



def  lowerCamelCase_	(      lowerCAmelCase__	:	list[int]			,	lowerCAmelCase__	:	list[int]				)       ->							tuple[float, float]:

							'''simple docstring'''






							if not len(lowerCAmelCase__				) == len(lowerCAmelCase__				) == 3:
														raise ValueError('Please enter a valid equation.'				)
							if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
														raise ValueError('Both a & b of two equations can\'t be zero.'				)

							# Extract the coefficients
							A						,   A						,   A      						=    equationa
							A						,   A						,   A      						=    equationa

							# Calculate the determinants of the matrices
							A      						=    aa * ba - aa * ba
							A      						=    ca * ba - ca * ba
							A      						=    aa * ca - aa * ca

							# Check if the system of linear equations has a solution (using Cramer's rule)
							if determinant == 0:
														if determinant_x == determinant_y == 0:
																					raise ValueError('Infinite solutions. (Consistent system)'				)
														else:
																					raise ValueError('No solution. (Inconsistent system)'				)
							else:
														if determinant_x == determinant_y == 0:
																					# Trivial solution (Inconsistent system)
																					return (0.0, 0.0)
														else:
																					A      						=    determinant_x / determinant
																					A      						=    determinant_y / determinant
																					# Non-Trivial Solution (Consistent system)
																					return (x, y)

'''simple docstring'''
import unittest

import torch

from diffusers import DDIMScheduler, DDPMScheduler, UNetaDModel
from diffusers.training_utils import set_seed
from diffusers.utils.testing_utils import slow


lowercase__											=False







class   a_ (      unittest.TestCase					):




			def 					lowerCAmelCase__					(       self					,   UpperCAmelCase=32	):
				set_seed(0	)
				a_      				=						UNetaDModel(sample_size=UpperCAmelCase					,   in_channels=3					,   out_channels=3	)
				a_      				=						torch.optim.SGD(model.parameters()					,   lr=0.00_01	)
				return model, optimizer






			@slow
			def 					lowerCAmelCase__					(       self	):
				a_      				=						"""cpu"""  # ensure full determinism without setting the CUBLAS_WORKSPACE_CONFIG env variable
				a_      				=						DDPMScheduler(
				    num_train_timesteps=10_00					,   beta_start=0.00_01					,   beta_end=0.02					,   beta_schedule="""linear"""					,   clip_sample=UpperCAmelCase					,   )
				a_      				=						DDIMScheduler(
				    num_train_timesteps=10_00					,   beta_start=0.00_01					,   beta_end=0.02					,   beta_schedule="""linear"""					,   clip_sample=UpperCAmelCase					,   )

				assert ddpm_scheduler.config.num_train_timesteps == ddim_scheduler.config.num_train_timesteps

				# shared batches for DDPM and DDIM
				set_seed(0	)
				a_      				=						[torch.randn((4, 3, 32, 32)	).clip(-1					,   1	).to(UpperCAmelCase	) for _ in range(4	)]
				a_      				=						[torch.randn((4, 3, 32, 32)	).to(UpperCAmelCase	) for _ in range(4	)]
				a_      				=						[torch.randint(0					,   10_00					,   (4,)	).long().to(UpperCAmelCase	) for _ in range(4	)]

				# train with a DDPM scheduler
				a_				,  a_      				=						self.get_model_optimizer(resolution=32	)
				model.train().to(UpperCAmelCase	)
				for i in range(4	):
					optimizer.zero_grad()
					a_      				=						ddpm_scheduler.add_noise(clean_images[i]					,   noise[i]					,   timesteps[i]	)
					a_      				=						model(UpperCAmelCase					,   timesteps[i]	).sample
					a_      				=						torch.nn.functional.mse_loss(UpperCAmelCase					,   noise[i]	)
					loss.backward()
					optimizer.step()
				del model, optimizer

				# recreate the model and optimizer, and retry with DDIM
				a_				,  a_      				=						self.get_model_optimizer(resolution=32	)
				model.train().to(UpperCAmelCase	)
				for i in range(4	):
					optimizer.zero_grad()
					a_      				=						ddim_scheduler.add_noise(clean_images[i]					,   noise[i]					,   timesteps[i]	)
					a_      				=						model(UpperCAmelCase					,   timesteps[i]	).sample
					a_      				=						torch.nn.functional.mse_loss(UpperCAmelCase					,   noise[i]	)
					loss.backward()
					optimizer.step()
				del model, optimizer

				self.assertTrue(torch.allclose(UpperCAmelCase					,   UpperCAmelCase					,   atol=1e-5	)	)
				self.assertTrue(torch.allclose(UpperCAmelCase					,   UpperCAmelCase					,   atol=1e-5	)	)
