HELLINGER3<-function(fitrot, alat, along, rho)
{
#hellinger triple junction data analysis for data in splus object fitrot
#initial guesses in the vectors alat, along, rho:
#first element is side 1 to 2, second element side 1 to 3
        call <- sys.call()
        nsect <- as.integer(fitrot$nsect)
        isect <- as.integer(fitrot$isect)
        iside <- as.integer(fitrot$iside)[isect<=nsect]
        ndat <- as.integer(length(iside))
        nrow <- as.integer(ndat)
        xlat<-fitrot$xlat[isect<=nsect]
        xlong<-fitrot$xlong[isect<=nsect]
        sd<-fitrot$sd[isect<=nsect]
        data <- cbind(xlat,xlong,sd,sd)
        isect<-isect[isect<=nsect]
        idata <- cbind(iside, isect)
        ndim <- as.integer(2 * nsect + 6)
        xmat <- matrix(0.1, nrow = ndat, ncol = ndim)
        hatkap <- 1.0
        etalat<-as.double(1:nsect)
        etalong<-etalat
        ier <- as.integer(0)
        alat2<-c(alat[1:2],.1)
        along2<-c(along[1:2],.1)
        rho2<-c(rho[1:2],.1)
        z2 <- .Fortran("hell4",
                ndat,
                nsect,
                nrow,
                idata,
                data,
                xmat,
                alat2,
                along2,
                rho2,
                hatkap,etalat,etalong,
                ier)
        alat2 <- z2[[7]]
        along2 <- z2[[8]]
        rho2 <- z2[[9]]
        ahat12 <- matrix(0.1, nrow = 3, ncol = 3)
        ahat12 <- .Fortran("trans7",
                alat2[1],
                along2[1],
                rho2[1],
                ahat12)[[4]]
        ahat13<-.Fortran("trans7",
                alat2[2],
                along2[2],
                rho2[2],ahat12)[[4]]
        ahat23<-.Fortran("trans7",
                alat2[3],
                along2[3],
                rho2[3],ahat12)[[4]]
        df <- as.double(ndat - 2 * nsect - 6)
        xmat <- z2[[6]]
        resi <- z2[[5]][, 4]
        xtx <- t(xmat) %*% xmat
        H11.2 <- xtx[1:6, 1:6] - xtx[1:6, 7:ndim] %*% solve(xtx[7:ndim, 7:ndim]
                ) %*% xtx[7:ndim, 1:6]
        c(fitrot,list(alat  = alat2, along = along2, rho = rho2, etalat=z2[[11]], 
etalong = z2[[12]], resi = resi, ahat12 = ahat12, ahat13=ahat13, ahat23=ahat23,
                kappahat = z2[[10]], df = df, Xmat = xmat, H11.2 = H11.2, ier
                 = z2[[13]], call = call, date = date()))
}