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NeutrinoDirectionality.cc
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NeutrinoDirectionality.cc
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#include "NeutrinoDirectionality.h"
#include "DetectorConfig.h"
#include "Formatting.h"
#include "Timer.h"
using std::cout, std::string, std::ifstream, std::array, std::getline;
void FillDetectorConfig()
{
// Filling values based on different periods
int noSegments = 154;
int noPeriods = 6;
for (int i = 0; i < noPeriods; i++)
{
int excludeSize = excludeList[i].size();
int counter = 0, tmp = 0;
vector<int> period;
for (int j = 0; j < noSegments; j++)
{
// Filling live segments by checking exclude list
tmp = excludeList[i][counter];
if (j == tmp)
{
period.push_back(0);
if (counter + 1 < excludeSize)
{
counter += 1;
}
}
else
{
period.push_back(1);
}
}
detectorConfig.push_back(period);
}
if (DETECTOR_VERBOSITY)
{
cout << "--------------------------------------------\n";
cout << "Below is the detector configuration.\n";
cout << "--------------------------------------------\n";
for (int i = 0; i < noPeriods; i++)
{
cout << "Detector configuration for period: " << i + 1 << '\n';
for (int j = 140; j >= 0; j -= 14)
{
for (int k = 0; k < 14; k++)
{
if (detectorConfig[i][j + k])
{
cout << "\u25A0 ";
}
else
{
cout << "\u25A1 ";
}
}
cout << '\n';
}
cout << '\n';
}
}
}
bool CheckNeighbor(int periodNo, int segment, char direction)
{
// Used for dead segment calculations
bool neighbor = false;
periodNo = periodNo - 1;
switch (direction)
{
case 'r':
neighbor = detectorConfig[periodNo][segment + 1];
break;
case 'l':
neighbor = detectorConfig[periodNo][segment - 1];
break;
case 'u':
neighbor = detectorConfig[periodNo][segment + 14];
break;
case 'd':
neighbor = detectorConfig[periodNo][segment - 14];
break;
default:
cout << "That direction doesn't exist!\n";
return false;
}
return neighbor;
}
Directionality::Directionality()
{
for (int dataset = Data; dataset < DatasetSize; dataset++) // Dataset
{
for (int signalSet = CorrelatedReactorOn; signalSet < TotalDifference; signalSet++) // Signal set
{
for (int direction = X; direction < DirectionSize; direction++)
{
// No reactor off for simulations
if ((dataset == Sim || dataset == SimUnbiased)
&& (signalSet == CorrelatedReactorOff || signalSet == AccidentalReactorOff))
continue;
string data = DatasetToString(dataset);
string signal = SignalToString(signalSet);
string axis = AxisToString(direction);
string histogramName = data + " " + signal + " " + axis;
histogram[dataset][signalSet][direction]
= TH1F(histogramName.c_str(), data.c_str(), bins, -histogramMax, histogramMax);
}
}
}
ResetLineNumber();
}
void Directionality::ReadFileList(int dataset, int periodNo)
{
char const* path;
switch (dataset)
{
case Data:
path = dataPath;
break;
case Sim:
path = simPath;
break;
case PerfSim:
path = perfSimPath;
break;
default:
path = dataPath;
break;
}
// Combining names into file list name
string fileList;
if (periodNo != 6)
fileList = Form(path, std::to_string(periodNo).c_str(), std::to_string(periodNo).c_str());
else
fileList = path;
// Opening and checking file list
ifstream file;
file.open(fileList, ifstream::in);
if (!(file.is_open() && file.good()))
{
cout << "File list not found! Exiting.\n";
cout << "Trying to find: " << fileList << '\n';
return;
}
while (file.good() && getline(file, files[lineNumber]))
{
lineNumber++;
}
files[lineNumber] = "Done";
lineNumber++;
}
void Directionality::SetUpHistograms(int dataset, int periodNo)
{
// Declaring some variables for use later
int totalLines = 0;
reactorOn = true;
dataSet = dataset;
period = periodNo;
char const* fileName;
switch (dataset)
{
case Data:
fileName = dataFileName;
break;
case Sim:
fileName = simFileName;
break;
case PerfSim:
fileName = perfSimFileName;
break;
default:
fileName = dataFileName;
break;
}
while (index < files.size())
{
if (files[index] == "Done")
{
index++;
return;
}
if (dataSet == Data || dataSet == DataUnbiased)
{
if (lineCounter % 100 == 0)
