SH.h File Reference

#include "math/legendre.h"
#include "math/least_squares.h"

Go to the source code of this file.

Classes
class	MR::Math::SH::Transform< ValueType >
class	MR::Math::SH::PrecomputedFraction< ValueType >
	used to speed up SH calculation More...
class	MR::Math::SH::PrecomputedAL< ValueType >
	Precomputed Associated Legrendre Polynomials - used to speed up SH calculation. More...
class	MR::Math::SH::aPSF< ValueType >
	a class to hold the coefficients for an apodised point-spread function. More...

Namespaces
namespace	MR
namespace	MR::Math
namespace	MR::Math::SH

Macros
#define	MAX_DIR_CHANGE   0.2
#define	ANGLE_TOLERANCE   1e-4

Functions
size_t	MR::Math::SH::NforL (int lmax)
	the number of (even-degree) coefficients for the given value of lmax More...
size_t	MR::Math::SH::index (int l, int m)
	compute the index for coefficient (l,m) More...
size_t	MR::Math::SH::NforL_mpos (int lmax)
	same as NforL(), but consider only non-negative orders m More...
size_t	MR::Math::SH::index_mpos (int l, int m)
	same as index(), but consider only non-negative orders m More...
size_t	MR::Math::SH::LforN (int N)
	returns the largest lmax given N parameters More...
template<class MatrixType >
Eigen::Matrix< typename MatrixType::Scalar, Eigen::Dynamic, Eigen::Dynamic >	MR::Math::SH::init_transform (const MatrixType &dirs, const int lmax)
	form the SH->amplitudes matrix More...
template<class MatrixType >
Eigen::Matrix< typename MatrixType::Scalar, Eigen::Dynamic, Eigen::Dynamic >	MR::Math::SH::init_transform_cart (const MatrixType &dirs, const int lmax)
	form the SH->amplitudes matrix More...
template<class MatrixType , class VectorType >
void	MR::Math::SH::scale_degrees_forward (MatrixType &SH2amp_mapping, const VectorType &coefs)
	scale the coefficients of each SH degree by the corresponding value in coefs More...
template<typename MatrixType , class VectorType >
void	MR::Math::SH::scale_degrees_inverse (MatrixType &amp2SH_mapping, const VectorType &coefs)
	scale the coefficients of each SH degree by the corresponding value in coefs More...
template<typename VectorType >
Eigen::Matrix< typename VectorType::Scalar, Eigen::Dynamic, 1 >	MR::Math::SH::invert (const VectorType &coefs)
	invert any non-zero coefficients in coefs More...
template<class VectorType >
VectorType::Scalar	MR::Math::SH::value (const VectorType &coefs, typename VectorType::Scalar cos_elevation, typename VectorType::Scalar cos_azimuth, typename VectorType::Scalar sin_azimuth, int lmax)
template<class VectorType >
VectorType::Scalar	MR::Math::SH::value (const VectorType &coefs, typename VectorType::Scalar cos_elevation, typename VectorType::Scalar azimuth, int lmax)
template<class VectorType1 , class VectorType2 >
VectorType1::Scalar	MR::Math::SH::value (const VectorType1 &coefs, const VectorType2 &unit_dir, int lmax)
template<class VectorType1 , class VectorType2 >
VectorType1 &	MR::Math::SH::delta (VectorType1 &delta_vec, const VectorType2 &unit_dir, int lmax)
template<class VectorType1 , class VectorType2 >
VectorType1 &	MR::Math::SH::SH2RH (VectorType1 &RH, const VectorType2 &sh)
template<class VectorType >
Eigen::Matrix< typename VectorType::Scalar, Eigen::Dynamic, 1 >	MR::Math::SH::SH2RH (const VectorType &sh)
template<class VectorType1 , class VectorType2 >
VectorType1 &	MR::Math::SH::sconv (VectorType1 &sh, const VectorType2 &RH)
	perform spherical convolution, in place More...
template<class VectorType1 , class VectorType2 , class VectorType3 >
VectorType1 &	MR::Math::SH::sconv (VectorType1 &C, const VectorType2 &RH, const VectorType3 &sh)
	perform spherical convolution More...
template<class MatrixType1 , class VectorType2 >
MatrixType1 &	MR::Math::SH::sconv_mat (MatrixType1 &sh, const VectorType2 &RH)
	perform spherical convolution, in place More...
template<class VectorType , class UnitVectorType , class ValueType = float>
VectorType::Scalar	MR::Math::SH::get_peak (const VectorType &sh, int lmax, UnitVectorType &unit_init_dir, PrecomputedAL< typename VectorType::Scalar > *precomputer=nullptr)
	estimate direction & amplitude of SH peak More...
template<class VectorType >
void	MR::Math::SH::derivatives (const VectorType &sh, const int lmax, const typename VectorType::Scalar elevation, const typename VectorType::Scalar azimuth, typename VectorType::Scalar &amplitude, typename VectorType::Scalar &dSH_del, typename VectorType::Scalar &dSH_daz, typename VectorType::Scalar &d2SH_del2, typename VectorType::Scalar &d2SH_deldaz, typename VectorType::Scalar &d2SH_daz2, PrecomputedAL< typename VectorType::Scalar > *precomputer)
	computes first and second order derivatives of SH series More...
template<class ImageType >
void	MR::Math::SH::check (const ImageType &H)
	convenience function to check if an input image can contain SH coefficients More...

Variables
const char *	MR::Math::SH::encoding_description
	a string containing a description of the SH storage convention More...

Macro Definition Documentation

ANGLE_TOLERANCE

#define ANGLE_TOLERANCE   1e-4

Definition at line 24 of file SH.h.

MAX_DIR_CHANGE

#define MAX_DIR_CHANGE   0.2

Definition at line 23 of file SH.h.