(Symmetric) Bordered Band Matrix. More...

#include <BorderedBandMatrix.h>

Public Member Functions
	BorderedBandMatrix ()
	Create bordered band matrix. More...

virtual	~BorderedBandMatrix ()

void	resize (unsigned int nSize, unsigned int nBorder=1, unsigned int nBand=7)
	Resize bordered band matrix. More...

void	setZero ()
	Set content to 0. More...

void	solveAndInvertBorderedBand (const VVector &aRightHandSide, VVector &aSolution)
	Solve linear equation system, partially calculate inverse. More...

void	addBlockMatrix (double aWeight, const std::vector< unsigned int > anIndex, const std::vector< double > aVector)
	Add symmetric block matrix. More...

void	addBlockMatrix (double aWeight, unsigned int nSimple, unsigned int anIndex, double aVector)
	Add symmetric block matrix. More...

Eigen::MatrixXd	getBlockMatrix (const std::vector< unsigned int > anIndex) const
	Retrieve symmetric block matrix. More...

Eigen::MatrixXd	getBlockMatrix (unsigned int aSize, unsigned int *anIndex) const
	Retrieve symmetric block matrix. More...

void	printMatrix () const
	Print bordered band matrix. More...

double	getBandCondition () const
	Get condition from band (decomposition) More...

Private Member Functions
void	decomposeBand ()
	(root free) Cholesky decomposition of band part: C=LDL^T More...

VVector	solveBand (const VVector &aRightHandSide) const
	Solve for band part. More...

VMatrix	solveBand (const VMatrix &aRightHandSide) const
	solve band part for mixed part (border rows). More...

VMatrix	invertBand ()
	Invert band part. More...

VMatrix	bandOfAVAT (const VMatrix &anArray, const VSymMatrix &aSymArray) const
	Calculate band part of: 'anArray * aSymArray * anArray.T'. More...

Private Attributes
unsigned int	numSize
	Matrix size. More...

unsigned int	numBorder
	Border size. More...

unsigned int	numBand
	Band width. More...

unsigned int	numCol
	Band matrix size. More...

VSymMatrix	theBorder
	Border part. More...

VMatrix	theMixed
	Mixed part. More...

VMatrix	theBand
	Band part. More...

Detailed Description

(Symmetric) Bordered Band Matrix.

Separate storage of border, mixed and band parts (as vector<double>).

*  Example for matrix size=8 with border size and band width of two
*
*     +-                                 -+
*     |  B11 B12 M13 M14 M15 M16 M17 M18  |
*     |  B12 B22 M23 M24 M25 M26 M27 M28  |
*     |  M13 M23 C33 C34 C35  0.  0.  0.  |
*     |  M14 M24 C34 C44 C45 C46  0.  0.  |
*     |  M15 M25 C35 C45 C55 C56 C57  0.  |
*     |  M16 M26  0. C46 C56 C66 C67 C68  |
*     |  M17 M27  0.  0. C57 C67 C77 C78  |
*     |  M18 M28  0.  0.  0. C68 C78 C88  |
*     +-                                 -+
*
*  Is stored as::
*
*     +-         -+     +-                         -+
*     |  B11 B12  |     |  M13 M14 M15 M16 M17 M18  |
*     |  B12 B22  |     |  M23 M24 M25 M26 M27 M28  |
*     +-         -+     +-                         -+
*
*                       +-                         -+
*                       |  C33 C44 C55 C66 C77 C88  |
*                       |  C34 C45 C56 C67 C78  0.  |
*                       |  C35 C46 C57 C68  0.  0.  |
*                       +-                         -+
*

Definition at line 76 of file BorderedBandMatrix.h.

Constructor & Destructor Documentation

◆ BorderedBandMatrix()

gbl::BorderedBandMatrix::BorderedBandMatrix ( )

Create bordered band matrix.

Definition at line 37 of file BorderedBandMatrix.cpp.

