


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       (      _UpperCAmelCase ):
     UpperCAmelCase__			:	torch.FloatTensor
     UpperCAmelCase__			:	Optional[torch.FloatTensor]       =						None



def      __lowerCAmelCase    (				snake_case						:     Optional[int]    ,   snake_case						:     Any=0.999    ,   snake_case						:     int="cosine"    ,   )							->				str:
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(snake_case						:     Optional[int]			):
         return math.cos((t + 0.008) / 1.008 * math.pi / 2			) ** 2

   elif alpha_transform_type == "exp":

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

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

   __lowerCamelCase:					Optional[Any]	 =						[]
   for i in range(snake_case			):
      __lowerCamelCase:					Dict	 =						i / num_diffusion_timesteps
      __lowerCamelCase:					Union[str, Any]	 =						(i + 1) / num_diffusion_timesteps
      betas.append(min(1 - alpha_bar_fn(snake_case			) / alpha_bar_fn(snake_case			)    ,   snake_case			)			)
   return torch.tensor(snake_case    ,   dtype=torch.floataa			)







class 							a       (      _UpperCAmelCase  ,_UpperCAmelCase ):
     UpperCAmelCase__			:	int       =						[e.name for e in KarrasDiffusionSchedulers]
     UpperCAmelCase__			:	Union[str, Any]       =						1





     @register_to_config
     def __init__(     self       :					Any     ,						SCREAMING_SNAKE_CASE_       :					int = 1000     ,						SCREAMING_SNAKE_CASE_       :					float = 0.0001     ,						SCREAMING_SNAKE_CASE_       :					float = 0.02     ,						SCREAMING_SNAKE_CASE_       :					str = "linear"     ,						SCREAMING_SNAKE_CASE_       :					Optional[Union[np.ndarray, List[float]]] = None     ,						SCREAMING_SNAKE_CASE_       :					Optional[bool] = False     ,						SCREAMING_SNAKE_CASE_       :					str = "epsilon"     ,						SCREAMING_SNAKE_CASE_       :					str = "linspace"     ,						SCREAMING_SNAKE_CASE_       :					int = 0     ,						):
        if trained_betas is not None:
           __lowerCamelCase:					int	 =						torch.tensor(SCREAMING_SNAKE_CASE_     ,						dtype=torch.floataa				)
        elif beta_schedule == "linear":
           __lowerCamelCase:					Union[str, 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.
           __lowerCamelCase:					int	 =						(
               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
           __lowerCamelCase:					List[Any]	 =						betas_for_alpha_bar(SCREAMING_SNAKE_CASE_				)
        else:
           raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'				)

        __lowerCamelCase:					Union[str, Any]	 =						1.0 - self.betas
        __lowerCamelCase:					str	 =						torch.cumprod(self.alphas     ,						dim=0				)

        __lowerCamelCase:					Tuple	 =						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
        __lowerCamelCase:					Optional[Any]	 =						np.concatenate([sigmas[::-1], [0.0]]				).astype(np.floataa				)
        __lowerCamelCase:					int	 =						torch.from_numpy(SCREAMING_SNAKE_CASE_				)

        # setable values
        __lowerCamelCase:					List[Any]	 =						None
        __lowerCamelCase:					Union[str, Any]	 =						use_karras_sigmas
        self.set_timesteps(SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_				)
        __lowerCamelCase:					Any	 =						[]
        __lowerCamelCase:					Tuple	 =						False





     @property
     def 			SCREAMING_SNAKE_CASE__							(     self       :					List[str]				):
        # 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 			SCREAMING_SNAKE_CASE__							(     self       :					Optional[Any]     ,						SCREAMING_SNAKE_CASE_       :					torch.FloatTensor     ,						SCREAMING_SNAKE_CASE_       :					Union[float, torch.FloatTensor]				):
        if isinstance(SCREAMING_SNAKE_CASE_     ,						torch.Tensor				):
           __lowerCamelCase:					Tuple	 =						timestep.to(self.timesteps.device				)
        __lowerCamelCase:					int	 =						(self.timesteps == timestep).nonzero().item()
        __lowerCamelCase:					List[str]	 =						self.sigmas[step_index]
        __lowerCamelCase:					Tuple	 =						sample / ((sigma**2 + 1) ** 0.5)
        __lowerCamelCase:					List[Any]	 =						True
        return sample





     def 			SCREAMING_SNAKE_CASE__							(     self       :					int     ,						SCREAMING_SNAKE_CASE_       :					str     ,						SCREAMING_SNAKE_CASE_       :					Union[str, Any]     ,						SCREAMING_SNAKE_CASE_       :					Dict				):

        def lms_derivative(SCREAMING_SNAKE_CASE_       :					List[str]				):
           __lowerCamelCase:					Any	 =						1.0
           for k in range(SCREAMING_SNAKE_CASE_				):
              if current_order == k:
                 continue
              prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
           return prod

