





import enum
import inspect
from typing import Iterable, List, Optional, Tuple, Union
class       UpperCamelCase_		(	enum.Enum       ):
					lowerCAmelCase_				=						'''timm'''
					lowerCAmelCase_				=						'''transformers'''





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[Iterable[str]]							,     UpperCamelCase__      :							Optional[Iterable[int]]							,     UpperCamelCase__      :							Optional[Iterable[str]]    )      ->			Optional[int]:



					'''simple docstring'''




					if stage_names is None:
										raise ValueError('Stage_names must be set for transformers backbones'    )

					if out_features is not None:
										if not isinstance(UpperCamelCase__							,     (list,)    ):
															raise ValueError(F'''out_features must be a list {type(UpperCamelCase__    )}'''    )
										if any(feat not in stage_names for feat in out_features    ):
															raise ValueError(F'''out_features must be a subset of stage_names: {stage_names} got {out_features}'''    )

					if out_indices is not None:
										if not isinstance(UpperCamelCase__							,     (list, tuple)    ):
															raise ValueError(F'''out_indices must be a list or tuple, got {type(UpperCamelCase__    )}'''    )
										if any(idx >= len(UpperCamelCase__    ) for idx in out_indices    ):
															raise ValueError('out_indices must be valid indices for stage_names {stage_names}, got {out_indices}'    )

					if out_features is not None and out_indices is not None:
										if len(UpperCamelCase__    ) != len(UpperCamelCase__    ):
															raise ValueError('out_features and out_indices should have the same length if both are set'    )
										if out_features != [stage_names[idx] for idx in out_indices]:
															raise ValueError('out_features and out_indices should correspond to the same stages if both are set'    )





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[List[str]]							,     UpperCamelCase__      :							Optional[Union[List[int], Tuple[int]]]							,     UpperCamelCase__      :							List[str]							,     )      ->			str:



					'''simple docstring'''




					if out_indices is None and out_features is None:
										_snake_case						=					[len(UpperCamelCase__    ) - 1]
										_snake_case						=					[stage_names[-1]]
					elif out_indices is None and out_features is not None:
										_snake_case						=					[stage_names.index(UpperCamelCase__    ) for layer in out_features]
					elif out_features is None and out_indices is not None:
										_snake_case						=					[stage_names[idx] for idx in out_indices]
					return out_features, out_indices





def     lowerCamelCase__  (  UpperCamelCase__      :							Optional[List[str]]							,     UpperCamelCase__      :							Optional[Union[List[int], Tuple[int]]]							,     UpperCamelCase__      :							List[str]							,     )      ->			Tuple[List[str], List[int]]:



					'''simple docstring'''




					verify_out_features_out_indices(out_features=UpperCamelCase__							,     out_indices=UpperCamelCase__							,     stage_names=UpperCamelCase__    )
					_snake_case				,  _snake_case						=					_align_output_features_output_indices(
					    out_features=UpperCamelCase__							,     out_indices=UpperCamelCase__							,     stage_names=UpperCamelCase__    )
					# Verify that the aligned out_features and out_indices are valid
					verify_out_features_out_indices(out_features=UpperCamelCase__							,     out_indices=UpperCamelCase__							,     stage_names=UpperCamelCase__    )
					return output_features, output_indices
class       UpperCamelCase_		:
					lowerCAmelCase_				=						None




					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				None:
										if getattr(self					,    '_backbone'					,    lowerCAmelCase_	) is None:
															raise ValueError('self._backbone must be set before calling _init_timm_backbone'	)

										# These will diagree with the defaults for the transformers models e.g. for resnet50
										# the transformer model has out_features = ['stem', 'stage1', 'stage2', 'stage3', 'stage4']
										# the timm model has out_features = ['act', 'layer1', 'layer2', 'layer3', 'layer4']
										_snake_case						=					[stage['module'] for stage in self._backbone.feature_info.info]
										_snake_case						=					[stage['num_chs'] for stage in self._backbone.feature_info.info]
										_snake_case						=					self._backbone.feature_info.out_indices
										_snake_case						=					self._backbone.feature_info.module_name()

										# We verify the out indices and out features are valid
										verify_out_features_out_indices(
										    out_features=lowerCAmelCase_					,    out_indices=lowerCAmelCase_					,    stage_names=self.stage_names	)
										_snake_case				,  _snake_case						=					out_features, out_indices




