# Compute gradient from residuals and Jacobian. For a nonlinear model originally expressed as an expression of the form lhs ~ formula_for_rhs assume we have a resfn and jacfn that compute the residuals and the Jacobian at a set of parameters. This routine computes the gradient, that is, t(Jacobian) . residuals. ```r modgr(prm, resfn, jacfn, ...) ``` ## Arguments - `prm`: A parameter vector. For our example, we could use start=c(b1=1, b2=2.345, b3=0.123) However, the names are NOT used, only positions in the vector. - `resfn`: A function to compute the residuals of our model at a parameter vector. - `jacfn`: A function to compute the Jacobian of the residuals at a paramter vector. - ``...``: Any data needed for computation of the residual vector from the expression rhsexpression - lhsvar. Note that this is the negative of the usual residual, but the sum of squares is the same. ## Details `modgr` calls resfn to compute residuals and jacfn to compute the Jacobian at the parameters `prm` using external data in the dot arguments. It then computes the gradient using t(Jacobian) . residuals. Note that it appears awkward to use this function in calls to optimization routines. The author would like to learn why. ## Returns The numeric vector with the gradient of the sum of squares at the paramters. ## References Nash, J. C. (1979, 1990) _Compact Numerical Methods for Computers. Linear Algebra and Function Minimisation._ Adam Hilger./Institute of Physics Publications ## Author(s) John C Nash ## Note Special notes, if any, will appear here. ## See Also Function `nls()`, packages `optim` and `optimx`. ## Examples ```r cat("See examples in nlmrt-package.Rd\n") y <- c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443, 38.558, 50.156, 62.948, 75.995, 91.972) # for testing tt <- seq_along(y) # for testing f <- y ~ b1/(1 + b2 * exp(-1 * b3 * tt)) p <- c(b1 = 1, b2 = 1, b3 = 1) myres <- model2resfun(f, p) myjac <- model2jacfun(f, p) mygr <- model2grfun(f, p) gr <- mygr(p, tt = tt, y = y) grm <- modgr(p, myres, myjac, tt = tt, y = y) cat("max(abs(grm - gr)) =",max(abs(grm-gr)),"\n") ```

modgr function