






'''simple docstring'''







# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin

class _lowercase	(				_lowercase				,      _lowercase		):
							a				      =       1




							@register_to_config
							def __init__(							self:				List[Any]			,							UpperCamelCase__:				Any=2_000			,							UpperCamelCase__:				Any=0.1			,							UpperCamelCase__:				Union[str, Any]=20			,							UpperCamelCase__:				int=1e-3     ):
														lowerCamelCase__					:	List[Any]         =       None
														lowerCamelCase__					:	Dict         =       None
														lowerCamelCase__					:	Dict         =       None




							def 		lowerCamelCase_				(							self:				int			,							UpperCamelCase__:				Union[str, Any]			,							UpperCamelCase__:				Union[str, torch.device] = None     ):
														lowerCamelCase__					:	List[Any]         =       torch.linspace(1			,							self.config.sampling_eps			,							UpperCamelCase__			,							device=UpperCamelCase__     )




							def 		lowerCamelCase_				(							self:				int			,							UpperCamelCase__:				str			,							UpperCamelCase__:				Dict			,							UpperCamelCase__:				Tuple			,							UpperCamelCase__:				List[Any]=None     ):
														if self.timesteps is None:
																					raise ValueError(
																					    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""     )

														# TODO(Patrick) better comments + non-PyTorch
														# postprocess model score
														lowerCamelCase__					:	Dict         =       (
														    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
														)
														lowerCamelCase__					:	Optional[int]         =       torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff     )     )
														lowerCamelCase__					:	Dict         =       std.flatten()
														while len(std.shape     ) < len(score.shape     ):
																					lowerCamelCase__					:	Any         =       std.unsqueeze(-1     )
														lowerCamelCase__					:	Dict         =       -score / std

														# compute
														lowerCamelCase__					:	Any         =       -1.0 / len(self.timesteps     )

														lowerCamelCase__					:	Optional[int]         =       self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
														lowerCamelCase__					:	List[str]         =       beta_t.flatten()
														while len(beta_t.shape     ) < len(x.shape     ):
																					lowerCamelCase__					:	Tuple         =       beta_t.unsqueeze(-1     )
														lowerCamelCase__					:	Union[str, Any]         =       -0.5 * beta_t * x

														lowerCamelCase__					:	List[str]         =       torch.sqrt(UpperCamelCase__     )
														lowerCamelCase__					:	List[Any]         =       drift - diffusion**2 * score
														lowerCamelCase__					:	Dict         =       x + drift * dt

														# add noise
														lowerCamelCase__					:	int         =       randn_tensor(x.shape			,							layout=x.layout			,							generator=UpperCamelCase__			,							device=x.device			,							dtype=x.dtype     )
														lowerCamelCase__					:	str         =       x_mean + diffusion * math.sqrt(-dt     ) * noise

														return x, x_mean




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


import numpy as np



def lowerCamelCase  (   SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE = 1e-12  ,			SCREAMING_SNAKE_CASE = 100  ,			):
    '''simple docstring'''







    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[1]
    # Ensure proper dimensionality.
    assert np.shape(SCREAMING_SNAKE_CASE	)[0] == np.shape(SCREAMING_SNAKE_CASE	)[0]
    # Ensure inputs are either both complex or both real
    assert np.iscomplexobj(SCREAMING_SNAKE_CASE	) == np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    __UpperCamelCase     :List[Any]			  =		np.iscomplexobj(SCREAMING_SNAKE_CASE	)
    if is_complex:
        # Ensure complex input_matrix is Hermitian
        assert np.array_equal(SCREAMING_SNAKE_CASE  ,			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.

    __UpperCamelCase     :str			  =		False
    __UpperCamelCase     :int			  =		0
    __UpperCamelCase     :Optional[Any]			  =		0
    __UpperCamelCase     :Union[str, Any]			  =		1e12

    while not convergence:
        # Multiple matrix by the vector.
        __UpperCamelCase     :List[str]			  =		np.dot(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)
        # Normalize the resulting output vector.
        __UpperCamelCase     :Tuple			  =		w / np.linalg.norm(SCREAMING_SNAKE_CASE	)
        # Find rayleigh quotient
        # (faster than usual b/c we know vector is normalized already)
        __UpperCamelCase     :int			  =		vector.conj().T if is_complex else vector.T
        __UpperCamelCase     :Optional[int]			  =		np.dot(SCREAMING_SNAKE_CASE  ,			np.dot(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)	)

        # Check convergence.
        __UpperCamelCase     :Optional[Any]			  =		np.abs(lambda_ - lambda_previous	) / lambda_
        iterations += 1

        if error <= error_tol or iterations >= max_iterations:
            __UpperCamelCase     :Dict			  =		True

        __UpperCamelCase     :List[Any]			  =		lambda_

    if is_complex:
        __UpperCamelCase     :Tuple			  =		np.real(lambda_	)

    return lambda_, vector



def lowerCamelCase  (   ):
    '''simple docstring'''







    __UpperCamelCase     :int			  =		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]	)
    __UpperCamelCase     :Optional[Any]			  =		np.array([41, 4, 20]	)
    __UpperCamelCase     :Any			  =		real_input_matrix.astype(np.complexaaa	)
    __UpperCamelCase     :Dict			  =		np.triu(1j * complex_input_matrix  ,			1	)
    complex_input_matrix += imag_matrix
    complex_input_matrix += -1 * imag_matrix.T
    __UpperCamelCase     :Optional[int]			  =		np.array([41, 4, 20]	).astype(np.complexaaa	)

    for problem_type in ["real", "complex"]:
        if problem_type == "real":
            __UpperCamelCase     :Any			  =		real_input_matrix
            __UpperCamelCase     :int			  =		real_vector
        elif problem_type == "complex":
            __UpperCamelCase     :Tuple			  =		complex_input_matrix
            __UpperCamelCase     :Optional[Any]			  =		complex_vector

        # Our implementation.
        __UpperCamelCase  ,       __UpperCamelCase     :Dict			  =		power_iteration(SCREAMING_SNAKE_CASE  ,			SCREAMING_SNAKE_CASE	)

        # Numpy implementation.

        # Get eigenvalues and eigenvectors using built-in numpy
        # eigh (eigh used for symmetric or hermetian matrices).
        __UpperCamelCase  ,       __UpperCamelCase     :List[Any]			  =		np.linalg.eigh(SCREAMING_SNAKE_CASE	)
        # Last eigenvalue is the maximum one.
        __UpperCamelCase     :List[Any]			  =		eigen_values[-1]
        # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
        __UpperCamelCase     :str			  =		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(SCREAMING_SNAKE_CASE	) - np.abs(SCREAMING_SNAKE_CASE	)	) <= 1e-6


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    test_power_iteration()





