
from typing import Any

import numpy as np







def 				UpperCAmelCase_(    a__   ):



    """simple docstring"""



    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.
    SCREAMING_SNAKE_CASE      ,							SCREAMING_SNAKE_CASE				:				Optional[Any]				      = 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 				UpperCAmelCase_(    a__   ):



    """simple docstring"""



    SCREAMING_SNAKE_CASE				:				Dict				      = np.random.randn(a__ ,						a__   )
    SCREAMING_SNAKE_CASE				:				Optional[int]				      = np.dot(a__ ,						random_matrix.T   )
    assert _is_matrix_spd(a__   )
    return spd_matrix







def 				UpperCAmelCase_(    a__ ,						a__ ,						a__ = 1_000 ,						a__ = 1e-8 ,						):



    """simple docstring"""



    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.
    SCREAMING_SNAKE_CASE				:				List[str]				      = np.zeros((np.shape(a__   )[0], 1)   )
    SCREAMING_SNAKE_CASE				:				Union[str, Any]				      = np.copy(a__   )
    SCREAMING_SNAKE_CASE				:				Optional[Any]				      = np.copy(a__   )

    # Set initial errors in solution guess and residual.
    SCREAMING_SNAKE_CASE				:				List[str]				      = 1e9
    SCREAMING_SNAKE_CASE				:				Dict				      = 1e9
    SCREAMING_SNAKE_CASE				:				Tuple				      = 1e9

    # Set iteration counter to threshold number of iterations.
    SCREAMING_SNAKE_CASE				:				Union[str, Any]				      = 0

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

        # The main algorithm.

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

        # Calculate errors.
        SCREAMING_SNAKE_CASE				:				int				      = np.linalg.norm(r - ra   )
        SCREAMING_SNAKE_CASE				:				Tuple				      = np.linalg.norm(x - xa   )
        SCREAMING_SNAKE_CASE				:				str				      = np.maximum(a__ ,						a__   )

        # Update variables.
        SCREAMING_SNAKE_CASE				:				str				      = np.copy(a__   )
        SCREAMING_SNAKE_CASE				:				Tuple				      = np.copy(a__   )
        SCREAMING_SNAKE_CASE				:				Optional[Any]				      = np.copy(a__   )

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

    return x







def 				UpperCAmelCase_(    ):



    """simple docstring"""



    SCREAMING_SNAKE_CASE				:				str				      = 3
    SCREAMING_SNAKE_CASE				:				str				      = _create_spd_matrix(a__   )
    SCREAMING_SNAKE_CASE				:				List[Any]				      = np.random.randn(a__ ,						1   )
    SCREAMING_SNAKE_CASE				:				Any				      = np.dot(a__ ,						a__   )

    # Numpy solution.
    SCREAMING_SNAKE_CASE				:				Dict				      = np.linalg.solve(a__ ,						a__   )

    # Our implementation.
    SCREAMING_SNAKE_CASE				:				Optional[Any]				      = 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 unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
				import torch

if is_vision_available():
				from PIL import Image

				from transformers import DeiTImageProcessor






class 							SCREAMING_SNAKE_CASE__     (				unittest.TestCase     ):

							"""simple docstring"""






							def __init__(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_=7  ,						SCREAMING_SNAKE_CASE_=3  ,						SCREAMING_SNAKE_CASE_=18  ,						SCREAMING_SNAKE_CASE_=30  ,						SCREAMING_SNAKE_CASE_=400  ,						SCREAMING_SNAKE_CASE_=True  ,						SCREAMING_SNAKE_CASE_=None  ,						SCREAMING_SNAKE_CASE_=True  ,						SCREAMING_SNAKE_CASE_=None  ,						SCREAMING_SNAKE_CASE_=True  ,						SCREAMING_SNAKE_CASE_=[0.5, 0.5, 0.5]  ,						SCREAMING_SNAKE_CASE_=[0.5, 0.5, 0.5]  ,						)-> List[str]:





													'''simple docstring'''






													__UpperCamelCase  	=      size if size is not None else {'''height''': 20, '''width''': 20}
													__UpperCamelCase  	=      crop_size if crop_size is not None else {'''height''': 18, '''width''': 18}

													__UpperCamelCase  	=      parent
													__UpperCamelCase  	=      batch_size
													__UpperCamelCase  	=      num_channels
													__UpperCamelCase  	=      image_size
													__UpperCamelCase  	=      min_resolution
													__UpperCamelCase  	=      max_resolution
													__UpperCamelCase  	=      do_resize
													__UpperCamelCase  	=      size
													__UpperCamelCase  	=      do_center_crop
													__UpperCamelCase  	=      crop_size
													__UpperCamelCase  	=      do_normalize
													__UpperCamelCase  	=      image_mean
													__UpperCamelCase  	=      image_std



							def      A__		(	self      )-> int:





													'''simple docstring'''






													return {
													    "do_resize": self.do_resize,
													    "size": self.size,
													    "do_center_crop": self.do_center_crop,
													    "crop_size": self.crop_size,
													    "do_normalize": self.do_normalize,
													    "image_mean": self.image_mean,
													    "image_std": self.image_std,
													}






@require_torch
@require_vision
class 							SCREAMING_SNAKE_CASE__     (				SCREAMING_SNAKE_CASE_ ,		unittest.TestCase     ):

							"""simple docstring"""






							_snake_case  		=	DeiTImageProcessor if is_vision_available() else None
							_snake_case  		=	True



							def      A__		(	self      )-> int:





													'''simple docstring'''






													__UpperCamelCase  	=      DeiTImageProcessingTester(self      )



							@property
							def      A__		(	self      )-> Any:





													'''simple docstring'''






													return self.image_processor_tester.prepare_image_processor_dict()



							def      A__		(	self      )-> Optional[Any]:





													'''simple docstring'''






													__UpperCamelCase  	=      self.image_processing_class(**self.image_processor_dict      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''do_resize'''      )      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''size'''      )      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''do_center_crop'''      )      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''center_crop'''      )      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''do_normalize'''      )      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''image_mean'''      )      )
													self.assertTrue(hasattr(SCREAMING_SNAKE_CASE_  ,						'''image_std'''      )      )



							def      A__		(	self      )-> int:





													'''simple docstring'''






													__UpperCamelCase  	=      self.image_processing_class.from_dict(self.image_processor_dict      )
													self.assertEqual(image_processor.size  ,						{'''height''': 20, '''width''': 20}      )
													self.assertEqual(image_processor.crop_size  ,						{'''height''': 18, '''width''': 18}      )

													__UpperCamelCase  	=      self.image_processing_class.from_dict(self.image_processor_dict  ,						size=42  ,						crop_size=84      )
													self.assertEqual(image_processor.size  ,						{'''height''': 42, '''width''': 42}      )
													self.assertEqual(image_processor.crop_size  ,						{'''height''': 84, '''width''': 84}      )



							def      A__		(	self      )-> Union[str, Any]:





													'''simple docstring'''






													pass



							def      A__		(	self      )-> str:





													'''simple docstring'''






													__UpperCamelCase  	=      self.image_processing_class(**self.image_processor_dict      )
													# create random PIL images
													__UpperCamelCase  	=      prepare_image_inputs(self.image_processor_tester  ,						equal_resolution=SCREAMING_SNAKE_CASE_      )
													for image in image_inputs:
																			self.assertIsInstance(SCREAMING_SNAKE_CASE_  ,						Image.Image      )

													# Test not batched input
													__UpperCamelCase  	=      image_processing(image_inputs[0]  ,						return_tensors='''pt'''      ).pixel_values
													self.assertEqual(
													    encoded_images.shape  ,						(
													        1,
													        self.image_processor_tester.num_channels,
													        self.image_processor_tester.crop_size['''height'''],
													        self.image_processor_tester.crop_size['''width'''],
													    )  ,						)

													# Test batched
													__UpperCamelCase  	=      image_processing(SCREAMING_SNAKE_CASE_  ,						return_tensors='''pt'''      ).pixel_values
													self.assertEqual(
													    encoded_images.shape  ,						(
													        self.image_processor_tester.batch_size,
													        self.image_processor_tester.num_channels,
													        self.image_processor_tester.crop_size['''height'''],
													        self.image_processor_tester.crop_size['''width'''],
													    )  ,						)



							def      A__		(	self      )-> List[str]:





													'''simple docstring'''






													__UpperCamelCase  	=      self.image_processing_class(**self.image_processor_dict      )
													# create random numpy tensors
													__UpperCamelCase  	=      prepare_image_inputs(self.image_processor_tester  ,						equal_resolution=SCREAMING_SNAKE_CASE_  ,						numpify=SCREAMING_SNAKE_CASE_      )
													for image in image_inputs:
																			self.assertIsInstance(SCREAMING_SNAKE_CASE_  ,						np.ndarray      )

													# Test not batched input
													__UpperCamelCase  	=      image_processing(image_inputs[0]  ,						return_tensors='''pt'''      ).pixel_values
													self.assertEqual(
													    encoded_images.shape  ,						(
													        1,
													        self.image_processor_tester.num_channels,
													        self.image_processor_tester.crop_size['''height'''],
													        self.image_processor_tester.crop_size['''width'''],
													    )  ,						)

													# Test batched
													__UpperCamelCase  	=      image_processing(SCREAMING_SNAKE_CASE_  ,						return_tensors='''pt'''      ).pixel_values
													self.assertEqual(
													    encoded_images.shape  ,						(
													        self.image_processor_tester.batch_size,
													        self.image_processor_tester.num_channels,
													        self.image_processor_tester.crop_size['''height'''],
													        self.image_processor_tester.crop_size['''width'''],
													    )  ,						)



							def      A__		(	self      )-> str:





													'''simple docstring'''






													__UpperCamelCase  	=      self.image_processing_class(**self.image_processor_dict      )
													# create random PyTorch tensors
													__UpperCamelCase  	=      prepare_image_inputs(self.image_processor_tester  ,						equal_resolution=SCREAMING_SNAKE_CASE_  ,						torchify=SCREAMING_SNAKE_CASE_      )
													for image in image_inputs:
																			self.assertIsInstance(SCREAMING_SNAKE_CASE_  ,						torch.Tensor      )

													# Test not batched input
													__UpperCamelCase  	=      image_processing(image_inputs[0]  ,						return_tensors='''pt'''      ).pixel_values
													self.assertEqual(
													    encoded_images.shape  ,						(
													        1,
													        self.image_processor_tester.num_channels,
													        self.image_processor_tester.crop_size['''height'''],
													        self.image_processor_tester.crop_size['''width'''],
													    )  ,						)

													# Test batched
													__UpperCamelCase  	=      image_processing(SCREAMING_SNAKE_CASE_  ,						return_tensors='''pt'''      ).pixel_values
													self.assertEqual(
													    encoded_images.shape  ,						(
													        self.image_processor_tester.batch_size,
													        self.image_processor_tester.num_channels,
													        self.image_processor_tester.crop_size['''height'''],
													        self.image_processor_tester.crop_size['''width'''],
													    )  ,						)




