| Re: I need a bit of help....Convol and functions [message #50412 is a reply to message #50395] |
Mon, 02 October 2006 14:59   |
JD Smith
Messages: 850
Registered: December 1999
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Senior Member |
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On Mon, 02 Oct 2006 13:00:17 -0700, kuyper wrote:
> JD Smith wrote:
>> 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".
>
> What you've written is indead the multiplication, and is therefore not a
> correct response to his request. The true mathematical convolution of f(x)
> and g(x) is y(x) = the integral over z from -infinity to +infinity of
> f(x-z)*g(z) dz. It's only possible to approximate the mathematical
> convolution numerically when you can approximate the infinite integral
> with acceptable accuracy by integrating over a finite range. That's why
> the numerical convolutions you've seen have involved small kernals.
Yes it is doing multiplication, as noted. I've found that many people use
the terminology "convolve x with y" when they mean "multiply x by y".
Sounds like that's not the case here, but anyway...
JD
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