




'''simple docstring'''
import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

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






@dataclass
class 			SCREAMING_SNAKE_CASE(							__A	):
       snake_case_					:	torch.FloatTensor
       snake_case_					:	torch.FloatTensor

def 							snake_case_    (  a__						:      Optional[Any]       ,a__						:      Optional[int]=0.9_9_9       ,a__						:      Tuple="cosine"       ,):



    """simple docstring"""




    if alpha_transform_type == "cosine":

        def alpha_bar_fn(a__						:      int     ):
            return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2     ) ** 2

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(a__						:      Union[str, Any]     ):
            return math.exp(t * -1_2.0     )

    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 			SCREAMING_SNAKE_CASE(							__A  , __A	):
       snake_case_					:	Tuple       =   1

       @register_to_config
       def __init__(       self   ,						lowerCamelCase__ = 1000   ,						lowerCamelCase__ = 0.00_01   ,						lowerCamelCase__ = 0.02   ,						lowerCamelCase__ = "linear"   ,						lowerCamelCase__ = 0.0   ,						lowerCamelCase__ = None   ,						lowerCamelCase__ = True   ,						)       ->   Optional[Any]:

           """simple docstring"""



           if trained_betas is not None:
               __lowercase     							=		torch.from_numpy(lowerCamelCase__	)
           elif beta_schedule == "linear":
               __lowercase     							=		torch.linspace(lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						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   ,						lowerCamelCase__   ,						dtype=torch.floataa	) ** 2
               )
           elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               __lowercase     							=		betas_for_alpha_bar(lowerCamelCase__	)
           elif beta_schedule == "sigmoid":
               # GeoDiff sigmoid schedule
               __lowercase     							=		torch.linspace(-6   ,						6   ,						lowerCamelCase__	)
               __lowercase     							=		torch.sigmoid(lowerCamelCase__	) * (beta_end - beta_start) + beta_start
           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	)
           __lowercase     							=		torch.tensor(1.0	)

           __lowercase     							=		torch.tensor(1.0	)

           # standard deviation of the initial noise distribution
           __lowercase     							=		1.0

           # setable values
           __lowercase     							=		None
           __lowercase     							=		torch.from_numpy(np.arange(0   ,						lowerCamelCase__	)[::-1].copy()	)

           __lowercase     							=		eta

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__ = None	)       ->   torch.FloatTensor:

           """simple docstring"""



           return sample

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__ = 10   ,						lowerCamelCase__ = 10   ,						lowerCamelCase__ = None   ,						)       ->   List[str]:

           """simple docstring"""



           __lowercase     							=		min(self.config.num_train_timesteps   ,						lowerCamelCase__	)
           __lowercase     							=		num_inference_steps

           __lowercase     							=		[]

           __lowercase     							=		{}
           for j in range(0   ,						num_inference_steps - jump_length   ,						lowerCamelCase__	):
               __lowercase     							=		jump_n_sample - 1

           __lowercase     							=		num_inference_steps
           while t >= 1:
               __lowercase     							=		t - 1
               timesteps.append(lowerCamelCase__	)

               if jumps.get(lowerCamelCase__   ,						0	) > 0:
                   __lowercase     							=		jumps[t] - 1
                   for _ in range(lowerCamelCase__	):
                       __lowercase     							=		t + 1
                       timesteps.append(lowerCamelCase__	)

           __lowercase     							=		np.array(lowerCamelCase__	) * (self.config.num_train_timesteps // self.num_inference_steps)
           __lowercase     							=		torch.from_numpy(lowerCamelCase__	).to(lowerCamelCase__	)

       def        snake_case__     (       self   ,						lowerCamelCase__	)       ->   Any:

           """simple docstring"""



           __lowercase     							=		t - self.config.num_train_timesteps // self.num_inference_steps

           __lowercase     							=		self.alphas_cumprod[t]
           __lowercase     							=		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
           __lowercase     							=		1 - alpha_prod_t
           __lowercase     							=		1 - alpha_prod_t_prev

           # For t > 0, compute predicted variance βt (see formula (6) and (7) from
           # https://arxiv.org/pdf/2006.11239.pdf) and sample from it to get
           # previous sample x_{t-1} ~ N(pred_prev_sample, variance) == add
           # variance to pred_sample
           # Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
           # without eta.
           # variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
           __lowercase     							=		(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

           return variance

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__ = None   ,						lowerCamelCase__ = True   ,						)       ->   Union[RePaintSchedulerOutput, Tuple]:

