Weighted least squares with minpack?

[Dave]

Hi all,

I'm fumbling around trying to figure out how to use minpack (lmstr)
for a weighted non-linear least squares fit and I know it shouldn't be
as tough as I'm making it. For weights, I'm using a full covariance
matrix, S, so in Bx = y the linear problem is:

(K^T S^(-1) K) x = K^T S^(-1) y

where K is the Jacobian matrix. My confusion is that lmstr (and most
similar routines) all expect you to provide:

m, n = rows, cols of K
x = initial guess (overwritten with solution)
y = data to fit
fcn = function to evaluate F(x) and Jacobian matrix (dF/dx)

It isn't obvious to me how to weight the data or write the model
function 'fcn' when weights are used?

Does anyone have a basic fortran example showing how to set this up?

Thanks,
Dave

[Duncan Muirhead]

If S = L*L' (cholesky) and you define A = inv(L)*B and z = inv(L)*y
then the unweighted ls problem with A and z will have the same solutions
as the weighted one.

[Peter Spellucci]

In article <1190222167....@o80g2000hse.googlegroups.com>,

in the function routine fcn, before exit multiply the function vector and
the Jacobian (if you do it analytically) by inv(L) where
S = L*L^T is the cCholesky decomposition of S
hth
peter