SamplerAnalysis.cc

/* 
Beam Delivery Simulation (BDSIM) Copyright (C) Royal Holloway, 
University of London 2001 - 2022.
 
This file is part of BDSIM.
 
BDSIM is free software: you can redistribute it and/or modify 
it under the terms of the GNU General Public License as published 
by the Free Software Foundation version 3 of the License.
 
BDSIM is distributed in the hope that it will be useful, but 
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.
 
You should have received a copy of the GNU General Public License
along with BDSIM.  If not, see <http://www.gnu.org/licenses/>.
*/
#include "SamplerAnalysis.hh"
#include "rebdsim.hh"
 
#include <cmath>
#include <vector>
 
double SamplerAnalysis::particleMass = 0;
 
SamplerAnalysis::SamplerAnalysis():
  s(nullptr),
  S(0),
  debug(false)
{
  CommonCtor();
}
 
#ifndef __ROOTDOUBLE__
SamplerAnalysis::SamplerAnalysis(BDSOutputROOTEventSampler<float> *samplerIn,
                                 bool debugIn):
#else 
SamplerAnalysis::SamplerAnalysis(BDSOutputROOTEventSampler<double> *samplerIn,
                                 bool debugIn):
#endif
  s(samplerIn),
  S(0),
  debug(debugIn)
{
  CommonCtor();
}
 
void SamplerAnalysis::UpdateMass(SamplerAnalysis* s)
{
  int id = s->s->partID[0];
  switch (std::abs(id))
    {
    case 11:
    case -11:
      {
        std::cout << "Primary particle: e-" << std::endl;
        particleMass = 0.000510999; break;}
    case 2212:
      {
        std::cout << "Primary particle: proton" << std::endl;
        particleMass = 0.938272; break;}
    default:
      {
        std::cout << "Primary particle: unknown -> m=0" << std::endl;
        particleMass = 0; break;}
    }
}
 
void SamplerAnalysis::UpdateMass(const std::string& particleName)
{
  if ((particleName == "e-") || (particleName == "e+"))
    {
      std::cout << "Primary particle: e-" << std::endl;
      particleMass = 0.000510999;;
    }
  else if (particleName == "proton")
    {
      std::cout << "Primary particle: proton" << std::endl;
      particleMass = 0.938272;
    }
  else
    {
      std::cout << "Primary particle: unknown -> m=0" << std::endl;
      particleMass = 0;
    }
}
 
void SamplerAnalysis::CommonCtor()
{
  npart = 0;
 
  // initialise a vector to store the coordinates of every event in a sampler
  coordinates.resize(6, 0);
 
  // initialise a vector to store the first values in a sampler for assumed mean subtraction
  offsets.resize(6, 0);
  
  optical.resize(3); // resize to 3 entries initialised to 0
  varOptical.resize(3);
  for(int i=0;i<3;++i)
    {
      optical[i].resize(25, 0);   // 12 for central values and 12 for errors and 1 for xy correlation
      varOptical[i].resize(12, 0);
    }
 
  covMats.resize(3);
  for(int i=0;i<3;++i)
  {
    covMats[i].resize(3);
    for(int j=0;j<3;++j)
      {covMats[i][j].resize(3, 0);}
  }
 
  derivMats.resize(3);
  for(int i=0;i<3;++i)
  {
    derivMats[i].resize(12);
    for(int j=0;j<12;++j)
      {derivMats[i][j].resize(3, 0);}
  }
  
  powSums.resize(6);
  cenMoms.resize(6);
 
  powSumsFirst.resize(6); // first sampler
  cenMomsFirst.resize(6);
 