        __lowerCamelCase:					List[Any]	 =						integrate.quad(SCREAMING_SNAKE_CASE_     ,						self.sigmas[t]     ,						self.sigmas[t + 1]     ,						epsrel=1E-4				)[0]

        return integrated_coeff





     def 			SCREAMING_SNAKE_CASE__							(     self       :					int     ,						SCREAMING_SNAKE_CASE_       :					int     ,						SCREAMING_SNAKE_CASE_       :					Union[str, torch.device] = None				):
        __lowerCamelCase:					Any	 =						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":
           __lowerCamelCase:					Optional[Any]	 =						np.linspace(0     ,						self.config.num_train_timesteps - 1     ,						SCREAMING_SNAKE_CASE_     ,						dtype=SCREAMING_SNAKE_CASE_				)[
               ::-1
           ].copy()
        elif self.config.timestep_spacing == "leading":
           __lowerCamelCase:					str	 =						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
           __lowerCamelCase:					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":
           __lowerCamelCase:					Union[str, Any]	 =						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
           __lowerCamelCase:					Union[str, Any]	 =						(np.arange(self.config.num_train_timesteps     ,						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\'.'				)

        __lowerCamelCase:					List[Any]	 =						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
        __lowerCamelCase:					List[Any]	 =						np.log(SCREAMING_SNAKE_CASE_				)
        __lowerCamelCase:					Any	 =						np.interp(SCREAMING_SNAKE_CASE_     ,						np.arange(0     ,						len(SCREAMING_SNAKE_CASE_				)				)     ,						SCREAMING_SNAKE_CASE_				)

        if self.use_karras_sigmas:
           __lowerCamelCase:					str	 =						self._convert_to_karras(in_sigmas=SCREAMING_SNAKE_CASE_				)
           __lowerCamelCase:					List[str]	 =						np.array([self._sigma_to_t(SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_				) for sigma in sigmas]				)

        __lowerCamelCase:					Any	 =						np.concatenate([sigmas, [0.0]]				).astype(np.floataa				)

        __lowerCamelCase:					int	 =						torch.from_numpy(SCREAMING_SNAKE_CASE_				).to(device=SCREAMING_SNAKE_CASE_				)
        if str(SCREAMING_SNAKE_CASE_				).startswith("""mps"""				):
           # mps does not support float64
           __lowerCamelCase:					Optional[int]	 =						torch.from_numpy(SCREAMING_SNAKE_CASE_				).to(SCREAMING_SNAKE_CASE_     ,						dtype=torch.floataa				)
        else:
           __lowerCamelCase:					int	 =						torch.from_numpy(SCREAMING_SNAKE_CASE_				).to(device=SCREAMING_SNAKE_CASE_				)

        __lowerCamelCase:					List[Any]	 =						[]





     def 			SCREAMING_SNAKE_CASE__							(     self       :					Optional[Any]     ,						SCREAMING_SNAKE_CASE_       :					Tuple     ,						SCREAMING_SNAKE_CASE_       :					Optional[Any]				):
        # get log sigma
        __lowerCamelCase:					str	 =						np.log(SCREAMING_SNAKE_CASE_				)

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

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

        __lowerCamelCase:					Any	 =						log_sigmas[low_idx]
        __lowerCamelCase:					int	 =						log_sigmas[high_idx]

        # interpolate sigmas
        __lowerCamelCase:					Any	 =						(low - log_sigma) / (low - high)
        __lowerCamelCase:					Tuple	 =						np.clip(SCREAMING_SNAKE_CASE_     ,						0     ,						1				)

        # transform interpolation to time range
        __lowerCamelCase:					Dict	 =						(1 - w) * low_idx + w * high_idx
        __lowerCamelCase:					Union[str, Any]	 =						t.reshape(sigma.shape				)
        return t





     def 			SCREAMING_SNAKE_CASE__							(     self       :					int     ,						SCREAMING_SNAKE_CASE_       :					torch.FloatTensor				):
        __lowerCamelCase:					float	 =						in_sigmas[-1].item()
        __lowerCamelCase:					float	 =						in_sigmas[0].item()

