RE: ugly Plot Eigenvalues ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg39666] RE: ugly Plot Eigenvalues ?*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 1 Mar 2003 02:47:22 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Pavel, Here is a routine from my DrawGraphics package that eliminates vertical lines. SplitLineOnSlope::usage = "SplitLineOnSlope[slope] is a rule which will split any Line primitives \ into multiple lines whenever two points give a slope whose absolute value is \ greater than the specified slope"; SplitLineOnSlope[slope_] := Line[a_] :> Line /@ Split[a, (Abs[Divide @@ Reverse[#2 - #1]] < slope &)] If you copy it into your notebook, you can then use it the following way... m1 = {{8., 8, 7}, {0, 5, 5}, {8, 0, 0}}; m2 = {{6., 0, 6}, {10, 8, 3}, {5, 8, 6}}; Show[Graphics[ {(Plot[Evaluate[Re[Eigenvalues[m1 + w*m2]]], {w, -3, 3}, DisplayFunction -> Identity] // First) /. SplitLineOnSlope[40]}], Frame -> True, ImageSize -> 500 Within DrawGraphics the plotting statement would be... Needs["DrawGraphics`DrawingMaster`"] Draw2D[ {Draw[Evaluate[Re[Eigenvalues[m1 + w*m2]]], {w, -3, 3}] /. SplitLineOnSlope[40]}, Frame -> True, ImageSize -> 500]; David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Pavel Pokorny [mailto:Pavel.Pokorny at vscht.cz] To: mathgroup at smc.vnet.net 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