BundleAdjust.cpp

 
/* SPDX-License-Identifier: CC0-1.0 */
 
#include "BundleAdjust.h"
 
// std lib
#include <iomanip>
#include <iostream>
#include <sstream>
 
// qt lib
#include <QCoreApplication>
#include <QDebug>
#include <QFile>
#include <QMutex>
 
// boost lib
#include <boost/lexical_cast.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
 
// Isis lib
#include "Application.h"
#include "BundleObservation.h"
#include "IsisBundleObservation.h"
#include "BundleObservationSolveSettings.h"
#include "BundleResults.h"
#include "BundleSettings.h"
#include "BundleSolutionInfo.h"
#include "BundleTargetBody.h"
#include "Camera.h"
#include "CameraDetectorMap.h"
#include "CameraDistortionMap.h"
#include "CameraFocalPlaneMap.h"
#include "CameraGroundMap.h"
#include "CSMCamera.h"
#include "Control.h"
#include "ControlPoint.h"
#include "CorrelationMatrix.h"
#include "Distance.h"
#include "ImageList.h"
#include "iTime.h"
#include "Latitude.h"
#include "Longitude.h"
#include "MaximumLikelihoodWFunctions.h"
#include "SpecialPixel.h"
#include "StatCumProbDistDynCalc.h"
#include "SurfacePoint.h"
#include "Target.h"
 
using namespace boost::numeric::ublas;
using namespace Isis;
 
namespace Isis {
 
 
  static void cholmodErrorHandler(int nStatus,
                                  const char* file,
                                  int nLineNo,
                                  const char* message) {
    QString errlog;
 
    errlog = "SPARSE: ";
    errlog += message;
 
    PvlGroup gp(errlog);
 
    gp += PvlKeyword("File",file);
    gp += PvlKeyword("Line_Number", toString(nLineNo));
    gp += PvlKeyword("Status", toString(nStatus));
 
//    Application::Log(gp);
 
    errlog += ". (See print.prt for details)";
 
//    throw IException(IException::Unknown, errlog, _FILEINFO_);
  }
 
 
  BundleAdjust::BundleAdjust(BundleSettingsQsp bundleSettings,
                             const QString &cnetFile,
                             const QString &cubeList,
                             bool printSummary) {
    m_abort = false;
    Progress progress;
    // initialize constructor dependent settings...
    // m_printSummary, m_cleanUp, m_cnetFileName, m_controlNet,
    // m_serialNumberList, m_bundleSettings
    m_printSummary = printSummary;
    m_cleanUp = true;
    m_cnetFileName = cnetFile;
    try {
      m_controlNet = ControlNetQsp( new ControlNet(cnetFile, &progress,
                                     bundleSettings->controlPointCoordTypeReports()) );
    }
    catch (IException &e) {
      throw;
    }
    m_bundleResults.setOutputControlNet(m_controlNet);
    m_serialNumberList = new SerialNumberList(cubeList);
    m_bundleSettings = bundleSettings;
    m_bundleTargetBody = bundleSettings->bundleTargetBody();
 
    init(&progress);
  }
 
 
  BundleAdjust::BundleAdjust(BundleSettingsQsp bundleSettings,
                             QString &cnetFile,
                             SerialNumberList &snlist,
                             bool printSummary) {
    // initialize constructor dependent settings...
    // m_printSummary, m_cleanUp, m_cnetFileName, m_controlNet,
    // m_serialNumberList, m_bundleSettings
    m_abort = false;
    Progress progress;
    m_printSummary = printSummary;
    m_cleanUp = false;
    m_cnetFileName = cnetFile;
    try {
      m_controlNet = ControlNetQsp( new ControlNet(cnetFile, &progress) );
    }
    catch (IException &e) {
      throw;
    }
    m_bundleResults.setOutputControlNet(m_controlNet);
    m_serialNumberList = &snlist;
    m_bundleSettings = bundleSettings;
    m_bundleTargetBody = bundleSettings->bundleTargetBody();
 
    init();
  }
 
 
  BundleAdjust::BundleAdjust(BundleSettingsQsp bundleSettings,
                             Control &cnet,
                             SerialNumberList &snlist,
                             bool printSummary) {
    // initialize constructor dependent settings...
    // m_printSummary, m_cleanUp, m_cnetFileName, m_controlNet,
    // m_serialNumberList, m_bundleSettings
    m_abort = false;
    Progress progress;
    m_printSummary = printSummary;
    m_cleanUp = false;
    m_cnetFileName = cnet.fileName();
    try {
      m_controlNet = ControlNetQsp( new ControlNet(cnet.fileName(), &progress) );
    }
    catch (IException &e) {
      throw;
    }
    m_bundleResults.setOutputControlNet(m_controlNet);
    m_serialNumberList = &snlist;
    m_bundleSettings = bundleSettings;
    m_bundleTargetBody = bundleSettings->bundleTargetBody();
 
    init();
  }
 
 
  BundleAdjust::BundleAdjust(BundleSettingsQsp bundleSettings,
                             ControlNet &cnet,
                             SerialNumberList &snlist,
                             bool printSummary) {
    // initialize constructor dependent settings...
    // m_printSummary, m_cleanUp, m_cnetFileName, m_controlNet,
    // m_serialNumberList, m_bundleSettings
    m_abort = false;
    m_printSummary = printSummary;
    m_cleanUp = false;
    m_cnetFileName = "";
    try {
      m_controlNet = ControlNetQsp( new ControlNet(cnet) );
    }
    catch (IException &e) {
      throw;
    }
    m_bundleResults.setOutputControlNet(m_controlNet);
    m_serialNumberList = &snlist;
    m_bundleSettings = bundleSettings;
    m_bundleTargetBody = bundleSettings->bundleTargetBody();
 
    init();
  }
 
 
  BundleAdjust::BundleAdjust(BundleSettingsQsp bundleSettings,
                             ControlNetQsp cnet,
                             const QString &cubeList,
                             bool printSummary) {
    m_abort = false;
    m_printSummary = printSummary;
    m_cleanUp = false;
    m_cnetFileName = "";
    try {
      m_controlNet = cnet;
    }
    catch (IException &e) {
      throw;
    }
    m_bundleResults.setOutputControlNet(m_controlNet);
    m_serialNumberList = new SerialNumberList(cubeList);
    m_bundleSettings = bundleSettings;
    m_bundleTargetBody = bundleSettings->bundleTargetBody();
 
    init();
  }
 
 
  BundleAdjust::BundleAdjust(BundleSettingsQsp bundleSettings,
                             Control &control,
                             QList<ImageList *> imgLists,
                             bool printSummary) {
    m_bundleSettings = bundleSettings;
 
    m_abort = false;
    try {
      m_controlNet = ControlNetQsp( new ControlNet(control.fileName()) );
    }
    catch (IException &e) {
      throw;
    }
    m_bundleResults.setOutputControlNet(m_controlNet);
 
    m_imageLists = imgLists;
 
    // this is too slow and we need to get rid of the serial number list anyway
    // should be unnecessary as Image class has serial number
    // could hang on to image list until creating BundleObservations?
    m_serialNumberList = new SerialNumberList;
 
    foreach (ImageList *imgList, imgLists) {
      foreach (Image *image, *imgList) {
        m_serialNumberList->add(image->fileName());
//      m_serialNumberList->add(image->serialNumber(), image->fileName());
      }
    }
 
    m_bundleTargetBody = bundleSettings->bundleTargetBody();
 
    m_printSummary = printSummary;
 
    m_cleanUp = false;
    m_cnetFileName = control.fileName();
 
    init();
  }
 
 
  BundleAdjust::~BundleAdjust() {
    // If we have ownership
    if (m_cleanUp) {
      delete m_serialNumberList;
    }
 
    freeCHOLMODLibraryVariables();
 
  }
 
 
  void BundleAdjust::init(Progress *progress) {
    emit(statusUpdate("Initialization"));
    m_previousNumberImagePartials = 0;
 
    // initialize
    //
    // JWB
    // - some of these not originally initialized.. better values???
    m_iteration = 0;
    m_rank = 0;
    m_iterationSummary = "";
 
    // Get the cameras set up for all images
    // NOTE - THIS IS NOT THE SAME AS "setImage" as called in BundleAdjust::computePartials
    // this call only does initializations; sets measure's camera pointer, etc
    // RENAME????????????
    m_controlNet->SetImages(*m_serialNumberList, progress);
 
    // clear JigsawRejected flags
    m_controlNet->ClearJigsawRejected();
 
    // initialize held variables
    int numImages = m_serialNumberList->size();
 
    // matrix stuff
    m_normalInverse.clear();
    m_RHS.clear();
    m_imageSolution.clear();
 
    // we don't want to call initializeCHOLMODLibraryVariables() here since mRank=0
    // m_cholmodCommon, m_sparseNormals are not initialized
    m_L = NULL;
    m_cholmodNormal = NULL;
    m_cholmodTriplet = NULL;
 
    // should we initialize objects m_xResiduals, m_yResiduals, m_xyResiduals
 
      // TESTING
      // TODO: code below should go into a separate method???
      // set up BundleObservations and assign solve settings for each from BundleSettings class
      for (int i = 0; i < numImages; i++) {
 
        Camera *camera = m_controlNet->Camera(i);
        QString observationNumber = m_serialNumberList->observationNumber(i);
        QString instrumentId = m_serialNumberList->spacecraftInstrumentId(i);
        QString serialNumber = m_serialNumberList->serialNumber(i);
        QString fileName = m_serialNumberList->fileName(i);
 
        // create a new BundleImage and add to new (or existing if observation mode is on)
        // BundleObservation
        BundleImageQsp image = BundleImageQsp(new BundleImage(camera, serialNumber, fileName));
 
        if (!image) {
          QString msg = "In BundleAdjust::init(): image " + fileName + "is null." + "\n";
          throw IException(IException::Programmer, msg, _FILEINFO_);
        }
 
        BundleObservationQsp observation =
            m_bundleObservations.addNew(image, observationNumber, instrumentId, m_bundleSettings);
 
        if (!observation) {
          QString msg = "In BundleAdjust::init(): observation "
                        + observationNumber + "is null." + "\n";
          throw IException(IException::Programmer, msg, _FILEINFO_);
        }
      }
 
      // set up vector of BundleControlPoints
      int numControlPoints = m_controlNet->GetNumPoints();
      for (int i = 0; i < numControlPoints; i++) {
        ControlPoint *point = m_controlNet->GetPoint(i);
        if (point->IsIgnored()) {
          continue;
        }
 
        BundleControlPointQsp bundleControlPoint(new BundleControlPoint
                            (m_bundleSettings, point));
        m_bundleControlPoints.append(bundleControlPoint);
 
        // set parent observation for each BundleMeasure
 
        int numMeasures = bundleControlPoint->size();
        for (int j=0; j < numMeasures; j++) {
          BundleMeasureQsp measure = bundleControlPoint->at(j);
          QString cubeSerialNumber = measure->cubeSerialNumber();
 
          BundleObservationQsp observation =
              m_bundleObservations.observationByCubeSerialNumber(cubeSerialNumber);
          BundleImageQsp image = observation->imageByCubeSerialNumber(cubeSerialNumber);
 
          measure->setParentObservation(observation);
          measure->setParentImage(image);
        }
      }
 
    //===========================================================================================//
    //==== Use the bundle settings to initialize more member variables and set up solutions =====//
    //===========================================================================================//
 
