'''simple docstring'''


from __future__ import annotations

from math import pi, pow


def    _lowerCamelCase       ( lowerCamelCase_   :				List[str]  ):



     """simple docstring"""





     if side_length < 0:
          raise ValueError('vol_cube() only accepts non-negative values'  )
     return pow(lowercase_      ,	3  )


def    _lowerCamelCase       ( lowerCamelCase_   :				Dict      ,	lowerCamelCase_   :				int  ):



     """simple docstring"""





     if height < 0 or radius < 0:
          raise ValueError('vol_spherical_cap() only accepts non-negative values'  )
     # Volume is 1/3 pi * height squared * (3 * radius - height)
     return 1 / 3 * pi * pow(lowercase_      ,	2  ) * (3 * radius - height)


def    _lowerCamelCase       ( lowerCamelCase_   :				Union[str, Any]      ,	lowerCamelCase_   :				List[str]      ,	lowerCamelCase_   :				int  ):



     """simple docstring"""





     if radius_a < 0 or radius_a < 0 or centers_distance < 0:
          raise ValueError('vol_spheres_intersect() only accepts non-negative values'  )
     if centers_distance == 0:
          return vol_sphere(min(lowercase_      ,	lowercase_  )  )

     UpperCAmelCase_				:  Union[str, Any]  = (
         (radius_a - radius_a + centers_distance)
         * (radius_a + radius_a - centers_distance)
         / (2 * centers_distance)
     )
     UpperCAmelCase_				:  Any  = (
         (radius_a - radius_a + centers_distance)
         * (radius_a + radius_a - centers_distance)
         / (2 * centers_distance)
     )

     return vol_spherical_cap(lowercase_      ,	lowercase_  ) + vol_spherical_cap(lowercase_      ,	lowercase_  )


def    _lowerCamelCase       ( lowerCamelCase_   :				List[Any]      ,	lowerCamelCase_   :				Union[str, Any]      ,	lowerCamelCase_   :				Union[str, Any]  ):



     """simple docstring"""





     if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
          raise ValueError(
              'vol_spheres_union() only accepts non-negative values, non-zero radius'  )

     if centers_distance == 0:
          return vol_sphere(max(lowercase_      ,	lowercase_  )  )

     return (
         vol_sphere(lowercase_  )
         + vol_sphere(lowercase_  )
         - vol_spheres_intersect(lowercase_      ,	lowercase_      ,	lowercase_  )
     )


def    _lowerCamelCase       ( lowerCamelCase_   :				Tuple      ,	lowerCamelCase_   :				Tuple      ,	lowerCamelCase_   :				List[Any]  ):



     """simple docstring"""





     if width < 0 or height < 0 or length < 0:
          raise ValueError('vol_cuboid() only accepts non-negative values'  )
     return float(width * height * length  )


def    _lowerCamelCase       ( lowerCamelCase_   :				Any      ,	lowerCamelCase_   :				str  ):



     """simple docstring"""





     if height < 0 or area_of_base < 0:
          raise ValueError('vol_cone() only accepts non-negative values'  )
     return area_of_base * height / 3.0


def    _lowerCamelCase       ( lowerCamelCase_   :				Tuple      ,	lowerCamelCase_   :				int  ):



     """simple docstring"""





     if height < 0 or radius < 0:
          raise ValueError('vol_right_circ_cone() only accepts non-negative values'  )
     return pi * pow(lowercase_      ,	2  ) * height / 3.0


def    _lowerCamelCase       ( lowerCamelCase_   :				str      ,	lowerCamelCase_   :				Dict  ):



     """simple docstring"""





     if height < 0 or area_of_base < 0:
          raise ValueError('vol_prism() only accepts non-negative values'  )
     return float(area_of_base * height  )


def    _lowerCamelCase       ( lowerCamelCase_   :				Optional[Any]      ,	lowerCamelCase_   :				List[Any]  ):



     """simple docstring"""





     if height < 0 or area_of_base < 0:
          raise ValueError('vol_pyramid() only accepts non-negative values'  )
     return area_of_base * height / 3.0


def    _lowerCamelCase       ( lowerCamelCase_   :				Dict  ):



     """simple docstring"""





     if radius < 0:
          raise ValueError('vol_sphere() only accepts non-negative values'  )
     # Volume is 4/3 * pi * radius cubed
     return 4 / 3 * pi * pow(lowercase_      ,	3  )


def    _lowerCamelCase       ( lowerCamelCase_   :				List[Any]  ):



     """simple docstring"""





     if radius < 0:
          raise ValueError('vol_hemisphere() only accepts non-negative values'  )
     # Volume is radius cubed * pi * 2/3
     return pow(lowercase_      ,	3  ) * pi * 2 / 3


def    _lowerCamelCase       ( lowerCamelCase_   :				List[str]      ,	lowerCamelCase_   :				List[str]  ):



