Derivation for tri-diagonal block matrix type. More...

#include <SurgSim/Math/LinearSolveAndInverse.h>

Inheritance diagram for SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >:

Public Member Functions
virtual void	operator() (const Matrix &A, const Vector &b, Vector x=nullptr, Matrix Ainv=nullptr) override
	Solve a linear system A.x=b and compute the matrix A^-1. More...

Public Member Functions inherited from SurgSim::Math::LinearSolveAndInverse
virtual	~LinearSolveAndInverse ()

Protected Member Functions
void	inverseTriDiagonalBlock (const SurgSim::Math::Matrix &A, SurgSim::Math::Matrix *inv, bool isSymmetric=false)
	Computes the inverse matrix. More...

Protected Attributes
Matrix	m_inverse
	Member variable to hold the inverse matrix in case only the solving is requested. More...

Private Types
typedef Eigen::Matrix< Matrix::Scalar, BlockSize, BlockSize, Matrix::Options >	Block

Private Member Functions
const Eigen::Block< const Matrix, BlockSize, BlockSize >	minusAi (const SurgSim::Math::Matrix &A, size_t i) const
	Gets a lower-diagonal block element (named -Ai in the algorithm) More...

const Eigen::Block< const Matrix, BlockSize, BlockSize >	Bi (const SurgSim::Math::Matrix &A, size_t i) const
	Gets a diagonal block element (named Bi in the algorithm) More...

const Eigen::Block< const Matrix, BlockSize, BlockSize >	minusCi (const SurgSim::Math::Matrix &A, size_t i) const
	Gets a upper-diagonal block element (named -Ci in the algorithm) More...

Private Attributes

std::vector< Block >	m_Di

std::vector< Block >	m_Ei

std::vector< Block >	m_Bi_AiDiminus1_inv

Detailed Description

template<int BlockSize>
class SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >

Derivation for tri-diagonal block matrix type.

Template Parameters

BlockSize Define the block size of the tri-diagonal block matrix

Member Typedef Documentation

template<int BlockSize>

typedef Eigen::Matrix<Matrix::Scalar, BlockSize, BlockSize, Matrix::Options> SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::Block

private

Member Function Documentation

template<int BlockSize>

const Eigen::Block< const Matrix, BlockSize, BlockSize > SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::Bi	(	const SurgSim::Math::Matrix &	A,
		size_t	i
	)		const

private

Gets a diagonal block element (named Bi in the algorithm)

Parameters

A	The matrix on which to retrieve the diagonal block element
i	The line index on which to retrieve the diagonal block element

Returns: The diagonal block element requested (i.e. block (i, i))

template<int BlockSize>

void SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::inverseTriDiagonalBlock	(	const SurgSim::Math::Matrix &	A,
		SurgSim::Math::Matrix *	inv,
		bool	isSymmetric = `false`
	)

protected

Computes the inverse matrix.

Parameters

	A	The matrix to inverse
[out]	inv	The inverse matrix
	isSymmetric	True if the matrix is symmetric, False otherwise

Note: isSymmetric is only indicative and helps optimizing the computation when the matrix is symmetric.; On the other side, if the flag is true and the matrix is not symmetric, the result will be wrong.; Assert on inverse matrix pointer (inv), on the matrix being square and on; proper size matching between the matrix size and the blockSize

template<int BlockSize>

const Eigen::Block< const Matrix, BlockSize, BlockSize > SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::minusAi	(	const SurgSim::Math::Matrix &	A,
		size_t	i
	)		const

private

Gets a lower-diagonal block element (named -Ai in the algorithm)

Parameters

A	The matrix on which to retrieve the lower-diagonal block element
i	The line index on which to retrieve the lower-diagonal block element

Returns: The lower-diagonal block element requested (i.e. block (i, i-1))

template<int BlockSize>

const Eigen::Block< const Matrix, BlockSize, BlockSize > SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::minusCi	(	const SurgSim::Math::Matrix &	A,
		size_t	i
	)		const

private

Gets a upper-diagonal block element (named -Ci in the algorithm)

Parameters

A	The matrix on which to retrieve the upper-diagonal block element
i	The line index on which to retrieve the upper-diagonal block element

Returns: The upper-diagonal block element requested (i.e. block (i, i+1))

template<int BlockSize>

void SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::operator()	(	const Matrix &	A,
		const Vector &	b,
		Vector *	x = `nullptr`,
		Matrix *	Ainv = `nullptr`
	)

overridevirtual

Solve a linear system A.x=b and compute the matrix A^-1.

Parameters

	A	Linear system matrix
	b	Linear system right-hand-side
[out]	x	Linear system unknown (if requested)
[out]	Ainv	Linear system matrix inverse = A^-1 (if requested)