


from typing import Any

import numpy as np




def   lowerCamelCase_       (					UpperCAmelCase__      ):



						"""simple docstring"""




						assert np.shape(UpperCAmelCase__      )[0] == np.shape(UpperCAmelCase__      )[1]

						# If matrix not symmetric, exit right away.
						if np.allclose(UpperCAmelCase__       ,    matrix.T      ) is False:
												return False

						# Get eigenvalues and eignevectors for a symmetric matrix.
						a_			,   a_					=		np.linalg.eigh(UpperCAmelCase__      )

						# Check sign of all eigenvalues.
						# np.all returns a value of type np.bool_
						return bool(np.all(eigen_values > 0      )      )




def   lowerCamelCase_       (					UpperCAmelCase__      ):



						"""simple docstring"""




						a_					=		np.random.randn(UpperCAmelCase__       ,    UpperCAmelCase__      )
						a_					=		np.dot(UpperCAmelCase__       ,    random_matrix.T      )
						assert _is_matrix_spd(UpperCAmelCase__      )
						return spd_matrix




def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__ = 1_000       ,    UpperCAmelCase__ = 1e-8       ,    ):



						"""simple docstring"""




						assert np.shape(UpperCAmelCase__      )[0] == np.shape(UpperCAmelCase__      )[1]
						assert np.shape(UpperCAmelCase__      )[0] == np.shape(UpperCAmelCase__      )[0]
						assert _is_matrix_spd(UpperCAmelCase__      )

						# Initialize solution guess, residual, search direction.
						a_					=		np.zeros((np.shape(UpperCAmelCase__      )[0], 1)      )
						a_					=		np.copy(UpperCAmelCase__      )
						a_					=		np.copy(UpperCAmelCase__      )

						# Set initial errors in solution guess and residual.
						a_					=		1e9
						a_					=		1e9
						a_					=		1e9

						# Set iteration counter to threshold number of iterations.
						a_					=		0

						while error > tol:
												# Save this value so we only calculate the matrix-vector product once.
												a_					=		np.dot(UpperCAmelCase__       ,    UpperCAmelCase__      )

												# The main algorithm.

												# Update search direction magnitude.
												a_					=		np.dot(ra.T       ,    UpperCAmelCase__      ) / np.dot(pa.T       ,    UpperCAmelCase__      )
												# Update solution guess.
												a_					=		xa + alpha * pa
												# Calculate new residual.
												a_					=		ra - alpha * w
												# Calculate new Krylov subspace scale.
												a_					=		np.dot(r.T       ,    UpperCAmelCase__      ) / np.dot(ra.T       ,    UpperCAmelCase__      )
												# Calculate new A conjuage search direction.
												a_					=		r + beta * pa

												# Calculate errors.
												a_					=		np.linalg.norm(r - ra      )
												a_					=		np.linalg.norm(x - xa      )
												a_					=		np.maximum(UpperCAmelCase__       ,    UpperCAmelCase__      )

												# Update variables.
												a_					=		np.copy(UpperCAmelCase__      )
												a_					=		np.copy(UpperCAmelCase__      )
												a_					=		np.copy(UpperCAmelCase__      )

												# Update number of iterations.
												iterations += 1
												if iterations > max_iterations:
																		break

						return x




def   lowerCamelCase_       (					):



						"""simple docstring"""




						a_					=		3
						a_					=		_create_spd_matrix(UpperCAmelCase__      )
						a_					=		np.random.randn(UpperCAmelCase__       ,    1      )
						a_					=		np.dot(UpperCAmelCase__       ,    UpperCAmelCase__      )

						# Numpy solution.
						a_					=		np.linalg.solve(UpperCAmelCase__       ,    UpperCAmelCase__      )

						# Our implementation.
						a_					=		conjugate_gradient(UpperCAmelCase__       ,    UpperCAmelCase__      )

						# Ensure both solutions are close to x_true (and therefore one another).
						assert np.linalg.norm(x_numpy - x_true      ) <= 1e-6
						assert np.linalg.norm(x_conjugate_gradient - x_true      ) <= 1e-6


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	test_conjugate_gradient()



import json
import os
import unittest

from transformers import BartTokenizer, BartTokenizerFast, BatchEncoding
from transformers.models.roberta.tokenization_roberta import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers, require_torch
from transformers.utils import cached_property

from ...test_tokenization_common import TokenizerTesterMixin, filter_roberta_detectors





