'''simple docstring'''

from typing import Any

import numpy as np


def 					UpperCAmelCase__      (							_lowerCAmelCase						: np.ndarray)						->		bool:



						"""simple docstring"""

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

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

						# Get eigenvalues and eignevectors for a symmetric matrix.
						snake_case							,				snake_case   :					List[str]							=						np.linalg.eigh(_lowerCAmelCase)

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


def 					UpperCAmelCase__      (							_lowerCAmelCase						: int)						->		Any:



						"""simple docstring"""

						snake_case   :					int							=						np.random.randn(_lowerCAmelCase,			_lowerCAmelCase)
						snake_case   :					Optional[Any]							=						np.dot(_lowerCAmelCase,			random_matrix.T)
						assert _is_matrix_spd(_lowerCAmelCase)
						return spd_matrix


def 					UpperCAmelCase__      (							_lowerCAmelCase						: np.ndarray,			_lowerCAmelCase						: np.ndarray,			_lowerCAmelCase						: int = 1000,			_lowerCAmelCase						: float = 1E-8,			)						->		Any:



						"""simple docstring"""

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

						# Initialize solution guess, residual, search direction.
						snake_case   :					List[Any]							=						np.zeros((np.shape(_lowerCAmelCase)[0], 1))
						snake_case   :					str							=						np.copy(_lowerCAmelCase)
						snake_case   :					Optional[int]							=						np.copy(_lowerCAmelCase)

						# Set initial errors in solution guess and residual.
						snake_case   :					Dict							=						1E9
						snake_case   :					Union[str, Any]							=						1E9
						snake_case   :					Optional[int]							=						1E9

						# Set iteration counter to threshold number of iterations.
						snake_case   :					Dict							=						0

						while error > tol:
												# Save this value so we only calculate the matrix-vector product once.
												snake_case   :					Optional[int]							=						np.dot(_lowerCAmelCase,			_lowerCAmelCase)

												# The main algorithm.

												# Update search direction magnitude.
												snake_case   :					Tuple							=						np.dot(ra.T,			_lowerCAmelCase) / np.dot(pa.T,			_lowerCAmelCase)
												# Update solution guess.
												snake_case   :					Union[str, Any]							=						xa + alpha * pa
												# Calculate new residual.
												snake_case   :					Tuple							=						ra - alpha * w
												# Calculate new Krylov subspace scale.
												snake_case   :					str							=						np.dot(r.T,			_lowerCAmelCase) / np.dot(ra.T,			_lowerCAmelCase)
												# Calculate new A conjuage search direction.
												snake_case   :					List[str]							=						r + beta * pa

												# Calculate errors.
												snake_case   :					Dict							=						np.linalg.norm(r - ra)
												snake_case   :					str							=						np.linalg.norm(x - xa)
												snake_case   :					Dict							=						np.maximum(_lowerCAmelCase,			_lowerCAmelCase)

												# Update variables.
												snake_case   :					List[Any]							=						np.copy(_lowerCAmelCase)
												snake_case   :					int							=						np.copy(_lowerCAmelCase)
												snake_case   :					List[str]							=						np.copy(_lowerCAmelCase)

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

						return x


def 					UpperCAmelCase__      (							)						->		None:



						"""simple docstring"""

						snake_case   :					int							=						3
						snake_case   :					Optional[int]							=						_create_spd_matrix(_lowerCAmelCase)
						snake_case   :					Dict							=						np.random.randn(_lowerCAmelCase,			1)
						snake_case   :					List[str]							=						np.dot(_lowerCAmelCase,			_lowerCAmelCase)

						# Numpy solution.
						snake_case   :					int							=						np.linalg.solve(_lowerCAmelCase,			_lowerCAmelCase)

						# Our implementation.
						snake_case   :					Optional[int]							=						conjugate_gradient(_lowerCAmelCase,			_lowerCAmelCase)

						# 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()






'''simple docstring'''

from typing import TYPE_CHECKING

from ..utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_tf_available, is_torch_available


