Run tests, where possible, on user objective function and (optionally) gradient and hessian

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Description

hesschk checks a user-provided R function, ffn.

Usage

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   hesschk(xpar, ffn, ggr, hhess, trace=0, testtol=(.Machine$double.eps)^(1/3), ...)

Arguments

xpar

parameters to the user objective and gradient functions ffn and ggr

ffn

User-supplied objective function

ggr

User-supplied gradient function

hhess

User-supplied Hessian function

trace

set >0 to provide output from grchk to the console, 0 otherwise

testtol

tolerance for equality tests

...

optional arguments passed to the objective function.

Details

Package: hesschk
Depends: R (>= 2.6.1)
License: GPL Version 2.

numDeriv is used to compute a numerical approximation to the Hessian matrix. If there is no analytic gradient, then the hessian() function from numDeriv is applied to the user function ffn. Otherwise, the jacobian() function of numDeriv is applied to the ggr function so that only one level of differencing is used.

Value

The function returns a single object hessOK which is TRUE if the analytic Hessian code returns a Hessian matrix that is "close" to the numerical approximation obtained via numDeriv; FALSE otherwise.

hessOK is returned with the following attributes:

  • "nullhess"Set TRUE if the user does not supply a function to compute the Hessian.

  • "asym"Set TRUE if the Hessian does not satisfy symmetry conditions to within a tolerance. See the hesschk for details.

  • "ha"The analytic Hessian computed at paramters xpar using hhess.

  • "hn"The numerical approximation to the Hessian computed at paramters xpar.

  • "msg"A text comment on the outcome of the tests.

Author(s)

John C. Nash

Examples

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# genrose function code
genrose.f<- function(x, gs=NULL){ # objective function
## One generalization of the Rosenbrock banana valley function (n parameters)
	n <- length(x)
        if(is.null(gs)) { gs=100.0 }
	fval<-1.0 + sum (gs*(x[1:(n-1)]^2 - x[2:n])^2 + (x[2:n] - 1)^2)
        return(fval)
}

genrose.g <- function(x, gs=NULL){
# vectorized gradient for genrose.f
# Ravi Varadhan 2009-04-03
	n <- length(x)
        if(is.null(gs)) { gs=100.0 }
	gg <- as.vector(rep(0, n))
	tn <- 2:n
	tn1 <- tn - 1
	z1 <- x[tn] - x[tn1]^2
	z2 <- 1 - x[tn]
	gg[tn] <- 2 * (gs * z1 - z2)
	gg[tn1] <- gg[tn1] - 4 * gs * x[tn1] * z1
	return(gg)
}

genrose.h <- function(x, gs=NULL) { ## compute Hessian
   if(is.null(gs)) { gs=100.0 }
	n <- length(x)
	hh<-matrix(rep(0, n*n),n,n)
	for (i in 2:n) {
		z1<-x[i]-x[i-1]*x[i-1]
#		z2<-1.0-x[i]
                hh[i,i]<-hh[i,i]+2.0*(gs+1.0)
                hh[i-1,i-1]<-hh[i-1,i-1]-4.0*gs*z1-4.0*gs*x[i-1]*(-2.0*x[i-1])
                hh[i,i-1]<-hh[i,i-1]-4.0*gs*x[i-1]
                hh[i-1,i]<-hh[i-1,i]-4.0*gs*x[i-1]
	}
        return(hh)
}

trad<-c(-1.2,1)
ans100<-hesschk(trad, genrose.f, genrose.g, genrose.h, trace=1)
print(ans100)
ans10<-hesschk(trad, genrose.f, genrose.g, genrose.h, trace=1, gs=10)
print(ans10)