{
cout << "Reading file: " << lineCounter << "/" << totalDataLines << '\r';
cout.flush();
}
}
else if (dataSet == Sim || dataSet == SimUnbiased)
{
if (lineCounter % 50 == 0)
{
cout << "Reading file: " << lineCounter << "/" << totalSimLines << '\r';
cout.flush();
}
}
else if (dataSet == PerfSim || dataSet == PerfSimUnbiased)
{
cout << "Reading file: " << lineCounter << "/" << totalPerfSimLines << '\r';
cout.flush();
}
// Combining names into root file name
TString rootFilename;
if (period != 6)
rootFilename = Form(fileName, std::to_string(period).c_str(), files[index].data());
else
rootFilename = Form(fileName, files[index].data());
if (rootFilename.Contains(" 0"))
{
rootFilename.ReplaceAll(" 0", "");
reactorOn = false;
}
else if (rootFilename.Contains(" 1"))
{
rootFilename.ReplaceAll(" 1", "");
reactorOn = true;
}
// Open the root file
auto rootFile = std::make_unique<TFile>(rootFilename);
// Going into empty scope to let the pointers die out for safety
{
TVectorD* runtime = (TVectorD*)rootFile->Get("runtime");
TVectorD* promptVeto = (TVectorD*)rootFile->Get("accumulated/P2kIBDPlugin.tveto_prompt"); // prompt veto deadtime
TVectorD* delayedVeto = (TVectorD*)rootFile->Get("accumulated/P2kIBDPlugin.tveto_delayed"); // delayed veto deadtime
xRx = runtime->Max() / (runtime->Max() - promptVeto->Max()) * runtime->Max() / (runtime->Max() - delayedVeto->Max());
if (reactorOn && dataSet == Data)
{
livetimeOn += runtime->Max() / xRx;
}
else if (dataSet == Data)
{
livetimeOff += runtime->Max() / xRx;
}
}
// Grab rootTree and cast to unique pointer
TTree* rootTree = (TTree*)rootFile->Get("P2kIBDPlugin/Tibd");
long nEntries = rootTree->GetEntries();
for (long i = 0; i < nEntries; i++)
{
rootTree->GetEntry(i);
for (direction = X; direction < DirectionSize; direction++)
{
// Grabbing relevant values from the rootTree entry
promptPosition = rootTree->GetLeaf("xyz")->GetValue(direction);
delayedPosition = rootTree->GetLeaf("n_xyz")->GetValue(direction);
promptSegment = rootTree->GetLeaf("maxseg")->GetValue(0);
delayedSegment = rootTree->GetLeaf("n_seg")->GetValue(0);
// We throw out events where the neutron moves in a direction we're not checking
if (promptSegment != delayedSegment && promptPosition == delayedPosition)
continue;
if (promptSegment == 32 || delayedSegment == 32)
continue;
if (direction != Z) // Cubical distance cuts in Z for X and Y
{
float zPromptPosition = rootTree->GetLeaf("xyz")->GetValue(Z);
float zDelayedPosition = rootTree->GetLeaf("n_xyz")->GetValue(Z);
float displacement = fabs(zPromptPosition - zDelayedPosition);
if (displacement > 60)
continue;
}
// Copying some loop values into current entry
Esmear = rootTree->GetLeaf("Esmear")->GetValue(0);
nCaptTime = rootTree->GetLeaf("ncapt_dt")->GetValue(0);
FillHistogram();
}
}
// Returns the next character in the input sequence, without extracting it: The character is left as the next character
// to be extracted from the stream
rootFile->Close();
lineCounter++;
index++;
}
}
void Directionality::FillHistogram()
{
// Applying energy cut
if (Esmear < 0.8 || Esmear > 7.4)
{
return;
}
int signalSet = 0;
if (nCaptTime > pow(10, 3) && nCaptTime < 120 * pow(10, 3)) // Correlated Dataset
{
// Calculate neutron displacement
double displacement = delayedPosition - promptPosition;
// Figure out whether the reactor is on and assign signal index
signalSet = reactorOn ? CorrelatedReactorOn : CorrelatedReactorOff;
// Fill regular dataset with displacement but Z only takes same segment
if (direction != Z)
{
// Correcting center to center displacment
if (displacement > 0)
displacement = segmentWidth;
else if (displacement < 0)
displacement = -segmentWidth;
histogram[dataSet][signalSet][direction].Fill(displacement);
}
// Fill dead segment correction dataset
FillHistogramUnbiased(signalSet);
}
else if (nCaptTime > pow(10, 6)) // Accidental Dataset
{
// Calculate neutron displacement
double displacement = delayedPosition - promptPosition;
// Figure out whether the reactor is on and assign signal index
