


'''simple docstring'''







from __future__ import annotations

from math import pow, sqrt






def 				lowerCAmelCase__					(    lowerCamelCase					:      float  ,lowerCamelCase					:      float  ,lowerCamelCase					:      float       ):
       if (resistance, reactance, impedance).count(0       ) != 1:
              raise ValueError('One and only one argument must be 0'       )
       if resistance == 0:
              return {"resistance": sqrt(pow(snake_case__  ,2       ) - pow(snake_case__  ,2       )       )}
       elif reactance == 0:
              return {"reactance": sqrt(pow(snake_case__  ,2       ) - pow(snake_case__  ,2       )       )}
       elif impedance == 0:
              return {"impedance": sqrt(pow(snake_case__  ,2       ) + pow(snake_case__  ,2       )       )}
       else:
              raise ValueError('Exactly one argument must be 0'       )


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''







import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput






def 				lowerCAmelCase__	(    lowerCamelCase					:      int  ,lowerCamelCase					:      str=0.999  ,lowerCamelCase					:      int="cosine"  ,):
       if alpha_transform_type == "cosine":

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

       elif alpha_transform_type == "exp":

              def alpha_bar_fn(lowerCamelCase					:      List[Any]       ):
                     return math.exp(t * -12.0       )

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

       _A					:     Tuple     = []
       for i in range(lowerCamelCase       ):
              _A					:     List[Any]     = i / num_diffusion_timesteps
              _A					:     List[str]     = (i + 1) / num_diffusion_timesteps
              betas.append(min(1 - alpha_bar_fn(lowerCamelCase       ) / alpha_bar_fn(lowerCamelCase       )  ,lowerCamelCase       )       )
       return torch.tensor(lowerCamelCase  ,dtype=torch.floataa       )


class 			__lowerCamelCase			(	a_    , a_	):
    """simple docstring"""
    a													=   [e.name for e in KarrasDiffusionSchedulers]
    a													=   2


    @register_to_config
    def __init__(  self      :							int				,							SCREAMING_SNAKE_CASE      :							int = 1000				,							SCREAMING_SNAKE_CASE      :							float = 0.0_0085				,							SCREAMING_SNAKE_CASE      :							float = 0.012				,							SCREAMING_SNAKE_CASE      :							str = "linear"				,							SCREAMING_SNAKE_CASE      :							Optional[Union[np.ndarray, List[float]]] = None				,							SCREAMING_SNAKE_CASE      :							str = "epsilon"				,							SCREAMING_SNAKE_CASE      :							str = "linspace"				,							SCREAMING_SNAKE_CASE      :							int = 0				,							):
           if trained_betas is not None:
                  _A					:     Optional[int]     = torch.tensor(SCREAMING_SNAKE_CASE				,							dtype=torch.floataa)
           elif beta_schedule == "linear":
                  _A					:     List[Any]     = torch.linspace(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE				,							dtype=torch.floataa)
           elif beta_schedule == "scaled_linear":
                  # this schedule is very specific to the latent diffusion model.
                  _A					:     Any     = (
                      torch.linspace(beta_start**0.5				,							beta_end**0.5				,							SCREAMING_SNAKE_CASE				,							dtype=torch.floataa) ** 2
                  )
           elif beta_schedule == "squaredcos_cap_v2":
                  # Glide cosine schedule
                  _A					:     Optional[Any]     = betas_for_alpha_bar(SCREAMING_SNAKE_CASE)
           else:
                  raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}')

           _A					:     Any     = 1.0 - self.betas
           _A					:     List[Any]     = torch.cumprod(self.alphas				,							dim=0)

           #  set all values
           self.set_timesteps(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE)


    def        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							Optional[int]				,							SCREAMING_SNAKE_CASE      :							Any=None):
           if schedule_timesteps is None:
                  _A					:     Dict     = self.timesteps

           _A					:     List[Any]     = (schedule_timesteps == timestep).nonzero()

           # The sigma index that is taken for the **very** first `step`
           # is always the second index (or the last index if there is only 1)
           # This way we can ensure we don't accidentally skip a sigma in
           # case we start in the middle of the denoising schedule (e.g. for image-to-image)
           if len(self._index_counter) == 0:
                  _A					:     Dict     = 1 if len(SCREAMING_SNAKE_CASE) > 1 else 0
           else:
                  _A					:     Union[str, Any]     = timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE) else timestep
                  _A					:     int     = self._index_counter[timestep_int]

           return indices[pos].item()


