smooth eigenvalues and eigenvectors as a function of frequency

*To*: mathgroup at smc.vnet.net*Subject*: [mg60312] smooth eigenvalues and eigenvectors as a function of frequency*From*: "Antonio Carlos Siqueira" <acsl at dee.ufrj.br>*Date*: Sat, 10 Sep 2005 22:36:35 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Dear MathGroup I am posting this message hoping that someone may have a better idea than me and point me in some direction to the solution. I have to fit a complex based function using a state-space approach and thus smooth eigenvectors and eigenfunctions are needed. Using Eigensystem I experienced some eigenvector/eigenvalues switchovers (from one frequency step to the next). I was wondering whether some sort of MapIndexed or some Sort can do the trick to switch the eigenvector back. I know that if I can track the direction of the eigenvalue.eigenvector dot product I might probably identify the switchover. Below I show the code I am using and a graph as an example of the switchover. Any help/comment is more than welcome! Thanks in advance Regards Antonio Here comes the code evalues = Table[0, {n, 1, nf}]; evectors= evects1; xc={-9.5, -9.5, -9.5, 9.5, 9.5, 9.5}; yc={26., 38.7, 51.4, 26., 38.7, 51.4}; nc=Length[xc]; compr = 25*10^3; rf = 0.0203454; rhoc = 4.169134020401465*^-8; rhosolo=100.0; mu = (4.*Pi)/10^7; epsilon = 8.854/10^12; freqlog[i_, f_, n_] := Table[N[10^(i + (x*(f - i))/(Floor[n] - 1))], {x, 0, n - 1}] length = 25000; npontos = 20; d1 = 0; d2 = 6; ndecadas = d2 - d1; nfd = ndecadas*npontos; f = freqlog[d1, d2, nfd]; nf = Length[f]; Do[{w = 2*Pi*f[[nm]], p = Sqrt[rhosolo/(I*w*µ)], etac = Sqrt[(I*w*µ)/rhoc], Z = Table[If[i != j, ((I*w*mu)* Log[Sqrt[(xc[[i]] - xc[[j]])^2 + (2*p + yc[[i]] + yc[[j]])^2]/ Sqrt[(xc[[i]] - xc[[j]])^2 + (yc[[i]] - yc[[j]])^2]])/(2*Pi), ((etac*rhoc)*BesselI[0, etac*rf])/((2*Pi*rf)*BesselI[1, etac*rf]) + ((I*w*mu)*Log[(2*p + 2*yc[[i]])/rf])/(2*Pi)], {i, 1, ncond}, {j, 1, ncond}], P = Table[If[i != j, Log[Sqrt[(xc[[i]] - xc[[j]])^2 + (yc[[i]] + yc[[j]])^2]/ Sqrt[(xc[[i]] - xc[[j]])^2 + (yc[[i]] - yc[[j]])^2]], Log[(2.*yc[[i]])/rf]], {i, 1, ncond}, {j, 1, ncond}], Y = I*w*2*Pi*epsilon*Inverse[P], {ll, T} = Eigensystem[Z . Y], {evalues[[nm]], evectors[[nm]]} = Transpose[Sort[Transpose[{ll, T}]]]}, {nm, 1, nf}]] DisplayTogether[ LogLinearListPlot[Transpose[{f, Re[evectors[[All,3,1]]]}]], LogLinearListPlot[Transpose[{f, Re[evectors[[All,3,2]]]}]], LogLinearListPlot[Transpose[{f, Re[evectors[[All,3,3]]]}]], LogLinearListPlot[Transpose[{f, Re[evectors[[All,3,4]]]}]]