signalSet = reactorOn ? AccidentalReactorOn : AccidentalReactorOff;
// Fill regular dataset with displacement but Z only takes same segment
if (direction != Z)
{
// Correcting center to center displacment
if (displacement > 0)
displacement = segmentWidth;
else if (displacement < 0)
displacement = -segmentWidth;
histogram[dataSet][signalSet][direction].Fill(displacement, xRx);
}
// Fill dead segment correction dataset
FillHistogramUnbiased(signalSet);
}
}
void Directionality::FillHistogramUnbiased(int signalSet)
{
bool posDirection = false, negDirection = false;
bool isDisplacement = false;
// Need to weight accidental datasets by deadtime correction factor
double weight = (signalSet == AccidentalReactorOff || signalSet == AccidentalReactorOn) ? xRx : 1;
isDisplacement = promptSegment != delayedSegment ? true : false;
if (isDisplacement && direction != Z)
{
// Calculate neutron displacement
double displacement = delayedPosition - promptPosition;
// Fill neutron displacement but only for x and y
histogram[dataSet + 1][signalSet][direction].Fill(displacement, weight);
}
// Check for live neighbors in different directions based on which axis we're filling
if (direction == X)
{
posDirection = CheckNeighbor(period, promptSegment, 'r');
negDirection = CheckNeighbor(period, promptSegment, 'l');
}
else if (direction == Y)
{
posDirection = CheckNeighbor(period, promptSegment, 'u');
negDirection = CheckNeighbor(period, promptSegment, 'd');
}
else if (direction == Z && !isDisplacement) // Fill Z with same segment events
{
double displacement = delayedPosition - promptPosition;
histogram[dataSet][signalSet][direction].Fill(displacement, weight);
}
// Dataset + 1 returns the unbiased version of that dataset
if (!isDisplacement)
{
if (posDirection && !negDirection)
{
histogram[dataSet + 1][signalSet][direction].Fill(1.0, weight);
if (dataSet == PerfSim && direction == X)
nxPlusPlusCounter[promptSegment]++;
else if (dataSet == PerfSim && direction == Y)
nyPlusPlusCounter[promptSegment]++;
}
else if (!posDirection && negDirection)
{
histogram[dataSet + 1][signalSet][direction].Fill(-1.0, weight);
if (dataSet == PerfSim && direction == X)
nxMinusMinusCounter[promptSegment]++;
else if (dataSet == PerfSim && direction == Y)
nyMinusMinusCounter[promptSegment]++;
}
else if (posDirection && negDirection)
{
histogram[dataSet + 1][signalSet][direction].Fill(0.0, weight);
if (dataSet == PerfSim && direction == X)
nxPlusMinusCounter[promptSegment]++;
else if (dataSet == PerfSim && direction == Y)
nyPlusMinusCounter[promptSegment]++;
}
}
}
void Directionality::SubtractBackgrounds()
{
/* IBD events = (Correlated - Accidental/100)_{reactor on} + (-livetimeOn/livetimeOff*Correlated +
livetimeOn/livetimeOff*Accidental/100)_{reactor off} */
// Defining variables for IBD background subtraction
double totalIBDs = 0, totalIBDErr = 0, effIBDs = 0;
// Doing n counts for comparison with/without background subtraction
double nPlus = 0, nPlusPlus = 0, nMinus = 0, nMinusMinus = 0, nPlusMinus = 0;
double nPlusError = 0, nPlusPlusError = 0, nMinusError = 0, nMinusMinusError = 0, nPlusMinusError = 0;
for (int dataset = DataUnbiased; dataset < DatasetSize; dataset += 2)
{
if (!NCOUNT_VERBOSITY)
continue;
for (int direction = X; direction < Z; direction++)
{
for (int signalSet = CorrelatedReactorOn; signalSet < SignalSize - 1; signalSet++)
{
// Grabbing data from filled bins, rest should be empty
nPlus = histogram[dataset][signalSet][direction].GetBinContent(296);
nPlusPlus = histogram[dataset][signalSet][direction].GetBinContent(152);
nMinus = histogram[dataset][signalSet][direction].GetBinContent(6);
nMinusMinus = histogram[dataset][signalSet][direction].GetBinContent(150);
nPlusMinus = histogram[dataset][signalSet][direction].GetBinContent(151);
nPlusError = histogram[dataset][signalSet][direction].GetBinError(296);
nPlusPlusError = histogram[dataset][signalSet][direction].GetBinError(152);
nMinusError = histogram[dataset][signalSet][direction].GetBinError(6);