◆ ~BorderedBandMatrix()

gbl::BorderedBandMatrix::~BorderedBandMatrix ( )

virtual

Definition at line 41 of file BorderedBandMatrix.cpp.

Member Function Documentation

◆ addBlockMatrix() [1/2]

void gbl::BorderedBandMatrix::addBlockMatrix	(	double	aWeight,
		const std::vector< unsigned int > *	anIndex,
		const std::vector< double > *	aVector
	)

Add symmetric block matrix.

Add (extended) block matrix defined by 'aVector * aWeight * aVector.T' to bordered band matrix: BBmatrix(anIndex(i),anIndex(j)) += aVector(i) * aWeight * aVector(j).

Parameters

aWeight	[in] Weight
anIndex	[in] List of rows/colums to be used
aVector	[in] Vector

Definition at line 77 of file BorderedBandMatrix.cpp.

References numBand, numBorder, theBand, theBorder, and theMixed.

Referenced by gbl::GblTrajectory::buildLinearEquationSystem().

◆ addBlockMatrix() [2/2]

void gbl::BorderedBandMatrix::addBlockMatrix	(	double	aWeight,
		unsigned int	aSize,
		unsigned int *	anIndex,
		double *	aVector
	)

Add symmetric block matrix.

Add (extended) block matrix defined by 'aVector * aWeight * aVector.T' to bordered band matrix: BBmatrix(anIndex(i),anIndex(j)) += aVector(i) * aWeight * aVector(j).

Parameters

aWeight	[in] Weight
aSize	[in] Size of block matrix
anIndex	[in] List of rows/colums to be used
aVector	[in] Vector

Definition at line 111 of file BorderedBandMatrix.cpp.

References numBand, numBorder, theBand, theBorder, and theMixed.

◆ bandOfAVAT()

VMatrix gbl::BorderedBandMatrix::bandOfAVAT	(	const VMatrix &	anArray,
		const VSymMatrix &	aSymArray
	)		const

private

Calculate band part of: 'anArray * aSymArray * anArray.T'.

Returns: Band part of product

Definition at line 398 of file BorderedBandMatrix.cpp.

References numBand, numBorder, and numCol.

Referenced by solveAndInvertBorderedBand().

◆ decomposeBand()

void gbl::BorderedBandMatrix::decomposeBand ( )

private

(root free) Cholesky decomposition of band part: C=LDL^T

Decompose band matrix into diagonal matrix D and lower triangular band matrix L (diagonal=1). Overwrite band matrix with D and off-diagonal part of L.

Exceptions

2	: matrix is singular.
3	: matrix is not positive definite.

Definition at line 281 of file BorderedBandMatrix.cpp.

References numBand, numCol, and theBand.

Referenced by solveAndInvertBorderedBand().

◆ getBandCondition()

double gbl::BorderedBandMatrix::getBandCondition ( ) const

Get condition from band (decomposition)

Definition at line 260 of file BorderedBandMatrix.cpp.

References numCol, and theBand.

Referenced by gbl::GblTrajectory::getBandCondition().

◆ getBlockMatrix() [1/2]

MatrixXd gbl::BorderedBandMatrix::getBlockMatrix ( const std::vector< unsigned int > anIndex ) const

Retrieve symmetric block matrix.

Get (compressed) block from bordered band matrix: aMatrix(i,j) = BBmatrix(anIndex(i),anIndex(j)).

Parameters

anIndex [in] List of rows/colums to be used

Definition at line 138 of file BorderedBandMatrix.cpp.

References numBorder, theBand, theBorder, and theMixed.

Referenced by gbl::GblTrajectory::getExtResults(), gbl::GblTrajectory::getResAndErr(), and gbl::GblTrajectory::getResults().

◆ getBlockMatrix() [2/2]

MatrixXd gbl::BorderedBandMatrix::getBlockMatrix	(	unsigned int	aSize,
		unsigned int *	anIndex
	)		const

Retrieve symmetric block matrix.

Get (compressed) block from bordered band matrix: aMatrix(i,j) = BBmatrix(anIndex(i),anIndex(j)).

