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

#include <SurgSim/Math/LinearSolveAndInverse.h>

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

Public Member Functions
void	setMatrix (const Matrix &matrix) override
	Set the linear solver matrix. More...

Vector	solve (const Vector &b) override
	Solve the linear system (matrix.x=b) using the matrix provided by the latest setMatrix call. More...

Matrix	getInverse () override

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<size_t 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

◆ Block

template<size_t BlockSize>

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

private

Member Function Documentation

◆ Bi()

template<size_t 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))

◆ getInverse()

template<size_t BlockSize>

Matrix SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::getInverse ( )

overridevirtual

Returns: The linear system's inverse matrix, i.e. the inverse of the matrix provided on the last setMatrix call

Implements SurgSim::Math::LinearSolveAndInverse.

◆ inverseTriDiagonalBlock()

template<size_t 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

◆ minusAi()

template<size_t 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))

◆ minusCi()

template<size_t 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))

◆ setMatrix()

template<size_t BlockSize>

void SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::setMatrix ( const Matrix & matrix )

overridevirtual

Set the linear solver matrix.

Parameters

matrix the new matrix to solve/inverse for

Implements SurgSim::Math::LinearSolveAndInverse.

Reimplemented in SurgSim::Math::LinearSolveAndInverseSymmetricTriDiagonalBlockMatrix< BlockSize >.

◆ solve()

template<size_t BlockSize>

Vector SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::solve ( const Vector & b )

overridevirtual

Solve the linear system (matrix.x=b) using the matrix provided by the latest setMatrix call.

Parameters

b	The rhs vector

Returns: The solution vector

Implements SurgSim::Math::LinearSolveAndInverse.

Member Data Documentation

◆ m_Bi_AiDiminus1_inv

template<size_t BlockSize>

std::vector<Block> SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::m_Bi_AiDiminus1_inv

private

Intermediate block matrices, helpful to construct the inverse matrix

◆ m_Di

template<size_t BlockSize>

std::vector<Block> SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::m_Di

private

Intermediate block matrices, helpful to construct the inverse matrix

◆ m_Ei

template<size_t BlockSize>

std::vector<Block> SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::m_Ei

private

Intermediate block matrices, helpful to construct the inverse matrix

◆ m_inverse

template<size_t BlockSize>

Matrix SurgSim::Math::LinearSolveAndInverseTriDiagonalBlockMatrix< BlockSize >::m_inverse

protected

Member variable to hold the inverse matrix in case only the solving is requested.

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

SurgSim/Math/LinearSolveAndInverse.h
SurgSim/Math/LinearSolveAndInverse-inl.h

Public Member Functions

Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Private Attributes

Detailed Description

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

Member Typedef Documentation

◆ Block

Member Function Documentation

◆ Bi()

◆ getInverse()

◆ inverseTriDiagonalBlock()

◆ minusAi()

◆ minusCi()

◆ setMatrix()

◆ solve()

Member Data Documentation

◆ m_Bi_AiDiminus1_inv

◆ m_Di

◆ m_Ei

◆ m_inverse

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