org.hps.recon.tracking.gbl.matrix

Class BorderedBandMatrix

java.lang.Object

org.hps.recon.tracking.gbl.matrix.BorderedBandMatrix

public class BorderedBandMatrix
extends Object

Separate storage of border, mixed and band parts (as vector). \verbatim 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. | +- -+ \endverbatim

Field Summary

Fields

Modifier and Type	Field and Description
private int	numBand
private int	numBorder
private int	numCol
private int	numSize
private VMatrix	theBand
private VSymMatrix	theBorder
private VMatrix	theMixed

Constructor Summary

Constructors

Constructor and Description
BorderedBandMatrix()

Method Summary

Modifier and Type	Method and Description
void	addBlockMatrix(double aWeight, int[] anIndex, double[] aVector) Add (extended) block matrix defined by 'aVector * aWeight * aVector.T' to bordered band matrix: BBmatrix(anIndex(i),anIndex(j)) += aVector(i) * aWeight * aVector(j).
private VMatrix	bandOfAVAT(VMatrix anArray, VSymMatrix aSymArray) \return Band part of product
private void	decomposeBand() Decompose band matrix into diagonal matrix D and lower triangular band matrix L (diagonal=1).
SymMatrix	getBlockMatrix(List<Integer> anIndex) Get (compressed) block from bordered band matrix: aMatrix(i,j) = BBmatrix(anIndex(i),anIndex(j)).
private VMatrix	invertBand() \return Inverted band
void	printMatrix()
void	resize(int nSize, int nBorder, int nBand) \param nSize [in] Size of matrix \param nBorder [in] Size of border (=1 for q/p + additional local parameters) \param nBand [in] Band width (usually = 5, for simplified jacobians = 4)
void	solveAndInvertBorderedBand(VVector aRightHandSide, VVector aSolution) Solve linear equation A*x=b system with bordered band matrix A, calculate bordered band part of inverse of A.
private VMatrix	solveBand(VMatrix aRightHandSide) Solve C*X=B for mixed part using decomposition C=LDL^T and forward and backward substitution.
private VVector	solveBand(VVector aRightHandSide) 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).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

numSize

private int numSize

numBorder

private int numBorder

numBand

private int numBand

numCol

private int numCol

theBorder

private VSymMatrix theBorder

theMixed

private VMatrix theMixed

theBand

private VMatrix theBand

Constructor Detail

BorderedBandMatrix

public BorderedBandMatrix()

Method Detail

resize

public void resize(int nSize,
                   int nBorder,
                   int nBand)

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

addBlockMatrix

public void addBlockMatrix(double aWeight,
                           int[] anIndex,
                           double[] aVector)

Add (extended) block matrix defined by 'aVector * aWeight * aVector.T' to bordered band matrix: BBmatrix(anIndex(i),anIndex(j)) += aVector(i) * aWeight * aVector(j). \param aWeight [in] Weight \param anIndex [in] List of rows/colums to be used \param aVector [in] Vector

getBlockMatrix

public SymMatrix getBlockMatrix(List<Integer> anIndex)

Get (compressed) block from bordered band matrix: aMatrix(i,j) = BBmatrix(anIndex(i),anIndex(j)). \param anIndex [in] List of rows/colums to be used

solveAndInvertBorderedBand

public void solveAndInvertBorderedBand(VVector aRightHandSide,
                                       VVector aSolution)

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

printMatrix

public void printMatrix()

decomposeBand

private void decomposeBand()

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

invertBand

private VMatrix invertBand()

\return Inverted band

solveBand

private VVector solveBand(VVector aRightHandSide)

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). \param [in] aRightHandSide Right hand side (vector) 'b' of C*x=b \return Solution (vector) 'x' of C*x=b

solveBand

private VMatrix solveBand(VMatrix aRightHandSide)

Solve C*X=B for mixed part using decomposition C=LDL^T and forward and backward substitution. \param [in] aRightHandSide Right hand side (matrix) 'B' of C*X=B \return Solution (matrix) 'X' of C*X=B

bandOfAVAT

private VMatrix bandOfAVAT(VMatrix anArray,
                           VSymMatrix aSymArray)

\return Band part of product