  // (x,xp,y,yp,E,t) (x,xp,y,yp,E,t) v1pow, v2pow
  for(int i=0;i<6;++i)
  {
    powSums[i].resize(6);
    cenMoms[i].resize(6);
 
    powSumsFirst[i].resize(6);
    cenMomsFirst[i].resize(6);
 
    for(int j=0;j<6;++j)
    {
      powSums[i][j].resize(5);
      cenMoms[i][j].resize(5);
 
      powSumsFirst[i][j].resize(5);
      cenMomsFirst[i][j].resize(5);
      
      for(int k=0;k<=4;++k)
      {
        powSums[i][j][k].resize(5, 0);
        cenMoms[i][j][k].resize(5, 0);
 
        powSumsFirst[i][j][k].resize(5, 0);
        cenMomsFirst[i][j][k].resize(5, 0);
      }
    }
  }
}
 
SamplerAnalysis::~SamplerAnalysis()
{;}
 
void SamplerAnalysis::Initialise()
{
  npart = 0;
}
 
void SamplerAnalysis::Process(bool firstTime)
{
  if(debug)
    {std::cout << __METHOD_NAME__ << "\"" << s->samplerName << "\" with " << s->n << " entries" << std::endl;}
 
  double m2 = std::pow(particleMass,2);
  
  // loop over all entries
  for(int i=0;i<s->n;++i)
  {
    if (i == 0)
      {S = s->S;} // update sampler on first round - do here so not to load default data
    if (s->parentID[i] != 0)
      {continue;} // select only primary particles
    if (s->turnNumber[i] > 1)
      {continue;} // only use first turn particles
    if (s->zp[i] <= 0)
      {continue;} // only forward going particles - sampler can intercept backwards particles
 
    coordinates[0] = s->x[i];
    coordinates[1] = s->xp[i];
    coordinates[2] = s->y[i];
    coordinates[3] = s->yp[i];
    coordinates[4] = std::sqrt(std::pow(s->energy[i],2) - m2); // p = sqrt(E^2 - M^2)
    coordinates[5] = s->T[i];
 
    if (firstTime)
      {offsets = coordinates;}
 
    // power sums
    for(int a=0;a<6;++a)
      {
        for(int b=0;b<6;++b)
          {
            for (int j = 0; j <= 4; ++j)
              {
                for (int k = 0; k <= 4; ++k)
                  {
                    powSums[a][b][j][k] += std::pow(coordinates[a]-offsets[a],j)*std::pow(coordinates[b]-offsets[b],k);
                  }
              }
          }
      }
  npart++;  
  }
}
 
std::vector<double> SamplerAnalysis::Terminate(std::vector<double> emittance,
                                               bool useEmittanceFromFirstSampler)
{
  if(debug)
    {std::cout << " " << __METHOD_NAME__ << s->modelID << " " << npart << std::flush;}
 
  // determine whether the input emittance is non-zero
  bool nonZeroEmittanceIn = !std::all_of(emittance.begin(), emittance.end(), [](double l) { return l==0; });
 
  // central moments
  for(int a=0;a<6;++a)
  {
    for(int b=0;b<6;++b)
      {
        for (int j = 0; j <= 4; ++j)
          {
            for (int k = 0; k <= 4; ++k)
              {
                cenMoms[a][b][j][k] = powSumToCentralMoment(powSums, npart, a, b, j, k);
              }
          }
      }
  }
 
  if (debug)
    {printBeamCorrelationMatrix(cenMoms);}
 
  // optical function calculation
  for(int i=0;i<3;++i)
  {
    int j = 0;
    if(i == 1) j = 2;
    if(i == 2) j = 4;
 
    // note: optical functions vector not populated in sequential order in order
    // to apply dispersion correction to lattice funcs.
 
    optical[i][6]  = cenMoms[j][j+1][1][0]; // mean spatial (transv.)/ mean P (longit.)
    optical[i][7]  = cenMoms[j][j+1][0][1]; // mean divergence (transv.)/ mean t (longit.)
    optical[i][8]  = sqrt(cenMoms[j][j+1][2][0]); // sigma spatial   (transv.)/ sigma P (longit.)
    optical[i][9]  = sqrt(cenMoms[j][j+1][0][2]); // sigma divergence (transv.)/ sigma t (longit.)
 
