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.

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

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)
#> Analytic hessian from function  genrose.h 
#> 
#> hn from hess() is reported non-symmetric with asymmetry ratio 5.09011128647231e-12 
print(ans100)
#> [1] TRUE
#> attr(,"asym")
#> [1] 5.090111e-12
#> attr(,"ha")
#>      [,1] [,2]
#> [1,] 1328  480
#> [2,]  480  202
#> attr(,"hn")
#>      [,1] [,2]
#> [1,] 1328  480
#> [2,]  480  202
ans10<-hesschk(trad, genrose.f, genrose.g, genrose.h, trace=1, gs=10)
#> Analytic hessian from function  genrose.h 
#> 
#> hn from hess() is reported non-symmetric with asymmetry ratio 5.83064342859778e-12 
print(ans10)
#> [1] TRUE
#> attr(,"asym")
#> [1] 5.830643e-12
#> attr(,"ha")
#>       [,1] [,2]
#> [1,] 132.8   48
#> [2,]  48.0   22
#> attr(,"hn")
#>       [,1] [,2]
#> [1,] 132.8   48
#> [2,]  48.0   22