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.Rhistory (UOS-17528's conflicted copy 2022-02-08)
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.packages()
knitr::opts_chunk$set(echo = TRUE)
rm(list = ls(all = TRUE))
library(lhs)
library(plgp, quietly=TRUE) # distance
eps <- sqrt(.Machine$double.eps)
sdx1 <- 0.5
sdx2 <- 0.5
sdy <- 1
sigma2.x1 <- sdx1^2
sigma2.x2 <- sdx2^2
sigma2.y <- sdy^2
nl <- function(par, D, Y)
{
theta <- par[1]
g <- par[2]
n <- length(Y)
K <- exp(-D/theta) + diag(g, n)
Ki <- solve(K)
ldetK <- determinant(K, logarithm=TRUE)$modulus
ll <- - (n/2)*log(t(Y) %*% Ki %*% Y) - (1/2)*ldetK
counter <<- counter + 1
return(-ll)
}
set.seed(1)
n <- 40
d <- 2
X <- randomLHS(n, d)
X[,1] <- (X[,1] - 0.5)*6 + 1
X[,2] <- (X[,2] - 0.5)*6 + 1
xlow <- -2
xupp <- 4 # for both dimensions
Xtilde <- X # n x d = 40 x 2
Xtilde2 <- rbind(Xtilde, Xtilde) # replication #
X <- Xtilde2[, 1] + rnorm(nrow(Xtilde2), sd=sdx1)
X <- cbind(X, Xtilde2[, 2] + rnorm(nrow(Xtilde2), sd=sdx2))
n <- nrow(X) # 80 # set.seed(1)
y <- X[,1]*exp(-X[,1]^2 - X[,2]^2) + rnorm(n, sd=sdy)
D <- distance(X)
counter <- 0
out <- optim(par=c(1, 0.1*var(y)), nl, method="L-BFGS-B", lower=eps,
upper=c(20, var(y)), D=D, Y=y) # p. 169 #
out$par # 0.4175349 1.1439083
thetahat <- out$par[1]
ghat <- out$par[2]
K <- exp(-D/thetahat) + diag(ghat, n) # Khat
Ki <- solve(K)
print(tau2hat <- drop(t(y) %*% Ki %*% y / n)) # 0.5294089 #
c(tau=sqrt(tau2hat), sigma=sqrt(tau2hat*ghat)) #0.7276049 0.7782000
xx <- seq(-2, 4, length=40) # 40 # n' = 1600
XX <- expand.grid(xx, xx) # n' x 2
DXX <- distance(XX) # n' x n'
KXX <- exp(-DXX/thetahat) + diag(ghat, nrow(DXX)) # n' x n'
DX <- distance(XX, X) # n' x n=1600x80
KX <- exp(-DX/thetahat) # n' x n = 1600*80
mup <- KX %*% Ki %*% y
Sigmap <- tau2hat*(KXX - KX %*% Ki %*% t(KX))
q1 <- mup+ qnorm(0.05, 0, sqrt(diag(Sigmap))) # 1600 #
q2 <- mup+ qnorm(0.95, 0, sqrt(diag(Sigmap)))
diff <- q2-q1
sdp <- sqrt(diag(Sigmap))
# Image plots of the posterior mean of the GP, and the posterior
# standard deviation
# points, and 5%, 95% confidence bands #
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(mup, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
image(xx, xx, matrix(sdp, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
YY <- XX[,1]*exp(-X[,1]^2 - X[,2]^2) # true function
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
YY
matrix(YY, ncol=length(xx))
XX[,1]*exp(-X[,1]^2 - X[,2]^2)
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
YY
XX
YY
matrix(YY, ncol=length(xx))
XX
matrix(YY, ncol=length(xx))
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
matrix(YY, ncol=length(xx), byrow =T)
image(xx, xx, matrix(YY, ncol=length(xx), byrow =T), xlab="x1", ylab="x2")
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
xx
xx <- seq(-2, 4, length=40) # 40 # n' = 1600
XX <- expand.grid(xx, xx) # n' x 2
DXX <- distance(XX) # n' x n'
KXX <- exp(-DXX/thetahat) + diag(ghat, nrow(DXX)) # n' x n'
DX <- distance(XX, X) # n' x n=1600x80
KX <- exp(-DX/thetahat) # n' x n = 1600*80
mup <- KX %*% Ki %*% y
Sigmap <- tau2hat*(KXX - KX %*% Ki %*% t(KX))
q1 <- mup+ qnorm(0.05, 0, sqrt(diag(Sigmap))) # 1600 #
q2 <- mup+ qnorm(0.95, 0, sqrt(diag(Sigmap)))
diff <- q2-q1
sdp <- sqrt(diag(Sigmap))
