R/laGP_sep.R

In laGP: Local Approximate Gaussian Process Regression

#*******************************************************************************
#
# 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
# License as published by the Free Software Foundation; either
# 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(ncol(Xref) != m) stop("bad dims")
  if(length(Z) != n) stop("bad dims")
  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
  }
  
  ## add ray info?
  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(ncol(Xref) != m) stop("bad dims")
  if(length(Z) != n) stop("bad dims")
  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
  
  ## add ray info?
  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)
    ## add mle info?
    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$mle <- mle
    ## add ray info?
    if(method == "alcray") r$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)), 
                numrays=ncol(X), omp.threads=1, verb=1)
  {
    ## 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
    if(length(omp.threads) != 1 || omp.threads < 1)
      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),
              omp.threads = as.integer(omp.threads),
              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)
    }

    ## add ray info?
    if(method == "alcray") outp$numrays <- numrays

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