    // TODO:  Need to have some validation code to make sure everything is
    // on the up-and-up with the control network.  Add checks for multiple
    // networks, images without any points, and points on images removed from
    // the control net (when we start adding software to remove points with high
    // residuals) and ?.  For "deltack" a single measure on a point is allowed
    // so skip the test.
    if (m_bundleSettings->validateNetwork()) {
      validateNetwork();
    }
    m_bundleResults.maximumLikelihoodSetUp(m_bundleSettings->maximumLikelihoodEstimatorModels());
 
    //===========================================================================================//
    //=============== End Bundle Settings =======================================================//
    //===========================================================================================//
 
    //===========================================================================================//
    //======================== initialize matrices and more parameters ==========================//
    //===========================================================================================//
 
    // size of reduced normals matrix
 
    // TODO
    // this should be determined from BundleSettings
    // m_rank will be the sum of observation, target, and self-cal parameters
    // TODO
    m_rank = m_bundleObservations.numberParameters();
 
    if (m_bundleSettings->solveTargetBody()) {
      m_rank += m_bundleSettings->numberTargetBodyParameters();
 
      if (m_bundleTargetBody->solveMeanRadius() || m_bundleTargetBody->solveTriaxialRadii()) {
        outputBundleStatus("Warning: Solving for the target body radii (triaxial or mean) "
                           "is NOT possible and likely increases error in the solve.\n");
      }
 
      if (m_bundleTargetBody->solveMeanRadius()){
        // Check if MeanRadiusValue is abnormal compared to observation
        bool isMeanRadiusValid = true;
        double localRadius, aprioriRadius;
 
        // Arbitrary control point containing an observed localRadius
        BundleControlPointQsp point = m_bundleControlPoints.at(0);
        SurfacePoint surfacepoint = point->adjustedSurfacePoint();
 
        localRadius = surfacepoint.GetLocalRadius().meters();
        aprioriRadius = m_bundleTargetBody->meanRadius().meters();
 
        // Ensure aprioriRadius is within some threshold
        // Considered potentially inaccurate if it's off by atleast a factor of two
        if (aprioriRadius >= 2 * localRadius || aprioriRadius <= localRadius / 2) {
            isMeanRadiusValid = false;
        }
 
        // Warn user for abnormal MeanRadiusValue
        if (!isMeanRadiusValid) {
          outputBundleStatus("Warning: User-entered MeanRadiusValue appears to be inaccurate. "
                             "This can cause a bundle failure.\n");
        }
      }
    }
 
    int num3DPoints = m_bundleControlPoints.size();
 
    m_bundleResults.setNumberUnknownParameters(m_rank + 3 * num3DPoints);
 
    m_imageSolution.resize(m_rank);
 
    //~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    // initializations for cholmod
    initializeCHOLMODLibraryVariables();
 
    // initialize normal equations matrix
    initializeNormalEquationsMatrix();
  }
 
 
  bool BundleAdjust::validateNetwork() {
 
    outputBundleStatus("\nValidating network...");
 
    int imagesWithInsufficientMeasures = 0;
    QString msg = "Images with one or less measures:\n";
    int numObservations = m_bundleObservations.size();
    for (int i = 0; i < numObservations; i++) {
      int numImages = m_bundleObservations.at(i)->size();
      for (int j = 0; j < numImages; j++) {
        BundleImageQsp bundleImage = m_bundleObservations.at(i)->at(j);
        int numMeasures = m_controlNet->
                              GetNumberOfValidMeasuresInImage(bundleImage->serialNumber());
 
        if (numMeasures > 1) {
          continue;
        }
 
        imagesWithInsufficientMeasures++;
        msg += bundleImage->fileName() + ": " + toString(numMeasures) + "\n";
      }
    }
 
    if ( imagesWithInsufficientMeasures > 0 ) {
      throw IException(IException::User, msg, _FILEINFO_);
    }
 
    outputBundleStatus("\nValidation complete!...\n");
 
    return true;
  }
 
  bool BundleAdjust::initializeCHOLMODLibraryVariables() {
    if ( m_rank <= 0 ) {
      return false;
    }
 
    m_cholmodTriplet = NULL;
 
    cholmod_start(&m_cholmodCommon);
 
    // set user-defined cholmod error handler
    m_cholmodCommon.error_handler = cholmodErrorHandler;
 
    // testing not using metis
    m_cholmodCommon.nmethods = 1;
    m_cholmodCommon.method[0].ordering = CHOLMOD_AMD;
 
    return true;
  }
 
 
  bool BundleAdjust::initializeNormalEquationsMatrix() {
 
    int nBlockColumns = m_bundleObservations.size();
 
    if (m_bundleSettings->solveTargetBody())
      nBlockColumns += 1;
 
    m_sparseNormals.setNumberOfColumns(nBlockColumns);
 
    m_sparseNormals.at(0)->setStartColumn(0);
 
    int nParameters = 0;
    if (m_bundleSettings->solveTargetBody()) {
      nParameters += m_bundleSettings->numberTargetBodyParameters();
      m_sparseNormals.at(1)->setStartColumn(nParameters);
 
      int observation = 0;
      for (int i = 2; i < nBlockColumns; i++) {
        nParameters += m_bundleObservations.at(observation)->numberParameters();
        m_sparseNormals.at(i)->setStartColumn(nParameters);
        observation++;
      }
    }
    else {
      for (int i = 0; i < nBlockColumns; i++) {
        m_sparseNormals.at(i)->setStartColumn(nParameters);
        nParameters += m_bundleObservations.at(i)->numberParameters();
      }
    }
 
    return true;
  }
 
 
  bool BundleAdjust::freeCHOLMODLibraryVariables() {
 
    cholmod_free_triplet(&m_cholmodTriplet, &m_cholmodCommon);
    cholmod_free_sparse(&m_cholmodNormal, &m_cholmodCommon);
    cholmod_free_factor(&m_L, &m_cholmodCommon);
 
    cholmod_finish(&m_cholmodCommon);
 
    return true;
  }
 
 
  BundleSolutionInfo* BundleAdjust::solveCholeskyBR() {
    solveCholesky();
    return bundleSolveInformation();
  }
 
 
  void BundleAdjust::abortBundle() {
    m_abort = true;
  }
 
 
  bool BundleAdjust::solveCholesky() {
    emit(statusBarUpdate("Solving"));
    try {
 
      // throw error if a frame camera is included AND
      // if m_bundleSettings->solveInstrumentPositionOverHermiteSpline()
      // is set to true (can only use for line scan or radar)
  //    if (m_bundleSettings->solveInstrumentPositionOverHermiteSpline() == true) {
  //      int numImages = images();
  //      for (int i = 0; i < numImages; i++) {
  //        if (m_controlNet->Camera(i)->GetCameraType() == 0) {
  //          QString msg = "At least one sensor is a frame camera. "
  //                        "Spacecraft Option OVERHERMITE is not valid for frame cameras\n";
  //          throw IException(IException::User, msg, _FILEINFO_);
  //        }
  //      }
  //    }
 
      // Compute the apriori coordinates for each nonheld point
      m_controlNet->ComputeApriori(); // original location
 
      // ken testing - if solving for target mean radius, set point radius to current mean radius
      // if solving for triaxial radii, set point radius to local radius
      if (m_bundleTargetBody && m_bundleTargetBody->solveMeanRadius()) {
        int numControlPoints = m_bundleControlPoints.size();
        for (int i = 0; i < numControlPoints; i++) {
          BundleControlPointQsp point = m_bundleControlPoints.at(i);
          SurfacePoint surfacepoint = point->adjustedSurfacePoint();
 
          surfacepoint.ResetLocalRadius(m_bundleTargetBody->meanRadius());
 
          point->setAdjustedSurfacePoint(surfacepoint);
        }
      }
 
      // Only use target body solution options when using Latitudinal coordinates
      if (m_bundleTargetBody && m_bundleTargetBody->solveTriaxialRadii()
         && m_bundleSettings->controlPointCoordTypeBundle() == SurfacePoint::Latitudinal) {
        int numControlPoints = m_bundleControlPoints.size();
        for (int i = 0; i < numControlPoints; i++) {
          BundleControlPointQsp point = m_bundleControlPoints.at(i);
          SurfacePoint surfacepoint = point->adjustedSurfacePoint();
 
          Distance localRadius = m_bundleTargetBody->localRadius(surfacepoint.GetLatitude(),
                                                                 surfacepoint.GetLongitude());
          surfacepoint.ResetLocalRadius(localRadius);
 
          point->setAdjustedSurfacePoint(surfacepoint);
        }
      }
 
      // Beginning of iterations
      m_iteration = 1;
      double vtpv = 0.0;
      double previousSigma0 = 0.0;
 
      // start the clock
      clock_t solveStartClock = clock();
 
      for (;;) {
 
        emit iterationUpdate(m_iteration);
 
        // testing
        if (m_abort) {
          m_bundleResults.setConverged(false);
          emit statusUpdate("\n aborting...");
          emit finished();
          return false;
        }
        // testing
 
        emit statusUpdate( QString("starting iteration %1\n").arg(m_iteration) );
 
        clock_t iterationStartClock = clock();
 
        // zero normals (after iteration 0)
        if (m_iteration != 1) {
          m_sparseNormals.zeroBlocks();
        }
 
        // form normal equations -- computePartials is called in here.
        if (!formNormalEquations()) {
          m_bundleResults.setConverged(false);
          break;
        }
 
        // testing
        if (m_abort) {
          m_bundleResults.setConverged(false);
          emit statusUpdate("\n aborting...");
          emit finished();
          return false;
        }
        // testing
 
        // solve the system
        if (!solveSystem()) {
          outputBundleStatus("\nsolve failed!");
          m_bundleResults.setConverged(false);
          break;
        }
 
        // testing
        if (m_abort) {
          m_bundleResults.setConverged(false);
          emit statusUpdate("\n aborting...");
          emit finished();
          return false;
        }
        // testing
 
        // apply parameter corrections
        applyParameterCorrections();
 
        // testing
        if (m_abort) {
          m_bundleResults.setConverged(false);
          emit statusUpdate("\n aborting...");
          emit finished();
          return false;
        }
        // testing
 
        // compute residuals
        vtpv = computeResiduals();
 
        // flag outliers
        if ( m_bundleSettings->outlierRejection() ) {
          computeRejectionLimit();
          flagOutliers();
        }
 
        // testing
        if (m_abort) {
          m_bundleResults.setConverged(false);
          emit statusUpdate("\n aborting...");
          emit finished();
          return false;
        }
        // testing
 
        // variance of unit weight (also reference variance, variance factor, etc.)
        m_bundleResults.computeSigma0(vtpv, m_bundleSettings->convergenceCriteria());
 
        // Set up formatting for status updates with doubles (e.g. Sigma0, Elapsed Time)
        int fieldWidth = 20;
        char format = 'f';
        int precision = 10;
 
        emit statusUpdate(QString("Iteration: %1 \n")
                                  .arg(m_iteration));
        emit statusUpdate(QString("Sigma0: %1 \n")
                                  .arg(m_bundleResults.sigma0(),
                                       fieldWidth,
                                       format,
                                       precision));
        emit statusUpdate(QString("Observations: %1 \n")
                                  .arg(m_bundleResults.numberObservations()));
        emit statusUpdate(QString("Constrained Parameters:%1 \n")
                                  .arg(m_bundleResults.numberConstrainedPointParameters()));
        emit statusUpdate(QString("Unknowns: %1 \n")
                                  .arg(m_bundleResults.numberUnknownParameters()));
        emit statusUpdate(QString("Degrees of Freedom: %1 \n")
                                  .arg(m_bundleResults.degreesOfFreedom()));
        emit iterationUpdate(m_iteration);
 
