VMatrix.cc

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/*
 * VMatrix.cpp
 *
 *  Created on: Feb 15, 2012
 *      Author: kleinwrt
 */
 
#include "VMatrix.h"
 
namespace gbl {
 
/*********** simple Matrix based on std::vector<double> **********/
 
VMatrix::VMatrix(const unsigned int nRows, const unsigned int nCols) :
        numRows(nRows), numCols(nCols), theVec(nRows * nCols) {
}
 
VMatrix::VMatrix(const VMatrix &aMatrix) :
        numRows(aMatrix.numRows), numCols(aMatrix.numCols), theVec(
                aMatrix.theVec) {
 
}
 
VMatrix::~VMatrix() {
}
 
 
void VMatrix::resize(const unsigned int nRows, const unsigned int nCols) {
    numRows = nRows;
    numCols = nCols;
    theVec.resize(nRows * nCols);
}
 
 
VMatrix VMatrix::transpose() const {
    VMatrix aResult(numCols, numRows);
    for (unsigned int i = 0; i < numRows; ++i) {
        for (unsigned int j = 0; j < numCols; ++j) {
            aResult(j, i) = theVec[numCols * i + j];
        }
    }
    return aResult;
}
 
 
unsigned int VMatrix::getNumRows() const {
    return numRows;
}
 
 
unsigned int VMatrix::getNumCols() const {
    return numCols;
}
 
void VMatrix::print() const {
    std::cout << " VMatrix: " << numRows << "*" << numCols << std::endl;
    for (unsigned int i = 0; i < numRows; ++i) {
        for (unsigned int j = 0; j < numCols; ++j) {
            if (j % 5 == 0) {
                std::cout << std::endl << std::setw(4) << i << ","
                        << std::setw(4) << j << "-" << std::setw(4)
                        << std::min(j + 4, numCols) << ":";
            }
            std::cout << std::setw(13) << theVec[numCols * i + j];
        }
    }
    std::cout << std::endl << std::endl;
}
 
VVector VMatrix::operator*(const VVector &aVector) const {
    VVector aResult(numRows);
    for (unsigned int i = 0; i < this->numRows; ++i) {
        double sum = 0.0;
        for (unsigned int j = 0; j < this->numCols; ++j) {
            sum += theVec[numCols * i + j] * aVector(j);
        }
        aResult(i) = sum;
    }
    return aResult;
}
 
VMatrix VMatrix::operator*(const VMatrix &aMatrix) const {
 
    VMatrix aResult(numRows, aMatrix.numCols);
    for (unsigned int i = 0; i < numRows; ++i) {
        for (unsigned int j = 0; j < aMatrix.numCols; ++j) {
            double sum = 0.0;
            for (unsigned int k = 0; k < numCols; ++k) {
                sum += theVec[numCols * i + k] * aMatrix(k, j);
            }
            aResult(i, j) = sum;
        }
    }
    return aResult;
}
 
VMatrix VMatrix::operator+(const VMatrix &aMatrix) const {
    VMatrix aResult(numRows, numCols);
    for (unsigned int i = 0; i < numRows; ++i) {
        for (unsigned int j = 0; j < numCols; ++j) {
            aResult(i, j) = theVec[numCols * i + j] + aMatrix(i, j);
        }
    }
    return aResult;
}
 
VMatrix &VMatrix::operator=(const VMatrix &aMatrix) {
    if (this != &aMatrix) {   // Gracefully handle self assignment
        numRows = aMatrix.getNumRows();
        numCols = aMatrix.getNumCols();
        theVec.resize(numRows * numCols);
        for (unsigned int i = 0; i < numRows; ++i) {
            for (unsigned int j = 0; j < numCols; ++j) {
                theVec[numCols * i + j] = aMatrix(i, j);
            }
        }
    }
    return *this;
}
 
/*********** simple symmetric Matrix based on std::vector<double> **********/
 
VSymMatrix::VSymMatrix(const unsigned int nRows) :
        numRows(nRows), theVec((nRows * nRows + nRows) / 2) {
}
 
VSymMatrix::~VSymMatrix() {
}
 
 
void VSymMatrix::resize(const unsigned int nRows) {
    numRows = nRows;
    theVec.resize((nRows * nRows + nRows) / 2);
}
 
 
unsigned int VSymMatrix::getNumRows() const {
    return numRows;
}
 
void VSymMatrix::print() const {
    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;
}
 
VSymMatrix VSymMatrix::operator-(const VMatrix &aMatrix) const {
    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;
}
 
VVector VSymMatrix::operator*(const VVector &aVector) const {
    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 VSymMatrix::operator*(const VMatrix &aMatrix) const {
    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;
}
 
/*********** simple Vector based on std::vector<double> **********/
 
VVector::VVector(const unsigned int nRows) :
        numRows(nRows), theVec(nRows) {
}
 
VVector::VVector(const VVector &aVector) :
        numRows(aVector.numRows), theVec(aVector.theVec) {
 
}
 
VVector::~VVector() {
}
 
 
void VVector::resize(const unsigned int nRows) {
    numRows = nRows;
    theVec.resize(nRows);
}
 
 
VVector VVector::getVec(unsigned int len, unsigned int start) const {
    VVector aResult(len);
    std::memcpy(&aResult.theVec[0], &theVec[start], sizeof(double) * len);
    return aResult;
}
 
 
void VVector::putVec(const VVector &aVector, unsigned int start) {
    std::memcpy(&theVec[start], &aVector.theVec[0],
            sizeof(double) * aVector.numRows);
}
 
 
unsigned int VVector::getNumRows() const {
    return numRows;
}
 
void VVector::print() const {
    std::cout << " VVector: " << numRows << std::endl;
    for (unsigned int i = 0; i < numRows; ++i) {
 
        if (i % 5 == 0) {
            std::cout << std::endl << std::setw(4) << i << "-" << std::setw(4)
                    << std::min(i + 4, numRows) << ":";
        }
        std::cout << std::setw(13) << theVec[i];
    }
    std::cout << std::endl << std::endl;
}
 
VVector VVector::operator-(const VVector &aVector) const {
    VVector aResult(numRows);
    for (unsigned int i = 0; i < numRows; ++i) {
        aResult(i) = theVec[i] - aVector(i);
    }
    return aResult;
}
 
VVector &VVector::operator=(const VVector &aVector) {
    if (this != &aVector) {   // Gracefully handle self assignment
        numRows = aVector.getNumRows();
        theVec.resize(numRows);
        for (unsigned int i = 0; i < numRows; ++i) {
            theVec[i] = aVector(i);
        }
    }
    return *this;
}
 
/*============================================================================
 from mpnum.F (MillePede-II by V. Blobel, Univ. Hamburg)
 ============================================================================*/
 
unsigned int VSymMatrix::invert() {
 
    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 jCandidate = first;
        int previous = 0;
        int last = previous;
        // look for pivot
        while (jCandidate > 0) {
            int jj = (jCandidate * jCandidate + jCandidate) / 2 - 1;
            if (fabs(theVec[jj]) > std::max(fabs(vkk), eps * diag[jCandidate - 1])) {
                vkk = theVec[jj];
                k = jCandidate;
                last = previous;
            }
            previous = jCandidate;
            jCandidate = next[jCandidate - 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 n = 1; n <= nSize; ++n) {
                if (next[n - 1] >= 0) {
                    int nn = (n * n - n) / 2 - 1;
                    for (int j = 1; j <= nSize; ++j) {
                        if (next[j - 1] >= 0) {
                            theVec[nn + 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;
}
}