
import mpmath  # for roots of unity
import numpy as np


class        lowercase      :



		def __init__(				self       ,   A_=None       ,   A_=None )						->      Any:
				"""simple docstring"""
				# Input as list
				UpperCamelCase						=  list(poly_a or [0] )[:]
				UpperCamelCase						=  list(poly_b or [0] )[:]

				# Remove leading zero coefficients
				while self.polyA[-1] == 0:
						self.polyA.pop()
				UpperCamelCase						=  len(self.polyA )

				while self.polyB[-1] == 0:
						self.polyB.pop()
				UpperCamelCase						=  len(self.polyB )

				# Add 0 to make lengths equal a power of 2
				UpperCamelCase						=  int(
				    2 ** np.ceil(np.loga(len(self.polyA ) + len(self.polyB ) - 1 ) ) )

				while len(self.polyA ) < self.c_max_length:
						self.polyA.append(0 )
				while len(self.polyB ) < self.c_max_length:
						self.polyB.append(0 )
				# A complex root used for the fourier transform
				UpperCamelCase						=  complex(mpmath.root(x=1       ,   n=self.c_max_length       ,   k=1 ) )

				# The product
				UpperCamelCase						=  self.__multiply()



		def __UpperCamelCase				(				self       ,   A_ )						->      str:
				"""simple docstring"""
				UpperCamelCase						=  [[x] for x in self.polyA] if which == "A" else [[x] for x in self.polyB]
				# Corner case
				if len(__A ) <= 1:
						return dft[0]
				#
				UpperCamelCase						=  self.c_max_length // 2
				while next_ncol > 0:
						UpperCamelCase						=  [[] for i in range(__A )]
						UpperCamelCase						=  self.root**next_ncol

						# First half of next step
						UpperCamelCase						=  1
						for j in range(self.c_max_length // (next_ncol * 2) ):
								for i in range(__A ):
										new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j] )
								current_root *= root
						# Second half of next step
						UpperCamelCase						=  1
						for j in range(self.c_max_length // (next_ncol * 2) ):
								for i in range(__A ):
										new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j] )
								current_root *= root
						# Update
						UpperCamelCase						=  new_dft
						UpperCamelCase						=  next_ncol // 2
				return dft[0]



		def __UpperCamelCase				(				self )						->      List[str]:
				"""simple docstring"""
				UpperCamelCase						=  self.__dft('A' )
				UpperCamelCase						=  self.__dft('B' )
				UpperCamelCase						=  [[dft_a[i] * dft_b[i] for i in range(self.c_max_length )]]
				del dft_a
				del dft_b

				# Corner Case
				if len(inverce_c[0] ) <= 1:
						return inverce_c[0]
				# Inverse DFT
				UpperCamelCase						=  2
				while next_ncol <= self.c_max_length:
						UpperCamelCase						=  [[] for i in range(__A )]
						UpperCamelCase						=  self.root ** (next_ncol // 2)
						UpperCamelCase						=  1
						# First half of next step
						for j in range(self.c_max_length // next_ncol ):
								for i in range(next_ncol // 2 ):
										# Even positions
										new_inverse_c[i].append(
										    (
										        inverce_c[i][j]
										        + inverce_c[i][j + self.c_max_length // next_ncol]
										    )
										    / 2 )
										# Odd positions
										new_inverse_c[i + next_ncol // 2].append(
										    (
										        inverce_c[i][j]
										        - inverce_c[i][j + self.c_max_length // next_ncol]
										    )
										    / (2 * current_root) )
								current_root *= root
						# Update
						UpperCamelCase						=  new_inverse_c
						next_ncol *= 2
				# Unpack
				UpperCamelCase						=  [round(x[0].real       ,   8 ) + round(x[0].imag       ,   8 ) * 1J for x in inverce_c]

