       Re: problems with NMinimize

• To: mathgroup at smc.vnet.net
• Subject: [mg109387] Re: problems with NMinimize
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 24 Apr 2010 04:03:06 -0400 (EDT)

```\[Beta][coeffs : {_?NumericQ ..}, z_?NumericQ] :=
coeffs[] + Sum[coeffs[[i]] ChebyshevT[i, z],
{i, 2, Length[coeffs]}];

Bob Hanlon

---- Neil Broderick <ngb at ecs.soton.ac.uk> wrote:

=============
Bob,
thanks for that. It is neater than my work around was that I defined the function recursively if the arguements weren't
numeric and then set the recursion limit to 2 to get it to halt. Do you know how I would handle a variable
number of arguments? Currently I have a function

\[Beta][coeffs_, z_] :=   coeffs[] +   Sum[coeffs[[i]] ChebyshevT[i, z], {i, 2, Length[coeffs]}];

and would like to be able minimise a function involving beta for an arbitrary number of arguments. So how
does the NumericQ trick work on a list of variables?

cheers,
Neil

On 22 Apr 2010, at 13:26, Bob Hanlon wrote:

>
> Define a function that only evaluates for numeric arguments
>
> f[a_?NumericQ, b_?NumericQ] :=
> Abs[NIntegrate[Sin[x], {x, -a, b}]]^2
>
> NMinimize[f[a, b], {a, b}]
>
> {7.56317*10^-19,{a->0.131888,b->-0.131888}}
>
>
> Bob Hanlon
>
> ---- Neil Broderick <ngb at ecs.soton.ac.uk> wrote:
>
> =============
> Hi,
> I am trying to use NMinimize to find the solutions to various numerical equations and I keep getting error
> messages concerning non-numerical values. For example consider the following:
>
> In:= NMinimize[Abs[NIntegrate[Sin[x], {x, -a, b}]]^2, {a, b}]
>
> During evaluation of In:= NIntegrate::nlim: x = -1. a is not a valid limit of integration. >>
>
> During evaluation of In:= NIntegrate::nlim: x = -1. a is not a valid limit of integration. >>
>
> During evaluation of In:= NIntegrate::nlim: x = -1. a is not a valid limit of integration. >>
>
> During evaluation of In:= General::stop: Further output of NIntegrate::nlim will be suppressed during this calculation. >>
>
> Out= {5.08978*10^-24, {a -> 0.0994414, b -> 0.0994414}}
>
> My actual problem involves taking Fourier transforms of lists of numbers but you get the picture. Why is
> NMinimize putting variables into the function rather than just numbers and is the likely to cause a problem
> in some cases?
>
> regards,
> Neil=

```

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