
'''simple docstring'''





from typing import Any

import numpy as np
def 	snake_case_							(				_a  :				np.ndarray      ):
      assert np.shape(_a      )[0] == np.shape(_a      )[1]

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

      # Get eigenvalues and eignevectors for a symmetric matrix.
      snake_case_							,						snake_case_    							=				np.linalg.eigh(_a      )

      # Check sign of all eigenvalues.
      # np.all returns a value of type np.bool_
      return bool(np.all(eigen_values > 0      )      )
def 	snake_case_							(				_a  :				int      ):
      snake_case_    							=				np.random.randn(_a			,       _a      )
      snake_case_    							=				np.dot(_a			,       random_matrix.T      )
      assert _is_matrix_spd(_a      )
      return spd_matrix
def 	snake_case_							(				_a  :				np.ndarray			,       _a  :				np.ndarray			,       _a  :				int = 1_000			,       _a  :				float = 1E-8			,       ):
      assert np.shape(_a      )[0] == np.shape(_a      )[1]
      assert np.shape(_a      )[0] == np.shape(_a      )[0]
      assert _is_matrix_spd(_a      )

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

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

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

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

            # The main algorithm.

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

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

            # Update variables.
            snake_case_    							=				np.copy(_a      )
            snake_case_    							=				np.copy(_a      )
            snake_case_    							=				np.copy(_a      )

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

      return x
def 	snake_case_							(				):
      snake_case_    							=				3
      snake_case_    							=				_create_spd_matrix(_a      )
      snake_case_    							=				np.random.randn(_a			,       1      )
      snake_case_    							=				np.dot(_a			,       _a      )

      # Numpy solution.
      snake_case_    							=				np.linalg.solve(_a			,       _a      )

      # Our implementation.
      snake_case_    							=				conjugate_gradient(_a			,       _a      )

      # 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()




import numpy as np
import PIL
import torch
import torchvision.transforms as T
import torchvision.transforms.functional as TF
from PIL import Image







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE=256					)							->   Optional[int]:

     """simple docstring"""







     _lowerCAmelCase :       Any	   =     min(img.size					)

     if s < target_image_size:
          raise ValueError(f'''min dim for image {s} < {target_image_size}'''					)

     _lowerCAmelCase :       Dict	   =     target_image_size / s
     _lowerCAmelCase :       Dict	   =     (round(r * img.size[1]					), round(r * img.size[0]					))
     _lowerCAmelCase :       Any	   =     TF.resize(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				interpolation=PIL.Image.LANCZOS					)
     _lowerCAmelCase :       str	   =     TF.center_crop(SCREAMING_SNAKE_CASE		,				output_size=2 * [target_image_size]					)
     _lowerCAmelCase :       int	   =     torch.unsqueeze(T.ToTensor()(SCREAMING_SNAKE_CASE					)		,				0					)
     return img







def 						_snake_case		(     SCREAMING_SNAKE_CASE					)							->   List[str]:

     """simple docstring"""







     _lowerCAmelCase :       List[Any]	   =     2.0 * x - 1.0
     return x







def 						_snake_case		(     SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE=True		,				SCREAMING_SNAKE_CASE="RGB"					)							->   int:

     """simple docstring"""







     _lowerCAmelCase :       Optional[int]	   =     x.detach().cpu()
     if process:
          _lowerCAmelCase :       List[Any]	   =     post_process_tensor(SCREAMING_SNAKE_CASE					)
     _lowerCAmelCase :       Optional[int]	   =     x.numpy()
     if process:
          _lowerCAmelCase :       List[Any]	   =     (255 * x).astype(np.uinta					)
     _lowerCAmelCase :       Optional[int]	   =     Image.fromarray(SCREAMING_SNAKE_CASE					)
     if not x.mode == mode:
          _lowerCAmelCase :       str	   =     x.convert(SCREAMING_SNAKE_CASE					)
     return x







def 						_snake_case		(     SCREAMING_SNAKE_CASE					)							->   Union[str, Any]:

     """simple docstring"""







     _lowerCAmelCase :       Any	   =     torch.clamp(SCREAMING_SNAKE_CASE		,				-1.0		,				1.0					)
     _lowerCAmelCase :       Any	   =     (x + 1.0) / 2.0
     _lowerCAmelCase :       List[Any]	   =     x.permute(1		,				2		,				0					)
     return x







def 						_snake_case		(     SCREAMING_SNAKE_CASE					)							->   Tuple:

     """simple docstring"""







     _lowerCAmelCase :       str	   =     post_process_tensor(x.squeeze()					)
     return x.permute(2		,				0		,				1					).unsqueeze(0					)






