



'''simple docstring'''





import numpy as np




def lowerCAmelCase  (__A  ,	__A  ,	__A = 1e-12  ,	__A = 100  ,	):



     """simple docstring"""



     assert np.shape(__A)[0] == np.shape(__A)[1]
     # Ensure proper dimensionality.
     assert np.shape(__A)[0] == np.shape(__A)[0]
     # Ensure inputs are either both complex or both real
     assert np.iscomplexobj(__A) == np.iscomplexobj(__A)
     _a      =  np.iscomplexobj(__A)
     if is_complex:
          # Ensure complex input_matrix is Hermitian
          assert np.array_equal(__A  ,	input_matrix.conj().T)

     # Set convergence to False. Will define convergence when we exceed max_iterations
     # or when we have small changes from one iteration to next.

     _a      =  False
     _a      =  0
     _a      =  0
     _a      =  1e12

     while not convergence:
          # Multiple matrix by the vector.
          _a      =  np.dot(__A  ,	__A)
          # Normalize the resulting output vector.
          _a      =  w / np.linalg.norm(__A)
          # Find rayleigh quotient
          # (faster than usual b/c we know vector is normalized already)
          _a      =  vector.conj().T if is_complex else vector.T
          _a      =  np.dot(__A  ,	np.dot(__A  ,	__A))

          # Check convergence.
          _a      =  np.abs(lambda_ - lambda_previous) / lambda_
          iterations += 1

          if error <= error_tol or iterations >= max_iterations:
               _a      =  True

          _a      =  lambda_

     if is_complex:
          _a      =  np.real(lambda_)

     return lambda_, vector




def lowerCAmelCase  ():



     """simple docstring"""



     _a      =  np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]])
     _a      =  np.array([41, 4, 20])
     _a      =  real_input_matrix.astype(np.complexaaa)
     _a      =  np.triu(1J * complex_input_matrix  ,	1)
     complex_input_matrix += imag_matrix
     complex_input_matrix += -1 * imag_matrix.T
     _a      =  np.array([41, 4, 20]).astype(np.complexaaa)

     for problem_type in ["real", "complex"]:
          if problem_type == "real":
               _a      =  real_input_matrix
               _a      =  real_vector
          elif problem_type == "complex":
               _a      =  complex_input_matrix
               _a      =  complex_vector

          # Our implementation.
          _a  ,    _a      =  power_iteration(__A  ,	__A)

          # Numpy implementation.

          # Get eigenvalues and eigenvectors using built-in numpy
          # eigh (eigh used for symmetric or hermetian matrices).
          _a  ,    _a      =  np.linalg.eigh(__A)
          # Last eigenvalue is the maximum one.
          _a      =  eigen_values[-1]
          # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
          _a      =  eigen_vectors[:, -1]

          # Check our implementation and numpy gives close answers.
          assert np.abs(eigen_value - eigen_value_max) <= 1e-6
          # Take absolute values element wise of each eigenvector.
          # as they are only unique to a minus sign.
          assert np.linalg.norm(np.abs(__A) - np.abs(__A)) <= 1e-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()








'''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 __A			:



 '''simple docstring'''







 __lowerCamelCase    :       CommonSchedulerState

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



 @classmethod
 def 					a__  (cls ,   A ,   A ,   A       )    ->     str:


      """simple docstring"""



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






@dataclass
class __A			(  A						):



 '''simple docstring'''







 __lowerCamelCase    :       DDPMSchedulerState






class __A			(  A   ,   A						):



 '''simple docstring'''







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

 __lowerCamelCase    :       jnp.dtype



 @property
 def 					a__  (self       )    ->     List[str]:


      """simple docstring"""



      return True



 @register_to_config
 def __init__(self ,   A = 1_000 ,   A = 0.0001 ,   A = 0.02 ,   A = "linear" ,   A = None ,   A = "fixed_small" ,   A = True ,   A = "epsilon" ,   A = jnp.floataa ,   )    ->     Union[str, Any]:


      """simple docstring"""



      _a      =  dtype



 def 					a__  (self ,   A = None       )    ->     DDPMSchedulerState:


      """simple docstring"""



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

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

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

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



 def 					a__  (self ,   A ,   A ,   A = None       )    ->     jnp.ndarray:


      """simple docstring"""



      return sample



 def 					a__  (self ,   A ,   A ,   A = ()       )    ->     DDPMSchedulerState:


      """simple docstring"""



      _a      =  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      =  (jnp.arange(0 ,   A       ) * step_ratio).round()[::-1]

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



 def 					a__  (self ,   A ,   A ,   A=None ,   A=None       )    ->     int:


      """simple docstring"""



      _a      =  state.common.alphas_cumprod[t]
      _a      =  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      =  (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

      if variance_type is None:
           _a      =  self.config.variance_type

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

      return variance



 def 					a__  (self ,   A ,   A ,   A ,   A ,   A = None ,   A = True ,   )    ->     Union[FlaxDDPMSchedulerOutput, Tuple]:


      """simple docstring"""



      _a      =  timestep

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

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

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

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

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

      _a      =  pred_prev_sample + variance

      if not return_dict:
           return (pred_prev_sample, state)

      return FlaxDDPMSchedulerOutput(prev_sample=A ,   state=A       )



 def 					a__  (self ,   A ,   A ,   A ,   A ,   )    ->     jnp.ndarray:


      """simple docstring"""



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



 def 					a__  (self ,   A ,   A ,   A ,   A ,   )    ->     jnp.ndarray:


      """simple docstring"""



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



 def __len__(self       )    ->     Tuple:


      """simple docstring"""



      return self.config.num_train_timesteps



