/// Encode translation and structure linear program with slack variables
///  in order to handle noisy measurements.
inline void EncodeTiXi_withNoise(const Mat & M, //Scene representation
                           const std::vector<Mat3> & Ri,
                           double sigma, // Start upper bound
                           sRMat & A, Vec & C,
                           std::vector<LP_Constraints::eLP_SIGN> & vec_sign,
                           std::vector<double> & vec_costs,
                           std::vector< std::pair<double,double> > & vec_bounds)
{
  // Build Constraint matrix.

  const size_t Ncam = (size_t) M.row(3).maxCoeff()+1;
  const size_t N3D  = (size_t) M.row(2).maxCoeff()+1;
  const size_t Nobs = M.cols();

  assert(Ncam == Ri.size());

  A.resize(5*Nobs+3, 3 * (Ncam + N3D + Nobs));

  C.resize(5 * Nobs + 3, 1);
  C.fill(0.0);
  vec_sign.resize(5*Nobs+3);

  const size_t transStart  = 0;
  const size_t pointStart  = transStart + 3*Ncam;
  const size_t offsetStart = pointStart + 3*N3D;
# define TVAR(i, el) (0 + 3*(i) + (el))
# define XVAR(j, el) (pointStart + 3*(j) + (el))
# define OFSVAR(k, el) (offsetStart + 3*(k) + (el))

  // Set objective coefficients.
  vec_costs = std::vector<double>(3 * (Ncam + N3D + Nobs), 0.0);
  for (size_t k = 0; k < Nobs; ++k)
  {
     vec_costs[OFSVAR(k, 0)] = 1.0;
     vec_costs[OFSVAR(k, 1)] = 1.0;
     vec_costs[OFSVAR(k, 2)] = 1.0;
  }

  // By default set free variable:
  vec_bounds = std::vector< std::pair<double,double> >(3 * (Ncam + N3D + Nobs));
  fill( vec_bounds.begin(), vec_bounds.end(), std::make_pair((double)-1e+30, (double)1e+30));
  // Change the offset to be positive
  for (size_t k = 0; k < 3*Nobs; ++k)
    vec_bounds[offsetStart + k].first = 0;

  size_t rowPos = 0;
  // Add the cheirality conditions (R_i*X_j + T_i)_3 >= 1
  for (size_t k = 0; k < Nobs; ++k)
  {
    const size_t indexPt3D = M(2,k);
    const size_t indexCam  = M(3,k);
    const Mat3 & R = Ri[indexCam];

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = 1.0;
    A.coeffRef(rowPos, OFSVAR(k, 2)) = 1.0;
    C(rowPos) = 1.0;
    vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
    ++rowPos;
  } // end for (k)

  // Add conic constraint:
  for (size_t k = 0; k < Nobs; ++k)
  {
    const Vec2 pt   = M.block<2,1>(0,k);
    const double u = pt(0);
    const double v = pt(1);
    const size_t indexPt3D = M(2,k);
    const size_t indexCam  = M(3,k);
    const Mat3 & R = Ri[indexCam];

    // x-residual =>
    // (R_i*X_j + T_i)_1 / (R_i*X_j + T_i)_3 - u >= -sigma
    // (R_i*X_j + T_i)_1 - u * (R_i*X_j + T_i)_3  + sigma (R_i*X_j + T_i)_3  >= 0.0
    // R_i_3 * (sigma-u) + R_i_1 + t_i_1 + t_i_3 * (sigma-u) >= 0

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(0,0) + (sigma-u) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(0,1) + (sigma-u) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(0,2) + (sigma-u) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 0)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = sigma-u;
    A.coeffRef(rowPos, OFSVAR(k, 0)) = 1.0;
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
    ++rowPos;

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(0,0) - (sigma+u) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(0,1) - (sigma+u) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(0,2) - (sigma+u) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 0)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = -(sigma + u);
    A.coeffRef(rowPos, OFSVAR(k, 0)) = -1.0;
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_LESS_OR_EQUAL;
    ++rowPos;

    // y-residual =>
    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(1,0) + (sigma-v) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(1,1) + (sigma-v) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(1,2) + (sigma-v) * R(2,2);
    A.coeffRef(rowPos, OFSVAR(k, 1)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 1)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = sigma-v;

