
'''simple docstring'''
import unittest

import numpy as np
import timeout_decorator  # noqa

from transformers import MBartConfig, is_flax_available
from transformers.testing_utils import require_flax, require_sentencepiece, require_tokenizers, slow
from transformers.utils import cached_property

from ...generation.test_flax_utils import FlaxGenerationTesterMixin
from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor


if is_flax_available():
						import os

						# The slow tests are often failing with OOM error on GPU
						# This makes JAX allocate exactly what is needed on demand, and deallocate memory that is no longer needed
						# but will be slower as stated here https://jax.readthedocs.io/en/latest/gpu_memory_allocation.html
						lowercase__						=			"platform"

						import jax
						import jax.numpy as jnp

						from transformers import AutoTokenizer
						from transformers.models.mbart.modeling_flax_mbart import (
						    FlaxMBartForConditionalGeneration,
						    FlaxMBartForQuestionAnswering,
						    FlaxMBartForSequenceClassification,
						    FlaxMBartModel,
						    shift_tokens_right,
						)




def       _UpperCamelCase	(					SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__   ,					SCREAMING_SNAKE_CASE__=None   ,					SCREAMING_SNAKE_CASE__=None   ,					SCREAMING_SNAKE_CASE__=None   ,					SCREAMING_SNAKE_CASE__=None   ,					SCREAMING_SNAKE_CASE__=None   ,					SCREAMING_SNAKE_CASE__=None   ,					)     ->       Dict:


		'''simple docstring'''


		if attention_mask is None:
				snake_case     :					Union[str, Any]     =	np.where(input_ids != config.pad_token_id   ,					1   ,					0 )
		if decoder_attention_mask is None:
				snake_case     :					str     =	np.where(decoder_input_ids != config.pad_token_id   ,					1   ,					0 )
		if head_mask is None:
				snake_case     :					int     =	np.ones((config.encoder_layers, config.encoder_attention_heads) )
		if decoder_head_mask is None:
				snake_case     :					Optional[Any]     =	np.ones((config.decoder_layers, config.decoder_attention_heads) )
		if cross_attn_head_mask is None:
				snake_case     :					Any     =	np.ones((config.decoder_layers, config.decoder_attention_heads) )
		return {
		    "input_ids": input_ids,
		    "decoder_input_ids": decoder_input_ids,
		    "attention_mask": attention_mask,
		    "decoder_attention_mask": decoder_attention_mask,
		}






class   snake_case__					(			unittest.TestCase				):







		"""simple docstring"""

		def __init__(			self							: List[Any]     ,  UpperCamelCase__							: Union[str, Any]     ,  UpperCamelCase__							: Union[str, Any]=13     ,  UpperCamelCase__							: str=7     ,  UpperCamelCase__							: Tuple=True     ,  UpperCamelCase__							: List[str]=False     ,  UpperCamelCase__							: Optional[int]=99     ,  UpperCamelCase__							: Optional[Any]=16     ,  UpperCamelCase__							: int=2     ,  UpperCamelCase__							: Any=4     ,  UpperCamelCase__							: Tuple=4     ,  UpperCamelCase__							: List[Any]="gelu"     ,  UpperCamelCase__							: Tuple=0.1     ,  UpperCamelCase__							: List[str]=0.1     ,  UpperCamelCase__							: int=32     ,  UpperCamelCase__							: Union[str, Any]=2     ,  UpperCamelCase__							: Optional[int]=1     ,  UpperCamelCase__							: Dict=0     ,  UpperCamelCase__							: Dict=2     ,  UpperCamelCase__							: List[str]=0.02     ,  )	-> List[str]:






