
"""simple docstring"""






import numpy as np






def 		_snake_case			(      lowercase__						:    Dict						)    ->							List[str]:


			'''simple docstring'''





			lowerCAmelCase_	,			lowerCAmelCase_       :List[Any]     	=    a.shape
			lowerCAmelCase_       :Union[str, Any]     	=    min(lowercase__ ,	lowercase__						)
			lowerCAmelCase_       :Union[str, Any]     	=    np.eye(lowercase__						)
			lowerCAmelCase_       :int     	=    a.copy()

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

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

						lowerCAmelCase_       :Union[str, Any]     	=    q @ q_k.T
						lowerCAmelCase_       :List[str]     	=    q_k @ r

			return q, r


if __name__ == "__main__":
				import doctest

				doctest.testmod()








"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


__UpperCAmelCase 					=    {
    'configuration_marian': ['MARIAN_PRETRAINED_CONFIG_ARCHIVE_MAP', 'MarianConfig', 'MarianOnnxConfig'],
}

try:
				if not is_sentencepiece_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase 					=    ['MarianTokenizer']

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase 					=    [
				    'MARIAN_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'MarianForCausalLM',
				    'MarianModel',
				    'MarianMTModel',
				    'MarianPreTrainedModel',
				]

try:
				if not is_tf_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase 					=    ['TFMarianModel', 'TFMarianMTModel', 'TFMarianPreTrainedModel']

try:
				if not is_flax_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase 					=    ['FlaxMarianModel', 'FlaxMarianMTModel', 'FlaxMarianPreTrainedModel']

if TYPE_CHECKING:
				from .configuration_marian import MARIAN_PRETRAINED_CONFIG_ARCHIVE_MAP, MarianConfig, MarianOnnxConfig

				try:
								if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_marian import MarianTokenizer

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_marian import (
								    MARIAN_PRETRAINED_MODEL_ARCHIVE_LIST,
								    MarianForCausalLM,
								    MarianModel,
								    MarianMTModel,
								    MarianPreTrainedModel,
								)

				try:
								if not is_tf_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_tf_marian import TFMarianModel, TFMarianMTModel, TFMarianPreTrainedModel

				try:
								if not is_flax_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_flax_marian import FlaxMarianModel, FlaxMarianMTModel, FlaxMarianPreTrainedModel

else:
				import sys

				__UpperCAmelCase 					=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)