    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
    ++rowPos;

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(1,0) - (sigma+v) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(1,1) - (sigma+v) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(1,2) - (sigma+v) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 1)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = -(sigma + v);
    A.coeffRef(rowPos, OFSVAR(k, 1)) = -1.0;
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_LESS_OR_EQUAL;
    ++rowPos;
  }
  // Fix the translation ambiguity. (set first cam at (0,0,0)
  //LP_EQUAL
  A.coeffRef(rowPos, TVAR(0, 0)) = 1.0; C(rowPos) = 0.0; vec_sign[rowPos] = LP_Constraints::LP_EQUAL; ++rowPos;
  A.coeffRef(rowPos, TVAR(0, 1)) = 1.0; C(rowPos) = 0.0; vec_sign[rowPos] = LP_Constraints::LP_EQUAL; ++rowPos;
  A.coeffRef(rowPos, TVAR(0, 2)) = 1.0; C(rowPos) = 0.0; vec_sign[rowPos] = LP_Constraints::LP_EQUAL; ++rowPos;

# undef TVAR
# undef XVAR
# undef OFSVAR
}
// Setup the linear program to solve the union of trifocal tensors heading
//  directions in a common global coordinate system.
//- Implementation of the LINEAR PROGRAM (9) page 5 of [1]:
//--
static void EncodeTi_from_tij_OneLambdaPerTrif(
    const size_t nTranslation,
    const std::vector<relativeInfo > & vec_relative,
    sRMat & A, Vec & C,
    std::vector<LP_Constraints::eLP_SIGN> & vec_sign,
    std::vector<double> & vec_costs,
    std::vector< std::pair<double,double> > & vec_bounds)
{
  // Build Constraint matrix.

  const size_t Ncam = (size_t) nTranslation;
  const size_t Nrelative = vec_relative.size();

  const size_t transStart  = 0;
  const size_t lambdaStart = 3 * Ncam;
  const size_t gammaStart = lambdaStart + Nrelative/3;

#undef TVAR
#undef LAMBDAVAR
#undef GAMMAVAR
# define TVAR(i, el) (transStart + 3*(i) + (el))  // translation (X,Y,Z)
# define LAMBDAVAR(j) (lambdaStart + (int)((j)/3)) // One per relative translation
# define GAMMAVAR gammaStart

  const size_t Nconstraint = Nrelative * 6;
  const size_t NVar = 3 * Ncam + Nrelative/3 + 1;

  A.resize(Nconstraint, NVar);

  C.resize(Nconstraint, 1);
  C.fill(0.0);
  vec_sign.resize(Nconstraint);

  // By default set free variable:
  vec_bounds = std::vector< std::pair<double,double> >(NVar);
  fill( vec_bounds.begin(), vec_bounds.end(),
    std::make_pair((double)-1e+30, (double)1e+30));
  //  Make first camera at origin (translation ambiguity)
  vec_bounds[TVAR(0,0)].first = vec_bounds[TVAR(0,0)].second = 0;
  vec_bounds[TVAR(0,1)].first = vec_bounds[TVAR(0,1)].second = 0;
  vec_bounds[TVAR(0,2)].first = vec_bounds[TVAR(0,2)].second = 0;
  // Make lambda variables between 1 and large number => constraint that lambda_ij > 1
  for (size_t k = 0; k < Nrelative/3; ++k)
    vec_bounds[lambdaStart + k].first = 1;

  // Setup gamma >= 0
  vec_bounds[vec_bounds.size()-1].first = 0.0;

  //-- Minimize gamma
  vec_costs.resize(NVar);
  std::fill(vec_costs.begin(), vec_costs.end(), 0.0);
  vec_costs[GAMMAVAR] = 1.0;
  //--

  size_t rowPos = 0;

  for (size_t k = 0; k < Nrelative; ++k)
  {
    const size_t i = vec_relative[k].first.first;
    const size_t j  = vec_relative[k].first.second;
    const Mat3 & Rij = vec_relative[k].second.first;
    const Vec3 & tij = vec_relative[k].second.second;

