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port unsupported modules to new API

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This commit is contained in:
Gael Guennebaud
2010-01-05 15:38:20 +01:00
parent cab85218db
commit 39209edd71
9 changed files with 189 additions and 189 deletions
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72
unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
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@@ -31,16 +31,16 @@
/** \ingroup MatrixFunctions_Module
*
* \brief Compute the matrix exponential.
* \brief Compute the matrix exponential.
*
* \param M matrix whose exponential is to be computed.
* \param M matrix whose exponential is to be computed.
* \param result pointer to the matrix in which to store the result.
*
* 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
* 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
@@ -54,17 +54,17 @@
* squaring. The degree of the Padé 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.
* 2005.
*
* Example: The following program checks that
* \f[ \exp \left[ \begin{array}{ccc}
* 0 & \frac14\pi & 0 \\
* \f[ \exp \left[ \begin{array}{ccc}
* 0 & \frac14\pi & 0 \\
* -\frac14\pi & 0 & 0 \\
* 0 & 0 & 0
* 0 & 0 & 0
* \end{array} \right] = \left[ \begin{array}{ccc}
* \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
* \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
@@ -76,11 +76,11 @@
* \include MatrixExponential.cpp
* Output: \verbinclude MatrixExponential.out
*
* \note \p M has to be a matrix of \c float, \c double,
* \note \p M has to be a matrix of \c float, \c double,
* \c complex<float> or \c complex<double> .
*/
template <typename Derived>
EIGEN_STRONG_INLINE void ei_matrix_exponential(const MatrixBase<Derived> &M,
EIGEN_STRONG_INLINE void ei_matrix_exponential(const MatrixBase<Derived> &M,
typename MatrixBase<Derived>::PlainMatrixType* result);
/** \ingroup MatrixFunctions_Module
@@ -90,13 +90,13 @@ template <typename MatrixType>
class MatrixExponential {
public:
/** \brief Compute the matrix exponential.
/** \brief Compute the matrix exponential.
*
* \param M matrix whose exponential is to be computed.
* \param M matrix whose exponential is to be computed.
* \param result pointer to the matrix in which to store the result.
*/
MatrixExponential(const MatrixType &M, MatrixType *result);
MatrixExponential(const MatrixType &M, MatrixType *result);
private:
@@ -105,7 +105,7 @@ class MatrixExponential {
MatrixExponential& operator=(const MatrixExponential&);
/** \brief Compute the (3,3)-Pad&eacute; approximant to the exponential.
*
*
* After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Pad&eacute;
* approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
*
@@ -114,7 +114,7 @@ class MatrixExponential {
void pade3(const MatrixType &A);
/** \brief Compute the (5,5)-Pad&eacute; approximant to the exponential.
*
*
* After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Pad&eacute;
* approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
*
@@ -123,7 +123,7 @@ class MatrixExponential {
void pade5(const MatrixType &A);
/** \brief Compute the (7,7)-Pad&eacute; approximant to the exponential.
*
*
* After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Pad&eacute;
* approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
*
@@ -132,7 +132,7 @@ class MatrixExponential {
void pade7(const MatrixType &A);
/** \brief Compute the (9,9)-Pad&eacute; approximant to the exponential.
*
*
* After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Pad&eacute;
* approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
*
@@ -141,7 +141,7 @@ class MatrixExponential {
void pade9(const MatrixType &A);
/** \brief Compute the (13,13)-Pad&eacute; approximant to the exponential.
*
*
* After exit, \f$ (V+U)(V-U)^{-1} \f$ is the Pad&eacute;
* approximant of \f$ \exp(A) \f$ around \f$ A = 0 \f$.
*
@@ -149,10 +149,10 @@ class MatrixExponential {
*/
void pade13(const MatrixType &A);
/** \brief Compute Pad&eacute; approximant to the exponential.
*
* Computes \c m_U, \c m_V and \c m_squarings such that
* \f$ (V+U)(V-U)^{-1} \f$ is a Pad&eacute; of
/** \brief Compute Pad&eacute; approximant to the exponential.
*
* Computes \c m_U, \c m_V and \c m_squarings such that
* \f$ (V+U)(V-U)^{-1} \f$ is a Pad&eacute; of
* \f$ \exp(2^{-\mbox{squarings}}M) \f$ around \f$ M = 0 \f$. The
* degree of the Pad&eacute; approximant and the value of
* squarings are chosen such that the approximation error is no
@@ -164,7 +164,7 @@ class MatrixExponential {
*/
void computeUV(double);
/** \brief Compute Pad&eacute; approximant to the exponential.
/** \brief Compute Pad&eacute; approximant to the exponential.
*
* \sa computeUV(double);
*/
@@ -174,7 +174,7 @@ class MatrixExponential {
typedef typename NumTraits<typename ei_traits<MatrixType>::Scalar>::Real RealScalar;
/** \brief Pointer to matrix whose exponential is to be computed. */
const MatrixType* m_M;
const MatrixType* m_M;
/** \brief Even-degree terms in numerator of Pad&eacute; approximant. */
MatrixType m_U;
@@ -200,14 +200,14 @@ class MatrixExponential {
template <typename MatrixType>
MatrixExponential<MatrixType>::MatrixExponential(const MatrixType &M, MatrixType *result) :
m_M(&M),
m_U(M.rows(),M.cols()),
m_V(M.rows(),M.cols()),
m_tmp1(M.rows(),M.cols()),
m_tmp2(M.rows(),M.cols()),
m_Id(MatrixType::Identity(M.rows(), M.cols())),
m_squarings(0),
m_l1norm(static_cast<float>(M.cwise().abs().colwise().sum().maxCoeff()))
m_M(&M),
m_U(M.rows(),M.cols()),
m_V(M.rows(),M.cols()),
m_tmp1(M.rows(),M.cols()),
m_tmp2(M.rows(),M.cols()),
m_Id(MatrixType::Identity(M.rows(), M.cols())),
m_squarings(0),
m_l1norm(static_cast<float>(M.cwiseAbs().colwise().sum().maxCoeff()))
{
computeUV(RealScalar());
m_tmp1 = m_U + m_V; // numerator of Pade approximant
@@ -267,8 +267,8 @@ EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade9(const MatrixType &
template <typename MatrixType>
EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade13(const MatrixType &A)
{
const Scalar b[] = {64764752532480000., 32382376266240000., 7771770303897600.,
1187353796428800., 129060195264000., 10559470521600., 670442572800.,
const Scalar b[] = {64764752532480000., 32382376266240000., 7771770303897600.,
1187353796428800., 129060195264000., 10559470521600., 670442572800.,
33522128640., 1323241920., 40840800., 960960., 16380., 182., 1.};
MatrixType A2 = A * A;
MatrixType A4 = A2 * A2;
@@ -317,7 +317,7 @@ void MatrixExponential<MatrixType>::computeUV(double)
}
template <typename Derived>
EIGEN_STRONG_INLINE void ei_matrix_exponential(const MatrixBase<Derived> &M,
EIGEN_STRONG_INLINE void ei_matrix_exponential(const MatrixBase<Derived> &M,
typename MatrixBase<Derived>::PlainMatrixType* result)
{
ei_assert(M.rows() == M.cols());