Compute the (17,17)-Padé approximant to the exponential. More...

#include <MatrixExponential.h>

Static Public Member Functions
static void	run (const MatrixType &arg, MatrixType &U, MatrixType &V, int &squarings)
	Compute Padé approximant to the exponential.

Detailed Description

template<typename MatrixType, typename RealScalar = typename NumTraits<typename traits<MatrixType>::Scalar>::Real>
struct Eigen::internal::matrix_exp_computeUV< MatrixType, RealScalar >

Compute the (17,17)-Padé approximant to the exponential.

After exit, $(V+U)(V-U)^{-1}$ is the Padé approximant of $\exp(A)$ around $ A = 0 $ .

This function activates only if your long double is double-double or quadruple.

Member Function Documentation

◆ run()

template<typename MatrixType , typename RealScalar = typename NumTraits<typename traits<MatrixType>::Scalar>::Real>

static void Eigen::internal::matrix_exp_computeUV< MatrixType, RealScalar >::run	(	const MatrixType &	arg,
		MatrixType &	U,
		MatrixType &	V,
		int &	squarings
	)

static

Compute Padé approximant to the exponential.

Computes U, V and squarings such that $(V+U)(V-U)^{-1}$ is a Padé approximant of $\exp(2^{-\mbox{squarings}}M)$ around $ M = 0 $ , where $ M $ denotes the matrix arg. The degree of the Padé approximant and the value of squarings are chosen such that the approximation error is no more than the round-off error.

The documentation for this struct was generated from the following file:

core/util/algorithms/eigen-3.4.0/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ run()