


# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left

@flax.struct.dataclass
class  UpperCamelCase__ :
      # setable values
      a__   :     Optional[jnp.ndarray]								=						None
      a__   :     Optional[jnp.ndarray]								=						None
      a__   :     Optional[jnp.ndarray]								=						None






      @classmethod
      def 	__lowercase(     cls					:   int   )  -> Optional[Any]:
           return cls()

@dataclass
class  UpperCamelCase__ ( __lowerCamelCase			):
      a__   :     ScoreSdeVeSchedulerState
      a__   :     jnp.ndarray
      a__   :     Optional[jnp.ndarray]								=						None

class  UpperCamelCase__ ( __lowerCamelCase							,						__lowerCamelCase			):






      @property
      def 	__lowercase(     self					:   int   )  -> Optional[Any]:
           return True






      @register_to_config
      def __init__(     self					:   Optional[Any],		__lowerCamelCase					:   int = 20_00,		__lowerCamelCase					:   float = 0.15,		__lowerCamelCase					:   float = 0.01,		__lowerCamelCase					:   float = 1348.0,		__lowerCamelCase					:   float = 1e-5,		__lowerCamelCase					:   int = 1,		)  -> Dict:
           pass






      def 	__lowercase(     self					:   Tuple   )  -> Union[str, Any]:
           UpperCamelCase__							:  Union[str, Any]								=     ScoreSdeVeSchedulerState.create()
           return self.set_sigmas(
               __lowerCamelCase,		self.config.num_train_timesteps,		self.config.sigma_min,		self.config.sigma_max,		self.config.sampling_eps,		)






      def 	__lowercase(     self					:   Dict,		__lowerCamelCase					:   ScoreSdeVeSchedulerState,		__lowerCamelCase					:   int,		__lowerCamelCase					:   Tuple = (),		__lowerCamelCase					:   float = None   )  -> ScoreSdeVeSchedulerState:
           UpperCamelCase__							:  Any								=     sampling_eps if sampling_eps is not None else self.config.sampling_eps

           UpperCamelCase__							:  Union[str, Any]								=     jnp.linspace(1,		__lowerCamelCase,		__lowerCamelCase   )
           return state.replace(timesteps=__lowerCamelCase   )






      def 	__lowercase(     self					:   Optional[Any],		__lowerCamelCase					:   ScoreSdeVeSchedulerState,		__lowerCamelCase					:   int,		__lowerCamelCase					:   float = None,		__lowerCamelCase					:   float = None,		__lowerCamelCase					:   float = None,		)  -> ScoreSdeVeSchedulerState:
           UpperCamelCase__							:  Tuple								=     sigma_min if sigma_min is not None else self.config.sigma_min
           UpperCamelCase__							:  Union[str, Any]								=     sigma_max if sigma_max is not None else self.config.sigma_max
           UpperCamelCase__							:  int								=     sampling_eps if sampling_eps is not None else self.config.sampling_eps
           if state.timesteps is None:
                UpperCamelCase__							:  Optional[Any]								=     self.set_timesteps(__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase   )

           UpperCamelCase__							:  Optional[Any]								=     jnp.exp(jnp.linspace(jnp.log(__lowerCamelCase   ),		jnp.log(__lowerCamelCase   ),		__lowerCamelCase   )   )
           UpperCamelCase__							:  Optional[Any]								=     jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]   )

           return state.replace(discrete_sigmas=__lowerCamelCase,		sigmas=__lowerCamelCase   )






      def 	__lowercase(     self					:   int,		__lowerCamelCase					:   Any,		__lowerCamelCase					:   str,		__lowerCamelCase					:   str   )  -> Optional[Any]:
           return jnp.where(timesteps == 0,		jnp.zeros_like(__lowerCamelCase   ),		state.discrete_sigmas[timesteps - 1]   )






      def 	__lowercase(     self					:   Dict,		__lowerCamelCase					:   ScoreSdeVeSchedulerState,		__lowerCamelCase					:   jnp.ndarray,		__lowerCamelCase					:   int,		__lowerCamelCase					:   jnp.ndarray,		__lowerCamelCase					:   random.KeyArray,		__lowerCamelCase					:   bool = True,		)  -> Union[FlaxSdeVeOutput, Tuple]:
           if state.timesteps is None:
                raise ValueError(
                    '''`state.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''   )

           UpperCamelCase__							:  Optional[int]								=     timestep * jnp.ones(
               sample.shape[0],		)
           UpperCamelCase__							:  Dict								=     (timestep * (len(state.timesteps   ) - 1)).long()

           UpperCamelCase__							:  int								=     state.discrete_sigmas[timesteps]
           UpperCamelCase__							:  Dict								=     self.get_adjacent_sigma(__lowerCamelCase,		__lowerCamelCase,		__lowerCamelCase   )
           UpperCamelCase__							:  Tuple								=     jnp.zeros_like(__lowerCamelCase   )
           UpperCamelCase__							:  Optional[int]								=     (sigma**2 - adjacent_sigma**2) ** 0.5

           # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
           # also equation 47 shows the analog from SDE models to ancestral sampling methods
           UpperCamelCase__							:  List[str]								=     diffusion.flatten()
           UpperCamelCase__							:  Any								=     broadcast_to_shape_from_left(__lowerCamelCase,		sample.shape   )
           UpperCamelCase__							:  Tuple								=     drift - diffusion**2 * model_output

           #  equation 6: sample noise for the diffusion term of
           UpperCamelCase__							:  Tuple								=     random.split(__lowerCamelCase,		num=1   )
           UpperCamelCase__							:  Union[str, Any]								=     random.normal(key=__lowerCamelCase,		shape=sample.shape   )
           UpperCamelCase__							:  Optional[int]								=     sample - drift  # subtract because `dt` is a small negative timestep
           # TODO is the variable diffusion the correct scaling term for the noise?
           UpperCamelCase__							:  Dict								=     prev_sample_mean + diffusion * noise  # add impact of diffusion field g

           if not return_dict:
                return (prev_sample, prev_sample_mean, state)

           return FlaxSdeVeOutput(prev_sample=__lowerCamelCase,		prev_sample_mean=__lowerCamelCase,		state=__lowerCamelCase   )






      def 	__lowercase(     self					:   int,		__lowerCamelCase					:   ScoreSdeVeSchedulerState,		__lowerCamelCase					:   jnp.ndarray,		__lowerCamelCase					:   jnp.ndarray,		__lowerCamelCase					:   random.KeyArray,		__lowerCamelCase					:   bool = True,		)  -> Union[FlaxSdeVeOutput, Tuple]:
           if state.timesteps is None:
                raise ValueError(
                    '''`state.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''   )

           # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
           # sample noise for correction
           UpperCamelCase__							:  Union[str, Any]								=     random.split(__lowerCamelCase,		num=1   )
           UpperCamelCase__							:  str								=     random.normal(key=__lowerCamelCase,		shape=sample.shape   )

           # compute step size from the model_output, the noise, and the snr
           UpperCamelCase__							:  Tuple								=     jnp.linalg.norm(__lowerCamelCase   )
           UpperCamelCase__							:  Optional[int]								=     jnp.linalg.norm(__lowerCamelCase   )
           UpperCamelCase__							:  Any								=     (self.config.snr * noise_norm / grad_norm) ** 2 * 2
           UpperCamelCase__							:  Dict								=     step_size * jnp.ones(sample.shape[0]   )

           # compute corrected sample: model_output term and noise term
           UpperCamelCase__							:  Any								=     step_size.flatten()
           UpperCamelCase__							:  List[str]								=     broadcast_to_shape_from_left(__lowerCamelCase,		sample.shape   )
           UpperCamelCase__							:  Dict								=     sample + step_size * model_output
           UpperCamelCase__							:  List[str]								=     prev_sample_mean + ((step_size * 2) ** 0.5) * noise

           if not return_dict:
                return (prev_sample, state)

           return FlaxSdeVeOutput(prev_sample=__lowerCamelCase,		state=__lowerCamelCase   )






      def __len__(     self					:   Tuple   )  -> Optional[int]:
           return self.config.num_train_timesteps








from __future__ import annotations

from math import pi, pow







def 						_lowercase       (     __lowerCamelCase			:					int | float			)  ->   float:





     '''simple docstring'''





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







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,2			) * (3 * radius - height)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,__lowerCamelCase			)			)

     UpperCamelCase__							:  Dict								=     (
         (radius_a - radius_a + centers_distance)
         * (radius_a + radius_a - centers_distance)
         / (2 * centers_distance)
     )
     UpperCamelCase__							:  Tuple								=     (
         (radius_a - radius_a + centers_distance)
         * (radius_a + radius_a - centers_distance)
         / (2 * centers_distance)
     )

     return vol_spherical_cap(__lowerCamelCase		,__lowerCamelCase			) + vol_spherical_cap(__lowerCamelCase		,__lowerCamelCase			)







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,__lowerCamelCase			)			)

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







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





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







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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 						_lowercase       (     __lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,3			)







def 						_lowercase       (     __lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





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







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,2			) * height * pi







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,2			) - pow(__lowerCamelCase		,2			)) * height







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''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(__lowerCamelCase		,2			) + pow(__lowerCamelCase		,2			) + radius_a * radius_a)
     )







def 						_lowercase       (     __lowerCamelCase			:					float		,__lowerCamelCase			:					float			)  ->   float:





     '''simple docstring'''





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







def 						_lowercase       (     )  ->   Tuple:





     '''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()