    // transverse optical function calculation skipped for longitudinal plane,
    // only mean and sigma of longit. coordinates recorded
    if (i==2)
      {continue;}
 
    optical[i][4]  = (cenMoms[4][4][1][0]*cenMoms[j][4][1][1])/cenMoms[4][4][2][0];    // eta
    optical[i][5]  = (cenMoms[4][4][1][0]*cenMoms[j+1][4][1][1])/cenMoms[4][4][2][0];  // eta prime
 
    // check for nans (expected if dP=0) and set disp=0 if found
    if (!std::isfinite(optical[i][4]))
      {optical[i][4] = 0;}
    if (!std::isfinite(optical[i][5]))
      {optical[i][5] = 0;}
 
    // temp variables to store dispersion corrected moments, aka moments without dispersion contribution
    double corrCentMom_2_0 = 0.0, corrCentMom_1_1 = 0.0;
    double corrCentMom_0_2 = 0.0;
 
    //Correction example: var[x]_corrected = var[x] - eta_x^2*sigma[dP/P]^2
    corrCentMom_2_0 =
      cenMoms[j][j+1][2][0] - std::pow(optical[i][4],2)*cenMoms[4][4][2][0]/std::pow(cenMoms[4][4][1][0],2);
 
    corrCentMom_0_2 =
      cenMoms[j][j+1][0][2] - std::pow(optical[i][5],2)*cenMoms[4][4][2][0]/std::pow(cenMoms[4][4][1][0],2);
 
    corrCentMom_1_1 =
      cenMoms[j][j+1][1][1] - (optical[i][4]*optical[i][5])*cenMoms[4][4][2][0]/std::pow(cenMoms[4][4][1][0],2);
 
    if(useEmittanceFromFirstSampler && nonZeroEmittanceIn)
      {optical[i][0]  = emittance[i];}
    else
      {optical[i][0] = sqrt(corrCentMom_2_0 * corrCentMom_0_2 - std::pow(corrCentMom_1_1, 2));}  //emittance
 
    optical[i][1]  = -corrCentMom_1_1/optical[i][0];                                             // alpha
    optical[i][2]  = corrCentMom_2_0/optical[i][0];                                              // beta
    optical[i][3]  = (1+std::pow(optical[i][1],2))/optical[i][2];                                // gamma
 
    optical[i][10] = S;
    optical[i][11] = npart;
  }
 
  // statistical error calculation
  
  // covariance matrix of central moments for optical functions.
  for(int i=0;i<3;++i)
    {
      for(int j=0;j<3;++j)
        {
          for(int k=0;k<3;++k)
            {
              covMats[i][j][k]=centMomToCovariance(cenMoms, npart, i, j, k);
            }
        }
    }
  
  // derivative matrix of parameters for optical functions. Each entry is
  // a first order derivative w.r.t central moments.  
  for(int i=0;i<3;++i)
    {
      for(int j=0;j<12;++j) //loop over optical functions.
        {
          for(int k=0;k<3;++k) //loop over derivative indices
            {
              derivMats[i][j][k]=centMomToDerivative(cenMoms, i, j, k);
            }
        }
    }
  
  // compute variances of optical functions
  for(int i=0;i<3;++i)      
    {
      for(int j=0;j<12;++j)
        {
          for(int k=0;k<3;++k)
            {
              for(int l=0;l<3;++l)
                {
                  varOptical[i][j] += derivMats[i][j][k]*derivMats[i][j][l]*covMats[i][k][l];
                }
            }
        }
    }
 
