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Re: FindMinimum[Print[]]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg86976] Re: FindMinimum[Print[]]
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Fri, 28 Mar 2008 03:13:28 -0500 (EST)
*Organization*: The Open University, Milton Keynes, UK
*References*: <fsg6o2$j61$1@smc.vnet.net>
MichaÃ«l Cadilhac wrote:
> I'm really new to Mathematica (though I can already say wow), and,
> following the tutorial[1] (which might be quite outdated), one of the
> exercise got me in trouble.
>
> The author asks to reformulate the following actions
>
> m = {{12, 1 + x, 4 - x, x},
> {4 - x, 11, 1 + x, x},
> {1 + x, 1 - x, 15, x},
> {x - 1, x - 1, x - 1, x - 1}};
> expr = Max[Re[Eigenvalues[m]]];
> FindMinimum[expr, {x, 0, 1}]
>
> into a more optimized version. In the course of doing that, I wanted
> to do something like
> FindMinimum[Print[x]; x^2, {x, 1}],
> hoping to see how is this whole thing is expanded/parsed. But, despite
> the fact that some articles on that newsgroup used the same form, this
> didn't print the iterations as expected.
>
> I wanted to understand how I should write
> FindMinimum[Max[Eigenvalues[m]], {x, 0, 1}]
> so that the eigenvalues are computed on the fully numerical
> (non-symbolic) matrix.
The option StepMonitor is what you are looking for.
In[1]:= FindMinimum[Exp[x] + 1/x, {x, 1},
StepMonitor :> Print["Step to x = ", x]]
During evaluation of In[1]:= Step to x = 0.788886
During evaluation of In[1]:= Step to x = 0.677316
During evaluation of In[1]:= Step to x = 0.706578
During evaluation of In[1]:= Step to x = 0.703587
During evaluation of In[1]:= Step to x = 0.703467
During evaluation of In[1]:= Step to x = 0.703467
Out[1]= {3.44228, {x -> 0.703467}}
In[2]:= m = {{12, 1 + x, 4 - x, x}, {4 - x, 11, 1 + x, x}, {1 + x,
1 - x, 15, x}, {x - 1, x - 1, x - 1, x - 1}};
expr = Max[Re[Eigenvalues[m]]];
FindMinimum[expr, {x, 0, 1}, StepMonitor :> Print["Step to x = ", x]]
During evaluation of In[2]:= Step to x = 0.362425
During evaluation of In[2]:= Step to x = 0.362425
During evaluation of In[2]:= Step to x = 0.362159
During evaluation of In[2]:= Step to x = 0.362151
Out[4]= {16.8343, {x -> 0.362151}}
HTH,
--
Jean-Marc
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