				# Remove leading 0's
				while inverce_c[-1] == 0:
						inverce_c.pop()
				return inverce_c



		def __str__(				self )						->      Optional[int]:
				"""simple docstring"""
				UpperCamelCase						=  "A = " + " + ".join(
				    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A] ) )
				UpperCamelCase						=  "B = " + " + ".join(
				    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B] ) )
				UpperCamelCase						=  "A*B = " + " + ".join(
				    F'''{coef}*x^{i}''' for coef, i in enumerate(self.product ) )

				return F'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
					import doctest

					doctest.testmod()

import torch

from diffusers import DDPMScheduler

from .test_schedulers import SchedulerCommonTest


class        lowercase      (	_SCREAMING_SNAKE_CASE     ):
		__lowercase : Dict			  =       (DDPMScheduler,)



		def __UpperCamelCase				(				self       ,   **A_ )						->      Dict:
				"""simple docstring"""
				UpperCamelCase						=  {
				    'num_train_timesteps': 1_000,
				    'beta_start': 0.0001,
				    'beta_end': 0.02,
				    'beta_schedule': 'linear',
				    'variance_type': 'fixed_small',
				    'clip_sample': True,
				}

				config.update(**A_ )
				return config



		def __UpperCamelCase				(				self )						->      List[Any]:
				"""simple docstring"""
				for timesteps in [1, 5, 100, 1_000]:
						self.check_over_configs(num_train_timesteps=A_ )



		def __UpperCamelCase				(				self )						->      str:
				"""simple docstring"""
				for beta_start, beta_end in zip([0.0001, 0.001, 0.01, 0.1]       ,   [0.002, 0.02, 0.2, 2] ):
						self.check_over_configs(beta_start=A_       ,   beta_end=A_ )



		def __UpperCamelCase				(				self )						->      Any:
				"""simple docstring"""
				for schedule in ["linear", "squaredcos_cap_v2"]:
						self.check_over_configs(beta_schedule=A_ )



		def __UpperCamelCase				(				self )						->      Tuple:
				"""simple docstring"""
				for variance in ["fixed_small", "fixed_large", "other"]:
						self.check_over_configs(variance_type=A_ )



		def __UpperCamelCase				(				self )						->      Union[str, Any]:
				"""simple docstring"""
				for clip_sample in [True, False]:
						self.check_over_configs(clip_sample=A_ )



		def __UpperCamelCase				(				self )						->      Optional[Any]:
				"""simple docstring"""
				self.check_over_configs(thresholding=A_ )
				for threshold in [0.5, 1.0, 2.0]:
						for prediction_type in ["epsilon", "sample", "v_prediction"]:
								self.check_over_configs(
								    thresholding=A_       ,   prediction_type=A_       ,   sample_max_value=A_       ,   )



		def __UpperCamelCase				(				self )						->      Optional[int]:
				"""simple docstring"""
				for prediction_type in ["epsilon", "sample", "v_prediction"]:
						self.check_over_configs(prediction_type=A_ )



		def __UpperCamelCase				(				self )						->      Optional[Any]:
				"""simple docstring"""
				for t in [0, 500, 999]:
						self.check_over_forward(time_step=A_ )



		def __UpperCamelCase				(				self )						->      List[str]:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config()
				UpperCamelCase						=  scheduler_class(**A_ )

				assert torch.sum(torch.abs(scheduler._get_variance(0 ) - 0.0 ) ) < 1e-5
				assert torch.sum(torch.abs(scheduler._get_variance(487 ) - 0.0_0979 ) ) < 1e-5
				assert torch.sum(torch.abs(scheduler._get_variance(999 ) - 0.02 ) ) < 1e-5



		def __UpperCamelCase				(				self )						->      List[Any]:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config()
				UpperCamelCase						=  scheduler_class(**A_ )

				UpperCamelCase						=  len(A_ )

				UpperCamelCase						=  self.dummy_model()
				UpperCamelCase						=  self.dummy_sample_deter
				UpperCamelCase						=  torch.manual_seed(0 )

				for t in reversed(range(A_ ) ):
						# 1. predict noise residual
						UpperCamelCase						=  model(A_       ,   A_ )

