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 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 = new EigenvalueDecomposition(covarMatrix);
    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 = new EigenvalueDecomposition(covarMatrix);
    return processEVD(evd);
  }

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Examples of org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition

    }
    startTime(TimingSection.TRIDIAG_DECOMP);


    log.info("Lanczos iteration complete - now to diagonalize the tri-diagonal auxiliary matrix.");
    // at this point, have tridiag all filled out, and basis is all filled out, and orthonormalized
    EigenvalueDecomposition decomp = new EigenvalueDecomposition(triDiag);


    DoubleMatrix2D eigenVects = decomp.getV();
    DoubleMatrix1D eigenVals = decomp.getRealEigenvalues();
    endTime(TimingSection.TRIDIAG_DECOMP);
    startTime(TimingSection.FINAL_EIGEN_CREATE);


    for (int i = 0; i < basis.numRows() - 1; i++) {
      Vector realEigen = new DenseVector(corpus.numCols());

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Examples of org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition

    }
    startTime(TimingSection.TRIDIAG_DECOMP);


    log.info("Lanczos iteration complete - now to diagonalize the tri-diagonal auxiliary matrix.");
    // at this point, have tridiag all filled out, and basis is all filled out, and orthonormalized
    EigenvalueDecomposition decomp = new EigenvalueDecomposition(triDiag);


    DoubleMatrix2D eigenVects = decomp.getV();
    DoubleMatrix1D eigenVals = decomp.getRealEigenvalues();
    endTime(TimingSection.TRIDIAG_DECOMP);
    startTime(TimingSection.FINAL_EIGEN_CREATE);
    for (int row = 0; row < i; row++) {
      Vector realEigen = null;
      // the eigenvectors live as columns of V, in reverse order.  Weird but true.

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Examples of org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition

    int desiredRank = 80;
    LanczosState state = new LanczosState(m, desiredRank, initialVector);
    // set initial vector?
    solver.solve(state, desiredRank, true);


    EigenvalueDecomposition decomposition = new EigenvalueDecomposition(m);
    DoubleMatrix1D eigenvalues = decomposition.getRealEigenvalues();


    float fractionOfEigensExpectedGood = 0.6f;
    for(int i = 0; i < fractionOfEigensExpectedGood * desiredRank; i++) {
      double s = state.getSingularValue(desiredRank - i - 1);
      double e = eigenvalues.get(eigenvalues.size() - i - 1);
      log.info("{} : L = {}, E = {}", new Object[] {i, s, e});
      assertTrue("Singular value differs from eigenvalue", Math.abs((s-e)/e) < ERROR_TOLERANCE);
      Vector v = state.getRightSingularVector(i);
      Vector v2 = decomposition.getV().viewColumn(eigenvalues.size() - i - 1).toVector();
      double error = 1 - Math.abs(v.dot(v2)/(v.norm(2) * v2.norm(2)));
      log.info("error: {}", error);
      assertTrue(i + ": 1 - cosAngle = " + error, error < ERROR_TOLERANCE);
    }
  }

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Examples of org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition

    }
    startTime(TimingSection.TRIDIAG_DECOMP);


    log.info("Lanczos iteration complete - now to diagonalize the tri-diagonal auxiliary matrix.");
    // at this point, have tridiag all filled out, and basis is all filled out, and orthonormalized
    EigenvalueDecomposition decomp = new EigenvalueDecomposition(triDiag);


    DoubleMatrix2D eigenVects = decomp.getV();
    DoubleMatrix1D eigenVals = decomp.getRealEigenvalues();
    endTime(TimingSection.TRIDIAG_DECOMP);
    startTime(TimingSection.FINAL_EIGEN_CREATE);


    for (int i = 0; i < basis.numRows() - 1; i++) {
      Vector realEigen = new DenseVector(corpus.numCols());

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Examples of org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition

    }
    startTime(TimingSection.TRIDIAG_DECOMP);


    log.info("Lanczos iteration complete - now to diagonalize the tri-diagonal auxiliary matrix.");
    // at this point, have tridiag all filled out, and basis is all filled out, and orthonormalized
    EigenvalueDecomposition decomp = new EigenvalueDecomposition(triDiag);


    DoubleMatrix2D eigenVects = decomp.getV();
    DoubleMatrix1D eigenVals = decomp.getRealEigenvalues();
    endTime(TimingSection.TRIDIAG_DECOMP);
    startTime(TimingSection.FINAL_EIGEN_CREATE);
    for (int row = 0; row < i; row++) {
      Vector realEigen = null;
      // the eigenvectors live as columns of V, in reverse order.  Weird but true.

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Examples of org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition

    LanczosSolver solver = new LanczosSolver();
    LanczosState state = new LanczosState(m, size, desiredRank, initialVector);
    // set initial vector?
    solver.solve(state, desiredRank, true);


    EigenvalueDecomposition decomposition = new EigenvalueDecomposition(m);
    DoubleMatrix1D eigenvalues = decomposition.getRealEigenvalues();


    float fractionOfEigensExpectedGood = 0.6f;
    for(int i = 0; i < fractionOfEigensExpectedGood * desiredRank; i++) {
      double s = state.getSingularValue(desiredRank - i - 1);
      double e = eigenvalues.get(eigenvalues.size() - i - 1);
      log.info(i + " : L = {}, E = {}", s, e);
      assertTrue("Singular value differs from eigenvalue", Math.abs((s-e)/e) < ERROR_TOLERANCE);
      Vector v = state.getRightSingularVector(i);
      Vector v2 = decomposition.getV().viewColumn(eigenvalues.size() - i - 1).toVector();
      double error = 1 - Math.abs(v.dot(v2)/(v.norm(2) * v2.norm(2)));
      log.info("error: {}", error);
      assertTrue(i + ": 1 - cosAngle = " + error, error < ERROR_TOLERANCE);
    }
  }

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Examples of org.encog.mathutil.matrices.decomposition.EigenvalueDecomposition

        {0,1,0,0},
        {0,0,1,0},
        {0,0,0,1} };
    Matrix matrix1 = new Matrix(m1);
      
    EigenvalueDecomposition e = new EigenvalueDecomposition(matrix1);
    
    double[] d1 = e.getImagEigenvalues();
    double[] d2 = e.getRealEigenvalues();
    Matrix mx = e.getV();
    
    Assert.assertEquals(1.0, mx.get(0,0));
    Assert.assertEquals(1.0, mx.get(1,1));
    Assert.assertEquals(1.0, mx.get(2,2));
    Assert.assertEquals(4, mx.getRows());

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Examples of org.encog.mathutil.matrices.decomposition.EigenvalueDecomposition

        {0,1,0,0},
        {0,0,1,0},
        {1,0,0,1} };
    Matrix matrix1 = new Matrix(m1);
      
    EigenvalueDecomposition e = new EigenvalueDecomposition(matrix1);
    
    double[] d1 = e.getImagEigenvalues();
    double[] d2 = e.getRealEigenvalues();
    Matrix mx = e.getV();
    
    Assert.assertEquals(0.0, mx.get(0,0));
    Assert.assertEquals(0.0, mx.get(1,1));
    Assert.assertEquals(1.0, mx.get(2,2));
    Assert.assertEquals(4, mx.getRows());

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