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Move documentation of MatrixBase methods in MatrixFunctions to module page.

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I think that because MatrixFunctions is in unsupported/ and MatrixBase is
not, doxygen does not include the MatrixBase methods defined and documented
in the MatrixFunctions module with the other MatrixBase methods. This is a
kludge, but at least the documentation is not lost.
This commit is contained in:
Jitse Niesen
2010-03-22 13:58:19 +00:00
parent 525d6b655f
commit 307c428253
3 changed files with 209 additions and 150 deletions
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50
unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
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@@ -330,56 +330,6 @@ struct ei_traits<MatrixExponentialReturnValue<Derived> >
typedef typename Derived::PlainObject ReturnType;
};
/** \ingroup MatrixFunctions_Module
*
* \brief Compute the matrix exponential.
*
* \param[in] M matrix whose exponential is to be computed.
* \returns expression representing the matrix exponential of \p M.
*
* The matrix exponential of \f$ M \f$ is defined by
* \f[ \exp(M) = \sum_{k=0}^\infty \frac{M^k}{k!}. \f]
* The matrix exponential can be used to solve linear ordinary
* differential equations: the solution of \f$ y' = My \f$ with the
* initial condition \f$ y(0) = y_0 \f$ is given by
* \f$ y(t) = \exp(M) y_0 \f$.
*
* The cost of the computation is approximately \f$ 20 n^3 \f$ for
* matrices of size \f$ n \f$. The number 20 depends weakly on the
* norm of the matrix.
*
* The matrix exponential is computed using the scaling-and-squaring
* method combined with Pad&eacute; approximation. The matrix is first
* rescaled, then the exponential of the reduced matrix is computed
* approximant, and then the rescaling is undone by repeated
* squaring. The degree of the Pad&eacute; approximant is chosen such
* that the approximation error is less than the round-off
* error. However, errors may accumulate during the squaring phase.
*
* Details of the algorithm can be found in: Nicholas J. Higham, "The
* scaling and squaring method for the matrix exponential revisited,"
* <em>SIAM J. %Matrix Anal. Applic.</em>, <b>26</b>:1179&ndash;1193,
* 2005.
*
* Example: The following program checks that
* \f[ \exp \left[ \begin{array}{ccc}
* 0 & \frac14\pi & 0 \\
* -\frac14\pi & 0 & 0 \\
* 0 & 0 & 0
* \end{array} \right] = \left[ \begin{array}{ccc}
* \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
* \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
* 0 & 0 & 1
* \end{array} \right]. \f]
* This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
* the z-axis.
*
* \include MatrixExponential.cpp
* Output: \verbinclude MatrixExponential.out
*
* \note \p M has to be a matrix of \c float, \c double,
* \c complex<float> or \c complex<double> .
*/
template <typename Derived>
const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const
{