Gaussian line profile using numeric python

[John J. Lee]

On 29 Mar 2001, Konrad Hinsen wrote:

> "Geoff Low" <geoff at ou043085.otago.ac.nz> writes:
>
> > I have an extensive set of xy data that I want to convolute with a gaussian
> > profile.  Below is my algorithm,  which doesn't work.  Can anyone see where
> > I'm being dumb?

What goes wrong?  Couldn't see your original message.

> To be honest, I am too lazy to look through this. However,

Me too.  :)  I do have some working routines that will do gaussian
convolution, using the standard Numeric FFT module -- very simple.  Or at
least would be if I didn't have a lot of stuff for using the FFTW library
in there, which doesn't actually work (the docs for the rfftw part of the
FFTW python wrapper seem to be wrong:  anybody got this working?).

> 1) The function Numeric.convolve is certainly a lot more efficient
>    than your code, and should make it simpler.

I seem to recall that it doesn't cover all the possibilities, though.  I
don't remember exactly why, but since I wrote my own functions to do this
there must have been a reason!

> 2) If you work with large data sets, you ought to use FFTs to
>    compute the convolution, that's O(N*log(N)) in the size of the
>    data set, instead of O(N**2) for the straightforward method.
>    Any good book on FFTs should explain how this works in detail.

but you probably don't need to know in detail, it boils down to

inv_FFT(FFT(data)*FFT(kernel))

But if you have small data sets it might be slower, of course.

> > P.S.  I'm no math wizard but this is my interpretation of the gaussian lineshape
> > function
> > G(v) = 1/(sqrt(2*PI)*FWHM)*exp(-(v-vo)^2/(2*FWHM^2))
>
> Assuming that FWHM stands for full width at half minimum, no, it's not
> correct. What you call FWHM is the variance sigma of the Gaussian, the
> FWHM is around 2.35*sigma (quick calculation, no guarantee).

That number is about right, from memory.


John