
from transformers import BertTokenizer, EncoderDecoderModel, SeqaSeqTrainer, SeqaSeqTrainingArguments
from transformers.testing_utils import TestCasePlus, require_torch, slow
from transformers.utils import is_datasets_available


if is_datasets_available():
					import datasets





class 							UpperCAmelCase      (  __SCREAMING_SNAKE_CASE  ):




	'''simple docstring'''





	@slow
	@require_torch
	def 				UpperCamelCase_  (       self					: List[Any] ):
					__A   			= EncoderDecoderModel.from_encoder_decoder_pretrained("prajjwal1/bert-tiny"							,"prajjwal1/bert-tiny" )
					__A   			= BertTokenizer.from_pretrained("bert-base-uncased" )

					__A   			= bertabert.config.encoder.vocab_size
					__A   			= tokenizer.sep_token_id
					__A   			= tokenizer.cls_token_id
					__A   			= 1_28

					__A   			= datasets.load_dataset("cnn_dailymail"							,"3.0.0"							,split="train[:1%]" )
					__A   			= datasets.load_dataset("cnn_dailymail"							,"3.0.0"							,split="validation[:1%]" )

					__A   			= train_dataset.select(range(32 ) )
					__A   			= val_dataset.select(range(16 ) )

					__A   			= 4

					def _map_to_encoder_decoder_inputs(A					: Optional[int] ):
									# Tokenizer will automatically set [BOS] <text> [EOS]
									__A   			= tokenizer(batch["article"]							,padding="max_length"							,truncation=A							,max_length=5_12 )
									__A   			= tokenizer(batch["highlights"]							,padding="max_length"							,truncation=A							,max_length=1_28 )
									__A   			= inputs.input_ids
									__A   			= inputs.attention_mask

									__A   			= outputs.input_ids
									__A   			= outputs.input_ids.copy()
									__A   			= [
									    [-1_00 if token == tokenizer.pad_token_id else token for token in labels] for labels in batch["labels"]
									]
									__A   			= outputs.attention_mask

									assert all(len(A ) == 5_12 for x in inputs.input_ids )
									assert all(len(A ) == 1_28 for x in outputs.input_ids )

									return batch

					def _compute_metrics(A					: Union[str, Any] ):
									__A   			= pred.label_ids
									__A   			= pred.predictions

									# all unnecessary tokens are removed
									__A   			= tokenizer.batch_decode(A							,skip_special_tokens=A )
									__A   			= tokenizer.batch_decode(A							,skip_special_tokens=A )

									__A   			= sum([int(pred_str[i] == label_str[i] ) for i in range(len(A ) )] ) / len(A )

									return {"accuracy": accuracy}

					# map train dataset
					__A   			= train_dataset.map(
					    _map_to_encoder_decoder_inputs							,batched=A							,batch_size=A							,remove_columns=["article", "highlights"]							,)
					train_dataset.set_format(
					    type="torch"							,columns=["input_ids", "attention_mask", "decoder_input_ids", "decoder_attention_mask", "labels"]							,)

					# same for validation dataset
					__A   			= val_dataset.map(
					    _map_to_encoder_decoder_inputs							,batched=A							,batch_size=A							,remove_columns=["article", "highlights"]							,)
					val_dataset.set_format(
					    type="torch"							,columns=["input_ids", "attention_mask", "decoder_input_ids", "decoder_attention_mask", "labels"]							,)

					__A   			= self.get_auto_remove_tmp_dir()

					__A   			= SeqaSeqTrainingArguments(
					    output_dir=A							,per_device_train_batch_size=A							,per_device_eval_batch_size=A							,predict_with_generate=A							,evaluation_strategy="steps"							,do_train=A							,do_eval=A							,warmup_steps=0							,eval_steps=2							,logging_steps=2							,)

					# instantiate trainer
					__A   			= SeqaSeqTrainer(
					    model=A							,args=A							,compute_metrics=_compute_metrics							,train_dataset=A							,eval_dataset=A							,tokenizer=A							,)

					# start training
					trainer.train()


import numpy as np


def 						UpperCAmelCase			(	a_		,   a_		,   a_ = 1E-12		,   a_ = 1_0_0		,   )		->	tuple[float, np.ndarray]:







				"""simple docstring"""



				assert np.shape(a_						)[0] == np.shape(a_						)[1]
				# Ensure proper dimensionality.
				assert np.shape(a_						)[0] == np.shape(a_						)[0]
				# Ensure inputs are either both complex or both real
				assert np.iscomplexobj(a_						) == np.iscomplexobj(a_						)
				__A   			= np.iscomplexobj(a_						)
				if is_complex:
								# Ensure complex input_matrix is Hermitian
								assert np.array_equal(a_		,   input_matrix.conj().T						)

				# Set convergence to False. Will define convergence when we exceed max_iterations
				# or when we have small changes from one iteration to next.

				__A   			= False
				__A   			= 0
				__A   			= 0
				__A   			= 1E12

				while not convergence:
								# Multiple matrix by the vector.
								__A   			= np.dot(a_		,   a_						)
								# Normalize the resulting output vector.
								__A   			= w / np.linalg.norm(a_						)
								# Find rayleigh quotient
								# (faster than usual b/c we know vector is normalized already)
								__A   			= vector.conj().T if is_complex else vector.T
								__A   			= np.dot(a_		,   np.dot(a_		,   a_						)						)

								# Check convergence.
								__A   			= np.abs(lambda_ - lambda_previous						) / lambda_
								iterations += 1

								if error <= error_tol or iterations >= max_iterations:
												__A   			= True

								__A   			= lambda_

				if is_complex:
								__A   			= np.real(lambda_						)

				return lambda_, vector


def 						UpperCAmelCase			(	)		->	None:







				"""simple docstring"""



				__A   			= np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]						)
				__A   			= np.array([4_1, 4, 2_0]						)
				__A   			= real_input_matrix.astype(np.complexaaa						)
				__A   			= np.triu(1J * complex_input_matrix		,   1						)
				complex_input_matrix += imag_matrix
				complex_input_matrix += -1 * imag_matrix.T
				__A   			= np.array([4_1, 4, 2_0]						).astype(np.complexaaa						)

				for problem_type in ["real", "complex"]:
								if problem_type == "real":
												__A   			= real_input_matrix
												__A   			= real_vector
								elif problem_type == "complex":
												__A   			= complex_input_matrix
												__A   			= complex_vector

								# Our implementation.
								__A			,							__A   			= power_iteration(a_		,   a_						)

								# Numpy implementation.

								# Get eigenvalues and eigenvectors using built-in numpy
								# eigh (eigh used for symmetric or hermetian matrices).
								__A			,							__A   			= np.linalg.eigh(a_						)
								# Last eigenvalue is the maximum one.
								__A   			= eigen_values[-1]
								# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
								__A   			= eigen_vectors[:, -1]

								# Check our implementation and numpy gives close answers.
								assert np.abs(eigen_value - eigen_value_max						) <= 1E-6
								# Take absolute values element wise of each eigenvector.
								# as they are only unique to a minus sign.
								assert np.linalg.norm(np.abs(a_						) - np.abs(a_						)						) <= 1E-6


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					test_power_iteration()