        // check for convergence
        if (m_bundleSettings->convergenceCriteria() == BundleSettings::Sigma0) {
          if (fabs(previousSigma0 - m_bundleResults.sigma0())
                <= m_bundleSettings->convergenceCriteriaThreshold()) {
            // convergence detected
 
            // if maximum likelihood tiers are being processed,
            // check to see if there's another tier to go.
            if (m_bundleResults.maximumLikelihoodModelIndex()
                   < m_bundleResults.numberMaximumLikelihoodModels() - 1
                && m_bundleResults.maximumLikelihoodModelIndex()
                     < 2) {
              // TODO is this second condition redundant???
              // should BundleResults require num models <= 3, so num models - 1 <= 2
              if (m_bundleResults.numberMaximumLikelihoodModels()
                      > m_bundleResults.maximumLikelihoodModelIndex() + 1) {
 
                // If there is another tier left we will increment the index.
                m_bundleResults.incrementMaximumLikelihoodModelIndex();
              }
            }
            else { // otherwise iterations are complete
              m_bundleResults.setConverged(true);
              emit statusUpdate("Bundle has converged\n");
              emit statusBarUpdate("Converged");
              break;
            }
          }
        }
        else {
          // bundleSettings.convergenceCriteria() == BundleSettings::ParameterCorrections
          int numConvergedParams = 0;
          int numImgParams = m_imageSolution.size();
          for (int ij = 0; ij < numImgParams; ij++) {
            if (fabs(m_imageSolution(ij)) > m_bundleSettings->convergenceCriteriaThreshold()) {
              break;
            }
            else
              numConvergedParams++;
          }
 
          if ( numConvergedParams == numImgParams ) {
            m_bundleResults.setConverged(true);
            emit statusUpdate("Bundle has converged\n");
            emit statusBarUpdate("Converged");
            break;
          }
        }
 
        m_bundleResults.printMaximumLikelihoodTierInformation();
        clock_t iterationStopClock = clock();
        double iterationTime = (iterationStopClock - iterationStartClock)
                                / (double)CLOCKS_PER_SEC;
        emit statusUpdate( QString("End of Iteration %1 \n").arg(m_iteration) );
        emit statusUpdate( QString("Elapsed Time: %1 \n").arg(iterationTime,
                                                           fieldWidth,
                                                           format,
                                                           precision) );
 
        // check for maximum iterations
        if (m_iteration >= m_bundleSettings->convergenceCriteriaMaximumIterations()) {
          emit(statusBarUpdate("Max Iterations Reached"));
          break;
        }
 
        // restart the dynamic calculation of the cumulative probility distribution of residuals
        // (in unweighted pixels) --so it will be up to date for the next iteration
        if (!m_bundleResults.converged()) {
          m_bundleResults.initializeResidualsProbabilityDistribution(101);
        }
        // TODO: is this necessary ???
        // probably all ready initialized to 101 nodes in bundle settings constructor...
 
        // if we're using CHOLMOD and still going, release cholmod_factor
        // (if we don't, memory leaks will occur), otherwise we need it for error propagation
        if (!m_bundleResults.converged() || !m_bundleSettings->errorPropagation()) {
          cholmod_free_factor(&m_L, &m_cholmodCommon);
        }
 
        iterationSummary();
 
        m_iteration++;
 
        previousSigma0 = m_bundleResults.sigma0();
      }
 
      if (m_bundleResults.converged() && m_bundleSettings->errorPropagation()) {
        clock_t errorPropStartClock = clock();
 
        outputBundleStatus("\nStarting Error Propagation");
 
        errorPropagation();
        emit statusUpdate("\n\nError Propagation Complete\n");
        clock_t errorPropStopClock = clock();
        m_bundleResults.setElapsedTimeErrorProp((errorPropStopClock - errorPropStartClock)
                                                / (double)CLOCKS_PER_SEC);
      }
 
      clock_t solveStopClock = clock();
      m_bundleResults.setElapsedTime((solveStopClock - solveStartClock)
                                     / (double)CLOCKS_PER_SEC);
 
      wrapUp();
 
      m_bundleResults.setIterations(m_iteration);
      m_bundleResults.setObservations(m_bundleObservations);
      m_bundleResults.setBundleControlPoints(m_bundleControlPoints);
 
      emit resultsReady(bundleSolveInformation());
 
      emit statusUpdate("\nBundle Complete\n");
 
      iterationSummary();
    }
    catch (IException &e) {
      m_bundleResults.setConverged(false);
      emit statusUpdate("\n aborting...");
      emit statusBarUpdate("Failed to Converge");
      emit finished();
      QString msg = "Could not solve bundle adjust.";
      throw IException(e, e.errorType(), msg, _FILEINFO_);
    }
 
    emit finished();
    return true;
  }
 
 
  BundleSolutionInfo *BundleAdjust::bundleSolveInformation() {
    BundleSolutionInfo *bundleSolutionInfo = new BundleSolutionInfo(m_bundleSettings,
                                                                    FileName(m_cnetFileName),
                                                                    m_bundleResults,
                                                                    imageLists());
    bundleSolutionInfo->setRunTime("");
    return bundleSolutionInfo;
  }
 
 
  bool BundleAdjust::formNormalEquations() {
    emit(statusBarUpdate("Forming Normal Equations"));
    bool status = false;
 
    m_bundleResults.setNumberObservations(0);// ???
    m_bundleResults.resetNumberConstrainedPointParameters();//???
 
    // Initialize auxilary matrices and vectors.
    static LinearAlgebra::Matrix coeffTarget;
    static LinearAlgebra::Matrix coeffImage;
    static LinearAlgebra::Matrix coeffPoint3D(2, 3);
    static LinearAlgebra::Vector coeffRHS(2);
    static boost::numeric::ublas::symmetric_matrix<double, upper> N22(3);
    SparseBlockColumnMatrix N12;
    static LinearAlgebra::Vector n2(3);
    boost::numeric::ublas::compressed_vector<double> n1(m_rank);
 
    m_RHS.resize(m_rank);
 
    // if solving for target body parameters, set size of coeffTarget
    // (note this size will not change through the adjustment).
    if (m_bundleSettings->solveTargetBody()) {
      int numTargetBodyParameters = m_bundleSettings->numberTargetBodyParameters();
      // TODO make sure numTargetBodyParameters is greater than 0
      coeffTarget.resize(2,numTargetBodyParameters);
    }
 
    // clear N12, n1, and nj
    N12.clear();
    n1.clear();
    m_RHS.clear();
 
    // clear static matrices
    coeffPoint3D.clear();
    coeffRHS.clear();
    N22.clear();
    n2.clear();
 
    // loop over 3D points
    int numGood3DPoints = 0;
    int numRejected3DPoints = 0;
    int pointIndex = 0;
    int num3DPoints = m_bundleControlPoints.size();
 
    outputBundleStatus("\n\n");
 
    for (int i = 0; i < num3DPoints; i++) {
      emit(pointUpdate(i+1));
      BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
      if (point->isRejected()) {
        numRejected3DPoints++;
 
        pointIndex++;
        continue;
      }
 
      if ( i != 0 ) {
        N22.clear();
        N12.wipe();
        n2.clear();
      }
 
      // loop over measures for this point
      int numMeasures = point->size();
      for (int j = 0; j < numMeasures; j++) {
        BundleMeasureQsp measure = point->at(j);
 
        // flagged as "JigsawFail" implies this measure has been rejected
        // TODO  IsRejected is obsolete -- replace code or add to ControlMeasure
        if (measure->isRejected()) {
          continue;
        }
 
        status = computePartials(coeffTarget, coeffImage, coeffPoint3D, coeffRHS, *measure,
                                     *point);
 
        if (!status) {
          // TODO should status be set back to true? JAM
          // TODO this measure should be flagged as rejected.
          continue;
        }
 
        // update number of observations
        int numObs = m_bundleResults.numberObservations();
        m_bundleResults.setNumberObservations(numObs + 2);
 
        formMeasureNormals(N22, N12, n1, n2, coeffTarget, coeffImage, coeffPoint3D, coeffRHS,
                             measure->observationIndex());
 
      } // end loop over this points measures
 
      formPointNormals(N22, N12, n2, m_RHS, point);
 
      pointIndex++;
 
      numGood3DPoints++;
 
  } // end loop over 3D points
 
  // finally, form the reduced normal equations
  formWeightedNormals(n1, m_RHS);
 
  // update number of unknown parameters
  m_bundleResults.setNumberUnknownParameters(m_rank + 3 * numGood3DPoints);
 
  return status;
}
 
 
  bool BundleAdjust::formMeasureNormals(symmetric_matrix<double, upper>&N22,
                                        SparseBlockColumnMatrix &N12,
                                        compressed_vector<double> &n1,
                                        vector<double> &n2,
                                        matrix<double> &coeffTarget,
                                        matrix<double> &coeffImage,
                                        matrix<double> &coeffPoint3D,
                                        vector<double> &coeffRHS,
                                        int observationIndex) {
 
    static symmetric_matrix<double, upper> N11;
    static matrix<double> N11TargetImage;
 
    int blockIndex = observationIndex;
 
    // if we are solving for target body parameters
    int numTargetPartials = coeffTarget.size2();
    if (m_bundleSettings->solveTargetBody()) {
      blockIndex++;
 
      static vector<double> n1Target(numTargetPartials);
      n1Target.resize(numTargetPartials);
      n1Target.clear();
 
      // form N11 (normals for target body)
      N11.resize(numTargetPartials);
      N11.clear();
 
      N11 = prod(trans(coeffTarget), coeffTarget);
 
      // insert submatrix at column, row
      m_sparseNormals.insertMatrixBlock(0, 0, numTargetPartials, numTargetPartials);
 
      (*(*m_sparseNormals[0])[0]) += N11;
 
      // form portion of N11 between target and image
      N11TargetImage.resize(numTargetPartials, coeffImage.size2());
      N11TargetImage.clear();
      N11TargetImage = prod(trans(coeffTarget),coeffImage);
 
      m_sparseNormals.insertMatrixBlock(blockIndex, 0,
                                        numTargetPartials, coeffImage.size2());
      (*(*m_sparseNormals[blockIndex])[0]) += N11TargetImage;
 
      // form N12 target portion
      static matrix<double> N12Target(numTargetPartials, 3);
      N12Target.clear();
 
      N12Target = prod(trans(coeffTarget), coeffPoint3D);
 
      // insert N12Target into N12
      N12.insertMatrixBlock(0, numTargetPartials, 3);
      *N12[0] += N12Target;
 
      // form n1Target
      n1Target = prod(trans(coeffTarget), coeffRHS);
 
      // insert n1Target into n1
      for (int i = 0; i < numTargetPartials; i++) {
        n1(i) += n1Target(i);
      }
    }
 
 
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ below is ok (2015-06-03)
// TODO - if solving for target (and/or self-cal) have to use not observationIndex below but
// observationIndex plus 1 or 2
 
    int numImagePartials = coeffImage.size2();
 
    static LinearAlgebra::Vector n1Image(numImagePartials);
    n1Image.resize(numImagePartials);
    n1Image.clear();
 
    // form N11 (normals for photo)
    N11.resize(numImagePartials);
    N11.clear();
 
    N11 = prod(trans(coeffImage), coeffImage);
 
    int t = m_sparseNormals.at(blockIndex)->startColumn();
 
    // insert submatrix at column, row
    m_sparseNormals.insertMatrixBlock(blockIndex, blockIndex,
                                      numImagePartials, numImagePartials);
 
    (*(*m_sparseNormals[blockIndex])[blockIndex]) += N11;
 
