'''simple docstring'''






from typing import Any

import numpy as np





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : np.ndarray							):
     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    _SCREAMING_SNAKE_CASE		(			__snake_case       : int							):
     _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    _SCREAMING_SNAKE_CASE		(			__snake_case       : np.ndarray      ,		__snake_case       : np.ndarray      ,		__snake_case       : int = 1_0_0_0      ,		__snake_case       : float = 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    _SCREAMING_SNAKE_CASE		(			):
     _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'''






import csv
import os

import pytest

from datasets import Dataset, DatasetDict, Features, NamedSplit, Value
from datasets.io.csv import CsvDatasetReader, CsvDatasetWriter

from ..utils import assert_arrow_memory_doesnt_increase, assert_arrow_memory_increases





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Optional[int]      ,		__snake_case       : List[str]							):
     assert isinstance(__snake_case      ,		__snake_case							)
     assert dataset.num_rows == 4
     assert dataset.num_columns == 3
     assert dataset.column_names == ["col_1", "col_2", "col_3"]
     for feature, expected_dtype in expected_features.items():
          assert dataset.features[feature].dtype == expected_dtype





@pytest.mark.parametrize('keep_in_memory'      ,		[False, True]							)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Union[str, Any]      ,		__snake_case       : List[Any]      ,		__snake_case       : List[str]							):
     _A								=     tmp_path / 'cache'
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
          _A								=     CsvDatasetReader(__snake_case      ,		cache_dir=__snake_case      ,		keep_in_memory=__snake_case							).read()
     _check_csv_dataset(__snake_case      ,		__snake_case							)





@pytest.mark.parametrize(
    'features'      ,		[
        None,
        {'col_1': 'string', 'col_2': 'int64', 'col_3': 'float64'},
        {'col_1': 'string', 'col_2': 'string', 'col_3': 'string'},
        {'col_1': 'int32', 'col_2': 'int32', 'col_3': 'int32'},
        {'col_1': 'float32', 'col_2': 'float32', 'col_3': 'float32'},
    ]      ,		)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : List[Any]      ,		__snake_case       : Any      ,		__snake_case       : Optional[Any]							):
     _A								=     tmp_path / 'cache'
     # CSV file loses col_1 string dtype information: default now is "int64" instead of "string"
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     _A								=     features.copy() if features else default_expected_features
     _A								=     (
         Features({feature: Value(__snake_case							) for feature, dtype in features.items()}							) if features is not None else None
     )
     _A								=     CsvDatasetReader(__snake_case      ,		features=__snake_case      ,		cache_dir=__snake_case							).read()
     _check_csv_dataset(__snake_case      ,		__snake_case							)





@pytest.mark.parametrize('split'      ,		[None, NamedSplit('train'							), 'train', 'test']							)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Tuple      ,		__snake_case       : str      ,		__snake_case       : int							):
     _A								=     tmp_path / 'cache'
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     _A								=     CsvDatasetReader(__snake_case      ,		cache_dir=__snake_case      ,		split=__snake_case							).read()
     _check_csv_dataset(__snake_case      ,		__snake_case							)
     assert dataset.split == split if split else "train"





@pytest.mark.parametrize('path_type'      ,		[str, list]							)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Tuple      ,		__snake_case       : int      ,		__snake_case       : Optional[int]							):
     if issubclass(__snake_case      ,		__snake_case							):
          _A								=     csv_path
     elif issubclass(__snake_case      ,		__snake_case							):
          _A								=     [csv_path]
     _A								=     tmp_path / 'cache'
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     _A								=     CsvDatasetReader(__snake_case      ,		cache_dir=__snake_case							).read()
     _check_csv_dataset(__snake_case      ,		__snake_case							)





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Optional[int]      ,		__snake_case       : int      ,		__snake_case       : int=("train",)							):
     assert isinstance(__snake_case      ,		__snake_case							)
     for split in splits:
          _A								=     dataset_dict[split]
          assert dataset.num_rows == 4
          assert dataset.num_columns == 3
          assert dataset.column_names == ["col_1", "col_2", "col_3"]
          for feature, expected_dtype in expected_features.items():
               assert dataset.features[feature].dtype == expected_dtype





