| Re: Challenging question - array curve fitting [message #53709 is a reply to message #53590] |
Tue, 24 April 2007 05:49   |
Qing
Messages: 12
Registered: February 2007
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Junior Member |
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On Apr 23, 12:49 pm, Craig Markwardt
<craigm...@REMOVEcow.physics.wisc.edu> wrote:
> Sorry for neglecting your post for so long!
>
> "Qing" <c...@bigpond.net.au> writes:
>> Hello Craig,
>
>> Thanks a lot for your comments and tips. It is intriguing for
>> "grouping multiple time series into a single large vector...". I can
>> manage to transform/ reform the data array into a large vector, but
>> my brain just can't think of a way to model the concatenated vector
>> independently. For example, I am using a Gaussian curve model with 3
>> fitting parameters for each curve. Typically Nx=Ny=128 and the
>> number of time points Nt=60. The thing is that my computer has two
>> CPUs, and it only uses about 50% total CPU when fitting the curve by
>> looping through each pixel.
>
> Your model function would still need to compute each light curve
> separately, which may involve a loop. But, for example, you could
> loop over time sample instead of light curve number, and in each
> iteration compute 128x128 model values at once (or fewer).
>
> Example:
> ; Compute NX x NY x NT light curve samples
> ; Model is simple linear P0 + P1*T
> ; Parameters are arranged like this:
> ; P0 = P(0:(NX*NY-1)) ;; For each pixel
> ; P1 = P(NX*NY:*) ;; For each pixel
> function lcmod, t, p, nx=nx, ny=ny
> ntot = nx*ny
> p0 = reform(p(0:ntot-1),nx,ny)
> p1 = reform(p(ntot-1:*),nx,ny)
> nt = n_elements(t)
> model = fltarr(nx,ny,nt)
> for i = 0, nt-1 do model(0,0,i) = p0 + p1*t(i)
> return, model
> end
>
> This only works because NX*NY is much larger than NT.
>
>> I though usually array operation is more efficient than looping
>> throug all elements individually, but I was not sure if that is the
>> case for a non-linear fitting task. Or at least, using array
>> operation can get better use of the CPUs upto 100%. Do you thing
>> using a large vector would be as efficient as using array?
>
> It all depends on how much work is done per iteration of the loop. If
> you can accomplish a lot of work in one iteration, then you will not
> save by vectorizing the loop. Since MPFIT has a lot of set-up and
> tear-down expenses, then I suspect you could indeed gain by grouping a
> several time series together.
>
>> Why does "the number of arithmetic operations required to perform
>> the fit scales as the number of pixels *cubed*"?, I thought it would
>> be a linear relation if using array just like looping through all
>> pixels one-by-one. Am I missing something?
>
> Actually it scales as M N^2 where M is the number of data points and N
> is the number of parameters. However, since this example involves
> grouping independent light curves with independent parameters into one
> block, M is also proportional to N, hence an overall N^3 dependence.
>
> Hope you succeeded!
> Craig
Hi Craig,
Champion! Thanks you soooooo much for the tips. I will try it to see
if this
can speed up my curve fittings!
Cheers :-))
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