    // form N12Image
    static matrix<double> N12Image(numImagePartials, 3);
    N12Image.resize(numImagePartials, 3);
    N12Image.clear();
 
    N12Image = prod(trans(coeffImage), coeffPoint3D);
 
    // insert N12Image into N12
    N12.insertMatrixBlock(blockIndex, numImagePartials, 3);
    *N12[blockIndex] += N12Image;
 
    // form n1
    n1Image = prod(trans(coeffImage), coeffRHS);
 
    // insert n1Image into n1
    // TODO - MUST ACCOUNT FOR TARGET BODY PARAMETERS
    // WHEN INSERTING INTO n1 HERE!!!!!
    for (int i = 0; i < numImagePartials; i++) {
      n1(i + t) += n1Image(i);
    }
 
    // form N22
    N22 += prod(trans(coeffPoint3D), coeffPoint3D);
 
    // form n2
    n2 += prod(trans(coeffPoint3D), coeffRHS);
 
    return true;
  }
 
 
  bool BundleAdjust::formPointNormals(symmetric_matrix<double, upper>&N22,
                                      SparseBlockColumnMatrix &N12,
                                      vector<double> &n2,
                                      vector<double> &nj,
                                      BundleControlPointQsp &bundleControlPoint) {
 
    boost::numeric::ublas::bounded_vector<double, 3> &NIC = bundleControlPoint->nicVector();
    SparseBlockRowMatrix &Q = bundleControlPoint->cholmodQMatrix();
 
    NIC.clear();
    Q.zeroBlocks();
 
    // weighting of 3D point parameters
    // Make sure weights are in the units corresponding to the bundle coordinate type
    boost::numeric::ublas::bounded_vector<double, 3> &weights
        = bundleControlPoint->weights();
    boost::numeric::ublas::bounded_vector<double, 3> &corrections
        = bundleControlPoint->corrections();
 
    if (weights(0) > 0.0) {
      N22(0,0) += weights(0);
      n2(0) += (-weights(0) * corrections(0));
      m_bundleResults.incrementNumberConstrainedPointParameters(1);
    }
 
    if (weights(1) > 0.0) {
      N22(1,1) += weights(1);
      n2(1) += (-weights(1) * corrections(1));
      m_bundleResults.incrementNumberConstrainedPointParameters(1);
    }
 
    if (weights(2) > 0.0) {
      N22(2,2) += weights(2);
      n2(2) += (-weights(2) * corrections(2));
      m_bundleResults.incrementNumberConstrainedPointParameters(1);
    }
 
    // invert N22
    invert3x3(N22);
 
    // save upper triangular covariance matrix for error propagation
    SurfacePoint SurfacePoint = bundleControlPoint->adjustedSurfacePoint();
    SurfacePoint.SetMatrix(m_bundleSettings->controlPointCoordTypeBundle(), N22);
    bundleControlPoint->setAdjustedSurfacePoint(SurfacePoint);
 
    // form Q (this is N22{-1} * N12{T})
    productATransB(N22, N12, Q);
 
    // form product of N22(inverse) and n2; store in NIC
    NIC = prod(N22, n2);
 
    // accumulate -R directly into reduced normal equations
    productAB(N12, Q);
 
    // accumulate -nj
    accumProductAlphaAB(-1.0, Q, n2, nj);
 
    return true;
  }
 
 
  bool BundleAdjust::formWeightedNormals(compressed_vector<double> &n1,
                                         vector<double> &nj) {
 
    m_bundleResults.resetNumberConstrainedImageParameters();
 
    int n = 0;
 
    for (int i = 0; i < m_sparseNormals.size(); i++) {
      LinearAlgebra::Matrix *diagonalBlock = m_sparseNormals.getBlock(i, i);
      if ( !diagonalBlock )
        continue;
 
      if (m_bundleSettings->solveTargetBody() && i == 0) {
        m_bundleResults.resetNumberConstrainedTargetParameters();
 
        // get parameter weights for target body
        vector<double> weights = m_bundleTargetBody->parameterWeights();
        vector<double> corrections = m_bundleTargetBody->parameterCorrections();
 
        int blockSize = diagonalBlock->size1();
        for (int j = 0; j < blockSize; j++) {
          if (weights[j] > 0.0) {
            (*diagonalBlock)(j,j) += weights[j];
            nj[n] -= weights[j] * corrections(j);
            m_bundleResults.incrementNumberConstrainedTargetParameters(1);
          }
          n++;
        }
      }
      else {
        BundleObservationQsp observation;
 
        // get parameter weights for this observation
        if (m_bundleSettings->solveTargetBody()) {
          observation = m_bundleObservations.at(i-1);
        }
        else {
          observation = m_bundleObservations.at(i);
        }
 
        LinearAlgebra::Vector weights = observation->parameterWeights();
        LinearAlgebra::Vector corrections = observation->parameterCorrections();
 
        int blockSize = diagonalBlock->size1();
        for (int j = 0; j < blockSize; j++) {
          if (weights(j) > 0.0) {
            (*diagonalBlock)(j,j) += weights(j);
            nj[n] -= weights(j) * corrections(j);
            m_bundleResults.incrementNumberConstrainedImageParameters(1);
          }
          n++;
        }
      }
    }
 
    // add n1 to nj
    nj += n1;
 
    return true;
  }
 
 
  bool BundleAdjust::productATransB(symmetric_matrix <double,upper> &N22,
                                    SparseBlockColumnMatrix &N12,
                                    SparseBlockRowMatrix &Q) {
 
    QMapIterator< int, LinearAlgebra::Matrix * > N12it(N12);
 
    while ( N12it.hasNext() ) {
      N12it.next();
 
      int rowIndex = N12it.key();
 
      // insert submatrix in Q at block "rowIndex"
      Q.insertMatrixBlock(rowIndex, 3, N12it.value()->size1());
 
      *(Q[rowIndex]) = prod(N22,trans(*(N12it.value())));
    }
 
    return true;
  }
 
 
  void BundleAdjust::productAB(SparseBlockColumnMatrix &N12,
                               SparseBlockRowMatrix &Q) {
    // iterators for N12 and Q
    QMapIterator<int, LinearAlgebra::Matrix*> N12it(N12);
    QMapIterator<int, LinearAlgebra::Matrix*> Qit(Q);
 
    // now multiply blocks and subtract from m_sparseNormals
    while ( N12it.hasNext() ) {
      N12it.next();
 
      int rowIndex = N12it.key();
      LinearAlgebra::Matrix *N12block = N12it.value();
 
      while ( Qit.hasNext() ) {
        Qit.next();
 
        int columnIndex = Qit.key();
 
        if ( rowIndex > columnIndex ) {
          continue;
        }
 
        LinearAlgebra::Matrix *Qblock = Qit.value();
 
        // insert submatrix at column, row
        m_sparseNormals.insertMatrixBlock(columnIndex, rowIndex,
                                          N12block->size1(), Qblock->size2());
 
        (*(*m_sparseNormals[columnIndex])[rowIndex]) -= prod(*N12block,*Qblock);
      }
      Qit.toFront();
    }
  }
 
 
  void BundleAdjust::accumProductAlphaAB(double alpha,
                                         SparseBlockRowMatrix &Q,
                                         vector<double> &n2,
                                         vector<double> &nj) {
 
    if (alpha == 0.0) {
      return;
    }
 
    int numParams;
 
    QMapIterator<int, LinearAlgebra::Matrix*> Qit(Q);
 
    while ( Qit.hasNext() ) {
      Qit.next();
 
      int columnIndex = Qit.key();
      LinearAlgebra::Matrix *Qblock = Qit.value();
 
      LinearAlgebra::Vector blockProduct = prod(trans(*Qblock),n2);
 
      numParams = m_sparseNormals.at(columnIndex)->startColumn();
 
      for (unsigned i = 0; i < blockProduct.size(); i++) {
        nj(numParams+i) += alpha*blockProduct(i);
      }
    }
  }
 
 
  bool BundleAdjust::solveSystem() {
 
    // load cholmod triplet
    if ( !loadCholmodTriplet() ) {
      QString msg = "CHOLMOD: Failed to load Triplet matrix";
      throw IException(IException::Programmer, msg, _FILEINFO_);
    }
 
    // convert triplet to sparse matrix
    m_cholmodNormal = cholmod_triplet_to_sparse(m_cholmodTriplet,
                                                m_cholmodTriplet->nnz,
                                                &m_cholmodCommon);
 
    // analyze matrix
    // TODO should we analyze just 1st iteration?
    m_L = cholmod_analyze(m_cholmodNormal, &m_cholmodCommon);
 
    // create cholmod cholesky factor
    // CHOLMOD will choose LLT or LDLT decomposition based on the characteristics of the matrix.
    cholmod_factorize(m_cholmodNormal, m_L, &m_cholmodCommon);
 
    // check for "matrix not positive definite" error
    if (m_cholmodCommon.status == CHOLMOD_NOT_POSDEF) {
      QString msg = "Matrix NOT positive-definite: failure at column " + toString((int) m_L->minor);
//    throw IException(IException::User, msg, _FILEINFO_);
      error(msg);
      emit(finished());
      return false;
    }
 
    // cholmod solution and right-hand side vectors
    cholmod_dense *x, *b;
 
    // initialize right-hand side vector
    b = cholmod_zeros(m_cholmodNormal->nrow, 1, m_cholmodNormal->xtype, &m_cholmodCommon);
 
    // copy right-hand side vector into b
    double *px = (double*)b->x;
    for (int i = 0; i < m_rank; i++) {
      px[i] = m_RHS[i];
    }
 
    // cholmod solve
    x = cholmod_solve(CHOLMOD_A, m_L, b, &m_cholmodCommon);
 
    // copy solution vector x out into m_imageSolution
    double *sx = (double*)x->x;
    for (int i = 0; i < m_rank; i++) {
      m_imageSolution[i] = sx[i];
    }
 
    // free cholmod structures
    cholmod_free_sparse(&m_cholmodNormal, &m_cholmodCommon);
    cholmod_free_dense(&b, &m_cholmodCommon);
    cholmod_free_dense(&x, &m_cholmodCommon);
 
    return true;
  }
 
 
  bool BundleAdjust::loadCholmodTriplet() {
 
    if ( m_iteration == 1 ) {
      int numElements = m_sparseNormals.numberOfElements();
      m_cholmodTriplet = cholmod_allocate_triplet(m_rank, m_rank, numElements,
                                                  -1, CHOLMOD_REAL, &m_cholmodCommon);
 
      if ( !m_cholmodTriplet ) {
        outputBundleStatus("\nTriplet allocation failure\n");
        return false;
      }
      m_cholmodTriplet->nnz = 0;
    }
 
    int *tripletColumns = (int*) m_cholmodTriplet->i;
    int *tripletRows = (int*) m_cholmodTriplet->j;
    double *tripletValues = (double*)m_cholmodTriplet->x;
 
    double entryValue;
 
    int numEntries = 0;
 
    int numBlockcolumns = m_sparseNormals.size();
    for (int columnIndex = 0; columnIndex < numBlockcolumns; columnIndex++) {
 
      SparseBlockColumnMatrix *normalsColumn = m_sparseNormals[columnIndex];
 
      if ( !normalsColumn ) {
        QString status = "\nSparseBlockColumnMatrix retrieval failure at column " +
                         QString::number(columnIndex);
        outputBundleStatus(status);
        return false;
      }
 
      int numLeadingColumns = normalsColumn->startColumn();
 
      QMapIterator< int, LinearAlgebra::Matrix * > it(*normalsColumn);
 
      while ( it.hasNext() ) {
        it.next();
 
        int rowIndex = it.key();
 
