- nonsymmetric matrix eigenvalue library for blackbox?

From: Campbell, Robert D (SELEX) (UK Edinburgh) <"Campbell,>
Date: Mon, 19 Jun 2006 13:04:29 +0100

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>Dear Robert Campbell

>I am working in a project that uses blackbox and winbugs at MIT. I need
to find a library that allows me to >compute eigenvalues and
eigenvectors for non-symmetric matrices. The library I could find at
oberon site is >eigensys which is limited to symmetric matrices.
>Can you tell me if there is any blackbox library that can compute
eigenvectors without the symmetry requirement? >Any suggestions?

>Thanks in advance

>Gui Liberali

Gui

I give an example below that shows how to extract the full
Complex eigensystem (values & vectors) from a non-symmetric
REAL matrix using the module LibEigenSys.

This in not stste-of-the-art stuff, but may suffice for casual
Use. If you find a more advanced library please let us know.
If your matrix is Complex I can't help.

Robert


PS - Don't expect it to work for repeated eigenvalues!








MODULE DemoEigenTest;

IMPORT Fmtrs := LibFmtrs, Vec := LibVectors, Mat := LibMatrices, Eigen
:= LibEigenSys,
        C := LibComplex, CVec := LibCVectors, CMat := LibCMatrices;


VAR
  f : Fmtrs.Fmtr;


PROCEDURE Do*;
  VAR
    mat, hes : Mat.Matrix;
    matC : CMat.Matrix;
    eigenBase, pntr : Eigen.EigenC;
    eValR : REAL;
    eVecR : Vec.Vector;
    eValC : C.Complex;
    eVecC : CVec.Vector;
  BEGIN
    f.SetToEnd;
    NEW (mat, 5);
    mat [0] := Vec.Set5 ( 3., -2., 5., 4., -7.);
    mat [1] := Vec.Set5 ( 2., 5., 1., 3., 2.);
    mat [2] := Vec.Set5 (-3., 3., -2., -3., 1.);
    mat [3] := Vec.Set5 ( 5., -1., -1., -5., -3.);
    mat [4] := Vec.Set5 (-2., -4., -3., 7., -9.);
    Mat.Wrt (f, mat, 9, 5, 0); f.Ln;

    hes := Mat.Copy (mat);
    matC := CMat.Float (mat, NIL);
    Eigen.ToHessian (hes, TRUE);
    Mat.Wrt (f, hes, 9, 5, 0);

    eigenBase := Eigen.HessQR (hes, TRUE, Eigen.absDecSort);

    pntr := eigenBase.First ()(Eigen.EigenC);
    WHILE pntr # eigenBase DO
     f.Ln;
     f.Str ('Eigen value : '); C.Wrt (f, pntr.val, 10, 6, TRUE);


      IF pntr.val.im = 0. THEN
        eValR := pntr.val.re;
        eVecR := Eigen.InvIterate (mat, eValR, 3, f);

        f.Str ('eValR * eVecR: ');
        Vec.Wrt (f, Vec.Scale (eValR, eVecR), 15, 10, 0);
        f.Str ('mat * eVecR : ');
        Vec.Wrt (f, Mat.MultMV (mat, eVecR), 15, 10, 0);
      ELSE
        eValC := pntr.val;
        eVecC := Eigen.InvIterateC (matC, eValC, 3, NIL);

        f.Str ('Eigen vector : '); CVec.Wrt (f, eVecC, 10, 6, 0);
        f.Str ('eValC * eVecC: ');
        CVec.Wrt (f, CVec.Scale (eValC, eVecC), 10, 6, 0);
        f.Str ('matC * eVecC : ');
        CVec.Wrt (f, CMat.MultMV (matC, eVecC), 10, 6, 0);
      END;
      pntr := pntr.Next ()(Eigen.EigenC)
    END
  END Do;


BEGIN
  f := Fmtrs.logFmtr;
END DemoEigenTest.


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Received on Mon Jun 19 2006 - 14:04:29 UTC