




from typing import Any

import numpy as np

def 			lowerCAmelCase_			(  lowerCamelCase:       np.ndarray						)					->			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.
      lowerCamelCase__  ,		lowerCamelCase__        =				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 			lowerCAmelCase_			(  lowerCamelCase:       int						)					->			Any:


      '''simple docstring'''




      lowerCamelCase__        =				np.random.randn(lowerCamelCase     ,				lowerCamelCase						)
      lowerCamelCase__        =				np.dot(lowerCamelCase     ,				random_matrix.T						)
      assert _is_matrix_spd(lowerCamelCase						)
      return spd_matrix

def 			lowerCAmelCase_			(  lowerCamelCase:       np.ndarray     ,				lowerCamelCase:       np.ndarray     ,				lowerCamelCase:       int = 10_00     ,				lowerCamelCase:       float = 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.
      lowerCamelCase__        =				np.zeros((np.shape(lowerCamelCase						)[0], 1)						)
      lowerCamelCase__        =				np.copy(lowerCamelCase						)
      lowerCamelCase__        =				np.copy(lowerCamelCase						)

      # 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(lowerCamelCase     ,				lowerCamelCase						)

            # The main algorithm.

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

            # Update variables.
            lowerCamelCase__        =				np.copy(lowerCamelCase						)
            lowerCamelCase__        =				np.copy(lowerCamelCase						)
            lowerCamelCase__        =				np.copy(lowerCamelCase						)

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

      return x

def 			lowerCAmelCase_			(  )					->			None:


      '''simple docstring'''




      lowerCamelCase__        =				3
      lowerCamelCase__        =				_create_spd_matrix(lowerCamelCase						)
      lowerCamelCase__        =				np.random.randn(lowerCamelCase     ,				1						)
      lowerCamelCase__        =				np.dot(lowerCamelCase     ,				lowerCamelCase						)

      # Numpy solution.
      lowerCamelCase__        =				np.linalg.solve(lowerCamelCase     ,				lowerCamelCase						)

      # Our implementation.
      lowerCamelCase__        =				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()





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 (
    get_resize_output_image_size,
    normalize,
    pad,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging
from ...utils.import_utils import is_vision_available


__SCREAMING_SNAKE_CASE    :   Tuple       =logging.get_logger(__name__)


if is_vision_available():
      import PIL






class 			A			(		_lowerCAmelCase		):
     """simple docstring"""

     _snake_case:	Dict     =["pixel_values"]




     def __init__(    self  :   Optional[Any]	,  A__  :   bool = True	,  A__  :   Dict[str, int] = None	,  A__  :   PILImageResampling = PILImageResampling.BILINEAR	,  A__  :   bool = True	,  A__  :   bool = False	,  A__  :   bool = True	,  A__  :   bool = True	,  A__  :   Union[int, float] = 1 / 2_5_5	,  A__  :   bool = True	,  A__  :   Optional[Union[float, List[float]]] = None	,  A__  :   Optional[Union[float, List[float]]] = None	,  **A__  :   List[str]	,  )				->       None:
           super().__init__(**A__			)

           lowerCamelCase__        =				size if size is not None else {'height': 2_5_6_0, 'width': 1_9_2_0}
           if isinstance(A__	,  (tuple, list)			):
                 # The previous feature extractor size parameter was in (width, height) format
                 lowerCamelCase__        =				size[::-1]
           lowerCamelCase__        =				get_size_dict(A__			)

           lowerCamelCase__        =				do_resize
           lowerCamelCase__        =				size
           lowerCamelCase__        =				resample
           lowerCamelCase__        =				do_thumbnail
           lowerCamelCase__        =				do_align_long_axis
           lowerCamelCase__        =				do_pad
           lowerCamelCase__        =				do_rescale
           lowerCamelCase__        =				rescale_factor
           lowerCamelCase__        =				do_normalize
           lowerCamelCase__        =				image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
           lowerCamelCase__        =				image_std if image_std is not None else IMAGENET_STANDARD_STD