           """simple docstring"""



           __lowercase     							=		timestep
           __lowercase     							=		timestep - self.config.num_train_timesteps // self.num_inference_steps

           # 1. compute alphas, betas
           __lowercase     							=		self.alphas_cumprod[t]
           __lowercase     							=		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
           __lowercase     							=		1 - alpha_prod_t

           # 2. compute predicted original sample from predicted noise also called
           # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
           __lowercase     							=		(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

           # 3. Clip "predicted x_0"
           if self.config.clip_sample:
               __lowercase     							=		torch.clamp(lowerCamelCase__   ,						-1   ,						1	)

           # We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
           # substitute formula (7) in the algorithm coming from DDPM paper
           # (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
           # DDIM schedule gives the same results as DDPM with eta = 1.0
           # Noise is being reused in 7. and 8., but no impact on quality has
           # been observed.

           # 5. Add noise
           __lowercase     							=		model_output.device
           __lowercase     							=		randn_tensor(model_output.shape   ,						generator=lowerCamelCase__   ,						device=lowerCamelCase__   ,						dtype=model_output.dtype	)
           __lowercase     							=		self.eta * self._get_variance(lowerCamelCase__	) ** 0.5

           __lowercase     							=		0
           if t > 0 and self.eta > 0:
               __lowercase     							=		std_dev_t * noise

           # 6. compute "direction pointing to x_t" of formula (12)
           # from https://arxiv.org/pdf/2010.02502.pdf
           __lowercase     							=		(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

           # 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
           __lowercase     							=		alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

           # 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
           __lowercase     							=		(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

           # 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
           __lowercase     							=		mask * prev_known_part + (1.0 - mask) * prev_unknown_part

           if not return_dict:
               return (
                   pred_prev_sample,
                   pred_original_sample,
               )

           return RePaintSchedulerOutput(prev_sample=lowerCamelCase__   ,						pred_original_sample=lowerCamelCase__	)

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__=None	)       ->   Optional[int]:

           """simple docstring"""



           __lowercase     							=		self.config.num_train_timesteps // self.num_inference_steps

           for i in range(lowerCamelCase__	):
               __lowercase     							=		self.betas[timestep + i]
               if sample.device.type == "mps":
                   # randn does not work reproducibly on mps
                   __lowercase     							=		randn_tensor(sample.shape   ,						dtype=sample.dtype   ,						generator=lowerCamelCase__	)
                   __lowercase     							=		noise.to(sample.device	)
               else:
                   __lowercase     							=		randn_tensor(sample.shape   ,						generator=lowerCamelCase__   ,						device=sample.device   ,						dtype=sample.dtype	)

               # 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
               __lowercase     							=		(1 - beta) ** 0.5 * sample + beta**0.5 * noise

           return sample

       def        snake_case__     (       self   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						lowerCamelCase__   ,						)       ->   torch.FloatTensor:

           """simple docstring"""



           raise NotImplementedError("""Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."""	)




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

           """simple docstring"""



           return self.config.num_train_timesteps










'''simple docstring'''
def 							snake_case_    (  a__						:      int     ):



    """simple docstring"""




    __lowercase     							=		1
    __lowercase     							=		0
    __lowercase     							=		1
    __lowercase     							=		1
    __lowercase     							=		3
    __lowercase     							=		3
    __lowercase     							=		limit
    __lowercase     							=		0

    __lowercase     							=		""""""
    while counter != decimal + 1:
        if 4 * q + r - t < n * t:
            result += str(a__     )
            if counter == 0:
                result += "."

            if decimal == counter:
                break

            counter += 1
            __lowercase     							=		10 * (r - n * t)
            __lowercase     							=		((10 * (3 * q + r)) // t) - 10 * n
            q *= 10
            __lowercase     							=		nr
        else:
            __lowercase     							=		(2 * q + r) * l
            __lowercase     							=		(q * (7 * k) + 2 + (r * l)) // (t * l)
            q *= k
            t *= l
            l += 2
            k += 1
            __lowercase     							=		nn
            __lowercase     							=		nr
    return result
def 							snake_case_    (  ):



    """simple docstring"""




    print(f'{calculate_pi(50     ) = }'     )
    import doctest

    doctest.testmod()


if __name__ == "__main__":
  main()




