## ---- include = FALSE--------------------------------------------------------- knitr::opts_chunk$set( collapse = TRUE, comment = "#>", echo=TRUE, results='hold', warning=F, cache=F, #dev = 'pdf', message=F, fig.width=5, fig.height=5, tidy.opts=list(width.cutoff=75), tidy=FALSE ) old <- options(scipen = 1, digits = 4) ## ----setup-------------------------------------------------------------------- library(GPFDA) require(MASS) ## ----------------------------------------------------------------------------- set.seed(123) n1 <- 30 # sample size for input coordinate 1 n2 <- 30 # sample size for input coordinate 2 n <- n1*n2 # total sample size # Creating evenly spaced spatial coordinates input <- list() input[[1]] <- seq(0,1,length.out = n1) input[[2]] <- seq(0,1,length.out = n2) inputMat <- as.matrix(expand.grid(input)) # inputs in matrix form # Creating the varying anisotropy matrix with spatially-varying parameters A11 <- function(s1,s2){ exp(6*cos(10*s1 - 5*s2)) } A22 <- function(s1,s2){ exp(sin(6*s1^3) + cos(6*s2^4)) } A12 <- function(s1,s2){ sqrt(A11(s1,s2)*A22(s1,s2))*tanh((s1^2+s2^2)/2) } A_List <- list() R12_vec <- rep(NA, n) for(i in 1:n){ s1 <- inputMat[i,1] s2 <- inputMat[i,2] A_i11 <- A11(s1=s1, s2=s2) A_i22 <- A22(s1=s1, s2=s2) A_i12 <- A12(s1=s1, s2=s2) A_i <- matrix(NA, 2, 2) A_i[1,1] <- A_i11 A_i[2,2] <- A_i22 A_i[1,2] <- A_i12 A_i[2,1] <- A_i12 A_List[[i]] <- A_i R12_vec[i] <- A_i12/sqrt(A_i11*A_i22) } # Constructing the (n x n) covariance matrix K ScaleDistMats <- calcScaleDistMats(A_List=A_List, coords=inputMat) Scale.mat <- ScaleDistMats$Scale.mat Dist.mat <- ScaleDistMats$Dist.mat corrModel <- "pow.ex" gamma <- 1 K <- Scale.mat*unscaledCorr(Dist.mat=Dist.mat, corrModel=corrModel, gamma=gamma) diag(K) <- diag(K) + 1e-8 # Generate response surfaces meanFunction <- rep(0, n) nrep <- 10 response <- t(mvtnorm::rmvnorm(nrep, meanFunction, K)) ## ----------------------------------------------------------------------------- ### NOT RUN # fit <- nsgpr(response = response, # input = input, # corrModel = corrModel, # gamma = gamma, # whichTau = c(T,T), # absBounds = 8, # nBasis = 6, # nInitCandidates = 1000, # cyclic = c(F,F), # unitSignalVariance = T, # zeroNoiseVariance = T, # sepCov = F) ## Taking ML estimates of B-spline coefficients # hp <- fit$MLEsts ### end NOT RUN hp <- c(5.60699, 1.14865, -6.61148, 8, -4.44439, -2.14159, 3.98823, 5.42213, -8, 6.91389, -0.17032, -6.29215, 0.48661, 8, -2.84537, -1.59173, 8, -2.55939, -8, -0.95508, 7.58644, -8, 4.86161, 8, -4.08238, -8, 8, -2.74033, -3.5963, 8, -1.30662, -8, 2.05985, 4.27012, -7.26238, 4.76814, 0.67189, 0.62838, 0.42846, 1.33653, -0.40139, 0.43309, -0.74954, 0.79752, -1.159, 3.31145, -0.87894, -0.99702, 1.72585, -0.29033, 2.41099, 0.46065, -0.95101, 2.0856, -1.39188, 0.57495, -0.39334, 3.24682, 1.09657, -1.90269, 1.5223, -2.87977, 1.54015, -3.89324, -1.67514, -0.18049, 3.93999, -1.50017, 1.18639, 2.16521, -6.93837, -1.88978, -2.06261, -0.80103, 3.17891, -3.68428, 1.64603, 0.58847, 0.86276, -2.38605, 3.99548, -0.52069, 1.33181, -0.10872, -0.43153, -4.91787, 2.56248, 1.90786, -5.382, 0.42587, 1.43742, 0.54047, -0.23679, 2.63721, -0.11159, 0.57184, -2.06124, 1.82977, -6.13951, 4.22915, -0.29822, -2.69144, -7.61238, 5.1746, -5.04487, 7.5953, 0.16564, -1.16696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23.02585) ## ----------------------------------------------------------------------------- # Creating test input points n1test <- n1*2 n2test <- n2*2 inputNew <- list() inputNew[[1]] <- seq(0,1,length.out = n1test) inputNew[[2]] <- seq(0,1,length.out = n2test) inputMatTest <- as.matrix(expand.grid(inputNew[[1]], inputNew[[2]])) pred <- nsgprPredict(hp=hp, response=response, input=input, inputNew=inputNew, noiseFreePred=F, nBasis=6, corrModel=corrModel, gamma=gamma, cyclic=c(F,F), whichTau=c(T,T)) ## ---- fig.width=6, fig.height=5----------------------------------------------- zlim <- range(c(pred$pred.mean, response)) plotImage(response = response, input = inputMat, realisation = 1, n1 = n1, n2 = n2, zlim = zlim, main = "observed") plotImage(response = pred$pred.mean, input = inputMatTest, realisation = 1, n1 = n1test, n2 = n2test, zlim = zlim, main = "prediction") ## ---- fig.width=10, fig.height=5---------------------------------------------- FittedCovMat <- nsgpCovMat(hp=hp, input=input, corrModel=corrModel, gamma=gamma, nBasis=6, cyclic=c(F,F), whichTau=c(T,T), calcCov=T)$Cov ## ---- fig.width=6, fig.height=5----------------------------------------------- # centre points for the covariance functions input1cent <- input[[1]][8] input2cent <- input[[2]][10] # half-width maxdist <- 0.2 zlim <- range(c(K, FittedCovMat)) + 0.2*c(-1,1) centre_idx <- which(inputMat[,1]==input1cent & inputMat[,2]==input2cent) other_idx <- which(inputMat[,1]>input1cent-maxdist & inputMat[,1]input2cent-maxdist & inputMat[,2]