Examples of EigenvalueDecomposition

Jama.EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix.
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.times(D.times(V.transpose())) and V.times(V.transpose()) 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.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
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).
de.lmu.ifi.dbs.elki.math.linearalgebra.EigenvalueDecomposition
Eigenvalues and eigenvectors of a real matrix.
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.times(D.timesTranspose(V)) and V.timesTranspose(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.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond(). @apiviz.uses Matrix - - transforms
org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition
@deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
org.encog.mathutil.matrices.decomposition.EigenvalueDecomposition
nist.gov/javanumerics/jama/
stallone.algebra.EigenvalueDecomposition
Data container for eigenvalue decomposition of a matrix @author noe
weka.core.matrix.EigenvalueDecomposition
nist.gov/javanumerics/jama/" target="_blank">JAMA package. @author The Mathworks and NIST @author Fracpete (fracpete at waikato dot ac dot nz) @version $Revision: 1.4 $

Examples of Jama.EigenvalueDecomposition


        double[] m = {xx, xy, xz, xy, yy, yz, xz, yz, zz};


        Matrix matrix = new Matrix(m, 3);


        EigenvalueDecomposition ed = matrix.eig();


        double x1 = ed.getV().get(0, 2);
        double y1 = ed.getV().get(1, 2);
        double z1 = ed.getV().get(2, 2);


        double length = Math.sqrt(x1 * x1 + y1 * y1 + z1 * z1);
        x1 /= length;
        y1 /= length;
        z1 /= length;

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Examples of Jama.EigenvalueDecomposition

    time = System.currentTimeMillis();


    //laplacianise(matrix);
    
    
    EigenvalueDecomposition evd = matrix.eig();
    System.out.println("evd in: " + (System.currentTimeMillis() - time));
    double [] evr = evd.getRealEigenvalues();    
    Matrix evm = evd.getV();


    int evnum = evr.length;


    for(int i=0;i<evr.length;i++) {
      if(evr[i] <= 1.0) {

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Examples of Jama.EigenvalueDecomposition

    public static void singularDecomposition(SSAData data) {
        double inclosureMatrix[][] = data.getInclosureMatrix();
        double transp[][] = transpositionMatrix(inclosureMatrix);
        Matrix S = new Matrix(inclosureMatrix).times(new Matrix(transp));
        //int d = new Matrix(inclosureMatrix).rank(); //ранг матрицы вложений
        EigenvalueDecomposition decomposition = new EigenvalueDecomposition(S);
        Matrix eigenvalue = decomposition.getD();   //матрица с собственными значениями
        Matrix eigenvec = decomposition.getV();     //матрица собственных векторов
        List<Double> eigenvalueList = new ArrayList<Double>();
        //формируем набор собственных значений, стоящих на диагонали
        for (int i = 0; i < eigenvalue.getRowDimension(); i++) {
            for (int j = 0; j < eigenvalue.getRowDimension(); j++) {
                if (i == j) {

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Examples of Jama.EigenvalueDecomposition

        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount,
                    "CholeskyDecomposition solve()...",
                    "incorrect Choleskydecomposition solve calculation");
        }
        EigenvalueDecomposition Eig = A.eig();
        Matrix D = Eig.getD();
        Matrix V = Eig.getV();


        try {
            check(A.times(V), V.times(D));
            try_success("EigenvalueDecomposition (symmetric)...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount,
                    "EigenvalueDecomposition (symmetric)...",
                    "incorrect symmetric Eigenvalue decomposition calculation");
        }
        A = new Matrix(evals);
        Eig = A.eig();
        D = Eig.getD();
        V = Eig.getV();
        try {
            check(A.times(V), V.times(D));
            try_success("EigenvalueDecomposition (nonsymmetric)...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount,

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Examples of Jama.EigenvalueDecomposition


            int t = (int) M.trace();


            print(fixedWidthIntegertoString(t, 10));


            EigenvalueDecomposition E = new EigenvalueDecomposition(
                    M.plus(M.transpose()).times(0.5));
            double[] d = E.getRealEigenvalues();


            print(fixedWidthDoubletoString(d[n - 1], 14, 3));


            int r = M.rank();

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Examples of Jama.EigenvalueDecomposition

    
    if (!isControllableCanonical(system)) {
      throw new IllegalArgumentException("System must be in controllable-canonical form");
    }
    
    EigenvalueDecomposition eig = new Matrix(MU.convert(system.getA(0f))).eig();
    double[] eigReal = eig.getRealEigenvalues(); 
    
    double slowest = eigReal[0];
    for (int i = 1; i < eig.getRealEigenvalues().length; i++) {
      if (Math.abs(eigReal[i]) < Math.abs(slowest)) slowest = eigReal[i];
    }
    
    //may be repeated / complex conjugate so change all slowest real eigenvalues
    for (int i = 0; i < eigReal.length; i++) {
      if (Math.abs(eigReal[i] - slowest) < .0001*Math.abs(slowest)) eigReal[i] = -1d / (double) tau;
    }
  
    //coefficients of new transfer function polynomial ...  
    double[] eigImag = eig.getImagEigenvalues();
    float[][] poly = new float[][]{new float[]{1f, (float) -eigReal[0]}, new float[]{0f, (float) -eigImag[0]}};
    for (int i = 1; i < eigReal.length; i++) {
      poly = prod(poly, new float[][]{new float[]{1f, (float) -eigReal[i]}, new float[]{0f, (float) -eigImag[i]}});
    }

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Examples of cern.colt.matrix.linalg.EigenvalueDecomposition

    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]);

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Examples of cern.colt.matrix.linalg.EigenvalueDecomposition

        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;

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Examples of de.lmu.ifi.dbs.elki.math.linearalgebra.EigenvalueDecomposition

   * @param covarMatrix the matrix used for performing pca
   * @return PCA result
   */
  public PCAResult processCovarMatrix(Matrix covarMatrix) {
    // TODO: add support for a different implementation to do EVD?
    EigenvalueDecomposition evd = covarMatrix.eig();
    return processEVD(evd);
  }

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Examples of de.lmu.ifi.dbs.elki.math.linearalgebra.EigenvalueDecomposition

   * @param covarMatrix the matrix used for performing PCA
   */
  @Override
  public PCAFilteredResult processCovarMatrix(Matrix covarMatrix) {
    // TODO: add support for a different implementation to do EVD?
    EigenvalueDecomposition evd = covarMatrix.eig();
    return processEVD(evd);
  }

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