					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				None:
										_snake_case						=					getattr(lowerCAmelCase_					,    'stage_names'	)
										_snake_case						=					getattr(lowerCAmelCase_					,    'out_features'					,    lowerCAmelCase_	)
										_snake_case						=					getattr(lowerCAmelCase_					,    'out_indices'					,    lowerCAmelCase_	)

										_snake_case						=					stage_names
										_snake_case				,  _snake_case						=					get_aligned_output_features_output_indices(
										    out_features=lowerCAmelCase_					,    out_indices=lowerCAmelCase_					,    stage_names=lowerCAmelCase_	)
										# Number of channels for each stage. This is set in the transformer backbone model init
										_snake_case						=					None




					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				None:
										_snake_case						=					config

										_snake_case						=					getattr(lowerCAmelCase_					,    'use_timm_backbone'					,    lowerCAmelCase_	)
										_snake_case						=					BackboneType.TIMM if self.use_timm_backbone else BackboneType.TRANSFORMERS

										if self.backbone_type == BackboneType.TIMM:
															self._init_timm_backbone(lowerCAmelCase_	)
										elif self.backbone_type == BackboneType.TRANSFORMERS:
															self._init_transformers_backbone(lowerCAmelCase_	)
										else:
															raise ValueError(F'''backbone_type {self.backbone_type} not supported.'''	)




					@property
					def 						lowerCAmelCase      (		self	)		->				List[str]:
										return self._out_features




					@out_features.setter
					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				Tuple:
										_snake_case				,  _snake_case						=					get_aligned_output_features_output_indices(
										    out_features=lowerCAmelCase_					,    out_indices=lowerCAmelCase_					,    stage_names=self.stage_names	)




					@property
					def 						lowerCAmelCase      (		self	)		->				Optional[int]:
										return self._out_indices




					@out_indices.setter
					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				str:
										_snake_case				,  _snake_case						=					get_aligned_output_features_output_indices(
										    out_features=lowerCAmelCase_					,    out_indices=lowerCAmelCase_					,    stage_names=self.stage_names	)




					@property
					def 						lowerCAmelCase      (		self	)		->				Optional[int]:
										# the current backbones will output the number of channels for each stage
										# even if that stage is not in the out_features list.
										return {stage: self.num_features[i] for i, stage in enumerate(self.stage_names	)}




					@property
					def 						lowerCAmelCase      (		self	)		->				Union[str, Any]:
										return [self.out_feature_channels[name] for name in self.out_features]




					def 						lowerCAmelCase      (		self					,    *lowerCAmelCase_					,    **lowerCAmelCase_	)		->				int:
										_snake_case						=					dict(inspect.signature(self.forward	).parameters	)
										_snake_case						=					{k: v for k, v in kwargs.items() if k in signature}
										return self(*lowerCAmelCase_					,    **lowerCAmelCase_	)




					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_					,    lowerCAmelCase_ = None					,    lowerCAmelCase_ = None					,    lowerCAmelCase_ = None					,    )		->				Union[str, Any]:
										raise NotImplementedError('This method should be implemented by the derived class.'	)






					def 						lowerCAmelCase      (		self	)		->				str:
										_snake_case						=					super().to_dict()
										_snake_case						=					output.pop('_out_features'	)
										_snake_case						=					output.pop('_out_indices'	)
										return output





class       UpperCamelCase_		:




					@property
					def 						lowerCAmelCase      (		self	)		->				int:
										return self._out_features




					@out_features.setter
					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				List[Any]:
										_snake_case				,  _snake_case						=					get_aligned_output_features_output_indices(
										    out_features=lowerCAmelCase_					,    out_indices=lowerCAmelCase_					,    stage_names=self.stage_names	)




					@property
					def 						lowerCAmelCase      (		self	)		->				Optional[int]:
										return self._out_indices




					@out_indices.setter
					def 						lowerCAmelCase      (		self					,    lowerCAmelCase_	)		->				Tuple:
										_snake_case				,  _snake_case						=					get_aligned_output_features_output_indices(
										    out_features=lowerCAmelCase_					,    out_indices=lowerCAmelCase_					,    stage_names=self.stage_names	)






					def 						lowerCAmelCase      (		self	)		->				Optional[Any]:
										_snake_case						=					super().to_dict()
										_snake_case						=					output.pop('_out_features'	)
										_snake_case						=					output.pop('_out_indices'	)
										return output










from typing import Any

import numpy as np





def     lowerCamelCase__  (  UpperCamelCase__      :							np.ndarray    )      ->			bool:



