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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
View File

@@ -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
{

96
unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
View File

@@ -536,56 +536,6 @@ struct ei_traits<MatrixFunctionReturnValue<Derived> >
/********** MatrixBase methods **********/
/** \ingroup MatrixFunctions_Module
*
* \brief Compute a matrix function.
*
* \param[in] M argument of matrix function, should be a square matrix.
* \param[in] f an entire function; \c f(x,n) should compute the n-th
* derivative of f at x.
* \returns expression representing \p f applied to \p M.
*
* Suppose that \p M is a matrix whose entries have type \c Scalar.
* Then, the second argument, \p f, should be a function with prototype
* \code
* ComplexScalar f(ComplexScalar, int)
* \endcode
* where \c ComplexScalar = \c std::complex<Scalar> if \c Scalar is
* real (e.g., \c float or \c double) and \c ComplexScalar =
* \c Scalar if \c Scalar is complex. The return value of \c f(x,n)
* should be \f$ f^{(n)}(x) \f$, the n-th derivative of f at x.
*
* This routine uses the algorithm described in:
* Philip Davies and Nicholas J. Higham,
* "A Schur-Parlett algorithm for computing matrix functions",
* <em>SIAM J. %Matrix Anal. Applic.</em>, <b>25</b>:464&ndash;485, 2003.
*
* The actual work is done by the MatrixFunction class.
*
* Example: The following program checks that
* \f[ \exp \left[ \begin{array}{ccc}
* 0 & \frac14\pi & 0 \\
* -\frac14\pi & 0 & 0 \\
* 0 & 0 & 0
* \end{array} \right] = \left[ \begin{array}{ccc}
* \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
* \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
* 0 & 0 & 1
* \end{array} \right]. \f]
* This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
* the z-axis. This is the same example as used in the documentation
* of MatrixBase::exp().
*
* \include MatrixFunction.cpp
* Output: \verbinclude MatrixFunction.out
*
* Note that the function \c expfn is defined for complex numbers
* \c x, even though the matrix \c A is over the reals. Instead of
* \c expfn, we could also have used StdStemFunctions::exp:
* \code
* A.matrixFunction(StdStemFunctions<std::complex<double> >::exp, &B);
* \endcode
*/
template <typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename ei_stem_function<typename ei_traits<Derived>::Scalar>::type f) const
{
@@ -593,18 +543,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typ
return MatrixFunctionReturnValue<Derived>(derived(), f);
}
/** \ingroup MatrixFunctions_Module
*
* \brief Compute the matrix sine.
*
* \param[in] M a square matrix.
* \returns expression representing \f$ \sin(M) \f$.
*
* This function calls matrixFunction() with StdStemFunctions::sin().
*
* \include MatrixSine.cpp
* Output: \verbinclude MatrixSine.out
*/
template <typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
{
@@ -613,17 +551,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sin);
}
/** \ingroup MatrixFunctions_Module
*
* \brief Compute the matrix cosine.
*
* \param[in] M a square matrix.
* \returns expression representing \f$ \cos(M) \f$.
*
* This function calls matrixFunction() with StdStemFunctions::cos().
*
* \sa ei_matrix_sin() for an example.
*/
template <typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
{
@@ -632,18 +559,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::cos);
}
/** \ingroup MatrixFunctions_Module
*
* \brief Compute the matrix hyperbolic sine.
*
* \param[in] M a square matrix.
* \returns expression representing \f$ \sinh(M) \f$
*
* This function calls matrixFunction() with StdStemFunctions::sinh().
*
* \include MatrixSinh.cpp
* Output: \verbinclude MatrixSinh.out
*/
template <typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
{
@@ -652,17 +567,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sinh);
}
/** \ingroup MatrixFunctions_Module
*
* \brief Compute the matrix hyberbolic cosine.
*
* \param[in] M a square matrix.
* \returns expression representing \f$ \cosh(M) \f$
*
* This function calls matrixFunction() with StdStemFunctions::cosh().
*
* \sa ei_matrix_sinh() for an example.
*/
template <typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const
{