        // note: as the normal equations matrix is symmetric, the # of leading rows for a block is
        //       equal to the # of leading columns for a block column at the "rowIndex" position
        int numLeadingRows = m_sparseNormals.at(rowIndex)->startColumn();
 
        LinearAlgebra::Matrix *normalsBlock = it.value();
        if ( !normalsBlock ) {
          QString status = "\nmatrix block retrieval failure at column ";
          status.append(columnIndex);
          status.append(", row ");
          status.append(rowIndex);
          outputBundleStatus(status);
          status = "Total # of block columns: " + QString::number(numBlockcolumns);
          outputBundleStatus(status);
          status = "Total # of blocks: " + QString::number(m_sparseNormals.numberOfBlocks());
          outputBundleStatus(status);
          return false;
        }
 
        if ( columnIndex == rowIndex )  {   // diagonal block (upper-triangular)
          for (unsigned ii = 0; ii < normalsBlock->size1(); ii++) {
            for (unsigned jj = ii; jj < normalsBlock->size2(); jj++) {
              entryValue = normalsBlock->at_element(ii,jj);
              int entryColumnIndex = jj + numLeadingColumns;
              int entryRowIndex = ii + numLeadingRows;
 
              if ( m_iteration == 1 ) {
                tripletColumns[numEntries] = entryColumnIndex;
                tripletRows[numEntries] = entryRowIndex;
                m_cholmodTriplet->nnz++;
              }
 
              tripletValues[numEntries] = entryValue;
 
              numEntries++;
            }
          }
        }
        else {                // off-diagonal block (square)
          for (unsigned ii = 0; ii < normalsBlock->size1(); ii++) {
            for (unsigned jj = 0; jj < normalsBlock->size2(); jj++) {
              entryValue = normalsBlock->at_element(ii,jj);
              int entryColumnIndex = jj + numLeadingColumns;
              int entryRowIndex = ii + numLeadingRows;
 
              if ( m_iteration ==1 ) {
                tripletColumns[numEntries] = entryRowIndex;
                tripletRows[numEntries] = entryColumnIndex;
                m_cholmodTriplet->nnz++;
              }
 
              tripletValues[numEntries] = entryValue;
 
              numEntries++;
            }
          }
        }
      }
    }
 
    return true;
  }
 
 
  bool BundleAdjust::cholmodInverse() {
    int i, j;
 
    // allocate matrix inverse
    m_normalInverse.resize(m_rank);
 
    cholmod_dense *x;        // solution vector
    cholmod_dense *b;        // right-hand side (column vectors of identity)
 
    b = cholmod_zeros ( m_rank, 1, CHOLMOD_REAL, &m_cholmodCommon ) ;
    double *pb = (double*)b->x;
 
    double *px = NULL;
 
    for (i = 0; i < m_rank; i++) {
      if ( i > 0 ) {
        pb[i-1] = 0.0;
      }
      pb[i] = 1.0;
 
      x = cholmod_solve ( CHOLMOD_A, m_L, b, &m_cholmodCommon ) ;
      px = (double*)x->x;
 
      // store solution in corresponding column of inverse
      for (j = 0; j <= i; j++) {
        m_normalInverse(j, i) = px[j];
      }
 
      cholmod_free_dense(&x,&m_cholmodCommon);
    }
 
    cholmod_free_dense(&b,&m_cholmodCommon);
 
    return true;
  }
 
 
  bool BundleAdjust::invert3x3(symmetric_matrix<double, upper> &m) {
    double det;
    double den;
 
    boost::numeric::ublas::symmetric_matrix< double, upper > c = m;
 
    den = m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1))
          - m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0))
          + m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0));
 
    // check for divide by zero
    if (fabs(den) < 1.0e-100) {
      return false;
    }
 
    det = 1.0 / den;
 
    m(0, 0) = (c(1, 1) * c(2, 2) - c(1, 2) * c(2, 1)) * det;
    m(0, 1) = (c(0, 2) * c(2, 1) - c(0, 1) * c(2, 2)) * det;
    m(0, 2) = (c(0, 1) * c(1, 2) - c(0, 2) * c(1, 1)) * det;
    m(1, 1) = (c(0, 0) * c(2, 2) - c(0, 2) * c(2, 0)) * det;
    m(1, 2) = (c(0, 2) * c(1, 0) - c(0, 0) * c(1, 2)) * det;
    m(2, 2) = (c(0, 0) * c(1, 1) - c(0, 1) * c(1, 0)) * det;
 
    return true;
  }
 
 
  bool BundleAdjust::computePartials(matrix<double> &coeffTarget,
                                     matrix<double> &coeffImage,
                                     matrix<double> &coeffPoint3D,
                                     vector<double> &coeffRHS,
                                     BundleMeasure &measure,
                                     BundleControlPoint &point) {
 
    Camera *measureCamera = measure.camera();
    BundleObservationQsp observation = measure.parentBundleObservation();
 
    int numImagePartials = observation->numberParameters();
 
    // we're saving the number of image partials in m_previousNumberImagePartials
    // to compare to the previous computePartials call to avoid unnecessary resizing of the
    // coeffImage matrix
    if (numImagePartials != m_previousNumberImagePartials) {
      coeffImage.resize(2,numImagePartials);
      m_previousNumberImagePartials = numImagePartials;
    }
 
    // No need to call SetImage for framing camera
    if (measureCamera->GetCameraType() != Camera::Framing) {
      // Set the Spice to the measured point.  A framing camera exposes the entire image at one time.
      // It will have a single set of Spice for the entire image.  Scanning cameras may populate a single
      // image with multiple exposures, each with a unique set of Spice.  SetImage needs to be called
      // repeatedly for these images to point to the Spice for the current pixel.
      measureCamera->SetImage(measure.sample(), measure.line());
    }
 
    // CSM Cameras do not have a ground map
    if (measureCamera->GetCameraType() != Camera::Csm) {
      // Compute the look vector in instrument coordinates based on time of observation and apriori
      // lat/lon/radius.  As of 05/15/2019, this call no longer does the back-of-planet test. An optional
      // bool argument was added CameraGroundMap::GetXY to turn off the test.
      double computedX, computedY;
      if (!(measureCamera->GroundMap()->GetXY(point.adjustedSurfacePoint(),
                                              &computedX, &computedY, false))) {
        QString msg = "Unable to map apriori surface point for measure ";
        msg += measure.cubeSerialNumber() + " on point " + point.id() + " into focal plane";
        throw IException(IException::User, msg, _FILEINFO_);
      }
    }
 
    if (m_bundleSettings->solveTargetBody()) {
      observation->computeTargetPartials(coeffTarget, measure, m_bundleSettings, m_bundleTargetBody);
    }
 
    observation->computeImagePartials(coeffImage, measure);
 
    // Complete partials calculations for 3D point (latitudinal or rectangular)
    // Retrieve the coordinate type (latitudinal or rectangular) and compute the partials for
    // the fixed point with respect to each coordinate in Body-Fixed
    SurfacePoint::CoordinateType coordType = m_bundleSettings->controlPointCoordTypeBundle();
    observation->computePoint3DPartials(coeffPoint3D, measure, coordType);
 
    // right-hand side (measured - computed)
    observation->computeRHSPartials(coeffRHS, measure);
 
    double deltaX = coeffRHS(0);
    double deltaY = coeffRHS(1);
 
    m_bundleResults.addResidualsProbabilityDistributionObservation(observation->computeObservationValue(measure, deltaX));
    m_bundleResults.addResidualsProbabilityDistributionObservation(observation->computeObservationValue(measure, deltaY));
 
    if (m_bundleResults.numberMaximumLikelihoodModels()
          > m_bundleResults.maximumLikelihoodModelIndex()) {
      // If maximum likelihood estimation is being used
      double residualR2ZScore = sqrt(deltaX * deltaX + deltaY * deltaY) / sqrt(2.0);
 
      // Dynamically build the cumulative probability distribution of the R^2 residual Z Scores
      m_bundleResults.addProbabilityDistributionObservation(residualR2ZScore);
 
      int currentModelIndex = m_bundleResults.maximumLikelihoodModelIndex();
      double observationWeight = m_bundleResults.maximumLikelihoodModelWFunc(currentModelIndex)
                            .sqrtWeightScaler(residualR2ZScore);
      coeffImage *= observationWeight;
      coeffPoint3D *= observationWeight;
      coeffRHS *= observationWeight;
 
      if (m_bundleSettings->solveTargetBody()) {
        coeffTarget *= observationWeight;
      }
    }
 
    return true;
  }
 
 
  void BundleAdjust::applyParameterCorrections() {
    emit(statusBarUpdate("Updating Parameters"));
    int t = 0;
 
    // TODO - update target body parameters if in solution
    // note these come before BundleObservation parameters in normal equations matrix
    if (m_bundleSettings->solveTargetBody()) {
      int numTargetBodyParameters = m_bundleTargetBody->numberParameters();
 
      m_bundleTargetBody->applyParameterCorrections(subrange(m_imageSolution,0,
                                                            numTargetBodyParameters));
 
      t += numTargetBodyParameters;
    }
 
    // Update spice for each BundleObservation
    int numObservations = m_bundleObservations.size();
    for (int i = 0; i < numObservations; i++) {
      BundleObservationQsp observation = m_bundleObservations.at(i);
 
      int numParameters = observation->numberParameters();
 
      observation->applyParameterCorrections(subrange(m_imageSolution,t,t+numParameters));
 
      if (m_bundleSettings->solveTargetBody()) {
        // TODO: needs to be updated for ISIS vs. CSM CSM has no updateBodyRotation]
        // TODO: this is no good.
        QSharedPointer<IsisBundleObservation> isisObservation = qSharedPointerDynamicCast<IsisBundleObservation>(observation);
        isisObservation->updateBodyRotation();
      }
 
      t += numParameters;
    }
    // TODO - When BundleXYZ gets merged into dev, go with Ken's version of merging the updating of
    //              of the adjusted surface point into BundleControlPoint.
 
    int pointIndex = 0;
    int numControlPoints = m_bundleControlPoints.size();
 
    for (int i = 0; i < numControlPoints; i++) {
      BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
      if (point->isRejected()) {
          pointIndex++;
          continue;
      }
 
      point->applyParameterCorrections(m_imageSolution, m_sparseNormals,
                                       m_bundleTargetBody);
      pointIndex++;
 
    } // end loop over point corrections
  }
 
 
  double BundleAdjust::computeResiduals() {
    emit(statusBarUpdate("Computing Residuals"));
    double vtpv = 0.0;
    double vtpvControl = 0.0;
    double vtpvImage = 0.0;
    double weight;
    double v, vx, vy;
 
    // clear residual stats vectors
    m_xResiduals.Reset();
    m_yResiduals.Reset();
    m_xyResiduals.Reset();
 
    // vtpv for image coordinates
    int numObjectPoints = m_bundleControlPoints.size();
 
    for (int i = 0; i < numObjectPoints; i++) {
 
      BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
      point->computeResiduals();
 
      int numMeasures = point->numberOfMeasures();
      for (int j = 0; j < numMeasures; j++) {
        const BundleMeasureQsp measure = point->at(j);
 
        weight = 1.4 * (measure->camera())->PixelPitch();
        weight = 1.0 / weight;
        weight *= weight;
 
        vx = measure->focalPlaneMeasuredX() - measure->focalPlaneComputedX();
        vy = measure->focalPlaneMeasuredY() - measure->focalPlaneComputedY();
 
