<s> """<STR_LIT>""" <EOL> from . rbf import RBF <EOL> from . stationary import Exponential <EOL> from . stationary import RatQuad <EOL> import numpy as np <EOL> import scipy as sp <EOL> class sde_RBF ( RBF ) : <EOL> """<STR_LIT>""" <EOL> def sde_update_gradient_full ( self , gradients ) : <EOL> """<STR_LIT>""" <EOL> self . variance . gradient = gradients [ <NUM_LIT:0> ] <EOL> self . lengthscale . gradient = gradients [ <NUM_LIT:1> ] <EOL> def sde ( self ) : <EOL> """<STR_LIT>""" <EOL> N = <NUM_LIT:10> <EOL> roots_rounding_decimals = <NUM_LIT:6> <EOL> fn = np . math . factorial ( N ) <EOL> kappa = <NUM_LIT:1.0> / <NUM_LIT> / self . lengthscale ** <NUM_LIT:2> <EOL> Qc = np . array ( ( self . variance * np . sqrt ( np . pi / kappa ) * fn * ( <NUM_LIT:4> * kappa ) ** N , ) , ) <EOL> pp = np . zeros ( ( <NUM_LIT:2> * N + <NUM_LIT:1> , ) ) <EOL> for n in range ( <NUM_LIT:0> , N + <NUM_LIT:1> ) : <EOL> pp [ <NUM_LIT:2> * ( N - n ) ] = fn * ( <NUM_LIT> * kappa ) ** ( N - n ) / np . math . factorial ( n ) * ( - <NUM_LIT:1> ) ** n <EOL> pp = sp . poly1d ( pp ) <EOL> roots = sp . roots ( pp ) <EOL> neg_real_part_roots = roots [ np . round ( np . real ( roots ) , roots_rounding_decimals ) < <NUM_LIT:0> ] <EOL> aa = sp . poly1d ( neg_real_part_roots , r = True ) . coeffs <EOL> F = np . diag ( np . ones ( ( N - <NUM_LIT:1> , ) ) , <NUM_LIT:1> ) <EOL> F [ - <NUM_LIT:1> , : ] = - aa [ - <NUM_LIT:1> : <NUM_LIT:0> : - <NUM_LIT:1> ] <EOL> L = np . zeros ( ( N , <NUM_LIT:1> ) ) <EOL> L [ N - <NUM_LIT:1> , <NUM_LIT:0> ] = <NUM_LIT:1> <EOL> H = np . zeros ( ( <NUM_LIT:1> , N ) ) <EOL> H [ <NUM_LIT:0> , <NUM_LIT:0> ] = <NUM_LIT:1> <EOL> Pinf = sp . linalg . solve_lyapunov ( F , - np . dot ( L , np . dot ( Qc [ <NUM_LIT:0> , <NUM_LIT:0> ] , L . T ) ) ) <EOL> Pinf = <NUM_LIT:0.5> * ( Pinf + Pinf . T ) <EOL> dF = np . empty ( [ F . shape [ <NUM_LIT:0> ] , F . shape [ <NUM_LIT:1> ] , <NUM_LIT:2> ] ) <EOL> dQc = np . empty ( [ Qc . shape [ <NUM_LIT:0> ] , Qc . shape [ <NUM_LIT:1> ] , <NUM_LIT:2> ] ) <EOL> dPinf = np . empty ( [ Pinf . shape [ <NUM_LIT:0> ] , Pinf . shape [ <NUM_LIT:1> ] , <NUM_LIT:2> ] ) <EOL> dFvariance = np . zeros ( F . shape ) <EOL> dFlengthscale = np . zeros ( F . shape ) <EOL> dFlengthscale [ - <NUM_LIT:1> , : ] = - aa [ - <NUM_LIT:1> : <NUM_LIT:0> : - <NUM_LIT:1> ] / self . lengthscale * np . arange ( - N , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> dQcvariance = Qc / self . variance <EOL> dQclengthscale = np . array ( ( ( self . variance * np . sqrt ( <NUM_LIT:2> * np . pi ) * fn * <NUM_LIT:2> ** N * self . lengthscale ** ( - <NUM_LIT:2> * N ) * ( <NUM_LIT:1> - <NUM_LIT:2> * N , ) , ) ) ) <EOL> dPinf_variance = Pinf / self . variance <EOL> lp = Pinf . shape [ <NUM_LIT:0> ] <EOL> coeff = np . arange ( <NUM_LIT:1> , lp + <NUM_LIT:1> ) . reshape ( lp , <NUM_LIT:1> ) + np . arange ( <NUM_LIT:1> , lp + <NUM_LIT:1> ) . reshape ( <NUM_LIT:1> , lp ) - <NUM_LIT:2> <EOL> coeff [ np . mod ( coeff , <NUM_LIT:2> ) != <NUM_LIT:0> ] = <NUM_LIT:0> <EOL> dPinf_lengthscale = - <NUM_LIT:1> / self . lengthscale * Pinf * coeff <EOL> dF [ : , : , <NUM_LIT:0> ] = dFvariance <EOL> dF [ : , : , <NUM_LIT:1> ] = dFlengthscale <EOL> dQc [ : , : , <NUM_LIT:0> ] = dQcvariance <EOL> dQc [ : , : , <NUM_LIT:1> ] = dQclengthscale <EOL> dPinf [ : , : , <NUM_LIT:0> ] = dPinf_variance <EOL> dPinf [ : , : , <NUM_LIT:1> ] = dPinf_lengthscale <EOL> P0 = Pinf . copy ( ) <EOL> dP0 = dPinf . copy ( ) <EOL> import GPy . models . state_space_main as ssm <EOL> ( F , L , Qc , H , Pinf , P0 , dF , dQc , dPinf , dP0 , T ) = ssm . balance_ss_model ( F , L , Qc , H , Pinf , P0 , dF , dQc , dPinf , dP0 ) <EOL> return ( F , L , Qc , H , Pinf , P0 , dF , dQc , dPinf , dP0 ) <EOL> class sde_Exponential ( Exponential ) : <EOL> """<STR_LIT>""" <EOL> def sde_update_gradient_full ( self , gradients ) : <EOL> """<STR_LIT>""" <EOL> self . variance . gradient = gradients [ <NUM_LIT:0> ] <EOL> self . lengthscale . gradient = gradients [ <NUM_LIT:1> ] <EOL> def sde ( self ) : <EOL> """<STR_LIT>""" <EOL> variance = float ( self . variance . values ) <EOL> lengthscale = float ( self . lengthscale ) <EOL> F = np . array ( ( ( - <NUM_LIT:1.0> / lengthscale , ) , ) ) <EOL> L = np . array ( ( ( <NUM_LIT:1.0> , ) , ) ) <EOL> Qc = np . array ( ( ( <NUM_LIT> * variance / lengthscale , ) , ) ) <EOL> H = np . array ( ( ( <NUM_LIT:1.0> , ) , ) ) <EOL> Pinf = np . array ( ( ( variance , ) , ) ) <EOL> P0 = Pinf . copy ( ) <EOL> dF = np . zeros ( ( <NUM_LIT:1> , <NUM_LIT:1> , <NUM_LIT:2> ) ) ; <EOL> dQc = np . zeros ( ( <NUM_LIT:1> , <NUM_LIT:1> , <NUM_LIT:2> ) ) ; <EOL> dPinf = np . zeros ( ( <NUM_LIT:1> , <NUM_LIT:1> , <NUM_LIT:2> ) ) ; <EOL> dF [ : , : , <NUM_LIT:0> ] = <NUM_LIT:0.0> <EOL> dF [ : , : , <NUM_LIT:1> ] = <NUM_LIT:1.0> / lengthscale ** <NUM_LIT:2> <EOL> dQc [ : , : , <NUM_LIT:0> ] = <NUM_LIT> / lengthscale <EOL> dQc [ : , : , <NUM_LIT:1> ] = - <NUM_LIT> * variance / lengthscale ** <NUM_LIT:2> <EOL> dPinf [ : , : , <NUM_LIT:0> ] = <NUM_LIT:1.0> <EOL> dPinf [ : , : , <NUM_LIT:1> ] = <NUM_LIT:0.0> <EOL> dP0 = dPinf . copy ( ) <EOL> return ( F , L , Qc , H , Pinf , P0 , dF , dQc , dPinf , dP0 ) <EOL> class sde_RatQuad ( RatQuad ) : <EOL> """<STR_LIT>""" <EOL> def sde ( self ) : <EOL> """<STR_LIT>""" <EOL> assert False , '<STR_LIT>' </s>