  // compute the sigmas of optical functions
  for(int i=0;i<3;++i)      
    {
      for(int j=0;j<12;++j)
        {
          if(j==6 || j==7)
            {optical[i][j+12]=optical[i][j+2]/sqrt(npart);} //errors of the means 
          else if(j == 10 || j == 11)
            {optical[i][j+12]= 0.0;}                        //no errors on S and Npart
          else if (j==0)
            {
                if(useEmittanceFromFirstSampler && nonZeroEmittanceIn)
                {
                    optical[i][j+12]=emittance[j+2];
                }
                else
                {
                    optical[i][j+12]=sqrt(varOptical[i][j]);
                }
            }
          else
            {optical[i][j+12]=sqrt(varOptical[i][j]);}
        }
    }
 
  // convert meanP back to meanE
  double m2 = std::pow(particleMass,2);
  double meanP = optical[2][6];
  optical[2][6] = std::sqrt(std::pow(meanP,2) + m2);
 
  //convert sigmaP back to SigmaE
  double gamma = optical[2][6] / particleMass;
  double beta = std::sqrt(1.0 - 1.0/std::pow(gamma,2));
  double sigmaP = optical[2][8];
  optical[2][8] = (sigmaP/meanP)*std::pow(beta,2);
 
  // write out the correlation x-y coefficient to the output as a matrix of horizontal-vertical coupling
  // writen only to the x vector, but 0 is added to y and z vectors to keep all vector sizes the same
  optical[0][24]=cenMoms[0][2][1][1]/std::sqrt(cenMoms[0][2][2][0]*cenMoms[0][2][0][2]);
 
  // emitt_x, emitt_y, err_emitt_x, err_emitt_y
  std::vector<double> emittanceOut = {optical[0][0],
                                      optical[1][0],
                                      optical[0][12],
                                      optical[1][12]};
 
  return emittanceOut;
}
 
double SamplerAnalysis::powSumToCentralMoment(fourDArray&   powSumsIn,
                                              long long int npartIn,
                                              int a,
                                              int b,
                                              int m,
                                              int n)
{
  double moment = 0.0;
 
  // Explicitly multiply out the number of particles to achieve the appropriate power.          
  // Typecast to a double is done to avoid integer overflow for large number of particles.
  double npartPow1 = (double)npartIn;
 
  // Done because of potential problems with the pow() funtion in C++ where some
  // arguments cause NaNs
  double npartPow2 = npartPow1 * npartPow1;
  double npartPow3 = npartPow2 * npartPow1;   
  double npartPow4 = npartPow3 * npartPow1;
 
  if((m == 1 && n == 0) || (m == 0 && n == 1))
    {
      double s_1_0 = powSumsIn[a][b][m][n];
      int k = m > n ? a : b;
 
      moment = s_1_0/npartIn+offsets[k];
    }
 
  else if((n == 2 && m == 0) || (n == 0 && m == 2))
    {
      double s_1_0 = 0.0, s_2_0 = 0.0;
      if(m == 2)
        {
          s_1_0 = powSumsIn[a][b][m-1][n];
          s_2_0 = powSumsIn[a][b][m][n];
        }
      else if(n == 2)
        {
          s_1_0 = powSumsIn[a][b][m][n-1];
          s_2_0 = powSumsIn[a][b][m][n];
        }
      
      moment =  (npartPow1*s_2_0 - std::pow(std::abs(s_1_0),2))/(npartPow1*(npartPow1-1));
    }
  
  else if(n == 1 && m == 1)
    {
      double s_1_0 = 0.0, s_0_1 = 0.0, s_1_1 = 0.0;
      
      s_1_0 = powSumsIn[a][b][m][n-1];
      s_0_1 = powSumsIn[a][b][m-1][n];
      s_1_1 = powSumsIn[a][b][m][n];
 
