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Minimization Problem
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More options Mar 27 2012, 2:52 am
Newsgroups: comp.lang.idl-pvwave
From: IDL beginner <moxam...@gmail.com>
Date: Mon, 26 Mar 2012 23:52:12 -0700 (PDT)
Local: Tues, Mar 27 2012 2:52 am
Subject: Minimization Problem
Dear All,

I need your help to solve the following problem using IDL. I need to
come up with an efficient way to find the minimum of a function. The
function is:

F(b) = (1 / la_determ((1 - b) * la_invert(v2) + b * la_invert(v1))) /
((la_determ(v1) ^ b) * (la_determ(v2) ^ (1 - b)))

Where v1 and v2 are given matrices and 0 < b < 1. So, what I need is
an efficient way of finding the value b for which the F(b) is
minimum.

I know that I can calculate for example 1000 values of b and for each
value I can find F(b) and search for the minimum. But this way is not
efficient in terms of accuracy and execution time.

Any help is appreciated.

MD

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More options Mar 27 2012, 8:44 am
Newsgroups: comp.lang.idl-pvwave
From: SonicKenking <ywa...@gmail.com>
Date: Tue, 27 Mar 2012 05:44:32 -0700 (PDT)
Local: Tues, Mar 27 2012 8:44 am
Subject: Re: Minimization Problem
On Mar 27, 5:52 pm, IDL beginner <moxam...@gmail.com> wrote:

You may wanna try TNMIN from the MPFIT package.

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More options Mar 27 2012, 9:24 am
Newsgroups: comp.lang.idl-pvwave
From: Craig Markwardt <craig.markwa...@gmail.com>
Date: Tue, 27 Mar 2012 06:24:42 -0700 (PDT)
Local: Tues, Mar 27 2012 9:24 am
Subject: Re: Minimization Problem

Don't throw out the grid method.  Depending on your application, doing a 1D grid search may be fine.  You can pre-compute LA_INVERT(V2), LA_INVERT(V1), LA_DETERM(V1) and LA_DETERM(V2).  The only thing that varies with B is the outer LA_DETERM(...).

The IDL Astronomy Library has a routine which brackets 1D minima, minf_bracket.pro.

You can also do this with MPFIT, it's one equation and one unknown.

Craig