


'''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    UpperCAmelCase_  :





    """simple docstring"""






    lowerCamelCase  :					CommonSchedulerState

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







    @classmethod
    def       lowercase_				(							cls			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     Optional[Any]:
         return cls(common=SCREAMING_SNAKE_CASE_			,     init_noise_sigma=SCREAMING_SNAKE_CASE_			,     timesteps=SCREAMING_SNAKE_CASE_	)







@dataclass
class    UpperCAmelCase_  (_UpperCAmelCase  ):





    """simple docstring"""






    lowerCamelCase  :					DDPMSchedulerState







class    UpperCAmelCase_  (_UpperCAmelCase					,		_UpperCAmelCase  ):





    """simple docstring"""






    lowerCamelCase  :					Dict							     =			[e.name for e in FlaxKarrasDiffusionSchedulers]

    lowerCamelCase  :					jnp.dtype







    @property
    def       lowercase_				(							self	)				->     Any:
         return True







    @register_to_config
    def __init__(							self			,     SCREAMING_SNAKE_CASE_ = 10_00			,     SCREAMING_SNAKE_CASE_ = 0.0_0_0_1			,     SCREAMING_SNAKE_CASE_ = 0.0_2			,     SCREAMING_SNAKE_CASE_ = "linear"			,     SCREAMING_SNAKE_CASE_ = None			,     SCREAMING_SNAKE_CASE_ = "fixed_small"			,     SCREAMING_SNAKE_CASE_ = True			,     SCREAMING_SNAKE_CASE_ = "epsilon"			,     SCREAMING_SNAKE_CASE_ = jnp.floataa			,     )				->     int:
         __lowerCamelCase   :	List[str]								=		dtype







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_ = None	)				->     DDPMSchedulerState:
         if common is None:
              __lowerCamelCase   :	Optional[int]								=		CommonSchedulerState.create(self	)

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

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

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







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = None	)				->     jnp.ndarray:
         return sample







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = ()	)				->     DDPMSchedulerState:
         __lowerCamelCase   :	int								=		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
         __lowerCamelCase   :	Union[str, Any]								=		(jnp.arange(0			,     SCREAMING_SNAKE_CASE_	) * step_ratio).round()[::-1]

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







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_=None			,     SCREAMING_SNAKE_CASE_=None	)				->     Tuple:
         __lowerCamelCase   :	Any								=		state.common.alphas_cumprod[t]
         __lowerCamelCase   :	Union[str, Any]								=		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
         __lowerCamelCase   :	Optional[int]								=		(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

         if variance_type is None:
              __lowerCamelCase   :	Union[str, Any]								=		self.config.variance_type

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

         return variance







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = None			,     SCREAMING_SNAKE_CASE_ = True			,     )				->     Union[FlaxDDPMSchedulerOutput, Tuple]:
         __lowerCamelCase   :	List[str]								=		timestep

         if key is None:
              __lowerCamelCase   :	Any								=		jax.random.PRNGKey(0	)

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

         # 1. compute alphas, betas
         __lowerCamelCase   :	str								=		state.common.alphas_cumprod[t]
         __lowerCamelCase   :	Union[str, Any]								=		jnp.where(t > 0			,     state.common.alphas_cumprod[t - 1]			,     jnp.array(1.0			,     dtype=self.dtype	)	)
         __lowerCamelCase   :	Union[str, Any]								=		1 - alpha_prod_t
         __lowerCamelCase   :	List[Any]								=		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":
              __lowerCamelCase   :	Any								=		(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
         elif self.config.prediction_type == "sample":
              __lowerCamelCase   :	str								=		model_output
         elif self.config.prediction_type == "v_prediction":
              __lowerCamelCase   :	Optional[Any]								=		(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:
              __lowerCamelCase   :	List[str]								=		jnp.clip(SCREAMING_SNAKE_CASE_			,     -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
         __lowerCamelCase   :	Tuple								=		(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
         __lowerCamelCase   :	List[Any]								=		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
         __lowerCamelCase   :	str								=		pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

         # 6. Add noise
         def random_variance():
              __lowerCamelCase   :	Union[str, Any]								=		jax.random.split(SCREAMING_SNAKE_CASE_			,     num=1	)
              __lowerCamelCase   :	Any								=		jax.random.normal(SCREAMING_SNAKE_CASE_			,     shape=model_output.shape			,     dtype=self.dtype	)
              return (self._get_variance(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     predicted_variance=SCREAMING_SNAKE_CASE_	) ** 0.5) * noise

         __lowerCamelCase   :	Optional[Any]								=		jnp.where(t > 0			,     random_variance()			,     jnp.zeros(model_output.shape			,     dtype=self.dtype	)	)

         __lowerCamelCase   :	List[str]								=		pred_prev_sample + variance

         if not return_dict:
              return (pred_prev_sample, state)

         return FlaxDDPMSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_			,     state=SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     )				->     jnp.ndarray:
         return add_noise_common(state.common			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     )				->     jnp.ndarray:
         return get_velocity_common(state.common			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)







    def __len__(							self	)				->     Any:
         return self.config.num_train_timesteps










'''simple docstring'''



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]							)     ->		str:
     __lowerCamelCase   :	Tuple								=		0
     __lowerCamelCase   :	Optional[int]								=		len(UpperCAmelCase_							)

     for i in range(n - 1							):
          for j in range(i + 1      ,    UpperCAmelCase_							):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		Optional[int]:
     if len(UpperCAmelCase_							) <= 1:
          return arr, 0
     __lowerCamelCase   :	str								=		len(UpperCAmelCase_							) // 2
     __lowerCamelCase   :	List[Any]								=		arr[0:mid]
     __lowerCamelCase   :	List[str]								=		arr[mid:]

     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Any								=		_count_cross_inversions(UpperCAmelCase_      ,    UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]      ,    UpperCAmelCase_    :				List[str]							)     ->		Optional[Any]:
     __lowerCamelCase   :	List[str]								=		[]
     __lowerCamelCase   :	Optional[int]								=		0
     while i < len(UpperCAmelCase_							) and j < len(UpperCAmelCase_							):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(UpperCAmelCase_							) - i
               r.append(q[j]							)
               j += 1
          else:
               r.append(p[i]							)
               i += 1

     if i < len(UpperCAmelCase_							):
          r.extend(p[i:]							)
     else:
          r.extend(q[j:]							)

     return r, num_inversion



def 			UpperCAmelCase__					(	)     ->		List[str]:
     __lowerCamelCase   :	Any								=		[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '      ,    UpperCAmelCase_							)

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)

     # an empty list should also have zero inversions
     __lowerCamelCase   :	Dict								=		[]
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Union[str, Any]								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)


if __name__ == "__main__":
      main()






