Re: fitting data to an integral

B.K. Chen wrote:


So you have data where the integral
is given as a function of x?

Yeah~ It's a function of x. My data points are (x, f(x) )

As long as a/b>=10 or so, I'd try a
Gauss-Hermite numerical quadrature
inside the objective function. Then
any optimizer will be fine. For
smaller values of a/b, I'd just use
quad over a finite set of limits,
base the upper limit on the value
of a/b.

In cftool(Create Custom Equation --> General Equations ),
it seems that we cannot input quadl directly , does it?

B.K.

I always thought I should learn to use
that toolbox. But I wrote my own little
gui tool for nonlinear regressions long
before it existed, so my incentive was
always pretty low. ;-)

You should be able to supply your own
function as an option. Have it call
quadl. BUT BEWARE!!!!

Do not try to integrate 0 to inf.
Furthermore, use of any adaptive
quadrature on an integrand that
involves a gaussian term and where
you cannot control the gaussian
parameters will likely cause serious
problems, culminating in a secondary
request to this newsgroup.

If you use a set of fixed integration
limits, the optimizer can pass in
any set of parameters (a,b) that it
"desires". If b is very small, the
Gaussian part of the kernel becomes
an effective Dirac delta, which the
numerical integration will fail to
"see".

This is why I suggested use of a
Gauss-Hermite for large a/b. Only
use quadl for the alternative case,
and use a carefully chosen upper
limit on the integration. You can
find a nice tool for this purpose
on the FEX:

<http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=32&objectType=file>

John
.

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