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

Package de.lmu.ifi.dbs.elki.math.linearalgebra

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

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

   * @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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   * @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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   * @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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   * @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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Related Classes of de.lmu.ifi.dbs.elki.math.linearalgebra.EigenvalueDecomposition

de.lmu.ifi.dbs.elki.math.linearalgebra.pca.PCAFilteredRunner

de.lmu.ifi.dbs.elki.math.linearalgebra.pca.PCARunner

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