      moment =  (npartPow1*s_1_1 - s_0_1*s_1_0)/(npartPow1*(npartPow1-1));
    }
  
  else if((n == 4 && m == 0) || (n == 0 && m == 4))
    {
      double s_1_0 = 0.0, s_2_0 = 0.0, s_3_0 = 0.0, s_4_0 = 0.0;
      if(m == 4)
        {
          s_1_0 = powSumsIn[a][b][m-3][n];
          s_2_0 = powSumsIn[a][b][m-2][n];
          s_3_0 = powSumsIn[a][b][m-1][n];
          s_4_0 = powSumsIn[a][b][m][n];
        }
      else if( n == 4)
        {
          s_1_0 = powSumsIn[a][b][m][n-3];
          s_2_0 = powSumsIn[a][b][m][n-2];
          s_3_0 = powSumsIn[a][b][m][n-1];
          s_4_0 = powSumsIn[a][b][m][n];
        }
      
      moment = - (3*std::pow(s_1_0,4))/npartPow4 + (6*std::pow(s_1_0,2)*s_2_0)/npartPow3
        - (4*s_1_0*s_3_0)/npartPow2 + s_4_0/npartPow1;
    }
  
  else if((m == 3 && n == 1) || (m == 1 && n ==3))
    {
      double s_1_0 = 0.0, s_0_1 = 0.0, s_1_1 = 0.0, s_2_0 = 0.0, s_2_1 = 0.0, s_3_0 = 0.0, s_3_1 = 0.0;
      
      if(m == 3)
        {
          s_1_0 = powSumsIn[a][b][m-2][n-1];
          s_0_1 = powSumsIn[a][b][m-3][n];
          s_1_1 = powSumsIn[a][b][m-2][n];
          s_2_0 = powSumsIn[a][b][m-1][n-1];
          s_2_1 = powSumsIn[a][b][m-1][n];
          s_3_0 = powSumsIn[a][b][m][n-1];
          s_3_1 = powSumsIn[a][b][m][n];
        }
      else if(n == 3)
        {
          s_1_0 = powSumsIn[a][b][m-1][n-2];
          s_0_1 = powSumsIn[a][b][m][n-3];
          s_1_1 = powSumsIn[a][b][m][n-2];
          s_2_0 = powSumsIn[a][b][m-1][n-1];
          s_2_1 = powSumsIn[a][b][m][n-1];
          s_3_0 = powSumsIn[a][b][m-1][n];
          s_3_1 = powSumsIn[a][b][m][n];
        }
      
      moment = - (3*s_0_1*std::pow(s_1_0,3))/npartPow4 + (3*s_1_0*s_1_0*s_1_1)/npartPow3
        + (3*s_0_1*s_1_0*s_2_0)/npartPow3 - (3*s_1_0*s_2_1)/npartPow2
        - (s_0_1*s_3_0)/npartPow2 + s_3_1/npartPow1;
    }
  
  else if(m == 2 && n == 2)
    {
      double s_1_0 = 0.0, s_0_1 = 0.0, s_1_1 = 0.0, s_2_0 = 0.0, s_0_2 = 0.0, s_1_2 = 0.0, s_2_1 = 0.0, s_2_2 = 0.0;
      
      s_1_0 = powSumsIn[a][b][m-1][n-2];
      s_0_1 = powSumsIn[a][b][m-2][n-1];
      s_1_1 = powSumsIn[a][b][m-1][n-1];
      s_2_0 = powSumsIn[a][b][m][n-2];
      s_0_2 = powSumsIn[a][b][m-2][n];
      s_1_2 = powSumsIn[a][b][m-1][n];
      s_2_1 = powSumsIn[a][b][m][n-1];
      s_2_2 = powSumsIn[a][b][m][n];
 
      moment = - (3*std::pow(s_0_1,2)*std::pow(s_1_0,2))/npartPow4 + (s_0_2*std::pow(s_1_0,2))/npartPow3
               + (4*s_0_1*s_1_0*s_1_1)/npartPow3 - (2*s_1_0*s_1_2)/npartPow2
               + (std::pow(s_0_1,2)*s_2_0)/npartPow3 - (2*s_0_1*s_2_1)/npartPow2 + s_2_2/npartPow1;
    }
 
