

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__	(  lowerCamelCase__      )  ->					List[Tuple[int, ...]]:
	__lowerCamelCase    :    List[Any] 	=			[]
	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        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__      )  ->					Tuple[int, ...]:
	__lowerCamelCase    :    Optional[Any] 	=			[]
	for d in reversed(lowerCamelCase__      ):
		idx.append(flat_idx % d      )
		__lowerCamelCase    :    List[str] 	=			flat_idx // d

	return tuple(reversed(lowerCamelCase__      )      )






@torch.jit.ignore
def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__ = None     ,			lowerCamelCase__ = 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__      ) -> None:
		__lowerCamelCase    :    List[Any] 	=			True
		for i in range(len(lowerCamelCase__      )      ):
			__lowerCamelCase    :    Dict 	=			-1 * (i + 1)
			l[reversed_idx] &= tally
			__lowerCamelCase    :    int 	=			l[reversed_idx]

	if start_edges is None:
		__lowerCamelCase    :    int 	=			[s == 0 for s in start]
		reduce_edge_list(lowerCamelCase__      )
	if end_edges is None:
		__lowerCamelCase    :    List[Any] 	=			[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      ),)]

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

	__lowerCamelCase    :    Tuple[slice, ...] 	=			tuple(lowerCamelCase__      )
	__lowerCamelCase    :    Dict 	=			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

		__lowerCamelCase    :    str 	=			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

		__lowerCamelCase    :    Optional[Any] 	=			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()      )
		__lowerCamelCase    :    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        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__      )  ->					torch.Tensor:
	__lowerCamelCase    :    str 	=			t.shape[:no_batch_dims]
	__lowerCamelCase    :    Optional[int] 	=			list(_flat_idx_to_idx(lowerCamelCase__     ,			lowerCamelCase__      )      )
	# _get_minimal_slice_set is inclusive
	__lowerCamelCase    :    int 	=			list(_flat_idx_to_idx(flat_end - 1     ,			lowerCamelCase__      )      )

	# Get an ordered list of slices to perform
	__lowerCamelCase    :    Optional[int] 	=			_get_minimal_slice_set(
	    lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)

	__lowerCamelCase    :    Optional[Any] 	=			[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__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__ = False     ,			lowerCamelCase__ = None     ,			lowerCamelCase__ = False     ,			)  ->					Any:
	if not (len(lowerCamelCase__      ) > 0):
		raise ValueError('Must provide at least one input'      )

	__lowerCamelCase    :    Tuple 	=			[shape[:no_batch_dims] for shape in _fetch_dims(lowerCamelCase__      )]
	__lowerCamelCase    :    Optional[Any] 	=			tuple([max(lowerCamelCase__      ) for s in zip(*lowerCamelCase__      )]      )

	def _prep_inputs(lowerCamelCase__      ) -> torch.Tensor:
		if not low_mem:
			if not sum(t.shape[:no_batch_dims]      ) == no_batch_dims:
				__lowerCamelCase    :    int 	=			t.expand(orig_batch_dims + t.shape[no_batch_dims:]      )
			__lowerCamelCase    :    Optional[int] 	=			t.reshape(-1     ,			*t.shape[no_batch_dims:]      )
		else:
			__lowerCamelCase    :    List[Any] 	=			t.expand(orig_batch_dims + t.shape[no_batch_dims:]      )
		return t

	__lowerCamelCase    :    Dict[str, Any] 	=			tensor_tree_map(_prep_inputs     ,			lowerCamelCase__      )
	__lowerCamelCase    :    Union[str, Any] 	=			None
	if _out is not None:
		__lowerCamelCase    :    Optional[int] 	=			tensor_tree_map(lambda lowerCamelCase__      : t.view([-1] + list(t.shape[no_batch_dims:]      )      )     ,			_out      )

	__lowerCamelCase    :    int 	=			1
	for d in orig_batch_dims:
		flat_batch_dim *= d

	__lowerCamelCase    :    Any 	=			flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

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

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

		__lowerCamelCase    :    Dict[str, Any] 	=			tensor_tree_map(lowerCamelCase__     ,			lowerCamelCase__      )

		# Run the layer on the chunk
		__lowerCamelCase    :    str 	=			layer(**lowerCamelCase__      )

		# Allocate space for the output
		if out is None:
			__lowerCamelCase    :    str 	=			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__     ,			lowerCamelCase__      ) -> 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:
							__lowerCamelCase    :    Optional[int] 	=			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:
					__lowerCamelCase    :    Optional[int] 	=			xa
		elif isinstance(lowerCamelCase__     ,			torch.Tensor      ):
			if _add_into_out:
				out[i : i + chunk_size] += output_chunk
			else:
				__lowerCamelCase    :    str 	=			output_chunk
		else:
			raise ValueError('Not supported'      )

		i += chunk_size

	__lowerCamelCase    :    str 	=			tensor_tree_map(lambda lowerCamelCase__      : t.view(orig_batch_dims + t.shape[1:]      )     ,			lowerCamelCase__      )

	return out






class 	A_		:
							def __init__(		self		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      int = 5_1_2       ,):
								__lowerCamelCase    :    Dict 	=			max_chunk_size
								__lowerCamelCase    :    Optional[int] 	=			None
								__lowerCamelCase    :    Optional[tuple] 	=			None
							def    lowerCAmelCase					(		self		:      Dict       ,SCREAMING_SNAKE_CASE__		:      Callable       ,SCREAMING_SNAKE_CASE__		:      tuple       ,SCREAMING_SNAKE_CASE__		:      int):
								logging.info('Tuning chunk size...')

