






"""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 		_a       (						lowercase_   ):





   '''simple docstring'''






   UpperCamelCase__      					=    42
   UpperCamelCase__      					=    42







def     A(  snake_case_						,       snake_case_=0.9_99						,       snake_case_="cosine"						,       ):
       """simple docstring"""





       if alpha_transform_type == "cosine":

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

       elif alpha_transform_type == "exp":

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

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

       lowercase__:    Dict        =      []
       for i in range(snake_case_		):
              lowercase__:    Optional[Any]        =      i / num_diffusion_timesteps
              lowercase__:    Dict        =      (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       (						lowercase_    ,					lowercase_   ):





   '''simple docstring'''






   UpperCamelCase__      					=    1





   @register_to_config
   def __init__(   self			,				UpperCAmelCase_ = 1_000			,				UpperCAmelCase_ = 0.00_01			,				UpperCAmelCase_ = 0.02			,				UpperCAmelCase_ = "linear"			,				UpperCAmelCase_ = 0.0			,				UpperCAmelCase_ = None			,				UpperCAmelCase_ = True			,				)	-> str:




          '''simple docstring'''




          if trained_betas is not None:
                 lowercase__:    Union[str, Any]        =      torch.from_numpy(UpperCAmelCase_)
          elif beta_schedule == "linear":
                 lowercase__:    List[str]        =      torch.linspace(UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				dtype=torch.floataa)
          elif beta_schedule == "scaled_linear":
                 # this schedule is very specific to the latent diffusion model.
                 lowercase__:    str        =      (
                     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__:    Tuple        =      betas_for_alpha_bar(UpperCAmelCase_)
          elif beta_schedule == "sigmoid":
                 # GeoDiff sigmoid schedule
                 lowercase__:    str        =      torch.linspace(-6			,				6			,				UpperCAmelCase_)
                 lowercase__:    Optional[int]        =      torch.sigmoid(UpperCAmelCase_) * (beta_end - beta_start) + beta_start
          else:
                 raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}""")

          lowercase__:    Tuple        =      1.0 - self.betas
          lowercase__:    List[Any]        =      torch.cumprod(self.alphas			,				dim=0)
          lowercase__:    int        =      torch.tensor(1.0)

          lowercase__:    str        =      torch.tensor(1.0)

          # standard deviation of the initial noise distribution
          lowercase__:    Any        =      1.0

          # setable values
          lowercase__:    str        =      None
          lowercase__:    int        =      torch.from_numpy(np.arange(0			,				UpperCAmelCase_)[::-1].copy())

          lowercase__:    Tuple        =      eta





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_ = None)	-> torch.FloatTensor:




          '''simple docstring'''




          return sample





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_ = 10			,				UpperCAmelCase_ = 10			,				UpperCAmelCase_ = None			,				)	-> Any:




          '''simple docstring'''




          lowercase__:    Optional[int]        =      min(self.config.num_train_timesteps			,				UpperCAmelCase_)
          lowercase__:    int        =      num_inference_steps

          lowercase__:    Tuple        =      []

          lowercase__:    Tuple        =      {}
          for j in range(0			,				num_inference_steps - jump_length			,				UpperCAmelCase_):
                 lowercase__:    Tuple        =      jump_n_sample - 1

          lowercase__:    Optional[int]        =      num_inference_steps
          while t >= 1:
                 lowercase__:    int        =      t - 1
                 timesteps.append(UpperCAmelCase_)

                 if jumps.get(UpperCAmelCase_			,				0) > 0:
                        lowercase__:    Optional[int]        =      jumps[t] - 1
                        for _ in range(UpperCAmelCase_):
                               lowercase__:    Optional[int]        =      t + 1
                               timesteps.append(UpperCAmelCase_)

          lowercase__:    Optional[Any]        =      np.array(UpperCAmelCase_) * (self.config.num_train_timesteps // self.num_inference_steps)
          lowercase__:    Union[str, Any]        =      torch.from_numpy(UpperCAmelCase_).to(UpperCAmelCase_)





   def __lowercase    (   self			,				UpperCAmelCase_)	-> int:




          '''simple docstring'''




          lowercase__:    List[Any]        =      t - self.config.num_train_timesteps // self.num_inference_steps

          lowercase__:    str        =      self.alphas_cumprod[t]
          lowercase__:    List[str]        =      self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
          lowercase__:    str        =      1 - alpha_prod_t
          lowercase__:    Dict        =      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__:    List[Any]        =      (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

          return variance





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




          '''simple docstring'''




          lowercase__:    Optional[Any]        =      timestep
          lowercase__:    Tuple        =      timestep - self.config.num_train_timesteps // self.num_inference_steps

          # 1. compute alphas, betas
          lowercase__:    List[Any]        =      self.alphas_cumprod[t]
          lowercase__:    List[Any]        =      self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
          lowercase__:    Union[str, Any]        =      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__:    Tuple        =      (sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

