





"""simple docstring"""





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

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin





@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 							_lowerCamelCase   (							_lowercase			):
						UpperCAmelCase_			=      42
						UpperCAmelCase_			=      None



def    a__       (       _SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE=0.9_99	,						_SCREAMING_SNAKE_CASE="cosine"	,						):




		"""simple docstring"""


		if alpha_transform_type == "cosine":

				def alpha_bar_fn(_SCREAMING_SNAKE_CASE     ):
						return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2     ) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(_SCREAMING_SNAKE_CASE     ):
						return math.exp(t * -12.0     )

		else:
				raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"     )

		UpperCamelCase =						[]
		for i in range(_SCREAMING_SNAKE_CASE     ):
				UpperCamelCase =						i / num_diffusion_timesteps
				UpperCamelCase =						(i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(_SCREAMING_SNAKE_CASE     ) / alpha_bar_fn(_SCREAMING_SNAKE_CASE     )	,						_SCREAMING_SNAKE_CASE     )     )
		return torch.tensor(_SCREAMING_SNAKE_CASE	,						dtype=torch.floataa     )






class 							_lowerCamelCase   (							_lowercase	,      _lowercase			):
						UpperCAmelCase_			=      [e.name for e in KarrasDiffusionSchedulers]
						UpperCAmelCase_			=      1


						@register_to_config
						def __init__(self ,				__a = 10_00 ,				__a = 0.0001 ,				__a = 0.02 ,				__a = "linear" ,				__a = None ,				__a = False ,				__a = "epsilon" ,				__a = "linspace" ,				__a = 0 ,				)			-> Any:
								if trained_betas is not None:
										UpperCamelCase =						torch.tensor(__a ,				dtype=torch.floataa		)
								elif beta_schedule == "linear":
										UpperCamelCase =						torch.linspace(__a ,				__a ,				__a ,				dtype=torch.floataa		)
								elif beta_schedule == "scaled_linear":
										# this schedule is very specific to the latent diffusion model.
										UpperCamelCase =						(
										    torch.linspace(beta_start**0.5 ,				beta_end**0.5 ,				__a ,				dtype=torch.floataa		) ** 2
										)
								elif beta_schedule == "squaredcos_cap_v2":
										# Glide cosine schedule
										UpperCamelCase =						betas_for_alpha_bar(__a		)
								else:
										raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"		)

								UpperCamelCase =						1.0 - self.betas
								UpperCamelCase =						torch.cumprod(self.alphas ,				dim=0		)

								UpperCamelCase =						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
								UpperCamelCase =						np.concatenate([sigmas[::-1], [0.0]]		).astype(np.floataa		)
								UpperCamelCase =						torch.from_numpy(__a		)

								# setable values
								UpperCamelCase =						None
								UpperCamelCase =						use_karras_sigmas
								self.set_timesteps(__a ,				__a		)
								UpperCamelCase =						[]
								UpperCamelCase =						False


						@property
						def      snake_case_ (self		)			-> List[Any]:
								# standard deviation of the initial noise distribution
								if self.config.timestep_spacing in ["linspace", "trailing"]:
										return self.sigmas.max()

								return (self.sigmas.max() ** 2 + 1) ** 0.5


						def      snake_case_ (self ,				__a ,				__a		)			-> torch.FloatTensor:
								if isinstance(__a ,				torch.Tensor		):
										UpperCamelCase =						timestep.to(self.timesteps.device		)
								UpperCamelCase =						(self.timesteps == timestep).nonzero().item()
								UpperCamelCase =						self.sigmas[step_index]
								UpperCamelCase =						sample / ((sigma**2 + 1) ** 0.5)
								UpperCamelCase =						True
								return sample


						def      snake_case_ (self ,				__a ,				__a ,				__a		)			-> Any:

								def lms_derivative(__a		):
										UpperCamelCase =						1.0
										for k in range(__a		):
												if current_order == k:
														continue
												prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
										return prod

