SoftGaussParticleConstraint.cc

/**************************************************************************
 * basf2 (Belle II Analysis Software Framework)                           *
 * Author: The Belle II Collaboration                                     *
 *                                                                        *
 * Forked from https://github.com/iLCSoft/MarlinKinfit                    *
 *                                                                        *
 * Further information about the fit engine and the user interface        *
 * provided in MarlinKinfit can be found at                               *
 * https://www.desy.de/~blist/kinfit/doc/html/                            *
 * and in the LCNotes LC-TOOL-2009-001 and LC-TOOL-2009-004 available     *
 * from http://www-flc.desy.de/lcnotes/                                   *
 *                                                                        *
 * See git log for contributors and copyright holders.                    *
 * This file is licensed under LGPL-3.0, see LICENSE.md.                  *
 **************************************************************************/
 
#include "analysis/OrcaKinFit/SoftGaussParticleConstraint.h"
#include "analysis/OrcaKinFit/ParticleFitObject.h"
#include <framework/logging/Logger.h>
#include <iostream>
#include <cmath>
using namespace std;
 
namespace Belle2 {
  namespace OrcaKinFit {
 
    SoftGaussParticleConstraint::SoftGaussParticleConstraint(double sigma_)
      : sigma(sigma_)
    {
      invalidateCache();
    }
 
    double SoftGaussParticleConstraint::getSigma() const
    {
      return sigma;
    }
 
    double SoftGaussParticleConstraint::setSigma(double sigma_)
    {
      if (sigma_ != 0) sigma = std::abs(sigma_);
      return sigma;
    }
 
    double SoftGaussParticleConstraint::getChi2() const
    {
      double r = getValue() / getSigma();
      return r * r;
    }
 
    double SoftGaussParticleConstraint::getError() const
    {
      double dgdpi[4];
      double error2 = 0;
      for (unsigned int i = 0; i < fitobjects.size(); ++i) {
        const ParticleFitObject* foi = fitobjects[i];
        assert(foi);
        if (firstDerivatives(i, dgdpi)) {
          error2 += foi->getError2(dgdpi, getVarBasis());
        }
      }
      return std::sqrt(std::abs(error2));
    }
 
    void SoftGaussParticleConstraint::add2ndDerivativesToMatrix(double* M, int idim) const
    {
 
      double s = getSigma();
      double fact = 2 * getValue() / (s * s);
 
      // Derivatives \f$\frac{\partial ^2 g}{\partial P_i \partial P_j}\f$ at fixed i, j
      // d2GdPidPj[4*ii+jj] is derivative w.r.t. P_i,ii and P_j,jj, where ii=0,1,2,3 for E,px,py,pz
      double d2GdPidPj[16];
      // Derivatives \f$\frac {\partial P_i}{\partial a_k}\f$ for all i;
      // k is local parameter number
      // dPidAk[KMAX*4*i + 4*k + ii] is \f$\frac {\partial P_{i,ii}}{\partial a_k}\f$,
      // with ii=0, 1, 2, 3 for E, px, py, pz
      const int KMAX = 4;
      const int n = fitobjects.size();
      auto* dPidAk = new double[n * KMAX * 4];
      bool* dPidAkval = new bool[n];
 
      for (int i = 0; i < n; ++i) dPidAkval[i] = false;
 
      // Derivatives \f$\frac{\partial ^2 g}{\partial P_i \partial a_l}\f$ at fixed i
      // d2GdPdAl[4*l + ii] is \f$\frac{\partial ^2 g}{\partial P_{i,ii} \partial a_l}\f$
      double d2GdPdAl[4 * KMAX];
      // Derivatives \f$\frac{\partial ^2 g}{\partial a_k \partial a_l}\f$
      double d2GdAkdAl[KMAX * KMAX] = {0};
 
      // Global parameter numbers: parglobal[KMAX*i+klocal]
      // is global parameter number of local parameter klocal of i-th Fit object
      int* parglobal = new int[KMAX * n];
 
      for (int i = 0; i < n; ++i) {
        const ParticleFitObject* foi = fitobjects[i];
        assert(foi);
        for (int klocal = 0; klocal < foi->getNPar(); ++klocal) {
          parglobal [KMAX * i + klocal] = foi->getGlobalParNum(klocal);
        }
      }
 
