itk::Math::detail Namespace Reference

Typedefs
template<typename TReal>
using	CholeskyRowMajor = Eigen::Matrix<TReal, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>
template<typename TReal>
using	CholeskyVector = Eigen::Matrix<TReal, Eigen::Dynamic, 1>

Functions
template<unsigned int VRows, unsigned int VColumns, typename TReal>
void	MatrixExponentialEigen (const TReal *inData, TReal *outData)
template<typename TReal>
void	MatrixExponentialEigen (const TReal *inData, TReal *outData, unsigned int n)

Detailed Description

Cholesky-based linear algebra for symmetric matrices, backed by Eigen.

Matrix exponential exp(A) for a real square matrix, backed by Eigen.

SolveSymmetricPositiveDefinite() uses Eigen's robust LDL^T (pivoted) factor, which handles near-semidefinite regularized Gram matrices. CholeskyLowerTriangle() returns the L of A = L L^T via Eigen's LLT.

Replacement for the removed vnl_matrix_exp. Delegates to Eigen's MatrixBase::exp(), which uses scaling-and-squaring with a degree-13 Pade approximant (Higham, SIAM J. Matrix Anal. Appl. 26(4), 2005) – more robust than the truncated Taylor series formerly provided by vnl_matrix_exp.

Typedef Documentation

CholeskyRowMajor

template<typename TReal>

using itk::Math::detail::CholeskyRowMajor = Eigen::Matrix<TReal, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>

Definition at line 44 of file itkCholeskySolve.h.

CholeskyVector

template<typename TReal>

using itk::Math::detail::CholeskyVector = Eigen::Matrix<TReal, Eigen::Dynamic, 1>

Definition at line 46 of file itkCholeskySolve.h.

Function Documentation

MatrixExponentialEigen() [1/2]

template<unsigned int VRows, unsigned int VColumns, typename TReal>

void itk::Math::detail::MatrixExponentialEigen	(	const TReal *	inData,
		TReal *	outData )

Definition at line 44 of file itkMatrixExponential.h.

Referenced by itk::Math::MatrixExponential(), itk::Math::MatrixExponential(), and itk::Math::MatrixExponential().

MatrixExponentialEigen() [2/2]

template<typename TReal>

void itk::Math::detail::MatrixExponentialEigen	(	const TReal *	inData,
		TReal *	outData,
		unsigned int	n )

Definition at line 54 of file itkMatrixExponential.h.