#include <VNLSparseLUSolverTraits.h>

Public Types
using	MatrixType = vnl_sparse_matrix< ValueType >

using	SolverType = vnl_sparse_lu

using	ValueType = T

using	VectorType = vnl_vector< ValueType >

Static Public Member Functions
static void	AddToMatrix (MatrixType &iA, const unsigned int &iR, const unsigned int &iC, const ValueType &iV)

static void	FillMatrix (MatrixType &iA, const unsigned int &iR, const unsigned int &iC, const ValueType &iV)

static MatrixType	InitializeSparseMatrix (const unsigned int &iN)

static MatrixType	InitializeSparseMatrix (const unsigned int &iRow, const unsigned int &iCol)

static VectorType	InitializeVector (const unsigned int &iN)

static bool	IsDirectSolver ()

static bool	Solve (const MatrixType &iA, const VectorType &iB, VectorType &oX)

static bool	Solve (const MatrixType &iA, const VectorType &iBx, const VectorType &iBy, const VectorType &iBz, VectorType &oX, VectorType &oY, VectorType &oZ)

static bool	Solve (const MatrixType &iA, const VectorType &iBx, const VectorType &iBy, VectorType &oX, VectorType &oY)

static void	Solve (SolverType &solver, const VectorType &iB, VectorType &oX)

static void	Solve (SolverType &solver, const VectorType &iBx, const VectorType &iBy, const VectorType &iBz, VectorType &oX, VectorType &oY, VectorType &oZ)

static void	Solve (SolverType &solver, const VectorType &iBx, const VectorType &iBy, VectorType &oX, VectorType &oY)

Detailed Description

template<typename T = double>
class VNLSparseLUSolverTraits< T >

Generic interface for sparse LU solver.

This generic interface (common to several sparse solvers), allow to interchange solver solutions when dealing with sparse linear systems. See itk::ParameterizationQuadEdgeMeshFilter for reference.

It internally uses the VNL library to represent and deal with vectors (vnl_vector) and sparse matrices (vnl_sparse_matrix). The solver by itself is made of a sparse LU decomposition followed by solving upper triangular system. see vnl_sparse_lu for more details on the method used.

See also: VNLIterativeSparseSolverTraits:w

Definition at line 42 of file VNLSparseLUSolverTraits.h.

Member Typedef Documentation

◆ MatrixType

template<typename T = double>

using VNLSparseLUSolverTraits< T >::MatrixType = vnl_sparse_matrix<ValueType>

Definition at line 46 of file VNLSparseLUSolverTraits.h.

◆ SolverType

template<typename T = double>

using VNLSparseLUSolverTraits< T >::SolverType = vnl_sparse_lu

Definition at line 48 of file VNLSparseLUSolverTraits.h.

◆ ValueType

template<typename T = double>

using VNLSparseLUSolverTraits< T >::ValueType = T

Definition at line 45 of file VNLSparseLUSolverTraits.h.

◆ VectorType

template<typename T = double>

using VNLSparseLUSolverTraits< T >::VectorType = vnl_vector<ValueType>

Definition at line 47 of file VNLSparseLUSolverTraits.h.

Member Function Documentation

◆ AddToMatrix()

template<typename T = double>

static void VNLSparseLUSolverTraits< T >::AddToMatrix	(	MatrixType &	iA,
		const unsigned int &	iR,
		const unsigned int &	iC,
		const ValueType &	iV
	)

inlinestatic

iA[iR][iC] += iV

Definition at line 87 of file VNLSparseLUSolverTraits.h.

◆ FillMatrix()

template<typename T = double>

static void VNLSparseLUSolverTraits< T >::FillMatrix	(	MatrixType &	iA,
		const unsigned int &	iR,
		const unsigned int &	iC,
		const ValueType &	iV
	)

inlinestatic

iA[iR][iC] = iV

Definition at line 80 of file VNLSparseLUSolverTraits.h.

◆ InitializeSparseMatrix() [1/2]

template<typename T = double>

static MatrixType VNLSparseLUSolverTraits< T >::InitializeSparseMatrix ( const unsigned int & iN )

inlinestatic

initialize a square sparse matrix of size iN x iN

Definition at line 59 of file VNLSparseLUSolverTraits.h.

◆ InitializeSparseMatrix() [2/2]

template<typename T = double>

static MatrixType VNLSparseLUSolverTraits< T >::InitializeSparseMatrix	(	const unsigned int &	iRow,
		const unsigned int &	iCol
	)

inlinestatic

initialize a sparse matrix of size iRow x iCol

Definition at line 66 of file VNLSparseLUSolverTraits.h.