@require_tokenizers
class        lowercase_				( UpperCamelCase__			,unittest.TestCase):






							"""simple docstring"""







							snake_case_        =		BartTokenizer
							snake_case_        =		BartTokenizerFast
							snake_case_        =		True
							snake_case_        =		filter_roberta_detectors


							def 						lowercase__     (   self		):







													"""simple docstring"""


													super().setUp()
													a_					=		[
													    """l""",
													    """o""",
													    """w""",
													    """e""",
													    """r""",
													    """s""",
													    """t""",
													    """i""",
													    """d""",
													    """n""",
													    """\u0120""",
													    """\u0120l""",
													    """\u0120n""",
													    """\u0120lo""",
													    """\u0120low""",
													    """er""",
													    """\u0120lowest""",
													    """\u0120newer""",
													    """\u0120wider""",
													    """<unk>""",
													]
													a_					=		dict(zip(_UpperCAmelCase			,    range(len(_UpperCAmelCase		)		)		)		)
													a_					=		["""#version: 0.2""", """\u0120 l""", """\u0120l o""", """\u0120lo w""", """e r""", """"""]
													a_					=		{"""unk_token""": """<unk>"""}

													a_					=		os.path.join(self.tmpdirname			,    VOCAB_FILES_NAMES["""vocab_file"""]		)
													a_					=		os.path.join(self.tmpdirname			,    VOCAB_FILES_NAMES["""merges_file"""]		)
													with open(self.vocab_file			,    """w"""			,    encoding="""utf-8"""		) as fp:
																			fp.write(json.dumps(_UpperCAmelCase		) + """\n"""		)
													with open(self.merges_file			,    """w"""			,    encoding="""utf-8"""		) as fp:
																			fp.write("""\n""".join(_UpperCAmelCase		)		)


							def 						lowercase__     (   self			,    **_UpperCAmelCase		):







													"""simple docstring"""


													kwargs.update(self.special_tokens_map		)
													return self.tokenizer_class.from_pretrained(self.tmpdirname			,    **_UpperCAmelCase		)


							def 						lowercase__     (   self			,    **_UpperCAmelCase		):







													"""simple docstring"""


													kwargs.update(self.special_tokens_map		)
													return self.rust_tokenizer_class.from_pretrained(self.tmpdirname			,    **_UpperCAmelCase		)


							def 						lowercase__     (   self			,    _UpperCAmelCase		):







													"""simple docstring"""


													return "lower newer", "lower newer"


							@cached_property
							def 						lowercase__     (   self		):







													"""simple docstring"""


													return BartTokenizer.from_pretrained("""facebook/bart-large"""		)


							@cached_property
							def 						lowercase__     (   self		):







													"""simple docstring"""


													return BartTokenizerFast.from_pretrained("""facebook/bart-large"""		)


							@require_torch
							def 						lowercase__     (   self		):







													"""simple docstring"""


													a_					=		["""A long paragraph for summarization.""", """Another paragraph for summarization."""]
													a_					=		[0, 250, 251, 17_818, 13, 39_186, 1_938, 4, 2]

													for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																			a_					=		tokenizer(_UpperCAmelCase			,    max_length=len(_UpperCAmelCase		)			,    padding=_UpperCAmelCase			,    return_tensors="""pt"""		)
																			self.assertIsInstance(_UpperCAmelCase			,    _UpperCAmelCase		)

																			self.assertEqual((2, 9)			,    batch.input_ids.shape		)
																			self.assertEqual((2, 9)			,    batch.attention_mask.shape		)
																			a_					=		batch.input_ids.tolist()[0]
																			self.assertListEqual(_UpperCAmelCase			,    _UpperCAmelCase		)
																			# Test that special tokens are reset


							@require_torch
							def 						lowercase__     (   self		):







													"""simple docstring"""


													a_					=		["""A long paragraph for summarization.""", """Another paragraph for summarization."""]
													for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																			a_					=		tokenizer(_UpperCAmelCase			,    padding=_UpperCAmelCase			,    return_tensors="""pt"""		)
																			# check if input_ids are returned and no labels
																			self.assertIn("""input_ids"""			,    _UpperCAmelCase		)
																			self.assertIn("""attention_mask"""			,    _UpperCAmelCase		)
																			self.assertNotIn("""labels"""			,    _UpperCAmelCase		)
																			self.assertNotIn("""decoder_attention_mask"""			,    _UpperCAmelCase		)