Parameters

aSize	[in] Matrix size
anIndex	[in] Array of rows/colums to be used

Definition at line 167 of file BorderedBandMatrix.cpp.

References numBorder, theBand, theBorder, and theMixed.

◆ invertBand()

VMatrix gbl::BorderedBandMatrix::invertBand ( )

private

Invert band part.

Returns: Inverted band

Definition at line 374 of file BorderedBandMatrix.cpp.

References numBand, numCol, and theBand.

Referenced by solveAndInvertBorderedBand().

◆ printMatrix()

void gbl::BorderedBandMatrix::printMatrix ( ) const

Print bordered band matrix.

Definition at line 250 of file BorderedBandMatrix.cpp.

References gbl::VMatrix::print(), gbl::VSymMatrix::print(), theBand, theBorder, and theMixed.

Referenced by gbl::GblTrajectory::printTrajectory().

◆ resize()

void gbl::BorderedBandMatrix::resize	(	unsigned int	nSize,
		unsigned int	nBorder = `1`,
		unsigned int	nBand = `7`
	)

Resize bordered band matrix.

Parameters

nSize	[in] Size of matrix
nBorder	[in] Size of border (=1 for q/p + additional local parameters)
nBand	[in] Band width (usually = 5, for simplified jacobians = 4, +2 for steps)

Definition at line 50 of file BorderedBandMatrix.cpp.

References numBand, numBorder, numCol, numSize, gbl::VSymMatrix::resize(), gbl::VMatrix::resize(), theBand, theBorder, and theMixed.

Referenced by gbl::GblTrajectory::buildLinearEquationSystem().

◆ setZero()

void gbl::BorderedBandMatrix::setZero ( )

Set content to 0.

Definition at line 62 of file BorderedBandMatrix.cpp.

References gbl::VMatrix::setZero(), gbl::VSymMatrix::setZero(), theBand, theBorder, and theMixed.

Referenced by gbl::GblTrajectory::buildLinearEquationSystem().

◆ solveAndInvertBorderedBand()

void gbl::BorderedBandMatrix::solveAndInvertBorderedBand	(	const VVector &	aRightHandSide,
		VVector &	aSolution
	)

Solve linear equation system, partially calculate inverse.

Solve linear equation A*x=b system with bordered band matrix A, calculate bordered band part of inverse of A. Use decomposition in border and band part for block matrix algebra:

| A  Ct |   | x1 |   | b1 |        , A  is the border part
|       | * |    | = |    |        , Ct is the mixed part
| C  D  |   | x2 |   | b2 |        , D  is the band part

Explicit inversion of D is avoided by using solution X of D*X=C (X=D^-1*C, obtained from Cholesky decomposition and forward/backward substitution)

| x1 |   | E*b1 - E*Xt*b2 |        , E^-1 = A-Ct*D^-1*C = A-Ct*X
|    | = |                |
| x2 |   |  x   - X*x1    |        , x is solution of D*x=b2 (x=D^-1*b2)

Inverse matrix is:

|  E   -E*Xt          |
|                     |            , only band part of (D^-1 + X*E*Xt)
| -X*E  D^-1 + X*E*Xt |              is calculated

Parameters

[in]	aRightHandSide	Right hand side (vector) 'b' of A*x=b
[out]	aSolution	Solution (vector) x of A*x=b

Definition at line 217 of file BorderedBandMatrix.cpp.

References bandOfAVAT(), decomposeBand(), gbl::VVector::getVec(), gbl::VSymMatrix::invert(), invertBand(), numBorder, numCol, gbl::VVector::putVec(), solveBand(), theBand, theBorder, theMixed, and gbl::VMatrix::transpose().

Referenced by gbl::GblTrajectory::fit().

◆ solveBand() [1/2]

VMatrix gbl::BorderedBandMatrix::solveBand ( const VMatrix & aRightHandSide ) const

private

solve band part for mixed part (border rows).

