GenericHouseholder.cc

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#include "Calibration/Tools/interface/GenericHouseholder.h"
#include <cfloat>
#include <cmath>

GenericHouseholder::GenericHouseholder(bool normalise) : normaliseFlag(normalise) {}

GenericHouseholder::~GenericHouseholder() {}

std::vector<float> GenericHouseholder::iterate(const std::vector<std::vector<float> >& eventMatrix,
                                               const std::vector<float>& energyVector,
                                               const int nIter) {
  std::vector<float> solution;
  std::vector<float> theCalibVector(energyVector.size(), 1.);
  std::vector<std::vector<float> > myEventMatrix(eventMatrix);
  int Nevents = eventMatrix.size();       // Number of events to calibrate with
  int Nchannels = eventMatrix[0].size();  // Number of channel coefficients

  // Iterate the correction
  for (int iter = 1; iter <= nIter; iter++) {
    // make one iteration
    solution = iterate(myEventMatrix, energyVector);

    if (solution.empty())
      return solution;
    // R.O.: or throw an exception, what's the standard CMS way ?

    // re-calibrate eventMatrix with solution
    for (int i = 0; i < Nchannels; i++) {
      for (int ievent = 0; ievent < Nevents; ievent++) {
        myEventMatrix[ievent][i] *= solution[i];
      }
      // save solution into theCalibVector
      theCalibVector[i] *= solution[i];
    }

  }  // end iterate the correction

  return theCalibVector;
}

std::vector<float> GenericHouseholder::iterate(const std::vector<std::vector<float> >& eventMatrix,
                                               const std::vector<float>& energyVector) {
  // An implementation of the Householder in-situ calibration algorithm
  // (Least squares minimisation of residual R=b-Ax, with QR decomposition of A)
  // A: matrix of channel response for all calib events
  // x: vector of channel calibration coefficients
  // b: vector of energies
  // adapted from the original code by Matt Probert 9/08/01.

  std::vector<float> solution;

  unsigned int m = eventMatrix.size();     // Number of events to calibrate with
  unsigned int n = eventMatrix[0].size();  // Number of channel coefficients to optimize

  std::cout << "Householder::runIter(): starting calibration optimization:" << std::endl;
  std::cout << "  Events:" << m << ", channels: " << n << std::endl;

  // Sanity check
  if (m != energyVector.size()) {
    std::cout << "Householder::runIter(): matrix dimensions non-conformant. " << std::endl;
    std::cout << "  energyVector.size()=" << energyVector.size() << std::endl;
    std::cout << "  eventMatrix[0].size()=" << eventMatrix[0].size() << std::endl;
    std::cout << " ******************    ERROR   *********************" << std::endl;
    return solution;  // empty vector
  }

  // Reserve workspace
  float e25p;
  unsigned int i, j;
  std::vector<std::vector<float> > A(eventMatrix);
  std::vector<float> energies(energyVector);

  float normalisation = 0.;

  // Normalise if normaliseFlag is set
  if (normaliseFlag) {
    std::cout << "Householder::iterate(): Normalising event data" << std::endl;
    std::cout << "  WARNING: assuming 5x5 filtering has already been done" << std::endl;

    for (i = 0; i < m; i++) {
      e25p = 0.;
      for (j = 0; j < n; j++) {
        e25p += eventMatrix[i][j];  // lorenzo -> trying to use ESetup which already performs calibs on rechits
      }
      e25p /= energyVector[i];
      normalisation += e25p;  // SUM e25p for all events
    }
    normalisation /= m;
    std::cout << "  Normalisation = " << normalisation << std::endl;

    for (i = 0; i < energies.size(); ++i)
      energies[i] *= normalisation;
  }

  // This is where the work goes on...
  // matrix decomposition
  std::vector<std::vector<float> > Acopy(A);
  std::vector<float> alpha(n);
  std::vector<int> pivot(n);
  if (!decompose(m, n, A, alpha, pivot)) {
    std::cout << "Householder::runIter(): Failed: Singular condition in decomposition." << std::endl;
    std::cout << "***************** PROBLEM in DECOMPOSITION *************************" << std::endl;
    return solution;  // empty vector
  }

  /* DBL_EPSILON: Difference between 1.0 and the minimum float greater than 1.0 */
  float etasqr = DBL_EPSILON * DBL_EPSILON;
  std::cout << "LOOK at DBL_EPSILON :" << DBL_EPSILON << std::endl;

  std::vector<float> r(energies);  // copy energies vector
  std::vector<float> e(n);

  // apply transformations to rhs - find solution vector
  solution.assign(n, 0.);
  solve(m, n, A, alpha, pivot, r, solution);

  // compute residual vector r
  for (i = 0; i < m; i++) {
    r[i] = energies[i];
    for (j = 0; j < n; j++)
      r[i] -= Acopy[i][j] * solution[j];
  }
  // compute first correction vector e
  solve(m, n, A, alpha, pivot, r, e);

  float normy0 = 0.;
  float norme1 = 0.;
  float norme0;

  for (i = 0; i < n; i++) {
    normy0 += solution[i] * solution[i];
    norme1 += e[i] * e[i];
  }

  std::cout << "Householder::runIter(): applying first correction" << std::endl;
  std::cout << " normy0 = " << normy0 << std::endl;
  std::cout << " norme1 = " << norme1 << std::endl;

