


'''simple docstring'''
# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
import jax.numpy as jnp

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

@flax.struct.dataclass
class 						_lowerCamelCase					:




 '''simple docstring'''
 __lowercase				:		CommonSchedulerState

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


 @classmethod
 def  snake_case__   (      cls      ,      __lowercase      ,      __lowercase      ,      __lowercase						):

       """simple docstring"""







       return cls(common=lowerCAmelCase_      ,      init_noise_sigma=lowerCAmelCase_      ,      timesteps=lowerCAmelCase_						)


@dataclass
class 						_lowerCamelCase					(    __lowerCAmelCase				):




 '''simple docstring'''
 __lowercase				:		DDPMSchedulerState


class 						_lowerCamelCase					(    __lowerCAmelCase    ,		__lowerCAmelCase				):




 '''simple docstring'''
 __lowercase				:		List[str]    							=						[e.name for e in FlaxKarrasDiffusionSchedulers]

 __lowercase				:		jnp.dtype


 @property
 def  snake_case__   (      self						):

       """simple docstring"""







       return True


 @register_to_config
 def __init__(      self      ,      __lowercase = 1_000      ,      __lowercase = 0.0_0_0_1      ,      __lowercase = 0.0_2      ,      __lowercase = "linear"      ,      __lowercase = None      ,      __lowercase = "fixed_small"      ,      __lowercase = True      ,      __lowercase = "epsilon"      ,      __lowercase = jnp.floataa      ,      ):

       """simple docstring"""







       __A  :		Optional[Any]       =			dtype


 def  snake_case__   (      self      ,      __lowercase = None						):

       """simple docstring"""







       if common is None:
             __A  :		Dict       =			CommonSchedulerState.create(self						)

       # standard deviation of the initial noise distribution
       __A  :		int       =			jnp.array(1.0      ,      dtype=self.dtype						)

       __A  :		Any       =			jnp.arange(0      ,      self.config.num_train_timesteps						).round()[::-1]

       return DDPMSchedulerState.create(
           common=lowerCAmelCase_      ,      init_noise_sigma=lowerCAmelCase_      ,      timesteps=lowerCAmelCase_      ,      )


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase = None						):

       """simple docstring"""







       return sample


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase = ()						):

       """simple docstring"""







       __A  :		List[str]       =			self.config.num_train_timesteps // num_inference_steps
       # creates integer timesteps by multiplying by ratio
       # rounding to avoid issues when num_inference_step is power of 3
       __A  :		Optional[int]       =			(jnp.arange(0      ,      lowerCAmelCase_						) * step_ratio).round()[::-1]

       return state.replace(
           num_inference_steps=lowerCAmelCase_      ,      timesteps=lowerCAmelCase_      ,      )


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase=None      ,      __lowercase=None						):

       """simple docstring"""







       __A  :		Optional[int]       =			state.common.alphas_cumprod[t]
       __A  :		List[str]       =			jnp.where(t > 0      ,      state.common.alphas_cumprod[t - 1]      ,      jnp.array(1.0      ,      dtype=self.dtype						)						)

       # 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  :		int       =			(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

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

       # hacks - were probably added for training stability
       if variance_type == "fixed_small":
             __A  :		int       =			jnp.clip(lowerCAmelCase_      ,      a_min=1E-20						)
       # for rl-diffuser https://arxiv.org/abs/2205.09991
       elif variance_type == "fixed_small_log":
             __A  :		Union[str, Any]       =			jnp.log(jnp.clip(lowerCAmelCase_      ,      a_min=1E-20						)						)
       elif variance_type == "fixed_large":
             __A  :		int       =			state.common.betas[t]
       elif variance_type == "fixed_large_log":
             # Glide max_log
             __A  :		Optional[int]       =			jnp.log(state.common.betas[t]						)
       elif variance_type == "learned":
             return predicted_variance
       elif variance_type == "learned_range":
             __A  :		List[str]       =			variance
             __A  :		List[Any]       =			state.common.betas[t]
             __A  :		Optional[Any]       =			(predicted_variance + 1) / 2
             __A  :		Optional[int]       =			frac * max_log + (1 - frac) * min_log

       return variance


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase      ,      __lowercase      ,      __lowercase = None      ,      __lowercase = True      ,      ):

       """simple docstring"""







