




'''simple docstring'''







import numpy as np






def 						_lowercase						(      lowercase_    ):



		'''simple docstring'''







		_snake_case			,       _snake_case      			=			a.shape
		_snake_case      			=			min(lowercase_		,				lowercase_    )
		_snake_case      			=			np.eye(lowercase_    )
		_snake_case      			=			a.copy()

		for k in range(t - 1    ):
				# select a column of modified matrix A':
				_snake_case      			=			r[k:, [k]]
				# construct first basis vector
				_snake_case      			=			np.zeros_like(lowercase_    )
				_snake_case      			=			1.0
				# determine scaling factor
				_snake_case      			=			np.linalg.norm(lowercase_    )
				# construct vector v for Householder reflection
				_snake_case      			=			x + np.sign(x[0]    ) * alpha * ea
				v /= np.linalg.norm(lowercase_    )

				# construct the Householder matrix
				_snake_case      			=			np.eye(m - k    ) - 2.0 * v @ v.T
				# pad with ones and zeros as necessary
				_snake_case      			=			np.block([[np.eye(lowercase_    ), np.zeros((k, m - k)    )], [np.zeros((m - k, k)    ), q_k]]    )

				_snake_case      			=			q @ q_k.T
				_snake_case      			=			q_k @ r

		return q, r


if __name__ == "__main__":
						import doctest

						doctest.testmod()











'''simple docstring'''







import enum
import inspect
from typing import Iterable, List, Optional, Tuple, Union





class 	lowerCamelCase_				(			enum.Enum				):




					'''simple docstring'''






					lowercase__       =					"""timm"""
					lowercase__       =					"""transformers"""






def 						_lowercase						(      lowercase_		,				lowercase_		,				lowercase_    ):



		'''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(lowercase_		,				(list,)    ):
						raise ValueError(f'''out_features must be a list {type(lowercase_    )}'''    )
				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(lowercase_		,				(list, tuple)    ):
						raise ValueError(f'''out_indices must be a list or tuple, got {type(lowercase_    )}'''    )
				if any(idx >= len(lowercase_    ) 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(lowercase_    ) != len(lowercase_    ):
						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 						_lowercase						(      lowercase_		,				lowercase_		,				lowercase_		,				):



		'''simple docstring'''







		if out_indices is None and out_features is None:
				_snake_case      			=			[len(lowercase_    ) - 1]
				_snake_case      			=			[stage_names[-1]]
		elif out_indices is None and out_features is not None:
				_snake_case      			=			[stage_names.index(lowercase_    ) 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 						_lowercase						(      lowercase_		,				lowercase_		,				lowercase_		,				):



		'''simple docstring'''







		verify_out_features_out_indices(out_features=lowercase_		,				out_indices=lowercase_		,				stage_names=lowercase_    )
		_snake_case			,       _snake_case      			=			_align_output_features_output_indices(
		    out_features=lowercase_		,				out_indices=lowercase_		,				stage_names=lowercase_    )
		# Verify that the aligned out_features and out_indices are valid
		verify_out_features_out_indices(out_features=lowercase_		,				out_indices=lowercase_		,				stage_names=lowercase_    )
		return output_features, output_indices





class 	lowerCamelCase_				:




					'''simple docstring'''






					lowercase__       =					None






					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							if getattr(self,    "_backbone",    __UpperCamelCase					) 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=__UpperCamelCase,    out_indices=__UpperCamelCase,    stage_names=self.stage_names					)
							_snake_case			,       _snake_case      			=			out_features, out_indices






					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							_snake_case      			=			getattr(__UpperCamelCase,    "stage_names"					)
							_snake_case      			=			getattr(__UpperCamelCase,    "out_features",    __UpperCamelCase					)
							_snake_case      			=			getattr(__UpperCamelCase,    "out_indices",    __UpperCamelCase					)

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






					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							_snake_case      			=			config

							_snake_case      			=			getattr(__UpperCamelCase,    "use_timm_backbone",    __UpperCamelCase					)
							_snake_case      			=			BackboneType.TIMM if self.use_timm_backbone else BackboneType.TRANSFORMERS

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






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return self._out_features






					@out_features.setter
					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							_snake_case			,       _snake_case      			=			get_aligned_output_features_output_indices(
							    out_features=__UpperCamelCase,    out_indices=__UpperCamelCase,    stage_names=self.stage_names					)






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return self._out_indices






					@out_indices.setter
					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							_snake_case			,       _snake_case      			=			get_aligned_output_features_output_indices(
							    out_features=__UpperCamelCase,    out_indices=__UpperCamelCase,    stage_names=self.stage_names					)






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							# 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 							__SCREAMING_SNAKE_CASE      (       self					):
							return [self.out_feature_channels[name] for name in self.out_features]






					def 							__SCREAMING_SNAKE_CASE      (       self,    *__UpperCamelCase,    **__UpperCamelCase					):
							_snake_case      			=			dict(inspect.signature(self.forward					).parameters					)
							_snake_case      			=			{k: v for k, v in kwargs.items() if k in signature}
							return self(*__UpperCamelCase,    **__UpperCamelCase					)






					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase,    __UpperCamelCase = None,    __UpperCamelCase = None,    __UpperCamelCase = None,    ):
							raise NotImplementedError("This method should be implemented by the derived class."					)






					def 							__SCREAMING_SNAKE_CASE      (       self					):
							_snake_case      			=			super().to_dict()
							_snake_case      			=			output.pop("_out_features"					)
							_snake_case      			=			output.pop("_out_indices"					)
							return output





class 	lowerCamelCase_				:




					'''simple docstring'''






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return self._out_features






					@out_features.setter
					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							_snake_case			,       _snake_case      			=			get_aligned_output_features_output_indices(
							    out_features=__UpperCamelCase,    out_indices=__UpperCamelCase,    stage_names=self.stage_names					)






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return self._out_indices






					@out_indices.setter
					def 							__SCREAMING_SNAKE_CASE      (       self,    __UpperCamelCase					):
							_snake_case			,       _snake_case      			=			get_aligned_output_features_output_indices(
							    out_features=__UpperCamelCase,    out_indices=__UpperCamelCase,    stage_names=self.stage_names					)






					def 							__SCREAMING_SNAKE_CASE      (       self					):
							_snake_case      			=			super().to_dict()
							_snake_case      			=			output.pop("_out_features"					)
							_snake_case      			=			output.pop("_out_indices"					)
							return output





