from typing import Any

import numpy as np


def SCREAMING_SNAKE_CASE					(  lowercase_:						np.ndarray					):
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[1]

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

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

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


def SCREAMING_SNAKE_CASE					(  lowercase_:						int					):
       _UpperCamelCase  :							Dict	    =	np.random.randn(lowercase_		,    lowercase_					)
       _UpperCamelCase  :							Any	    =	np.dot(lowercase_		,    random_matrix.T					)
       assert _is_matrix_spd(lowercase_					)
       return spd_matrix


def SCREAMING_SNAKE_CASE					(  lowercase_:						np.ndarray		,    lowercase_:						np.ndarray		,    lowercase_:						int = 1000		,    lowercase_:						float = 1e-8		,    ):
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[1]
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[0]
       assert _is_matrix_spd(lowercase_					)

       # Initialize solution guess, residual, search direction.
       _UpperCamelCase  :							Dict	    =	np.zeros((np.shape(lowercase_					)[0], 1)					)
       _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)
       _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)

       # Set initial errors in solution guess and residual.
       _UpperCamelCase  :							Tuple	    =	1e9
       _UpperCamelCase  :							Optional[int]	    =	1e9
       _UpperCamelCase  :							List[str]	    =	1e9

       # Set iteration counter to threshold number of iterations.
       _UpperCamelCase  :							List[str]	    =	0

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

              # The main algorithm.

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

              # Calculate errors.
              _UpperCamelCase  :							int	    =	np.linalg.norm(r - ra					)
              _UpperCamelCase  :							Union[str, Any]	    =	np.linalg.norm(x - xa					)
              _UpperCamelCase  :							Dict	    =	np.maximum(lowercase_		,    lowercase_					)

              # Update variables.
              _UpperCamelCase  :							Union[str, Any]	    =	np.copy(lowercase_					)
              _UpperCamelCase  :							Any	    =	np.copy(lowercase_					)
              _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)

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

       return x


def SCREAMING_SNAKE_CASE					(  ):
       _UpperCamelCase  :							Optional[Any]	    =	3
       _UpperCamelCase  :							List[str]	    =	_create_spd_matrix(lowercase_					)
       _UpperCamelCase  :							Tuple	    =	np.random.randn(lowercase_		,    1					)
       _UpperCamelCase  :							List[Any]	    =	np.dot(lowercase_		,    lowercase_					)

       # Numpy solution.
       _UpperCamelCase  :							int	    =	np.linalg.solve(lowercase_		,    lowercase_					)

       # Our implementation.
       _UpperCamelCase  :							List[Any]	    =	conjugate_gradient(lowercase_		,    lowercase_					)

       # 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_tf_available,
    is_torch_available,
    is_vision_available,
)


__SCREAMING_SNAKE_CASE		:  Tuple        =      {
    'configuration_segformer': ['SEGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP', 'SegformerConfig', 'SegformerOnnxConfig']
}

try:
					if not is_vision_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					__SCREAMING_SNAKE_CASE		:  Dict        =      ['SegformerFeatureExtractor']
					__SCREAMING_SNAKE_CASE		:  str        =      ['SegformerImageProcessor']

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					__SCREAMING_SNAKE_CASE		:  List[str]        =      [
					    'SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
					    'SegformerDecodeHead',
					    'SegformerForImageClassification',
					    'SegformerForSemanticSegmentation',
					    'SegformerLayer',
					    'SegformerModel',
					    'SegformerPreTrainedModel',
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					__SCREAMING_SNAKE_CASE		:  List[str]        =      [
					    'TF_SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
					    'TFSegformerDecodeHead',
					    'TFSegformerForImageClassification',
					    'TFSegformerForSemanticSegmentation',
					    'TFSegformerModel',
					    'TFSegformerPreTrainedModel',
					]


if TYPE_CHECKING:
					from .configuration_segformer import SEGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, SegformerConfig, SegformerOnnxConfig

					try:
										if not is_vision_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .feature_extraction_segformer import SegformerFeatureExtractor
										from .image_processing_segformer import SegformerImageProcessor

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_segformer import (
										    SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
										    SegformerDecodeHead,
										    SegformerForImageClassification,
										    SegformerForSemanticSegmentation,
										    SegformerLayer,
										    SegformerModel,
										    SegformerPreTrainedModel,
										)
					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_segformer import (
										    TF_SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TFSegformerDecodeHead,
										    TFSegformerForImageClassification,
										    TFSegformerForSemanticSegmentation,
										    TFSegformerModel,
										    TFSegformerPreTrainedModel,
										)

else:
					import sys

					__SCREAMING_SNAKE_CASE		:  Optional[Any]        =      _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)