				"""simple docstring"""







				snake_case     :					Union[str, Any]     =	parent
				snake_case     :					int     =	batch_size
				snake_case     :					Optional[int]     =	seq_length
				snake_case     :					Optional[Any]     =	is_training
				snake_case     :					Dict     =	use_labels
				snake_case     :					Dict     =	vocab_size
				snake_case     :					List[str]     =	hidden_size
				snake_case     :					int     =	num_hidden_layers
				snake_case     :					Optional[Any]     =	num_attention_heads
				snake_case     :					Dict     =	intermediate_size
				snake_case     :					Tuple     =	hidden_act
				snake_case     :					Dict     =	hidden_dropout_prob
				snake_case     :					List[Any]     =	attention_probs_dropout_prob
				snake_case     :					Optional[Any]     =	max_position_embeddings
				snake_case     :					List[Any]     =	eos_token_id
				snake_case     :					Union[str, Any]     =	pad_token_id
				snake_case     :					int     =	bos_token_id
				snake_case     :					str     =	decoder_start_token_id
				snake_case     :					Union[str, Any]     =	initializer_range



		def 			lowerCAmelCase							(			self							: Optional[Any]			)	-> Tuple:






				"""simple docstring"""







				snake_case     :					str     =	np.clip(ids_tensor([self.batch_size, self.seq_length - 1]     ,  self.vocab_size			)     ,  3     ,  self.vocab_size			)
				snake_case     :					str     =	np.concatenate((input_ids, 2 * np.ones((self.batch_size, 1)     ,  dtype=np.intaa			))     ,  -1			)

				snake_case     :					Optional[Any]     =	shift_tokens_right(UpperCamelCase__     ,  1			)

				snake_case     :					str     =	MBartConfig(
				    vocab_size=self.vocab_size     ,  d_model=self.hidden_size     ,  encoder_layers=self.num_hidden_layers     ,  decoder_layers=self.num_hidden_layers     ,  encoder_attention_heads=self.num_attention_heads     ,  decoder_attention_heads=self.num_attention_heads     ,  encoder_ffn_dim=self.intermediate_size     ,  decoder_ffn_dim=self.intermediate_size     ,  dropout=self.hidden_dropout_prob     ,  attention_dropout=self.attention_probs_dropout_prob     ,  max_position_embeddings=self.max_position_embeddings     ,  eos_token_id=self.eos_token_id     ,  bos_token_id=self.bos_token_id     ,  pad_token_id=self.pad_token_id     ,  decoder_start_token_id=self.decoder_start_token_id     ,  initializer_range=self.initializer_range     ,  use_cache=UpperCamelCase__     ,  )
				snake_case     :					List[Any]     =	prepare_mbart_inputs_dict(UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__			)
				return config, inputs_dict



		def 			lowerCAmelCase							(			self							: List[str]			)	-> int:






				"""simple docstring"""







				snake_case ,snake_case     :					int     =	self.prepare_config_and_inputs()
				return config, inputs_dict



		def 			lowerCAmelCase							(			self							: List[str]     ,  UpperCamelCase__							: List[Any]     ,  UpperCamelCase__							: Dict     ,  UpperCamelCase__							: List[str]			)	-> int:






				"""simple docstring"""







				snake_case     :					Tuple     =	20
				snake_case     :					Optional[Any]     =	model_class_name(UpperCamelCase__			)

				snake_case     :					str     =	model.encode(inputs_dict['''input_ids''']			)

				snake_case ,snake_case     :					Any     =	(
				    inputs_dict['''decoder_input_ids'''],
				    inputs_dict['''decoder_attention_mask'''],
				)

				snake_case     :					Optional[int]     =	model.init_cache(decoder_input_ids.shape[0]     ,  UpperCamelCase__     ,  UpperCamelCase__			)
				snake_case     :					Optional[int]     =	jnp.ones((decoder_input_ids.shape[0], max_decoder_length)     ,  dtype='''i4'''			)

				snake_case     :					Optional[int]     =	jnp.broadcast_to(
				    jnp.arange(decoder_input_ids.shape[-1] - 1			)[None, :]     ,  (decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)     ,  )
				snake_case     :					Any     =	model.decode(
				    decoder_input_ids[:, :-1]     ,  UpperCamelCase__     ,  decoder_attention_mask=UpperCamelCase__     ,  past_key_values=UpperCamelCase__     ,  decoder_position_ids=UpperCamelCase__     ,  )

				snake_case     :					Union[str, Any]     =	jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]     ,  dtype='''i4'''			)
				snake_case     :					Optional[int]     =	model.decode(
				    decoder_input_ids[:, -1:]     ,  UpperCamelCase__     ,  decoder_attention_mask=UpperCamelCase__     ,  past_key_values=outputs_cache.past_key_values     ,  decoder_position_ids=UpperCamelCase__     ,  )