        __lowerCamelCase:					Dict	 =						7.0  # 7.0 is the value used in the paper
        __lowerCamelCase:					Dict	 =						np.linspace(0     ,						1     ,						self.num_inference_steps				)
        __lowerCamelCase:					Tuple	 =						sigma_min ** (1 / rho)
        __lowerCamelCase:					Optional[Any]	 =						sigma_max ** (1 / rho)
        __lowerCamelCase:					Tuple	 =						(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return sigmas





     def 			SCREAMING_SNAKE_CASE__							(     self       :					Optional[int]     ,						SCREAMING_SNAKE_CASE_       :					torch.FloatTensor     ,						SCREAMING_SNAKE_CASE_       :					Union[float, torch.FloatTensor]     ,						SCREAMING_SNAKE_CASE_       :					torch.FloatTensor     ,						SCREAMING_SNAKE_CASE_       :					int = 4     ,						SCREAMING_SNAKE_CASE_       :					bool = True     ,						):
        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(SCREAMING_SNAKE_CASE_     ,						torch.Tensor				):
           __lowerCamelCase:					Any	 =						timestep.to(self.timesteps.device				)
        __lowerCamelCase:					int	 =						(self.timesteps == timestep).nonzero().item()
        __lowerCamelCase:					Optional[int]	 =						self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
           __lowerCamelCase:					Any	 =						sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
           # * c_out + input * c_skip
           __lowerCamelCase:					Any	 =						model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        elif self.config.prediction_type == "sample":
           __lowerCamelCase:					Optional[Any]	 =						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
        __lowerCamelCase:					List[Any]	 =						(sample - pred_original_sample) / sigma
        self.derivatives.append(SCREAMING_SNAKE_CASE_				)
        if len(self.derivatives				) > order:
           self.derivatives.pop(0				)

        # 3. Compute linear multistep coefficients
        __lowerCamelCase:					Dict	 =						min(step_index + 1     ,						SCREAMING_SNAKE_CASE_				)
        __lowerCamelCase:					str	 =						[self.get_lms_coefficient(SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_				) for curr_order in range(SCREAMING_SNAKE_CASE_				)]

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

        if not return_dict:
           return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_     ,						pred_original_sample=SCREAMING_SNAKE_CASE_				)





     def 			SCREAMING_SNAKE_CASE__							(     self       :					int     ,						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
        __lowerCamelCase:					Union[str, Any]	 =						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
           __lowerCamelCase:					str	 =						self.timesteps.to(original_samples.device     ,						dtype=torch.floataa				)
           __lowerCamelCase:					Optional[int]	 =						timesteps.to(original_samples.device     ,						dtype=torch.floataa				)
        else:
           __lowerCamelCase:					Optional[Any]	 =						self.timesteps.to(original_samples.device				)
           __lowerCamelCase:					str	 =						timesteps.to(original_samples.device				)

        __lowerCamelCase:					Dict	 =						[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

        __lowerCamelCase:					Union[str, Any]	 =						original_samples + noise * sigma
        return noisy_samples







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






_A		:					Optional[int]          =							{
    '''+''': lambda x, y: x + y,
    '''-''': lambda x, y: x - y,
    '''*''': lambda x, y: x * y,
    '''/''': lambda x, y: x / y,
}



def      __lowerCAmelCase    (				snake_case						:     Union[str, Any]			)							->				str:
   return c.isdigit()



def      __lowerCAmelCase    (				snake_case						:     Optional[Any]			)							->				str:
   __lowerCamelCase:					List[str]	 =						[]

   # iterate over the string in reverse order
   for c in expression.split()[::-1]:
      # push operand to stack
      if is_operand(snake_case			):
         stack.append(int(snake_case			)			)

      else:
         # pop values from stack can calculate the result
         # push the result onto the stack again
         __lowerCamelCase:					Any	 =						stack.pop()
         __lowerCamelCase:					int	 =						stack.pop()
         stack.append(calc[c](snake_case    ,   snake_case			)			)

   return stack.pop()


# Driver code
if __name__ == "__main__":
   _A		:					int          =							'''+ 9 * 2 6'''
   print(evaluate(test_expression))

   _A		:					str          =							'''/ * 10 2 + 4 1 '''
   print(evaluate(test_expression))


