:	int    ,							lowerCAmelCase:	int				)->		torch.Tensor:
  _snake_case   :				int														=	t.shape[:no_batch_dims]
  _snake_case   :				str														=	list(_flat_idx_to_idx(lowerCAmelCase    ,							lowerCAmelCase				)				)
  # _get_minimal_slice_set is inclusive
  _snake_case   :				List[str]														=	list(_flat_idx_to_idx(flat_end - 1    ,							lowerCAmelCase				)				)

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

  _snake_case   :				str														=	[t[s] for s in slices]

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


def     lowerCamelCase_	(      lowerCAmelCase:	Callable    ,							lowerCAmelCase:	Dict[str, Any]    ,							lowerCAmelCase:	int    ,							lowerCAmelCase:	int    ,							lowerCAmelCase:	bool = False    ,							lowerCAmelCase:	Any = None    ,							lowerCAmelCase:	bool = False    ,							)->		Any:
  if not (len(lowerCAmelCase				) > 0):
    raise ValueError('Must provide at least one input'				)

  _snake_case   :				List[Any]														=	[shape[:no_batch_dims] for shape in _fetch_dims(lowerCAmelCase				)]
  _snake_case   :				Optional[int]														=	tuple([max(lowerCAmelCase				) for s in zip(*lowerCAmelCase				)]				)

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

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

  _snake_case   :				Optional[Any]														=	1
  for d in orig_batch_dims:
    flat_batch_dim *= d

  _snake_case   :				List[Any]														=	flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

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

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

    _snake_case   :				Dict[str, Any]														=	tensor_tree_map(lowerCAmelCase    ,							lowerCAmelCase				)

    # Run the layer on the chunk
    _snake_case   :				str														=	layer(**lowerCAmelCase				)

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

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

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

      assign(lowerCAmelCase    ,							lowerCAmelCase				)
    elif isinstance(lowerCAmelCase    ,							lowerCAmelCase				):
      for xa, xa in zip(lowerCAmelCase    ,							lowerCAmelCase				):
        if _add_into_out:
          xa[i : i + chunk_size] += xa
        else:
          _snake_case   :				Tuple														=	xa
    elif isinstance(lowerCAmelCase    ,							torch.Tensor				):
      if _add_into_out:
        out[i : i + chunk_size] += output_chunk
      else:
        _snake_case   :				str														=	output_chunk
    else:
      raise ValueError('Not supported'				)

    i += chunk_size

  _snake_case   :				int														=	tensor_tree_map(lambda lowerCAmelCase				: t.view(orig_batch_dims + t.shape[1:]				)    ,							lowerCAmelCase				)

  return out







class        _lowerCAmelCase    :


  '''simple docstring'''







  def __init__(      self      :					str      ,				UpperCamelCase      :					int = 5_12      ,				):


    '''simple docstring'''





    _snake_case   :				Dict														=	max_chunk_size
    _snake_case   :				Optional[int]														=	None
    _snake_case   :				Optional[tuple]														=	None







  def UpperCamelCase_ (      self      :					Optional[int]      ,				UpperCamelCase      :					Callable      ,				UpperCamelCase      :					tuple      ,				UpperCamelCase      :					int							):


    '''simple docstring'''





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

    if min_chunk_size >= self.max_chunk_size:
      return min_chunk_size

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

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

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

    return candidates[min_viable_chunk_size_index]







  def UpperCamelCase_ (      self      :					Tuple      ,				UpperCamelCase      :					Iterable      ,				UpperCamelCase      :					Iterable							):


    '''simple docstring'''





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

    return consistent







  def UpperCamelCase_ (      self      :					Optional[Any]      ,				UpperCamelCase      :					Callable      ,				UpperCamelCase      :					tuple      ,				UpperCamelCase      :					int      ,				):


    '''simple docstring'''





    _snake_case   :				int														=	True
    _snake_case   :				tuple														=	tree_map(lambda UpperCamelCase							: a.shape if isinstance(UpperCamelCase      ,				torch.Tensor							) else a      ,				UpperCamelCase      ,				UpperCamelCase							)
    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(UpperCamelCase							)
      _snake_case   :				Tuple														=	self._compare_arg_caches(self.cached_arg_data      ,				UpperCamelCase							)
    else:
      # Otherwise, we can reuse the precomputed value
      _snake_case   :				Dict														=	False

    if not consistent:
      _snake_case   :				Optional[int]														=	self._determine_favorable_chunk_size(
          UpperCamelCase      ,				UpperCamelCase      ,				UpperCamelCase      ,				)
      _snake_case   :				Any														=	arg_data

