Re: FindMinimum[Print[]]
- To: mathgroup at smc.vnet.net
- Subject: [mg86987] Re: FindMinimum[Print[]]
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Fri, 28 Mar 2008 03:15:36 -0500 (EST)
- Organization: University of Bergen
- References: <fsg6o2$j61$1@smc.vnet.net>
Michaël Cadilhac wrote: > Hello list ! > > 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 following the tutorial[1] (which might be quite outdated), one of the 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. > > Thanks in advance for any information on that simple matter. > > Footnotes: > [1] http://library.wolfram.com/conferences/devconf99/withoff/ Hi, One solution is to define a function that only evaluates with numerical (not symbolic) arguments: expr[x_?NumericQ] := Max[Re[Eigenvalues[{{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}}]]] FindMinimum[expr[x], {x, 1}] You can use the same technique to print each x value while FindMinimum is working, or you could use the EvaluationMonitor option.