# R/laGP_sep.R In laGP: Local Approximate Gaussian Process Regression

#### Documented in aGPsepaGPsep.RlaGPseplaGPsep.R

```#*******************************************************************************
#
# Local Approximate Gaussian Process Regression
# Copyright (C) 2013, The University of Chicago
#
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# version 2.1 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with this library; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301 USA
#
# Questions? Contact Robert B. Gramacy (rbg@vt.edu)
#
#*******************************************************************************

## laGPsep:
##
## C-version of sequential design loop for prediction at Xref

laGPsep <- function(Xref, start, end, X, Z, d=NULL, g=1/10000,
method=c("alc", "alcopt", "alcray", "nn"), Xi.ret=TRUE,
close=min((1000+end)*if(method[1] %in% c("alcray", "alcopt")) 10 else 1, nrow(X)),
alc.gpu=FALSE, numstart=if(method[1] == "alcray") ncol(X) else 1,
rect=NULL, lite=TRUE, verb=0)
{
## argument matching and numerifying
method <- match.arg(method)
if(method == "alc") imethod <- 1
else if(method == "alcopt") imethod <- 2
else if(method == "alcray") imethod <- 3
## else if(method == "mspe") imethod <- 4
## else if(method == "fish") imethod <- 5
else imethod <- 6

## massage Xref
m <- ncol(X)
if(!is.matrix(Xref)) Xref <- data.matrix(Xref)
nref <- nrow(Xref)

## calculate rectangle if using alcray
if(method == "alcray" || method == "alcopt") {
if(is.null(rect)) rect <- matrix(0, nrow=2, ncol=m);
if(method == "alcray" && nref != 1)
stop("alcray only implemented for nrow(Xref) = 1")
if(nrow(rect) != 2 || ncol(rect) != m)
stop("bad rect dimensions, must be 2 x ncol(X)")
if(length(numstart) != 1 || numstart < 1)
stop("numstart should be an integer scalar >= 1")
} else {
if(!is.null(rect)) warning("rect only used by alcray and alcopt methods");
rect <- 0
}

## sanity checks on input dims
n <- nrow(X)
if(start < 6 || end <= start) stop("must have 6 <= start < end")
if(start >= end || n <= end)
stop("start >= end or nrow(X) <= end, so nothing to do")
if(close <= end || close > n) stop("must have end < close <= n")
if(!lite) {
if(nref == 1) {
warning("lite = FALSE only allowed for nref > 1")
lite <- TRUE
}
else s2dim <- nref*nref
} else s2dim <- nref

## process the d argument
d <- darg(d, X)
if(length(d\$start) == 1) d\$start <- rep(d\$start, ncol(X))
else if(length(d\$start) != ncol(X))
stop("d\$start should be scalar or length ncol(X)")
## process the g argument
g <- garg(g, Z)
if(length(g\$start) != 1) stop("g\$start should be scalar")

## convert to doubles
m <- ncol(X)
dd <- c(d\$start, d\$mle, rep(d\$min, m), rep(d\$max, m), d\$ab)
dg <- c(g\$start, g\$mle, g\$min, g\$max, g\$ab)

## sanity checks on controls
if(!(is.logical(Xi.ret) && length(Xi.ret) == 1))
stop("Xi.ret not a scalar logical")
if(length(alc.gpu) > 1 || alc.gpu < 0)
stop("alc.gpu should be a scalar logical or scalar non-negative integer")

## for timing
tic <- proc.time()[3]

out <- .C("laGPsep_R",
m = as.integer(ncol(Xref)),
start = as.integer(start),
end = as.integer(end),
Xref = as.double(t(Xref)),
nref = as.integer(nref),
n = as.integer(n),
X = as.double(t(X)),
Z = as.double(Z),
d = as.double(dd),
g = as.double(dg),
imethod = as.integer(imethod),
