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 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 m = 1; m <= nSize; ++m) { // elimination
        if (m == k) {
          jk = kk;
          jl += m;
        } else {
          if (m < k) {
            ++jk;
          } else {
            jk += m - 1;
          }
 
          double vjk = theVec[jk];
          theVec[jk] = vkk * vjk;
          int lk = kk - k;
          if (m >= 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 <= m; ++l) {
              ++jl;
              lk += l - 1;
              theVec[jl] -= theVec[lk] * vjk;
            }
          } else {
            for (int l = 1; l <= m; ++l) {
              ++jl;
              ++lk;
              theVec[jl] -= theVec[lk] * vjk;
            }
          }
        }
      }
    } else {
      for (int m = 1; m <= nSize; ++m) {
        if (next[m - 1] >= 0) {
          int kk = (m * m - m) / 2 - 1;
          for (int n = 1; n <= nSize; ++n) {
            if (next[n - 1] >= 0) {
              theVec[kk + n] = 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;
}
}