C_tr {activegp}

Expected variance of trace of C

Description

Expected variance of trace of C

Usage

C_tr(C, xnew, grad = FALSE)

Arguments

C

A const_C object, the result of a call to C_GP.

xnew

The new design point

grad

If FALSE, calculate variance of trace after update. If TRUE, returns the gradient.

Value

A real number giving the expected variance of the trace of C given the current design.

References

N. Wycoff, M. Binois, S. Wild (2019+), Sequential Learning of Active Subspaces, preprint.

Examples

################################################################################
### Variance of trace criterion landscape
################################################################################
    library(hetGP)
    set.seed(42)
    nvar <- 2
    n <- 20

    # theta gives the subspace direction
    f <- function(x, theta = pi/6, nugget = 1e-6){
     if(is.null(dim(x))) x <- matrix(x, 1)
     xact <- cos(theta) * x[,1] - sin(theta) * x[,2]
     return(hetGP::f1d(xact) + 
       rnorm(n = nrow(x), sd = rep(nugget, nrow(x))))
    }

    design <- matrix(signif(runif(nvar*n), 2), ncol = nvar)
    response <- apply(design, 1, f)
    model <- mleHomGP(design, response, lower = rep(1e-4, nvar),
                      upper = rep(0.5,nvar), known = list(g = 1e-4))
                      
    C_hat <- C_GP(model)

    ngrid <- 101
    xgrid <- seq(0, 1,, ngrid)
    Xgrid <- as.matrix(expand.grid(xgrid, xgrid))
    filled.contour(matrix(f(Xgrid), ngrid))

    Ctr_grid <- apply(Xgrid, 1, C_tr, C = C_hat)
    filled.contour(matrix(Ctr_grid, ngrid), color.palette = terrain.colors,
                   plot.axes = {axis(1); axis(2); points(design, pch = 20)})