    return moment;
}
 
double SamplerAnalysis::centMomToCovariance(fourDArray&   centMoms,
                                            long long int npartIn,
                                            int k,
                                            int i,
                                            int j)
{  
  double cov = 0.0;
 
  int a = 0;
  if(k == 1) {a=2;}
  if(k == 2) {a=4;}
 
  if((i == 0 && j == 0) || (i == 1 && j == 1))
    {
      double m_4_0 = 0.0, m_2_0 = 0.0;
      
      if(i == 0)
        {       
          m_4_0 = centMoms[a][a+1][4][0];
          m_2_0 = centMoms[a][a+1][2][0];
        }
      
      else if(i == 1)
        {
          m_4_0 = centMoms[a][a+1][0][4];
              m_2_0 = centMoms[a][a+1][0][2];
        }
 
      cov = -((npartIn-3)*std::pow(m_2_0,2))/(npartIn*(npartIn-1)) + m_4_0/npartIn;
    }
  
  else if(i == 2 && j == 2)
    {
      double m_1_1 = 0.0, m_2_0 = 0.0, m_0_2 = 0.0, m_2_2 = 0.0;
 
      m_1_1 = centMoms[a][a+1][1][1];
      m_2_0 = centMoms[a][a+1][2][0];
      m_0_2 = centMoms[a][a+1][0][2];
      m_2_2 = centMoms[a][a+1][2][2];
 
      cov = -((npartIn-2)*std::pow(m_1_1,2))/(npartIn*(npartIn-1)) + (m_0_2*m_2_0)/(npartIn*(npartIn-1)) + m_2_2/npartIn;
    }
 
  else if((i == 0 && j == 2) || (i == 1 && j == 2) || (i == 2 && j == 0) || (i == 2 && j == 1))
  {
    double m_1_1 = 0.0, m_2_0 = 0.0, m_3_1 = 0.0;
 
    if((i == 0 && j == 2) || (i == 2 && j == 0 ))
    {
      m_1_1 = centMoms[a][a+1][1][1];
      m_2_0 = centMoms[a][a+1][2][0];
      m_3_1 = centMoms[a][a+1][3][1];
    }
    else if((i == 1 && j == 2) || (i == 2 && j == 1))
    {
      m_1_1 = centMoms[a][a+1][1][1];
      m_2_0 = centMoms[a][a+1][0][2];
      m_3_1 = centMoms[a][a+1][1][3];
    }
 
    cov = -((npartIn-3)*m_1_1*m_2_0)/(npartIn*(npartIn-1)) + m_3_1/npartIn;
  }
  else if((i == 0 && j == 1) || (i == 1 && j == 0) )
  {
    double m_1_1 = 0.0, m_2_0 = 0.0, m_0_2 = 0.0,  m_2_2 = 0.0;
      
    m_1_1 = centMoms[a][a+1][1][1];
    m_2_0 = centMoms[a][a+1][0][2];
    m_0_2 = centMoms[a][a+1][2][0];
    m_2_2 = centMoms[a][a+1][2][2];
 
    cov = 2*std::pow(m_1_1,2)/(npartIn*(npartIn-1)) - m_2_0*m_0_2/npartIn + m_2_2/npartIn;
  }
 
  return cov;
}
 
double SamplerAnalysis::centMomToDerivative(fourDArray& centMoms,
                                            int k,
                                            int t,
                                            int i)
 