nMinusMinusError = histogram[dataset][signalSet][direction].GetBinError(150);
nPlusMinusError = histogram[dataset][signalSet][direction].GetBinError(151);
cout << "N (with background) counts for: " << boldOn << DatasetToString(dataset) << " "
<< AxisToString(direction) << " " << SignalToString(signalSet) << ":\n";
cout << "N+: " << resetFormats << nPlus << '\n';
cout << boldOn << "N-: " << resetFormats << nMinus << '\n';
cout << boldOn << "N++: " << resetFormats << nPlusPlus << '\n';
cout << boldOn << "N--: " << resetFormats << nMinusMinus << '\n';
cout << boldOn << "N+-: " << resetFormats << nPlusMinus << '\n';
cout << "--------------------------------------------\n";
cout << "N (with background) count errors for: " << boldOn << DatasetToString(dataset) << " "
<< AxisToString(direction) << " " << SignalToString(signalSet) << ":\n";
cout << "N+: " << resetFormats << nPlusError << '\n';
cout << boldOn << "N-: " << resetFormats << nMinusError << '\n';
cout << boldOn << "N++: " << resetFormats << nPlusPlusError << '\n';
cout << boldOn << "N--: " << resetFormats << nMinusMinusError << '\n';
cout << boldOn << "N+-: " << resetFormats << nPlusMinusError << '\n';
cout << "--------------------------------------------\n";
}
}
}
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
for (int direction = X; direction < DirectionSize; direction++)
{
string histogramName;
string data = DatasetToString(dataset);
histogramName = data + " Total Difference " + AxisToString(direction);
// Copying Correlated Reactor On to start
histogram[dataset][TotalDifference][direction] = TH1F(histogram[dataset][CorrelatedReactorOn][direction]);
histogram[dataset][TotalDifference][direction].SetNameTitle(histogramName.c_str(), data.c_str());
histogram[dataset][TotalDifference][direction].Add(&histogram[dataset][AccidentalReactorOn][direction], -1. / 100);
if (dataset == Data || dataset == DataUnbiased)
{
histogram[dataset][TotalDifference][direction].Add(&histogram[dataset][CorrelatedReactorOff][direction],
-livetimeOn * atmosphericScaling / livetimeOff);
histogram[dataset][TotalDifference][direction].Add(&histogram[dataset][AccidentalReactorOff][direction],
livetimeOn * atmosphericScaling / (100 * livetimeOff));
}
totalIBDs = histogram[dataset][TotalDifference][direction].IntegralAndError(
0, histogram[dataset][TotalDifference][direction].GetNbinsX() + 1, totalIBDErr);
effIBDs = pow(totalIBDs, 2) / pow(totalIBDErr, 2); // Effective IBD counts. Done by Poisson Distribution
// N^2/(sqrt(N)^2) = N; Eff. counts = counts^2/counts_err^2
totalIBD[dataset][direction] = totalIBDs;
totalIBDError[dataset][direction] = totalIBDErr;
if (direction == Z)
{
effectiveIBD[dataset][direction] = effIBDs;
continue;
}
if (dataset == Data || dataset == Sim || dataset == PerfSim)
{
mean[dataset][direction] = histogram[dataset][TotalDifference][direction].GetMean();
sigma[dataset][direction] = histogram[dataset][TotalDifference][direction].GetStdDev() / sqrt(effIBDs);
effectiveIBD[dataset][direction] = effIBDs;
}
else
{
effectiveIBD[dataset][direction] = effIBDs;
}
}
if (dataset == DataUnbiased || dataset == SimUnbiased)
continue;
// Z is fit to a Guassian and only takes same segment inputs
// Possible thanks to 1mm resolution in Z
TF1 gaussian("Fit", "gaus", -140, 140);
histogram[dataset][TotalDifference][Z].Fit("Fit", "RQ");
float zMean = gaussian.GetParameter(1);
float zError = gaussian.GetParError(1);
mean[dataset][Z] = zMean;
sigma[dataset][Z] = zError;
// Deleting fit because we don't want the plot options stuck here
delete histogram[dataset][TotalDifference][Z].GetListOfFunctions()->FindObject("Fit");
}
// Printing out values
if (IBDCOUNT_VERBOSITY)
{
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
cout << "Total and Effective IBD Events for: " << boldOn << DatasetToString(dataset) << resetFormats << '\n';
for (int direction = X; direction < DirectionSize; direction++)
{
cout << boldOn << AxisToString(direction) << ": " << resetFormats << totalIBD[dataset][direction] << " ± "