    assert self.cached_chunk_size is not None

    return self.cached_chunk_size











import math
import random
from typing import Any

from .hill_climbing import SearchProblem


def     lowerCamelCase_	(      lowerCAmelCase:	Tuple    ,							lowerCAmelCase:	bool = True    ,							lowerCAmelCase:	float = math.inf    ,							lowerCAmelCase:	float = -math.inf    ,							lowerCAmelCase:	float = math.inf    ,							lowerCAmelCase:	float = -math.inf    ,							lowerCAmelCase:	bool = False    ,							lowerCAmelCase:	float = 1_00    ,							lowerCAmelCase:	float = 0.0_1    ,							lowerCAmelCase:	float = 1    ,							)->		Any:
  _snake_case   :				int														=	False
  _snake_case   :				Any														=	search_prob
  _snake_case   :				Tuple														=	start_temperate
  _snake_case   :				Any														=	[]
  _snake_case   :				List[str]														=	0
  _snake_case   :				Optional[Any]														=	None

  while not search_end:
    _snake_case   :				List[Any]														=	current_state.score()
    if best_state is None or current_score > best_state.score():
      _snake_case   :				Dict														=	current_state
    scores.append(lowerCAmelCase				)
    iterations += 1
    _snake_case   :				Optional[int]														=	None
    _snake_case   :				Union[str, Any]														=	current_state.get_neighbors()
    while (
        next_state is None and neighbors
    ):  # till we do not find a neighbor that we can move to
      _snake_case   :				Dict														=	random.randint(0    ,							len(lowerCAmelCase				) - 1				)  # picking a random neighbor
      _snake_case   :				int														=	neighbors.pop(lowerCAmelCase				)
      _snake_case   :				Union[str, Any]														=	picked_neighbor.score() - current_score

      if (
          picked_neighbor.x > max_x
          or picked_neighbor.x < min_x
          or picked_neighbor.y > max_y
          or picked_neighbor.y < min_y
      ):
        continue  # neighbor outside our bounds

      if not find_max:
        _snake_case   :				Union[str, Any]														=	change * -1  # in case we are finding minimum
      if change > 0:  # improves the solution
        _snake_case   :				Union[str, Any]														=	picked_neighbor
      else:
        _snake_case   :				Optional[Any]														=	(math.e) ** (
            change / current_temp
        )  # probability generation function
        if random.random() < probability:  # random number within probability
          _snake_case   :				int														=	picked_neighbor
    _snake_case   :				List[Any]														=	current_temp - (current_temp * rate_of_decrease)

    if current_temp < threshold_temp or next_state is None:
      # temperature below threshold, or could not find a suitable neighbor
      _snake_case   :				List[str]														=	True
    else:
      _snake_case   :				Union[str, Any]														=	next_state

  if visualization:
    from matplotlib import pyplot as plt

    plt.plot(range(lowerCAmelCase				)    ,							lowerCAmelCase				)
    plt.xlabel('Iterations'				)
    plt.ylabel('Function values'				)
    plt.show()
  return best_state


if __name__ == "__main__":


      def     lowerCamelCase_	(      lowerCAmelCase:	Any    ,							lowerCAmelCase:	List[Any]				)->		List[Any]:
        return (x**2) + (y**2)

      # starting the problem with initial coordinates (12, 47)
      lowerCAmelCase_						   =    SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
      lowerCAmelCase_						   =    simulated_annealing(
          prob, find_max=False, max_x=100, min_x=5, max_y=50, min_y=-5, visualization=True
      )
      print(
          """The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
          F"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
      )

      # starting the problem with initial coordinates (12, 47)
      lowerCAmelCase_						   =    SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
      lowerCAmelCase_						   =    simulated_annealing(
          prob, find_max=True, max_x=100, min_x=5, max_y=50, min_y=-5, visualization=True
      )
      print(
          """The maximum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
          F"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
      )


      def     lowerCamelCase_	(      lowerCAmelCase:	Any    ,							lowerCAmelCase:	Dict				)->		Dict:
        return (3 * x**2) - (6 * y)

      lowerCAmelCase_						   =    SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
      lowerCAmelCase_						   =    simulated_annealing(prob, find_max=False, visualization=True)
      print(
          """The minimum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: """
          F"""{local_min.score()}"""
      )

      lowerCAmelCase_						   =    SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
      lowerCAmelCase_						   =    simulated_annealing(prob, find_max=True, visualization=True)







      print(
          """The maximum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: """
          F"""{local_min.score()}"""
      )