A_        =   {
    "configuration_utils": ["GenerationConfig"],
    "streamers": ["TextIteratorStreamer", "TextStreamer"],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_        =   [
						    "Constraint",
						    "ConstraintListState",
						    "DisjunctiveConstraint",
						    "PhrasalConstraint",
						]
						A_        =   [
						    "BeamHypotheses",
						    "BeamScorer",
						    "BeamSearchScorer",
						    "ConstrainedBeamSearchScorer",
						]
						A_        =   [
						    "EpsilonLogitsWarper",
						    "EtaLogitsWarper",
						    "ForcedBOSTokenLogitsProcessor",
						    "ForcedEOSTokenLogitsProcessor",
						    "HammingDiversityLogitsProcessor",
						    "InfNanRemoveLogitsProcessor",
						    "LogitsProcessor",
						    "LogitsProcessorList",
						    "LogitsWarper",
						    "MinLengthLogitsProcessor",
						    "MinNewTokensLengthLogitsProcessor",
						    "NoBadWordsLogitsProcessor",
						    "NoRepeatNGramLogitsProcessor",
						    "PrefixConstrainedLogitsProcessor",
						    "RepetitionPenaltyLogitsProcessor",
						    "SequenceBiasLogitsProcessor",
						    "EncoderRepetitionPenaltyLogitsProcessor",
						    "TemperatureLogitsWarper",
						    "TopKLogitsWarper",
						    "TopPLogitsWarper",
						    "TypicalLogitsWarper",
						    "EncoderNoRepeatNGramLogitsProcessor",
						    "ExponentialDecayLengthPenalty",
						    "LogitNormalization",
						]
						A_        =   [
						    "MaxNewTokensCriteria",
						    "MaxLengthCriteria",
						    "MaxTimeCriteria",
						    "StoppingCriteria",
						    "StoppingCriteriaList",
						    "validate_stopping_criteria",
						]
						A_        =   [
						    "GenerationMixin",
						    "top_k_top_p_filtering",
						    "GreedySearchEncoderDecoderOutput",
						    "GreedySearchDecoderOnlyOutput",
						    "SampleEncoderDecoderOutput",
						    "SampleDecoderOnlyOutput",
						    "BeamSearchEncoderDecoderOutput",
						    "BeamSearchDecoderOnlyOutput",
						    "BeamSampleEncoderDecoderOutput",
						    "BeamSampleDecoderOnlyOutput",
						    "ContrastiveSearchEncoderDecoderOutput",
						    "ContrastiveSearchDecoderOnlyOutput",
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_        =   [
						    "TFForcedBOSTokenLogitsProcessor",
						    "TFForcedEOSTokenLogitsProcessor",
						    "TFLogitsProcessor",
						    "TFLogitsProcessorList",
						    "TFLogitsWarper",
						    "TFMinLengthLogitsProcessor",
						    "TFNoBadWordsLogitsProcessor",
						    "TFNoRepeatNGramLogitsProcessor",
						    "TFRepetitionPenaltyLogitsProcessor",
						    "TFTemperatureLogitsWarper",
						    "TFTopKLogitsWarper",
						    "TFTopPLogitsWarper",
						    "TFForceTokensLogitsProcessor",
						    "TFSuppressTokensAtBeginLogitsProcessor",
						    "TFSuppressTokensLogitsProcessor",
						]
						A_        =   [
						    "TFGenerationMixin",
						    "tf_top_k_top_p_filtering",
						    "TFGreedySearchDecoderOnlyOutput",
						    "TFGreedySearchEncoderDecoderOutput",
						    "TFSampleEncoderDecoderOutput",
						    "TFSampleDecoderOnlyOutput",
						    "TFBeamSearchEncoderDecoderOutput",
						    "TFBeamSearchDecoderOnlyOutput",
						    "TFBeamSampleEncoderDecoderOutput",
						    "TFBeamSampleDecoderOnlyOutput",
						    "TFContrastiveSearchEncoderDecoderOutput",
						    "TFContrastiveSearchDecoderOnlyOutput",
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_        =   [
						    "FlaxForcedBOSTokenLogitsProcessor",
						    "FlaxForcedEOSTokenLogitsProcessor",
						    "FlaxLogitsProcessor",
						    "FlaxLogitsProcessorList",
						    "FlaxLogitsWarper",
						    "FlaxMinLengthLogitsProcessor",
						    "FlaxTemperatureLogitsWarper",
						    "FlaxTopKLogitsWarper",
						    "FlaxTopPLogitsWarper",
						]
						A_        =   [
						    "FlaxGenerationMixin",
						    "FlaxGreedySearchOutput",
						    "FlaxSampleOutput",
						    "FlaxBeamSearchOutput",
						]

if TYPE_CHECKING:
						from .configuration_utils import GenerationConfig
						from .streamers import TextIteratorStreamer, TextStreamer