								UpperCamelCase =						integrate.quad(__a ,				self.sigmas[t] ,				self.sigmas[t + 1] ,				epsrel=1e-4		)[0]

								return integrated_coeff


						def      snake_case_ (self ,				__a ,				__a = None		)			-> str:
								UpperCamelCase =						num_inference_steps

								# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
								if self.config.timestep_spacing == "linspace":
										UpperCamelCase =						np.linspace(0 ,				self.config.num_train_timesteps - 1 ,				__a ,				dtype=__a		)[
										    ::-1
										].copy()
								elif self.config.timestep_spacing == "leading":
										UpperCamelCase =						self.config.num_train_timesteps // self.num_inference_steps
										# creates integer timesteps by multiplying by ratio
										# casting to int to avoid issues when num_inference_step is power of 3
										UpperCamelCase =						(np.arange(0 ,				__a		) * step_ratio).round()[::-1].copy().astype(__a		)
										timesteps += self.config.steps_offset
								elif self.config.timestep_spacing == "trailing":
										UpperCamelCase =						self.config.num_train_timesteps / self.num_inference_steps
										# creates integer timesteps by multiplying by ratio
										# casting to int to avoid issues when num_inference_step is power of 3
										UpperCamelCase =						(np.arange(self.config.num_train_timesteps ,				0 ,				-step_ratio		)).round().copy().astype(__a		)
										timesteps -= 1
								else:
										raise ValueError(
										    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."		)

								UpperCamelCase =						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
								UpperCamelCase =						np.log(__a		)
								UpperCamelCase =						np.interp(__a ,				np.arange(0 ,				len(__a		)		) ,				__a		)

								if self.use_karras_sigmas:
										UpperCamelCase =						self._convert_to_karras(in_sigmas=__a		)
										UpperCamelCase =						np.array([self._sigma_to_t(__a ,				__a		) for sigma in sigmas]		)

								UpperCamelCase =						np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)

								UpperCamelCase =						torch.from_numpy(__a		).to(device=__a		)
								if str(__a		).startswith("mps"		):
										# mps does not support float64
										UpperCamelCase =						torch.from_numpy(__a		).to(__a ,				dtype=torch.floataa		)
								else:
										UpperCamelCase =						torch.from_numpy(__a		).to(device=__a		)

								UpperCamelCase =						[]


						def      snake_case_ (self ,				__a ,				__a		)			-> int:
								# get log sigma
								UpperCamelCase =						np.log(__a		)

								# get distribution
								UpperCamelCase =						log_sigma - log_sigmas[:, np.newaxis]

								# get sigmas range
								UpperCamelCase =						np.cumsum((dists >= 0) ,				axis=0		).argmax(axis=0		).clip(max=log_sigmas.shape[0] - 2		)
								UpperCamelCase =						low_idx + 1

								UpperCamelCase =						log_sigmas[low_idx]
								UpperCamelCase =						log_sigmas[high_idx]

								# interpolate sigmas
								UpperCamelCase =						(low - log_sigma) / (low - high)
								UpperCamelCase =						np.clip(__a ,				0 ,				1		)

								# transform interpolation to time range
								UpperCamelCase =						(1 - w) * low_idx + w * high_idx
								UpperCamelCase =						t.reshape(sigma.shape		)
								return t


						def      snake_case_ (self ,				__a		)			-> torch.FloatTensor:
								UpperCamelCase =						in_sigmas[-1].item()
								UpperCamelCase =						in_sigmas[0].item()

								UpperCamelCase =						7.0  # 7.0 is the value used in the paper
								UpperCamelCase =						np.linspace(0 ,				1 ,				self.num_inference_steps		)
								UpperCamelCase =						sigma_min ** (1 / rho)
								UpperCamelCase =						sigma_max ** (1 / rho)
								UpperCamelCase =						(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
								return sigmas


						def      snake_case_ (self ,				__a ,				__a ,				__a ,				__a = 4 ,				__a = True ,				)			-> Union[LMSDiscreteSchedulerOutput, Tuple]:
								if not self.is_scale_input_called:
										warnings.warn(
										    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
										    "See `StableDiffusionPipeline` for a usage example."		)

								if isinstance(__a ,				torch.Tensor		):
										UpperCamelCase =						timestep.to(self.timesteps.device		)
								UpperCamelCase =						(self.timesteps == timestep).nonzero().item()
								UpperCamelCase =						self.sigmas[step_index]

								# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
								if self.config.prediction_type == "epsilon":
										UpperCamelCase =						sample - sigma * model_output
								elif self.config.prediction_type == "v_prediction":
										# * c_out + input * c_skip
										UpperCamelCase =						model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
								elif self.config.prediction_type == "sample":
										UpperCamelCase =						model_output
								else:
										raise ValueError(
										    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"		)

								# 2. Convert to an ODE derivative
								UpperCamelCase =						(sample - pred_original_sample) / sigma
								self.derivatives.append(__a		)
								if len(self.derivatives		) > order:
										self.derivatives.pop(0		)

								# 3. Compute linear multistep coefficients
								UpperCamelCase =						min(step_index + 1 ,				__a		)
								UpperCamelCase =						[self.get_lms_coefficient(__a ,				__a ,				__a		) for curr_order in range(__a		)]

								# 4. Compute previous sample based on the derivatives path
								UpperCamelCase =						sample + sum(
								    coeff * derivative for coeff, derivative in zip(__a ,				reversed(self.derivatives		)		)		)

								if not return_dict:
										return (prev_sample,)

								return LMSDiscreteSchedulerOutput(prev_sample=__a ,				pred_original_sample=__a		)


						def      snake_case_ (self ,				__a ,				__a ,				__a ,				)			-> torch.FloatTensor:
								# Make sure sigmas and timesteps have the same device and dtype as original_samples
								UpperCamelCase =						self.sigmas.to(device=original_samples.device ,				dtype=original_samples.dtype		)
								if original_samples.device.type == "mps" and torch.is_floating_point(__a		):
										# mps does not support float64
										UpperCamelCase =						self.timesteps.to(original_samples.device ,				dtype=torch.floataa		)
										UpperCamelCase =						timesteps.to(original_samples.device ,				dtype=torch.floataa		)
								else:
										UpperCamelCase =						self.timesteps.to(original_samples.device		)
										UpperCamelCase =						timesteps.to(original_samples.device		)

								UpperCamelCase =						[(schedule_timesteps == t).nonzero().item() for t in timesteps]

								UpperCamelCase =						sigmas[step_indices].flatten()
								while len(sigma.shape		) < len(original_samples.shape		):
										UpperCamelCase =						sigma.unsqueeze(-1		)

								UpperCamelCase =						original_samples + noise * sigma
								return noisy_samples




						def __len__(self		)			-> Dict:
								return self.config.num_train_timesteps













"""simple docstring"""





def    a__       (       _SCREAMING_SNAKE_CASE	,						_SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						sorted(_SCREAMING_SNAKE_CASE	,						key=lambda _SCREAMING_SNAKE_CASE     : value[2]	,						reverse=_SCREAMING_SNAKE_CASE     )

		# Create a list of size equal to the maximum deadline
		# and initialize it with -1
		UpperCamelCase =						max(_SCREAMING_SNAKE_CASE	,						key=lambda _SCREAMING_SNAKE_CASE     : value[1]     )[1]
		UpperCamelCase =						[-1] * max_deadline

		# Finding the maximum profit and the count of jobs
		UpperCamelCase =						0
		UpperCamelCase =						0
		for job in jobs:
				# Find a free time slot for this job
				# (Note that we start from the last possible slot)
				for i in range(job[1] - 1	,						-1	,						-1     ):
						if time_slots[i] == -1:
								UpperCamelCase =						job[0]
								count += 1
								max_profit += job[2]
								break
		return [count, max_profit]


if __name__ == "__main__":
						import doctest

						doctest.testmod()






