




from collections import OrderedDict
from dataclasses import fields
from typing import Any, Tuple

import numpy as np

from .import_utils import is_torch_available




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						Dict:

    """simple docstring"""


    if is_torch_available():
        import torch

        if isinstance(lowercase_       ,  torch.Tensor   ):
            return True

    return isinstance(lowercase_       ,  np.ndarray   )


class 			_lowerCamelCase    (      _SCREAMING_SNAKE_CASE ):

      """simple docstring"""

      def    snake_case						(  self       :			Optional[Any]					):
          __UpperCamelCase			=    fields(self					)

          # Safety and consistency checks
          if not len(snake_case					):
              raise ValueError(F"{self.__class__.__name__} has no fields."					)

          __UpperCamelCase			=    getattr(self			,							class_fields[0].name					)
          __UpperCamelCase			=    all(getattr(self			,							field.name					) is None for field in class_fields[1:]					)

          if other_fields_are_none and isinstance(snake_case			,							snake_case					):
              for key, value in first_field.items():
                  __UpperCamelCase			=    value
          else:
              for field in class_fields:
                  __UpperCamelCase			=    getattr(self			,							field.name					)
                  if v is not None:
                      __UpperCamelCase			=    v







      def __delitem__(  self       :			Union[str, Any]			,							*snake_case       :			List[str]			,							**snake_case       :			List[str]					):
          raise Exception(F"You cannot use ``__delitem__`` on a {self.__class__.__name__} instance."					)







      def    snake_case						(  self       :			List[Any]			,							*snake_case       :			Optional[int]			,							**snake_case       :			Tuple					):
          raise Exception(F"You cannot use ``setdefault`` on a {self.__class__.__name__} instance."					)







      def    snake_case						(  self       :			Optional[int]			,							*snake_case       :			Union[str, Any]			,							**snake_case       :			str					):
          raise Exception(F"You cannot use ``pop`` on a {self.__class__.__name__} instance."					)







      def    snake_case						(  self       :			Any			,							*snake_case       :			Optional[Any]			,							**snake_case       :			int					):
          raise Exception(F"You cannot use ``update`` on a {self.__class__.__name__} instance."					)







      def __getitem__(  self       :			str			,							snake_case       :			List[str]					):
          if isinstance(snake_case			,							snake_case					):
              __UpperCamelCase			=    dict(self.items()					)
              return inner_dict[k]
          else:
              return self.to_tuple()[k]







      def __setattr__(  self       :			Dict			,							snake_case       :			List[Any]			,							snake_case       :			List[Any]					):
          if name in self.keys() and value is not None:
              # Don't call self.__setitem__ to avoid recursion errors
              super().__setitem__(snake_case			,							snake_case					)
          super().__setattr__(snake_case			,							snake_case					)







      def __setitem__(  self       :			Dict			,							snake_case       :			Optional[Any]			,							snake_case       :			Optional[Any]					):
          # Will raise a KeyException if needed
          super().__setitem__(snake_case			,							snake_case					)
          # Don't call self.__setattr__ to avoid recursion errors
          super().__setattr__(snake_case			,							snake_case					)







      def    snake_case						(  self       :			Any					):
          return tuple(self[k] for k in self.keys()					)











from typing import Any

import numpy as np




def    UpperCAmelCase					(  lowercase__						:					np.ndarray	):



			'''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    UpperCAmelCase					(  lowercase__						:					int	):



			'''simple docstring'''





			a__					=  np.random.randn(lowercase__				,					lowercase__	)
			a__					=  np.dot(lowercase__				,					random_matrix.T	)
			assert _is_matrix_spd(lowercase__	)
			return spd_matrix




def    UpperCAmelCase					(  lowercase__						:					np.ndarray				,					lowercase__						:					np.ndarray				,					lowercase__						:					int = 1000				,					lowercase__						:					float = 1e-8				,					):



			'''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    UpperCAmelCase					(  ):



			'''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()