							@require_torch
							def 						lowercase__     (   self		):







													"""simple docstring"""


													a_					=		[
													    """Summary of the text.""",
													    """Another summary.""",
													]
													for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																			a_					=		tokenizer(text_target=_UpperCAmelCase			,    max_length=32			,    padding="""max_length"""			,    return_tensors="""pt"""		)
																			self.assertEqual(32			,    targets["""input_ids"""].shape[1]		)


							@require_torch
							def 						lowercase__     (   self		):







													"""simple docstring"""


													for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																			a_					=		tokenizer(
																			    ["""I am a small frog""" * 1_024, """I am a small frog"""]			,    padding=_UpperCAmelCase			,    truncation=_UpperCAmelCase			,    return_tensors="""pt"""		)
																			self.assertIsInstance(_UpperCAmelCase			,    _UpperCAmelCase		)
																			self.assertEqual(batch.input_ids.shape			,    (2, 1_024)		)


							@require_torch
							def 						lowercase__     (   self		):







													"""simple docstring"""


													a_					=		["""A long paragraph for summarization."""]
													a_					=		[
													    """Summary of the text.""",
													]
													for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
																			a_					=		tokenizer(_UpperCAmelCase			,    return_tensors="""pt"""		)
																			a_					=		tokenizer(text_target=_UpperCAmelCase			,    return_tensors="""pt"""		)
																			a_					=		inputs["""input_ids"""]
																			a_					=		targets["""input_ids"""]
																			self.assertTrue((input_ids[:, 0] == tokenizer.bos_token_id).all().item()		)
																			self.assertTrue((labels[:, 0] == tokenizer.bos_token_id).all().item()		)
																			self.assertTrue((input_ids[:, -1] == tokenizer.eos_token_id).all().item()		)
																			self.assertTrue((labels[:, -1] == tokenizer.eos_token_id).all().item()		)


							def 						lowercase__     (   self		):







													"""simple docstring"""


													pass






							def 						lowercase__     (   self		):







													"""simple docstring"""


													for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
																			with self.subTest(f"{tokenizer.__class__.__name__} ({pretrained_name})"		):
																									a_					=		self.rust_tokenizer_class.from_pretrained(_UpperCAmelCase			,    **_UpperCAmelCase		)
																									a_					=		self.tokenizer_class.from_pretrained(_UpperCAmelCase			,    **_UpperCAmelCase		)
																									a_					=		"""A, <mask> AllenNLP sentence."""
																									a_					=		tokenizer_r.encode_plus(_UpperCAmelCase			,    add_special_tokens=_UpperCAmelCase			,    return_token_type_ids=_UpperCAmelCase		)
																									a_					=		tokenizer_p.encode_plus(_UpperCAmelCase			,    add_special_tokens=_UpperCAmelCase			,    return_token_type_ids=_UpperCAmelCase		)

																									# token_type_ids should put 0 everywhere
																									self.assertEqual(sum(tokens_r["""token_type_ids"""]		)			,    sum(tokens_p["""token_type_ids"""]		)		)

																									# attention_mask should put 1 everywhere, so sum over length should be 1
																									self.assertEqual(
																									    sum(tokens_r["""attention_mask"""]		) / len(tokens_r["""attention_mask"""]		)			,    sum(tokens_p["""attention_mask"""]		) / len(tokens_p["""attention_mask"""]		)			,    )

																									a_					=		tokenizer_r.convert_ids_to_tokens(tokens_r["""input_ids"""]		)
																									a_					=		tokenizer_p.convert_ids_to_tokens(tokens_p["""input_ids"""]		)

																									# Rust correctly handles the space before the mask while python doesnt
																									self.assertSequenceEqual(tokens_p["""input_ids"""]			,    [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]		)
																									self.assertSequenceEqual(tokens_r["""input_ids"""]			,    [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]		)

																									self.assertSequenceEqual(
																									    _UpperCAmelCase			,    ["""<s>""", """A""", """,""", """<mask>""", """ĠAllen""", """N""", """LP""", """Ġsentence""", """.""", """</s>"""]		)
																									self.assertSequenceEqual(
																									    _UpperCAmelCase			,    ["""<s>""", """A""", """,""", """<mask>""", """ĠAllen""", """N""", """LP""", """Ġsentence""", """.""", """</s>"""]		)