     def  __snake_case   (    self  :   str	,  A__  :   np.ndarray	,  A__  :   Dict[str, int]	,  A__  :   Optional[Union[str, ChannelDimension]] = None			)				->       np.ndarray:
           lowerCamelCase__  ,		lowerCamelCase__        =				get_image_size(A__			)
           lowerCamelCase__  ,		lowerCamelCase__        =				size['height'], size['width']

           if (output_width < output_height and input_width > input_height) or (
               output_width > output_height and input_width < input_height
           ):
                 lowerCamelCase__        =				np.rotaa(A__	,  3			)

           if data_format is not None:
                 lowerCamelCase__        =				to_channel_dimension_format(A__	,  A__			)

           return image




     def  __snake_case   (    self  :   Tuple	,  A__  :   np.ndarray	,  A__  :   Dict[str, int]	,  A__  :   bool = False	,  A__  :   Optional[Union[str, ChannelDimension]] = None	,  )				->       np.ndarray:
           lowerCamelCase__  ,		lowerCamelCase__        =				size['height'], size['width']
           lowerCamelCase__  ,		lowerCamelCase__        =				get_image_size(A__			)

           lowerCamelCase__        =				output_width - input_width
           lowerCamelCase__        =				output_height - input_height

           if random_padding:
                 lowerCamelCase__        =				np.random.randint(low=0	,  high=delta_height + 1			)
                 lowerCamelCase__        =				np.random.randint(low=0	,  high=delta_width + 1			)
           else:
                 lowerCamelCase__        =				delta_height // 2
                 lowerCamelCase__        =				delta_width // 2

           lowerCamelCase__        =				delta_height - pad_top
           lowerCamelCase__        =				delta_width - pad_left

           lowerCamelCase__        =				((pad_top, pad_bottom), (pad_left, pad_right))
           return pad(A__	,  A__	,  data_format=A__			)




     def  __snake_case   (    self  :   int	,  *A__  :   Tuple	,  **A__  :   Dict			)				->       List[Any]:
           logger.info('pad is deprecated and will be removed in version 4.27. Please use pad_image instead.'			)
           return self.pad_image(*A__	,  **A__			)




     def  __snake_case   (    self  :   Any	,  A__  :   np.ndarray	,  A__  :   Dict[str, int]	,  A__  :   PILImageResampling = PILImageResampling.BICUBIC	,  A__  :   Optional[Union[str, ChannelDimension]] = None	,  **A__  :   Any	,  )				->       np.ndarray:
           lowerCamelCase__  ,		lowerCamelCase__        =				get_image_size(A__			)
           lowerCamelCase__  ,		lowerCamelCase__        =				size['height'], size['width']

           # We always resize to the smallest of either the input or output size.
           lowerCamelCase__        =				min(A__	,  A__			)
           lowerCamelCase__        =				min(A__	,  A__			)

           if height == input_height and width == input_width:
                 return image

           if input_height > input_width:
                 lowerCamelCase__        =				int(input_width * height / input_height			)
           elif input_width > input_height:
                 lowerCamelCase__        =				int(input_height * width / input_width			)

           return resize(
               A__	,  size=(height, width)	,  resample=A__	,  reducing_gap=2.0	,  data_format=A__	,  **A__			)




     def  __snake_case   (    self  :   List[str]	,  A__  :   np.ndarray	,  A__  :   Dict[str, int]	,  A__  :   PILImageResampling = PILImageResampling.BICUBIC	,  A__  :   Optional[Union[str, ChannelDimension]] = None	,  **A__  :   Any	,  )				->       np.ndarray:
           lowerCamelCase__        =				get_size_dict(A__			)
           lowerCamelCase__        =				min(size['height']	,  size['width']			)
           lowerCamelCase__        =				get_resize_output_image_size(A__	,  size=A__	,  default_to_square=A__			)
           lowerCamelCase__        =				resize(A__	,  size=A__	,  resample=A__	,  data_format=A__	,  **A__			)
           return resized_image