<< totalIBDError[dataset][direction] << boldOn << ". Effective IBD counts: " << resetFormats
<< effectiveIBD[dataset][direction] << ".\n";
}
cout << "--------------------------------------------\n";
}
}
cout << boldOn << cyanOn << "Subtracted backgrounds.\n" << resetFormats;
cout << "--------------------------------------------\n";
CalculateUnbiasing();
}
void Directionality::CalculateUnbiasing()
{
// Defining variables used in calculation. Check the error propagation technote for details on the method
double rPlus = 0, rMinus = 0;
double p = 0, pError = 0;
double nPlus = 0, nPlusPlus = 0, nMinus = 0, nMinusMinus = 0, nPlusMinus = 0;
double nPlusError = 0, nPlusPlusError = 0, nMinusError = 0, nMinusMinusError = 0, nPlusMinusError = 0;
for (int dataset = DataUnbiased; dataset < DatasetSize; dataset += 2)
{
for (int direction = X; direction < Z; direction++)
{
// Dataset - 1 returns the biased dataset counts
// Grabbing data from filled bins, rest should be empty
nPlus = histogram[dataset][TotalDifference][direction].GetBinContent(296);
nPlusPlus = histogram[dataset][TotalDifference][direction].GetBinContent(152);
nMinus = histogram[dataset][TotalDifference][direction].GetBinContent(6);
nMinusMinus = histogram[dataset][TotalDifference][direction].GetBinContent(150);
nPlusMinus = histogram[dataset][TotalDifference][direction].GetBinContent(151);
nPlusError = histogram[dataset][TotalDifference][direction].GetBinError(296);
nPlusPlusError = histogram[dataset][TotalDifference][direction].GetBinError(152);
nMinusError = histogram[dataset][TotalDifference][direction].GetBinError(6);
nMinusMinusError = histogram[dataset][TotalDifference][direction].GetBinError(150);
nPlusMinusError = histogram[dataset][TotalDifference][direction].GetBinError(151);
rPlus = nPlus / (nPlusPlus + nPlusMinus);
rMinus = nMinus / (nMinusMinus + nPlusMinus);
p = segmentWidth * (rPlus - rMinus) / (rPlus + rMinus + 1);
pError
= segmentWidth
* pow(1 / ((nMinus * (nPlusMinus + nPlusPlus) + (nMinusMinus + nPlusMinus) * (nPlus + nPlusMinus + nPlusPlus))),
2)
* sqrt(
pow((nMinusMinus + nPlusMinus) * (nPlusMinus + nPlusPlus), 2)
* (pow(nPlusError * (2 * nMinus + nMinusMinus + nPlusMinus), 2)
+ pow(nMinusError * (2 * nPlus + nPlusPlus + nPlusMinus), 2))
+ pow((nPlus * (nPlusMinus + nMinusMinus) * (2 * nMinus + nMinusMinus + nPlusMinus) * nPlusPlusError), 2)
+ pow((nPlusMinusError
* (nPlus * pow((nMinusMinus + nPlusMinus), 2)
+ nMinus * (2 * nMinusMinus * nPlus - 2 * nPlus * nPlusPlus - pow((nPlusMinus + nPlusPlus), 2)))),
2)
+ pow((nMinus * (nPlusMinus + nPlusPlus) * (2 * nPlus + nPlusMinus + nPlusPlus) * nMinusMinusError), 2));
mean[dataset][direction] = p;
sigma[dataset][direction] = pError;
if (NCOUNT_VERBOSITY)
{
cout << "N counts for: " << boldOn << DatasetToString(dataset) << " " << AxisToString(direction) << ":\n";
cout << "N+: " << resetFormats << nPlus << '\n';
cout << boldOn << "N-: " << resetFormats << nMinus << '\n';
cout << boldOn << "N++: " << resetFormats << nPlusPlus << '\n';
cout << boldOn << "N--: " << resetFormats << nMinusMinus << '\n';
cout << boldOn << "N+-: " << resetFormats << nPlusMinus << '\n';
cout << "--------------------------------------------\n";
cout << "N count errors for: " << boldOn << DatasetToString(dataset) << " " << AxisToString(direction) << ":\n";
cout << "N+: " << resetFormats << nPlusError << '\n';
cout << boldOn << "N-: " << resetFormats << nMinusError << '\n';
cout << boldOn << "N++: " << resetFormats << nPlusPlusError << '\n';
cout << boldOn << "N--: " << resetFormats << nMinusMinusError << '\n';
cout << boldOn << "N+-: " << resetFormats << nPlusMinusError << '\n';
cout << "--------------------------------------------\n";
}
double stdDev = (segmentWidth / (rPlus + rMinus + 1)) * sqrt(4 * rPlus * rMinus + rPlus + rMinus);
cout << "Standard Deviation for " << boldOn << DatasetToString(dataset) << " " << AxisToString(direction);
cout << resetFormats << " " << stdDev << "\n";
cout << "--------------------------------------------\n";
}
