


"""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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class 						_A  (  _a  ):







    """simple docstring"""




    UpperCAmelCase       :							torch.FloatTensor
    UpperCAmelCase       :							Optional[torch.FloatTensor]	=       None






def      lowercase			(				A_  ,   A_=0.9_9_9  ,   A_="cosine"  ,   )->      Any:
  '''simple docstring'''







  if alpha_transform_type == "cosine":

    def alpha_bar_fn(A_       ):
      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_       ):
      return math.exp(t * -1_2.0       )

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

  a						:		Tuple      							=			[]
  for i in range(A_       ):
    a						:		List[Any]      							=			i / num_diffusion_timesteps
    a						:		Any      							=			(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 						_A  (  _a    ,_a  ):







    """simple docstring"""




    @register_to_config
    def __init__(					self				:    Union[str, Any]				, __UpperCAmelCase				:    int = 1000				, __UpperCAmelCase				:    str = "fixed_small_log"				, __UpperCAmelCase				:    bool = True				, __UpperCAmelCase				:    Optional[float] = 1.0				, __UpperCAmelCase				:    str = "epsilon"				, __UpperCAmelCase				:    str = "squaredcos_cap_v2"				, ):
      if beta_schedule != "squaredcos_cap_v2":
        raise ValueError("UnCLIPScheduler only supports `beta_schedule`: 'squaredcos_cap_v2'")

      a						:		Tuple      							=			betas_for_alpha_bar(__UpperCAmelCase)

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

      # standard deviation of the initial noise distribution
      a						:		str      							=			1.0

      # setable values
      a						:		Dict      							=			None
      a						:		Optional[Any]      							=			torch.from_numpy(np.arange(0				, __UpperCAmelCase)[::-1].copy())

      a						:		Optional[Any]      							=			variance_type






    def 	__snake_case							(					self				:    Dict				, __UpperCAmelCase				:    torch.FloatTensor				, __UpperCAmelCase				:    Optional[int] = None):
      return sample






    def 	__snake_case							(					self				:    Union[str, Any]				, __UpperCAmelCase				:    int				, __UpperCAmelCase				:    Union[str, torch.device] = None):
      a						:		int      							=			num_inference_steps
      a						:		str      							=			(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
      a						:		Optional[int]      							=			(np.arange(0				, __UpperCAmelCase) * step_ratio).round()[::-1].copy().astype(np.intaa)
      a						:		List[Any]      							=			torch.from_numpy(__UpperCAmelCase).to(__UpperCAmelCase)






    def 	__snake_case							(					self				:    Union[str, Any]				, __UpperCAmelCase				:    Optional[int]				, __UpperCAmelCase				:    str=None				, __UpperCAmelCase				:    Optional[int]=None				, __UpperCAmelCase				:    str=None):
      if prev_timestep is None:
        a						:		Union[str, Any]      							=			t - 1

      a						:		str      							=			self.alphas_cumprod[t]
      a						:		str      							=			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
      a						:		int      							=			1 - alpha_prod_t
      a						:		Union[str, Any]      							=			1 - alpha_prod_t_prev

      if prev_timestep == t - 1:
        a						:		Optional[Any]      							=			self.betas[t]
      else:
        a						:		Any      							=			1 - alpha_prod_t / 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
      a						:		List[str]      							=			beta_prod_t_prev / beta_prod_t * beta

      if variance_type is None:
        a						:		Any      							=			self.config.variance_type

      # hacks - were probably added for training stability
      if variance_type == "fixed_small_log":
        a						:		Union[str, Any]      							=			torch.log(torch.clamp(__UpperCAmelCase				, min=1e-20))
        a						:		Any      							=			torch.exp(0.5 * variance)
      elif variance_type == "learned_range":
        # NOTE difference with DDPM scheduler
        a						:		List[str]      							=			variance.log()
        a						:		Union[str, Any]      							=			beta.log()

        a						:		Any      							=			(predicted_variance + 1) / 2
        a						:		Tuple      							=			frac * max_log + (1 - frac) * min_log

      return variance






    def 	__snake_case							(					self				:    Union[str, Any]				, __UpperCAmelCase				:    torch.FloatTensor				, __UpperCAmelCase				:    int				, __UpperCAmelCase				:    torch.FloatTensor				, __UpperCAmelCase				:    Optional[int] = None				, __UpperCAmelCase				:    Union[str, Any]=None				, __UpperCAmelCase				:    bool = True				, ):
      a						:		Any      							=			timestep

      if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
        a							,		a						:		List[Any]      							=			torch.split(__UpperCAmelCase				, sample.shape[1]				, dim=1)
      else:
        a						:		List[Any]      							=			None

