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Re: I need a bit of help....Convol and functions [message #50432 is a reply to message #50421] Mon, 02 October 2006 10:14 Go to previous messageGo to previous message
JD Smith is currently offline  JD Smith
Messages: 850
Registered: December 1999
Senior Member
On Sun, 01 Oct 2006 03:42:34 -0700, D.Kochman@gmail.com wrote:

> So, I'm fairly new to IDL (and an organic chemist so programming is not my
> forte), but I'm chunking my way through it. I'm currently in the process
> of modifying a program that fits exponential decays given the impulse
> response function and the decay curve.
>
> I have to remodel it to fit another much more complex function than an
> exponential decay, however with a similar number of parameters. I've
> already fixed the GUI, and changed all the references to the widgets,
> along with adjusting the appropriate arrays. It now compiles after many
> hours of debugging and displays itself appropriately with a dummy function
> with the appropriate amount of parameters.
>
> I'm stuck with now implementing the function itself, any help on the
> implementation will be *highly* appreciated.
>
> The function is an infinite sum convolved with an exponential decay. I've
> done modeling with the sum, and it converges fairly rapidly, and I can
> limit it to 10 terms or so and still get accuracy to 6 decimal places.
>
> Approximately it is:
>
> Sum[(-1)^n*cos(n*P(1)*X)*exp(-(2n)^2*P(2)*X), n ->0 to 10] convol
> exp[-X/P(4)]
>
> *whew*
>
> anyways, I've been working through the documentation on convol, and I find
> it a bit cryptic. I have very few clues how to implement this function in
> code. I'm guessing the first portion (the sum portion) needs to be
> recursively defined in a for loop. Is this the case, or is their a
> shortcut with a sigma type function built in?
>
> However, how do I easily convolve the two functions if they are functions
> and not arrays? Should I just go to fourier space?
>
> Thanks for any help. I don't expect anyone to code this for me, just a
> gentle (or violent) shove in the appropriate direction will be infinately
> helpful.

For the sum, you can use a total over an array:

nx=n_elements(X)
n=rebin(transpose(lindgen(11)),nx,11)
func=total((-1.)^n*cos(n*P[1]*X)*exp(-(2.*n)^2*P[2]*X),2)*ex p(-X/P[4])

Are you sure it's really a convolution? When the kernel size is the
same as the thing its convolving, I almost always think
"multiplication" not "convolution". Otherwise, it has no scale. If
it occurred over some fixed scale X0, then a convolution would be more
understandable.

For speed, you could cache the "n" array above to avoid having to
recreate it, assuming nx doesn't change.

JD

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