close = as.integer(close),
numstart = as.integer(numstart),
rect = as.double(t(rect)),
lite = as.integer(lite),
verb = as.integer(verb),
Xi.ret = as.integer(Xi.ret),
Xi = integer(end*Xi.ret),
mean = double(nref),
s2 = double(s2dim),
df = double(1),
dmle = double(m * d\$mle),
dits = integer(1 * d\$mle),
gmle = double(1 * g\$mle),
gits = integer(1 * g\$mle),
llik = double(1),
PACKAGE = "laGP")

## put timing in
toc <- proc.time()[3]

## assemble output and return
outp <- list(mean=out\$mean, s2=out\$s2, df=out\$df, llik=out\$llik,
time=toc-tic, method=method, d=d, g=g, close=close)

## possibly add mle and Xi info
mle <- NULL
if(d\$mle) mle <- data.frame(d=matrix(out\$dmle, nrow=1), dits=out\$dits)
if(g\$mle) mle <- cbind(mle, data.frame(g=out\$gmle, gits=out\$gits))
outp\$mle <- mle
if(Xi.ret) outp\$Xi <- out\$Xi + 1

## check for lite and possibly make s2 into Sigma
if(!lite) {
outp\$Sigma <- matrix(out\$s2, ncol=nref)
outp\$s2 <- NULL
}

if(method == "alcray" || method == "alcopt")
outp\$numstart <- numstart

##return
return(outp)
}

## laGPsep.R:
##
## and R-loop version of the laGPsep function; the main reason this is
## much slower than the C-version (laGPsep) is that it must pass/copy
## a big X-matrix each time it is called

laGPsep.R <- function(Xref, start, end, X, Z, d=NULL, g=1/10000,
method=c("alc", "alcopt", "alcray", "nn"),
Xi.ret=TRUE, pall=FALSE,
close=min((1000+end)*if(method[1] %in% c("alcray", "alcopt")) 10 else 1, nrow(X)),
parallel=c("none", "omp", "gpu"),
numstart=if(method[1] == "alcray") ncol(X) else 1,
rect=NULL, lite=TRUE, verb=0)
{
## argument matching
method <- match.arg(method)
parallel <- match.arg(parallel)

## massage Xref
m <- ncol(X)
if(!is.matrix(Xref)) Xref <- data.matrix(Xref)

## sanity checks
n <- nrow(X)
if(start < 6 || end <= start) stop("must have 6 <= start < end")
if(start >= end || n <= end)
stop("start >= end or nrow(X) <= end, so nothing to do")
if(close <= end || close > n) stop("must have end < close <= n")
if(!lite && nrow(Xref) == 1)
warning("lite = TRUE only allowed for nrow(Xref) > 1")

## calculate rectangle if using alcray
if(method %in% c("alcray", "alcopt")) {
if(method == "alcray" && nrow(Xref) != 1)
stop("alcray only implemented for nrow(Xref) = 1")
if(length(numstart) != 1 || numstart < 1)
stop("numstart should be an integer scalar >= 1")
}

## process the d argument
d <- darg(d, X)
if(length(d\$start) == 1) d\$start <- rep(d\$start, ncol(X))
else if(length(d\$start) != ncol(X))
stop("d\$start should be scalar or length ncol(X)")
## process the g argument
g <- garg(g, Z)
if(length(g\$start) != 1) stop("g\$start should be scalar")

## check Xi.ret argument
if(!( is.logical(Xi.ret) && length(Xi.ret) == 1))
stop("Xi.ret not a scalar logical")
if(Xi.ret) Xi.ret <- rep(NA, end)
else Xi.ret <- NULL

## for timing
tic <- proc.time()[3]

## sorting to Xref location
dst <- drop(distance(Xref, X))
if(is.matrix(dst)) dst <- apply(dst, 2, min)
cands <- order(dst)
Xi <- cands[1:start]

## building a new GP with closest Xs to Xref
gpsepi <- newGPsep(X[Xi,,drop=FALSE], Z[Xi], d=d\$start, g=g\$start,
dK=!(method %in% c("alc", "alcray", "alcopt", "nn")))

## for the output object
if(!is.null(Xi.ret)) Xi.ret[1:start] <- Xi

## if pall, then predict after every iteration
## ONLY AVAILABLE IN THE R VERSION
if(pall) {