     """simple docstring"""





     if height < 0 or radius < 0:
          raise ValueError('vol_circular_cylinder() only accepts non-negative values'  )
     # Volume is radius squared * height * pi
     return pow(lowercase_      ,	2  ) * height * pi


def    _lowerCamelCase       ( lowerCamelCase_   :				Dict      ,	lowerCamelCase_   :				int      ,	lowerCamelCase_   :				Dict  ):



     """simple docstring"""





     if inner_radius < 0 or outer_radius < 0 or height < 0:
          raise ValueError(
              'vol_hollow_circular_cylinder() only accepts non-negative values'  )
     if outer_radius <= inner_radius:
          raise ValueError('outer_radius must be greater than inner_radius'  )
     return pi * (pow(lowercase_      ,	2  ) - pow(lowercase_      ,	2  )) * height


def    _lowerCamelCase       ( lowerCamelCase_   :				Optional[int]      ,	lowerCamelCase_   :				int      ,	lowerCamelCase_   :				Any  ):



     """simple docstring"""





     if radius_a < 0 or radius_a < 0 or height < 0:
          raise ValueError('vol_conical_frustum() only accepts non-negative values'  )
     return (
         1
         / 3
         * pi
         * height
         * (pow(lowercase_      ,	2  ) + pow(lowercase_      ,	2  ) + radius_a * radius_a)
     )


def    _lowerCamelCase       ( lowerCamelCase_   :				Optional[int]      ,	lowerCamelCase_   :				Any  ):



     """simple docstring"""





     if torus_radius < 0 or tube_radius < 0:
          raise ValueError('vol_torus() only accepts non-negative values'  )
     return 2 * pow(lowercase_      ,	2  ) * torus_radius * pow(lowercase_      ,	2  )


def    _lowerCamelCase       ( ):



     """simple docstring"""





     print('Volumes:'  )
     print(F'''Cube: {vol_cube(2  ) = }'''  )  # = 8
     print(F'''Cuboid: {vol_cuboid(2      ,	2      ,	2  ) = }'''  )  # = 8
     print(F'''Cone: {vol_cone(2      ,	2  ) = }'''  )  # ~= 1.33
     print(F'''Right Circular Cone: {vol_right_circ_cone(2      ,	2  ) = }'''  )  # ~= 8.38
     print(F'''Prism: {vol_prism(2      ,	2  ) = }'''  )  # = 4
     print(F'''Pyramid: {vol_pyramid(2      ,	2  ) = }'''  )  # ~= 1.33
     print(F'''Sphere: {vol_sphere(2  ) = }'''  )  # ~= 33.5
     print(F'''Hemisphere: {vol_hemisphere(2  ) = }'''  )  # ~= 16.75
     print(F'''Circular Cylinder: {vol_circular_cylinder(2      ,	2  ) = }'''  )  # ~= 25.1
     print(F'''Torus: {vol_torus(2      ,	2  ) = }'''  )  # ~= 157.9
     print(F'''Conical Frustum: {vol_conical_frustum(2      ,	2      ,	4  ) = }'''  )  # ~= 58.6
     print(F'''Spherical cap: {vol_spherical_cap(1      ,	2  ) = }'''  )  # ~= 5.24
     print(F'''Spheres intersetion: {vol_spheres_intersect(2      ,	2      ,	1  ) = }'''  )  # ~= 21.21
     print(F'''Spheres union: {vol_spheres_union(2      ,	2      ,	1  ) = }'''  )  # ~= 45.81
     print(
         F'''Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1      ,	2      ,	3  ) = }'''  )  # ~= 28.3


if __name__ == "__main__":
 main()












from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)

@flax.struct.dataclass
class 			_lowerCamelCase    :

      """simple docstring"""

      lowerCAmelCase__      :			CommonSchedulerState

      # setable values
      lowerCAmelCase__      :			jnp.ndarray
      lowerCAmelCase__      :			jnp.ndarray
      lowerCAmelCase__      :			jnp.ndarray
      lowerCAmelCase__      :			Optional[int]     =       None

      # running values
      lowerCAmelCase__      :			Optional[jnp.ndarray]     =       None







      @classmethod
      def    snake_case						(  cls       :			str			,							snake_case       :			CommonSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray					):
          return cls(common=snake_case			,							init_noise_sigma=snake_case			,							timesteps=snake_case			,							sigmas=snake_case					)







@dataclass
class 			_lowerCamelCase    (      _SCREAMING_SNAKE_CASE ):

      """simple docstring"""

      lowerCAmelCase__      :			LMSDiscreteSchedulerState







class 			_lowerCamelCase    (      _SCREAMING_SNAKE_CASE				,      _SCREAMING_SNAKE_CASE ):

      """simple docstring"""

      lowerCAmelCase__      :			List[Any]     =       [e.name for e in FlaxKarrasDiffusionSchedulers]

      lowerCAmelCase__      :			jnp.dtype







      @property
      def    snake_case						(  self       :			Any					):
          return True







