calcMin: Calculate the Minimum of a User-Defined Function

In PBSmodelling: GUI Tools Made Easy: Interact with Models and Explore Data

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)
})

PBSmodelling documentation built on Nov. 9, 2023, 5:07 p.m.