



import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput

@dataclass
class  __snake_case      (   lowerCAmelCase__):







							'''simple docstring'''






							UpperCamelCase__				:      torch.FloatTensor
							UpperCamelCase__				:      torch.FloatTensor




class  __snake_case      (   lowerCAmelCase__			,lowerCAmelCase__):







							'''simple docstring'''






							UpperCamelCase__				:      Any         =					1


							@register_to_config
							def __init__(							self  ,  a_ = 2_000  ,  a_ = 0.15  ,  a_ = 0.01  ,  a_ = 1_348.0  ,  a_ = 1E-5  ,  a_ = 1  ,  ):
											a__				      =		sigma_max

											# setable values
											a__				      =		None

											self.set_sigmas(_lowerCamelCase  ,  _lowerCamelCase  ,  _lowerCamelCase  ,  _lowerCamelCase		)


							def _a      (							self  ,  a_  ,  a_ = None		):
											return sample


							def _a      (							self  ,  a_  ,  a_ = None  ,  a_ = None		):
											a__				      =		sampling_eps if sampling_eps is not None else self.config.sampling_eps

											a__				      =		torch.linspace(1  ,  _lowerCamelCase  ,  _lowerCamelCase  ,  device=_lowerCamelCase		)


							def _a      (							self  ,  a_  ,  a_ = None  ,  a_ = None  ,  a_ = None		):
											a__				      =		sigma_min if sigma_min is not None else self.config.sigma_min
											a__				      =		sigma_max if sigma_max is not None else self.config.sigma_max
											a__				      =		sampling_eps if sampling_eps is not None else self.config.sampling_eps
											if self.timesteps is None:
															self.set_timesteps(_lowerCamelCase  ,  _lowerCamelCase		)

											a__				      =		sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
											a__				      =		torch.exp(torch.linspace(math.log(_lowerCamelCase		)  ,  math.log(_lowerCamelCase		)  ,  _lowerCamelCase		)		)
											a__				      =		torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]		)


							def _a      (							self  ,  a_  ,  a_		):
											return torch.where(
											    timesteps == 0  ,  torch.zeros_like(t.to(timesteps.device		)		)  ,  self.discrete_sigmas[timesteps - 1].to(timesteps.device		)  ,  )


							def _a      (							self  ,  a_  ,  a_  ,  a_  ,  a_ = None  ,  a_ = True  ,  ):





											if self.timesteps is None:
															raise ValueError(
															    """`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler"""		)

											a__				      =		timestep * torch.ones(
											    sample.shape[0]  ,  device=sample.device		)  # torch.repeat_interleave(timestep, sample.shape[0])
											a__				      =		(timestep * (len(self.timesteps		) - 1)).long()

											# mps requires indices to be in the same device, so we use cpu as is the default with cuda
											a__				      =		timesteps.to(self.discrete_sigmas.device		)

											a__				      =		self.discrete_sigmas[timesteps].to(sample.device		)
											a__				      =		self.get_adjacent_sigma(_lowerCamelCase  ,  _lowerCamelCase		).to(sample.device		)
											a__				      =		torch.zeros_like(_lowerCamelCase		)
											a__				      =		(sigma**2 - adjacent_sigma**2) ** 0.5

											# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
											# also equation 47 shows the analog from SDE models to ancestral sampling methods
											a__				      =		diffusion.flatten()
											while len(diffusion.shape		) < len(sample.shape		):
															a__				      =		diffusion.unsqueeze(-1		)
											a__				      =		drift - diffusion**2 * model_output

											#  equation 6: sample noise for the diffusion term of
											a__				      =		randn_tensor(
											    sample.shape  ,  layout=sample.layout  ,  generator=_lowerCamelCase  ,  device=sample.device  ,  dtype=sample.dtype		)
											a__				      =		sample - drift  # subtract because `dt` is a small negative timestep
											# TODO is the variable diffusion the correct scaling term for the noise?
											a__				      =		prev_sample_mean + diffusion * noise  # add impact of diffusion field g

											if not return_dict:
															return (prev_sample, prev_sample_mean)

											return SdeVeOutput(prev_sample=_lowerCamelCase  ,  prev_sample_mean=_lowerCamelCase		)


							def _a      (							self  ,  a_  ,  a_  ,  a_ = None  ,  a_ = True  ,  ):





											if self.timesteps is None:
															raise ValueError(
															    """`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler"""		)

											# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
											# sample noise for correction
											a__				      =		randn_tensor(sample.shape  ,  layout=sample.layout  ,  generator=_lowerCamelCase		).to(sample.device		)

											# compute step size from the model_output, the noise, and the snr
											a__				      =		torch.norm(model_output.reshape(model_output.shape[0]  ,  -1		)  ,  dim=-1		).mean()
											a__				      =		torch.norm(noise.reshape(noise.shape[0]  ,  -1		)  ,  dim=-1		).mean()
											a__				      =		(self.config.snr * noise_norm / grad_norm) ** 2 * 2
											a__				      =		step_size * torch.ones(sample.shape[0]		).to(sample.device		)
											# self.repeat_scalar(step_size, sample.shape[0])

											# compute corrected sample: model_output term and noise term
											a__				      =		step_size.flatten()
											while len(step_size.shape		) < len(sample.shape		):
															a__				      =		step_size.unsqueeze(-1		)
											a__				      =		sample + step_size * model_output
											a__				      =		prev_sample_mean + ((step_size * 2) ** 0.5) * noise

											if not return_dict:
															return (prev_sample,)

											return SchedulerOutput(prev_sample=_lowerCamelCase		)


							def _a      (							self  ,  a_  ,  a_  ,  a_  ,  ):
											a__				      =		timesteps.to(original_samples.device		)
											a__				      =		self.discrete_sigmas.to(original_samples.device		)[timesteps]
											a__				      =		(
											    noise * sigmas[:, None, None, None]
											    if noise is not None
											    else torch.randn_like(_lowerCamelCase		) * sigmas[:, None, None, None]
											)
											a__				      =		noise + original_samples
											return noisy_samples



							def __len__(							self		):
											return self.config.num_train_timesteps






from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
UpperCAmelCase							 =					299_792_458

# Symbols
UpperCAmelCase ,       UpperCAmelCase ,       UpperCAmelCase ,       UpperCAmelCase							 =					symbols("""ct x y z""")

def 			A_      (	__a     :				float		):

				"""simple docstring"""
				if velocity > c:
								raise ValueError("""Speed must not exceed light speed 299,792,458 [m/s]!"""		)
				elif velocity < 1:
								# Usually the speed should be much higher than 1 (c order of magnitude)
								raise ValueError("""Speed must be greater than or equal to 1!"""		)

				return velocity / c

def 			A_      (	__a     :				float		):

				"""simple docstring"""
				return 1 / sqrt(1 - beta(__a		) ** 2		)

def 			A_      (	__a     :				float		):

				"""simple docstring"""
				return np.array(
				    [
				        [gamma(__a		), -gamma(__a		) * beta(__a		), 0, 0],
				        [-gamma(__a		) * beta(__a		), gamma(__a		), 0, 0],
				        [0, 0, 1, 0],
				        [0, 0, 0, 1],
				    ]		)

def 			A_      (	__a     :				float ,		__a     :				np.ndarray | None = None		):

				"""simple docstring"""
				# Ensure event is not empty
				if event is None:
								a__				      =		np.array([ct, x, y, z]		)  # Symbolic four vector
				else:
								event[0] *= c  # x0 is ct (speed of light * time)

				return transformation_matrix(__a		) @ event


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	# Example of symbolic vector:
	UpperCAmelCase							 =					transform(29_979_245)
	print("""Example of four vector: """)
	print(f"""ct' = {four_vector[0]}""")
	print(f"""x' = {four_vector[1]}""")
	print(f"""y' = {four_vector[2]}""")
	print(f"""z' = {four_vector[3]}""")

	# Substitute symbols with numerical values
	UpperCAmelCase							 =					{ct: c, x: 1, y: 1, z: 1}
	UpperCAmelCase							 =					[four_vector[i].subs(sub_dict) for i in range(4)]

	print(f"""\n{numerical_vector}""")