       __A  :		Dict       =			timestep

       if key is None:
             __A  :		int       =			jax.random.PRNGKey(0						)

       if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
             __A     ,__A  :		Any       =			jnp.split(lowerCAmelCase_      ,      sample.shape[1]      ,      axis=1						)
       else:
             __A  :		Any       =			None

       # 1. compute alphas, betas
       __A  :		str       =			state.common.alphas_cumprod[t]
       __A  :		List[str]       =			jnp.where(t > 0      ,      state.common.alphas_cumprod[t - 1]      ,      jnp.array(1.0      ,      dtype=self.dtype						)						)
       __A  :		List[Any]       =			1 - alpha_prod_t
       __A  :		int       =			1 - alpha_prod_t_prev

       # 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  :		Any       =			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
       elif self.config.prediction_type == "sample":
             __A  :		int       =			model_output
       elif self.config.prediction_type == "v_prediction":
             __A  :		Optional[int]       =			(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
       else:
             raise ValueError(
                 F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` """
                 ' for the FlaxDDPMScheduler.'						)

       # 3. Clip "predicted x_0"
       if self.config.clip_sample:
             __A  :		Union[str, Any]       =			jnp.clip(lowerCAmelCase_      ,      -1      ,      1						)

       # 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 * state.common.betas[t]) / beta_prod_t
       __A  :		int       =			state.common.alphas[t] ** 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  :		Union[str, Any]       =			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

       # 6. Add noise
       def random_variance():
             __A  :		Dict       =			jax.random.split(lowerCAmelCase_      ,      num=1						)
             __A  :		Any       =			jax.random.normal(lowerCAmelCase_      ,      shape=model_output.shape      ,      dtype=self.dtype						)
             return (self._get_variance(lowerCAmelCase_      ,      lowerCAmelCase_      ,      predicted_variance=lowerCAmelCase_						) ** 0.5) * noise

       __A  :		str       =			jnp.where(t > 0      ,      random_variance()      ,      jnp.zeros(model_output.shape      ,      dtype=self.dtype						)						)

       __A  :		int       =			pred_prev_sample + variance

       if not return_dict:
             return (pred_prev_sample, state)

       return FlaxDDPMSchedulerOutput(prev_sample=lowerCAmelCase_      ,      state=lowerCAmelCase_						)


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase      ,      __lowercase      ,      ):

       """simple docstring"""







       return add_noise_common(state.common      ,      lowerCAmelCase_      ,      lowerCAmelCase_      ,      lowerCAmelCase_						)


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase      ,      __lowercase      ,      ):

       """simple docstring"""







       return get_velocity_common(state.common      ,      lowerCAmelCase_      ,      lowerCAmelCase_      ,      lowerCAmelCase_						)







 def __len__(      self						):

       """simple docstring"""







       return self.config.num_train_timesteps










'''simple docstring'''
from math import pi, sqrt, tan


def 			_lowercase       (				UpperCamelCase__       :					float			):
 if side_length < 0:
  raise ValueError('surface_area_cube() only accepts non-negative values'			)
 return 6 * side_length**2


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if length < 0 or breadth < 0 or height < 0:
  raise ValueError('surface_area_cuboid() only accepts non-negative values'			)
 return 2 * ((length * breadth) + (breadth * height) + (length * height))


def 			_lowercase       (				UpperCamelCase__       :					float			):
 if radius < 0:
  raise ValueError('surface_area_sphere() only accepts non-negative values'			)
 return 4 * pi * radius**2


def 			_lowercase       (				UpperCamelCase__       :					float			):
 if radius < 0:
  raise ValueError('surface_area_hemisphere() only accepts non-negative values'			)
 return 3 * pi * radius**2


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if radius < 0 or height < 0:
  raise ValueError('surface_area_cone() only accepts non-negative values'			)
 return pi * radius * (radius + (height**2 + radius**2) ** 0.5)


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if radius_a < 0 or radius_a < 0 or height < 0:
  raise ValueError(
      'surface_area_conical_frustum() only accepts non-negative values'			)
 __A  :		Optional[Any]       =			(height**2 + (radius_a - radius_a) ** 2) ** 0.5
 return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if radius < 0 or height < 0:
  raise ValueError('surface_area_cylinder() only accepts non-negative values'			)
 return 2 * pi * radius * (height + radius)


