






# 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 	a_:



     """simple docstring"""



     __snake_case		:				Optional[jnp.ndarray]  					=None
     __snake_case		:				Optional[jnp.ndarray]  					=None
     __snake_case		:				Optional[jnp.ndarray]  					=None





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

      """simple docstring"""
      return cls()

@dataclass
class 	a_(		lowercase__	):



     """simple docstring"""



     __snake_case		:				ScoreSdeVeSchedulerState
     __snake_case		:				jnp.ndarray
     __snake_case		:				Optional[jnp.ndarray]  					=None

class 	a_(		lowercase__			,							lowercase__	):



     """simple docstring"""



     @property
     def     __UpperCamelCase						(		self					:	Tuple)							->	str:

      """simple docstring"""
      return True





     @register_to_config
     def __init__(		self					:	Optional[Any]  ,  lowerCAmelCase__					:	int = 2_0_0_0  ,  lowerCAmelCase__					:	float = 0.15  ,  lowerCAmelCase__					:	float = 0.01  ,  lowerCAmelCase__					:	float = 13_48.0  ,  lowerCAmelCase__					:	float = 1e-5  ,  lowerCAmelCase__					:	int = 1  ,  )							->	str:

      """simple docstring"""
      pass





     def     __UpperCamelCase						(		self					:	Optional[Any])							->	List[Any]:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		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     __UpperCamelCase						(		self					:	Optional[Any]  ,  lowerCAmelCase__					:	ScoreSdeVeSchedulerState  ,  lowerCAmelCase__					:	int  ,  lowerCAmelCase__					:	Tuple = ()  ,  lowerCAmelCase__					:	float = None)							->	ScoreSdeVeSchedulerState:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		sampling_eps if sampling_eps is not None else self.config.sampling_eps

      SCREAMING_SNAKE_CASE				    =		jnp.linspace(1  ,  lowerCAmelCase__  ,  lowerCAmelCase__)
      return state.replace(timesteps=lowerCAmelCase__)





     def     __UpperCamelCase						(		self					:	Any  ,  lowerCAmelCase__					:	ScoreSdeVeSchedulerState  ,  lowerCAmelCase__					:	int  ,  lowerCAmelCase__					:	float = None  ,  lowerCAmelCase__					:	float = None  ,  lowerCAmelCase__					:	float = None  ,  )							->	ScoreSdeVeSchedulerState:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		sigma_min if sigma_min is not None else self.config.sigma_min
      SCREAMING_SNAKE_CASE				    =		sigma_max if sigma_max is not None else self.config.sigma_max
      SCREAMING_SNAKE_CASE				    =		sampling_eps if sampling_eps is not None else self.config.sampling_eps
      if state.timesteps is None:
       SCREAMING_SNAKE_CASE				    =		self.set_timesteps(lowerCAmelCase__  ,  lowerCAmelCase__  ,  lowerCAmelCase__)

      SCREAMING_SNAKE_CASE				    =		jnp.exp(jnp.linspace(jnp.log(lowerCAmelCase__)  ,  jnp.log(lowerCAmelCase__)  ,  lowerCAmelCase__))
      SCREAMING_SNAKE_CASE				    =		jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps])

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





     def     __UpperCamelCase						(		self					:	Optional[Any]  ,  lowerCAmelCase__					:	List[Any]  ,  lowerCAmelCase__					:	int  ,  lowerCAmelCase__					:	Dict)							->	Dict:

      """simple docstring"""
      return jnp.where(timesteps == 0  ,  jnp.zeros_like(lowerCAmelCase__)  ,  state.discrete_sigmas[timesteps - 1])





     def     __UpperCamelCase						(		self					:	Any  ,  lowerCAmelCase__					:	ScoreSdeVeSchedulerState  ,  lowerCAmelCase__					:	jnp.ndarray  ,  lowerCAmelCase__					:	int  ,  lowerCAmelCase__					:	jnp.ndarray  ,  lowerCAmelCase__					:	random.KeyArray  ,  lowerCAmelCase__					:	bool = True  ,  )							->	Union[FlaxSdeVeOutput, Tuple]:

      """simple docstring"""
      if state.timesteps is None:
       raise ValueError(
           '`state.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler')

      SCREAMING_SNAKE_CASE				    =		timestep * jnp.ones(
          sample.shape[0]  ,  )
      SCREAMING_SNAKE_CASE				    =		(timestep * (len(state.timesteps) - 1)).long()

      SCREAMING_SNAKE_CASE				    =		state.discrete_sigmas[timesteps]
      SCREAMING_SNAKE_CASE				    =		self.get_adjacent_sigma(lowerCAmelCase__  ,  lowerCAmelCase__  ,  lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		jnp.zeros_like(lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		(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
      SCREAMING_SNAKE_CASE				    =		diffusion.flatten()
      SCREAMING_SNAKE_CASE				    =		broadcast_to_shape_from_left(lowerCAmelCase__  ,  sample.shape)
      SCREAMING_SNAKE_CASE				    =		drift - diffusion**2 * model_output

