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| Re: Solution of Nonlinear System of Equations (BROYDEN etc.) [message #31908 is a reply to message #31894] |
Sun, 25 August 2002 07:00  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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Here I am, replying to my own post. As David can attest, this is a
sure sign of madness.
Craig Markwardt <craigmnet@cow.physics.wisc.edu> writes:
...
> 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.
...
I wanted to add that if you define your function BROYFUNC, as it is
defined in the BROYDEN documentation, then you can use MPFIT directly
with no additional changes. The benefit is that you can also use the
nice FUNCTARGS features of MPFIT to pass named values to your function.
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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| 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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