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

                                   {  0.5608, -0.2016,  0.1152, -0.2976 },
                                   { -0.2016,  0.4432, -0.2304,  0.1152 },
                                   {  0.1152, -0.2304,  0.3088, -0.1344 },
                                   { -0.2976,  0.1152, -0.1344,  0.3872 }
                               });
        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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        }
        Arrays.sort(ref);
        TriDiagonalTransformer t =
            new TriDiagonalTransformer(createTestMatrix(r, ref));
        EigenDecomposition ed =
            new EigenDecompositionImpl(t.getMainDiagonalRef(),
                                       t.getSecondaryDiagonalRef(),
                                       MathUtils.SAFE_MIN);
        double[] eigenValues = ed.getRealEigenvalues();
        assertEquals(ref.length, eigenValues.length);
        for (int i = 0; i < ref.length; ++i) {
            assertEquals(ref[ref.length - i - 1], eigenValues[i], 2.0e-14);
        }

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    }


    /** test dimensions */
    public void testDimensions() {
        final int m = matrix.getRowDimension();
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        assertEquals(m, ed.getV().getRowDimension());
        assertEquals(m, ed.getV().getColumnDimension());
        assertEquals(m, ed.getD().getColumnDimension());
        assertEquals(m, ed.getD().getColumnDimension());
        assertEquals(m, ed.getVT().getRowDimension());
        assertEquals(m, ed.getVT().getColumnDimension());
    }

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        assertEquals(m, ed.getVT().getColumnDimension());
    }


    /** test eigenvalues */
    public void testEigenvalues() {
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        double[] eigenValues = ed.getRealEigenvalues();
        assertEquals(refValues.length, eigenValues.length);
        for (int i = 0; i < refValues.length; ++i) {
            assertEquals(refValues[i], eigenValues[i], 3.0e-15);
        }
    }

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        for (int i = 0; i < bigValues.length; ++i) {
            bigValues[i] = 2 * r.nextDouble() - 1;
        }
        Arrays.sort(bigValues);
        EigenDecomposition ed =
            new EigenDecompositionImpl(createTestMatrix(r, bigValues), MathUtils.SAFE_MIN);
        double[] eigenValues = ed.getRealEigenvalues();
        assertEquals(bigValues.length, eigenValues.length);
        for (int i = 0; i < bigValues.length; ++i) {
            assertEquals(bigValues[bigValues.length - i - 1], eigenValues[i], 2.0e-14);
        }
    }

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        }
    }


    /** test eigenvectors */
    public void testEigenvectors() {
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        for (int i = 0; i < matrix.getRowDimension(); ++i) {
            double lambda = ed.getRealEigenvalue(i);
            RealVector v  = ed.getEigenvector(i);
            RealVector mV = matrix.operate(v);
            assertEquals(0, mV.subtract(v.mapMultiplyToSelf(lambda)).getNorm(), 1.0e-13);
        }
    }

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        }
    }


    /** test A = VDVt */
    public void testAEqualVDVt() {
        EigenDecomposition ed = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN);
        RealMatrix v  = ed.getV();
        RealMatrix d  = ed.getD();
        RealMatrix vT = ed.getVT();
        double norm = v.multiply(d).multiply(vT).subtract(matrix).getNorm();
        assertEquals(0, norm, 6.0e-13);
    }

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        assertEquals(0, norm, 6.0e-13);
    }


    /** test that V is orthogonal */
    public void testVOrthogonal() {
        RealMatrix v = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN).getV();
        RealMatrix vTv = v.transpose().multiply(v);
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(vTv.getRowDimension());
        assertEquals(0, vTv.subtract(id).getNorm(), 2.0e-13);
    }

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    /** test diagonal matrix */
    public void testDiagonal() {
        double[] diagonal = new double[] { -3.0, -2.0, 2.0, 5.0 };
        RealMatrix m = createDiagonalMatrix(diagonal, diagonal.length, diagonal.length);
        EigenDecomposition ed = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN);
        assertEquals(diagonal[0], ed.getRealEigenvalue(3), 2.0e-15);
        assertEquals(diagonal[1], ed.getRealEigenvalue(2), 2.0e-15);
        assertEquals(diagonal[2], ed.getRealEigenvalue(1), 2.0e-15);
        assertEquals(diagonal[3], ed.getRealEigenvalue(0), 2.0e-15);
    }

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  private final double[] eigenvalues;
  private final double[][] uHat;


  public EigenSolverWrapper(double[][] bbt) {
    int dim = bbt.length;
    EigenDecomposition evd2 = new EigenDecompositionImpl(
        new Array2DRowRealMatrix(bbt), 0);
    eigenvalues = evd2.getRealEigenvalues();
    RealMatrix uHatrm = evd2.getV();
    uHat = new double[dim][];
    for (int i = 0; i < dim; i++) {
      uHat[i] = uHatrm.getRow(i);
    }
  }

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