nav <- rep(NA, end-start)
pall <- data.frame(mean=nav, s2=nav, df=nav, llik=nav)
} else pall <- NULL

## determine remaining candidates
if(close >= n) close <- 0
if(close > 0) {
if(close >= n-start)
stop("close not less than remaining cands")
cands <- cands[(start+1):close]
} else cands <- cands[-(1:start)]

# set up rect from cands if not specified
if(method %in% c("alcray", "alcopt")) {
if(is.null(rect)) rect <- apply(X[cands,,drop=FALSE], 2, range)
else if(nrow(rect) != 2 || ncol(rect) != m)
stop("bad rect dimensions, must be 2 x ncol(X)")
} else if(!is.null(rect))
warning("rect only used by alcray and alcopt methods")

## set up the start and end times
for(t in (start+1):end) {

## if pall then predict after each iteration
if(!is.null(pall))
pall[t-start,] <- predGPsep(gpsepi, Xref, lite=TRUE)

## calc ALC to reference
if(method == "alcray") {
offset <- ((t-start) %% floor(sqrt(t-start))) + 1
w <- lalcrayGPsep(gpsepi, Xref, X[cands,,drop=FALSE], rect, offset, numstart,
verb=verb-2)
} else if(method == "alcopt") {
offset <- ((t-start)) # %% floor(sqrt(t-start))) + 1
w <- lalcoptGPsep.R(gpsepi, Xref, X[cands,,drop=FALSE], rect, offset, numstart,
verb=verb-2)
} else {
if(method == "alc")
als <- alcGPsep(gpsepi, X[cands,,drop=FALSE], Xref, parallel=parallel,
verb=verb-2)
else als <- c(1, rep(0, length(cands)-1)) ## nearest neighbor
als[!is.finite(als)] <- NA
w <- which.max(als)
}

## add the chosen point to the GP fit
updateGPsep(gpsepi, matrix(X[cands[w],], nrow=1), Z[cands[w]], verb=verb-1)
if(!is.null(Xi.ret)) Xi.ret[t] <- cands[w]
cands <- cands[-w]
}

## maybe do post-MLE calculation
mle <- mleGPsep.switch(gpsepi, method, d, g, verb)

## Obtain final prediction
outp <- predGPsep(gpsepi, Xref, lite=lite)
if(!is.null(pall)) outp <- as.list(rbind(pall, outp))

## put timing and X info in
toc <- proc.time()[3]
outp\$time <- toc - tic
outp\$Xi <- Xi.ret
outp\$method <- method
outp\$close <- close

## assign d & g
outp\$d <- d
## assign g
outp\$g <- g
## assign mle
outp\$mle <- mle

if(method == "alcray" || method == "alcopt")
outp\$numstart <- numstart

## clean up
deleteGPsep(gpsepi)

return(outp)
}

## aGPsep.R:
##
## loops over all predictive locations XX and obtains adaptive approx
## kriging equations for each based on localized subsets of (X,Z);
## the main reason this is much slower than the C-version (aGPsep) is
## that it must pass/copy a big X-matrix each time it is called

aGPsep.R <- function(X, Z, XX, start=6, end=50, d=NULL, g=1/10000,
method=c("alc", "alcray", "nn"), Xi.ret=TRUE,
close=min((1000+end)*if(method[1] == "alcray") 10 else 1, nrow(X)),
numrays=ncol(X), laGPsep=laGPsep.R, verb=1)
{
## sanity checks
nn <- nrow(XX)
m <- ncol(X)
if(ncol(XX) != ncol(X)) stop("mismatch XX and X cols")
if(nrow(X) != length(Z)) stop("length(Z) != nrow(X)")
if(end-start <= 0) stop("nothing to do")

## check method argument
method <- match.arg(method)

## calculate rectangle if using alcray
if(method == "alcray") {
rect <- apply(X, 2, range)
if(nrow(rect) != 2 || ncol(rect) != ncol(X))
stop("bad rect dimensions, must be 2 x ncol(X)")
if(length(numrays) != 1 || numrays < 1)
stop("numrays should be an integer scalar >= 1")
} else rect <- NULL

## memory for each set of approx kriging equations
ZZ.var <- ZZ.mean <- rep(NA, nrow(XX))

