calcMin: 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, ...)

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.

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.

Author

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

Details

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

Examples

Run this code

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)
})

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