      # 1. compute alphas, betas
      if prev_timestep is None:
        a						:		int      							=			t - 1

      a						:		Optional[Any]      							=			self.alphas_cumprod[t]
      a						:		Union[str, Any]      							=			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
      a						:		List[Any]      							=			1 - alpha_prod_t
      a						:		str      							=			1 - alpha_prod_t_prev

      if prev_timestep == t - 1:
        a						:		str      							=			self.betas[t]
        a						:		Optional[int]      							=			self.alphas[t]
      else:
        a						:		List[Any]      							=			1 - alpha_prod_t / alpha_prod_t_prev
        a						:		Optional[Any]      							=			1 - beta

      # 2. compute predicted original sample from predicted noise also called
      # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
      if self.config.prediction_type == "epsilon":
        a						:		Union[str, Any]      							=			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
      elif self.config.prediction_type == "sample":
        a						:		Optional[int]      							=			model_output
      else:
        raise ValueError(
            f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`'''
            " for the UnCLIPScheduler.")

      # 3. Clip "predicted x_0"
      if self.config.clip_sample:
        a						:		List[str]      							=			torch.clamp(
            __UpperCAmelCase				, -self.config.clip_sample_range				, self.config.clip_sample_range)

      # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
      # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
      a						:		Union[str, Any]      							=			(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
      a						:		List[Any]      							=			alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

      # 5. Compute predicted previous sample µ_t
      # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
      a						:		Tuple      							=			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

      # 6. Add noise
      a						:		Optional[Any]      							=			0
      if t > 0:
        a						:		List[Any]      							=			randn_tensor(
            model_output.shape				, dtype=model_output.dtype				, generator=__UpperCAmelCase				, device=model_output.device)

        a						:		Any      							=			self._get_variance(
            __UpperCAmelCase				, predicted_variance=__UpperCAmelCase				, prev_timestep=__UpperCAmelCase				, )

        if self.variance_type == "fixed_small_log":
          a						:		int      							=			variance
        elif self.variance_type == "learned_range":
          a						:		Any      							=			(0.5 * variance).exp()
        else:
          raise ValueError(
              f'''variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`'''
              " for the UnCLIPScheduler.")

        a						:		List[str]      							=			variance * variance_noise

      a						:		List[Any]      							=			pred_prev_sample + variance

      if not return_dict:
        return (pred_prev_sample,)

      return UnCLIPSchedulerOutput(prev_sample=__UpperCAmelCase				, pred_original_sample=__UpperCAmelCase)






    def 	__snake_case							(					self				:    int				, __UpperCAmelCase				:    torch.FloatTensor				, __UpperCAmelCase				:    torch.FloatTensor				, __UpperCAmelCase				:    torch.IntTensor				, ):
      # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
      a						:		Dict      							=			self.alphas_cumprod.to(device=original_samples.device				, dtype=original_samples.dtype)
      a						:		Union[str, Any]      							=			timesteps.to(original_samples.device)

      a						:		int      							=			alphas_cumprod[timesteps] ** 0.5
      a						:		Optional[Any]      							=			sqrt_alpha_prod.flatten()
      while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
        a						:		Any      							=			sqrt_alpha_prod.unsqueeze(-1)

      a						:		str      							=			(1 - alphas_cumprod[timesteps]) ** 0.5
      a						:		Tuple      							=			sqrt_one_minus_alpha_prod.flatten()
      while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
        a						:		Optional[int]      							=			sqrt_one_minus_alpha_prod.unsqueeze(-1)

      a						:		List[Any]      							=			sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
      return noisy_samples










"""simple docstring"""







from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray


def      lowercase			(				A_  ,   A_  ,   A_ = False       )->      list[float]:
  '''simple docstring'''







  if radian_mode:
    return [magnitude * cos(A_       ), magnitude * sin(A_       )]
  return [magnitude * cos(radians(A_       )       ), magnitude * sin(radians(A_       )       )]


def      lowercase			(				A_  ,   A_  ,   A_ = 10**-1       )->      bool:
  '''simple docstring'''







  a						:		NDArray[floataa]      							=			cross(A_  ,   A_       )
  a						:		float      							=			sum(A_       )
  return abs(A_       ) < eps


if __name__ == "__main__":
 # Test to check if it works
 __lowercase    					=      array(
     [
         polar_force(7_18.4, 180 - 30),
         polar_force(8_79.54, 45),
         polar_force(100, -90),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem 1 in image_data/2D_problems.jpg
 __lowercase    					=      array(
     [
         polar_force(30 * 9.81, 15),
         polar_force(215, 180 - 45),
         polar_force(264, 90 - 30),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem in image_data/2D_problems_1.jpg
 __lowercase    					=      array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

 __lowercase    					=      array([[0, 0], [6, 0], [10, 0], [12, 0]])

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()