				snake_case     :					Optional[int]     =	model.decode(UpperCamelCase__     ,  UpperCamelCase__			)

				snake_case     :					Optional[Any]     =	np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])			)			)
				self.parent.assertTrue(diff < 1e-3     ,  msg=f'Max diff is {diff}'			)



		def 			lowerCAmelCase							(			self							: str     ,  UpperCamelCase__							: Union[str, Any]     ,  UpperCamelCase__							: Union[str, Any]     ,  UpperCamelCase__							: Optional[Any]			)	-> Dict:






				"""simple docstring"""







				snake_case     :					str     =	20
				snake_case     :					Dict     =	model_class_name(UpperCamelCase__			)

				snake_case     :					Dict     =	model.encode(inputs_dict['''input_ids''']			)

				snake_case ,snake_case     :					int     =	(
				    inputs_dict['''decoder_input_ids'''],
				    inputs_dict['''decoder_attention_mask'''],
				)

				snake_case     :					List[Any]     =	jnp.concatenate(
				    [
				        decoder_attention_mask,
				        jnp.zeros((decoder_attention_mask.shape[0], max_decoder_length - decoder_attention_mask.shape[1])			),
				    ]     ,  axis=-1     ,  )

				snake_case     :					Optional[Any]     =	model.init_cache(decoder_input_ids.shape[0]     ,  UpperCamelCase__     ,  UpperCamelCase__			)
				snake_case     :					int     =	jnp.broadcast_to(
				    jnp.arange(decoder_input_ids.shape[-1] - 1			)[None, :]     ,  (decoder_input_ids.shape[0], decoder_input_ids.shape[-1] - 1)     ,  )

				snake_case     :					Optional[Any]     =	model.decode(
				    decoder_input_ids[:, :-1]     ,  UpperCamelCase__     ,  decoder_attention_mask=UpperCamelCase__     ,  past_key_values=UpperCamelCase__     ,  decoder_position_ids=UpperCamelCase__     ,  )
				snake_case     :					Optional[Any]     =	jnp.array(decoder_input_ids.shape[0] * [[decoder_input_ids.shape[-1] - 1]]     ,  dtype='''i4'''			)
				snake_case     :					List[str]     =	model.decode(
				    decoder_input_ids[:, -1:]     ,  UpperCamelCase__     ,  past_key_values=outputs_cache.past_key_values     ,  decoder_attention_mask=UpperCamelCase__     ,  decoder_position_ids=UpperCamelCase__     ,  )

				snake_case     :					List[str]     =	model.decode(UpperCamelCase__     ,  UpperCamelCase__     ,  decoder_attention_mask=UpperCamelCase__			)

				snake_case     :					Tuple     =	np.max(np.abs((outputs_cache_next[0][:, -1, :5] - outputs[0][:, -1, :5])			)			)
				self.parent.assertTrue(diff < 1e-3     ,  msg=f'Max diff is {diff}'			)







@require_flax
class   snake_case__					(			unittest.TestCase				):







		"""simple docstring"""

		lowerCamelCase           =	99



		def 			lowerCAmelCase							(			self							: Tuple			)	-> Union[str, Any]:






				"""simple docstring"""







				snake_case     :					List[Any]     =	np.array(
				    [
				        [71, 82, 18, 33, 46, 91, 2],
				        [68, 34, 26, 58, 30, 82, 2],
				        [5, 97, 17, 39, 94, 40, 2],
				        [76, 83, 94, 25, 70, 78, 2],
				        [87, 59, 41, 35, 48, 66, 2],
				        [55, 13, 16, 58, 5, 2, 1],  # note padding
				        [64, 27, 31, 51, 12, 75, 2],
				        [52, 64, 86, 17, 83, 39, 2],
				        [48, 61, 9, 24, 71, 82, 2],
				        [26, 1, 60, 48, 22, 13, 2],
				        [21, 5, 62, 28, 14, 76, 2],
				        [45, 98, 37, 86, 59, 48, 2],
				        [70, 70, 50, 9, 28, 0, 2],
				    ]     ,  dtype=np.intaa     ,  )

