
from typing import Any

import numpy as np


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	assert np.shape(SCREAMING_SNAKE_CASE_							)[0] == np.shape(SCREAMING_SNAKE_CASE_							)[1]

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

	# Get eigenvalues and eignevectors for a symmetric matrix.
	snake_case_		   =					np.linalg.eigh(SCREAMING_SNAKE_CASE_							)

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


def 						lowerCamelCase__   (		_A							):







	'''simple docstring'''





	snake_case_		   =					np.random.randn(SCREAMING_SNAKE_CASE_					,     SCREAMING_SNAKE_CASE_							)
	snake_case_		   =					np.dot(SCREAMING_SNAKE_CASE_					,     random_matrix.T							)
	assert _is_matrix_spd(SCREAMING_SNAKE_CASE_							)
	return spd_matrix


def 						lowerCamelCase__   (		_A					,     _A					,     _A = 1000					,     _A = 1E-8					,     ):







	'''simple docstring'''





	assert np.shape(SCREAMING_SNAKE_CASE_							)[0] == np.shape(SCREAMING_SNAKE_CASE_							)[1]
	assert np.shape(SCREAMING_SNAKE_CASE_							)[0] == np.shape(SCREAMING_SNAKE_CASE_							)[0]
	assert _is_matrix_spd(SCREAMING_SNAKE_CASE_							)

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

	# Set initial errors in solution guess and residual.
	snake_case_		   =					1E9
	snake_case_		   =					1E9
	snake_case_		   =					1E9

	# Set iteration counter to threshold number of iterations.
	snake_case_		   =					0

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

		# The main algorithm.

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

		# Calculate errors.
		snake_case_		   =					np.linalg.norm(r - ra							)
		snake_case_		   =					np.linalg.norm(x - xa							)
		snake_case_		   =					np.maximum(SCREAMING_SNAKE_CASE_					,     SCREAMING_SNAKE_CASE_							)

		# Update variables.
		snake_case_		   =					np.copy(SCREAMING_SNAKE_CASE_							)
		snake_case_		   =					np.copy(SCREAMING_SNAKE_CASE_							)
		snake_case_		   =					np.copy(SCREAMING_SNAKE_CASE_							)

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

	return x


def 						lowerCamelCase__   (		):







	'''simple docstring'''





	snake_case_		   =					3
	snake_case_		   =					_create_spd_matrix(SCREAMING_SNAKE_CASE_							)
	snake_case_		   =					np.random.randn(SCREAMING_SNAKE_CASE_					,     1							)
	snake_case_		   =					np.dot(SCREAMING_SNAKE_CASE_					,     SCREAMING_SNAKE_CASE_							)

	# Numpy solution.
	snake_case_		   =					np.linalg.solve(SCREAMING_SNAKE_CASE_					,     SCREAMING_SNAKE_CASE_							)

	# Our implementation.
	snake_case_		   =					conjugate_gradient(SCREAMING_SNAKE_CASE_					,     SCREAMING_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()






import torch

from diffusers import EulerAncestralDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest
class 		UpperCAmelCase       (    UpperCAmelCase__      ):







						'''simple docstring'''





						lowerCAmelCase_							=       (EulerAncestralDiscreteScheduler,)
						lowerCAmelCase_							=       10






						def 	snake_case__						(						self							:					Tuple	,     **__lowercase							:					int						):






							"""simple docstring"""






							snake_case_		   =					{
							    "num_train_timesteps": 11_00,
							    "beta_start": 0.0001,
							    "beta_end": 0.02,
							    "beta_schedule": "linear",
							}

							config.update(**__lowercase						)
							return config






						def 	snake_case__						(						self							:					Union[str, Any]						):






							"""simple docstring"""






							for timesteps in [10, 50, 1_00, 10_00]:
								self.check_over_configs(num_train_timesteps=__lowercase						)






						def 	snake_case__						(						self							:					List[str]						):






							"""simple docstring"""






							for beta_start, beta_end in zip([0.0_0001, 0.0001, 0.001]	,     [0.0002, 0.002, 0.02]						):
								self.check_over_configs(beta_start=__lowercase	,     beta_end=__lowercase						)






						def 	snake_case__						(						self							:					List[str]						):