# Image plots of the posterior mean of the GP, and the posterior
# standard deviation
# points, and 5%, 95% confidence bands #
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(mup, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
image(xx, xx, matrix(sdp, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
YY <- XX[,1]*exp(-X[,1]^2 - X[,2]^2) # true function
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
points(X[, 1], X[, 2])
mup
y
YY
cbind(X, y)
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
points(X[, 1], X[, 2])
YY
matrix(YY, ncol=length(xx))
matrix(YY, ncol=length(xx))[1, ]
cbind(X, y)
YY <- XX[,1]*exp(-XX[,1]^2 - XX[,2]^2) # true function
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
points(X[, 1], X[, 2])
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
xx <- seq(-2, 4, length=40) # 40 # n' = 1600
XX <- expand.grid(xx, xx) # n' x 2
DXX <- distance(XX) # n' x n'
KXX <- exp(-DXX/thetahat) + diag(ghat, nrow(DXX)) # n' x n'
DX <- distance(XX, X) # n' x n=1600x80
KX <- exp(-DX/thetahat) # n' x n = 1600*80
mup <- KX %*% Ki %*% y
Sigmap <- tau2hat*(KXX - KX %*% Ki %*% t(KX))
q1 <- mup+ qnorm(0.05, 0, sqrt(diag(Sigmap))) # 1600 #
q2 <- mup+ qnorm(0.95, 0, sqrt(diag(Sigmap)))
diff <- q2-q1
sdp <- sqrt(diag(Sigmap))
# Image plots of the posterior mean of the GP, and the posterior
# standard deviation
# points, and 5%, 95% confidence bands #
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(mup, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
image(xx, xx, matrix(sdp, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
YY <- XX[,1]*exp(-XX[,1]^2 - XX[,2]^2) # true function
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
points(X[, 1], X[, 2])
rm(list = ls(all = TRUE))
library(lhs)
library(plgp, quietly=TRUE) # distance
eps <- sqrt(.Machine$double.eps)
sdx1 <- 0.5
sdx2 <- 0.5
sdy <- 0
sigma2.x1 <- sdx1^2
sigma2.x2 <- sdx2^2
sigma2.y <- sdy^2
nl <- function(par, D, Y)
{
theta <- par[1]
g <- par[2]
n <- length(Y)
K <- exp(-D/theta) + diag(g, n)
Ki <- solve(K)
ldetK <- determinant(K, logarithm=TRUE)$modulus
ll <- - (n/2)*log(t(Y) %*% Ki %*% Y) - (1/2)*ldetK
counter <<- counter + 1
return(-ll)
}
set.seed(1)
n <- 40
d <- 2
X <- randomLHS(n, d)
X[,1] <- (X[,1] - 0.5)*6 + 1
X[,2] <- (X[,2] - 0.5)*6 + 1
xlow <- -2
xupp <- 4 # for both dimensions
Xtilde <- X # n x d = 40 x 2
Xtilde2 <- rbind(Xtilde, Xtilde) # replication #
X <- Xtilde2[, 1] + rnorm(nrow(Xtilde2), sd=sdx1)
X <- cbind(X, Xtilde2[, 2] + rnorm(nrow(Xtilde2), sd=sdx2))
n <- nrow(X) # 80 # set.seed(1)
y <- X[,1]*exp(-X[,1]^2 - X[,2]^2) + rnorm(n, sd=sdy)
D <- distance(X)
counter <- 0
out <- optim(par=c(1, 0.1*var(y)), nl, method="L-BFGS-B", lower=eps,
upper=c(20, var(y)), D=D, Y=y) # p. 169 #
out$par # 0.4175349 1.1439083
thetahat <- out$par[1]
ghat <- out$par[2]
K <- exp(-D/thetahat) + diag(ghat, n) # Khat
Ki <- solve(K)
print(tau2hat <- drop(t(y) %*% Ki %*% y / n)) # 0.5294089 #
c(tau=sqrt(tau2hat), sigma=sqrt(tau2hat*ghat)) #0.7276049 0.7782000
xx <- seq(-2, 4, length=40) # 40 # n' = 1600
XX <- expand.grid(xx, xx) # n' x 2
DXX <- distance(XX) # n' x n'
KXX <- exp(-DXX/thetahat) + diag(ghat, nrow(DXX)) # n' x n'
DX <- distance(XX, X) # n' x n=1600x80
KX <- exp(-DX/thetahat) # n' x n = 1600*80
mup <- KX %*% Ki %*% y
Sigmap <- tau2hat*(KXX - KX %*% Ki %*% t(KX))