        // if rejected, don't include in statistics
        if (measure->isRejected()) {
          continue;
        }
 
        m_xResiduals.AddData(vx);
        m_yResiduals.AddData(vy);
        m_xyResiduals.AddData(vx);
        m_xyResiduals.AddData(vy);
 
        vtpv += vx * vx * weight + vy * vy * weight;
      }
    }
 
    // add vtpv from constrained 3D points
    int pointIndex = 0;   // *** TODO *** This does not appear to be used.  Delete? DAC 07-14-2017
    for (int i = 0; i < numObjectPoints; i++) {
      BundleControlPointQsp bundleControlPoint = m_bundleControlPoints.at(i);
 
      // get weight and correction vector for this point
      boost::numeric::ublas::bounded_vector<double, 3> weights = bundleControlPoint->weights();
      boost::numeric::ublas::bounded_vector<double, 3> corrections =
                                                             bundleControlPoint->corrections();
 
      if ( weights(0) > 0.0 ) {
          vtpvControl += corrections(0) * corrections(0) * weights(0);
      }
      if ( weights(1) > 0.0 ) {
          vtpvControl += corrections(1) * corrections(1) * weights(1);
      }
      if ( weights(2) > 0.0 ) {
          vtpvControl += corrections(2) * corrections(2) * weights(2);
      }
 
      pointIndex++;
    }
 
    // add vtpv from constrained image parameters
    for (int i = 0; i < m_bundleObservations.size(); i++) {
      BundleObservationQsp observation = m_bundleObservations.at(i);
 
      // get weight and correction vector for this observation
      const LinearAlgebra::Vector &weights = observation->parameterWeights();
      const LinearAlgebra::Vector &corrections = observation->parameterCorrections();
 
      for (int j = 0; j < (int)corrections.size(); j++) {
        if (weights[j] > 0.0) {
          v = corrections[j];
          vtpvImage += v * v * weights[j];
        }
      }
    }
 
    // TODO - add vtpv from constrained target body parameters
    double vtpvTargetBody = 0.0;
    if ( m_bundleTargetBody) {
      vtpvTargetBody = m_bundleTargetBody->vtpv();
    }
 
   vtpv = vtpv + vtpvControl + vtpvImage + vtpvTargetBody;
 
    // Compute rms for all image coordinate residuals
    // separately for x, y, then x and y together
    m_bundleResults.setRmsXYResiduals(m_xResiduals.Rms(), m_yResiduals.Rms(), m_xyResiduals.Rms());
 
    return vtpv;
  }
 
 
  bool BundleAdjust::wrapUp() {
    // compute residuals in pixels
 
    // vtpv for image coordinates
    for (int i = 0;  i < m_bundleControlPoints.size(); i++) {
      BundleControlPointQsp point = m_bundleControlPoints.at(i);
      point->computeResiduals();
    }
 
    computeBundleStatistics();
 
    return true;
  }
 
 
  bool BundleAdjust::computeRejectionLimit() {
      double vx, vy;
 
      int numResiduals = m_bundleResults.numberObservations() / 2;
 
      std::vector<double> residuals;
 
      residuals.resize(numResiduals);
 
      // load magnitude (squared) of residual vector
      int residualIndex = 0;
      int numObjectPoints = m_bundleControlPoints.size();
      for (int i = 0; i < numObjectPoints; i++) {
 
          const BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
          if ( point->isRejected() ) {
            continue;
          }
 
          int numMeasures = point->numberOfMeasures();
          for (int j = 0; j < numMeasures; j++) {
 
              const BundleMeasureQsp measure = point->at(j);
 
              if ( measure->isRejected() ) {
                  continue;
              }
 
              vx = measure->sampleResidual();
              vy = measure->lineResidual();
 
              residuals[residualIndex] = sqrt(vx*vx + vy*vy);
 
              residualIndex++;
          }
      }
 
      // sort vectors
      std::sort(residuals.begin(), residuals.end());
 
      double median;
      double medianDev;
      double mad;
 
      int midpointIndex = numResiduals / 2;
 
      if ( numResiduals % 2 == 0 ) {
        median = (residuals[midpointIndex - 1] + residuals[midpointIndex]) / 2;
      }
      else {
        median = residuals[midpointIndex];
      }
 
      // compute M.A.D.
      for (int i = 0; i < numResiduals; i++) {
          residuals[i] = fabs(residuals[i] - median);
      }
 
      std::sort(residuals.begin(), residuals.end());
 
      if ( numResiduals % 2 == 0 ) {
        medianDev = (residuals[midpointIndex - 1] + residuals[midpointIndex]) / 2;
      }
      else {
        medianDev = residuals[midpointIndex];
      }
 
      QString status = "\nmedian deviation: ";
      status.append(QString("%1").arg(medianDev));
      status.append("\n");
      outputBundleStatus(status);
 
      mad = 1.4826 * medianDev;
 
      status = "\nmad: ";
      status.append(QString("%1").arg(mad));
      status.append("\n");
      outputBundleStatus(status);
 
      m_bundleResults.setRejectionLimit(median
                                        + m_bundleSettings->outlierRejectionMultiplier() * mad);
 
      status = "\nRejection Limit: ";
      status.append(QString("%1").arg(m_bundleResults.rejectionLimit()));
      status.append("\n");
      outputBundleStatus(status);
 
      return true;
  }
 
 
  bool BundleAdjust::flagOutliers() {
    double vx, vy;
    int numRejected;
    int totalNumRejected = 0;
 
    int maxResidualIndex;
    double maxResidual;
    double sumSquares;
    double usedRejectionLimit = m_bundleResults.rejectionLimit();
 
    // TODO What to do if usedRejectionLimit is too low?
 
    int numComingBack = 0;
 
    int numObjectPoints = m_bundleControlPoints.size();
 
    outputBundleStatus("\n");
    for (int i = 0; i < numObjectPoints; i++) {
      BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
      point->zeroNumberOfRejectedMeasures();
 
      numRejected = 0;
      maxResidualIndex = -1;
      maxResidual = -1.0;
 
      int numMeasures = point->numberOfMeasures();
      for (int j = 0; j < numMeasures; j++) {
 
        BundleMeasureQsp measure = point->at(j);
 
        vx = measure->sampleResidual();
        vy = measure->lineResidual();
 
        sumSquares = sqrt(vx*vx + vy*vy);
 
        // measure is good
        if ( sumSquares <= usedRejectionLimit ) {
 
          // was it previously rejected?
          if ( measure->isRejected() ) {
            QString status = "Coming back in: ";
            status.append(QString("%1").arg(point->id().toLatin1().data()));
            status.append("\r");
            outputBundleStatus(status);
            numComingBack++;
            m_controlNet->DecrementNumberOfRejectedMeasuresInImage(measure->cubeSerialNumber());
          }
 
          measure->setRejected(false);
          continue;
        }
 
        // if it's still rejected, skip it
        if ( measure->isRejected() ) {
          numRejected++;
          totalNumRejected++;
          continue;
        }
 
        if ( sumSquares > maxResidual ) {
          maxResidual = sumSquares;
          maxResidualIndex = j;
        }
      }
 
      // no observations above the current rejection limit for this 3D point
      if ( maxResidual == -1.0 || maxResidual <= usedRejectionLimit ) {
          point->setNumberOfRejectedMeasures(numRejected);
          continue;
      }
 
      // this is another kluge - if we only have two observations
      // we won't reject (for now)
      if ((numMeasures - (numRejected + 1)) < 2) {
          point->setNumberOfRejectedMeasures(numRejected);
          continue;
      }
 
      // otherwise, we have at least one observation
      // for this point whose residual is above the
      // current rejection limit - we'll flag the
      // worst of these as rejected
      BundleMeasureQsp rejected = point->at(maxResidualIndex);
      rejected->setRejected(true);
      numRejected++;
      point->setNumberOfRejectedMeasures(numRejected);
      m_controlNet->IncrementNumberOfRejectedMeasuresInImage(rejected->cubeSerialNumber());
      totalNumRejected++;
 
      // do we still have sufficient remaining observations for this 3D point?
      if ( ( numMeasures-numRejected ) < 2 ) {
          point->setRejected(true);
          QString status = "Rejecting Entire Point: ";
          status.append(QString("%1").arg(point->id().toLatin1().data()));
          status.append("\r");
          outputBundleStatus(status);
      }
      else
          point->setRejected(false);
 
    }
 
    int numberRejectedObservations = 2*totalNumRejected;
 
    QString status = "\nRejected Observations:";
    status.append(QString("%1").arg(numberRejectedObservations));
    status.append(" (Rejection Limit:");
    status.append(QString("%1").arg(usedRejectionLimit));
    status.append(")\n");
    outputBundleStatus(status);
 
    m_bundleResults.setNumberRejectedObservations(numberRejectedObservations);
 
    status = "\nMeasures that came back: ";
    status.append(QString("%1").arg(numComingBack));
    status.append("\n");
    outputBundleStatus(status);
 
    return true;
  }
 
 
  QList<ImageList *> BundleAdjust::imageLists() {
 
    if (m_imageLists.count() > 0) {
      return m_imageLists;
    }
    else if (m_serialNumberList->size() > 0) {
      ImageList *imgList = new ImageList;
      try {
        for (int i = 0; i < m_serialNumberList->size(); i++) {
          Image *image = new Image(m_serialNumberList->fileName(i));
          imgList->append(image);
          image->closeCube();
        }
        m_imageLists.append(imgList);
      }
      catch (IException &e) {
        QString msg = "Invalid image in serial number list\n";
        throw IException(IException::Programmer, msg, _FILEINFO_);
      }
    }
    else {
      QString msg = "No images used in bundle adjust\n";
      throw IException(IException::Programmer, msg, _FILEINFO_);
    }
 
    return m_imageLists;
  }
 
 
  bool BundleAdjust::errorPropagation() {
    emit(statusBarUpdate("Error Propagation"));
    // free unneeded memory
    cholmod_free_triplet(&m_cholmodTriplet, &m_cholmodCommon);
    cholmod_free_sparse(&m_cholmodNormal, &m_cholmodCommon);
 
    LinearAlgebra::Matrix T(3, 3);
    // *** TODO ***
    // Can any of the control point specific code be moved to BundleControlPoint?
 
    double sigma0Squared = m_bundleResults.sigma0() * m_bundleResults.sigma0();
 
    int numObjectPoints = m_bundleControlPoints.size();
 
    std::string currentTime = iTime::CurrentLocalTime().toLatin1().data();
 
    QString status = "     Time: ";
    status.append(currentTime.c_str());
    status.append("\n\n");
    outputBundleStatus(status);
 
    // create and initialize array of 3x3 matrices for all object points
    std::vector< symmetric_matrix<double> > pointCovariances(numObjectPoints,
                                                             symmetric_matrix<double>(3));
    for (int d = 0; d < numObjectPoints; d++) {
      pointCovariances[d].clear();
    }
 
    cholmod_dense *x;        // solution vector
    cholmod_dense *b;        // right-hand side (column vectors of identity)
 
    b = cholmod_zeros ( m_rank, 1, CHOLMOD_REAL, &m_cholmodCommon );
    double *pb = (double*)b->x;
 
    double *px = NULL;
 
    SparseBlockColumnMatrix inverseMatrix;
 
    // Create unique file name
    FileName matrixFile(m_bundleSettings->outputFilePrefix() + "inverseMatrix.dat");
    //???FileName matrixFile = FileName::createTempFile(m_bundleSettings.outputFilePrefix()
    //???                                               + "inverseMatrix.dat");
    // Create file handle
    QFile matrixOutput(matrixFile.expanded());
 