 
      for (int i = 0; i < n; ++i) {
        const ParticleFitObject* foi = fitobjects[i];
        assert(foi);
        for (int j = 0; j < n; ++j) {
          const ParticleFitObject* foj = fitobjects[j];
          assert(foj);
          if (secondDerivatives(i, j, d2GdPidPj)) {
            if (!dPidAkval[i]) {
              foi->getDerivatives(dPidAk + i * (KMAX * 4), KMAX * 4);
              dPidAkval[i] = true;
            }
            if (!dPidAkval[j]) {
              foj->getDerivatives(dPidAk + j * (KMAX * 4), KMAX * 4);
              dPidAkval[j] = true;
            }
            // Now sum over E/px/Py/Pz for object j:
            // \f[
            //   \frac{\partial ^2 g}{\partial P_{i,ii} \partial a_l}
            //   = (sum_{j}) sum_{jj} frac{\partial ^2 g}{\partial P_{i,ii} \partial P_{j,jj}}
            //     \cdot \frac{\partial P_{j,jj}}{\partial a_l}
            // \f]
            // We're summing over jj here
            for (int llocal = 0; llocal < foj->getNPar(); ++llocal) {
              for (int ii = 0; ii < 4; ++ii) {
                int ind1 = 4 * ii;
                int ind2 = (KMAX * 4) * j + 4 * llocal;
                double& r = d2GdPdAl[4 * llocal + ii];
                r  = d2GdPidPj[  ind1] * dPidAk[  ind2];   // E
                r += d2GdPidPj[++ind1] * dPidAk[++ind2];   // px
                r += d2GdPidPj[++ind1] * dPidAk[++ind2];   // py
                r += d2GdPidPj[++ind1] * dPidAk[++ind2];   // pz
              }
            }
            // Now sum over E/px/Py/Pz for object i, i.e. sum over ii:
            // \f[
            // \frac{\partial ^2 g}{\partial a_k \partial a_l}
            //      = \sum_{ii} \frac{\partial ^2 g}{\partial P_{i,ii} \partial a_l} \cdot
            //        \frac{\partial P_{i,ii}}{\partial a_k}
            // \f]
            for (int klocal = 0; klocal < foi->getNPar(); ++klocal) {
              for (int llocal = 0; llocal < foj->getNPar(); ++llocal) {
                int ind1 = 4 * llocal;
                int ind2 = (KMAX * 4) * i + 4 * klocal;
                double& r = d2GdAkdAl[KMAX * klocal + llocal];
                r  = d2GdPdAl[  ind1] * dPidAk[  ind2];    //E
                r += d2GdPdAl[++ind1] * dPidAk[++ind2];   // px
                r += d2GdPdAl[++ind1] * dPidAk[++ind2];   // py
                r += d2GdPdAl[++ind1] * dPidAk[++ind2];   // pz
              }
            }
            // Now expand the local parameter numbers to global ones
            for (int klocal = 0; klocal < foi->getNPar(); ++klocal) {
              int kglobal = parglobal [KMAX * i + klocal];
              for (int llocal = 0; llocal < foj->getNPar(); ++llocal) {
                int lglobal = parglobal [KMAX * j + llocal];
                M [idim * kglobal + lglobal] += fact * d2GdAkdAl[KMAX * klocal + llocal];
              }
            }
          }
        }
      }
      auto* v = new double[idim];
      for (int i = 0; i < idim; ++i) v[i] = 0;
      double sqrtfact2 = sqrt(2.0) / s;
 
      double dgdpi[4];
      for (int i = 0; i < n; ++i) {
        const ParticleFitObject* foi = fitobjects[i];
        assert(foi);
        if (firstDerivatives(i, dgdpi)) {
          foi->addTo2ndDerivatives(M, idim, fact, dgdpi, getVarBasis());
          foi->addToGlobalChi2DerVector(v, idim, sqrtfact2, dgdpi, getVarBasis());
        }
      }
 
      for (int i = 0; i < idim; ++i) {
        if (double vi = v[i]) {
          int ioffs = i * idim;
          for (double* pvj = v; pvj < v + idim; ++pvj) {
            M[ioffs++] += vi * (*pvj);
          }
        }
      }
 
 
      delete[] dPidAk;
      delete[] dPidAkval;
      delete[] parglobal;
      delete[] v;
    }
 
    void SoftGaussParticleConstraint::addToGlobalChi2DerVector(double* y, int idim) const
    {
      double dgdpi[4];
      double s = getSigma();
      double r = 2 * getValue() / (s * s);
      for (unsigned int i = 0; i < fitobjects.size(); ++i) {
        const ParticleFitObject* foi = fitobjects[i];
        assert(foi);
        if (firstDerivatives(i, dgdpi)) {
          foi->addToGlobalChi2DerVector(y, idim, r, dgdpi, getVarBasis());
        }
      }
    }
 