      #  equation 6: sample noise for the diffusion term of
      SCREAMING_SNAKE_CASE				    =		random.split(lowerCAmelCase__  ,  num=1)
      SCREAMING_SNAKE_CASE				    =		random.normal(key=lowerCAmelCase__  ,  shape=sample.shape)
      SCREAMING_SNAKE_CASE				    =		sample - drift  # subtract because `dt` is a small negative timestep
      # TODO is the variable diffusion the correct scaling term for the noise?
      SCREAMING_SNAKE_CASE				    =		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     __UpperCamelCase						(		self					:	Dict  ,  lowerCAmelCase__					:	ScoreSdeVeSchedulerState  ,  lowerCAmelCase__					:	jnp.ndarray  ,  lowerCAmelCase__					:	jnp.ndarray  ,  lowerCAmelCase__					:	random.KeyArray  ,  lowerCAmelCase__					:	bool = True  ,  )							->	Union[FlaxSdeVeOutput, Tuple]:

      """simple docstring"""
      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
      SCREAMING_SNAKE_CASE				    =		random.split(lowerCAmelCase__  ,  num=1)
      SCREAMING_SNAKE_CASE				    =		random.normal(key=lowerCAmelCase__  ,  shape=sample.shape)

      # compute step size from the model_output, the noise, and the snr
      SCREAMING_SNAKE_CASE				    =		jnp.linalg.norm(lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		jnp.linalg.norm(lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		(self.config.snr * noise_norm / grad_norm) ** 2 * 2
      SCREAMING_SNAKE_CASE				    =		step_size * jnp.ones(sample.shape[0])

      # compute corrected sample: model_output term and noise term
      SCREAMING_SNAKE_CASE				    =		step_size.flatten()
      SCREAMING_SNAKE_CASE				    =		broadcast_to_shape_from_left(lowerCAmelCase__  ,  sample.shape)
      SCREAMING_SNAKE_CASE				    =		sample + step_size * model_output
      SCREAMING_SNAKE_CASE				    =		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					:	Any)							->	List[Any]:

      """simple docstring"""
      return self.config.num_train_timesteps








from typing import Any

import numpy as np






def  _UpperCAmelCase						( __lowerCamelCase							)		->bool:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]

 # If matrix not symmetric, exit right away.
 if np.allclose(__lowerCamelCase			,  matrix.T							) is False:
  return False

 # Get eigenvalues and eignevectors for a symmetric matrix.
 snake_case	,       snake_case :			int							=   np.linalg.eigh(__lowerCamelCase							)

 # Check sign of all eigenvalues.
 # np.all returns a value of type np.bool_
 return bool(np.all(eigen_values > 0							)							)






def  _UpperCAmelCase						( __lowerCamelCase							)		->Any:


 '''simple docstring'''
 snake_case :			Dict							=   np.random.randn(__lowerCamelCase			,  __lowerCamelCase							)
 snake_case :			List[Any]							=   np.dot(__lowerCamelCase			,  random_matrix.T							)
 assert _is_matrix_spd(__lowerCamelCase							)
 return spd_matrix






def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = 1000			,  __lowerCamelCase = 1E-8			,  )		->Any:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[0]
 assert _is_matrix_spd(__lowerCamelCase							)

 # Initialize solution guess, residual, search direction.
 snake_case :			Any							=   np.zeros((np.shape(__lowerCamelCase							)[0], 1)							)
 snake_case :			Optional[int]							=   np.copy(__lowerCamelCase							)
 snake_case :			Optional[Any]							=   np.copy(__lowerCamelCase							)

 # Set initial errors in solution guess and residual.
 snake_case :			Optional[Any]							=   1E9
 snake_case :			List[Any]							=   1E9
 snake_case :			List[str]							=   1E9

 # Set iteration counter to threshold number of iterations.
 snake_case :			List[str]							=   0

 while error > tol:
  # Save this value so we only calculate the matrix-vector product once.
  snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

  # The main algorithm.

  # Update search direction magnitude.
  snake_case :			List[str]							=   np.dot(ra.T			,  __lowerCamelCase							) / np.dot(pa.T			,  __lowerCamelCase							)
  # Update solution guess.
  snake_case :			Optional[int]							=   xa + alpha * pa
  # Calculate new residual.
  snake_case :			str							=   ra - alpha * w
  # Calculate new Krylov subspace scale.
  snake_case :			List[str]							=   np.dot(r.T			,  __lowerCamelCase							) / np.dot(ra.T			,  __lowerCamelCase							)
  # Calculate new A conjuage search direction.
  snake_case :			List[Any]							=   r + beta * pa

  # Calculate errors.
  snake_case :			List[Any]							=   np.linalg.norm(r - ra							)
  snake_case :			Any							=   np.linalg.norm(x - xa							)
  snake_case :			str							=   np.maximum(__lowerCamelCase			,  __lowerCamelCase							)

  # Update variables.
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			List[str]							=   np.copy(__lowerCamelCase							)

  # Update number of iterations.
  iterations += 1
  if iterations > max_iterations:
   break

 return x






def  _UpperCAmelCase						( )		->None:


 '''simple docstring'''
 snake_case :			str							=   3
 snake_case :			Dict							=   _create_spd_matrix(__lowerCamelCase							)
 snake_case :			str							=   np.random.randn(__lowerCamelCase			,  1							)
 snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

 # Numpy solution.
 snake_case :			Any							=   np.linalg.solve(__lowerCamelCase			,  __lowerCamelCase							)

 # Our implementation.
 snake_case :			List[str]							=   conjugate_gradient(__lowerCamelCase			,  __lowerCamelCase							)

 # Ensure both solutions are close to x_true (and therefore one another).
 assert np.linalg.norm(x_numpy - x_true							) <= 1E-6
 assert np.linalg.norm(x_conjugate_gradient - x_true							) <= 1E-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_conjugate_gradient()