          # 3. Clip "predicted x_0"
          if self.config.clip_sample:
                 lowercase__:    Dict        =      torch.clamp(UpperCAmelCase_			,				-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__:    Any        =      model_output.device
          lowercase__:    str        =      randn_tensor(model_output.shape			,				generator=UpperCAmelCase_			,				device=UpperCAmelCase_			,				dtype=model_output.dtype)
          lowercase__:    List[str]        =      self.eta * self._get_variance(UpperCAmelCase_) ** 0.5

          lowercase__:    Optional[Any]        =      0
          if t > 0 and self.eta > 0:
                 lowercase__:    Optional[Any]        =      std_dev_t * noise

          # 6. compute "direction pointing to x_t" of formula (12)
          # from https://arxiv.org/pdf/2010.02502.pdf
          lowercase__:    Any        =      (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__:    Any        =      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__:    Any        =      (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__:    Any        =      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=UpperCAmelCase_			,				pred_original_sample=UpperCAmelCase_)





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_=None)	-> List[str]:




          '''simple docstring'''




          lowercase__:    Union[str, Any]        =      self.config.num_train_timesteps // self.num_inference_steps

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

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

          return sample





   def __lowercase    (   self			,				UpperCAmelCase_			,				UpperCAmelCase_			,				UpperCAmelCase_			,				)	-> torch.FloatTensor:




          '''simple docstring'''




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





   def __len__(   self)	-> Any:




          '''simple docstring'''




          return self.config.num_train_timesteps














"""simple docstring"""





import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

UpperCamelCase			=      0.25 + 0.0j
UpperCamelCase			=      -0.4 + 0.6j
UpperCamelCase			=      -0.1 + 0.651j
UpperCamelCase			=      -2.0
UpperCamelCase			=      56
UpperCamelCase			=      2.0
UpperCamelCase			=      6_66






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return numpy.exp(snake_case_		) + c_parameter






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       return z_values * z_values + c_parameter






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__:    str        =      numpy.linspace(-window_size						,       snake_case_						,       snake_case_		)
       lowercase__:    Union[str, Any]        =      x.reshape((nb_pixels, 1)		)
       lowercase__:    Any        =      numpy.linspace(-window_size						,       snake_case_						,       snake_case_		)
       lowercase__:    List[Any]        =      y.reshape((1, nb_pixels)		)
       return x + 1.0J * y






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       snake_case_						,       snake_case_ = None						,       ):
       """simple docstring"""





       lowercase__:    List[Any]        =      z_a.astype("complex64"		)
       for _ in range(snake_case_		):
              lowercase__:    Any        =      eval_function(snake_case_						,       snake_case_		)
              if infinity is not None:
                     numpy.nan_to_num(snake_case_						,       copy=snake_case_						,       nan=snake_case_		)
                     lowercase__:    Union[str, Any]        =      infinity
       return z_n






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       snake_case_						,       ):
       """simple docstring"""





       lowercase__:    Union[str, Any]        =      (abs(snake_case_		)).transpose()
       lowercase__:    List[Any]        =      abs_z_final[::-1, :]
       pyplot.matshow(abs_z_final < escape_radius		)
       pyplot.title(F"""Julia set of ${function_label}$, $c={function_params}$"""		)
       pyplot.show()






def     A(  ):
       """simple docstring"""





       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in multiply"		)
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="invalid value encountered in multiply"						,       )
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in absolute"		)
       warnings.filterwarnings(
           "ignore"						,       category=snake_case_						,       message="overflow encountered in exp"		)


if __name__ == "__main__":
  UpperCamelCase			=      prepare_grid(window_size, nb_pixels)

  ignore_overflow_warnings()  # See file header for explanations

  UpperCamelCase			=      24
  UpperCamelCase			=      2 * abs(c_cauliflower) + 1
  UpperCamelCase			=      iterate_function(
      eval_quadratic_polynomial,
      c_cauliflower,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("""z^2+c""", c_cauliflower, escape_radius, z_final)

  UpperCamelCase			=      64
  UpperCamelCase			=      2 * abs(c_polynomial_a) + 1
  UpperCamelCase			=      iterate_function(
      eval_quadratic_polynomial,
      c_polynomial_a,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)

  UpperCamelCase			=      1_61
  UpperCamelCase			=      2 * abs(c_polynomial_a) + 1
  UpperCamelCase			=      iterate_function(
      eval_quadratic_polynomial,
      c_polynomial_a,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)

  UpperCamelCase			=      12
  UpperCamelCase			=      10_000.0
  UpperCamelCase			=      iterate_function(
      eval_exponential,
      c_exponential,
      nb_iterations,
      z_a + 2,
      infinity=1.0e10,
  )
  show_results("""e^z+c""", c_exponential, escape_radius, z_final)