    // | T_j - R_ij T_i - Lambda_ij t_ij | < Gamma
    // Absolute constraint transformed in two sign constraints
    //   T_j - R_ij T_i - Lambda_ij t_ij < Gamma
    //   T_j - R_ij T_i - Lambda_ij t_ij > - Gamma

    // For X, Y, Z axis:
    for (int l = 0; l < 3; ++l)
    {
      // T_j
      A.coeffRef(rowPos, TVAR(j, l)) = 1;

      //- R_ij T_i
      A.coeffRef(rowPos, TVAR(i, 0)) = - Rij(l, 0);
      A.coeffRef(rowPos, TVAR(i, 1)) = - Rij(l, 1);
      A.coeffRef(rowPos, TVAR(i, 2)) = - Rij(l, 2);

      // - Lambda_ij t_ij
      A.coeffRef(rowPos, LAMBDAVAR(k)) = - tij(l);

      // - gamma
      A.coeffRef(rowPos, GAMMAVAR) = -1;

      // < 0
      vec_sign[rowPos] = LP_Constraints::LP_LESS_OR_EQUAL;
      C(rowPos) = 0;
      ++rowPos;

      // ---------
      // Opposite constraint
      //   T_j - R_ij T_i - Lambda_ij t_ij > - Gamma
      // ---------

      // T_j
      A.coeffRef(rowPos, TVAR(j, l)) = 1;

      //- R_ij T_i
      A.coeffRef(rowPos, TVAR(i, 0)) = - Rij(l, 0);
      A.coeffRef(rowPos, TVAR(i, 1)) = - Rij(l, 1);
      A.coeffRef(rowPos, TVAR(i, 2)) = - Rij(l, 2);

      // - Lambda_ij t_ij
      A.coeffRef(rowPos, LAMBDAVAR(k)) = - tij(l);

      // + gamma
      A.coeffRef(rowPos, GAMMAVAR) = 1;

      // > 0
      vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
      C(rowPos) = 0;
      ++rowPos;
    }
  } // end for (k)
#undef TVAR
#undef LAMBDAVAR
#undef GAMMAVAR
}
Exemplo n.º 3
0
/// Encode translation and structure linear program
static void EncodeTiXi(const Mat & M, //Scene representation
                           const std::vector<Mat3> & Ri,
                           double sigma, // Start upper bound
                           sRMat & A, Vec & C,
                           std::vector<LP_Constraints::eLP_SIGN> & vec_sign,
                           std::vector<double> & vec_costs,
                           std::vector< std::pair<double,double> > & vec_bounds)
{
  // Build Constraint matrix.
  const size_t Ncam = (size_t) M.row(3).maxCoeff()+1;
  const size_t N3D  = (size_t) M.row(2).maxCoeff()+1;
  const size_t Nobs = M.cols();

  assert(Ncam == Ri.size());

  A.resize(5 * Nobs, 3 * (N3D + Ncam));

  C.resize(5 * Nobs, 1);
  C.fill(0.0);
  vec_sign.resize(5 * Nobs + 3);

  const size_t transStart  = 0;
  const size_t pointStart  = transStart + 3*Ncam;
# define TVAR(i, el) (0 + 3*(i) + (el))
# define XVAR(j, el) (pointStart + 3*(j) + (el))

  // By default set free variable:
  vec_bounds = std::vector< std::pair<double,double> >(3 * (N3D + Ncam));
  fill( vec_bounds.begin(), vec_bounds.end(), std::make_pair((double)-1e+30, (double)1e+30));
  // Fix the translation ambiguity. (set first cam at (0,0,0))
  vec_bounds[0] = vec_bounds[1] = vec_bounds[2] = std::make_pair(0,0);

  size_t rowPos = 0;
  // Add the cheirality conditions (R_i*X_j + T_i)_3 + Z_ij >= 1
  for (size_t k = 0; k < Nobs; ++k)
  {
    const size_t indexPt3D = M(2,k);
    const size_t indexCam  = M(3,k);
    const Mat3 & R = Ri[indexCam];

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = 1.0;
    C(rowPos) = 1.0;
    vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
    ++rowPos;

    const Vec2 pt   = M.block<2,1>(0,k);
    const double u = pt(0);
    const double v = pt(1);

