"""simple docstring"""



from typing import Any

import numpy as np

def    _A(		lowerCAmelCase       ):
							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.
							A__					:    str														= 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    _A(		lowerCAmelCase       ):
							A__					:    str														= np.random.randn(lowerCAmelCase ,     lowerCAmelCase       )
							A__					:    Dict														= np.dot(lowerCAmelCase ,     random_matrix.T       )
							assert _is_matrix_spd(lowerCAmelCase       )
							return spd_matrix

def    _A(		lowerCAmelCase ,     lowerCAmelCase ,     lowerCAmelCase = 1000 ,     lowerCAmelCase = 1E-8 ,     ):
							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.
							A__					:    str														= np.zeros((np.shape(lowerCAmelCase       )[0], 1)       )
							A__					:    int														= np.copy(lowerCAmelCase       )
							A__					:    str														= np.copy(lowerCAmelCase       )

							# Set initial errors in solution guess and residual.
							A__					:    Tuple														= 1E9
							A__					:    Dict														= 1E9
							A__					:    Optional[Any]														= 1E9

							# Set iteration counter to threshold number of iterations.
							A__					:    Any														= 0

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

														# The main algorithm.

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

														# Calculate errors.
														A__					:    Any														= np.linalg.norm(r - ra       )
														A__					:    Optional[Any]														= np.linalg.norm(x - xa       )
														A__					:    Any														= np.maximum(lowerCAmelCase ,     lowerCAmelCase       )

														# Update variables.
														A__					:    Tuple														= np.copy(lowerCAmelCase       )
														A__					:    Any														= np.copy(lowerCAmelCase       )
														A__					:    Optional[int]														= np.copy(lowerCAmelCase       )

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

							return x

def    _A(		):
							A__					:    List[str]														= 3
							A__					:    Tuple														= _create_spd_matrix(lowerCAmelCase       )
							A__					:    Optional[int]														= np.random.randn(lowerCAmelCase ,     1       )
							A__					:    List[Any]														= np.dot(lowerCAmelCase ,     lowerCAmelCase       )

							# Numpy solution.
							A__					:    int														= np.linalg.solve(lowerCAmelCase ,     lowerCAmelCase       )

							# Our implementation.
							A__					:    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 inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_multi_gpu,
    require_single_gpu,
    test_sync,
)
from accelerate.utils import patch_environment
class 	__UpperCAmelCase						(unittest.TestCase    ):







			'''simple docstring'''





			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										A__					:    Optional[int]														= inspect.getfile(accelerate.test_utils       )
										A__					:    Tuple														= os.path.sep.join(mod_file.split(os.path.sep       )[:-1] + ["""scripts""", """test_sync.py"""]       )





			@require_cpu
			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										debug_launcher(test_sync.main      ,			num_processes=1       )





			@require_cpu
			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										debug_launcher(test_sync.main       )





			@require_single_gpu
			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										test_sync.main()





			@require_multi_gpu
			def 		lowerCamelCase				( self       ):







										'''simple docstring'''


										print(F'''Found {torch.cuda.device_count()} devices.'''       )
										A__					:    List[str]														= ["""torchrun""", F'''--nproc_per_node={torch.cuda.device_count()}''', self.test_file_path]
										with patch_environment(omp_num_threads=1       ):
																	execute_subprocess_async(snake_case_      ,			env=os.environ.copy()       )





