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

   */
  @Override
  public DoubleMatrix2D getPower(final Matrix<?> m, final double p) {
    if (m instanceof DoubleMatrix2D) {
      final RealMatrix temp = CommonsMathWrapper.wrap((DoubleMatrix2D) m);
      final EigenDecomposition eigen = new EigenDecompositionImpl(temp, 0.0);
      final double[] rEigenValues = eigen.getRealEigenvalues();
      final double[] iEigenValues = eigen.getImagEigenvalues();
      final int n = rEigenValues.length;
      final double[][] d = new double[n][n];
      for (int i = n - 1; i >= 0; --i) {
        d[i][i] = Math.pow(rEigenValues[i], p);
        if (iEigenValues[i] != 0.0) {
          throw new NotImplementedException("Cannot handle complex eigenvalues in getPower");
        }
      }
      final RealMatrix res = eigen.getV().multiply((new Array2DRowRealMatrix(d)).multiply(eigen.getVT()));
      return CommonsMathWrapper.unwrap(res);
    }
    throw new IllegalArgumentException("Can only find pow of DoubleMatrix2D; have " + m.getClass());
  }

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