Examples of cern.colt.matrix.linalg.EigenvalueDecomposition

cern.colt.matrix.linalg.EigenvalueDecomposition

Eigenvalues and eigenvectors of a real matrix A.

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.mult(D.mult(transpose(V))) and V.mult(transpose(V)) equals the identity matrix.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.mult(V) equals V.mult(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon Algebra.cond(V).

    double[][] mN = MatrixMath.multiply(dataDifference,
        MatrixMath.transpose(dataDifference));
    
    // eigenvaluedecomosition from cern
    DenseDoubleMatrix2D d = new DenseDoubleMatrix2D(mN);
    EigenvalueDecomposition e = new EigenvalueDecomposition(d);
    double[] eigenValues = MatrixMath.diag(e.getD().toArray());
    double[][] eigenVectors = e.getV().viewDice().toArray();
    
    // sorting
    Vector<EigenPair> eigenPairs = new Vector<EigenPair>();
    for (int i = 0; i < eigenValues.length; i++) {
      EigenPair ep = new EigenPair(eigenValues[i], eigenVectors[i]);

        if (i != l - 1) {
          hessian.setQuick(i + 1, i, 1);
        }
      }
    }
    final double[] d = new EigenvalueDecomposition(hessian).getRealEigenvalues().toArray();
    final Double[] result = new Double[d.length];
    for (int i = 0; i < d.length; i++) {
      result[i] = d[i];
    }
    return result;

Examples of cern.colt.matrix.linalg.EigenvalueDecomposition

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