[MATH-318] wrong result in eigen decomposition

• Type: Bug
• Status: Closed
• Priority: Major
• Resolution: Fixed
• Affects Version/s: 2.0
• Fix Version/s: 2.1
• Assignee: Unassigned
• Reporter: Luc Maisonobe
• Created: 06/Nov/09 15:09
• Updated: 03/Apr/10 20:49
• Resolved: 06/Nov/09 15:12

Description

Some results computed by EigenDecompositionImpl are wrong. The following case computed by Fortran Lapack fails with version 2.0

    public void testMathpbx02() {

        double[] mainTridiagonal = {
        	  7484.860960227216, 18405.28129035345, 13855.225609560746,
        	 10016.708722343366, 559.8117399576674, 6750.190788301587, 
        	    71.21428769782159
        };
        double[] secondaryTridiagonal = {
        	 -4175.088570476366,1975.7955858241994,5193.178422374075, 
        	  1995.286659169179,75.34535882933804,-234.0808002076056
        };

        // the reference values have been computed using routine DSTEMR
        // from the fortran library LAPACK version 3.2.1
        double[] refEigenValues = {
        		20654.744890306974412,16828.208208485466457,
        		6893.155912634994820,6757.083016675340332,
        		5887.799885688558788,64.309089923240379,
        		57.992628792736340
        };
        RealVector[] refEigenVectors = {
        		new ArrayRealVector(new double[] {-0.270356342026904, 0.852811091326997, 0.399639490702077, 0.198794657813990, 0.019739323307666, 0.000106983022327, -0.000001216636321}),
        		new ArrayRealVector(new double[] {0.179995273578326,-0.402807848153042,0.701870993525734,0.555058211014888,0.068079148898236,0.000509139115227,-0.000007112235617}),
        		new ArrayRealVector(new double[] {-0.399582721284727,-0.056629954519333,-0.514406488522827,0.711168164518580,0.225548081276367,0.125943999652923,-0.004321507456014}),
        		new ArrayRealVector(new double[] {0.058515721572821,0.010200130057739,0.063516274916536,-0.090696087449378,-0.017148420432597,0.991318870265707,-0.034707338554096}),
        		new ArrayRealVector(new double[] {0.855205995537564,0.327134656629775,-0.265382397060548,0.282690729026706,0.105736068025572,-0.009138126622039,0.000367751821196}),
        		new ArrayRealVector(new double[] {-0.002913069901144,-0.005177515777101,0.041906334478672,-0.109315918416258,0.436192305456741,0.026307315639535,0.891797507436344}),
        		new ArrayRealVector(new double[] {-0.005738311176435,-0.010207611670378,0.082662420517928,-0.215733886094368,0.861606487840411,-0.025478530652759,-0.451080697503958})
        };

        // the following line triggers the exception
        EigenDecomposition decomposition =
            new EigenDecompositionImpl(mainTridiagonal, secondaryTridiagonal, MathUtils.SAFE_MIN);

        double[] eigenValues = decomposition.getRealEigenvalues();
        for (int i = 0; i < refEigenValues.length; ++i) {
            assertEquals(refEigenValues[i], eigenValues[i], 1.0e-3);
            if (refEigenVectors[i].dotProduct(decomposition.getEigenvector(i)) < 0) {
                assertEquals(0, refEigenVectors[i].add(decomposition.getEigenvector(i)).getNorm(), 1.0e-5);
            } else {
                assertEquals(0, refEigenVectors[i].subtract(decomposition.getEigenvector(i)).getNorm(), 1.0e-5);
            }
        }

    }