'''simple docstring'''




from typing import Any

import numpy as np






def __lowerCAmelCase				(							UpperCamelCase__       )			->					bool:
    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.
    __lowerCamelCase			,						__lowerCamelCase						=						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__       )			->					Any:
    __lowerCamelCase						=						np.random.randn(UpperCamelCase__       ,						UpperCamelCase__       )
    __lowerCamelCase						=						np.dot(UpperCamelCase__       ,						random_matrix.T       )
    assert _is_matrix_spd(UpperCamelCase__       )
    return spd_matrix






def __lowerCAmelCase				(							UpperCamelCase__       ,						UpperCamelCase__       ,						UpperCamelCase__ = 10_00       ,						UpperCamelCase__ = 1E-8       ,						)			->					Any:
    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.
    __lowerCamelCase						=						np.zeros((np.shape(UpperCamelCase__       )[0], 1)       )
    __lowerCamelCase						=						np.copy(UpperCamelCase__       )
    __lowerCamelCase						=						np.copy(UpperCamelCase__       )

    # Set initial errors in solution guess and residual.
    __lowerCamelCase						=						1E9
    __lowerCamelCase						=						1E9
    __lowerCamelCase						=						1E9

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

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

        # The main algorithm.

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

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

        # Update variables.
        __lowerCamelCase						=						np.copy(UpperCamelCase__       )
        __lowerCamelCase						=						np.copy(UpperCamelCase__       )
        __lowerCamelCase						=						np.copy(UpperCamelCase__       )

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

    return x






def __lowerCAmelCase				(							)			->					None:
    __lowerCamelCase						=						3
    __lowerCamelCase						=						_create_spd_matrix(UpperCamelCase__       )
    __lowerCamelCase						=						np.random.randn(UpperCamelCase__       ,						1       )
    __lowerCamelCase						=						np.dot(UpperCamelCase__       ,						UpperCamelCase__       )

    # Numpy solution.
    __lowerCamelCase						=						np.linalg.solve(UpperCamelCase__       ,						UpperCamelCase__       )

    # Our implementation.
    __lowerCamelCase						=						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()

'''simple docstring'''




from typing import TYPE_CHECKING

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


__UpperCAmelCase  							={
    "configuration_rwkv": ["RWKV_PRETRAINED_CONFIG_ARCHIVE_MAP", "RwkvConfig", "RwkvOnnxConfig"],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __UpperCAmelCase  							=[
      "RWKV_PRETRAINED_MODEL_ARCHIVE_LIST",
      "RwkvForCausalLM",
      "RwkvModel",
      "RwkvPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_rwkv import RWKV_PRETRAINED_CONFIG_ARCHIVE_MAP, RwkvConfig, RwkvOnnxConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_rwkv import (
        RWKV_PRETRAINED_MODEL_ARCHIVE_LIST,
        RwkvForCausalLM,
        RwkvModel,
        RwkvPreTrainedModel,
    )
else:
  import sys

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