     def  __snake_case   (    self  :   Optional[int]	,  A__  :   np.ndarray	,  A__  :   Union[int, float]	,  A__  :   Optional[Union[str, ChannelDimension]] = None	,  **A__  :   Optional[int]	,  )				->       Tuple:
           return rescale(A__	,  scale=A__	,  data_format=A__	,  **A__			)




     def  __snake_case   (    self  :   Any	,  A__  :   np.ndarray	,  A__  :   Union[float, List[float]]	,  A__  :   Union[float, List[float]]	,  A__  :   Optional[Union[str, ChannelDimension]] = None	,  **A__  :   Union[str, Any]	,  )				->       np.ndarray:
           return normalize(A__	,  mean=A__	,  std=A__	,  data_format=A__	,  **A__			)




     def  __snake_case   (    self  :   Union[str, Any]	,  A__  :   ImageInput	,  A__  :   bool = None	,  A__  :   Dict[str, int] = None	,  A__  :   PILImageResampling = None	,  A__  :   bool = None	,  A__  :   bool = None	,  A__  :   bool = None	,  A__  :   bool = False	,  A__  :   bool = None	,  A__  :   float = None	,  A__  :   bool = None	,  A__  :   Optional[Union[float, List[float]]] = None	,  A__  :   Optional[Union[float, List[float]]] = None	,  A__  :   Optional[Union[str, TensorType]] = None	,  A__  :   Optional[ChannelDimension] = ChannelDimension.FIRST	,  **A__  :   Any	,  )				->       PIL.Image.Image:
           lowerCamelCase__        =				do_resize if do_resize is not None else self.do_resize
           lowerCamelCase__        =				size if size is not None else self.size
           if isinstance(A__	,  (tuple, list)			):
                 # Previous feature extractor had size in (width, height) format
                 lowerCamelCase__        =				size[::-1]
           lowerCamelCase__        =				get_size_dict(A__			)
           lowerCamelCase__        =				resample if resample is not None else self.resample
           lowerCamelCase__        =				do_thumbnail if do_thumbnail is not None else self.do_thumbnail
           lowerCamelCase__        =				do_align_long_axis if do_align_long_axis is not None else self.do_align_long_axis
           lowerCamelCase__        =				do_pad if do_pad is not None else self.do_pad
           lowerCamelCase__        =				do_rescale if do_rescale is not None else self.do_rescale
           lowerCamelCase__        =				rescale_factor if rescale_factor is not None else self.rescale_factor
           lowerCamelCase__        =				do_normalize if do_normalize is not None else self.do_normalize
           lowerCamelCase__        =				image_mean if image_mean is not None else self.image_mean
           lowerCamelCase__        =				image_std if image_std is not None else self.image_std

           lowerCamelCase__        =				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:
                 raise ValueError('Size must be specified if do_resize is True.'			)

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

           if do_pad and size is None:
                 raise ValueError('Size must be specified if do_pad 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.
           lowerCamelCase__        =				[to_numpy_array(A__			) for image in images]

           if do_align_long_axis:
                 lowerCamelCase__        =				[self.align_long_axis(A__	,  size=A__			) for image in images]

           if do_resize:
                 lowerCamelCase__        =				[self.resize(image=A__	,  size=A__	,  resample=A__			) for image in images]

           if do_thumbnail:
                 lowerCamelCase__        =				[self.thumbnail(image=A__	,  size=A__			) for image in images]

           if do_pad:
                 lowerCamelCase__        =				[self.pad_image(image=A__	,  size=A__	,  random_padding=A__			) for image in images]

           if do_rescale:
                 lowerCamelCase__        =				[self.rescale(image=A__	,  scale=A__			) for image in images]

           if do_normalize:
                 lowerCamelCase__        =				[self.normalize(image=A__	,  mean=A__	,  std=A__			) for image in images]

           lowerCamelCase__        =				[to_channel_dimension_format(A__	,  A__			) for image in images]

           lowerCamelCase__        =				{'pixel_values': images}
           return BatchFeature(data=A__	,  tensor_type=A__			)