    void SoftGaussParticleConstraint::test1stDerivatives()
    {
      B2INFO("SoftGaussParticleConstraint::test1stDerivatives for " << getName());
      double y[100];
      for (double& i : y) i = 0;
      addToGlobalChi2DerVector(y, 100);
      double eps = 0.00001;
      for (unsigned int ifo = 0; ifo < fitobjects.size(); ++ifo) {
        ParticleFitObject* fo = fitobjects[ifo];
        assert(fo);
        for (int ilocal = 0; ilocal < fo->getNPar(); ++ilocal) {
          int iglobal = fo->getGlobalParNum(ilocal);
          double calc = y[iglobal];
          double num = num1stDerivative(ifo, ilocal, eps);
          B2INFO("fo: " << fo->getName() << " par " << ilocal << "/"
                 << iglobal << " (" << fo->getParamName(ilocal)
                 << ") calc: " << calc << " - num: " << num << " = " << calc - num);
        }
      }
    }
    void SoftGaussParticleConstraint::test2ndDerivatives()
    {
      B2INFO("SoftGaussParticleConstraint::test2ndDerivatives for " << getName());
      const int idim = 100;
      auto* M = new double[idim * idim];
      for (int i = 0; i < idim * idim; ++i) M[i] = 0;
      add2ndDerivativesToMatrix(M, idim);
      double eps = 0.0001;
      B2INFO("eps=" << eps);
 
      for (unsigned int ifo1 = 0; ifo1 < fitobjects.size(); ++ifo1) {
        ParticleFitObject* fo1 = fitobjects[ifo1];
        assert(fo1);
        for (unsigned int ifo2 = ifo1; ifo2 < fitobjects.size(); ++ifo2) {
          ParticleFitObject* fo2 = fitobjects[ifo2];
          assert(fo2);
          for (int ilocal1 = 0; ilocal1 < fo1->getNPar(); ++ilocal1) {
            int iglobal1 = fo1->getGlobalParNum(ilocal1);
            for (int ilocal2 = (ifo1 == ifo2 ? ilocal1 : 0); ilocal2 < fo2->getNPar(); ++ilocal2) {
              int iglobal2 = fo2->getGlobalParNum(ilocal2);
              double calc = M[idim * iglobal1 + iglobal2];
              double num = num2ndDerivative(ifo1, ilocal1, eps, ifo2, ilocal2, eps);
              B2INFO("fo1: " << fo1->getName() << " par " << ilocal1 << "/"
                     << iglobal1 << " (" << fo1->getParamName(ilocal1)
                     << "), fo2: " << fo2->getName() << " par " << ilocal2 << "/"
                     << iglobal2 << " (" << fo2->getParamName(ilocal2)
                     << ") calc: " << calc << " - num: " << num << " = " << calc - num);
            }
          }
        }
      }
      delete[] M;
    }
 
 
    double SoftGaussParticleConstraint::num1stDerivative(int ifo, int ilocal, double eps)
    {
      ParticleFitObject* fo = fitobjects[ifo];
      assert(fo);
      double save = fo->getParam(ilocal);
      fo->setParam(ilocal, save + eps);
      double v1 = getChi2();
      fo->setParam(ilocal, save - eps);
      double v2 = getChi2();
      double result = (v1 - v2) / (2 * eps);
      fo->setParam(ilocal, save);
      return result;
    }
 
    double SoftGaussParticleConstraint::num2ndDerivative(int ifo1, int ilocal1, double eps1,
                                                         int ifo2, int ilocal2, double eps2)
    {
      double result;
 
      if (ifo1 == ifo2 && ilocal1 == ilocal2) {
        ParticleFitObject* fo = fitobjects[ifo1];
        assert(fo);
        double save = fo->getParam(ilocal1);
        double v0 = getChi2();
        fo->setParam(ilocal1, save + eps1);
        double v1 = getChi2();
        fo->setParam(ilocal1, save - eps1);
        double v2 = getChi2();
        result = (v1 + v2 - 2 * v0) / (eps1 * eps1);
        fo->setParam(ilocal1, save);
      } else {
        ParticleFitObject* fo1 = fitobjects[ifo1];
        assert(fo1);
        ParticleFitObject* fo2 = fitobjects[ifo2];
        assert(fo2);
        double save1 = fo1->getParam(ilocal1);
        double save2 = fo2->getParam(ilocal2);
        fo1->setParam(ilocal1, save1 + eps1);
        fo2->setParam(ilocal2, save2 + eps2);
        double v11 = getChi2();
        fo2->setParam(ilocal2, save2 - eps2);
        double v12 = getChi2();
        fo1->setParam(ilocal1, save1 - eps1);
        double v22 = getChi2();
        fo2->setParam(ilocal2, save2 + eps2);
        double v21 = getChi2();
        result = (v11 + v22 - v12 - v21) / (4 * eps1 * eps2);
        fo1->setParam(ilocal1, save1);
        fo2->setParam(ilocal2, save2);
      }
      return result;
    }
 
    int SoftGaussParticleConstraint::getVarBasis() const
    {
      return VAR_BASIS;
    }
  }// end OrcaKinFit namespace
} // end Belle2 namespace