gbl::VSymMatrix Class Reference

Simple symmetric Matrix based on std::vector<double> More...

#include <VMatrix.h>

Public Member Functions
unsigned int	getNumRows () const
	Get number of rows (= number of colums). More...
unsigned int	invert ()
	Matrix inversion. More...
double &	operator() (unsigned int i, unsigned int j)
	access element (i,j) assuming i>=j More...
double	operator() (unsigned int i, unsigned int j) const
	access element (i,j) assuming i>=j More...
VVector	operator* (const VVector &aVector) const
	Multiplication SymMatrix*Vector. More...
VMatrix	operator* (const VMatrix &aMatrix) const
	Multiplication SymMatrix*Matrix. More...
VSymMatrix	operator- (const VMatrix &aMatrix) const
	Subtraction SymMatrix-(sym)Matrix. More...
void	print () const
	Print matrix. More...
void	resize (const unsigned int nRows)
	Resize symmetric matrix. More...
	VSymMatrix (const unsigned int nRows=0)
virtual	~VSymMatrix ()

Private Attributes
unsigned int	numRows
	Number of rows. More...
std::vector< double >	theVec
	Data (symmetric storage) More...

Detailed Description

Simple symmetric Matrix based on std::vector<double>

Definition at line 64 of file VMatrix.h.

Constructor & Destructor Documentation

gbl::VSymMatrix::VSymMatrix

(

const unsigned int

nRows = 0

)

Definition at line 142 of file VMatrix.cc.

                                               :
        numRows(nRows), theVec((nRows * nRows + nRows) / 2) {
}

gbl::VSymMatrix::~VSymMatrix ( )

virtual

Definition at line 146 of file VMatrix.cc.

                        {
}

Member Function Documentation

unsigned int gbl::VSymMatrix::getNumRows

(

)

const

Get number of rows (= number of colums).

Returns

Number of rows.

Definition at line 162 of file VMatrix.cc.

References numRows.

                                          {
    return numRows;
}

unsigned int gbl::VSymMatrix::invert

(

)

Matrix inversion.

Invert symmetric N-by-N matrix V in symmetric storage mode V(1) = V11, V(2) = V12, V(3) = V22, V(4) = V13, . . . replaced by inverse matrix

Method of solution is by elimination selecting the pivot on the diagonal each stage. The rank of the matrix is returned in NRANK. For NRANK ne N, all remaining rows and cols of the resulting matrix V are set to zero.

Exceptions

1	: matrix is singular.

Returns

Rank of matrix.

Definition at line 326 of file VMatrix.cc.

References plotBeamSpotDB::first, i, j, findQualityFiles::jj, relval_2017::k, GetRecoTauVFromDQM_MC_cff::kk, cmsLHEtoEOSManager::l, plotBeamSpotDB::last, bookConverter::max, GetRecoTauVFromDQM_MC_cff::next, numRows, and theVec.

Referenced by gbl::BorderedBandMatrix::solveAndInvertBorderedBand().

                                {

    const double eps = 1.0E-10;
    unsigned int aSize = numRows;
    std::vector<int> next(aSize);
    std::vector<double> diag(aSize);
    int nSize = aSize;

    int first = 1;
    for (int i = 1; i <= nSize; ++i) {
        next[i - 1] = i + 1; // set "next" pointer
        diag[i - 1] = fabs(theVec[(i * i + i) / 2 - 1]); // save abs of diagonal elements
    }
    next[aSize - 1] = -1; // end flag

    unsigned int nrank = 0;
    for (int i = 1; i <= nSize; ++i) { // start of loop
        int k = 0;
        double vkk = 0.0;

        int j = first;
        int previous = 0;
        int last = previous;
        // look for pivot
        while (j > 0) {
            int jj = (j * j + j) / 2 - 1;
            if (fabs(theVec[jj]) > std::max(fabs(vkk), eps * diag[j - 1])) {
                vkk = theVec[jj];
                k = j;
                last = previous;
            }
            previous = j;
            j = next[j - 1];
        }
        // pivot found
        if (k > 0) {
            int kk = (k * k + k) / 2 - 1;
            if (last <= 0) {
                first = next[k - 1];
            } else {
                next[last - 1] = next[k - 1];
            }
            next[k - 1] = 0; // index is used, reset
            nrank++; // increase rank and ...

            vkk = 1.0 / vkk;
            theVec[kk] = -vkk;
            int jk = kk - k;
            int jl = -1;
            for (int j = 1; j <= nSize; ++j) { // elimination
                if (j == k) {
                    jk = kk;
                    jl += j;
                } else {
                    if (j < k) {
                        ++jk;
                    } else {
                        jk += j - 1;
                    }

                    double vjk = theVec[jk];
                    theVec[jk] = vkk * vjk;
                    int lk = kk - k;
                    if (j >= k) {
                        for (int l = 1; l <= k - 1; ++l) {
                            ++jl;
                            ++lk;
                            theVec[jl] -= theVec[lk] * vjk;
                        }
                        ++jl;
                        lk = kk;
                        for (int l = k + 1; l <= j; ++l) {
                            ++jl;
                            lk += l - 1;
                            theVec[jl] -= theVec[lk] * vjk;
                        }
                    } else {
                        for (int l = 1; l <= j; ++l) {
                            ++jl;
                            ++lk;
                            theVec[jl] -= theVec[lk] * vjk;
                        }
                    }
                }
            }
        } else {
            for (int k = 1; k <= nSize; ++k) {
                if (next[k - 1] >= 0) {
                    int kk = (k * k - k) / 2 - 1;
                    for (int j = 1; j <= nSize; ++j) {
                        if (next[j - 1] >= 0) {
                            theVec[kk + j] = 0.0; // clear matrix row/col
                        }
                    }
                }
            }
            throw 1; // singular
        }
    }
    for (int ij = 0; ij < (nSize * nSize + nSize) / 2; ++ij) {
        theVec[ij] = -theVec[ij]; // finally reverse sign of all matrix elements
    }
    return nrank;
}

double & gbl::VSymMatrix::operator() ( unsigned int  i, unsigned int  j  )

inline

access element (i,j) assuming i>=j

Definition at line 103 of file VMatrix.h.