Solve C*X=B for mixed part using decomposition C=LDL^T and forward and backward substitution.

Parameters

[in] aRightHandSide Right hand side (matrix) 'B' of C*X=B

Returns: Solution (matrix) 'X' of C*X=B

Definition at line 345 of file BorderedBandMatrix.cpp.

References gbl::VMatrix::getNumCols(), gbl::VMatrix::getNumRows(), numBorder, and theBand.

◆ solveBand() [2/2]

VVector gbl::BorderedBandMatrix::solveBand ( const VVector & aRightHandSide ) const

private

Solve for band part.

Solve C*x=b for band part using decomposition C=LDL^T and forward (L*z=b) and backward substitution (L^T*x=D^-1*z).

Parameters

[in] aRightHandSide Right hand side (vector) 'b' of C*x=b

Returns: Solution (vector) 'x' of C*x=b

Definition at line 316 of file BorderedBandMatrix.cpp.

References gbl::VMatrix::getNumCols(), gbl::VMatrix::getNumRows(), and theBand.

Referenced by solveAndInvertBorderedBand().

Member Data Documentation

◆ numBand

unsigned int gbl::BorderedBandMatrix::numBand

private

Band width.

Definition at line 100 of file BorderedBandMatrix.h.

Referenced by addBlockMatrix(), bandOfAVAT(), decomposeBand(), invertBand(), and resize().

◆ numBorder

unsigned int gbl::BorderedBandMatrix::numBorder

private

Border size.

Definition at line 99 of file BorderedBandMatrix.h.

Referenced by addBlockMatrix(), bandOfAVAT(), getBlockMatrix(), resize(), solveAndInvertBorderedBand(), and solveBand().

◆ numCol

unsigned int gbl::BorderedBandMatrix::numCol

private

Band matrix size.

Definition at line 101 of file BorderedBandMatrix.h.

Referenced by bandOfAVAT(), decomposeBand(), getBandCondition(), invertBand(), resize(), and solveAndInvertBorderedBand().

◆ numSize

unsigned int gbl::BorderedBandMatrix::numSize

private

Matrix size.

Definition at line 98 of file BorderedBandMatrix.h.

Referenced by resize().

◆ theBand

VMatrix gbl::BorderedBandMatrix::theBand

private

Band part.

Definition at line 104 of file BorderedBandMatrix.h.

Referenced by addBlockMatrix(), decomposeBand(), getBandCondition(), getBlockMatrix(), invertBand(), printMatrix(), resize(), setZero(), solveAndInvertBorderedBand(), and solveBand().

◆ theBorder

VSymMatrix gbl::BorderedBandMatrix::theBorder

private

Border part.

Definition at line 102 of file BorderedBandMatrix.h.

Referenced by addBlockMatrix(), getBlockMatrix(), printMatrix(), resize(), setZero(), and solveAndInvertBorderedBand().

◆ theMixed

VMatrix gbl::BorderedBandMatrix::theMixed

private

Mixed part.

Definition at line 103 of file BorderedBandMatrix.h.

Referenced by addBlockMatrix(), getBlockMatrix(), printMatrix(), resize(), setZero(), and solveAndInvertBorderedBand().

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

src/BorderedBandMatrix.h
src/BorderedBandMatrix.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BorderedBandMatrix()

◆ ~BorderedBandMatrix()

Member Function Documentation

◆ addBlockMatrix() [1/2]

◆ addBlockMatrix() [2/2]

◆ bandOfAVAT()

◆ decomposeBand()

◆ getBandCondition()

◆ getBlockMatrix() [1/2]

◆ getBlockMatrix() [2/2]

◆ invertBand()

◆ printMatrix()

◆ resize()

◆ setZero()

◆ solveAndInvertBorderedBand()

◆ solveBand() [1/2]

◆ solveBand() [2/2]

Member Data Documentation

◆ numBand

◆ numBorder

◆ numCol

◆ numSize

◆ theBand

◆ theBorder

◆ theMixed