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .beam_constraints import Constraint, ConstraintListState, DisjunctiveConstraint, PhrasalConstraint
												from .beam_search import BeamHypotheses, BeamScorer, BeamSearchScorer, ConstrainedBeamSearchScorer
												from .logits_process import (
												    EncoderNoRepeatNGramLogitsProcessor,
												    EncoderRepetitionPenaltyLogitsProcessor,
												    EpsilonLogitsWarper,
												    EtaLogitsWarper,
												    ExponentialDecayLengthPenalty,
												    ForcedBOSTokenLogitsProcessor,
												    ForcedEOSTokenLogitsProcessor,
												    HammingDiversityLogitsProcessor,
												    InfNanRemoveLogitsProcessor,
												    LogitNormalization,
												    LogitsProcessor,
												    LogitsProcessorList,
												    LogitsWarper,
												    MinLengthLogitsProcessor,
												    MinNewTokensLengthLogitsProcessor,
												    NoBadWordsLogitsProcessor,
												    NoRepeatNGramLogitsProcessor,
												    PrefixConstrainedLogitsProcessor,
												    RepetitionPenaltyLogitsProcessor,
												    SequenceBiasLogitsProcessor,
												    TemperatureLogitsWarper,
												    TopKLogitsWarper,
												    TopPLogitsWarper,
												    TypicalLogitsWarper,
												)
												from .stopping_criteria import (
												    MaxLengthCriteria,
												    MaxNewTokensCriteria,
												    MaxTimeCriteria,
												    StoppingCriteria,
												    StoppingCriteriaList,
												    validate_stopping_criteria,
												)
												from .utils import (
												    BeamSampleDecoderOnlyOutput,
												    BeamSampleEncoderDecoderOutput,
												    BeamSearchDecoderOnlyOutput,
												    BeamSearchEncoderDecoderOutput,
												    ContrastiveSearchDecoderOnlyOutput,
												    ContrastiveSearchEncoderDecoderOutput,
												    GenerationMixin,
												    GreedySearchDecoderOnlyOutput,
												    GreedySearchEncoderDecoderOutput,
												    SampleDecoderOnlyOutput,
												    SampleEncoderDecoderOutput,
												    top_k_top_p_filtering,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tf_logits_process import (
												    TFForcedBOSTokenLogitsProcessor,
												    TFForcedEOSTokenLogitsProcessor,
												    TFForceTokensLogitsProcessor,
												    TFLogitsProcessor,
												    TFLogitsProcessorList,
												    TFLogitsWarper,
												    TFMinLengthLogitsProcessor,
												    TFNoBadWordsLogitsProcessor,
												    TFNoRepeatNGramLogitsProcessor,
												    TFRepetitionPenaltyLogitsProcessor,
												    TFSuppressTokensAtBeginLogitsProcessor,
												    TFSuppressTokensLogitsProcessor,
												    TFTemperatureLogitsWarper,
												    TFTopKLogitsWarper,
												    TFTopPLogitsWarper,
												)
												from .tf_utils import (
												    TFBeamSampleDecoderOnlyOutput,
												    TFBeamSampleEncoderDecoderOutput,
												    TFBeamSearchDecoderOnlyOutput,
												    TFBeamSearchEncoderDecoderOutput,
												    TFContrastiveSearchDecoderOnlyOutput,
												    TFContrastiveSearchEncoderDecoderOutput,
												    TFGenerationMixin,
												    TFGreedySearchDecoderOnlyOutput,
												    TFGreedySearchEncoderDecoderOutput,
												    TFSampleDecoderOnlyOutput,
												    TFSampleEncoderDecoderOutput,
												    tf_top_k_top_p_filtering,
												)

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .flax_logits_process import (
												    FlaxForcedBOSTokenLogitsProcessor,
												    FlaxForcedEOSTokenLogitsProcessor,
												    FlaxLogitsProcessor,
												    FlaxLogitsProcessorList,
												    FlaxLogitsWarper,
												    FlaxMinLengthLogitsProcessor,
												    FlaxTemperatureLogitsWarper,
												    FlaxTopKLogitsWarper,
												    FlaxTopPLogitsWarper,
												)
												from .flax_utils import FlaxBeamSearchOutput, FlaxGenerationMixin, FlaxGreedySearchOutput, FlaxSampleOutput
else:
						import sys

						A_        =   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