effectiveIBD[dataset][Z] = effectiveIBD[dataset - 1][Z];
mean[dataset][Z] = mean[dataset - 1][Z];
sigma[dataset][Z] = sigma[dataset - 1][Z];
}
cout << boldOn << cyanOn << "Calculated Means.\n" << resetFormats;
cout << "--------------------------------------------\n";
// Printing out values
if (MEAN_VERBOSITY)
{
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
cout << "Mean and sigma values for: " << boldOn << DatasetToString(dataset) << resetFormats << '\n';
for (int direction = X; direction < DirectionSize; direction++)
{
cout << boldOn << "p" << AxisToString(direction) << ": " << resetFormats << mean[dataset][direction] << " ± "
<< sigma[dataset][direction] << '\n';
}
cout << "--------------------------------------------\n";
}
}
}
void Directionality::AddSystematics()
{
// Systematics extracted from BiPo study
// Defining variables for readability of code
double sigmaX, sigmaY, sigmaZ;
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
sigmaX = sigma[dataset][X];
sigmaY = sigma[dataset][Y];
sigmaZ = sigma[dataset][Z];
sigmaSystematics[dataset][X] = sqrt(pow(sigmaX, 2) + pow(0.25, 2) + pow(0.08, 2));
sigmaSystematics[dataset][Y] = sqrt(pow(sigmaY, 2) + pow(0.39, 2) + pow(0.08, 2));
sigmaSystematics[dataset][Z] = sqrt(pow(sigmaZ, 2) + pow(0.06, 2) + pow(0.06, 2));
}
cout << boldOn << cyanOn << "Added Systematics.\n" << resetFormats;
cout << "--------------------------------------------\n";
// Printing out values
if (SYSTEMATIC_MEAN_VERBOSITY)
{
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
cout << "Mean and sigma values for: " << boldOn << DatasetToString(dataset) << resetFormats << '\n';
for (int direction = X; direction < DirectionSize; direction++)
{
cout << boldOn << "p" << AxisToString(direction) << ": " << resetFormats << mean[dataset][direction] << " ± "
<< sigmaSystematics[dataset][direction] << '\n';
}
cout << "--------------------------------------------\n";
}
}
}
void Directionality::CalculateAngles()
{
// Defining variables for readability of code
double px, py, pz;
double sigmaX, sigmaY, sigmaZ;
double sigmaXSystematics, sigmaYSystematics, sigmaZSystematics;
double effIBDX, effIBDY, effIBDZ;
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
// Grabbing values from current dataset
px = mean[dataset][X];
py = mean[dataset][Y];
pz = mean[dataset][Z];
sigmaX = sigma[dataset][X];
sigmaY = sigma[dataset][Y];
sigmaZ = sigma[dataset][Z];
sigmaXSystematics = sigmaSystematics[dataset][X];
sigmaYSystematics = sigmaSystematics[dataset][Y];
sigmaZSystematics = sigmaSystematics[dataset][Z];
effIBDX = effectiveIBD[dataset][X];
effIBDY = effectiveIBD[dataset][Y];
effIBDZ = effectiveIBD[dataset][Z];
// phi = arctan(y / x)
double tanPhi = py / px;
double phiTemp = atan(tanPhi) * 180.0 / pi;
double tanPhiError = sqrt(pow((sigmaX * py) / pow(px, 2), 2) + pow(sigmaY / px, 2));
double phiErrorTemp = (tanPhiError / (1 + pow(tanPhi, 2))) * 180.0 / pi;
double tanPhiErrorSystematics = sqrt(pow((sigmaXSystematics * py) / pow(px, 2), 2) + pow(sigmaYSystematics / px, 2));
double phiErrorSystematicsTemp = (tanPhiErrorSystematics / (1 + pow(tanPhi, 2))) * 180.0 / pi;
// theta = arctan(z / sqrt(x^2 + y^2))
double tanTheta = pz / sqrt(pow(px, 2) + pow(py, 2));
double thetaTemp = atan(tanTheta) * 180.0 / pi;
double tanThetaError = sqrt((1 / (px * px + py * py))
* (pow((px * pz * sigmaX / (px * px + py * py)), 2)
+ pow((py * pz * sigmaY / (px * px + py * py)), 2) + pow(sigmaZ, 2)));
double thetaErrorTemp = (tanThetaError / (1 + pow(tanTheta, 2))) * 180.0 / pi;
double tanThetaErrorSystematics
= sqrt((1 / (px * px + py * py))
* (pow((px * pz * sigmaXSystematics / (px * px + py * py)), 2)
+ pow((py * pz * sigmaYSystematics / (px * px + py * py)), 2) + pow(sigmaZSystematics, 2)));
double thetaErrorSystematicsTemp = (tanThetaErrorSystematics / (1 + pow(tanTheta, 2))) * 180.0 / pi;
// Storing values
phi[dataset] = phiTemp;
phiError[dataset] = phiErrorTemp;
phiErrorSystematics[dataset] = phiErrorSystematicsTemp;
theta[dataset] = thetaTemp;