    @property
    def        A   (  self      :							Optional[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        A   (  self      :							List[Any]				,							SCREAMING_SNAKE_CASE      :							torch.FloatTensor				,							SCREAMING_SNAKE_CASE      :							Union[float, torch.FloatTensor]				,							):
           _A					:     Tuple     = self.index_for_timestep(SCREAMING_SNAKE_CASE)

           if self.state_in_first_order:
                  _A					:     Any     = self.sigmas[step_index]
           else:
                  _A					:     int     = self.sigmas_interpol[step_index]

           _A					:     Union[str, Any]     = sample / ((sigma**2 + 1) ** 0.5)
           return sample


    def        A   (  self      :							Tuple				,							SCREAMING_SNAKE_CASE      :							int				,							SCREAMING_SNAKE_CASE      :							Union[str, torch.device] = None				,							SCREAMING_SNAKE_CASE      :							Optional[int] = None				,							):
           _A					:     Optional[Any]     = num_inference_steps

           _A					:     int     = num_train_timesteps or self.config.num_train_timesteps

           # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
           if self.config.timestep_spacing == "linspace":
                  _A					:     Tuple     = np.linspace(0				,							num_train_timesteps - 1				,							SCREAMING_SNAKE_CASE				,							dtype=SCREAMING_SNAKE_CASE)[::-1].copy()
           elif self.config.timestep_spacing == "leading":
                  _A					:     Optional[Any]     = 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
                  _A					:     int     = (np.arange(0				,							SCREAMING_SNAKE_CASE) * step_ratio).round()[::-1].copy().astype(SCREAMING_SNAKE_CASE)
                  timesteps += self.config.steps_offset
           elif self.config.timestep_spacing == "trailing":
                  _A					:     List[str]     = 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
                  _A					:     str     = (np.arange(SCREAMING_SNAKE_CASE				,							0				,							-step_ratio)).round().copy().astype(SCREAMING_SNAKE_CASE)
                  timesteps -= 1
           else:
                  raise ValueError(
                      F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.')

           _A					:     List[str]     = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
           _A					:     Optional[int]     = torch.from_numpy(np.log(SCREAMING_SNAKE_CASE)).to(SCREAMING_SNAKE_CASE)

           _A					:     str     = np.interp(SCREAMING_SNAKE_CASE				,							np.arange(0				,							len(SCREAMING_SNAKE_CASE))				,							SCREAMING_SNAKE_CASE)
           _A					:     str     = np.concatenate([sigmas, [0.0]]).astype(np.floataa)
           _A					:     Union[str, Any]     = torch.from_numpy(SCREAMING_SNAKE_CASE).to(device=SCREAMING_SNAKE_CASE)

           # interpolate sigmas
           _A					:     Optional[int]     = sigmas.log().lerp(sigmas.roll(1).log()				,							0.5).exp()

           _A					:     Any     = torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2), sigmas[-1:]])
           _A					:     List[Any]     = torch.cat(
               [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2), sigmas_interpol[-1:]])

           if str(SCREAMING_SNAKE_CASE).startswith('mps'):
                  # mps does not support float64
                  _A					:     Union[str, Any]     = torch.from_numpy(SCREAMING_SNAKE_CASE).to(SCREAMING_SNAKE_CASE				,							dtype=torch.floataa)
           else:
                  _A					:     Dict     = torch.from_numpy(SCREAMING_SNAKE_CASE).to(SCREAMING_SNAKE_CASE)

           # interpolate timesteps
           _A					:     Optional[int]     = self.sigma_to_t(SCREAMING_SNAKE_CASE).to(SCREAMING_SNAKE_CASE				,							dtype=timesteps.dtype)
           _A					:     Union[str, Any]     = torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])				,							dim=-1).flatten()

           _A					:     Optional[Any]     = torch.cat([timesteps[:1], interleaved_timesteps])

           _A					:     str     = None

           # for exp beta schedules, such as the one for `pipeline_shap_e.py`
           # we need an index counter
           _A					:     Union[str, Any]     = defaultdict(SCREAMING_SNAKE_CASE)


    def        A   (  self      :							Union[str, Any]				,							SCREAMING_SNAKE_CASE      :							Union[str, Any]):
           # get log sigma
           _A					:     Dict     = sigma.log()

           # get distribution
           _A					:     Any     = log_sigma - self.log_sigmas[:, None]

           # get sigmas range
           _A					:     Tuple     = dists.ge(0).cumsum(dim=0).argmax(dim=0).clamp(max=self.log_sigmas.shape[0] - 2)
           _A					:     Union[str, Any]     = low_idx + 1

           _A					:     Dict     = self.log_sigmas[low_idx]
           _A					:     List[Any]     = self.log_sigmas[high_idx]

           # interpolate sigmas
           _A					:     Dict     = (low - log_sigma) / (low - high)
           _A					:     Union[str, Any]     = w.clamp(0				,							1)

