
'''simple docstring'''
from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import center_crop, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
     import PIL


A__ :		Union[str, Any]					=logging.get_logger(__name__)







class 			__A					(			_SCREAMING_SNAKE_CASE      ):
 lowerCamelCase												=['''pixel_values''']
 def __init__( self      :     Tuple					, lowerCamelCase      :     Optional[int] = True					, lowerCamelCase      :     Optional[Any] = None					, lowerCamelCase      :     Optional[Any] = PIL.Image.NEAREST					, lowerCamelCase      :     Union[str, Any] = False					, lowerCamelCase      :     Optional[int] = None					, lowerCamelCase      :     Optional[Any] = 1 / 2_55					, lowerCamelCase      :     Any = False					, lowerCamelCase      :     Optional[Any] = True					, lowerCamelCase      :     Optional[int] = True					, lowerCamelCase      :     int = None					, lowerCamelCase      :     Union[str, Any] = None					, lowerCamelCase      :     Union[str, Any] = True					, **lowerCamelCase      :     Union[str, Any]					, ):



   """simple docstring"""





   super().__init__(**a__							)
   __A		:  Any       				=		size if size is not None else {'''height''': 3_46, '''width''': 3_46}
   __A		:  Optional[int]       				=		get_size_dict(a__							)
   __A		:  List[Any]       				=		crop_size if crop_size is not None else {'''height''': 2_89, '''width''': 2_89}
   __A		:  Optional[Any]       				=		get_size_dict(a__					, param_name="""crop_size"""							)

   __A		:  int       				=		do_resize
   __A		:  List[Any]       				=		size
   __A		:  int       				=		resample
   __A		:  str       				=		do_center_crop
   __A		:  List[str]       				=		crop_size
   __A		:  int       				=		do_rescale
   __A		:  Dict       				=		rescale_factor
   __A		:  int       				=		rescale_offset
   __A		:  int       				=		do_normalize
   __A		:  List[str]       				=		image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
   __A		:  Any       				=		image_std if image_std is not None else IMAGENET_STANDARD_STD
   __A		:  Optional[Any]       				=		include_top
 def 		lowercase_( self      :     Any					, lowerCamelCase      :     int					, lowerCamelCase      :     Union[str, Any]					, lowerCamelCase      :     List[str] = PIL.Image.NEAREST					, lowerCamelCase      :     Optional[int] = None					, **lowerCamelCase      :     Optional[int]					, ):



   """simple docstring"""





   __A		:  str       				=		get_size_dict(a__							)
   if "height" not in size or "width" not in size:
     raise ValueError(f"The size dictionary must have keys \'height\' and \'width\'. Got {size.keys()}"							)
   return resize(
       a__					, size=(size["""height"""], size["""width"""])					, resample=a__					, data_format=a__					, **a__							)
 def 		lowercase_( self      :     List[Any]					, lowerCamelCase      :     Any					, lowerCamelCase      :     Union[str, Any]					, lowerCamelCase      :     int = None					, **lowerCamelCase      :     int					, ):



   """simple docstring"""





   __A		:  Optional[Any]       				=		get_size_dict(a__							)
   if "height" not in size or "width" not in size:
     raise ValueError(f"The size dictionary must have keys \'height\' and \'width\'. Got {size.keys()}"							)
   return center_crop(a__					, size=(size["""height"""], size["""width"""])					, data_format=a__					, **a__							)
 def 		lowercase_( self      :     Dict					, lowerCamelCase      :     int					, lowerCamelCase      :     List[str]					, lowerCamelCase      :     int = True					, lowerCamelCase      :     Any = None					, **lowerCamelCase      :     List[Any]					, ):



   """simple docstring"""





   if offset:
     __A		:  str       				=		(image - 127.5) * scale
     if data_format is not None:
       __A		:  List[str]       				=		to_channel_dimension_format(a__					, a__							)
     __A		:  List[Any]       				=		rescaled_image.astype(np.floataa							)
   else:
     __A		:  Optional[int]       				=		rescale(a__					, scale=a__					, data_format=a__					, **a__							)
   return rescaled_image
 def 		lowercase_( self      :     Optional[Any]					, lowerCamelCase      :     int					, lowerCamelCase      :     str					, lowerCamelCase      :     Optional[Any]					, lowerCamelCase      :     Tuple = None					, **lowerCamelCase      :     Optional[int]					, ):



   """simple docstring"""





   return normalize(a__					, mean=a__					, std=a__					, data_format=a__					, **a__							)






 def 		lowercase_( self      :     str					, lowerCamelCase      :     List[str]					, lowerCamelCase      :     List[Any] = None					, lowerCamelCase      :     Optional[Any] = None					, lowerCamelCase      :     Optional[Any]=None					, lowerCamelCase      :     Union[str, Any] = None					, lowerCamelCase      :     Union[str, Any] = None					, lowerCamelCase      :     Tuple = None					, lowerCamelCase      :     Union[str, Any] = None					, lowerCamelCase      :     int = None					, lowerCamelCase      :     List[Any] = None					, lowerCamelCase      :     str = None					, lowerCamelCase      :     int = None					, lowerCamelCase      :     str = None					, lowerCamelCase      :     str = None					, lowerCamelCase      :     Tuple = ChannelDimension.FIRST					, **lowerCamelCase      :     str					, ):



   """simple docstring"""





