




import math
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 SchedulerMixin, SchedulerOutput
class 						UpperCAmelCase  (							lowerCAmelCase_			,  lowerCAmelCase_     ):







						'''simple docstring'''





						lowerCAmelCase_							=  1






						@register_to_config
						def __init__(		self				:	List[Any]			,      __lowercase				:	int = 10_00			,      __lowercase				:	Optional[Union[np.ndarray, List[float]]] = None		):






							"""simple docstring"""






							self.set_timesteps(__lowerCAmelCase		)

							# standard deviation of the initial noise distribution
							snake_case_						       =	1.0

							# For now we only support F-PNDM, i.e. the runge-kutta method
							# For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
							# mainly at formula (9), (12), (13) and the Algorithm 2.
							snake_case_						       =	4

							# running values
							snake_case_						       =	[]






						def 			snake_case__		(		self				:	Union[str, Any]			,      __lowercase				:	int			,      __lowercase				:	Union[str, torch.device] = None		):






							"""simple docstring"""






							snake_case_						       =	num_inference_steps
							snake_case_						       =	torch.linspace(1			,      0			,      num_inference_steps + 1		)[:-1]
							snake_case_						       =	torch.cat([steps, torch.tensor([0.0]		)]		)

							if self.config.trained_betas is not None:
								snake_case_						       =	torch.tensor(self.config.trained_betas			,      dtype=torch.floataa		)
							else:
								snake_case_						       =	torch.sin(steps * math.pi / 2		) ** 2

							snake_case_						       =	(1.0 - self.betas**2) ** 0.5

							snake_case_						       =	(torch.atana(self.betas			,      self.alphas		) / math.pi * 2)[:-1]
							snake_case_						       =	timesteps.to(__lowerCAmelCase		)

							snake_case_						       =	[]






						def 			snake_case__		(		self				:	Optional[int]			,      __lowercase				:	torch.FloatTensor			,      __lowercase				:	int			,      __lowercase				:	torch.FloatTensor			,      __lowercase				:	bool = True			,      ):






							"""simple docstring"""






							if self.num_inference_steps is None:
								raise ValueError(
								    "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"		)

							snake_case_						       =	(self.timesteps == timestep).nonzero().item()
							snake_case_						       =	timestep_index + 1

							snake_case_						       =	sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
							self.ets.append(__lowerCAmelCase		)

							if len(self.ets		) == 1:
								snake_case_						       =	self.ets[-1]
							elif len(self.ets		) == 2:
								snake_case_						       =	(3 * self.ets[-1] - self.ets[-2]) / 2
							elif len(self.ets		) == 3:
								snake_case_						       =	(23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
							else:
								snake_case_						       =	(1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

							snake_case_						       =	self._get_prev_sample(__lowerCAmelCase			,      __lowerCAmelCase			,      __lowerCAmelCase			,      __lowerCAmelCase		)

							if not return_dict:
								return (prev_sample,)

							return SchedulerOutput(prev_sample=__lowerCAmelCase		)






						def 			snake_case__		(		self				:	Optional[int]			,      __lowercase				:	torch.FloatTensor			,      *__lowercase				:	Any			,      **__lowercase				:	Dict		):






							"""simple docstring"""






							return sample






						def 			snake_case__		(		self				:	int			,      __lowercase				:	int			,      __lowercase				:	int			,      __lowercase				:	List[str]			,      __lowercase				:	str		):






							"""simple docstring"""






							snake_case_						       =	self.alphas[timestep_index]
							snake_case_						       =	self.betas[timestep_index]

							snake_case_						       =	self.alphas[prev_timestep_index]
							snake_case_						       =	self.betas[prev_timestep_index]

							snake_case_						       =	(sample - sigma * ets) / max(__lowerCAmelCase			,      1E-8		)
							snake_case_						       =	next_alpha * pred + ets * next_sigma

							return prev_sample






						def __len__(		self				:	Dict		):






							"""simple docstring"""






							return self.config.num_train_timesteps

"""simple docstring"""


from __future__ import annotations

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






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase = False		):







  """simple docstring"""
  if radian_mode:
    return [magnitude * cos(lowercase		), magnitude * sin(lowercase		)]
  return [magnitude * cos(radians(lowercase		)		), magnitude * sin(radians(lowercase		)		)]






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase = 10**-1		):







  """simple docstring"""
  _UpperCAmelCase    			=   cross(lowercase ,lowercase		)
  _UpperCAmelCase    			=   sum(lowercase		)
  return abs(lowercase		) < eps


if __name__ == "__main__":
    # Test to check if it works
    UpperCAmelCase__			=    array(
        [
            polar_force(718.4, 1_8_0 - 3_0),
            polar_force(879.54, 4_5),
            polar_force(1_0_0, -9_0),
        ]
    )

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

    assert in_static_equilibrium(forces, location)

    # Problem 1 in image_data/2D_problems.jpg
    UpperCAmelCase__			=    array(
        [
            polar_force(3_0 * 9.81, 1_5),
            polar_force(2_1_5, 1_8_0 - 4_5),
            polar_force(2_6_4, 9_0 - 3_0),
        ]
    )

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

    assert in_static_equilibrium(forces, location)

    # Problem in image_data/2D_problems_1.jpg
    UpperCAmelCase__			=    array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

    UpperCAmelCase__			=    array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()