{
  double deriv = 0.0;
 
  int a = 0;
  if(k == 1) {a=2;}
  if(k == 2) {a=4;}
  
  switch(t)   
    {
    case 0:
      //emittance
      if(i == 0 && k < 2)  // k<2 check selects transverse planes, longitudinal parameters are not calculated
      {
        deriv = centMoms[a][a+1][0][2]/(2*sqrt(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2)));
      }
      else if(i == 1 && k < 2)
      {
        deriv = centMoms[a][a+1][2][0]/(2*sqrt(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2)));
      }
      else if(i == 2 && k < 2)
      {
        deriv = -centMoms[a][a+1][1][1]/(sqrt(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2)));
      }
      else {deriv=0;}
      
      return deriv;
      break;
      
    case 1:
      //alpha
      if(i == 0 && k < 2) 
      {
        deriv = centMoms[a][a+1][0][2]*centMoms[a][a+1][1][1]/(2*std::pow(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2),3./2.));
      }
      else if(i == 1 && k < 2)
      {
        deriv = centMoms[a][a+1][2][0]*centMoms[a][a+1][1][1]/(2*std::pow(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2),3./2.)); 
      }
      else if(i == 2 && k < 2)
      {
        deriv = - centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]/std::pow(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2),3./2.);
      }
      else {deriv=0;}
      
      return deriv;
      break;
 
    case 2:
      //beta
      if(i == 0 && k < 2) 
      {
        deriv = (centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-2*std::pow(centMoms[a][a+1][1][1],2))/(2*std::pow(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2),3./2.)); 
      }
      else if(i == 1 && k < 2)
      {
        deriv = - std::pow(centMoms[a][a+1][2][0],2)/(2*std::pow(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2),3./2.));
      }
      else if(i == 2 && k < 2)
      {
        deriv = centMoms[a][a+1][2][0]*centMoms[a][a+1][1][1]/std::pow(centMoms[a][a+1][2][0]*centMoms[a][a+1][0][2]-std::pow(centMoms[a][a+1][1][1],2),3./2.);
      }
      else {deriv=0;}
      
      return deriv;
      break;
 
 
    case 3:
      //gamma
      return 0; // TODO
      break;
 
    case 4:
      //eta
      if(i == 0 && k < 2)
      {
        deriv = 0;
      }
      else if(i == 1 && k < 2)
      {
        deriv = -centMoms[a][4][1][1]/std::pow(centMoms[4][4][2][0],2);
      }
      else if(i == 2 && k < 2)
      {
        deriv = 1/centMoms[4][4][2][0];
      }
      else {deriv=0;}
      
      return deriv;
      break;
 
    case 5:
      //eta prime
      if(i == 0 && k < 2)
      {
        deriv = 0;
      }
      else if(i == 1 && k < 2)
      {
        deriv = -centMoms[a+1][4][1][1]/std::pow(centMoms[4][4][2][0],2);
      }
      else if(i == 2 && k < 2)
      {
        deriv = 1/centMoms[4][4][2][0];
      }
      else {deriv=0;}
      
      return deriv;
      break;
 
    case 6:                // mean derivatives are all 0 as they don't depend on second order moments
      //mean spatial    
      return 0;              
      break;
 
    case 7:
      //mean divergence
      return 0;
      break;
 
    case 8:
      //sigma spatial
      if(i == 0)
      {
        deriv = 1/(2*sqrt(centMoms[a][a+1][2][0]));
      }
      
      else {deriv=0;}
      
      return deriv;
      break;
 
    case 9:
      //sigma divergence
      if(i == 1)
      {
        deriv = 1/(2*sqrt(centMoms[a][a+1][0][2]));
      }
      
      else {deriv=0;}
      
      return deriv;
      break;
      
    default:
      return 0;
      break;
    }
}
 
 
void SamplerAnalysis::printBeamCorrelationMatrix(fourDArray&   centMoms)
{
  std::cout<<"\nCorrelation matrix for sampler: "<<s->samplerName<<std::endl;
  double corr = 0.0;
  for (int i=0; i<6; i++)
    {
      for(int j=0; j<6; j++)
        {
          corr = centMoms[i][j][1][1]/std::sqrt(centMoms[i][j][2][0]*centMoms[i][j][0][2]);
          std::printf("%- *.6e ", 12, corr);
        }
      std::printf("\n");
    }
 
}