




'''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      _a    (      __a					):
       __a							:	torch.FloatTensor
       __a							:	Optional[torch.FloatTensor]  							=   None






def 		snake_case_				(_a      :				Optional[int]       ,  _a      :				Optional[Any]=0.999       ,  _a      :				Optional[int]="cosine"       ,  ):
    if alpha_transform_type == "cosine":

        def alpha_bar_fn(_a      :				Any	):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2	) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(_a      :				Optional[int]	):
            return math.exp(t * -12.0	)

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

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







class      _a    (      __a				,				__a					):
       __a							:	Union[str, Any]  							=   [e.name for e in KarrasDiffusionSchedulers]
       __a							:	Optional[int]  							=   1
       @register_to_config
       def __init__(      self		:      Union[str, Any]  ,							lowercase		:      int = 1_000  ,							lowercase		:      float = 0.0001  ,							lowercase		:      float = 0.02  ,							lowercase		:      str = "linear"  ,							lowercase		:      Optional[Union[np.ndarray, List[float]]] = None  ,							lowercase		:      Optional[bool] = False  ,							lowercase		:      str = "epsilon"  ,							lowercase		:      str = "linspace"  ,							lowercase		:      int = 0  ,							):



           '''simple docstring'''

           if trained_betas is not None:
               UpperCAmelCase     			=						torch.tensor(lowercase  ,							dtype=torch.floataa							)
           elif beta_schedule == "linear":
               UpperCAmelCase     			=						torch.linspace(lowercase  ,							lowercase  ,							lowercase  ,							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  ,							lowercase  ,							dtype=torch.floataa							) ** 2
               )
           elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               UpperCAmelCase     			=						betas_for_alpha_bar(lowercase							)
           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(lowercase							)

           # setable values
           UpperCAmelCase     			=						None
           UpperCAmelCase     			=						use_karras_sigmas
           self.set_timesteps(lowercase  ,							lowercase							)
           UpperCAmelCase     			=						[]
           UpperCAmelCase     			=						False
       @property
       def        A (      self		:      Union[str, Any]							):



           '''simple docstring'''

           if self.config.timestep_spacing in ["linspace", "trailing"]:
               return self.sigmas.max()

           return (self.sigmas.max() ** 2 + 1) ** 0.5
       def        A (      self		:      Optional[int]  ,							lowercase		:      torch.FloatTensor  ,							lowercase		:      Union[float, torch.FloatTensor]							):



           '''simple docstring'''

           if isinstance(lowercase  ,							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        A (      self		:      Optional[Any]  ,							lowercase		:      Optional[Any]  ,							lowercase		:      Optional[Any]  ,							lowercase		:      List[str]							):



           '''simple docstring'''

           def lms_derivative(lowercase		:      List[Any]							):
               UpperCAmelCase     			=						1.0
               for k in range(lowercase							):
                   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(lowercase  ,							self.sigmas[t]  ,							self.sigmas[t + 1]  ,							epsrel=1E-4							)[0]

           return integrated_coeff
       def        A (      self		:      Any  ,							lowercase		:      int  ,							lowercase		:      Union[str, torch.device] = None							):



           '''simple docstring'''

           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  ,							lowercase  ,							dtype=lowercase							)[
                   ::-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  ,							lowercase							) * step_ratio).round()[::-1].copy().astype(lowercase							)
               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(lowercase							)
               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(lowercase							)
           UpperCAmelCase     			=						np.interp(lowercase  ,							np.arange(0  ,							len(lowercase							)							)  ,							lowercase							)

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

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

           UpperCAmelCase     			=						torch.from_numpy(lowercase							).to(device=lowercase							)
           if str(lowercase							).startswith('''mps'''							):
               # mps does not support float64
               UpperCAmelCase     			=						torch.from_numpy(lowercase							).to(lowercase  ,							dtype=torch.floataa							)
           else:
               UpperCAmelCase     			=						torch.from_numpy(lowercase							).to(device=lowercase							)

           UpperCAmelCase     			=						[]
       def        A (      self		:      int  ,							lowercase		:      List[str]  ,							lowercase		:      Union[str, Any]							):



           '''simple docstring'''

           UpperCAmelCase     			=						np.log(lowercase							)

           # 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(lowercase  ,							0  ,							1							)

           # transform interpolation to time range
           UpperCAmelCase     			=						(1 - w) * low_idx + w * high_idx
           UpperCAmelCase     			=						t.reshape(sigma.shape							)
           return t
       def        A (      self		:      Any  ,							lowercase		:      torch.FloatTensor							):



           '''simple docstring'''

           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        A (      self		:      Union[str, Any]  ,							lowercase		:      torch.FloatTensor  ,							lowercase		:      Union[float, torch.FloatTensor]  ,							lowercase		:      torch.FloatTensor  ,							lowercase		:      int = 4  ,							lowercase		:      bool = True  ,							):



           '''simple docstring'''

           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(lowercase  ,							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(lowercase							)
           if len(self.derivatives							) > order:
               self.derivatives.pop(0							)

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

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

           if not return_dict:
               return (prev_sample,)

           return LMSDiscreteSchedulerOutput(prev_sample=lowercase  ,							pred_original_sample=lowercase							)
       def        A (      self		:      Optional[Any]  ,							lowercase		:      torch.FloatTensor  ,							lowercase		:      torch.FloatTensor  ,							lowercase		:      torch.FloatTensor  ,							):



           '''simple docstring'''

           UpperCAmelCase     			=						self.sigmas.to(device=original_samples.device  ,							dtype=original_samples.dtype							)
           if original_samples.device.type == "mps" and torch.is_floating_point(lowercase							):
               # 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		:      Optional[int]							):



           '''simple docstring'''

           return self.config.num_train_timesteps










'''simple docstring'''







def 		snake_case_				(_a      :				Any       ,  _a      :				Union[str, Any]	):
    if n < 0:
        return 0
    # table[i] represents the number of ways to get to amount i
    UpperCAmelCase     			=						[0] * (n + 1)

    # There is exactly 1 way to get to zero(You pick no coins).
    UpperCAmelCase     			=						1

    # Pick all coins one by one and update table[] values
    # after the index greater than or equal to the value of the
    # picked coin
    for coin_val in s:
        for j in range(_a       ,  n + 1	):
            table[j] += table[j - coin_val]

    return table[n]


if __name__ == "__main__":
   import doctest

   doctest.testmod()