@pytest.mark.parametrize('keep_in_memory'      ,		[False, True]							)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Dict      ,		__snake_case       : Any      ,		__snake_case       : Optional[Any]							):
     _A								=     tmp_path / 'cache'
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     with assert_arrow_memory_increases() if keep_in_memory else assert_arrow_memory_doesnt_increase():
          _A								=     CsvDatasetReader({'train': csv_path}      ,		cache_dir=__snake_case      ,		keep_in_memory=__snake_case							).read()
     _check_csv_datasetdict(__snake_case      ,		__snake_case							)





@pytest.mark.parametrize(
    'features'      ,		[
        None,
        {'col_1': 'string', 'col_2': 'int64', 'col_3': 'float64'},
        {'col_1': 'string', 'col_2': 'string', 'col_3': 'string'},
        {'col_1': 'int32', 'col_2': 'int32', 'col_3': 'int32'},
        {'col_1': 'float32', 'col_2': 'float32', 'col_3': 'float32'},
    ]      ,		)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Union[str, Any]      ,		__snake_case       : List[str]      ,		__snake_case       : str							):
     _A								=     tmp_path / 'cache'
     # CSV file loses col_1 string dtype information: default now is "int64" instead of "string"
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     _A								=     features.copy() if features else default_expected_features
     _A								=     (
         Features({feature: Value(__snake_case							) for feature, dtype in features.items()}							) if features is not None else None
     )
     _A								=     CsvDatasetReader({'train': csv_path}      ,		features=__snake_case      ,		cache_dir=__snake_case							).read()
     _check_csv_datasetdict(__snake_case      ,		__snake_case							)





@pytest.mark.parametrize('split'      ,		[None, NamedSplit('train'							), 'train', 'test']							)
def    _SCREAMING_SNAKE_CASE		(			__snake_case       : List[Any]      ,		__snake_case       : Union[str, Any]      ,		__snake_case       : int							):
     if split:
          _A								=     {split: csv_path}
     else:
          _A								=     {'train': csv_path, 'test': csv_path}
     _A								=     tmp_path / 'cache'
     _A								=     {'col_1': 'int64', 'col_2': 'int64', 'col_3': 'float64'}
     _A								=     CsvDatasetReader(__snake_case      ,		cache_dir=__snake_case							).read()
     _check_csv_datasetdict(__snake_case      ,		__snake_case      ,		splits=list(path.keys()							)							)
     assert all(dataset[split].split == split for split in path.keys()							)





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : List[str]							):
     with open(__snake_case      ,		encoding='utf-8'							) as csvfile:
          yield from csv.reader(__snake_case							)





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Any      ,		__snake_case       : Optional[Any]							):
     _A								=     tmp_path / 'cache'
     _A								=     os.path.join(__snake_case      ,		'tmp.csv'							)
     _A								=     CsvDatasetReader({'train': csv_path}      ,		cache_dir=__snake_case							).read()
     CsvDatasetWriter(dataset['train']      ,		__snake_case      ,		num_proc=1							).write()

     _A								=     iter_csv_file(__snake_case							)
     _A								=     iter_csv_file(__snake_case							)

     for rowa, rowa in zip(__snake_case      ,		__snake_case							):
          assert rowa == rowa





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Dict      ,		__snake_case       : Optional[Any]							):
     _A								=     tmp_path / 'cache'
     _A								=     os.path.join(__snake_case      ,		'tmp.csv'							)
     _A								=     CsvDatasetReader({'train': csv_path}      ,		cache_dir=__snake_case							).read()
     CsvDatasetWriter(dataset['train']      ,		__snake_case      ,		num_proc=2							).write()

     _A								=     iter_csv_file(__snake_case							)
     _A								=     iter_csv_file(__snake_case							)

     for rowa, rowa in zip(__snake_case      ,		__snake_case							):
          assert rowa == rowa





def    _SCREAMING_SNAKE_CASE		(			__snake_case       : Optional[Any]      ,		__snake_case       : Tuple							):
     _A								=     tmp_path / 'cache'
     _A								=     os.path.join(__snake_case      ,		'tmp.csv'							)
     _A								=     CsvDatasetReader({'train': csv_path}      ,		cache_dir=__snake_case							).read()
     with pytest.raises(__snake_case							):
          CsvDatasetWriter(dataset['train']      ,		__snake_case      ,		num_proc=0							)