      @register_to_config
      def __init__(  self       :			Union[str, Any]			,							snake_case       :			int = 1000			,							snake_case       :			float = 0.00_01			,							snake_case       :			float = 0.02			,							snake_case       :			str = "linear"			,							snake_case       :			Optional[jnp.ndarray] = None			,							snake_case       :			str = "epsilon"			,							snake_case       :			jnp.dtype = jnp.floataa			,							):
          __UpperCamelCase			=    dtype







      def    snake_case						(  self       :			int			,							snake_case       :			Optional[CommonSchedulerState] = None					):
          if common is None:
              __UpperCamelCase			=    CommonSchedulerState.create(self					)

          __UpperCamelCase			=    jnp.arange(0			,							self.config.num_train_timesteps					).round()[::-1]
          __UpperCamelCase			=    ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

          # standard deviation of the initial noise distribution
          __UpperCamelCase			=    sigmas.max()

          return LMSDiscreteSchedulerState.create(
              common=snake_case			,							init_noise_sigma=snake_case			,							timesteps=snake_case			,							sigmas=snake_case			,							)







      def    snake_case						(  self       :			str			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			int					):
          ((__UpperCamelCase)		,   )			=    jnp.where(state.timesteps == timestep			,							size=1					)
          __UpperCamelCase			=    step_index[0]

          __UpperCamelCase			=    state.sigmas[step_index]
          __UpperCamelCase			=    sample / ((sigma**2 + 1) ** 0.5)
          return sample







      def    snake_case						(  self       :			Optional[Any]			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			str			,							snake_case       :			Tuple			,							snake_case       :			int					):

          def lms_derivative(snake_case       :			int					):
              __UpperCamelCase			=    1.0
              for k in range(snake_case					):
                  if current_order == k:
                      continue
                  prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
              return prod

          __UpperCamelCase			=    integrate.quad(snake_case			,							state.sigmas[t]			,							state.sigmas[t + 1]			,							epsrel=1E-4					)[0]

          return integrated_coeff







      def    snake_case						(  self       :			int			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			int			,							snake_case       :			Tuple = ()					):
          __UpperCamelCase			=    jnp.linspace(self.config.num_train_timesteps - 1			,							0			,							snake_case			,							dtype=self.dtype					)

          __UpperCamelCase			=    jnp.floor(snake_case					).astype(jnp.intaa					)
          __UpperCamelCase			=    jnp.ceil(snake_case					).astype(jnp.intaa					)

          __UpperCamelCase			=    jnp.mod(snake_case			,							1.0					)

          __UpperCamelCase			=    ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
          __UpperCamelCase			=    (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
          __UpperCamelCase			=    jnp.concatenate([sigmas, jnp.array([0.0]			,							dtype=self.dtype					)]					)

          __UpperCamelCase			=    timesteps.astype(jnp.intaa					)

          # initial running values
          __UpperCamelCase			=    jnp.zeros((0,) + shape			,							dtype=self.dtype					)

          return state.replace(
              timesteps=snake_case			,							sigmas=snake_case			,							num_inference_steps=snake_case			,							derivatives=snake_case			,							)







      def    snake_case						(  self       :			Tuple			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			int			,							snake_case       :			jnp.ndarray			,							snake_case       :			int = 4			,							snake_case       :			bool = True			,							):
          if state.num_inference_steps is None:
              raise ValueError(
                  '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''					)

          __UpperCamelCase			=    state.sigmas[timestep]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
              __UpperCamelCase			=    sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
              # * c_out + input * c_skip
              __UpperCamelCase			=    model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          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
          __UpperCamelCase			=    (sample - pred_original_sample) / sigma
          __UpperCamelCase			=    state.replace(derivatives=jnp.append(state.derivatives			,							snake_case					)					)
          if len(state.derivatives					) > order:
              __UpperCamelCase			=    state.replace(derivatives=jnp.delete(state.derivatives			,							0					)					)

          # 3. Compute linear multistep coefficients
          __UpperCamelCase			=    min(timestep + 1			,							snake_case					)
          __UpperCamelCase			=    [self.get_lms_coefficient(snake_case			,							snake_case			,							snake_case			,							snake_case					) for curr_order in range(snake_case					)]

          # 4. Compute previous sample based on the derivatives path
          __UpperCamelCase			=    sample + sum(
              coeff * derivative for coeff, derivative in zip(snake_case			,							reversed(state.derivatives					)					)					)

          if not return_dict:
              return (prev_sample, state)

          return FlaxLMSSchedulerOutput(prev_sample=snake_case			,							state=snake_case					)







      def    snake_case						(  self       :			Dict			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray			,							):
          __UpperCamelCase			=    state.sigmas[timesteps].flatten()
          __UpperCamelCase			=    broadcast_to_shape_from_left(snake_case			,							noise.shape					)

          __UpperCamelCase			=    original_samples + noise * sigma

          return noisy_samples







      def __len__(  self       :			Optional[Any]					):
          return self.config.num_train_timesteps






