# Run tests, where possible, on user objective function and (optionally) gradient and hessian `hesschk` checks a user-provided R function, `ffn`. ```r 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 ```r # 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) ```

hesschk function