| Re: Solution of Nonlinear System of Equations (BROYDEN etc.) [message #31909 is a reply to message #31908] |
Sun, 25 August 2002 06:34  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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air_jlin@yahoo.com (Johnny Lin) writes:
> Hi all,
>
> I've this system of nonlinear equations that I want to solve
> iteratively and was planning on using BROYDEN to do it. What I'm
> wondering is how do I implement the function in BROYDEN so that I can
> change parameters on the fly. For instance, in the example in the
> help file, one of the equations is:
>
> 3x - COS(yz) - 1/2 = 0
>
> They then hard-wire the constants (3, 1/2, etc.) into BROYFUNC. But
> let's say I want to be able to change the 3x to ax where "a" is a
> constant I specify and change as the program runs. Is there a way to
> do this in a way the BROYDEN call will understand? I couldn't find
> the source code for BROYDEN to see if this is possible.
Hi Johnny--
One "solution" would be to use a common block to pass relevant
parameters to your function. We all know that is a pretty bad
solution, since it entails all of the ugliness associated with common
blocks. The RSI-supplied numerical routines are pretty bad all
around, when it comes to user-level flexibility.
One thing that people might not realize is that the MPFIT family of
functions can also be used to solve systems of non-linear equations.
Normally MPFIT is used to minimize the summed squared residuals in a
curve fitting application. However it can also be used to minimize
the error in a non-linear equation solution.
Here is an example using MPFITEXPR, but you could also use MPFIT
directly. All you need to do is return the vector of non-linear
function values. Here is an example based on the BROYDEN
documentation. I have set X and Y to zero because the expression,
EXPR, computes the residuals directly.
; Vector of non-linear functions to minimize
expr = '[3.0 * P[0] - COS(P[1]*P[2]) - 0.5, '+$
' P[0]^2 - 81.0*(P[1] + 0.1)^2 + SIN(P[2]) + 1.06, '+$
' EXP(-P[0]*P[1]) + 20.0 * P[2] + (10.0*!DPI - 3.0)/3.0]'
p0 = [-1.,1,2]
p = mpfitexpr(expr, 0, 0, 1, p0)
Now you may say to yourself, but Craig didn't answer my question! You
wanted to know how to change the hard-coded values.
Possibility number 1 is simply to re-write the expression when you
need to. This is much easier than trying to recompile an IDL
function.
Possibility number 2 is to use FUNCTARGS to pass information to the
expression. I have recently enhanced MPFITEXPR to allow this more
usefully, and it is documented. Essentially, during execution of the
expression, FUNCTARGS appears as a structure called PRIVATE which you
can access in any way you wish.
Good luck!
Craig
--
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Craig B. Markwardt, Ph.D. EMAIL: craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
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