






from typing import Any

import numpy as np


def 						_UpperCamelCase							(     snake_case__							):
      assert np.shape(snake_case__							)[0] == np.shape(snake_case__							)[1]

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

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

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


def 						_UpperCamelCase							(     snake_case__							):
      __A		   =      np.random.randn(snake_case__							,			snake_case__							)
      __A		   =      np.dot(snake_case__							,			random_matrix.T							)
      assert _is_matrix_spd(snake_case__							)
      return spd_matrix


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							,			snake_case__ = 1_000							,			snake_case__ = 1E-8							,			):
      assert np.shape(snake_case__							)[0] == np.shape(snake_case__							)[1]
      assert np.shape(snake_case__							)[0] == np.shape(snake_case__							)[0]
      assert _is_matrix_spd(snake_case__							)

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

      # 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(snake_case__							,			snake_case__							)

            # The main algorithm.

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

            # Update variables.
            __A		   =      np.copy(snake_case__							)
            __A		   =      np.copy(snake_case__							)
            __A		   =      np.copy(snake_case__							)

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

      return x


def 						_UpperCamelCase							(     ):
      __A		   =      3
      __A		   =      _create_spd_matrix(snake_case__							)
      __A		   =      np.random.randn(snake_case__							,			1							)
      __A		   =      np.dot(snake_case__							,			snake_case__							)

      # Numpy solution.
      __A		   =      np.linalg.solve(snake_case__							,			snake_case__							)

      # Our implementation.
      __A		   =      conjugate_gradient(snake_case__							,			snake_case__							)

      # 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()










'''simple docstring'''







from typing import List

import datasets
from datasets.tasks import ImageClassification

from ..folder_based_builder import folder_based_builder


__A      :       Tuple      =	datasets.utils.logging.get_logger(__name__)






class 					a__    (			folder_based_builder.FolderBasedBuilderConfig						):
     '''simple docstring'''







     _snake_case             =  None
     _snake_case             =  None







class 					a__    (			folder_based_builder.FolderBasedBuilder						):
     '''simple docstring'''







     _snake_case             =  datasets.Image()
     _snake_case             =  'image'
     _snake_case             =  ImageFolderConfig
     _snake_case             =  42  # definition at the bottom of the script
     _snake_case             =  ImageClassification(image_column='image' ,						label_column='label'						)







__A      :       Any      =	[
    '.blp',
    '.bmp',
    '.dib',
    '.bufr',
    '.cur',
    '.pcx',
    '.dcx',
    '.dds',
    '.ps',
    '.eps',
    '.fit',
    '.fits',
    '.fli',
    '.flc',
    '.ftc',
    '.ftu',
    '.gbr',
    '.gif',
    '.grib',
    '.h5',
    '.hdf',
    '.png',
    '.apng',
    '.jp2',
    '.j2k',
    '.jpc',
    '.jpf',
    '.jpx',
    '.j2c',
    '.icns',
    '.ico',
    '.im',
    '.iim',
    '.tif',
    '.tiff',
    '.jfif',
    '.jpe',
    '.jpg',
    '.jpeg',
    '.mpg',
    '.mpeg',
    '.msp',
    '.pcd',
    '.pxr',
    '.pbm',
    '.pgm',
    '.ppm',
    '.pnm',
    '.psd',
    '.bw',
    '.rgb',
    '.rgba',
    '.sgi',
    '.ras',
    '.tga',
    '.icb',
    '.vda',
    '.vst',
    '.webp',
    '.wmf',
    '.emf',
    '.xbm',
    '.xpm',
]
__A      :       List[Any]      =	IMAGE_EXTENSIONS


