(Symmetric) Bordered Band Matrix. More...

#include <BorderedBandMatrix.h>

Collaboration diagram for BorderedBandMatrix:

[legend]

Public Member Functions
	BorderedBandMatrix ()
	Create bordered band matrix.

void	resize (unsigned int nSize, unsigned int nBorder=1, unsigned int nBand=5)
	Resize bordered band matrix. 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...

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

void	printMatrix () const
	Print bordered band matrix.

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.

unsigned int	numBorder
	Border size.

unsigned int	numBand
	Band width.

unsigned int	numCol
	Band matrix size.

VSymMatrix	theBorder
	Border part.

VMatrix	theMixed
	Mixed part.

VMatrix	theBand
	Band part.

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 79 of file BorderedBandMatrix.h.

Member Function Documentation

◆ addBlockMatrix()

void 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 68 of file BorderedBandMatrix.cc.

                                       {
   int nBorder = numBorder;
   for (unsigned int i = 0; i < anIndex->size(); ++i) {
     int iIndex = (*anIndex)[i] - 1; // anIndex has to be sorted
     for (unsigned int j = 0; j <= i; ++j) {
       int jIndex = (*anIndex)[j] - 1;
       if (iIndex < nBorder) {
         theBorder(iIndex, jIndex) += (*aVector)[i] * aWeight
             * (*aVector)[j];
       } else if (jIndex < nBorder) {
         theMixed(jIndex, iIndex - nBorder) += (*aVector)[i] * aWeight
             * (*aVector)[j];
       } else {
         unsigned int nBand = iIndex - jIndex;
         theBand(nBand, jIndex - nBorder) += (*aVector)[i] * aWeight
             * (*aVector)[j];
         numBand = std::max(numBand, nBand); // update band width
       }
     }
   }
 }

◆ bandOfAVAT()

VMatrix 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 316 of file BorderedBandMatrix.cc.

◆ decomposeBand()

void 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 199 of file BorderedBandMatrix.cc.

◆ getBlockMatrix()

TMatrixDSym 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 97 of file BorderedBandMatrix.cc.

◆ invertBand()

VMatrix invertBand ( )

private

Invert band part.

Returns: Inverted band

Definition at line 292 of file BorderedBandMatrix.cc.

◆ resize()

void resize	(	unsigned int	nSize,
		unsigned int	nBorder = `1`,
		unsigned int	nBand = `5`
	)

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)

Definition at line 48 of file BorderedBandMatrix.cc.

◆ solveAndInvertBorderedBand()

void 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 147 of file BorderedBandMatrix.cc.

◆ solveBand() [1/2]

VMatrix 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 263 of file BorderedBandMatrix.cc.

◆ solveBand() [2/2]

VVector 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 234 of file BorderedBandMatrix.cc.

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

genfit2/code2/GBL/include/BorderedBandMatrix.h
genfit2/code2/GBL/src/BorderedBandMatrix.cc

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Function Documentation

◆ addBlockMatrix()

◆ bandOfAVAT()

◆ decomposeBand()

◆ getBlockMatrix()

◆ invertBand()

◆ resize()

◆ solveAndInvertBorderedBand()

◆ solveBand() [1/2]

◆ solveBand() [2/2]