



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   (						A__						,  A__=0.9_99						,  A__="cosine"						,  ):
      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

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

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

      lowercase__     =  []
      for i in range(a_	):
            lowercase__     =  i / num_diffusion_timesteps
            lowercase__     =  (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       UpperCAmelCase__(							_UpperCamelCase     ,							_UpperCamelCase	):

   '''simple docstring'''




   A    :  int       				=    [e.name for e in KarrasDiffusionSchedulers]
   A    :  Dict       				=    2


   @register_to_config
   def __init__(						self  :			Optional[int]			,				lowerCAmelCase  :			Dict = 10_00			,				lowerCAmelCase  :			Tuple = 0.0_00_85			,				lowerCAmelCase  :			List[str] = 0.0_12			,				lowerCAmelCase  :			Optional[int] = "linear"			,				lowerCAmelCase  :			List[str] = None			,				lowerCAmelCase  :			Any = "epsilon"			,				lowerCAmelCase  :			List[Any] = "linspace"			,				lowerCAmelCase  :			List[str] = 0			,				)	->				Optional[int]:




         """simple docstring"""

         if trained_betas is not None:
               lowercase__     =  torch.tensor(_UpperCAmelCase			,				dtype=torch.floataa)
         elif beta_schedule == "linear":
               lowercase__     =  torch.linspace(_UpperCAmelCase			,				_UpperCAmelCase			,				_UpperCAmelCase			,				dtype=torch.floataa)
         elif beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               lowercase__     =  (
                   torch.linspace(beta_start**0.5			,				beta_end**0.5			,				_UpperCAmelCase			,				dtype=torch.floataa) ** 2
               )
         elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               lowercase__     =  betas_for_alpha_bar(_UpperCAmelCase)
         else:
               raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}''')

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

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


   def 			UpperCAmelCase		(						self  :			Optional[int]			,				lowerCAmelCase  :			List[Any]			,				lowerCAmelCase  :			Optional[int]=None)	->				str:




         """simple docstring"""

         if schedule_timesteps is None:
               lowercase__     =  self.timesteps

         lowercase__     =  (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:
               lowercase__     =  1 if len(_UpperCAmelCase) > 1 else 0
         else:
               lowercase__     =  timestep.cpu().item() if torch.is_tensor(_UpperCAmelCase) else timestep
               lowercase__     =  self._index_counter[timestep_int]

         return indices[pos].item()


   @property
   def 			UpperCAmelCase		(						self  :			Any)	->				Optional[Any]:




         """simple docstring"""

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

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


   def 			UpperCAmelCase		(						self  :			Optional[Any]			,				lowerCAmelCase  :			Optional[Any]			,				lowerCAmelCase  :			str			,				)	->				Dict:




         """simple docstring"""

         lowercase__     =  self.index_for_timestep(_UpperCAmelCase)

         if self.state_in_first_order:
               lowercase__     =  self.sigmas[step_index]
         else:
               lowercase__     =  self.sigmas_interpol[step_index]

         lowercase__     =  sample / ((sigma**2 + 1) ** 0.5)
         return sample


   def 			UpperCAmelCase		(						self  :			Optional[Any]			,				lowerCAmelCase  :			Optional[Any]			,				lowerCAmelCase  :			List[Any] = None			,				lowerCAmelCase  :			Optional[Any] = None			,				)	->				List[Any]:




         """simple docstring"""

         lowercase__     =  num_inference_steps

         lowercase__     =  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":
               lowercase__     =  np.linspace(0			,				num_train_timesteps - 1			,				_UpperCAmelCase			,				dtype=_UpperCAmelCase)[::-1].copy()
         elif self.config.timestep_spacing == "leading":
               lowercase__     =  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
               lowercase__     =  (np.arange(0			,				_UpperCAmelCase) * step_ratio).round()[::-1].copy().astype(_UpperCAmelCase)
               timesteps += self.config.steps_offset
         elif self.config.timestep_spacing == "trailing":
               lowercase__     =  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
               lowercase__     =  (np.arange(_UpperCAmelCase			,				0			,				-step_ratio)).round().copy().astype(_UpperCAmelCase)
               timesteps -= 1
         else:
               raise ValueError(
                   f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.''')

         lowercase__     =  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
         lowercase__     =  torch.from_numpy(np.log(_UpperCAmelCase)).to(_UpperCAmelCase)

         lowercase__     =  np.interp(_UpperCAmelCase			,				np.arange(0			,				len(_UpperCAmelCase))			,				_UpperCAmelCase)
         lowercase__     =  np.concatenate([sigmas, [0.0]]).astype(np.floataa)
         lowercase__     =  torch.from_numpy(_UpperCAmelCase).to(device=_UpperCAmelCase)

