C_var2 | R Documentation |
Defined as E[(C - E[C])^2], where A^2 = AA (not elementwise multiplication).
C_var2(C, xnew, grad = FALSE)
C |
A const_C object, the result of a call to |
xnew |
The new design point |
grad |
If |
A real number giving the expected variance of C defined via matrix multiplication given the current design.
N. Wycoff, M. Binois, S. Wild (2019+), Sequential Learning of Active Subspaces, preprint.
################################################################################ ### Norm of the variance of C 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 <- 51 xgrid <- seq(0, 1,, ngrid) Xgrid <- as.matrix(expand.grid(xgrid, xgrid)) filled.contour(matrix(f(Xgrid), ngrid)) cvar_crit <- function(C, xnew){ return(sqrt(sum(C_var(C, xnew)^2))) } Cvar_grid <- apply(Xgrid, 1, cvar_crit, C = C_hat) filled.contour(matrix(Cvar_grid, ngrid), color.palette = terrain.colors, plot.axes = {axis(1); axis(2); points(design, pch = 20)})
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