'''simple docstring'''


from typing import Any

import numpy as np


def    _lowerCamelCase       ( lowerCamelCase_   :				np.ndarray  ):



     """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.
     UpperCAmelCase_  ,     UpperCAmelCase_				:  List[Any]  = 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  ):



     """simple docstring"""





     UpperCAmelCase_				:  int  = np.random.randn(lowerCamelCase_      ,	lowerCamelCase_  )
     UpperCAmelCase_				:  Union[str, Any]  = np.dot(lowerCamelCase_      ,	random_matrix.T  )
     assert _is_matrix_spd(lowerCamelCase_  )
     return spd_matrix


def    _lowerCamelCase       ( lowerCamelCase_   :				np.ndarray      ,	lowerCamelCase_   :				np.ndarray      ,	lowerCamelCase_   :				int = 1000      ,	lowerCamelCase_   :				float = 1e-8      ,	):



     """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.
     UpperCAmelCase_				:  Union[str, Any]  = np.zeros((np.shape(lowerCamelCase_  )[0], 1)  )
     UpperCAmelCase_				:  Union[str, Any]  = np.copy(lowerCamelCase_  )
     UpperCAmelCase_				:  str  = np.copy(lowerCamelCase_  )

     # Set initial errors in solution guess and residual.
     UpperCAmelCase_				:  Tuple  = 1e9
     UpperCAmelCase_				:  int  = 1e9
     UpperCAmelCase_				:  Union[str, Any]  = 1e9

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

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

          # The main algorithm.

          # Update search direction magnitude.
          UpperCAmelCase_				:  Any  = np.dot(ra.T      ,	lowerCamelCase_  ) / np.dot(pa.T      ,	lowerCamelCase_  )
          # Update solution guess.
          UpperCAmelCase_				:  Dict  = xa + alpha * pa
          # Calculate new residual.
          UpperCAmelCase_				:  Dict  = ra - alpha * w
          # Calculate new Krylov subspace scale.
          UpperCAmelCase_				:  str  = np.dot(r.T      ,	lowerCamelCase_  ) / np.dot(ra.T      ,	lowerCamelCase_  )
          # Calculate new A conjuage search direction.
          UpperCAmelCase_				:  Tuple  = r + beta * pa

          # Calculate errors.
          UpperCAmelCase_				:  Dict  = np.linalg.norm(r - ra  )
          UpperCAmelCase_				:  str  = np.linalg.norm(x - xa  )
          UpperCAmelCase_				:  Union[str, Any]  = np.maximum(lowerCamelCase_      ,	lowerCamelCase_  )

          # Update variables.
          UpperCAmelCase_				:  Optional[int]  = np.copy(lowerCamelCase_  )
          UpperCAmelCase_				:  List[str]  = np.copy(lowerCamelCase_  )
          UpperCAmelCase_				:  Any  = np.copy(lowerCamelCase_  )

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

     return x


def    _lowerCamelCase       ( ):



     """simple docstring"""





     UpperCAmelCase_				:  Union[str, Any]  = 3
     UpperCAmelCase_				:  List[str]  = _create_spd_matrix(lowerCamelCase_  )
     UpperCAmelCase_				:  List[Any]  = np.random.randn(lowerCamelCase_      ,	1  )
     UpperCAmelCase_				:  int  = np.dot(lowerCamelCase_      ,	lowerCamelCase_  )

     # Numpy solution.
     UpperCAmelCase_				:  Dict  = np.linalg.solve(lowerCamelCase_      ,	lowerCamelCase_  )

     # Our implementation.
     UpperCAmelCase_				:  Union[str, Any]  = 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()







'''simple docstring'''


import re
import tempfile
import unittest
from pathlib import Path

from datasets.utils.metadata import DatasetMetadata


def    _lowerCamelCase       ( lowerCamelCase_   :				str  ):



     """simple docstring"""





     UpperCAmelCase_				:  str  = min(re.search('^ +'      ,	lowerCamelCase_  ).end() if t.startswith(' '  ) else 0 for t in string.splitlines()  )
     return "\n".join([line[indent_level:] for line in string.splitlines() if indent_level < len(lowerCamelCase_  )]  )


snake_case__	:     Dict      =    '''\
---
language:
- zh
- en
task_ids:
- sentiment-classification
---
# Begin of markdown