         # interpolate sigmas
         lowercase__     =  sigmas.log().lerp(sigmas.roll(1).log()			,				0.5).exp()

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

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

         # interpolate timesteps
         lowercase__     =  self.sigma_to_t(_UpperCAmelCase).to(_UpperCAmelCase			,				dtype=timesteps.dtype)
         lowercase__     =  torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])			,				dim=-1).flatten()

         lowercase__     =  torch.cat([timesteps[:1], interleaved_timesteps])

         lowercase__     =  None

         # for exp beta schedules, such as the one for `pipeline_shap_e.py`
         # we need an index counter
         lowercase__     =  defaultdict(_UpperCAmelCase)


   def 			UpperCAmelCase		(						self  :			Union[str, Any]			,				lowerCAmelCase  :			Any)	->				Optional[Any]:




         """simple docstring"""

         lowercase__     =  sigma.log()

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

         # get sigmas range
         lowercase__     =  dists.ge(0).cumsum(dim=0).argmax(dim=0).clamp(max=self.log_sigmas.shape[0] - 2)
         lowercase__     =  low_idx + 1

         lowercase__     =  self.log_sigmas[low_idx]
         lowercase__     =  self.log_sigmas[high_idx]

         # interpolate sigmas
         lowercase__     =  (low - log_sigma) / (low - high)
         lowercase__     =  w.clamp(0			,				1)

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


   @property
   def 			UpperCAmelCase		(						self  :			Optional[Any])	->				Any:




         """simple docstring"""

         return self.sample is None


   def 			UpperCAmelCase		(						self  :			Optional[int]			,				lowerCAmelCase  :			Tuple			,				lowerCAmelCase  :			List[Any]			,				lowerCAmelCase  :			Tuple			,				lowerCAmelCase  :			Optional[Any] = True			,				)	->				int:




         """simple docstring"""

         lowercase__     =  self.index_for_timestep(_UpperCAmelCase)

         # advance index counter by 1
         lowercase__     =  timestep.cpu().item() if torch.is_tensor(_UpperCAmelCase) else timestep
         self._index_counter[timestep_int] += 1

         if self.state_in_first_order:
               lowercase__     =  self.sigmas[step_index]
               lowercase__     =  self.sigmas_interpol[step_index + 1]
               lowercase__     =  self.sigmas[step_index + 1]
         else:
               # 2nd order / KDPM2's method
               lowercase__     =  self.sigmas[step_index - 1]
               lowercase__     =  self.sigmas_interpol[step_index]
               lowercase__     =  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
         lowercase__     =  0
         lowercase__     =  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":
               lowercase__     =  sigma_hat if self.state_in_first_order else sigma_interpol
               lowercase__     =  sample - sigma_input * model_output
         elif self.config.prediction_type == "v_prediction":
               lowercase__     =  sigma_hat if self.state_in_first_order else sigma_interpol
               lowercase__     =  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
               lowercase__     =  (sample - pred_original_sample) / sigma_hat
               # 3. delta timestep
               lowercase__     =  sigma_interpol - sigma_hat

               # store for 2nd order step
               lowercase__     =  sample
         else:
               # DPM-Solver-2
               # 2. Convert to an ODE derivative for 2nd order
               lowercase__     =  (sample - pred_original_sample) / sigma_interpol

               # 3. delta timestep
               lowercase__     =  sigma_next - sigma_hat

               lowercase__     =  self.sample
               lowercase__     =  None

         lowercase__     =  sample + derivative * dt

         if not return_dict:
               return (prev_sample,)

         return SchedulerOutput(prev_sample=_UpperCAmelCase)


   def 			UpperCAmelCase		(						self  :			Optional[int]			,				lowerCAmelCase  :			str			,				lowerCAmelCase  :			List[str]			,				lowerCAmelCase  :			Dict			,				)	->				List[Any]:




         """simple docstring"""

         lowercase__     =  self.sigmas.to(device=original_samples.device			,				dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(_UpperCAmelCase):
               # mps does not support float64
               lowercase__     =  self.timesteps.to(original_samples.device			,				dtype=torch.floataa)
               lowercase__     =  timesteps.to(original_samples.device			,				dtype=torch.floataa)
         else:
               lowercase__     =  self.timesteps.to(original_samples.device)
               lowercase__     =  timesteps.to(original_samples.device)

         lowercase__     =  [self.index_for_timestep(_UpperCAmelCase			,				_UpperCAmelCase) for t in timesteps]

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

         lowercase__     =  original_samples + noise * sigma
         return noisy_samples



   def __len__(						self  :			List[str])	->				Tuple:




         """simple docstring"""

         return self.config.num_train_timesteps





def   _lowerCAmelCase   (						A__						,  A__						,  A__	):
      if principal <= 0:
            raise Exception('Principal borrowed must be > 0'	)
      if rate_per_annum < 0:
            raise Exception('Rate of interest must be >= 0'	)
      if years_to_repay <= 0 or not isinstance(A__						,  A__	):
            raise Exception('Years to repay must be an integer > 0'	)

      # Yearly rate is divided by 12 to get monthly rate
      lowercase__     =  rate_per_annum / 12

      # Years to repay is multiplied by 12 to get number of payments as payment is monthly
      lowercase__     =  years_to_repay * 12

      return (
          principal
          * rate_per_month
          * (1 + rate_per_month) ** number_of_payments
          / ((1 + rate_per_month) ** number_of_payments - 1)
      )


if __name__ == "__main__":
       import doctest

       doctest.testmod()