## other args checked in laGP.R; allocate Xi space (?)
N <- length(ZZ.mean)
if(Xi.ret) Xi <- matrix(NA, nrow=N, ncol=end)
else Xi <- NULL

## get d and g arguments
d <- darg(d, X)
g <- garg(g, Z)

## check d\$start
ds.norep <- d\$start
if(length(d\$start) == 1)
d\$start <- matrix(rep(d\$start, m), ncol=m, nrow=nn, byrow=TRUE)
else if(length(d\$start) == m)
d\$start <- matrix(d\$start, nrow=nn, byrow=TRUE)
else if(nrow(d\$start) != nn || ncol(d\$start) != m)
stop("d\$start must be a scalar, or a vector of length ncol(X), or an nrow(XX) x ncol(X) matrix")
## check gstart
if(length(g\$start) > 1 && length(g\$start) != nn)
stop("g\$start must be a scalar or a vector of length nrow(XX)")
gs.norep <- g\$start
if(length(g\$start) != nrow(XX)) g\$start <- rep(g\$start, nrow(XX))

## check mle
if(d\$mle) {
dits <- ZZ.var
dmle <- matrix(NA, nrow=nrow(XX), ncol=ncol(X))
} else dits <- dmle <- NULL
if(g\$mle) gits <- gmle <- ZZ.var
else gits <- gmle <- NULL

## for timing
tic <- proc.time()[3]

## now do copies and local updates for each reference location
for(i in 1:N) {

## local calculation, (add/remove .R in laGP.R for R/C version)
di <- list(start=d\$start[i,], mle=d\$mle, min=d\$min, max=d\$max, ab=d\$ab)
gi <- list(start=g\$start[i], mle=g\$mle, min=g\$min, max=g\$max, ab=g\$ab)
outp <- laGPsep(XX[i,,drop=FALSE], start, end, X, Z, d=di, g=gi,
method=method, Xi.ret=Xi.ret, close=close, numrays=numrays,
rect=rect, verb=verb-1)

## save MLE outputs and update gpi to use new dmle
if(!is.null(dmle)) { dmle[i,] <- as.numeric(outp\$mle[1:ncol(X)]); dits[i] <- outp\$mle\$dits }
if(!is.null(gmle)) { gmle[i] <- outp\$mle\$g; gits[i] <- outp\$mle\$gits }

## extract predictive equations
ZZ.mean[i] <- outp\$mean
ZZ.var[i] <- outp\$s2 * outp\$df / (outp\$df-2)

## save Xi; Xi.ret checked in laGP.R
if(Xi.ret) Xi[i,] <- outp\$Xi

## print progress
if(verb > 0) {
cat("i = ", i, " (of ", N, ")", sep="")
if(d\$mle) cat(", d = (", paste(signif(dmle[i,], 5), collapse=", "), "), its = ", dits[i], sep="")
if(g\$mle) cat(", g = ", gmle[i], ", its = ", gits[i], sep="")
cat("\n", sep="")
}
}

## for timing
toc <- proc.time()[3]

## assemble output
d\$start <- ds.norep
g\$start <- gs.norep
r <- list(Xi=Xi, mean=ZZ.mean, var=ZZ.var, d=d, g=g,
time=toc-tic, method=method, close=close)
mle <- NULL
if(d\$mle) mle <- data.frame(d=dmle, dits=dits)
if(g\$mle) mle <- cbind(mle, data.frame(g=gmle, gits=gits))
r\$mle <- mle
if(method == "alcray") r\$numrays <- numrays

## done
return(r)
}

## aGPsep:
##
## using C: loops over all predictive locations XX and obtains adaptive
## approx kriging equations for each based on localized subsets of (X,Z)

aGPsep <- function(X, Z, XX, start=6, end=50, d=NULL, g=1/10000,
method=c("alc", "alcray", "nn"), Xi.ret=TRUE,
close=min((1000+end)*if(method[1] == "alcray") 10 else 1, nrow(X)),
{
## sanity checks
nn <- nrow(XX)
m <- ncol(X)
n <- nrow(X)
if(ncol(XX) != m) stop("mismatch XX and X cols")
if(n != length(Z)) stop("length(Z) != nrow(X)")
