





from typing import Any

import numpy as np





def  __UpperCamelCase   (     a)			->bool:
					assert np.shape(a)[0] == np.shape(a)[1]

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

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

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





def  __UpperCamelCase   (     a)			->Any:
					lowerCamelCase__      =							np.random.randn(a,  a)
					lowerCamelCase__      =							np.dot(a,  random_matrix.T)
					assert _is_matrix_spd(a)
					return spd_matrix





def  __UpperCamelCase   (     a,  a,  a = 1000,  a = 1E-8,  )			->Any:
					assert np.shape(a)[0] == np.shape(a)[1]
					assert np.shape(a)[0] == np.shape(a)[0]
					assert _is_matrix_spd(a)

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

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

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

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

										# The main algorithm.

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

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

										# Update variables.
										lowerCamelCase__      =							np.copy(a)
										lowerCamelCase__      =							np.copy(a)
										lowerCamelCase__      =							np.copy(a)

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

					return x





def  __UpperCamelCase   (     )			->None:
					lowerCamelCase__      =							3
					lowerCamelCase__      =							_create_spd_matrix(a)
					lowerCamelCase__      =							np.random.randn(a,  1)
					lowerCamelCase__      =							np.dot(a,  a)

					# Numpy solution.
					lowerCamelCase__      =							np.linalg.solve(a,  a)

					# Our implementation.
					lowerCamelCase__      =							conjugate_gradient(a,  a)

					# 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 SCREAMING_SNAKE_CASE_			:





					"""simple docstring"""


					A__								=     42

					# setable values
					A__								=     42
					A__								=     42
					A__								=     42
					A__								=     None

					# running values
					A__								=     None





					@classmethod
					def        __magic_name__			(			cls						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						):
										return cls(common=_lowerCAmelCase						,	init_noise_sigma=_lowerCAmelCase						,	timesteps=_lowerCAmelCase						,	sigmas=_lowerCAmelCase						)

@dataclass
class SCREAMING_SNAKE_CASE_			(       lowercase_ ):





					"""simple docstring"""


					A__								=     42

class SCREAMING_SNAKE_CASE_			(       lowercase_				,							lowercase_ ):





					"""simple docstring"""


					A__								=     [e.name for e in FlaxKarrasDiffusionSchedulers]

					A__								=     42





					@property
					def        __magic_name__			(			self						):
										return True





					@register_to_config
					def __init__(			self						,	_lowerCAmelCase = 1000						,	_lowerCAmelCase = 0.0_001						,	_lowerCAmelCase = 0.02						,	_lowerCAmelCase = "linear"						,	_lowerCAmelCase = None						,	_lowerCAmelCase = "epsilon"						,	_lowerCAmelCase = jnp.floataa						,	):
										lowerCamelCase__      =							dtype





					def        __magic_name__			(			self						,	_lowerCAmelCase = None						):
										if common is None:
															lowerCamelCase__      =							CommonSchedulerState.create(self						)

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

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

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





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						):
										((lowerCamelCase__)     ,		)      =							jnp.where(state.timesteps == timestep						,	size=1						)
										lowerCamelCase__      =							step_index[0]

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





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						):

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

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

										return integrated_coeff





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase = ()						):
										lowerCamelCase__      =							jnp.linspace(self.config.num_train_timesteps - 1						,	0						,	_lowerCAmelCase						,	dtype=self.dtype						)

										lowerCamelCase__      =							jnp.floor(_lowerCAmelCase						).astype(jnp.intaa						)
										lowerCamelCase__      =							jnp.ceil(_lowerCAmelCase						).astype(jnp.intaa						)

										lowerCamelCase__      =							jnp.mod(_lowerCAmelCase						,	1.0						)

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

										lowerCamelCase__      =							timesteps.astype(jnp.intaa						)

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

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





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase = 4						,	_lowerCAmelCase = 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"						)

										lowerCamelCase__      =							state.sigmas[timestep]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
															lowerCamelCase__      =							sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
															# * c_out + input * c_skip
															lowerCamelCase__      =							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
										lowerCamelCase__      =							(sample - pred_original_sample) / sigma
										lowerCamelCase__      =							state.replace(derivatives=jnp.append(state.derivatives						,	_lowerCAmelCase						)						)
										if len(state.derivatives						) > order:
															lowerCamelCase__      =							state.replace(derivatives=jnp.delete(state.derivatives						,	0						)						)

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

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

										if not return_dict:
															return (prev_sample, state)

										return FlaxLMSSchedulerOutput(prev_sample=_lowerCAmelCase						,	state=_lowerCAmelCase						)





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	):
										lowerCamelCase__      =							state.sigmas[timesteps].flatten()
										lowerCamelCase__      =							broadcast_to_shape_from_left(_lowerCAmelCase						,	noise.shape						)

										lowerCamelCase__      =							original_samples + noise * sigma

										return noisy_samples






					def __len__(			self						):
										return self.config.num_train_timesteps