    // Check to see if creating the inverse correlation matrix is turned on
    if (m_bundleSettings->createInverseMatrix()) {
      // Open file to write to
      matrixOutput.open(QIODevice::WriteOnly);
    }
    QDataStream outStream(&matrixOutput);
 
    int i, j, k;
    int columnIndex = 0;
    int numColumns = 0;
    int numBlockColumns = m_sparseNormals.size();
    for (i = 0; i < numBlockColumns; i++) {
 
      // columns in this column block
      SparseBlockColumnMatrix *normalsColumn = m_sparseNormals.at(i);
      if (i == 0) {
        numColumns = normalsColumn->numberOfColumns();
        int numRows = normalsColumn->numberOfRows();
        inverseMatrix.insertMatrixBlock(i, numRows, numColumns);
        inverseMatrix.zeroBlocks();
      }
      else {
        if (normalsColumn->numberOfColumns() == numColumns) {
          int numRows = normalsColumn->numberOfRows();
          inverseMatrix.insertMatrixBlock(i, numRows, numColumns);
          inverseMatrix.zeroBlocks();
        }
        else {
          numColumns = normalsColumn->numberOfColumns();
 
          // reset inverseMatrix
          inverseMatrix.wipe();
 
          // insert blocks
          for (j = 0; j < (i+1); j++) {
            SparseBlockColumnMatrix *normalsRow = m_sparseNormals.at(j);
            int numRows = normalsRow->numberOfRows();
 
            inverseMatrix.insertMatrixBlock(j, numRows, numColumns);
          }
        }
      }
 
      int localCol = 0;
 
      // solve for inverse for nCols
      for (j = 0; j < numColumns; j++) {
        if ( columnIndex > 0 ) {
          pb[columnIndex - 1] = 0.0;
        }
        pb[columnIndex] = 1.0;
 
        x = cholmod_solve ( CHOLMOD_A, m_L, b, &m_cholmodCommon );
        px = (double*)x->x;
        int rp = 0;
 
        // store solution in corresponding column of inverse
        for (k = 0; k < inverseMatrix.size(); k++) {
          LinearAlgebra::Matrix *matrix = inverseMatrix.value(k);
 
          int sz1 = matrix->size1();
 
          for (int ii = 0; ii < sz1; ii++) {
            (*matrix)(ii,localCol) = px[ii + rp];
          }
          rp += matrix->size1();
        }
 
        columnIndex++;
        localCol++;
 
        cholmod_free_dense(&x,&m_cholmodCommon);
      }
 
      // save adjusted target body sigmas if solving for target
      if (m_bundleSettings->solveTargetBody() && i == 0) {
        vector< double > &adjustedSigmas = m_bundleTargetBody->adjustedSigmas();
        matrix< double > *targetCovMatrix = inverseMatrix.value(i);
 
        for (int z = 0; z < numColumns; z++)
          adjustedSigmas[z] = sqrt((*targetCovMatrix)(z,z))*m_bundleResults.sigma0();
      }
      // save adjusted image sigmas
      else {
        BundleObservationQsp observation;
        if (m_bundleSettings->solveTargetBody()) {
          observation = m_bundleObservations.at(i-1);
        }
        else {
          observation = m_bundleObservations.at(i);
        }
        vector< double > &adjustedSigmas = observation->adjustedSigmas();
        matrix< double > *imageCovMatrix = inverseMatrix.value(i);
        for ( int z = 0; z < numColumns; z++) {
          adjustedSigmas[z] = sqrt((*imageCovMatrix)(z,z))*m_bundleResults.sigma0();
        }
      }
 
      // Output the inverse matrix if requested
      if (m_bundleSettings->createInverseMatrix()) {
        outStream << inverseMatrix;
      }
 
      // now loop over all object points to sum contributions into 3x3 point covariance matrix
      int pointIndex = 0;
      for (j = 0; j < numObjectPoints; j++) {
        emit(pointUpdate(j+1));
        BundleControlPointQsp point = m_bundleControlPoints.at(pointIndex);
        if ( point->isRejected() ) {
          continue;
        }
 
        // only update point every 100 points
        if (j%100 == 0) {
          QString status = "\rError Propagation: Inverse Block ";
          status.append(QString::number(i+1));
          status.append(" of ");
          status.append(QString::number(numBlockColumns));
          status.append("; Point ");
          status.append(QString::number(j+1));
          status.append(" of ");
          status.append(QString::number(numObjectPoints));
          outputBundleStatus(status);
        }
 
        // get corresponding Q matrix
        // NOTE: we are getting a reference to the Q matrix stored
        //       in the BundleControlPoint for speed (without the & it is dirt slow)
        SparseBlockRowMatrix &Q = point->cholmodQMatrix();
 
        T.clear();
 
        // get corresponding point covariance matrix
        boost::numeric::ublas::symmetric_matrix<double> &covariance = pointCovariances[pointIndex];
 
        // get firstQBlock - index i is the key into Q for firstQBlock
        LinearAlgebra::Matrix *firstQBlock = Q.value(i);
        if (!firstQBlock) {
          pointIndex++;
          continue;
        }
 
        // iterate over Q
        // secondQBlock is current map value
        QMapIterator< int, LinearAlgebra::Matrix * > it(Q);
        while ( it.hasNext() ) {
          it.next();
 
          int nKey = it.key();
 
          if (it.key() > i) {
            break;
          }
 
          LinearAlgebra::Matrix *secondQBlock = it.value();
 
          if ( !secondQBlock ) {// should never be NULL
            continue;
          }
 
          LinearAlgebra::Matrix *inverseBlock = inverseMatrix.value(it.key());
 
          if ( !inverseBlock ) {// should never be NULL
            continue;
          }
 
          T = prod(*inverseBlock, trans(*firstQBlock));
          T = prod(*secondQBlock,T);
 
          if (nKey != i) {
            T += trans(T);
          }
 
          try {
            covariance += T;
          }
 
          catch (std::exception &e) {
            outputBundleStatus("\n\n");
            QString msg = "Input data and settings are not sufficiently stable "
                          "for error propagation.";
            throw IException(IException::User, msg, _FILEINFO_);
          }
        }
        pointIndex++;
      }
    }
 
    if (m_bundleSettings->createInverseMatrix()) {
      // Close the file.
      matrixOutput.close();
      // Save the location of the "covariance" matrix
      m_bundleResults.setCorrMatCovFileName(matrixFile);
    }
 
    // can free sparse normals now
    m_sparseNormals.wipe();
 
    // free b (right-hand side vector
    cholmod_free_dense(&b,&m_cholmodCommon);
 
    outputBundleStatus("\n\n");
 
    currentTime = Isis::iTime::CurrentLocalTime().toLatin1().data();
 
    status = "\rFilling point covariance matrices: Time ";
    status.append(currentTime.c_str());
    outputBundleStatus(status);
    outputBundleStatus("\n\n");
 
    // now loop over points again and set final covariance stuff
    // *** TODO *** Can this loop go into BundleControlPoint
    int pointIndex = 0;
    for (j = 0; j < numObjectPoints; j++) {
 
      BundleControlPointQsp point = m_bundleControlPoints.at(pointIndex);
 
      if ( point->isRejected() ) {
        continue;
      }
 
      if (j%100 == 0) {
        status = "\rError Propagation: Filling point covariance matrices ";
        status.append(QString("%1").arg(j+1));
        status.append(" of ");
        status.append(QString("%1").arg(numObjectPoints));
        status.append("\r");
        outputBundleStatus(status);
      }
 
      // get corresponding point covariance matrix
      boost::numeric::ublas::symmetric_matrix<double> &covariance = pointCovariances[pointIndex];
 
      // Update and reset the matrix
      // Get the Limiting Error Propagation uncertainties:  sigmas for coordinate 1, 2, and 3 in meters
      //
      SurfacePoint SurfacePoint = point->adjustedSurfacePoint();
 
      // Get the TEP by adding the corresponding members of pCovar and covariance
      boost::numeric::ublas::symmetric_matrix <double,boost::numeric::ublas::upper> pCovar;
 
      if (m_bundleSettings->controlPointCoordTypeBundle() == SurfacePoint::Latitudinal) {
        pCovar = SurfacePoint.GetSphericalMatrix(SurfacePoint::Kilometers);
      }
      else {
        // Assume Rectangular coordinates
        pCovar = SurfacePoint.GetRectangularMatrix(SurfacePoint::Kilometers);
      }
      pCovar += covariance;
      pCovar *= sigma0Squared;
 
      // debug lines
      // if (j < 3) {
      //   std::cout << " Adjusted surface point ..." << std::endl;
      //   std:: cout << "     sigmaLat (radians) = " << sqrt(pCovar(0,0)) << std::endl;
      //   std:: cout << "     sigmaLon (radians) = " << sqrt(pCovar(1,1)) << std::endl;
      //   std:: cout << "     sigmaRad (km) = " << sqrt(pCovar(2,2)) << std::endl;
      // std::cout <<  "      Adjusted matrix = " << std::endl;
      // std::cout << "       " << pCovar(0,0) << "   " << pCovar(0,1) << "   "
      //           << pCovar(0,2) << std::endl;
      // std::cout << "        " << pCovar(1,0) << "   " << pCovar(1,1) << "   "
      //           << pCovar(1,2) << std::endl;
      // std::cout << "        " << pCovar(2,0) << "   " << pCovar(2,1) << "   "
      //           << pCovar(2,2) << std::endl;
      // }
      // end debug
 
      // Distance units are km**2
      SurfacePoint.SetMatrix(m_bundleSettings->controlPointCoordTypeBundle(),pCovar);
      point->setAdjustedSurfacePoint(SurfacePoint);
      // // debug lines
      // if (j < 3) {
      //   boost::numeric::ublas::symmetric_matrix <double,boost::numeric::ublas::upper> recCovar;
      //   recCovar = SurfacePoint.GetRectangularMatrix(SurfacePoint::Meters);
      //   std:: cout << "     sigmaLat (meters) = " <<
      //     point->adjustedSurfacePoint().GetSigmaDistance(SurfacePoint::Latitudinal,
      //     SurfacePoint::One).meters() << std::endl;
      //   std:: cout << "     sigmaLon (meters) = " <<
      //     point->adjustedSurfacePoint().GetSigmaDistance(SurfacePoint::Latitudinal,
      //     SurfacePoint::Two).meters() << std::endl;
      //   std:: cout << "   sigmaRad (km) = " << sqrt(pCovar(2,2)) << std::endl;
      //   std::cout << "Rectangular matrix with radius in meters" << std::endl;
      //   std::cout << "       " << recCovar(0,0) << "   " << recCovar(0,1) << "   "
      //           << recCovar(0,2) << std::endl;
      //   std::cout << "        " << recCovar(1,0) << "   " << recCovar(1,1) << "   "
      //           << recCovar(1,2) << std::endl;
      //   std::cout << "        " << recCovar(2,0) << "   " << recCovar(2,1) << "   "
      //           << recCovar(2,2) << std::endl;
      // }
      // // end debug
 
      pointIndex++;
    }
 
    return true;
  }
 
 
  ControlNetQsp BundleAdjust::controlNet() {
    return m_controlNet;
  }
 
 
  SerialNumberList *BundleAdjust::serialNumberList() {
    return m_serialNumberList;
  }
 
 
  int BundleAdjust::numberOfImages() const {
    return m_serialNumberList->size();
  }
 
 
  // TODO: probably don't need this, can get from BundleObservation
  QString BundleAdjust::fileName(int i) {
    return m_serialNumberList->fileName(i);
  }
 
 
  double BundleAdjust::iteration() const {
    return m_iteration;
  }
 
 
  Table BundleAdjust::cMatrix(int i) {
    return m_controlNet->Camera(i)->instrumentRotation()->Cache("InstrumentPointing");
  }
 