if(end-start <= 0) stop("nothing to do")
if(close <= end || close > n) stop("must have end < close <= n")

## numerify method
method <- match.arg(method)
if(method == "alc") imethod <- 1
else if(method == "alcray") imethod <- 3
else imethod <- 6

## calculate rectangle if using alcray
if(method == "alcray") {
rect <- apply(X, 2, range)
if(nrow(rect) != 2 || ncol(rect) != m)
stop("bad rect dimensions, must be 2 x ncol(X)")
if(length(numrays) != 1 || numrays < 1)
stop("numrays should be an integer scalar >= 1")
} else rect <- 0

## check Xi.ret argument
if(!(is.logical(Xi.ret) && length(Xi.ret) == 1))
stop("Xi.ret not a scalar logical")

## get d and g arguments
d <- darg(d, X)
dd <- c(d\$mle, rep(d\$min, m), rep(d\$max, m), d\$ab)
g <- garg(g, Z)
dg <- c(g\$mle, g\$min, g\$max, g\$ab)

## check d\$start
ds.norep <- d\$start
if(length(d\$start) == 1)
d\$start <- matrix(rep(d\$start, m), ncol=m, nrow=nn, byrow=TRUE)
else if(length(d\$start) == m)
d\$start <- matrix(rep(d\$start, nn), ncol=m, byrow=TRUE)
else if(nrow(d\$start) != nn || ncol(d\$start) != m)
stop("d\$start must be a scalar, or a vector of length ncol(X), or an nrow(XX) x ncol(X) matrix")
## check gstart
if(length(g\$start) > 1 && length(g\$start) != nn)
stop("g\$start must be a scalar or a vector of length nrow(XX)")
gs.norep <- g\$start
if(length(g\$start) != nrow(XX)) g\$start <- rep(g\$start, nrow(XX))

## check OMP argument
stop("omp.threads should be a positive scalar integer")

## for timing
tic <- proc.time()[3]

## calculate the kriging equations separately
out <- .C("aGPsep_R",
m = as.integer(m),
start = as.integer(start),
end = as.integer(end),
XX = as.double(t(XX)),
nn = as.integer(nn),
n = as.integer(n),
X = as.double(t(X)),
Z = as.double(Z),
dstart = as.double(t(d\$start)),
darg = as.double(dd),
g = as.double(g\$start),
garg = as.double(dg),
imethod = as.integer(imethod),
close = as.integer(close),
numrays = as.integer(numrays),
rect = as.double(t(rect)),
verb = as.integer(verb),
Xi.ret = as.integer(Xi.ret),
Xi = integer(end*Xi.ret*nn),
mean = double(nn),
var = double(nn),
dmle = double(nn * d\$mle * m),
dits = integer(nn * d\$mle),
gmle = double(nn * g\$mle),
gits = integer(nn * g\$mle),
llik = double(nn),
PACKAGE = "laGP")

## for timing
toc <- proc.time()[3]

## all done, return
d\$start <- ds.norep
g\$start <- gs.norep
outp <- list(mean=out\$mean, var=out\$var, llik=out\$llik, d=d, g=g,
time=toc-tic, method=method, close=close)

## copy MLE outputs
outp\$mle <- NULL
if(d\$mle) {
outp\$mle <- data.frame(d=matrix(out\$dmle, ncol=m, byrow=TRUE),
dits=out\$dits)
}
if(g\$mle) {
if(d\$mle) outp\$mle <- cbind(outp\$mle, data.frame(g=out\$gmle, gits=out\$gits))
else outp\$mle <- data.frame(g=out\$gmle, gits=out\$gits)
}

if(method == "alcray") outp\$numrays <- numrays

## copy XI
if(Xi.ret) outp\$Xi <- matrix(out\$Xi+1, nrow=nn, byrow=TRUE)

return(outp)
}
```

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laGP documentation built on June 27, 2022, 9:05 a.m.