q1 <- mup+ qnorm(0.05, 0, sqrt(diag(Sigmap))) # 1600 #
q2 <- mup+ qnorm(0.95, 0, sqrt(diag(Sigmap)))
diff <- q2-q1
sdp <- sqrt(diag(Sigmap))
# Image plots of the posterior mean of the GP, and the posterior
# standard deviation
# points, and 5%, 95% confidence bands #
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(mup, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
image(xx, xx, matrix(sdp, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
YY <- XX[,1]*exp(-XX[,1]^2 - XX[,2]^2) # true function
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(YY, ncol=length(xx)), xlab="x1", ylab="x2")
points(X[, 1], X[, 2])
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128)
image(xx, xx, matrix(q1, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
image(xx, xx, matrix(q2, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
image(xx, xx, matrix(diff, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
# NI Fitted Model: 2d
# ############################### #
Lambda <- thetahat/2
alphavec <- (Ki %*% y)/tau2hat
Delta.fbar.mat <- matrix(NA, nrow=n, ncol=d) # n=80
for(l in 1:n) # l <- 1
{
xstar <- X[l, , drop=FALSE] # 1 x d
kxstar.X <- tau2hat*K[l, , drop=FALSE] # 1 x n
Xtilde.star.tras <- t(matrix(xstar, nrow=n, ncol=d, byrow=TRUE)-X) # d x n
Delta.fbar.mat[l, ] <- (-1/Lambda) * Xtilde.star.tras %*% (t(kxstar.X) * alphavec)
}
# Posterior mean and posterior variance-covariance function.
K.ni <- tau2hat*K + diag(sigma2.y, n) + diag(diag(Delta.fbar.mat %*% diag(c(sigma2.x1, sigma2.x2), 2) %*% t(Delta.fbar.mat)), n)
K.ni.i <- solve(K.ni)
mup.ni <- tau2hat*KX %*% K.ni.i %*% y
Sigmap.ni <- (tau2hat*KXX - tau2hat*KX %*% K.ni.i %*% t(tau2hat*KX)) # 100 100
q1.ni <- mup.ni + qnorm(0.05, 0, sqrt(diag(Sigmap.ni))) # 100
q2.ni <- mup.ni + qnorm(0.95, 0, sqrt(diag(Sigmap.ni)))
diff.grad <- q2.ni-q1.ni
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
par(mgp=c(1.5, 0.8, 0), mar=c(8, 2, 1, 2)+0.1)
cols <- heat.colors(128) # white: highest, red: lowest
image(xx, xx, matrix(mup.ni, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
sdp.ni <- sqrt(diag(Sigmap.ni))
image(xx, xx, matrix(sdp.ni, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
par(mfrow=c(1, 2))
par(las=1, cex.axis=2, cex.lab=2)
cols <- heat.colors(128)
image(xx, xx, matrix(q1.ni, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
image(xx, xx, matrix(q2.ni, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
image(xx, xx, matrix(diff.grad, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
par(mfrow=c(1, 1))
par(las=1, cex.axis=2, cex.lab=2)
image(xx, xx, matrix(diff.grad-diff, ncol=length(xx)), xlab="x1", ylab="x2", col=cols)
points(X[, 1], X[, 2])
usethis::create_github_token()
gitcreds::gitcreds_set()
usethis::use_github_action(url = "https://raw.githubusercontent.com/ropenscilabs/actions_sandbox/master/.github/workflows/deploy_bookdown.yml")
usethis::use_github_action(url = "https://raw.githubusercontent.com/ropenscilabs/actions_sandbox/master/.github/workflows/deploy_bookdown.yml")
usethis::use_github_action(url = "https://raw.githubusercontent.com/ropenscilabs/actions_sandbox/master/.github/workflows/deploy_bookdown.yml")
renv::snapshot()
usethis::use_github_action("bookdown")
?bookdown::render_book
16/70
factor(4)
factor(1:4)
