




from typing import Any

import numpy as np




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						bool:

    """simple docstring"""


    assert np.shape(lowercase_   )[0] == np.shape(lowercase_   )[1]

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

    # Get eigenvalues and eignevectors for a symmetric matrix.
    __UpperCamelCase		,   __UpperCamelCase			=    np.linalg.eigh(lowercase_   )

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




def        __SCREAMING_SNAKE_CASE (	lowercase_   )							->						Any:

    """simple docstring"""


    __UpperCamelCase			=    np.random.randn(lowercase_       ,  lowercase_   )
    __UpperCamelCase			=    np.dot(lowercase_       ,  random_matrix.T   )
    assert _is_matrix_spd(lowercase_   )
    return spd_matrix




def        __SCREAMING_SNAKE_CASE (	lowercase_       ,  lowercase_       ,  lowercase_ = 10_00       ,  lowercase_ = 1E-8       ,  )							->						Any:

    """simple docstring"""


    assert np.shape(lowercase_   )[0] == np.shape(lowercase_   )[1]
    assert np.shape(lowercase_   )[0] == np.shape(lowercase_   )[0]
    assert _is_matrix_spd(lowercase_   )

    # Initialize solution guess, residual, search direction.
    __UpperCamelCase			=    np.zeros((np.shape(lowercase_   )[0], 1)   )
    __UpperCamelCase			=    np.copy(lowercase_   )
    __UpperCamelCase			=    np.copy(lowercase_   )

    # Set initial errors in solution guess and residual.
    __UpperCamelCase			=    1E9
    __UpperCamelCase			=    1E9
    __UpperCamelCase			=    1E9

    # Set iteration counter to threshold number of iterations.
    __UpperCamelCase			=    0

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

        # The main algorithm.

        # Update search direction magnitude.
        __UpperCamelCase			=    np.dot(ra.T       ,  lowercase_   ) / np.dot(pa.T       ,  lowercase_   )
        # Update solution guess.
        __UpperCamelCase			=    xa + alpha * pa
        # Calculate new residual.
        __UpperCamelCase			=    ra - alpha * w
        # Calculate new Krylov subspace scale.
        __UpperCamelCase			=    np.dot(r.T       ,  lowercase_   ) / np.dot(ra.T       ,  lowercase_   )
        # Calculate new A conjuage search direction.
        __UpperCamelCase			=    r + beta * pa

        # Calculate errors.
        __UpperCamelCase			=    np.linalg.norm(r - ra   )
        __UpperCamelCase			=    np.linalg.norm(x - xa   )
        __UpperCamelCase			=    np.maximum(lowercase_       ,  lowercase_   )

        # Update variables.
        __UpperCamelCase			=    np.copy(lowercase_   )
        __UpperCamelCase			=    np.copy(lowercase_   )
        __UpperCamelCase			=    np.copy(lowercase_   )

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

    return x




def        __SCREAMING_SNAKE_CASE (	)							->						None:

    """simple docstring"""


    __UpperCamelCase			=    3
    __UpperCamelCase			=    _create_spd_matrix(lowercase_   )
    __UpperCamelCase			=    np.random.randn(lowercase_       ,  1   )
    __UpperCamelCase			=    np.dot(lowercase_       ,  lowercase_   )

    # Numpy solution.
    __UpperCamelCase			=    np.linalg.solve(lowercase_       ,  lowercase_   )

    # Our implementation.
    __UpperCamelCase			=    conjugate_gradient(lowercase_       ,  lowercase_   )

    # 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()












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

import flax
import jax.numpy as jnp
from scipy import integrate

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

@flax.struct.dataclass
class 			_lowerCamelCase    :

      """simple docstring"""

      lowerCAmelCase__      :			CommonSchedulerState

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

      # running values
      lowerCAmelCase__      :			Optional[jnp.ndarray]     =       None







      @classmethod
      def    snake_case						(  cls       :			str			,							snake_case       :			CommonSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray					):
          return cls(common=snake_case			,							init_noise_sigma=snake_case			,							timesteps=snake_case			,							sigmas=snake_case					)







@dataclass
class 			_lowerCamelCase    (      _SCREAMING_SNAKE_CASE ):

      """simple docstring"""

      lowerCAmelCase__      :			LMSDiscreteSchedulerState







class 			_lowerCamelCase    (      _SCREAMING_SNAKE_CASE				,      _SCREAMING_SNAKE_CASE ):

      """simple docstring"""

      lowerCAmelCase__      :			List[Any]     =       [e.name for e in FlaxKarrasDiffusionSchedulers]

      lowerCAmelCase__      :			jnp.dtype







      @property
      def    snake_case						(  self       :			Any					):
          return True







