| mpfit: what's different [message #58600] |
Wed, 06 February 2008 08:35  |
Wox
Messages: 184
Registered: August 2006
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Senior Member |
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Hi everyone,
Is there any documentation on the theory behind Craig Markwardt's
mpfit? What's different from the Levenberg-Marquardt algorithm as
given in "Numerical Recipes in C" (used in IDL's curvefit)?
Is it a difference in choosing the damping factor in the modified
curvature matrix or is there more to it?
Thanks,
Wout
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| Re: mpfit: what's different [message #58638 is a reply to message #58600] |
Mon, 11 February 2008 05:39  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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Wox <nomail@hotmail.com> writes:
> Hi everyone,
>
> Is there any documentation on the theory behind Craig Markwardt's
> mpfit? What's different from the Levenberg-Marquardt algorithm as
> given in "Numerical Recipes in C" (used in IDL's curvefit)?
>
Hi, I'm back!
First off, I should say that MPFIT is based on MINPACK (by Jose More'
et al), so I don't take any of the credit for the underlying algorithm.
Basically, Numerical Recipes is a quick and dirty implementation of
Levenberg Marquardt, so what you get are quick and dirty results.
Some of it boils down to how the normal equations are determined
(MPFIT doesn't; it uses direct QR factorization of the Jacobian, which
improves numerical precision); how the LM parameter and trust region
are determined (Numerical Recipes doesn't really have a concept of
"trust region"); and the convergence criteria.
Also, as David points out, MPFIT has more features than CURVEFIT, such
as the abillity to fix or vary certain parameters, the ability to set
simple parameter boundaries, to tie parameters together, and some
advanced options for keeping track of the fit status. The MPFIT*
library also has a few different flavors of the main routine, to make
things easy in certain cases (1d fitting, 2d fitting, using an
expression insted of a function, and so on).
> Is it a difference in choosing the damping factor in the modified
> curvature matrix or is there more to it?
I'm not sure what this means. I encourage you to consult the primary
references in the mpfit.pro documentation section.
Good luck, and happy fitting,
Craig Markwardt
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| Re: mpfit: what's different [message #58703 is a reply to message #58600] |
Tue, 12 February 2008 09:40 |
Wox
Messages: 184
Registered: August 2006
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Senior Member |
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Btw, can it be that mpcurvefit expects a different analytical
derivative (dResid/dP) than curvefit (dFunc/dP)? I think this should
be added in mpcurvefit_eval:
;; Compute the deviates, applying the weights
result = (y-f)*wts
if n_params() GT 1 then $
dp*=rebin(wts,n_elements(x),n_elements(p),/sample)
Actually, it should be
dp*=rebin(-wts,n_elements(x),n_elements(p),/sample)
but since mpfit_fdjac2 flips the sign (why?), we have to do it here to
correct for that.
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| Re: mpfit: what's different [message #58713 is a reply to message #58627] |
Tue, 12 February 2008 02:19 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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Wox <nomail@hotmail.com> writes:
> On 11 Feb 2008 08:39:28 -0500, Craig Markwardt
> <craigmnet@REMOVEcow.physics.wisc.edu> wrote:
>
> <snip>
>> I'm not sure what this means. I encourage you to consult the primary
>> references in the mpfit.pro documentation section.
>
> Thanks, I will.
>
> One question: Is there a way to make sure that the sum of certain
> parameters stays below 1? I was looking at the tied and limit
> possibilities, but I don't thing they can do this...
Not really. MPFIT only supports simple boundary constraints on
individual parameters. If you can re-write your problem so that a new
parameter is the sum of original parameters, then you can do it.
Craig
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