Examples of org.apache.commons.math.linear.EigenDecompositionImpl

org.apache.commons.math.linear.EigenDecompositionImpl
Calculates the eigen decomposition of a real symmetric matrix.
The eigen decomposition of matrix A is a set of two matrices: V and D such that A = V D V^T. A, V and D are all m × m matrices.

As of 2.0, this class supports only symmetric matrices, and hence computes only real realEigenvalues. This implies the D matrix returned by {@link #getD()} is always diagonal and the imaginary values returned{@link #getImagEigenvalue(int)} and {@link #getImagEigenvalues()} are alwaysnull.

When called with a {@link RealMatrix} argument, this implementation only usesthe upper part of the matrix, the part below the diagonal is not accessed at all.

This implementation is based on the paper by A. Drubrulle, R.S. Martin and J.H. Wilkinson 'The Implicit QL Algorithm' in Wilksinson and Reinsch (1971) Handbook for automatic computation, vol. 2, Linear algebra, Springer-Verlag, New-York
@version $Revision: 1002040 $ $Date: 2010-09-28 09:18:31 +0200 (mar. 28 sept. 2010) $ @since 2.0

    /** test non invertible matrix */
    public void testNonInvertible() {
        Random r = new Random(9994100315209l);
        RealMatrix m =
            EigenDecompositionImplTest.createTestMatrix(r, new double[] { 1.0, 0.0, -1.0, -2.0, -3.0 });
        DecompositionSolver es = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN).getSolver();
        assertFalse(es.isNonSingular());
        try {
            es.getInverse();
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {

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    /** test invertible matrix */
    public void testInvertible() {
        Random r = new Random(9994100315209l);
        RealMatrix m =
            EigenDecompositionImplTest.createTestMatrix(r, new double[] { 1.0, 0.5, -1.0, -2.0, -3.0 });
        DecompositionSolver es = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN).getSolver();
        assertTrue(es.isNonSingular());
        RealMatrix inverse = es.getInverse();
        RealMatrix error =
            m.multiply(inverse).subtract(MatrixUtils.createRealIdentityMatrix(m.getRowDimension()));
        assertEquals(0, error.getNorm(), 4.0e-15);

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        assertEquals(0, error.getNorm(), 4.0e-15);
    }


    /** test solve dimension errors */
    public void testSolveDimensionErrors() {
        DecompositionSolver es = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            es.solve(b);
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {

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                { 29, -1, 12,  9, 21,  8 },
                { 32,  0,  9, 14,  9,  0 },
                { 40,  2, 21,  9, 51, 19 },
                { 14, -1,  8,  0, 19, 14 }
        });
        DecompositionSolver es = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { 1561, 269, 188 },
                {   69, -21,  70 },
                {  739, 108,  63 },
                {  324,  86,  59 },

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        RealMatrix repeated = MatrixUtils.createRealMatrix(new double[][] {
                {3,  2,  4},
                {2,  0,  2},
                {4,  2,  3}
        }); 
        EigenDecomposition ed = new EigenDecompositionImpl(repeated, MathUtils.SAFE_MIN);
        checkEigenValues((new double[] {8, -1, -1}), ed, 1E-12);
        checkEigenVector((new double[] {2, 1, 2}), ed, 1E-12);
    }

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        RealMatrix distinct = MatrixUtils.createRealMatrix(new double[][] {
                {3, 1, -4},  
                {1, 3, -4}, 
                {-4, -4, 8}
        });
        EigenDecomposition ed = new EigenDecompositionImpl(distinct, MathUtils.SAFE_MIN);
        checkEigenValues((new double[] {2, 0, 12}), ed, 1E-12);
        checkEigenVector((new double[] {1, -1, 0}), ed, 1E-12);
        checkEigenVector((new double[] {1, 1, 1}), ed, 1E-12);
        checkEigenVector((new double[] {-1, -1, 2}), ed, 1E-12);
    }

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    }


    public void testDimension1() {
        RealMatrix matrix =
            MatrixUtils.createRealMatrix(new double[][] { { 1.5 } });
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        assertEquals(1.5, ed.getRealEigenvalue(0), 1.0e-15);
    }

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        RealMatrix matrix =
            MatrixUtils.createRealMatrix(new double[][] {
                    { 59.0, 12.0 },
                    { 12.0, 66.0 }
            });
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        assertEquals(75.0, ed.getRealEigenvalue(0), 1.0e-15);
        assertEquals(50.0, ed.getRealEigenvalue(1), 1.0e-15);
    }

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            MatrixUtils.createRealMatrix(new double[][] {
                                   {  39632.0, -4824.0, -16560.0 },
                                   {  -4824.0,  8693.0,   7920.0 },
                                   { -16560.0,  7920.0,  17300.0 }
                               });
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        assertEquals(50000.0, ed.getRealEigenvalue(0), 3.0e-11);
        assertEquals(12500.0, ed.getRealEigenvalue(1), 3.0e-11);
        assertEquals( 3125.0, ed.getRealEigenvalue(2), 3.0e-11);
    }

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                                   {  0.784, -0.288,  0.000,  0.000 },
                                   { -0.288,  0.616,  0.000,  0.000 },
                                   {  0.000,  0.000,  0.164, -0.048 },
                                   {  0.000,  0.000, -0.048,  0.136 }
                               });
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        assertEquals(1.0, ed.getRealEigenvalue(0), 1.0e-15);
        assertEquals(0.4, ed.getRealEigenvalue(1), 1.0e-15);
        assertEquals(0.2, ed.getRealEigenvalue(2), 1.0e-15);
        assertEquals(0.1, ed.getRealEigenvalue(3), 1.0e-15);
    }

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