GitHub-Proxy/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2025-08-05 11:40:40 +08:00
Code Issues Packages Projects Releases Wiki Activity

add compatibility with long double

Browse Source
This commit is contained in:
Chen-Pang He 2011-08-20 12:33:51 +08:00
parent ea4a1960f0
commit 6d7a32231d
3 changed files with 113 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

1
unsupported/Eigen/MatrixFunctions
View File

@ -25,6 +25,7 @@
#ifndef EIGEN_MATRIX_FUNCTIONS
#define EIGEN_MATRIX_FUNCTIONS
#include <cfloat>
#include <list>
#include <functional>
#include <iterator>

116
unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
View File

@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2009, 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@ -107,6 +108,17 @@ class MatrixExponential {
*/
void pade13(const MatrixType &A);
/** \brief Compute the (17,17)-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$.
*
* This function activates only if your long double is double-double or quadruple.
*
* \param[in] A Argument of matrix exponential
*/
void pade17(const MatrixType &A);
/** \brief Compute Pad&eacute; approximant to the exponential.
*
* Computes \c m_U, \c m_V and \c m_squarings such that
@ -128,16 +140,22 @@ class MatrixExponential {
*/
void computeUV(float);
/** \brief Compute Pad&eacute; approximant to the exponential.
*
* \sa computeUV(double);
*/
void computeUV(long double);
typedef typename internal::traits<MatrixType>::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
/** \brief Reference to matrix whose exponential is to be computed. */
typename internal::nested<MatrixType>::type m_M;
/** \brief Even-degree terms in numerator of Pad&eacute; approximant. */
/** \brief Odd-degree terms in numerator of Pad&eacute; approximant. */
MatrixType m_U;
/** \brief Odd-degree terms in numerator of Pad&eacute; approximant. */
/** \brief Even-degree terms in numerator of Pad&eacute; approximant. */
MatrixType m_V;
/** \brief Used for temporary storage. */
@ -153,7 +171,7 @@ class MatrixExponential {
int m_squarings;
/** \brief L1 norm of m_M. */
float m_l1norm;
RealScalar m_l1norm;
};
template <typename MatrixType>
@ -247,6 +265,30 @@ EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade13(const MatrixType
m_V += b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;
}
#if LDBL_MANT_DIG > 64
template <typename MatrixType>
EIGEN_STRONG_INLINE void MatrixExponential<MatrixType>::pade17(const MatrixType &A)
{
const Scalar b[] = {830034394580628357120000.L, 415017197290314178560000.L,
100610229646136770560000.L, 15720348382208870400000.L,
1774878043152614400000.L, 153822763739893248000.L, 10608466464820224000.L,
595373117923584000.L, 27563570274240000.L, 1060137318240000.L,
33924394183680.L, 899510451840.L, 19554575040.L, 341863200.L, 4651200.L,
46512.L, 306.L, 1.L};
MatrixType A2 = A * A;
MatrixType A4 = A2 * A2;
MatrixType A6 = A4 * A2;
m_tmp1.noalias() = A4 * A4;
m_V = b[17]*m_tmp1 + b[15]*A6 + b[13]*A4 + b[11]*A2; // used for temporary storage
m_tmp2.noalias() = m_tmp1 * m_V;
m_tmp2 += b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;
m_U.noalias() = A * m_tmp2;
m_tmp2 = b[16]*m_tmp1 + b[14]*A6 + b[12]*A4 + b[10]*A2;
m_V.noalias() = m_tmp1 * m_tmp2;
m_V += b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;
}
#endif
template <typename MatrixType>
void MatrixExponential<MatrixType>::computeUV(float)
{
@ -260,7 +302,7 @@ void MatrixExponential<MatrixType>::computeUV(float)
} else {
const float maxnorm = 3.925724783138660f;
m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm)));
MatrixType A = m_M / pow(Scalar(2), Scalar(static_cast<RealScalar>(m_squarings)));
MatrixType A = m_M / pow(Scalar(2), m_squarings);
pade7(A);
}
}
@ -282,11 +324,75 @@ void MatrixExponential<MatrixType>::computeUV(double)
} else {
const double maxnorm = 5.371920351148152;
m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm)));
MatrixType A = m_M / pow(Scalar(2), Scalar(m_squarings));
MatrixType A = m_M / pow(Scalar(2), m_squarings);
pade13(A);
}
}
template <typename MatrixType>
void MatrixExponential<MatrixType>::computeUV(long double)
{
using std::max;
using std::pow;
using std::ceil;
#if LDBL_MANT_DIG == 53 // double precision
computeUV(0.);
#elif LDBL_MANT_DIG <= 64 // extended precision
if (m_l1norm < 4.1968497232266989671e-003L) {
pade3(m_M);
} else if (m_l1norm < 1.1848116734693823091e-001L) {
pade5(m_M);
} else if (m_l1norm < 5.5170388480686700274e-001L) {
pade7(m_M);
} else if (m_l1norm < 1.3759868875587845383e+000L) {
pade9(m_M);
} else {
const double maxnorm = 4.0246098906697353063L;
m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm)));
MatrixType A = m_M / pow(Scalar(2), m_squarings);
pade13(A);
}
#elif LDBL_MANT_DIG <= 106 // double-double
if (m_l1norm < 3.2787892205607026992947488108213e-005L) {
pade3(m_M);
} else if (m_l1norm < 6.4467025060072760084130906076332e-003L) {
pade5(m_M);
} else if (m_l1norm < 6.8988028496595374751374122881143e-002L) {
pade7(m_M);
} else if (m_l1norm < 2.7339737518502231741495857201670e-001L) {
pade9(m_M);
} else if (m_l1norm < 1.3203382096514474905666448850278e+000L) {
pade13(m_M);
} else {
const double maxnorm = 3.2579440895405400856599663723517L;
m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm)));
MatrixType A = m_M / pow(Scalar(2), m_squarings);
pade17(A);
}
#elif LDBL_MANT_DIG <= 112 // quadruple precison
if (m_l1norm < 1.639394610288918690547467954466970e-005L) {
pade3(m_M);
} else if (m_l1norm < 4.253237712165275566025884344433009e-003L) {
pade5(m_M);
} else if (m_l1norm < 5.125804063165764409885122032933142e-002L) {
pade7(m_M);
} else if (m_l1norm < 2.170000765161155195453205651889853e-001L) {
pade9(m_M);
} else if (m_l1norm < 1.125358383453143065081397882891878e+000L) {
pade13(m_M);
} else {
const double maxnorm = 2.884233277829519311757165057717815L;
m_squarings = (max)(0, (int)ceil(log2(m_l1norm / maxnorm)));
MatrixType A = m_M / pow(Scalar(2), m_squarings);
pade17(A);
}
#else // should never happen
MatrixType A = m_M / Scalar(2);
m_U = m_M.sinh();
m_V = m_M.cosh();
#endif
}
/** \ingroup MatrixFunctions_Module
*
* \brief Proxy for the matrix exponential of some matrix (expression).

2
unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
View File

@ -26,7 +26,7 @@
#define EIGEN_MATRIX_LOGARITHM
#ifndef M_PI
#define M_PI 3.14159265358979323846
#define M_PI 3.14159265358979323846264338327950L
#endif
/** \ingroup MatrixFunctions_Module