hesschk function

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

hesschk checks a user-provided R function, ffn.

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 hesschk 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.

Returns

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

# 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)