
'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


lowercase__						=		{
    "configuration_flava": [
        "FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "FlavaConfig",
        "FlavaImageCodebookConfig",
        "FlavaImageConfig",
        "FlavaMultimodalConfig",
        "FlavaTextConfig",
    ],
}

try:
						if not is_vision_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						=		["FlavaFeatureExtractor"]
						lowercase__						=		["FlavaImageProcessor"]
						lowercase__						=		["FlavaProcessor"]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						=		[
						    "FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "FlavaForPreTraining",
						    "FlavaImageCodebook",
						    "FlavaImageModel",
						    "FlavaModel",
						    "FlavaMultimodalModel",
						    "FlavaPreTrainedModel",
						    "FlavaTextModel",
						]

if TYPE_CHECKING:
						from .configuration_flava import (
						    FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP,
						    FlavaConfig,
						    FlavaImageCodebookConfig,
						    FlavaImageConfig,
						    FlavaMultimodalConfig,
						    FlavaTextConfig,
						)

						try:
												if not is_vision_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .feature_extraction_flava import FlavaFeatureExtractor
												from .image_processing_flava import FlavaImageProcessor
												from .processing_flava import FlavaProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flava import (
												    FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST,
												    FlavaForPreTraining,
												    FlavaImageCodebook,
												    FlavaImageModel,
												    FlavaModel,
												    FlavaMultimodalModel,
												    FlavaPreTrainedModel,
												    FlavaTextModel,
												)

else:
						import sys

						lowercase__						=		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




'''simple docstring'''
import numpy as np




def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__ )     ->       Optional[Any]:


		'''simple docstring'''


		snake_case ,snake_case     :					str     =	a.shape
		snake_case     :					Union[str, Any]     =	min(SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__ )
		snake_case     :					List[Any]     =	np.eye(SCREAMING_SNAKE_CASE__ )
		snake_case     :					Union[str, Any]     =	a.copy()

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

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

				snake_case     :					int     =	q @ q_k.T
				snake_case     :					Dict     =	q_k @ r

		return q, r


if __name__ == "__main__":
						import doctest

						doctest.testmod()


