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

 From: Patrick Alken Subject: Re: [Help-gsl] linear least squares fitting for complex data set Date: Tue, 07 Aug 2012 16:49:55 -0600 User-agent: Mozilla/5.0 (X11; Linux i686 on x86_64; rv:14.0) Gecko/20120713 Thunderbird/14.0

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.
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```
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.
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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

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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

```
```

```