    // x-residual =>
    // (R_i*X_j + T_i)_1 / (R_i*X_j + T_i)_3 - u >= -sigma
    // (R_i*X_j + T_i)_1 - u * (R_i*X_j + T_i)_3  + sigma (R_i*X_j + T_i)_3  >= 0.0
    // R_i_3 * (sigma-u) + R_i_1 + t_i_1 + t_i_3 * (sigma-u) >= 0

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(0,0) + (sigma-u) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(0,1) + (sigma-u) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(0,2) + (sigma-u) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 0)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = sigma-u;
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
    ++rowPos;

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(0,0) - (sigma+u) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(0,1) - (sigma+u) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(0,2) - (sigma+u) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 0)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = -(sigma + u);
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_LESS_OR_EQUAL;
    ++rowPos;

    // y-residual =>
    // (R_i*X_j + T_i)_2 / (R_i*X_j + T_i)_3 - v >= -sigma
    // (R_i*X_j + T_i)_2 - v * (R_i*X_j + T_i)_3  + sigma (R_i*X_j + T_i)_3  >= 0.0
    // R_i_3 * (sigma-v) + R_i_2 + t_i_2 + t_i_3 * (sigma-v) >= 0
    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(1,0) + (sigma-v) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(1,1) + (sigma-v) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(1,2) + (sigma-v) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 1)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = sigma-v;
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_GREATER_OR_EQUAL;
    ++rowPos;

    A.coeffRef(rowPos, XVAR(indexPt3D, 0)) = R(1,0) - (sigma+v) * R(2,0);
    A.coeffRef(rowPos, XVAR(indexPt3D, 1)) = R(1,1) - (sigma+v) * R(2,1);
    A.coeffRef(rowPos, XVAR(indexPt3D, 2)) = R(1,2) - (sigma+v) * R(2,2);
    A.coeffRef(rowPos, TVAR(indexCam, 1)) = 1.0;
    A.coeffRef(rowPos, TVAR(indexCam, 2)) = -(sigma + v);
    C(rowPos) = 0.0;
    vec_sign[rowPos] = LP_Constraints::LP_LESS_OR_EQUAL;
    ++rowPos;
  }
# undef TVAR
# undef XVAR
}
// Implementation of the formula (1) of [1] with 10 quantiles.
//-- L_infinity alignment of pair of histograms over a graph thanks to a linear program.
static void Encode_histo_relation(
    const size_t nImage,
    const std::vector<relativeColorHistogramEdge > & vec_relativeHistograms,
    const std::vector<size_t> & vec_indexToFix,
    sRMat & A, Vec & C,
    std::vector<linearProgramming::LP_Constraints::eLP_SIGN> & vec_sign,
    std::vector<double> & vec_costs,
    std::vector< std::pair<double,double> > & vec_bounds)
{
  const size_t Nima = (size_t) nImage;
  const size_t Nrelative = vec_relativeHistograms.size();

# define GVAR(i) (2*(i))
# define OFFSETVAR(i) (2*(i)+1)
# define GAMMAVAR (2*Nima)

  const size_t nbQuantile = 10;

  const size_t Nconstraint = nbQuantile * Nrelative * 2;
  const size_t NVar = 2 * Nima+ 1;

  A.resize(Nconstraint, NVar);

  C.resize(Nconstraint, 1);
  C.fill(0.0);
  vec_sign.resize(Nconstraint);

  // By default set free variable:
  vec_bounds = std::vector< std::pair<double,double> >(NVar);
  fill( vec_bounds.begin(), vec_bounds.end(),
    std::make_pair((double)-1e+30, (double)1e+30));

  // Set gain as positive values
  for (size_t i = 0; i < Nima; ++i)
  {
    vec_bounds[GVAR(i)].first = 0.0;
  }

  //-- Fix the required image to known gain and offset value
  for (std::vector<size_t>::const_iterator iter = vec_indexToFix.begin();
    iter != vec_indexToFix.end(); ++iter)
  {
    vec_bounds[GVAR(*iter)] = std::make_pair(1.0, 1.0);      // gain = 1.0
    vec_bounds[OFFSETVAR(*iter)] = std::make_pair(0.0, 0.0); // offset = 0
  }

  // Setup gamma >= 0
  vec_bounds[GAMMAVAR].first = 0.0;