					'''simple docstring'''




					assert np.shape(UpperCamelCase__    )[0] == np.shape(UpperCamelCase__    )[1]

					# If matrix not symmetric, exit right away.
					if np.allclose(UpperCamelCase__							,     matrix.T    ) is False:
										return False

					# Get eigenvalues and eignevectors for a symmetric matrix.
					_snake_case				,  _snake_case						=					np.linalg.eigh(UpperCamelCase__    )

					# Check sign of all eigenvalues.
					# np.all returns a value of type np.bool_
					return bool(np.all(eigen_values > 0    )    )





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			Any:



					'''simple docstring'''




					_snake_case						=					np.random.randn(UpperCamelCase__							,     UpperCamelCase__    )
					_snake_case						=					np.dot(UpperCamelCase__							,     random_matrix.T    )
					assert _is_matrix_spd(UpperCamelCase__    )
					return spd_matrix





def     lowerCamelCase__  (  UpperCamelCase__      :							np.ndarray							,     UpperCamelCase__      :							np.ndarray							,     UpperCamelCase__      :							int = 1_000							,     UpperCamelCase__      :							float = 1e-8							,     )      ->			Any:



					'''simple docstring'''




					assert np.shape(UpperCamelCase__    )[0] == np.shape(UpperCamelCase__    )[1]
					assert np.shape(UpperCamelCase__    )[0] == np.shape(UpperCamelCase__    )[0]
					assert _is_matrix_spd(UpperCamelCase__    )

					# Initialize solution guess, residual, search direction.
					_snake_case						=					np.zeros((np.shape(UpperCamelCase__    )[0], 1)    )
					_snake_case						=					np.copy(UpperCamelCase__    )
					_snake_case						=					np.copy(UpperCamelCase__    )

					# Set initial errors in solution guess and residual.
					_snake_case						=					1e9
					_snake_case						=					1e9
					_snake_case						=					1e9

					# Set iteration counter to threshold number of iterations.
					_snake_case						=					0

					while error > tol:
										# Save this value so we only calculate the matrix-vector product once.
										_snake_case						=					np.dot(UpperCamelCase__							,     UpperCamelCase__    )

										# The main algorithm.

										# Update search direction magnitude.
										_snake_case						=					np.dot(ra.T							,     UpperCamelCase__    ) / np.dot(pa.T							,     UpperCamelCase__    )
										# Update solution guess.
										_snake_case						=					xa + alpha * pa
										# Calculate new residual.
										_snake_case						=					ra - alpha * w
										# Calculate new Krylov subspace scale.
										_snake_case						=					np.dot(r.T							,     UpperCamelCase__    ) / np.dot(ra.T							,     UpperCamelCase__    )
										# Calculate new A conjuage search direction.
										_snake_case						=					r + beta * pa

										# Calculate errors.
										_snake_case						=					np.linalg.norm(r - ra    )
										_snake_case						=					np.linalg.norm(x - xa    )
										_snake_case						=					np.maximum(UpperCamelCase__							,     UpperCamelCase__    )

										# Update variables.
										_snake_case						=					np.copy(UpperCamelCase__    )
										_snake_case						=					np.copy(UpperCamelCase__    )
										_snake_case						=					np.copy(UpperCamelCase__    )

										# Update number of iterations.
										iterations += 1
										if iterations > max_iterations:
															break

					return x





def     lowerCamelCase__  (  )      ->			None:



					'''simple docstring'''




					_snake_case						=					3
					_snake_case						=					_create_spd_matrix(UpperCamelCase__    )
					_snake_case						=					np.random.randn(UpperCamelCase__							,     1    )
					_snake_case						=					np.dot(UpperCamelCase__							,     UpperCamelCase__    )

					# Numpy solution.
					_snake_case						=					np.linalg.solve(UpperCamelCase__							,     UpperCamelCase__    )

					# Our implementation.
					_snake_case						=					conjugate_gradient(UpperCamelCase__							,     UpperCamelCase__    )

					# Ensure both solutions are close to x_true (and therefore one another).
					assert np.linalg.norm(x_numpy - x_true    ) <= 1e-6
					assert np.linalg.norm(x_conjugate_gradient - x_true    ) <= 1e-6


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					test_conjugate_gradient()