						# 2. predict previous mean of sample x_t-1
						UpperCamelCase						=  scheduler.step(A_       ,   A_       ,   A_       ,   generator=A_ ).prev_sample

						# if t > 0:
						#     noise = self.dummy_sample_deter
						#     variance = scheduler.get_variance(t) ** (0.5) * noise
						#
						# sample = pred_prev_sample + variance
						UpperCamelCase						=  pred_prev_sample

				UpperCamelCase						=  torch.sum(torch.abs(A_ ) )
				UpperCamelCase						=  torch.mean(torch.abs(A_ ) )

				assert abs(result_sum.item() - 258.9606 ) < 1e-2
				assert abs(result_mean.item() - 0.3372 ) < 1e-3



		def __UpperCamelCase				(				self )						->      Tuple:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config(prediction_type='v_prediction' )
				UpperCamelCase						=  scheduler_class(**A_ )

				UpperCamelCase						=  len(A_ )

				UpperCamelCase						=  self.dummy_model()
				UpperCamelCase						=  self.dummy_sample_deter
				UpperCamelCase						=  torch.manual_seed(0 )

				for t in reversed(range(A_ ) ):
						# 1. predict noise residual
						UpperCamelCase						=  model(A_       ,   A_ )

						# 2. predict previous mean of sample x_t-1
						UpperCamelCase						=  scheduler.step(A_       ,   A_       ,   A_       ,   generator=A_ ).prev_sample

						# if t > 0:
						#     noise = self.dummy_sample_deter
						#     variance = scheduler.get_variance(t) ** (0.5) * noise
						#
						# sample = pred_prev_sample + variance
						UpperCamelCase						=  pred_prev_sample

				UpperCamelCase						=  torch.sum(torch.abs(A_ ) )
				UpperCamelCase						=  torch.mean(torch.abs(A_ ) )

				assert abs(result_sum.item() - 202.0296 ) < 1e-2
				assert abs(result_mean.item() - 0.2631 ) < 1e-3



		def __UpperCamelCase				(				self )						->      Union[str, Any]:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config()
				UpperCamelCase						=  scheduler_class(**A_ )

				UpperCamelCase						=  [100, 87, 50, 1, 0]

				scheduler.set_timesteps(timesteps=A_ )

				UpperCamelCase						=  scheduler.timesteps

				for i, timestep in enumerate(A_ ):
						if i == len(A_ ) - 1:
								UpperCamelCase						=  -1
						else:
								UpperCamelCase						=  timesteps[i + 1]

						UpperCamelCase						=  scheduler.previous_timestep(A_ )
						UpperCamelCase						=  prev_t.item()

						self.assertEqual(A_       ,   A_ )



		def __UpperCamelCase				(				self )						->      Tuple:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config()
				UpperCamelCase						=  scheduler_class(**A_ )

				UpperCamelCase						=  [100, 87, 50, 51, 0]

				with self.assertRaises(A_       ,   msg='`custom_timesteps` must be in descending order.' ):
						scheduler.set_timesteps(timesteps=A_ )



		def __UpperCamelCase				(				self )						->      Union[str, Any]:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config()
				UpperCamelCase						=  scheduler_class(**A_ )

				UpperCamelCase						=  [100, 87, 50, 1, 0]
				UpperCamelCase						=  len(A_ )

				with self.assertRaises(A_       ,   msg='Can only pass one of `num_inference_steps` or `custom_timesteps`.' ):
						scheduler.set_timesteps(num_inference_steps=A_       ,   timesteps=A_ )



		def __UpperCamelCase				(				self )						->      int:
				"""simple docstring"""
				UpperCamelCase						=  self.scheduler_classes[0]
				UpperCamelCase						=  self.get_scheduler_config()
				UpperCamelCase						=  scheduler_class(**A_ )

				UpperCamelCase						=  [scheduler.config.num_train_timesteps]

				with self.assertRaises(
				    A_       ,   msg='`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}'       ,   ):
						scheduler.set_timesteps(timesteps=A_ )