References theVec.

                                                                          {
    return theVec[(iRow * iRow + iRow) / 2 + iCol]; // assuming iCol <= iRow
}

double gbl::VSymMatrix::operator() ( unsigned int  i, unsigned int  j  ) const

inline

access element (i,j) assuming i>=j

Definition at line 108 of file VMatrix.h.

References theVec.

                                 {
    return theVec[(iRow * iRow + iRow) / 2 + iCol]; // assuming iCol <= iRow
}

VVector gbl::VSymMatrix::operator*

(

const VVector &

aVector

)

const

Multiplication SymMatrix*Vector.

Definition at line 194 of file VMatrix.cc.

References i, j, numRows, and theVec.

                                                          {
    VVector aResult(numRows);
    for (unsigned int i = 0; i < numRows; ++i) {
        aResult(i) = theVec[(i * i + i) / 2 + i] * aVector(i);
        for (unsigned int j = 0; j < i; ++j) {
            aResult(j) += theVec[(i * i + i) / 2 + j] * aVector(i);
            aResult(i) += theVec[(i * i + i) / 2 + j] * aVector(j);
        }
    }
    return aResult;
}

VMatrix gbl::VSymMatrix::operator*

(

const VMatrix &

aMatrix

)

const

Multiplication SymMatrix*Matrix.

Definition at line 207 of file VMatrix.cc.

References gbl::VMatrix::getNumCols(), i, j, cmsLHEtoEOSManager::l, numRows, and theVec.

                                                          {
    unsigned int nCol = aMatrix.getNumCols();
    VMatrix aResult(numRows, nCol);
    for (unsigned int l = 0; l < nCol; ++l) {
        for (unsigned int i = 0; i < numRows; ++i) {
            aResult(i, l) = theVec[(i * i + i) / 2 + i] * aMatrix(i, l);
            for (unsigned int j = 0; j < i; ++j) {
                aResult(j, l) += theVec[(i * i + i) / 2 + j] * aMatrix(i, l);
                aResult(i, l) += theVec[(i * i + i) / 2 + j] * aMatrix(j, l);
            }
        }
    }
    return aResult;
}

VSymMatrix gbl::VSymMatrix::operator-

(

const VMatrix &

aMatrix

)

const

Subtraction SymMatrix-(sym)Matrix.

Definition at line 183 of file VMatrix.cc.

References i, j, numRows, and theVec.

                                                             {
    VSymMatrix aResult(numRows);
    for (unsigned int i = 0; i < numRows; ++i) {
        for (unsigned int j = 0; j <= i; ++j) {
            aResult(i, j) = theVec[(i * i + i) / 2 + j] - aMatrix(i, j);
        }
    }
    return aResult;
}

void gbl::VSymMatrix::print

(

void

)

const

Print matrix.

Definition at line 167 of file VMatrix.cc.

References gather_cfg::cout, i, j, min(), numRows, and theVec.

Referenced by gbl::BorderedBandMatrix::printMatrix().

                             {
    std::cout << " VSymMatrix: " << numRows << "*" << numRows << std::endl;
    for (unsigned int i = 0; i < numRows; ++i) {
        for (unsigned int j = 0; j <= i; ++j) {
            if (j % 5 == 0) {
                std::cout << std::endl << std::setw(4) << i << ","
                        << std::setw(4) << j << "-" << std::setw(4)
                        << std::min(j + 4, i) << ":";
            }
            std::cout << std::setw(13) << theVec[(i * i + i) / 2 + j];
        }
    }
    std::cout << std::endl << std::endl;
}

void gbl::VSymMatrix::resize

(

const unsigned int

nRows

)

Resize symmetric matrix.

Parameters

[in]

nRows

Number of rows.

Definition at line 153 of file VMatrix.cc.

References numRows, and theVec.

Referenced by Vispa.Gui.TextDialog.TextDialog::__init__(), Vispa.Plugins.ConfigEditor.ToolDialog.ToolDialog::__init__(), Vispa.Main.MainWindow.MainWindow::_loadIni(), gbl::BorderedBandMatrix::resize(), and Vispa.Gui.PortConnection.PointToPointConnection::updateConnection().

                                                {
    numRows = nRows;
    theVec.resize((nRows * nRows + nRows) / 2);
}

Member Data Documentation

unsigned int gbl::VSymMatrix::numRows

private

Number of rows.

Definition at line 78 of file VMatrix.h.

Referenced by getNumRows(), invert(), operator*(), operator-(), print(), and resize().

std::vector<double> gbl::VSymMatrix::theVec

private

Data (symmetric storage)

Definition at line 79 of file VMatrix.h.

Referenced by invert(), operator()(), operator*(), operator-(), print(), and resize().