[R] Compute in C a loop with the lm() function and back to R

[Javier López de Lacalle Beltrán de Heredia]

I want to do the computations from a loop by means of
a C routine that will be called from R. The lm()
function is entailed in that loop.

As a guidance, I have taken the following example from
http://www.math.mcgill.ca/steele/ (As far as my
question is concerned, I get similar information from
"writing R extensions" and the book "Econometrics in
R" by G.V Farnsworth):

Let convolve.rfun an R function

convolve.rfun <- function(a,b)
{
  ab <- rep(0, length(a)+length(b)-1)
  for(i in seq(along=a)){
    for(j in seq(along=b))
      ab[i+j-1] <- ab[i+j-1] + a[i]*b[j]
  }
  ab
}

then the following C code do the computations of
convolve.rfun,

void convolve(double *a, int *na, double *b, int *nb,
double *ab)
{
 int i, j, nab = *na + *nb - 1;

 for(i = 0; i < nab; i = i+1){
   ab[i] = 0.0;
 }

 for(i = 0; i < *na; i = i + 1){
  for(j = 0; j < *nb; j = j + 1){
    ab[i + j] = ab[i+j] +  a[i] * b[j];
   }
 }
}

which after being compiled (R CMD SHLIB convolve.c)
can be called from R:

dyn.load("convolve.so")
conv <- function(a, b){
  .C("convolve", as.double(a), as.integer(length(a)),
as.double(b),
    as.integer(length(b)),
ab=double(length(a)+length(b)-1))$ab
}

My question is: How should I write the corresponding C
code if the lm() R-function is entailed in the
computations of the loop in convolve.rfun() . How
could I get the OLS estimates in C?. Is there any
routine that I should include in the header of the C
file? Where to find it?

Thank you.