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MathGroup Archive 2003

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RE: ugly Plot Eigenvalues ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39717] RE: [mg39670] ugly Plot Eigenvalues ?
  • From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
  • Date: Mon, 3 Mar 2003 23:48:50 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: Pavel Pokorny [mailto:Pavel.Pokorny at vscht.cz]
To: mathgroup at smc.vnet.net
>Sent: Friday, February 28, 2003 10:46 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg39717] [mg39670] ugly Plot Eigenvalues ?
>
>
>    Dear Mathematica friends,
>
>How can I plot Re Eigenvalues as a function of a parameter
>without unwanted ugly connections between branches?
>In the example (computed by Mathematica 4.2 for HP-UX PA-RISC)
>
>   m1={{8., 8, 7}, {0, 5, 5}, {8, 0, 0}}
>   m2={{6., 0, 6}, {10, 8, 3}, {5, 8, 6}}
>   Plot[Evaluate[Re[Eigenvalues[m1+w*m2]]], {w,-3,3}];
>
>for w approximately -0.4 there is an unwanted vertical bar.
>This is related to "ordering" of solutions to equation.
>
>Is there a simple nice solution for this and related examples?
>(taking exact numbers in the example above avoids the unwanted 
>connection,
>but this is not a good solution for a general machine 
>precission problem)
>
>-- 
>Pavel Pokorny
>Math Dept, Prague Institute of Chemical Technology
>http://staffold.vscht.cz/mat/Pavel.Pokorny
>

A suggestion:

ev = Re[Eigenvalues[m1 + w*m2]];

evs := Sort[ev]

Plot[{evs[[1]], evs[[2]], evs[[3]]}, {w, -3, 3}]

Of course a problem of reference still remains.


--
Hartmut Wolf



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