   __A		:  Optional[int]       				=		do_resize if do_resize is not None else self.do_resize
   __A		:  Any       				=		resample if resample is not None else self.resample
   __A		:  List[Any]       				=		do_center_crop if do_center_crop is not None else self.do_center_crop
   __A		:  List[Any]       				=		do_rescale if do_rescale is not None else self.do_rescale
   __A		:  Optional[int]       				=		rescale_factor if rescale_factor is not None else self.rescale_factor
   __A		:  int       				=		rescale_offset if rescale_offset is not None else self.rescale_offset
   __A		:  str       				=		do_normalize if do_normalize is not None else self.do_normalize
   __A		:  List[Any]       				=		image_mean if image_mean is not None else self.image_mean
   __A		:  List[Any]       				=		image_std if image_std is not None else self.image_std
   __A		:  Tuple       				=		include_top if include_top is not None else self.include_top

   __A		:  Union[str, Any]       				=		size if size is not None else self.size
   __A		:  Optional[Any]       				=		get_size_dict(a__							)
   __A		:  Any       				=		crop_size if crop_size is not None else self.crop_size
   __A		:  Optional[int]       				=		get_size_dict(a__					, param_name="""crop_size"""							)

   __A		:  Dict       				=		make_list_of_images(a__							)

   if not valid_images(a__							):
     raise ValueError(
         """Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, """
         """torch.Tensor, tf.Tensor or jax.ndarray."""							)

   if do_resize and size is None or resample is None:
     raise ValueError("""Size and resample must be specified if do_resize is True."""							)

   if do_center_crop and crop_size is None:
     raise ValueError("""Crop size must be specified if do_center_crop is True."""							)

   if do_rescale and rescale_factor is None:
     raise ValueError("""Rescale factor must be specified if do_rescale is True."""							)

   if do_normalize and (image_mean is None or image_std is None):
     raise ValueError("""Image mean and std must be specified if do_normalize is True."""							)

   # All transformations expect numpy arrays.
   __A		:  Tuple       				=		[to_numpy_array(a__							) for image in images]

   if do_resize:
     __A		:  str       				=		[self.resize(image=a__					, size=a__					, resample=a__							) for image in images]

   if do_center_crop:
     __A		:  Union[str, Any]       				=		[self.center_crop(image=a__					, size=a__							) for image in images]

   if do_rescale:
     __A		:  Dict       				=		[self.rescale(image=a__					, scale=a__					, offset=a__							) for image in images]

   if do_normalize:
     __A		:  int       				=		[self.normalize(image=a__					, mean=a__					, std=a__							) for image in images]

   if include_top:
     __A		:  List[str]       				=		[self.normalize(image=a__					, mean=[0, 0, 0]					, std=a__							) for image in images]

   __A		:  int       				=		[to_channel_dimension_format(a__					, a__							) for image in images]

   __A		:  Union[str, Any]       				=		{'''pixel_values''': images}
   return BatchFeature(data=a__					, tensor_type=a__							)







from typing import Any

import numpy as np






def  _UpperCAmelCase						( __lowerCamelCase							)		->bool:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]

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

 # Get eigenvalues and eignevectors for a symmetric matrix.
 snake_case	,       snake_case :			int							=   np.linalg.eigh(__lowerCamelCase							)

 # Check sign of all eigenvalues.
 # np.all returns a value of type np.bool_
 return bool(np.all(eigen_values > 0							)							)






def  _UpperCAmelCase						( __lowerCamelCase							)		->Any:


 '''simple docstring'''
 snake_case :			Dict							=   np.random.randn(__lowerCamelCase			,  __lowerCamelCase							)
 snake_case :			List[Any]							=   np.dot(__lowerCamelCase			,  random_matrix.T							)
 assert _is_matrix_spd(__lowerCamelCase							)
 return spd_matrix






def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = 1000			,  __lowerCamelCase = 1E-8			,  )		->Any:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[0]
 assert _is_matrix_spd(__lowerCamelCase							)

 # Initialize solution guess, residual, search direction.
 snake_case :			Any							=   np.zeros((np.shape(__lowerCamelCase							)[0], 1)							)
 snake_case :			Optional[int]							=   np.copy(__lowerCamelCase							)
 snake_case :			Optional[Any]							=   np.copy(__lowerCamelCase							)

 # Set initial errors in solution guess and residual.
 snake_case :			Optional[Any]							=   1E9
 snake_case :			List[Any]							=   1E9
 snake_case :			List[str]							=   1E9

 # Set iteration counter to threshold number of iterations.
 snake_case :			List[str]							=   0

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

  # The main algorithm.

  # Update search direction magnitude.
  snake_case :			List[str]							=   np.dot(ra.T			,  __lowerCamelCase							) / np.dot(pa.T			,  __lowerCamelCase							)
  # Update solution guess.
  snake_case :			Optional[int]							=   xa + alpha * pa
  # Calculate new residual.
  snake_case :			str							=   ra - alpha * w
  # Calculate new Krylov subspace scale.
  snake_case :			List[str]							=   np.dot(r.T			,  __lowerCamelCase							) / np.dot(ra.T			,  __lowerCamelCase							)
  # Calculate new A conjuage search direction.
  snake_case :			List[Any]							=   r + beta * pa

  # Calculate errors.
  snake_case :			List[Any]							=   np.linalg.norm(r - ra							)
  snake_case :			Any							=   np.linalg.norm(x - xa							)
  snake_case :			str							=   np.maximum(__lowerCamelCase			,  __lowerCamelCase							)

  # Update variables.
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			List[str]							=   np.copy(__lowerCamelCase							)

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

 return x






def  _UpperCAmelCase						( )		->None:


 '''simple docstring'''
 snake_case :			str							=   3
 snake_case :			Dict							=   _create_spd_matrix(__lowerCamelCase							)
 snake_case :			str							=   np.random.randn(__lowerCamelCase			,  1							)
 snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

 # Numpy solution.
 snake_case :			Any							=   np.linalg.solve(__lowerCamelCase			,  __lowerCamelCase							)

 # Our implementation.
 snake_case :			List[str]							=   conjugate_gradient(__lowerCamelCase			,  __lowerCamelCase							)

 # 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()