Some cool dataset card
'''

snake_case__	:     Union[str, Any]      =    '''\
---
---
# Begin of markdown

Some cool dataset card
'''


snake_case__	:     int      =    '''\
# Begin of markdown

Some cool dataset card
'''






class 	__SCREAMING_SNAKE_CASE		(			unittest.TestCase			):







  '''simple docstring'''






  def _UpperCamelCase	(					self		):




       '''simple docstring'''

       with tempfile.TemporaryDirectory() as tmp_dir:
            UpperCAmelCase_				:  Tuple  = Path(snake_case_		) / 'README.md'
            with open(snake_case_ ,						'w+'		) as readme_file:
                 readme_file.write(snake_case_		)
            UpperCAmelCase_				:  Optional[Any]  = DatasetMetadata.from_readme(snake_case_		)
            self.assertDictEqual(snake_case_ ,						{'language': ['zh', 'en'], 'task_ids': ['sentiment-classification']}		)

            with open(snake_case_ ,						'w+'		) as readme_file:
                 readme_file.write(snake_case_		)
            UpperCAmelCase_				:  Union[str, Any]  = DatasetMetadata.from_readme(snake_case_		)
            self.assertDictEqual(snake_case_ ,						{}		)

            with open(snake_case_ ,						'w+'		) as readme_file:
                 readme_file.write(snake_case_		)
            UpperCAmelCase_				:  List[str]  = DatasetMetadata.from_readme(snake_case_		)
            self.assertEqual(snake_case_ ,						{}		)






  def _UpperCamelCase	(					self		):




       '''simple docstring'''

       UpperCAmelCase_				:  int  = _dedent(
           '\\n            annotations_creators:\n            - found\n            language_creators:\n            - found\n            language:\n            - en\n            license:\n            - unknown\n            multilinguality:\n            - monolingual\n            pretty_name: Test Dataset\n            size_categories:\n            - 10K<n<100K\n            source_datasets:\n            - extended|other-yahoo-webscope-l6\n            task_categories:\n            - question-answering\n            task_ids:\n            - open-domain-qa\n            '		)
       assert DatasetMetadata.from_yaml_string(snake_case_		)

       UpperCAmelCase_				:  int  = _dedent(
           '\\n            annotations_creators:\n            - found\n            language:\n            - en\n            license:\n            - unknown\n            multilinguality:\n            - monolingual\n            pretty_name: Test Dataset\n            size_categories:\n            - 10K<n<100K\n            source_datasets:\n            - extended|other-yahoo-webscope-l6\n            task_categories:\n            - question-answering\n            task_ids:\n            - open-domain-qa\n            task_ids:\n            - open-domain-qa\n            '		)
       with self.assertRaises(snake_case_		):
            DatasetMetadata.from_yaml_string(snake_case_		)

       UpperCAmelCase_				:  str  = _dedent(
           '\\n            annotations_creators:\n            - found\n            language_creators:\n            - found\n            language:\n            - en\n            license:\n            - unknown\n            multilinguality:\n            - monolingual\n            pretty_name: Test Dataset\n            size_categories:\n            - 10K<n<100K\n            source_datasets:\n            - extended|other-yahoo-webscope-l6\n            task_categories:\n            - text-classification\n            task_ids:\n            - multi-class-classification\n            paperswithcode_id:\n            - squad\n            configs:\n            - en\n            train-eval-index:\n            - config: en\n              task: text-classification\n              task_id: multi_class_classification\n              splits:\n                train_split: train\n                eval_split: test\n              col_mapping:\n                text: text\n                label: target\n              metrics:\n                - type: accuracy\n                  name: Accuracy\n            extra_gated_prompt: |\n              By clicking on “Access repository” below, you also agree to ImageNet Terms of Access:\n              [RESEARCHER_FULLNAME] (the "Researcher") has requested permission to use the ImageNet database (the "Database") at Princeton University and Stanford University. In exchange for such permission, Researcher hereby agrees to the following terms and conditions:\n              1. Researcher shall use the Database only for non-commercial research and educational purposes.\n            extra_gated_fields:\n              Company: text\n              Country: text\n              I agree to use this model for non-commerical use ONLY: checkbox\n            '		)
       assert DatasetMetadata.from_yaml_string(snake_case_		)