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if torus_radius < 0 or tube_radius < 0:
  raise ValueError('surface_area_torus() only accepts non-negative values'			)
 if torus_radius < tube_radius:
  raise ValueError(
      'surface_area_torus() does not support spindle or self intersecting tori'			)
 return 4 * pow(UpperCamelCase__,				2			) * torus_radius * tube_radius


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if length < 0 or width < 0:
  raise ValueError('area_rectangle() only accepts non-negative values'			)
 return length * width


def 			_lowercase       (				UpperCamelCase__       :					float			):
 if side_length < 0:
  raise ValueError('area_square() only accepts non-negative values'			)
 return side_length**2


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if base < 0 or height < 0:
  raise ValueError('area_triangle() only accepts non-negative values'			)
 return (base * height) / 2


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if sidea < 0 or sidea < 0 or sidea < 0:
  raise ValueError('area_triangle_three_sides() only accepts non-negative values'			)
 elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
  raise ValueError('Given three sides do not form a triangle'			)
 __A  :		int       =			(sidea + sidea + sidea) / 2
 __A  :		List[Any]       =			sqrt(
     semi_perimeter
     * (semi_perimeter - sidea)
     * (semi_perimeter - sidea)
     * (semi_perimeter - sidea)			)
 return area


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if base < 0 or height < 0:
  raise ValueError('area_parallelogram() only accepts non-negative values'			)
 return base * height


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if basea < 0 or basea < 0 or height < 0:
  raise ValueError('area_trapezium() only accepts non-negative values'			)
 return 1 / 2 * (basea + basea) * height


def 			_lowercase       (				UpperCamelCase__       :					float			):
 if radius < 0:
  raise ValueError('area_circle() only accepts non-negative values'			)
 return pi * radius**2


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if radius_x < 0 or radius_y < 0:
  raise ValueError('area_ellipse() only accepts non-negative values'			)
 return pi * radius_x * radius_y


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if diagonal_a < 0 or diagonal_a < 0:
  raise ValueError('area_rhombus() only accepts non-negative values'			)
 return 1 / 2 * diagonal_a * diagonal_a


def 			_lowercase       (				UpperCamelCase__       :					int,				UpperCamelCase__       :					float			):
 if not isinstance(UpperCamelCase__,				UpperCamelCase__			) or sides < 3:
  raise ValueError(
      'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'			)
 elif length < 0:
  raise ValueError(
      'area_reg_polygon() only accepts non-negative values as \
length of a side'			)
 return (sides * length**2) / (4 * tan(pi / sides			))
 return (sides * length**2) / (4 * tan(pi / sides			))


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

 print('[DEMO] Areas of various geometric shapes: \n')
 print(f'''Rectangle: {area_rectangle(1_0, 2_0) = }''')
 print(f'''Square: {area_square(1_0) = }''')
 print(f'''Triangle: {area_triangle(1_0, 1_0) = }''')
 print(f'''Triangle: {area_triangle_three_sides(5, 1_2, 1_3) = }''')
 print(f'''Parallelogram: {area_parallelogram(1_0, 2_0) = }''')
 print(f'''Rhombus: {area_rhombus(1_0, 2_0) = }''')
 print(f'''Trapezium: {area_trapezium(1_0, 2_0, 3_0) = }''')
 print(f'''Circle: {area_circle(2_0) = }''')
 print(f'''Ellipse: {area_ellipse(1_0, 2_0) = }''')
 print('\nSurface Areas of various geometric shapes: \n')
 print(f'''Cube: {surface_area_cube(2_0) = }''')
 print(f'''Cuboid: {surface_area_cuboid(1_0, 2_0, 3_0) = }''')
 print(f'''Sphere: {surface_area_sphere(2_0) = }''')
 print(f'''Hemisphere: {surface_area_hemisphere(2_0) = }''')
 print(f'''Cone: {surface_area_cone(1_0, 2_0) = }''')
 print(f'''Conical Frustum: {surface_area_conical_frustum(1_0, 2_0, 3_0) = }''')
 print(f'''Cylinder: {surface_area_cylinder(1_0, 2_0) = }''')
 print(f'''Torus: {surface_area_torus(2_0, 1_0) = }''')
 print(f'''Equilateral Triangle: {area_reg_polygon(3, 1_0) = }''')
 print(f'''Square: {area_reg_polygon(4, 1_0) = }''')
 print(f'''Reqular Pentagon: {area_reg_polygon(5, 1_0) = }''')