      @register_to_config
      def __init__(  self       :			Union[str, Any]			,							snake_case       :			int = 1000			,							snake_case       :			float = 0.00_01			,							snake_case       :			float = 0.02			,							snake_case       :			str = "linear"			,							snake_case       :			Optional[jnp.ndarray] = None			,							snake_case       :			str = "epsilon"			,							snake_case       :			jnp.dtype = jnp.floataa			,							):
          __UpperCamelCase			=    dtype







      def    snake_case						(  self       :			int			,							snake_case       :			Optional[CommonSchedulerState] = None					):
          if common is None:
              __UpperCamelCase			=    CommonSchedulerState.create(self					)

          __UpperCamelCase			=    jnp.arange(0			,							self.config.num_train_timesteps					).round()[::-1]
          __UpperCamelCase			=    ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

          # standard deviation of the initial noise distribution
          __UpperCamelCase			=    sigmas.max()

          return LMSDiscreteSchedulerState.create(
              common=snake_case			,							init_noise_sigma=snake_case			,							timesteps=snake_case			,							sigmas=snake_case			,							)







      def    snake_case						(  self       :			str			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			int					):
          ((__UpperCamelCase)		,   )			=    jnp.where(state.timesteps == timestep			,							size=1					)
          __UpperCamelCase			=    step_index[0]

          __UpperCamelCase			=    state.sigmas[step_index]
          __UpperCamelCase			=    sample / ((sigma**2 + 1) ** 0.5)
          return sample







      def    snake_case						(  self       :			Optional[Any]			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			str			,							snake_case       :			Tuple			,							snake_case       :			int					):

          def lms_derivative(snake_case       :			int					):
              __UpperCamelCase			=    1.0
              for k in range(snake_case					):
                  if current_order == k:
                      continue
                  prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
              return prod

          __UpperCamelCase			=    integrate.quad(snake_case			,							state.sigmas[t]			,							state.sigmas[t + 1]			,							epsrel=1E-4					)[0]

          return integrated_coeff







      def    snake_case						(  self       :			int			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			int			,							snake_case       :			Tuple = ()					):
          __UpperCamelCase			=    jnp.linspace(self.config.num_train_timesteps - 1			,							0			,							snake_case			,							dtype=self.dtype					)

          __UpperCamelCase			=    jnp.floor(snake_case					).astype(jnp.intaa					)
          __UpperCamelCase			=    jnp.ceil(snake_case					).astype(jnp.intaa					)

          __UpperCamelCase			=    jnp.mod(snake_case			,							1.0					)

          __UpperCamelCase			=    ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
          __UpperCamelCase			=    (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
          __UpperCamelCase			=    jnp.concatenate([sigmas, jnp.array([0.0]			,							dtype=self.dtype					)]					)

          __UpperCamelCase			=    timesteps.astype(jnp.intaa					)

          # initial running values
          __UpperCamelCase			=    jnp.zeros((0,) + shape			,							dtype=self.dtype					)

          return state.replace(
              timesteps=snake_case			,							sigmas=snake_case			,							num_inference_steps=snake_case			,							derivatives=snake_case			,							)







      def    snake_case						(  self       :			Tuple			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			int			,							snake_case       :			jnp.ndarray			,							snake_case       :			int = 4			,							snake_case       :			bool = True			,							):
          if state.num_inference_steps is None:
              raise ValueError(
                  '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''					)

          __UpperCamelCase			=    state.sigmas[timestep]

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          if self.config.prediction_type == "epsilon":
              __UpperCamelCase			=    sample - sigma * model_output
          elif self.config.prediction_type == "v_prediction":
              # * c_out + input * c_skip
              __UpperCamelCase			=    model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          else:
              raise ValueError(
                  F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"					)

          # 2. Convert to an ODE derivative
          __UpperCamelCase			=    (sample - pred_original_sample) / sigma
          __UpperCamelCase			=    state.replace(derivatives=jnp.append(state.derivatives			,							snake_case					)					)
          if len(state.derivatives					) > order:
              __UpperCamelCase			=    state.replace(derivatives=jnp.delete(state.derivatives			,							0					)					)

          # 3. Compute linear multistep coefficients
          __UpperCamelCase			=    min(timestep + 1			,							snake_case					)
          __UpperCamelCase			=    [self.get_lms_coefficient(snake_case			,							snake_case			,							snake_case			,							snake_case					) for curr_order in range(snake_case					)]

          # 4. Compute previous sample based on the derivatives path
          __UpperCamelCase			=    sample + sum(
              coeff * derivative for coeff, derivative in zip(snake_case			,							reversed(state.derivatives					)					)					)

          if not return_dict:
              return (prev_sample, state)

          return FlaxLMSSchedulerOutput(prev_sample=snake_case			,							state=snake_case					)







      def    snake_case						(  self       :			Dict			,							snake_case       :			LMSDiscreteSchedulerState			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray			,							snake_case       :			jnp.ndarray			,							):
          __UpperCamelCase			=    state.sigmas[timesteps].flatten()
          __UpperCamelCase			=    broadcast_to_shape_from_left(snake_case			,							noise.shape					)

          __UpperCamelCase			=    original_samples + noise * sigma

          return noisy_samples







      def __len__(  self       :			Optional[Any]					):
          return self.config.num_train_timesteps