				snake_case     :					str     =	input_ids.shape[0]
				snake_case     :					Dict     =	MBartConfig(
				    vocab_size=self.vocab_size     ,  d_model=24     ,  encoder_layers=2     ,  decoder_layers=2     ,  encoder_attention_heads=2     ,  decoder_attention_heads=2     ,  encoder_ffn_dim=32     ,  decoder_ffn_dim=32     ,  max_position_embeddings=48     ,  eos_token_id=2     ,  pad_token_id=1     ,  bos_token_id=0     ,  )
				return config, input_ids, batch_size



		def 			lowerCAmelCase							(			self							: Optional[int]			)	-> Union[str, Any]:






				"""simple docstring"""







				snake_case ,snake_case ,snake_case     :					Optional[Any]     =	self._get_config_and_data()
				snake_case     :					List[Any]     =	FlaxMBartForSequenceClassification(UpperCamelCase__			)
				snake_case     :					Tuple     =	model(input_ids=UpperCamelCase__     ,  decoder_input_ids=UpperCamelCase__			)
				snake_case     :					Any     =	(batch_size, config.num_labels)
				self.assertEqual(outputs['''logits'''].shape     ,  UpperCamelCase__			)



		def 			lowerCAmelCase							(			self							: Optional[int]			)	-> List[Any]:






				"""simple docstring"""







				snake_case ,snake_case ,snake_case     :					Union[str, Any]     =	self._get_config_and_data()
				snake_case     :					List[str]     =	FlaxMBartForQuestionAnswering(UpperCamelCase__			)
				snake_case     :					Optional[int]     =	model(input_ids=UpperCamelCase__			)

				self.assertEqual(outputs['''start_logits'''].shape     ,  input_ids.shape			)
				self.assertEqual(outputs['''end_logits'''].shape     ,  input_ids.shape			)



		def 			lowerCAmelCase							(			self							: Any			)	-> Dict:






				"""simple docstring"""







				snake_case ,snake_case ,snake_case     :					List[Any]     =	self._get_config_and_data()
				snake_case     :					Any     =	FlaxMBartForConditionalGeneration(UpperCamelCase__			)
				snake_case     :					List[str]     =	lm_model(input_ids=UpperCamelCase__			)
				snake_case     :					int     =	(batch_size, input_ids.shape[1], config.vocab_size)
				self.assertEqual(outputs['''logits'''].shape     ,  UpperCamelCase__			)



		def 			lowerCAmelCase							(			self							: Optional[Any]			)	-> List[Any]:






				"""simple docstring"""







				snake_case     :					int     =	MBartConfig(
				    vocab_size=self.vocab_size     ,  d_model=14     ,  encoder_layers=2     ,  decoder_layers=2     ,  encoder_attention_heads=2     ,  decoder_attention_heads=2     ,  encoder_ffn_dim=8     ,  decoder_ffn_dim=8     ,  max_position_embeddings=48     ,  )
				snake_case     :					Optional[int]     =	FlaxMBartForConditionalGeneration(UpperCamelCase__			)
				snake_case     :					Tuple     =	np.array([[71, 82, 18, 33, 46, 91, 2], [68, 34, 26, 58, 30, 2, 1]]     ,  dtype=np.intaa			)
				snake_case     :					Any     =	np.array([[82, 71, 82, 18, 2], [58, 68, 2, 1, 1]]     ,  dtype=np.intaa			)
				snake_case     :					int     =	lm_model(input_ids=UpperCamelCase__     ,  decoder_input_ids=UpperCamelCase__			)
				snake_case     :					List[str]     =	(*summary.shape, config.vocab_size)
				self.assertEqual(outputs['''logits'''].shape     ,  UpperCamelCase__			)



		def 			lowerCAmelCase							(			self							: str			)	-> List[str]:






				"""simple docstring"""







				snake_case     :					Optional[int]     =	np.array([[71, 82, 18, 33, 2, 1, 1], [68, 34, 26, 58, 30, 82, 2]]     ,  dtype=np.intaa			)
				snake_case     :					Union[str, Any]     =	shift_tokens_right(UpperCamelCase__     ,  1			)
				snake_case     :					Any     =	np.equal(UpperCamelCase__     ,  1			).astype(np.floataa			).sum()
				snake_case     :					Tuple     =	np.equal(UpperCamelCase__     ,  1			).astype(np.floataa			).sum()
				self.assertEqual(shifted.shape     ,  input_ids.shape			)
				self.assertEqual(UpperCamelCase__     ,  n_pad_before - 1			)
				self.assertTrue(np.equal(shifted[:, 0]     ,  2			).all()			)







@require_flax
class   snake_case__					(			__SCREAMING_SNAKE_CASE						,				unittest.TestCase						,				__SCREAMING_SNAKE_CASE				):







		"""simple docstring"""

		lowerCamelCase           =	True
		lowerCamelCase           =	(
		    (
		        FlaxMBartModel,
		        FlaxMBartForConditionalGeneration,
		        FlaxMBartForSequenceClassification,
		        FlaxMBartForQuestionAnswering,
		    )
		    if is_flax_available()
		    else ()
		)
		lowerCamelCase           =	(FlaxMBartForConditionalGeneration,) if is_flax_available() else ()



		def 			lowerCAmelCase							(			self							: List[Any]			)	-> Optional[Any]:






				"""simple docstring"""







				snake_case     :					Dict     =	FlaxMBartModelTester(self			)



		def 			lowerCAmelCase							(			self							: Dict			)	-> List[str]:






				"""simple docstring"""







				snake_case ,snake_case     :					str     =	self.model_tester.prepare_config_and_inputs()
				for model_class in self.all_model_classes:
						self.model_tester.check_use_cache_forward(UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__			)



		def 			lowerCAmelCase							(			self							: Any			)	-> List[str]:






				"""simple docstring"""







				snake_case ,snake_case     :					Optional[Any]     =	self.model_tester.prepare_config_and_inputs()
				for model_class in self.all_model_classes:
						self.model_tester.check_use_cache_forward_with_attn_mask(UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__			)



		def 			lowerCAmelCase							(			self							: List[Any]			)	-> Tuple:






				"""simple docstring"""







				snake_case ,snake_case     :					Optional[int]     =	self.model_tester.prepare_config_and_inputs_for_common()

				for model_class in self.all_model_classes:
						with self.subTest(model_class.__name__			):
								snake_case     :					Tuple     =	self._prepare_for_class(UpperCamelCase__     ,  UpperCamelCase__			)
								snake_case     :					Optional[int]     =	model_class(UpperCamelCase__			)

								@jax.jit
								def encode_jitted(UpperCamelCase__							: List[Any]     ,  UpperCamelCase__							: Tuple=None     ,  **UpperCamelCase__							: List[Any]			):
										return model.encode(input_ids=UpperCamelCase__     ,  attention_mask=UpperCamelCase__			)

								with self.subTest('''JIT Enabled'''			):
										snake_case     :					str     =	encode_jitted(**UpperCamelCase__			).to_tuple()

								with self.subTest('''JIT Disabled'''			):
										with jax.disable_jit():
												snake_case     :					int     =	encode_jitted(**UpperCamelCase__			).to_tuple()

								self.assertEqual(len(UpperCamelCase__			)     ,  len(UpperCamelCase__			)			)
								for jitted_output, output in zip(UpperCamelCase__     ,  UpperCamelCase__			):
										self.assertEqual(jitted_output.shape     ,  output.shape			)



		def 			lowerCAmelCase							(			self							: Any			)	-> Union[str, Any]:






				"""simple docstring"""







				snake_case ,snake_case     :					int     =	self.model_tester.prepare_config_and_inputs_for_common()

				for model_class in self.all_model_classes:
						with self.subTest(model_class.__name__			):
								snake_case     :					Tuple     =	model_class(UpperCamelCase__			)
								snake_case     :					Any     =	model.encode(inputs_dict['''input_ids''']     ,  inputs_dict['''attention_mask''']			)

								snake_case     :					List[Any]     =	{
								    '''decoder_input_ids''': inputs_dict['''decoder_input_ids'''],
								    '''decoder_attention_mask''': inputs_dict['''decoder_attention_mask'''],
								    '''encoder_outputs''': encoder_outputs,
								}