thetaError[dataset] = thetaErrorTemp;
thetaErrorSystematics[dataset] = thetaErrorSystematicsTemp;
}
// Calculating "true" neutrino direction
// Based on Figure 1, https://doi.org/10.1103/PhysRevD.103.032001
float xTrue = -5.97, yTrue = -5.09, zTrue = 1.19;
float xTrueError = 0.1, yTrueError = 0.1, zTrueError = 0.1;
// Scaling by average prompt location
xTrue += 50.99 / 1000;
yTrue -= 23.31 / 1000;
zTrue -= 0.33 / 1000;
// Same angle calculation as above
float tanPhiTrue = yTrue / xTrue;
phiTrue = atan(tanPhiTrue) * 180.0 / pi;
float tanPhiTrueError = sqrt(pow((yTrue * xTrueError) / (xTrue * xTrue), 2) + pow(yTrueError / xTrue, 2));
phiTrueError = tanPhiTrueError / (1 + pow(tanPhiTrue, 2)) * 180.0 / pi;
float tanThetaTrue = zTrue / sqrt(pow(xTrue, 2) + pow(yTrue, 2));
thetaTrue = atan(tanThetaTrue) * 180.0 / pi;
float tanThetaTrueError
= sqrt(pow(1 / sqrt(xTrue * xTrue + yTrue * yTrue), 2)
* (pow(xTrue * zTrue / (xTrue * xTrue + yTrue * yTrue) * xTrueError, 2)
+ pow(yTrue * zTrue / (xTrue * xTrue + yTrue * yTrue) * yTrueError, 2) + pow(zTrueError, 2)));
thetaTrueError = tanThetaTrueError / (1 + pow(tanPhiTrue, 2)) * 180.0 / pi;
}
void Directionality::CalculateCovariances()
{
// Calculating covariances
array<array<float, 2>, 2> covarianceMatrix;
array<array<float, 2>, 2> covarianceMatrixSystematics;
// Defining variables for readability
float px, py, pz;
float sigmaX, sigmaY, sigmaZ;
float sigmaXSystematics, sigmaYSystematics, sigmaZSystematics;
float phiTemp, thetaTemp;
// From error propagation document
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
// Grabbing values of current dataset from struct
px = mean[dataset][X];
py = mean[dataset][Y];
pz = mean[dataset][Z];
sigmaX = sigma[dataset][X];
sigmaY = sigma[dataset][Y];
sigmaZ = sigma[dataset][Z];
sigmaXSystematics = sigmaSystematics[dataset][X];
sigmaYSystematics = sigmaSystematics[dataset][Y];
sigmaZSystematics = sigmaSystematics[dataset][Z];
phiTemp = phi[dataset];
thetaTemp = theta[dataset];
// Filling out first matrix
covarianceMatrix[0][0] = (pow(sigmaX, 2) * pow(py, 2) / (pow(px, 4))) + pow(sigmaY, 2) / pow(px, 2);
covarianceMatrix[0][1] = (pow(pz, 2) / (px * pow(pow(px, 2) + pow(py, 2), (3. / 2.))))
* (pow(sigmaY, 2) - pow(sigmaX, 2));
covarianceMatrix[1][0] = ((py * pz) / (px * pow(pow(px, 2) + pow(py, 2), (3. / 2.)))) * (pow(sigmaY, 2) - pow(sigmaX, 2));
covarianceMatrix[1][1] = ((pow(px, 2) * pow(pz, 2) * pow(sigmaX, 2) + pow(py, 2) * pow(pz, 2) * pow(sigmaY, 2))
/ (pow(pow(px, 2) + pow(py, 2), 3)))
+ (pow(sigmaZ, 2)) / (pow(px, 2) + pow(py, 2));
covarianceMatrixSystematics[0][0] = (pow(sigmaXSystematics, 2) * pow(py, 2) / (pow(px, 4)))
+ pow(sigmaYSystematics, 2) / pow(px, 2);
covarianceMatrixSystematics[0][1] = (pow(pz, 2) / (px * pow(pow(px, 2) + pow(py, 2), (3. / 2.))))
* (pow(sigmaYSystematics, 2) - pow(sigmaXSystematics, 2));
covarianceMatrixSystematics[1][0] = ((py * pz) / (px * pow(pow(px, 2) + pow(py, 2), (3. / 2.))))
* (pow(sigmaYSystematics, 2) - pow(sigmaXSystematics, 2));
covarianceMatrixSystematics[1][1]
= ((pow(px, 2) * pow(pz, 2) * pow(sigmaXSystematics, 2) + pow(py, 2) * pow(pz, 2) * pow(sigmaYSystematics, 2))
/ (pow(pow(px, 2) + pow(py, 2), 3)))
+ (pow(sigmaZSystematics, 2)) / (pow(px, 2) + pow(py, 2));
// Including angles
covarianceMatrix[0][0] = covarianceMatrix[0][0] * pow(cos(phiTemp * pi / 180), 4);
covarianceMatrix[0][1] = covarianceMatrix[0][1] * pow(cos(phiTemp * pi / 180), 2) * pow(cos(thetaTemp * pi / 180), 2);
covarianceMatrix[1][0] = covarianceMatrix[1][0] * pow(cos(phiTemp * pi / 180), 2) * pow(cos(thetaTemp * pi / 180), 2);
covarianceMatrix[1][1] = covarianceMatrix[1][1] * pow(cos(thetaTemp * pi / 180), 4);
covarianceMatrixSystematics[0][0] = covarianceMatrixSystematics[0][0] * pow(cos(phiTemp * pi / 180), 4);
covarianceMatrixSystematics[0][1] = covarianceMatrixSystematics[0][1] * pow(cos(phiTemp * pi / 180), 2)
* pow(cos(thetaTemp * pi / 180), 2);
covarianceMatrixSystematics[1][0] = covarianceMatrixSystematics[1][0] * pow(cos(phiTemp * pi / 180), 2)