							"""simple docstring"""






							for schedule in ["linear", "scaled_linear"]:
								self.check_over_configs(beta_schedule=__lowercase						)






						def 	snake_case__						(						self							:					Union[str, Any]						):






							"""simple docstring"""






							for prediction_type in ["epsilon", "v_prediction"]:
								self.check_over_configs(prediction_type=__lowercase						)






						def 	snake_case__						(						self							:					Optional[Any]						):






							"""simple docstring"""






							snake_case_		   =					self.scheduler_classes[0]
							snake_case_		   =					self.get_scheduler_config()
							snake_case_		   =					scheduler_class(**__lowercase						)

							scheduler.set_timesteps(self.num_inference_steps						)

							snake_case_		   =					torch.manual_seed(0						)

							snake_case_		   =					self.dummy_model()
							snake_case_		   =					self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
							snake_case_		   =					sample.to(__lowercase						)

							for i, t in enumerate(scheduler.timesteps						):
								snake_case_		   =					scheduler.scale_model_input(__lowercase	,     __lowercase						)

								snake_case_		   =					model(__lowercase	,     __lowercase						)

								snake_case_		   =					scheduler.step(__lowercase	,     __lowercase	,     __lowercase	,     generator=__lowercase						)
								snake_case_		   =					output.prev_sample

							snake_case_		   =					torch.sum(torch.abs(__lowercase						)						)
							snake_case_		   =					torch.mean(torch.abs(__lowercase						)						)

							assert abs(result_sum.item() - 152.3192						) < 1E-2
							assert abs(result_mean.item() - 0.1983						) < 1E-3






						def 	snake_case__						(						self							:					List[Any]						):






							"""simple docstring"""






							snake_case_		   =					self.scheduler_classes[0]
							snake_case_		   =					self.get_scheduler_config(prediction_type="v_prediction"						)
							snake_case_		   =					scheduler_class(**__lowercase						)

							scheduler.set_timesteps(self.num_inference_steps						)

							snake_case_		   =					torch.manual_seed(0						)

							snake_case_		   =					self.dummy_model()
							snake_case_		   =					self.dummy_sample_deter * scheduler.init_noise_sigma
							snake_case_		   =					sample.to(__lowercase						)

							for i, t in enumerate(scheduler.timesteps						):
								snake_case_		   =					scheduler.scale_model_input(__lowercase	,     __lowercase						)

								snake_case_		   =					model(__lowercase	,     __lowercase						)

								snake_case_		   =					scheduler.step(__lowercase	,     __lowercase	,     __lowercase	,     generator=__lowercase						)
								snake_case_		   =					output.prev_sample

							snake_case_		   =					torch.sum(torch.abs(__lowercase						)						)
							snake_case_		   =					torch.mean(torch.abs(__lowercase						)						)

							assert abs(result_sum.item() - 108.4439						) < 1E-2
							assert abs(result_mean.item() - 0.1412						) < 1E-3






						def 	snake_case__						(						self							:					Optional[int]						):






							"""simple docstring"""






							snake_case_		   =					self.scheduler_classes[0]
							snake_case_		   =					self.get_scheduler_config()
							snake_case_		   =					scheduler_class(**__lowercase						)

							scheduler.set_timesteps(self.num_inference_steps	,     device=__lowercase						)
							snake_case_		   =					torch.manual_seed(0						)

							snake_case_		   =					self.dummy_model()
							snake_case_		   =					self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
							snake_case_		   =					sample.to(__lowercase						)

							for t in scheduler.timesteps:
								snake_case_		   =					scheduler.scale_model_input(__lowercase	,     __lowercase						)

								snake_case_		   =					model(__lowercase	,     __lowercase						)

								snake_case_		   =					scheduler.step(__lowercase	,     __lowercase	,     __lowercase	,     generator=__lowercase						)
								snake_case_		   =					output.prev_sample

							snake_case_		   =					torch.sum(torch.abs(__lowercase						)						)
							snake_case_		   =					torch.mean(torch.abs(__lowercase						)						)

							assert abs(result_sum.item() - 152.3192						) < 1E-2
							assert abs(result_mean.item() - 0.1983						) < 1E-3
