sim.dpp.modal.fast.seq {demu}

Draw sequential samples from the conditional DPP given previously sampled points already in the design.

Description

sim.dpp.modal.fast.seq() is similar to sim.dpp.modal.fast but sequentially selects n additional points to add to the design given that the points in curpts are alread in the design from previous sequential iterations. It uses the C++ codepath that makes use of SPAM's sparse matrices to enable faster computation. It implements the DPP-based design emulator of Pratola et al. (2018) to draw a sequential sample of the n-run additional optimal design points for a Gaussian process regression model with compact correlation function r(x,x^\prime), where the entries of R are formed by evaluating r(x,x^\prime) over a grid of candidate locations.

Usage

sim.dpp.modal.fast.seq(curpts, R,n)

Arguments

curpts

A vector of indices to the candidate points that already appear in the design.

R

A sparse correlation matrix evaluated over a grid of candidate design sites. The sparse matrix should be of type dgCMatrix (see package spam).

n

Size of the design to sample.

Details

For more details on the method, see Pratola et al. (2018). Detailed examples demonstrating the method are available at http://www.matthewpratola.com/software.

Value

A vector of indices to the sampled design sites.

References

Pratola, Matthew T., Lin, C. Devon, and Craigmile, Peter. (2018) Optimal Design Emulators: A Point Process Approach. arXiv:1804.02089.

See Also

demu-package sim.dpp.modal.fast sim.dpp.modal

Examples

library(demu)
library(fields)
library(spam)
library(Matrix)

n1=3
n2=3
n3=3
rho=0.2
ngrid=10

x=seq(0,1,length=ngrid)
X=as.matrix(expand.grid(x,x))
l.d=makedistlist(X)

# Initial design
R.spam=wendland.cov(X,X,theta=rho,k=3)
R=as.dgCMatrix.spam(R.spam)
pts.1=sim.dpp.modal.fast(R,n1)
pts.1.proj=remove.projections(pts.1,X)

# Next sequential step, removing projections
pts.2=sim.dpp.modal.fast.seq(pts.1.proj$allpts,R,n2)
design=c(pts.1,pts.2$pts.new)
pts.2.proj=remove.projections(design,X)

# Next sequential step, removing projections
pts.3=sim.dpp.modal.fast.seq(pts.2.proj$allpts,R,n3)
design=c(design,pts.3$pts.new)


# Or, starting with the initial design, don't remove projections
pts.2=sim.dpp.modal.fast.seq(pts.1,R,n2)
designB=c(pts.1,pts.2$pts.new)

pts.3=sim.dpp.modal.fast.seq(designB,R,n3)
designB=c(designB,pts.3$pts.new)


# Plot the result:
#par(mfrow=c(1,3))
#plot(X,xlim=c(0,1),ylim=c(0,1),main="Initial Design")
#points(X[pts.1,],pch=20,cex=2)
#
#plot(X,xlim=c(0,1),ylim=c(0,1),main="+3x2 remove projections")
#points(X[design,],pch=20,cex=2)
#
#plot(X,xlim=c(0,1),ylim=c(0,1),main="+3x2 not removing projections")
#points(X[designB,],pch=20,cex=2)