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gbl::BorderedBandMatrix Class Reference

(Symmetric) Bordered Band Matrix. More...

#include <GenFit/blob/master/GBL/include/BorderedBandMatrix.h>

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Public Member Functions

 BorderedBandMatrix ()
 Create bordered band matrix.
 
virtual ~BorderedBandMatrix ()
 
void resize (unsigned int nSize, unsigned int nBorder=1, unsigned int nBand=5)
 Resize bordered band matrix.
 
void solveAndInvertBorderedBand (const VVector &aRightHandSide, VVector &aSolution)
 Solve linear equation system, partially calculate inverse.
 
void addBlockMatrix (double aWeight, const std::vector< unsigned int > *anIndex, const std::vector< double > *aVector)
 Add symmetric block matrix.
 
TMatrixDSym getBlockMatrix (const std::vector< unsigned int > &anIndex) const
 Retrieve symmetric block matrix.
 
void printMatrix () const
 Print bordered band matrix.
 

Private Member Functions

void decomposeBand ()
 (root free) Cholesky decomposition of band part: C=LDL^T
 
VVector solveBand (const VVector &aRightHandSide) const
 Solve for band part.
 
VMatrix solveBand (const VMatrix &aRightHandSide) const
 solve band part for mixed part (border rows).
 
VMatrix invertBand ()
 Invert band part.
 
VMatrix bandOfAVAT (const VMatrix &anArray, const VSymMatrix &aSymArray) const
 Calculate band part of: 'anArray * aSymArray * anArray.T'.
 

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.

View newest version in sPHENIX GitHub at line 79 of file BorderedBandMatrix.h

Constructor & Destructor Documentation

gbl::BorderedBandMatrix::BorderedBandMatrix ( )

Create bordered band matrix.

Definition at line 36 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 36 of file BorderedBandMatrix.cc

gbl::BorderedBandMatrix::~BorderedBandMatrix ( )
virtual

Definition at line 39 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 39 of file BorderedBandMatrix.cc

Member Function Documentation

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 68 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 68 of file BorderedBandMatrix.cc

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

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

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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 316 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 316 of file BorderedBandMatrix.cc

References i, j, k, numBand, numBorder, numCol, and sum().

Referenced by solveAndInvertBorderedBand().

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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 199 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 199 of file BorderedBandMatrix.cc

References i, j, k, Acts::UnitConstants::min, numBand, numCol, and theBand.

Referenced by solveAndInvertBorderedBand().

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TMatrixDSym 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 97 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 97 of file BorderedBandMatrix.cc

References i, j, numBorder, theBand, theBorder, and theMixed.

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

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VMatrix gbl::BorderedBandMatrix::invertBand ( )
private

Invert band part.

Returns
Inverted band

Definition at line 292 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 292 of file BorderedBandMatrix.cc

References i, j, k, Acts::UnitConstants::min, numBand, numCol, and theBand.

Referenced by solveAndInvertBorderedBand().

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void gbl::BorderedBandMatrix::printMatrix ( ) const

Print bordered band matrix.

Definition at line 180 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 180 of file BorderedBandMatrix.cc

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

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

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void gbl::BorderedBandMatrix::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.

View newest version in sPHENIX GitHub at line 48 of file BorderedBandMatrix.cc

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

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

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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]aRightHandSideRight hand side (vector) 'b' of A*x=b
[out]aSolutionSolution (vector) x of A*x=b

Definition at line 147 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 147 of file BorderedBandMatrix.cc

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().

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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]aRightHandSideRight hand side (vector) 'b' of C*x=b
Returns
Solution (vector) 'x' of C*x=b

Definition at line 234 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 234 of file BorderedBandMatrix.cc

References gbl::VMatrix::getNumCols(), gbl::VMatrix::getNumRows(), i, j, Acts::UnitConstants::min, and theBand.

Referenced by solveAndInvertBorderedBand().

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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]aRightHandSideRight hand side (matrix) 'B' of C*X=B
Returns
Solution (matrix) 'X' of C*X=B

Definition at line 263 of file BorderedBandMatrix.cc.

View newest version in sPHENIX GitHub at line 263 of file BorderedBandMatrix.cc

References gbl::VMatrix::getNumCols(), gbl::VMatrix::getNumRows(), i, j, Acts::UnitConstants::min, numBorder, and theBand.

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Member Data Documentation

unsigned int gbl::BorderedBandMatrix::numBand
private

Band width.

Definition at line 96 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 96 of file BorderedBandMatrix.h

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

unsigned int gbl::BorderedBandMatrix::numBorder
private

Border size.

Definition at line 95 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 95 of file BorderedBandMatrix.h

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

unsigned int gbl::BorderedBandMatrix::numCol
private

Band matrix size.

Definition at line 97 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 97 of file BorderedBandMatrix.h

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

unsigned int gbl::BorderedBandMatrix::numSize
private

Matrix size.

Definition at line 94 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 94 of file BorderedBandMatrix.h

Referenced by resize().

VMatrix gbl::BorderedBandMatrix::theBand
private

Band part.

Definition at line 100 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 100 of file BorderedBandMatrix.h

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

VSymMatrix gbl::BorderedBandMatrix::theBorder
private

Border part.

Definition at line 98 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 98 of file BorderedBandMatrix.h

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

VMatrix gbl::BorderedBandMatrix::theMixed
private

Mixed part.

Definition at line 99 of file BorderedBandMatrix.h.

View newest version in sPHENIX GitHub at line 99 of file BorderedBandMatrix.h

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

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