Calculate Hessian for a GP with Gaussian correlation

Usage

Gaussian_hessianR(XX, X, Z, Kinv, mu_hat, theta)

Arguments

XX: The vector at which to calculate the Hessian
X: The input points
Z: The output values
Kinv: The inverse of the correlation matrix
mu_hat: Estimate of mu
theta: Theta parameters for the correlation

Value

Matrix, the Hessian at XX

Examples

set.seed(0)
n <- 40
x <- matrix(runif(n*2), ncol=2)
f1 <- function(a) {sin(2*pi*a[1]) + sin(6*pi*a[2])}
y <- apply(x,1,f1) + rnorm(n,0,.01)
gp <- GauPro(x,y, verbose=2, parallel=FALSE);gp$theta
#> Optimizing
#> 	Initial values:
#> $par
#> [1]  0  0 -6
#> 
#> $value
#> [1] 230.1134
#> 
#> 	Restart (parallel): starts pars = 0 0 -6 
#> 	Restart (parallel): starts pars = 2.508166 1.544284 -4.654356 
#> 	Restart (parallel): starts pars = -0.8496206 -0.8379602 -5.318771 
#> 	Restart (parallel): starts pars = -0.5515561 2.512038 -5.517843 
#> 	Restart (parallel): starts pars = 2.598625 -1.746524 -5.993321 
#> 	Restart (parallel): starts pars = -1.761743 1.192518 -5.904707 
#>                start                  end    value func_evals grad_evals
#> 1             0,0,-6                   NA 230.1134          1         NA
#> 2             0,0,-6 0.662,-0.0899,0.0118  114.978         NA         NA
#> 3    2.51,1.54,-4.65     0.527,1.45,-5.64 41.38313         NA         NA
#> 4 -0.85,-0.838,-5.32 0.662,-0.0899,0.0118  114.978         NA         NA
#> 5  -0.552,2.51,-5.52     0.528,1.45,-5.64 41.38313         NA         NA
#> 6    2.6,-1.75,-5.99     0.527,1.45,-5.64 41.38313         NA         NA
#> 7    -1.76,1.19,-5.9    0.654,-4.65,0.148 116.6973         NA         NA
#>   convergence message
#> 1          NA      NA
#> 2           0      NA
#> 3           0      NA
#> 4           0      NA
#> 5           0      NA
#> 6           0      NA
#> 7       -1001      NA
#> [1]  3.368992 28.355167
gp$hessian(c(.2,.75), useC=FALSE) # Should be -38.3, -5.96, -5.96, -389.4 as 2x2 matrix
#>            [,1]        [,2]
#> [1,] -38.669255    8.040595
#> [2,]   8.040595 -319.909255