  // not attempt at obtaining the solution is made unless the norm of the first
  // correction  is significantly smaller than the norm of the initial solution
  if (norme1 > (0.0625 * normy0)) {
    std::cout << "Householder::runIter(): first correction is too large. Failed." << std::endl;
  }

  // improve the solution
  for (i = 0; i < n; i++)
    solution[i] += e[i];

  std::cout << "Householder::runIter(): improving solution...." << std::endl;

  // only continue iteration if the correction was significant
  while (norme1 > (etasqr * normy0)) {
    std::cout << "Householder::runIter(): norme1 = " << norme1 << std::endl;

    for (i = 0; i < m; i++) {
      r[i] = energies[i];
      for (j = 0; j < n; j++)
        r[i] -= Acopy[i][j] * solution[j];
    }

    // compute next correction vector
    solve(m, n, A, alpha, pivot, r, e);

    norme0 = norme1;
    norme1 = 0.;
    for (i = 0; i < n; i++)
      norme1 += e[i] * e[i];

    // terminate iteration if the norm of the new correction failed to decrease
    // significantly compared to the norm of the previous correction
    if (norme1 > (0.0625 * norme0))
      break;

    // apply correction vector
    for (i = 0; i < n; i++)
      solution[i] += e[i];
  }

  return solution;
}

bool GenericHouseholder::decompose(const int m,
                                   const int n,
                                   std::vector<std::vector<float> >& qr,
                                   std::vector<float>& alpha,
                                   std::vector<int>& pivot) {
  int i, j, jbar, k;
  float beta, sigma, alphak, qrkk;
  std::vector<float> y(n);
  std::vector<float> sum(n);

  std::cout << "Householder::decompose() started" << std::endl;

  for (j = 0; j < n; j++) {
    // jth column sum

    sum[j] = 0.;
    for (i = 0; i < m; i++)
      //      std::cout << "0: qr[i][j]" << qr[i][j] << " i = " << i << " j = " << j << std::endl;
      sum[j] += qr[i][j] * qr[i][j];

    pivot[j] = j;
  }

  for (k = 0; k < n; k++) {
    // kth Householder transformation

    sigma = sum[k];
    jbar = k;

    for (j = k + 1; j < n; j++) {
      if (sigma < sum[j]) {
        sigma = sum[j];
        jbar = j;
      }
    }

    if (jbar != k) {
      // column interchange
      i = pivot[k];
      pivot[k] = pivot[jbar];
      pivot[jbar] = i;
      sum[jbar] = sum[k];
      sum[k] = sigma;

      for (i = 0; i < m; i++) {
        sigma = qr[i][k];
        qr[i][k] = qr[i][jbar];
        //      std::cout << "A: qr[i][k]" << qr[i][k] << " i = " << i << " k = " << k << std::endl;
        qr[i][jbar] = sigma;
        //      std::cout << "B: qr[i][jbar]" << qr[i][k] << " i = " << i << " jbar = " << jbar << std::endl;
      }
    }  // end column interchange

    sigma = 0.;
    for (i = k; i < m; i++) {
      sigma += qr[i][k] * qr[i][k];
      //      std::cout << "C: qr[i][k]" << qr[i][k] << " i = " << i << " k = " << k << std::endl;
    }

    if (sigma == 0.) {
      std::cout << "Householder::decompose() failed" << std::endl;
      return false;
    }

    qrkk = qr[k][k];

    if (qrkk < 0.)
      alpha[k] = sqrt(sigma);
    else
      alpha[k] = sqrt(sigma) * (-1.);
    alphak = alpha[k];

    beta = 1 / (sigma - qrkk * alphak);
    qr[k][k] = qrkk - alphak;

    for (j = k + 1; j < n; j++) {
      y[j] = 0.;
      for (i = k; i < m; i++)
        y[j] += qr[i][k] * qr[i][j];
      y[j] *= beta;
    }

    for (j = k + 1; j < n; j++) {
      for (i = k; i < m; i++) {
        qr[i][j] -= qr[i][k] * y[j];
        sum[j] -= qr[k][j] * qr[k][j];
      }
    }
  }  // end of kth householder transformation

  std::cout << "Householder::decompose() finished" << std::endl;

  return true;
}

void GenericHouseholder::solve(int m,
                               int n,
                               const std::vector<std::vector<float> >& qr,
                               const std::vector<float>& alpha,
                               const std::vector<int>& pivot,
                               std::vector<float>& r,
                               std::vector<float>& y) {
  std::vector<float> z(n, 0.);

  float gamma;
  int i, j;

  std::cout << "Householder::solve() begin" << std::endl;

  for (j = 0; j < n; j++) {
    // apply jth transformation to the right hand side
    gamma = 0.;
    for (i = j; i < m; i++)
      gamma += qr[i][j] * r[i];
    gamma /= (alpha[j] * qr[j][j]);

    for (i = j; i < m; i++)
      r[i] += gamma * qr[i][j];
  }

  //  std::cout<<"OK1:"<<std::endl;
  z[n - 1] = r[n - 1] / alpha[n - 1];
  //  std::cout<<"OK2:"<<std::endl;

  for (i = n - 2; i >= 0; i--) {
    z[i] = r[i];
    for (j = i + 1; j < n; j++)
      z[i] -= qr[i][j] * z[j];
    z[i] /= alpha[i];
  }
  //  std::cout<<"OK3:"<<std::endl;

  for (i = 0; i < n; i++)
    y[pivot[i]] = z[i];

  std::cout << "Householder::solve() finished." << std::endl;
}