[R] eliminate t() and %*% using crossprod() and solve(A,b)

[Robin Hankin]

Hi

I have a square matrix Ainv of size N-by-N where N ~  1000
I have a rectangular matrix H of size N by n where n ~ 4.
I have a vector d of length N.

I need   X  = solve(t(H) %*% Ainv %*% H) %*% t(H) %*% Ainv %*% d

and

H %*% X.

It is possible to rewrite X in the recommended crossprod way:

X <-  solve(quad.form(Ainv, H), crossprod(crossprod(Ainv, H), d))

where quad.form() is a little function that evaluates a quadratic form:

  quad.form <- function (M, x){
         jj <- crossprod(M, x)
         return(drop(crossprod(jj, jj)))
}


QUESTION:

how  to calculate

H %*% X

in the recommended crossprod way?  (I don't want to take a transpose
because t() is expensive, and I know that %*% is slow).





--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743