optextras (version 2013-10.27)

ugr: Wrapper for user gradient function for optimization tools

Description

Provides a wrapper around user gradient function for nonlinear optimization to try to control for inadmissible arguments to user objective, gradient or hessian functions, as well as provide for maximization.

Usage

ugr(par, fnuser)

Arguments

par

A vector of parameters to the user-supplied function fn

fnuser

A user-supplied function object that has three sub-functions fn, gr, and hess. fn generates the scalar numerical value of the objective function, gr its vector valued gradient (or is NULL) and hess a numerical matrix for the Hes

Value

• ugr returns a vector numeric value, but all elements are set to the R constant .Machine$double.xmax if the inputs to the function are inadmissible and the computation of gr fails. The returned value has an attribute inadmissible which is returned TRUE in this case, but otherwise is FALSE.

encoding

UTF-8

concept

• minimization
• maximization

Details

The usual dot arguments (...) are subsumed in fnuser$dots to save complexity in the function call. Note that we need to unlist() these is the call to the actual user function.

Examples

cat("Show how ugr works
")
cat("matrix function
")
aa<-matrix(c(2,1,1,2),nrow=2)

myxp<-function(par, A=NULL){
   if(is.null(A))stop("MUST have matrix A")
   f<-as.numeric((t(par) %*% A) %*% par)+(as.numeric(crossprod(par))-1)^2
}

myxpg<-function(par, A=NULL){
   if(is.null(A))stop("MUST have matrix A")
   gg<-2.0*as.vector(A %*% par)+4.0*(as.numeric(crossprod(par))-1)*par
}
npar<-2
opxfn<-list2env(list(fn=myxp, gr=myxpg, hess=NULL, MAXIMIZE=FALSE, PARSCALE=rep(1,npar), FNSCALE=1,
       KFN=0, KGR=0, KHESS=0, dots=list(A=aa)))

x0<-c(1,1)
g0<-myxpg(x0, A=aa)
print(g0)

cat("using numDeriv on myxp
")
gn<-grad(myxp, x0, A=aa)
print(gn)

cat("using ugr with myxpg
")
g0u<-ugr(x0,opxfn)
print(g0u)
rm(opxfn)
cat("using ugr with numderiv "grnd"
")
opxfn<-list2env(list(fn=myxp, gr="grnd", hess=NULL, MAXIMIZE=FALSE, PARSCALE=rep(1,npar), FNSCALE=1,
       KFN=0, KGR=0, KHESS=0, dots=list(A=aa)))

g0un<-ugr(x0,opxfn)
print(g0un)


tmp<-readline("next")
rm(opxfn)
cat("=====================================

")

badlogf<-function(x, skale=10){
#   cat("in badlogf, skale=",skale,"\n")
   sq<-seq(1:length(x))
   r<-(10-x)^2 + skale*log(x-sq)
   f<-as.double(crossprod(r))
} # note that this will fail when length(x)>x for some element of x

badlogg<-function(x, skale=10){# This is the gradient of badlogf
   sq<-seq(1:length(x))
   r<-(10-x)^2 + skale*log(x-sq)
   g<-2*r*(-2*(10-x)+skale/(x-sq))
} # note that this will fail when length(x)>x for some element of x

#badlogh<-function(x, skale=10){
#   sq<-seq(1:length(x))
#   r<-(10-x)^2 + skale*log(x-sq)
#   H<-r\%*\%t(r) # WRONG!
#   2*r*(-2*(10-x)+skale/(x-sq))
## NOT YET SET UP PROPERLY #  
#} # note that this will fail when length(x)>x for some element of x


x0<-rep(20, 4)
npar<-4
opxargs<-list(fn=badlogf, gr=badlogg, hess=NULL, MAXIMIZE=FALSE, 
 PARSCALE=rep(1,npar), FNSCALE=1, KFN=0, KGR=0, KHESS=0, dots=NULL)
opxfn<-list2env(opxargs)

ps1<-rep(1,4)
cat("skale= NULL, parameters:")
print(x0)
cat("Calling analytical badlogg:")
gval0<-badlogg(x0)
print(gval0)
gvalu<-ugr(x0, opxfn)
cat("result:")
print(gvalu)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grfwd"
gvalunf<-ugr(x0, opxfn)
cat("result from grfwd:")
print(gvalunf)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grcentral"
gvalunc<-ugr(x0, opxfn)
cat("result from grcentral:")
print(gvalunc)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grback"
gvalunb<-ugr(x0, opxfn)
cat("result from grback:")
print(gvalunb)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grnd"
gvalund<-ugr(x0, opxfn)
cat("result from grnd:")
print(gvalund)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

cat("======================================
")
tmp<-readline("change parameter scaling")

x0<-rep(20, 4)
npar<-4
opxargs<-list(fn=badlogf, gr=badlogg, hess=NULL, MAXIMIZE=FALSE,
    PARSCALE=rep(1,npar), FNSCALE=1, KFN=0, KGR=0, KHESS=0, dots=NULL)
opxfn<-list2env(opxargs)

ps1<-1/(1:4)
opxfn$PARSCALE<-ps1
cat("skale= NULL, parameters:")
print(x0)
cat("parscale:")
print(ps1)
cat("and in opxfn:")
print(opxfn$PARSCALE)
cat("Calling badlogg function:
")
gval0<-badlogg(x0)
print(gval0)
cat("grad on badlogf:
")
print(grad(badlogf,x0))

x0s<-x0/ps1
cat("x0s:")
print(x0s)

gvalu<-ugr(x0s, opxfn)
cat("result of ugr:
")
print(gvalu)
cat("rescaled:")
print(gvalu/ps1)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")


opxfn$gr<-"grfwd"
gvalunf<-ugr(x0s, opxfn)
cat("result from grfwd:")
print(gvalunf)
cat("rescaled:")
print(gvalunf/ps1)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grcentral"
gvalunc<-ugr(x0s, opxfn)
cat("result from grcentral:")
print(gvalunc)
cat("rescaled:")
print(gvalunc/ps1)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grback"
gvalunb<-ugr(x0s, opxfn)
cat("result from grback:")
print(gvalunb)
cat("rescaled:")
print(gvalunb/ps1)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

opxfn$gr<-"grnd"
gvalund<-ugr(x0s, opxfn)
cat("result from grnd:")
print(gvalund)
cat("rescaled:")
print(gvalund/ps1)
cat("counter: kfn=",opxfn$KFN,"kgr=",opxfn$KGR,"")

cat("======================================
")