



'''simple docstring'''


from typing import Any

import numpy as np






def 			UpperCAmelCase_							(		lowercase__							):


     '''simple docstring'''







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

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

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

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






def 			UpperCAmelCase_							(		lowercase__							):


     '''simple docstring'''







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






def 			UpperCAmelCase_							(		lowercase__							,						lowercase__							,						lowercase__ = 1_0_0_0							,						lowercase__ = 1E-8							,						):


     '''simple docstring'''







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

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

     # 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(SCREAMING_SNAKE_CASE_							,						SCREAMING_SNAKE_CASE_							)

          # The main algorithm.

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

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

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

     return x






def 			UpperCAmelCase_							(		):


     '''simple docstring'''







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

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

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

     # 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()




from typing import TYPE_CHECKING

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


lowerCamelCase__        =						{"""configuration_regnet""": ["""REGNET_PRETRAINED_CONFIG_ARCHIVE_MAP""", """RegNetConfig"""]}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						[
					    """REGNET_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """RegNetForImageClassification""",
					    """RegNetModel""",
					    """RegNetPreTrainedModel""",
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						[
					    """TF_REGNET_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """TFRegNetForImageClassification""",
					    """TFRegNetModel""",
					    """TFRegNetPreTrainedModel""",
					]

try:
					if not is_flax_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						[
					    """FlaxRegNetForImageClassification""",
					    """FlaxRegNetModel""",
					    """FlaxRegNetPreTrainedModel""",
					]


if TYPE_CHECKING:
					from .configuration_regnet import REGNET_PRETRAINED_CONFIG_ARCHIVE_MAP, RegNetConfig

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_regnet import (
										    REGNET_PRETRAINED_MODEL_ARCHIVE_LIST,
										    RegNetForImageClassification,
										    RegNetModel,
										    RegNetPreTrainedModel,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_regnet import (
										    TF_REGNET_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TFRegNetForImageClassification,
										    TFRegNetModel,
										    TFRegNetPreTrainedModel,
										)

					try:
										if not is_flax_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_flax_regnet import (
										    FlaxRegNetForImageClassification,
										    FlaxRegNetModel,
										    FlaxRegNetPreTrainedModel,
										)


else:
					import sys

					lowerCamelCase__        =						_LazyModule(__name__, globals()["""__file__"""], _import_structure)