






'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCamelCase_							      =      {
    '''configuration_decision_transformer''': [
        '''DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''DecisionTransformerConfig''',
    ],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCamelCase_							      =      [
        '''DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''DecisionTransformerGPT2Model''',
        '''DecisionTransformerGPT2PreTrainedModel''',
        '''DecisionTransformerModel''',
        '''DecisionTransformerPreTrainedModel''',
    ]


if TYPE_CHECKING:
    from .configuration_decision_transformer import (
        DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
        DecisionTransformerConfig,
    )

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_decision_transformer import (
            DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
            DecisionTransformerGPTaModel,
            DecisionTransformerGPTaPreTrainedModel,
            DecisionTransformerModel,
            DecisionTransformerPreTrainedModel,
        )


else:
    import sys

    lowerCamelCase_							      =      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)













'''simple docstring'''




from typing import Any

import numpy as np

def       __lowercase		(    __lowercase ) ->		bool:

      '''simple docstring'''


      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.
      _A  ,			_A      =			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       __lowercase		(    __lowercase ) ->		Any:

      '''simple docstring'''


      _A      =			np.random.randn(__lowercase     ,						__lowercase )
      _A      =			np.dot(__lowercase     ,						random_matrix.T )
      assert _is_matrix_spd(__lowercase )
      return spd_matrix

def       __lowercase		(    __lowercase     ,						__lowercase     ,						__lowercase = 1000     ,						__lowercase = 1e-8     ,						) ->		Any:

      '''simple docstring'''


      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.
      _A      =			np.zeros((np.shape(__lowercase )[0], 1) )
      _A      =			np.copy(__lowercase )
      _A      =			np.copy(__lowercase )

      # 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(__lowercase     ,						__lowercase )

            # The main algorithm.

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

            # Update variables.
            _A      =			np.copy(__lowercase )
            _A      =			np.copy(__lowercase )
            _A      =			np.copy(__lowercase )

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

      return x

def       __lowercase		(    ) ->		None:

      '''simple docstring'''


      _A      =			3
      _A      =			_create_spd_matrix(__lowercase )
      _A      =			np.random.randn(__lowercase     ,						1 )
      _A      =			np.dot(__lowercase     ,						__lowercase )

      # Numpy solution.
      _A      =			np.linalg.solve(__lowercase     ,						__lowercase )

      # Our implementation.
      _A      =			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()





