calcMin {PBSmodelling}

Calculate the Minimum of a User-Defined Function

Description

Minimization based on the R-stat functions nlm, nlminb, and optim. Model parameters are scaled and can be active or not in the minimization.

Usage

calcMin(pvec, func, method="nlm", trace=0, maxit=1000, reltol=1e-8,
        steptol=1e-6, temp=10, repN=0, ...)

Arguments

pvec

Initial values of the model parameters to be optimized. pvec is a data frame comprising four columns ( "val","min","max","active") and as many rows as there are model parameters. The "active" field (logical) determines whether the parameters are estimated (T) or remain fixed (F).

func

The user-defined function to be minimized (or maximized). The function should return a scalar result.

method

The minimization method to use: one of nlm, nlminb, Nelder-Mead, BFGS, CG, L-BFGS-B, or SANN. Default is nlm.

trace

Non-negative integer. If positive, tracing information on the progress of the minimization is produced. Higher values may produce more tracing information: for method "L-BFGS-B" there are six levels of tracing. Default is 0.

maxit

The maximum number of iterations. Default is 1000.

reltol

Relative convergence tolerance. The algorithm stops if it is unable to reduce the value by a factor of reltol*(abs(val)+reltol) at a step. Default is 1e-8.

steptol

A positive scalar providing the minimum allowable relative step length. Default is 1e-6.

temp

Temperature controlling the "SANN" method. It is the starting temperature for the cooling schedule. Default is 10.

repN

Reports the parameter and objective function values on the R-console every repN evaluations. Default is 0 for no reporting.

...

Further arguments to be passed to the optimizing function chosen: nlm, nlminb, or optim. Beware of partial matching to earlier arguments.

Details

See optim for details on the following methods: Nelder-Mead, BFGS, CG, L-BFGS-B, and SANN.

Value

A list with components:

Fout

The output list from the optimizer function chosen through method.

iters

Number of iterations.

evals

Number of evaluations.

cpuTime

The user CPU time to execute the minimization.

elapTime

The total elapsed time to execute the minimization.

fminS

The objective function value calculated at the start of the minimization.

fminE

The objective function value calculated at the end of the minimization.

Pstart

Starting values for the model parameters.

Pend

Final values estimated for the model parameters from the minimization.

AIC

Akaike's Information Criterion

message

Convergence message from the minimization routine.

Note

Some arguments to calcMin have no effect depending on the method chosen.

Author(s)

Jon T. Schnute, Pacific Biological Station, Fisheries and Oceans Canada, Nanaimo BC

See Also

scalePar, restorePar, calcMin, GT0
In the stats package: nlm, nlminb, and optim.

Examples

local(envir=.PBSmodEnv,expr={
Ufun <- function(P) {
  Linf <- P[1]; K <- P[2]; t0 <- P[3]; obs <- afile$len;
  pred <- Linf * (1 - exp(-K*(afile$age-t0)));
  n <- length(obs); ssq <- sum((obs-pred)^2 );
  return(n*log(ssq)); };

oldpar = par(no.readonly = TRUE)
afile <- data.frame(age=1:16,len=c(7.36,14.3,21.8,27.6,31.5,35.3,39,
  41.1,43.8,45.1,47.4,48.9,50.1,51.7,51.7,54.1));
pvec <- data.frame(val=c(70,0.5,0),min=c(40,0.01,-2),max=c(100,2,2),
  active=c(TRUE,TRUE,TRUE),row.names=c("Linf","K","t0"),
  stringsAsFactors=FALSE);
alist <- calcMin(pvec=pvec,func=Ufun,method="nlm",steptol=1e-4,repN=10);
print(alist[-1]); P <- alist$Pend;
#resetGraph(); 
expandGraph();
xnew <- seq(afile$age[1],afile$age[nrow(afile)],len=100);
ynew <- P[1] * (1 - exp(-P[2]*(xnew-P[3])) );
plot(afile); lines(xnew,ynew,col="red",lwd=2); 
addLabel(.05,.88,paste(paste(c("Linf","K","t0"),round(P,c(2,4,4)),
  sep=" = "),collapse="\n"),adj=0,cex=0.9);
par(oldpar)
})