  //-- Minimize gamma
  vec_costs.resize(NVar);
  std::fill(vec_costs.begin(), vec_costs.end(), 0.0);
  vec_costs[GAMMAVAR] = 1.0;
  //--

  size_t rowPos = 0;
  double incrementPourcentile = 1./(double) nbQuantile;

  for (size_t i = 0; i < Nrelative; ++i)
  {
    std::vector<relativeColorHistogramEdge>::const_iterator iter = vec_relativeHistograms.begin();
    std::advance(iter, i);

    const relativeColorHistogramEdge & edge = *iter;

    //-- compute the two cumulated and normalized histogram

    const std::vector< size_t > & vec_histoI = edge.histoI;
    const std::vector< size_t > & vec_histoJ = edge.histoJ;

    const size_t nBuckets = vec_histoI.size();

    // Normalize histogram
    std::vector<double> ndf_I(nBuckets), ndf_J(nBuckets);
    histogram::normalizeHisto(vec_histoI, ndf_I);
    histogram::normalizeHisto(vec_histoJ, ndf_J);

    // Compute cumulative distribution functions (cdf)
    std::vector<double> cdf_I(nBuckets), cdf_J(nBuckets);
    histogram::cdf(ndf_I, cdf_I);
    histogram::cdf(ndf_J, cdf_J);

    double currentPourcentile = 5./100.;

    //-- Compute pourcentile and their positions
    std::vector<double> vec_pourcentilePositionI, vec_pourcentilePositionJ;
    vec_pourcentilePositionI.reserve(1.0/incrementPourcentile);
    vec_pourcentilePositionJ.reserve(1.0/incrementPourcentile);

    std::vector<double>::const_iterator cdf_I_IterBegin = cdf_I.begin();
    std::vector<double>::const_iterator cdf_J_IterBegin = cdf_J.begin();
    while( currentPourcentile < 1.0)
    {
      std::vector<double>::const_iterator iterFI = std::lower_bound(cdf_I.begin(), cdf_I.end(), currentPourcentile);
      const size_t positionI = std::distance(cdf_I_IterBegin, iterFI);

      std::vector<double>::const_iterator iterFJ = std::lower_bound(cdf_J.begin(), cdf_J.end(), currentPourcentile);
      const size_t positionJ = std::distance(cdf_J_IterBegin, iterFJ);

      vec_pourcentilePositionI.push_back(positionI);
      vec_pourcentilePositionJ.push_back(positionJ);

      currentPourcentile += incrementPourcentile;
    }

    //-- Add the constraints:
    // pos * ga + offa - pos * gb - offb <= gamma
    // pos * ga + offa - pos * gb - offb >= - gamma

    for(size_t k = 0; k < vec_pourcentilePositionI.size(); ++k)
    {
      A.coeffRef(rowPos, GVAR(edge.I)) = vec_pourcentilePositionI[k];
      A.coeffRef(rowPos, OFFSETVAR(edge.I)) = 1.0;

      A.coeffRef(rowPos, GVAR(edge.J)) = - vec_pourcentilePositionJ[k];
      A.coeffRef(rowPos, OFFSETVAR(edge.J)) = - 1.0;

      // - gamma (side change)
      A.coeffRef(rowPos, GAMMAVAR) = -1;
      // <= gamma
      vec_sign[rowPos] = linearProgramming::LP_Constraints::LP_LESS_OR_EQUAL;
      C(rowPos) = 0;
      ++rowPos;

      A.coeffRef(rowPos, GVAR(edge.I)) = vec_pourcentilePositionI[k];
      A.coeffRef(rowPos, OFFSETVAR(edge.I)) = 1.0;

      A.coeffRef(rowPos, GVAR(edge.J)) = - vec_pourcentilePositionJ[k];
      A.coeffRef(rowPos, OFFSETVAR(edge.J)) = - 1.0;

      // + gamma (side change)
      A.coeffRef(rowPos, GAMMAVAR) = 1;
      // >= - gamma
      vec_sign[rowPos] = linearProgramming::LP_Constraints::LP_GREATER_OR_EQUAL;
      C(rowPos) = 0;
      ++rowPos;
    }
  }
#undef GVAR
#undef OFFSETVAR
#undef GAMMAVAR
}