           # transform interpolation to time range
           _A					:     int     = (1 - w) * low_idx + w * high_idx
           _A					:     Any     = t.view(sigma.shape)
           return t


    @property
    def        A   (  self      :							Any):
           return self.sample is None


    def        A   (  self      :							int				,							SCREAMING_SNAKE_CASE      :							Union[torch.FloatTensor, np.ndarray]				,							SCREAMING_SNAKE_CASE      :							Union[float, torch.FloatTensor]				,							SCREAMING_SNAKE_CASE      :							Union[torch.FloatTensor, np.ndarray]				,							SCREAMING_SNAKE_CASE      :							bool = True				,							):
           _A					:     Optional[int]     = self.index_for_timestep(SCREAMING_SNAKE_CASE)

           # advance index counter by 1
           _A					:     Dict     = timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE) else timestep
           self._index_counter[timestep_int] += 1

           if self.state_in_first_order:
                  _A					:     Tuple     = self.sigmas[step_index]
                  _A					:     Dict     = self.sigmas_interpol[step_index + 1]
                  _A					:     Union[str, Any]     = self.sigmas[step_index + 1]
           else:
                  # 2nd order / KDPM2's method
                  _A					:     int     = self.sigmas[step_index - 1]
                  _A					:     Union[str, Any]     = self.sigmas_interpol[step_index]
                  _A					:     Dict     = self.sigmas[step_index]

           # currently only gamma=0 is supported. This usually works best anyways.
           # We can support gamma in the future but then need to scale the timestep before
           # passing it to the model which requires a change in API
           _A					:     List[Any]     = 0
           _A					:     Dict     = sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

           # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
           if self.config.prediction_type == "epsilon":
                  _A					:     Tuple     = sigma_hat if self.state_in_first_order else sigma_interpol
                  _A					:     Tuple     = sample - sigma_input * model_output
           elif self.config.prediction_type == "v_prediction":
                  _A					:     Any     = sigma_hat if self.state_in_first_order else sigma_interpol
                  _A					:     Union[str, Any]     = model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
                      sample / (sigma_input**2 + 1)
                  )
           elif self.config.prediction_type == "sample":
                  raise NotImplementedError('prediction_type not implemented yet: sample')
           else:
                  raise ValueError(
                      F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`')

           if self.state_in_first_order:
                  # 2. Convert to an ODE derivative for 1st order
                  _A					:     int     = (sample - pred_original_sample) / sigma_hat
                  # 3. delta timestep
                  _A					:     str     = sigma_interpol - sigma_hat

                  # store for 2nd order step
                  _A					:     List[str]     = sample
           else:
                  # DPM-Solver-2
                  # 2. Convert to an ODE derivative for 2nd order
                  _A					:     List[Any]     = (sample - pred_original_sample) / sigma_interpol

                  # 3. delta timestep
                  _A					:     Optional[int]     = sigma_next - sigma_hat

                  _A					:     str     = self.sample
                  _A					:     Any     = None

           _A					:     Tuple     = sample + derivative * dt

           if not return_dict:
                  return (prev_sample,)

           return SchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE)


    def        A   (  self      :							Any				,							SCREAMING_SNAKE_CASE      :							torch.FloatTensor				,							SCREAMING_SNAKE_CASE      :							torch.FloatTensor				,							SCREAMING_SNAKE_CASE      :							torch.FloatTensor				,							):
           # Make sure sigmas and timesteps have the same device and dtype as original_samples
           _A					:     str     = self.sigmas.to(device=original_samples.device				,							dtype=original_samples.dtype)
           if original_samples.device.type == "mps" and torch.is_floating_point(SCREAMING_SNAKE_CASE):
                  # mps does not support float64
                  _A					:     Any     = self.timesteps.to(original_samples.device				,							dtype=torch.floataa)
                  _A					:     List[str]     = timesteps.to(original_samples.device				,							dtype=torch.floataa)
           else:
                  _A					:     str     = self.timesteps.to(original_samples.device)
                  _A					:     str     = timesteps.to(original_samples.device)

           _A					:     int     = [self.index_for_timestep(SCREAMING_SNAKE_CASE				,							SCREAMING_SNAKE_CASE) for t in timesteps]

           _A					:     Tuple     = sigmas[step_indices].flatten()
           while len(sigma.shape) < len(original_samples.shape):
                  _A					:     List[Any]     = sigma.unsqueeze(-1)

           _A					:     Dict     = original_samples + noise * sigma
           return noisy_samples


    def __len__(  self      :							List[Any]):
           return self.config.num_train_timesteps