								if min_chunk_size >= self.max_chunk_size:
									return min_chunk_size

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

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

								__lowerCamelCase    :    Union[str, Any] 	=			0
								__lowerCamelCase    :    Optional[int] 	=			len(SCREAMING_SNAKE_CASE__) - 1
								while i > min_viable_chunk_size_index:
									__lowerCamelCase    :    Optional[int] 	=			test_chunk_size(candidates[i])
									if not viable:
										__lowerCamelCase    :    Tuple 	=			(min_viable_chunk_size_index + i) // 2
									else:
										__lowerCamelCase    :    Dict 	=			i
										__lowerCamelCase    :    Optional[Any] 	=			(i + len(SCREAMING_SNAKE_CASE__) - 1) // 2

								return candidates[min_viable_chunk_size_index]
							def    lowerCAmelCase					(		self		:      Optional[int]       ,SCREAMING_SNAKE_CASE__		:      Iterable       ,SCREAMING_SNAKE_CASE__		:      Iterable):
								__lowerCamelCase    :    List[Any] 	=			True
								for aa, aa in zip(SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__):
									assert type(SCREAMING_SNAKE_CASE__) == type(SCREAMING_SNAKE_CASE__)
									if isinstance(SCREAMING_SNAKE_CASE__       ,(list, tuple)):
										consistent &= self._compare_arg_caches(SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__)
									elif isinstance(SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__):
										__lowerCamelCase    :    int 	=			[v for _, v in sorted(aa.items()       ,key=lambda SCREAMING_SNAKE_CASE__: x[0])]
										__lowerCamelCase    :    str 	=			[v for _, v in sorted(aa.items()       ,key=lambda SCREAMING_SNAKE_CASE__: x[0])]
										consistent &= self._compare_arg_caches(SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__)
									else:
										consistent &= aa == aa

								return consistent


							def    lowerCAmelCase					(		self		:      Any       ,SCREAMING_SNAKE_CASE__		:      Callable       ,SCREAMING_SNAKE_CASE__		:      tuple       ,SCREAMING_SNAKE_CASE__		:      int       ,):
								__lowerCamelCase    :    int 	=			True
								__lowerCamelCase    :    tuple 	=			tree_map(lambda SCREAMING_SNAKE_CASE__: a.shape if isinstance(SCREAMING_SNAKE_CASE__       ,torch.Tensor) else a       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__)
								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(SCREAMING_SNAKE_CASE__)
									__lowerCamelCase    :    Optional[int] 	=			self._compare_arg_caches(self.cached_arg_data       ,SCREAMING_SNAKE_CASE__)
								else:
									# Otherwise, we can reuse the precomputed value
									__lowerCamelCase    :    int 	=			False

								if not consistent:
									__lowerCamelCase    :    List[str] 	=			self._determine_favorable_chunk_size(
									    SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,)
									__lowerCamelCase    :    Optional[int] 	=			arg_data

								assert self.cached_chunk_size is not None

								return self.cached_chunk_size







from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					List[Any]:

	# A local function to see if a dot lands in the circle.
	def is_in_circle(lowerCamelCase__     ,			lowerCamelCase__      ) -> bool:
		__lowerCamelCase    :    Dict 	=			sqrt((x**2) + (y**2)      )
		# Our circle has a radius of 1, so a distance
		# greater than 1 would land outside the circle.
		return distance_from_centre <= 1

	# The proportion of guesses that landed in the circle
	__lowerCamelCase    :    Optional[int] 	=			mean(
	    int(is_in_circle(uniform(-1.0     ,			1.0      )     ,			uniform(-1.0     ,			1.0      )      )      )
	    for _ in range(lowerCamelCase__      )      )
	# The ratio of the area for circle to square is pi/4.
	__lowerCamelCase    :    Any 	=			proportion * 4
	print(F"The estimated value of pi is {pi_estimate}"      )
	print(F"The numpy value of pi is {pi}"      )
	print(F"The total error is {abs(pi - pi_estimate      )}"      )






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__ = 0.0     ,			lowerCamelCase__ = 1.0     ,			)  ->					float:
	return mean(
	    function_to_integrate(uniform(lowerCamelCase__     ,			lowerCamelCase__      )      ) for _ in range(lowerCamelCase__      )      ) * (max_value - min_value)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__ = 0.0     ,			lowerCamelCase__ = 1.0      )  ->					None:

	def identity_function(lowerCamelCase__      ) -> float:
		return x

	__lowerCamelCase    :    str 	=			area_under_curve_estimator(
	    lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__      )
	__lowerCamelCase    :    int 	=			(max_value * max_value - min_value * min_value) / 2

	print('******************'      )
	print(F"Estimating area under y=x where x varies from {min_value} to {max_value}"      )
	print(F"Estimated value is {estimated_value}"      )
	print(F"Expected value is {expected_value}"      )
	print(F"Total error is {abs(estimated_value - expected_value      )}"      )
	print('******************'      )






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					None:

	def function_to_integrate(lowerCamelCase__      ) -> float:
		return sqrt(4.0 - x * x      )

	__lowerCamelCase    :    Any 	=			area_under_curve_estimator(
	    lowerCamelCase__     ,			lowerCamelCase__     ,			0.0     ,			2.0      )

	print('******************'      )
	print('Estimating pi using area_under_curve_estimator'      )
	print(F"Estimated value is {estimated_value}"      )
	print(F"Expected value is {pi}"      )
	print(F"Total error is {abs(estimated_value - pi      )}"      )
	print('******************'      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()




