Re: [Help-gsl] linear least squares fitting for complex data set

[Patrick Alken]

Yes that is possible. However you need to be very careful because lets 
say you have a model:

sum_{lm} A_{lm} X_{lm} = Y_{lm}

and lets say that A_{lm} is real everytime m = 0 (this is quite common 
in spherical harmonic expansions), then if you naively pack the matrix 
as real imag..., the matrix will be singular because it will have 0 for 
the imag part whenever m = 0.

This is why I suggest using the LAPACK complex routines, unless you have 
a very simple problem and you know the matrix won't be singular.

On 08/07/2012 04:42 PM, Apurv Bhartia wrote:
> "In principle you could order a real matrix and coeff and rhs vectors 
> as: real imag real imag, etc."
>
> Sorry I'm new to GSL. In my dataset, X is real and Y, A are complex. 
> Just to make sure, do you mean that it can be done by having X, Y and 
> A as complex data sets, and packing them into a real vector by 
> alternating real and imaginary values?
> This way, is it then possible to use gsl_multifit_linear(x, y, a, cov, 
> chisq, ws)?
>
> Thanks,
> Apurv
>
> On Tue, Aug 7, 2012 at 4:56 PM, Patrick Alken 
> <address@hidden <mailto:address@hidden>> wrote:
>
>     There aren't any native complex implementations of the multifit
>     routines. In principle you could order a real matrix and coeff and
>     rhs vectors as: real imag real imag, etc. But its probably easiest
>     to use the complex LAPACK routines for this.
>
>
>     On 08/07/2012 03:29 PM, Apurv Bhartia wrote:
>
>         Hi,
>
>         Is there a way to use least squares fit for complex data sets?
>         All of the
>         *_multifit_* variants seem to require non-complex data. If
>         not, then any
>         advice on how I can somehow get this done?
>
>         Thanks,
>         Apurv