

"""simple docstring"""




from typing import TYPE_CHECKING

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


__A	:       List[str]        =						{
    'configuration_xlm_prophetnet': ['XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP', 'XLMProphetNetConfig'],
}

try:
	if not is_sentencepiece_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__A	:       int        =						['XLMProphetNetTokenizer']

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__A	:       List[Any]        =						[
	    'XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST',
	    'XLMProphetNetDecoder',
	    'XLMProphetNetEncoder',
	    'XLMProphetNetForCausalLM',
	    'XLMProphetNetForConditionalGeneration',
	    'XLMProphetNetModel',
	    'XLMProphetNetPreTrainedModel',
	]


if TYPE_CHECKING:
	from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

	try:
		if not is_sentencepiece_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_xlm_prophetnet import (
		    XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
		    XLMProphetNetDecoder,
		    XLMProphetNetEncoder,
		    XLMProphetNetForCausalLM,
		    XLMProphetNetForConditionalGeneration,
		    XLMProphetNetModel,
		    XLMProphetNetPreTrainedModel,
		)

else:
	import sys

	__A	:       List[str]        =						_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)











'''simple docstring'''
import numpy as np
def 							snake_case_    (  a__						:      Tuple     ):



    """simple docstring"""




    __lowercase							,__lowercase     							=		a.shape
    __lowercase     							=		min(a__       ,a__     )
    __lowercase     							=		np.eye(a__     )
    __lowercase     							=		a.copy()

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

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

        __lowercase     							=		q @ q_k.T
        __lowercase     							=		q_k @ r

    return q, r


if __name__ == "__main__":
  import doctest

  doctest.testmod()




