nlsr (version 2021.8.19)

resgr: Compute gradient from residuals and Jacobian.

Description

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.

Usage

resgr(prm, resfn, jacfn, ...)

Value

The numeric vector with the gradient of the sum of squares at the paramters.

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.

Author

John C Nash <[e-mail]>

Details

resgr 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.

References

Nash, J. C. (1979, 1990) _Compact Numerical Methods for Computers. Linear Algebra and Function Minimisation._ Adam Hilger./Institute of Physics Publications

See Also

Function nls(), packages optim and optimx.

Examples

shobbs.res  <-  function(x){ # scaled Hobbs weeds problem -- residual
  # This variant uses looping
  if(length(x) != 3) stop("hobbs.res -- parameter vector n!=3")
  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)
  tt  <-  1:12
  res  <-  100.0*x[1]/(1+x[2]*10.*exp(-0.1*x[3]*tt)) - y
}

shobbs.jac  <-  function(x) { # scaled Hobbs weeds problem -- Jacobian
  jj  <-  matrix(0.0, 12, 3)
  tt  <-  1:12
  yy  <-  exp(-0.1*x[3]*tt)
  zz  <-  100.0/(1+10.*x[2]*yy)
  jj[tt,1]   <-   zz
  jj[tt,2]   <-   -0.1*x[1]*zz*zz*yy
  jj[tt,3]   <-   0.01*x[1]*zz*zz*yy*x[2]*tt
  attr(jj, "gradient") <- jj
  jj
}

st  <-  c(b1=1, b2=1, b3=1)
RG <- resgr(st, shobbs.res, shobbs.jac)
RG