◆ InitializeVector()

template<typename T = double>

static VectorType VNLSparseLUSolverTraits< T >::InitializeVector ( const unsigned int & iN )

inlinestatic

initialize a vector of size iN

Definition at line 73 of file VNLSparseLUSolverTraits.h.

◆ IsDirectSolver()

template<typename T = double>

static bool VNLSparseLUSolverTraits< T >::IsDirectSolver ( )

inlinestatic

Returns: false (it is not a direct solver, it is an iterative solver)

Definition at line 52 of file VNLSparseLUSolverTraits.h.

◆ Solve() [1/6]

template<typename T = double>

static bool VNLSparseLUSolverTraits< T >::Solve	(	const MatrixType &	iA,
		const VectorType &	iB,
		VectorType &	oX
	)

inlinestatic

Solve the linear system $iA \cdot oX = iB$ .

Definition at line 94 of file VNLSparseLUSolverTraits.h.

Referenced by VNLSparseLUSolverTraits< T >::Solve().

◆ Solve() [2/6]

template<typename T = double>

static bool VNLSparseLUSolverTraits< T >::Solve	(	const MatrixType &	iA,
		const VectorType &	iBx,
		const VectorType &	iBy,
		const VectorType &	iBz,
		VectorType &	oX,
		VectorType &	oY,
		VectorType &	oZ
	)

inlinestatic

Solve the linear systems: $iA \cdot oX = iBx$ , $iA \cdot oY = iBy$ , $iA \cdot oZ = iBz$ .

Definition at line 105 of file VNLSparseLUSolverTraits.h.

References VNLSparseLUSolverTraits< T >::Solve().

◆ Solve() [3/6]

template<typename T = double>

static bool VNLSparseLUSolverTraits< T >::Solve	(	const MatrixType &	iA,
		const VectorType &	iBx,
		const VectorType &	iBy,
		VectorType &	oX,
		VectorType &	oY
	)

inlinestatic

Solve the linear systems: $iA \cdot oX = iBx$ , $iA \cdot oY = iBy$ .

Definition at line 121 of file VNLSparseLUSolverTraits.h.

References VNLSparseLUSolverTraits< T >::Solve().

◆ Solve() [4/6]

template<typename T = double>

static void VNLSparseLUSolverTraits< T >::Solve	(	SolverType &	solver,
		const VectorType &	iB,
		VectorType &	oX
	)

inlinestatic

Solve the linear system $iA \cdot oX = iB$ factoring the internal matrix if needed.

Definition at line 131 of file VNLSparseLUSolverTraits.h.

◆ Solve() [5/6]

template<typename T = double>

static void VNLSparseLUSolverTraits< T >::Solve	(	SolverType &	solver,
		const VectorType &	iBx,
		const VectorType &	iBy,
		const VectorType &	iBz,
		VectorType &	oX,
		VectorType &	oY,
		VectorType &	oZ
	)

inlinestatic

Solve the linear systems: $iA \cdot oX = iBx$ , $iA \cdot oY = iBy$ , $iA \cdot oZ = iBz$ factoring the internal matrix if needed.

Definition at line 139 of file VNLSparseLUSolverTraits.h.

◆ Solve() [6/6]

template<typename T = double>

static void VNLSparseLUSolverTraits< T >::Solve	(	SolverType &	solver,
		const VectorType &	iBx,
		const VectorType &	iBy,
		VectorType &	oX,
		VectorType &	oY
	)

inlinestatic

Solve the linear systems: $iA \cdot oX = iBx$ , $iA \cdot oY = iBy$ factoring the internal matrix if needed.

Definition at line 155 of file VNLSparseLUSolverTraits.h.

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

VNLSparseLUSolverTraits.h

Public Types

Static Public Member Functions

Detailed Description

template<typename T = double> class VNLSparseLUSolverTraits< T >

Member Typedef Documentation

◆ MatrixType

◆ SolverType

◆ ValueType

◆ VectorType

Member Function Documentation

◆ AddToMatrix()

◆ FillMatrix()

◆ InitializeSparseMatrix() [1/2]

◆ InitializeSparseMatrix() [2/2]

◆ InitializeVector()

◆ IsDirectSolver()

◆ Solve() [1/6]

◆ Solve() [2/6]

◆ Solve() [3/6]

◆ Solve() [4/6]

◆ Solve() [5/6]

◆ Solve() [6/6]

template<typename T = double>
class VNLSparseLUSolverTraits< T >