# Empirical linked GASP plot Function plots the empirical true linked emulator in case of one-dimensional input. ```r emp_GASP_plot(em, fun, data, emul_type, exp.ql, exp.qu, labels, ylab, xlab, ylim, col_CI_area, col_points, col_fun, col_mean, points) ``` ## Arguments - `em`: the returned output from the function eval_type1_GASP(...) or eval_type2_GASP(...). - `fun`: Simulator function. Currently only one-dimensional input is supported. - `data`: Training data and smoothness. The same as supplied to eval_GASP_RFP(...) for construction of the GASP. - `emul_type`: A text string which provides description of an emulator. - `exp.ql`: Quantile 0.025 - `exp.qu`: Quantile 0.975 - `labels`: As in standard R plot. - `ylab`: As in standard R plot. - `xlab`: As in standard R plot. - `ylim`: As in standard R plot. - `col_CI_area`: Color of a credible area. - `col_points`: Color of the training points. - `col_fun`: Color of a simulator function. - `col_mean`: Color of the emulator of the GASP mean. - `points`: Default is FALSE. To plot or not the training points. ## Returns Plot ## Author(s) Ksenia N. Kyzyurova, kseniak.ucoz.net ## Examples ```r ## Function f1 is a simulator f1<-function(x){sin(pi*x)} ## Function f2 is a simulator f2<-function(x){cos(5*x)} ## Function f2(f1) is a simulator of a composite model f2f1 <- function(x){f2(f1(x))} ## One-dimensional inputs are x1 x1 <- seq(-1,1,.37) ## The following contains the list of data inputs (training) and outputs (fD) together with the ## assumed fixed smoothness of a computer model output. data.f1 <- list(training = x1,fD = f1(x1), smooth = 1.99) ## Evaluation of GASP parameters f1_MLEs = eval_GASP_RFP(data.f1,list(function(x){x^0},function(x){x^1}),1,FALSE) ## Evaluate the emulator xn = seq(-1,1,.01) GASP_type2_f1 <- eval_type2_GASP(as.matrix(xn),f1_MLEs) par(mfrow = c(1,1)) par(mar = c(6.1, 6.1, 5.1, 2.1)) ylim = c(-1.5,1.5) GASP_plot(GASP_type2_f1,f1,data.f1,"Type 2 GASP",ylab = " f",xlab = "x", ylim = ylim, plot_training = TRUE) s = GASP_type2_f1$mu s.var = diag(GASP_type2_f1$var) x2 = seq(-0.95,0.95,length = 6)#f1(x1) data.f2 <- list(training = x2,fD = f2(x2), smooth = 2) # linking requires this emulator ## to have smoothness parameter equal to 2 f2_MLEs = eval_GASP_RFP(data.f2,list(function(x){x^0},function(x){x^1}),1,FALSE) GASP_type1_f2 <- eval_type1_GASP(as.matrix(seq(-3.5,3.5,.01)),f2_MLEs) GASP_type2_f2 <- eval_type2_GASP(as.matrix(seq(-1,1,.01)),f2_MLEs) TGASP_f2 <- eval_TGASP(as.matrix(seq(-1,1,.01)),f2_MLEs) ylim = c(-1.5,1.5) # labels = c(expression(phantom(x)*phantom(x)*phantom(x)*f(x[1])), # expression(f(x[2])*phantom(x)*phantom(x)*phantom(x)), # expression(f(x[3])),expression(f(x[4])), # expression(f(x[5])),expression(f(x[6]))) par(mar = c(6.1, 6.1, 5.1, 2.1)) GASP_plot(GASP_type2_f2,f2,data.f2, "Type 2 GASP",labels = x2,xlab= "z",ylab = " g", ylim = ylim,plot_training = TRUE) le <- link(f1_MLEs, f2_MLEs, as.matrix(xn)) ## Construct an empirical emulator n.samples = 100 em2.runs<-mat.or.vec(n.samples,length(s)) library(MASS) for(i in 1:n.samples) { GASP = eval_type2_GASP(as.matrix(mvrnorm(1,s,diag(s.var))),f2_MLEs) em2.runs[i,] <- mvrnorm(1,GASP$mu, GASP$var) } ## Plot the empirical GASP emulator data.f2f1 <- list(training = x1,fD = f2f1(x1), smooth = 2) par(mar = c(6.1, 6.1, 5.1, 2.1)) emp_GASP_plot(le$em2,f2f1,data.f2f1,"Linked",apply(em2.runs,2,quantile,probs = 0.025), apply(em2.runs,2,quantile,probs = 0.975), ylab = expression("g" ~ scriptscriptstyle(O) ~ "f"),xlab = "x, input",ylim = ylim) ```

emp_GASP_plot function