 
  Table BundleAdjust::spVector(int i) {
    return m_controlNet->Camera(i)->instrumentPosition()->Cache("InstrumentPosition");
  }
 
 
  QString BundleAdjust::modelState(int i) {
    Camera *imageCam = m_controlNet->Camera(i);
    if (imageCam->GetCameraType() != Camera::Csm) {
      QString msg = "Cannot get model state for image [" + toString(i) +
                    "] because it is not a CSM camera model.";
      throw IException(IException::Programmer, msg, _FILEINFO_);
    }
 
    CSMCamera *csmCamera = dynamic_cast<CSMCamera*>(imageCam);
    return csmCamera->getModelState();
  }
 
 
  void BundleAdjust::iterationSummary() {
    QString iterationNumber;
 
    if ( m_bundleResults.converged() ) {
        iterationNumber = "Iteration" + toString(m_iteration) + ": Final";
    }
    else {
        iterationNumber = "Iteration" + toString(m_iteration);
    }
 
    PvlGroup summaryGroup(iterationNumber);
 
    summaryGroup += PvlKeyword("Sigma0",
                               toString( m_bundleResults.sigma0() ) );
    summaryGroup += PvlKeyword("Observations",
                               toString( m_bundleResults.numberObservations() ) );
    summaryGroup += PvlKeyword("Constrained_Point_Parameters",
                               toString( m_bundleResults.numberConstrainedPointParameters() ) );
    summaryGroup += PvlKeyword("Constrained_Image_Parameters",
                               toString( m_bundleResults.numberConstrainedImageParameters() ) );
    if (m_bundleSettings->bundleTargetBody()) {
      summaryGroup += PvlKeyword("Constrained_Target_Parameters",
                                toString( m_bundleResults.numberConstrainedTargetParameters() ) );
    }
    summaryGroup += PvlKeyword("Unknown_Parameters",
                               toString( m_bundleResults.numberUnknownParameters() ) );
    summaryGroup += PvlKeyword("Degrees_of_Freedom",
                               toString( m_bundleResults.degreesOfFreedom() ) );
    summaryGroup += PvlKeyword( "Rejected_Measures",
                                toString( m_bundleResults.numberRejectedObservations()/2) );
 
    if ( m_bundleResults.numberMaximumLikelihoodModels() >
         m_bundleResults.maximumLikelihoodModelIndex() ) {
      // if maximum likelihood estimation is being used
 
      summaryGroup += PvlKeyword("Maximum_Likelihood_Tier: ",
                                 toString( m_bundleResults.maximumLikelihoodModelIndex() ) );
      summaryGroup += PvlKeyword("Median_of_R^2_residuals: ",
                                 toString( m_bundleResults.maximumLikelihoodMedianR2Residuals() ) );
    }
 
    if ( m_bundleResults.converged() ) {
      summaryGroup += PvlKeyword("Converged", "TRUE");
      summaryGroup += PvlKeyword("TotalElapsedTime", toString( m_bundleResults.elapsedTime() ) );
 
      if (m_bundleSettings->errorPropagation()) {
        summaryGroup += PvlKeyword("ErrorPropagationElapsedTime",
                                   toString( m_bundleResults.elapsedTimeErrorProp() ) );
      }
    }
 
    std::ostringstream ostr;
    ostr << summaryGroup << std::endl;
    m_iterationSummary += QString::fromStdString( ostr.str() );
 
    if (m_printSummary && iApp != NULL) {
      Application::Log(summaryGroup);
    }
    else {
      std::cout << summaryGroup << std::endl;
    }
  }
 
 
  bool BundleAdjust::isConverged() {
    return m_bundleResults.converged();
  }
 
 
  bool BundleAdjust::isAborted() {
    return m_abort;
  }
 
 
  QString BundleAdjust::iterationSummaryGroup() const {
    return m_iterationSummary;
  }
 
 
  void BundleAdjust::outputBundleStatus(QString status) {
    if (iApp == NULL) { // in a function call
      printf("%s", status.toStdString().c_str());
    }
    else if (QCoreApplication::applicationName() != "ipce") {
      printf("%s", status.toStdString().c_str());
    }
  }
 
 
 
  bool BundleAdjust::computeBundleStatistics() {
 
    // use qvectors so that we can set the size.
    // this will be useful later when adding data.
    // data may added out of index order
    int numberImages = m_serialNumberList->size();
    QVector<Statistics> rmsImageSampleResiduals(numberImages);
    QVector<Statistics> rmsImageLineResiduals(numberImages);
    QVector<Statistics> rmsImageResiduals(numberImages);
 
    int numObjectPoints = m_bundleControlPoints.size();
    for (int i = 0; i < numObjectPoints; i++) {
 
      const BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
      if (point->isRejected()) {
        continue;
      }
 
      int numMeasures = point->numberOfMeasures();
      for (int j = 0; j < numMeasures; j++) {
 
        const BundleMeasureQsp measure = point->at(j);
 
        if (measure->isRejected()) {
          continue;
        }
 
        double sampleResidual = fabs(measure->sampleResidual());
        double lineResidual = fabs(measure->lineResidual());
 
        // Determine the index for this measure's serial number
        int imageIndex = m_serialNumberList->serialNumberIndex(measure->cubeSerialNumber());
 
        // add residual data to the statistics object at the appropriate serial number index
        rmsImageSampleResiduals[imageIndex].AddData(sampleResidual);
        rmsImageLineResiduals[imageIndex].AddData(lineResidual);
        rmsImageResiduals[imageIndex].AddData(lineResidual);
        rmsImageResiduals[imageIndex].AddData(sampleResidual);
      }
    }
 
 
    if (m_bundleSettings->errorPropagation()) {
 
      // initialize body-fixed coordinate boundaries
 
      // Latitude or X
      Distance minSigmaCoord1Dist;
      QString  minSigmaCoord1PointId = "";
 
      Distance maxSigmaCoord1Dist;
      QString  maxSigmaCoord1PointId = "";
 
      // Longitude or Y
      Distance minSigmaCoord2Dist;
      QString  minSigmaCoord2PointId = "";
 
      Distance maxSigmaCoord2Dist;
      QString  maxSigmaCoord2PointId = "";
 
      // Radius or Z
      Distance minSigmaCoord3Dist;
      QString  minSigmaCoord3PointId = "";
 
      Distance maxSigmaCoord3Dist;
      QString  maxSigmaCoord3PointId = "";
 
      // compute stats for point sigmas
      Statistics sigmaCoord1Stats;
      Statistics sigmaCoord2Stats;
      Statistics sigmaCoord3Stats;
 
      Distance sigmaCoord1Dist, sigmaCoord2Dist, sigmaCoord3Dist;
      SurfacePoint::CoordinateType type = m_bundleSettings->controlPointCoordTypeReports();
 
      int numPoints = m_bundleControlPoints.size();
      // initialize max and min values to those from first valid point
      for (int i = 0; i < numPoints; i++) {
 
        const BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
        maxSigmaCoord1Dist = point->adjustedSurfacePoint().GetSigmaDistance(type,
                                                                            SurfacePoint::One);
        minSigmaCoord1Dist = maxSigmaCoord1Dist;
 
        maxSigmaCoord2Dist = point->adjustedSurfacePoint().GetSigmaDistance(type,
                                                                            SurfacePoint::Two);
        minSigmaCoord2Dist = maxSigmaCoord2Dist;
 
        maxSigmaCoord1PointId = point->id();
        maxSigmaCoord2PointId = maxSigmaCoord1PointId;
        minSigmaCoord1PointId = maxSigmaCoord1PointId;
        minSigmaCoord2PointId = maxSigmaCoord1PointId;
 
        // Get stats for coordinate 3 if used
        if (m_bundleSettings->solveRadius() || type == SurfacePoint::Rectangular) {
          maxSigmaCoord3Dist = point->adjustedSurfacePoint().GetSigmaDistance(type,
                                                                              SurfacePoint::Three);
          minSigmaCoord3Dist = maxSigmaCoord3Dist;
 
          maxSigmaCoord3PointId = maxSigmaCoord1PointId;
          minSigmaCoord3PointId = maxSigmaCoord1PointId;
        }
        break;
      }
 
      for (int i = 0; i < numPoints; i++) {
 
        const BundleControlPointQsp point = m_bundleControlPoints.at(i);
 
        sigmaCoord1Dist = point->adjustedSurfacePoint().GetSigmaDistance(type,
                                                                         SurfacePoint::One);
        sigmaCoord2Dist = point->adjustedSurfacePoint().GetSigmaDistance(type,
                                                                         SurfacePoint::Two);
        sigmaCoord3Dist = point->adjustedSurfacePoint().GetSigmaDistance(type,
                                                                         SurfacePoint::Three);
 
        sigmaCoord1Stats.AddData(sigmaCoord1Dist.meters());
        sigmaCoord2Stats.AddData(sigmaCoord2Dist.meters());
        sigmaCoord3Stats.AddData(sigmaCoord3Dist.meters());
 
        if (sigmaCoord1Dist > maxSigmaCoord1Dist) {
          maxSigmaCoord1Dist = sigmaCoord1Dist;
          maxSigmaCoord1PointId = point->id();
        }
        if (sigmaCoord2Dist > maxSigmaCoord2Dist) {
          maxSigmaCoord2Dist = sigmaCoord2Dist;
          maxSigmaCoord2PointId = point->id();
        }
        if (m_bundleSettings->solveRadius() || type == SurfacePoint::Rectangular) {
          if (sigmaCoord3Dist > maxSigmaCoord3Dist) {
            maxSigmaCoord3Dist = sigmaCoord3Dist;
            maxSigmaCoord3PointId = point->id();
          }
        }
        if (sigmaCoord1Dist < minSigmaCoord1Dist) {
          minSigmaCoord1Dist = sigmaCoord1Dist;
          minSigmaCoord1PointId = point->id();
        }
        if (sigmaCoord2Dist < minSigmaCoord2Dist) {
          minSigmaCoord2Dist = sigmaCoord2Dist;
          minSigmaCoord2PointId = point->id();
        }
        if (m_bundleSettings->solveRadius() || type == SurfacePoint::Rectangular) {
          if (sigmaCoord3Dist < minSigmaCoord3Dist) {
            minSigmaCoord3Dist = sigmaCoord3Dist;
            minSigmaCoord3PointId = point->id();
          }
        }
      }
 
      // update bundle results
      m_bundleResults.resizeSigmaStatisticsVectors(numberImages);
 
      m_bundleResults.setSigmaCoord1Range(minSigmaCoord1Dist, maxSigmaCoord1Dist,
                                            minSigmaCoord1PointId, maxSigmaCoord1PointId);
 
      m_bundleResults.setSigmaCoord2Range(minSigmaCoord2Dist, maxSigmaCoord2Dist,
                                             minSigmaCoord2PointId, maxSigmaCoord2PointId);
 
      m_bundleResults.setSigmaCoord3Range(minSigmaCoord3Dist, maxSigmaCoord3Dist,
                                          minSigmaCoord3PointId, maxSigmaCoord3PointId);
 
      m_bundleResults.setRmsFromSigmaStatistics(sigmaCoord1Stats.Rms(),
                                                sigmaCoord2Stats.Rms(),
                                                sigmaCoord3Stats.Rms());
    }
    m_bundleResults.setRmsImageResidualLists(rmsImageLineResiduals.toList(),
                                             rmsImageSampleResiduals.toList(),
                                             rmsImageResiduals.toList());
 
    return true;
  }
 
}