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     :       int  						=  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     :       Optional[int]  						=  np.random.randn(lowercase_		,						lowercase_				)
       _UpperCamelCase     :       int  						=  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     :       int  						=  np.zeros((np.shape(lowercase_				)[0], 1)				)
       _UpperCamelCase     :       Union[str, Any]  						=  np.copy(lowercase_				)
       _UpperCamelCase     :       str  						=  np.copy(lowercase_				)

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

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

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

              # The main algorithm.

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

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

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

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

       return x


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

       # Numpy solution.
       _UpperCamelCase     :       List[str]  						=  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()




from .chunk_utils import chunk_layer
from .data_transforms import make_atomaa_masks
from .feats import atomaa_to_atomaa, frames_and_literature_positions_to_atomaa_pos, torsion_angles_to_frames
from .loss import compute_predicted_aligned_error, compute_tm
from .protein import Protein as OFProtein
from .protein import to_pdb
from .rigid_utils import Rigid, Rotation
from .tensor_utils import dict_multimap, flatten_final_dims, permute_final_dims