rep(factor(1:4), 5)
pulp <- data.frame(operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)
pulp <- data.frame(run = 1:20, operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)
pulp <- data.frame(repetition = rep(1:4, rep(5, 5)), operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
pulp <- data.frame(repetition = rep(1:4, rep(5, 4)), operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)
pulp <- data.frame(repetition = rep(1:4, rep(5, 4)), operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)
rep(1:4, rep(5, 4)
rep(1:4, rep(5, 4))
pulp <- data.frame(run = 1:20, repetition = rep(1:4, rep(5, 4)), operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, id_col = run, names_from = operator, values_from = reflectance)
pulp <- data.frame(run = 1:20, repetition = rep(1:4, rep(5, 4)), operator = rep(factor(1:4), 5),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
pulp
pulp <- data.frame(operator = rep(factor(1:4), 5),
repetition = rep(1:4, rep(5, 4)),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
pulp
pulp <- data.frame(operator = rep(factor(1:4), 5),
repetition = rep(1:4, rep(5, 4)),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)
pulp <- data.frame(operator = rep(factor(1:4), 5),
repetition = rep(1:5, rep(4, 5)),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)
?knitr::kable
pulp <- data.frame(operator = rep(factor(1:4), 5),
repetition = rep(1:5, rep(4, 5)),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
knitr::kable(
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance),
col.names = paste("Operator", 1:4),
caption = "Pulp experiment: reflectance values from four different operators."
)
paste("Operator", 1:4)
pulp <- data.frame(operator = rep(factor(1:4), 5),
repetition = rep(1:5, rep(4, 5)),
reflectance = c(59.8, 59.8, 60.7, 61.0, 60.0, 60.2, 60.7, 60.8,
60.8, 60.4, 60.5, 60.6, 60.8, 59.9, 60.9, 60.5, 59.8, 60.0, 60.3, 60.5)
)
knitr::kable(
tidyr::pivot_wider(pulp, names_from = operator, values_from = reflectance)[, -1],
col.names = paste("Operator", 1:4),
caption = "Pulp experiment: reflectance values from four different operators."
)
?boxplot
boxplot(reflectance ~ operator)
boxplot(reflectance ~ operator, data = pulp)
getwd()
?purl
purl("01-intro.Rmd", documentation = 0, output = "../R")
knitr::purl("01-intro.Rmd", documentation = 0, output = "../R")
knitr::purl("01-intro.Rmd", documentation = 0, output = "../R/01-intro.R")
renv::activate()
renv::restore()
renv::snapshot()
renv::snapshot()
renv::snapshot()
renv::snapshot()
renev:deactivate()
renv:deactivate()
renv::deactivate()
renv::snapshot()
renv::snapshot()
renv::dependencies()
?renv::dependencies()
renv::snapshot()
renv::settings$snapshot.type("all")
renv::snapshot()
renv::deactivate()
renv::activate()
renv::snapshot()
?renv::settings
renv::settings$snapshot.type("implicit")
renv::init()
renv::snapshot()
install.packages("bookdown")
renev::status()
install.packages(c("renev", "tidyr"))
install.packages(c("renv", "tidyr"))
install.packages(c("renv", "tidyr"))
install.packages(c("renv", "tidyr"))
install.packages(c("generics"))
install.packages("generics")
?install.packages
install.packages("generics", type = "mac.binary")
install.packages("pillar", type = "mac.binary")
renv::status()
renv::restore()
warnings()