								@jax.jit
								def decode_jitted(UpperCamelCase__							: Tuple     ,  UpperCamelCase__							: List[str]     ,  UpperCamelCase__							: List[Any]			):
										return model.decode(
										    decoder_input_ids=UpperCamelCase__     ,  decoder_attention_mask=UpperCamelCase__     ,  encoder_outputs=UpperCamelCase__     ,  )

								with self.subTest('''JIT Enabled'''			):
										snake_case     :					List[str]     =	decode_jitted(**UpperCamelCase__			).to_tuple()

								with self.subTest('''JIT Disabled'''			):
										with jax.disable_jit():
												snake_case     :					Dict     =	decode_jitted(**UpperCamelCase__			).to_tuple()

								self.assertEqual(len(UpperCamelCase__			)     ,  len(UpperCamelCase__			)			)
								for jitted_output, output in zip(UpperCamelCase__     ,  UpperCamelCase__			):
										self.assertEqual(jitted_output.shape     ,  output.shape			)



		@slow
		def 			lowerCAmelCase							(			self							: List[str]			)	-> Union[str, Any]:






				"""simple docstring"""







				for model_class_name in self.all_model_classes:
						snake_case     :					int     =	model_class_name.from_pretrained('''facebook/mbart-large-cc25'''     ,  from_pt=UpperCamelCase__			)
						# FlaxMBartForSequenceClassification expects eos token in input_ids
						snake_case     :					Tuple     =	np.ones((1, 1)			) * model.config.eos_token_id
						snake_case     :					List[Any]     =	model(UpperCamelCase__			)
						self.assertIsNotNone(UpperCamelCase__			)







@require_flax
@require_sentencepiece
@require_tokenizers
class   snake_case__					(			unittest.TestCase				):







		"""simple docstring"""

		lowerCamelCase           =	[
		    """ UN Chief Says There Is No Military Solution in Syria""",
		]
		lowerCamelCase           =	[
		    """Şeful ONU declară că nu există o soluţie militară în Siria""",
		]
		lowerCamelCase           =	"""facebook/mbart-large-en-ro"""



		@cached_property
		def 			lowerCAmelCase							(			self							: Dict			)	-> Optional[Any]:






				"""simple docstring"""







				return AutoTokenizer.from_pretrained(self.model_name			)



		@cached_property
		def 			lowerCAmelCase							(			self							: Optional[Any]			)	-> Optional[Any]:






				"""simple docstring"""







				snake_case     :					str     =	FlaxMBartForConditionalGeneration.from_pretrained(self.model_name     ,  from_pt=UpperCamelCase__			)
				return model



		def 			lowerCAmelCase							(			self							: int     ,  **UpperCamelCase__							: Union[str, Any]			)	-> Tuple:






				"""simple docstring"""







				snake_case     :					Any     =	self.translate_src_text(**UpperCamelCase__			)
				self.assertListEqual(self.expected_text     ,  UpperCamelCase__			)



		def 			lowerCAmelCase							(			self							: List[Any]     ,  **UpperCamelCase__							: str			)	-> str:






				"""simple docstring"""







				snake_case     :					int     =	self.tokenizer(self.src_text     ,  **UpperCamelCase__     ,  return_tensors='''np'''			)
				snake_case     :					Any     =	self.model.generate(
				    model_inputs.input_ids     ,  attention_mask=model_inputs.attention_mask     ,  decoder_start_token_id=self.tokenizer.lang_code_to_id['''ro_RO''']     ,  early_stopping=UpperCamelCase__     ,  num_beams=2     ,  ).sequences
				snake_case     :					List[Any]     =	self.tokenizer.batch_decode(UpperCamelCase__     ,  skip_special_tokens=UpperCamelCase__			)
				return generated_words



		@slow
		def 			lowerCAmelCase							(			self							: str			)	-> Union[str, Any]:






				"""simple docstring"""







				self._assert_generated_batch_equal_expected()




'''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()