* pow(cos(thetaTemp * pi / 180), 2);
covarianceMatrixSystematics[1][1] = covarianceMatrixSystematics[1][1] * pow(cos(thetaTemp * pi / 180), 4);
// Eigenvalues
float a = covarianceMatrix[0][0], aSystematics = covarianceMatrixSystematics[0][0];
float b = covarianceMatrix[0][1], bSystematics = covarianceMatrixSystematics[0][1];
float c = covarianceMatrix[1][0], cSystematics = covarianceMatrixSystematics[1][0];
float d = covarianceMatrix[1][1], dSystematics = covarianceMatrixSystematics[1][1];
float lambda1 = ((a + d) + sqrt(pow(a, 2) - 2 * a * d + 4 * b * c + pow(d, 2))) / 2;
float lambda2 = ((a + d) - sqrt(pow(a, 2) - 2 * a * d + 4 * b * c + pow(d, 2))) / 2;
float lambda1Sytematics = ((aSystematics + dSystematics)
+ sqrt(pow(aSystematics, 2) - 2 * aSystematics * dSystematics
+ 4 * bSystematics * cSystematics + pow(dSystematics, 2)))
/ 2;
float lambda2Sytematics = ((aSystematics + dSystematics)
- sqrt(pow(aSystematics, 2) - 2 * aSystematics * dSystematics
+ 4 * bSystematics * cSystematics + pow(dSystematics, 2)))
/ 2;
// Eigenvector to calculate tilt
float vector1_1 = lambda1 - d;
float vector1_2 = c;
float normalizer = 1.0 / c;
vector1_1 *= normalizer;
vector1_2 *= normalizer;
float tiltTemp = atan(vector1_1) * 180.0 / pi;
tiltTemp += 90;
float vector1_1Systematics = lambda1Sytematics - dSystematics;
float vector1_2Systematics = cSystematics;
float normalizerSystematics = 1.0 / cSystematics;
vector1_1Systematics *= normalizerSystematics;
vector1_2Systematics *= normalizerSystematics;
float tiltSystematicsTemp = atan(vector1_1Systematics) * 180.0 / pi;
tiltSystematicsTemp += 90;
// Calculating final angle errors
float phiErrorTemp = sqrt(2.291 * lambda1) * 180.0 / pi;
float thetaErrorTemp = sqrt(2.291 * lambda2) * 180.0 / pi;
float phiErrorSystematicsTemp = sqrt(2.291 * lambda1Sytematics) * 180.0 / pi;
float thetaErrorSystematicsTemp = sqrt(2.291 * lambda2Sytematics) * 180.0 / pi;
// Filling array
phiEllipseError[dataset] = phiErrorTemp;
phiEllipseErrorSystematics[dataset] = phiErrorSystematicsTemp;
thetaEllipseError[dataset] = thetaErrorTemp;
thetaEllipseErrorSystematics[dataset] = thetaErrorSystematicsTemp;
tilt[dataset] = tiltTemp;
tiltSystematics[dataset] = tiltSystematicsTemp;
}
// Prints out the 1 sigma values if COVARIANCE_VERBOSITY is set to 1
// Change at top of file
if (COVARIANCE_VERBOSITY)
{
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
cout << "The 1 sigma ellipse for: " << boldOn << DatasetToString(dataset) << resetFormats << " with systematics.\n";
cout << greenOn;
cout << boldOn << underlineOn << "Phi:" << resetFormats << greenOn << " " << phi[dataset] << "\u00B0 ± "
<< phiEllipseErrorSystematics[dataset] << "\u00B0.\n";
cout << boldOn << underlineOn << "Theta:" << resetFormats << greenOn << " " << theta[dataset] << "\u00B0 ± "
<< thetaEllipseErrorSystematics[dataset] << "\u00B0.\n";
cout << boldOn << underlineOn << "Tilt:" << resetFormats << greenOn << " " << tiltSystematics[dataset] << "\u00B0.\n"
<< resetFormats;
cout << "--------------------------------------------\n";
cout << "The 1 sigma ellipse for: " << boldOn << DatasetToString(dataset) << resetFormats
<< " without systematics.\n";
cout << greenOn;
cout << boldOn << underlineOn << "Phi:" << resetFormats << greenOn << " " << phi[dataset] << "\u00B0 ± "
<< phiEllipseError[dataset] << "\u00B0.\n";
cout << boldOn << underlineOn << "Theta:" << resetFormats << greenOn << " " << theta[dataset] << "\u00B0 ± "
<< thetaEllipseError[dataset] << "\u00B0.\n";
cout << boldOn << underlineOn << "Tilt:" << resetFormats << greenOn << " " << tilt[dataset] << "\u00B0.\n"
<< resetFormats;
cout << "--------------------------------------------\n";
}
}
// Final cone of uncertainty
float a = phiEllipseError[DataUnbiased];
float b = thetaEllipseError[DataUnbiased];
thetaTemp = 90 - theta[DataUnbiased];
float solidAngle = pi * a * b * sin(thetaTemp * pi / 180.0);
float solidAngleRadians = solidAngle * pow((pi / 180.0), 2);
float coneAngle = acos(1 - (solidAngleRadians / (2 * pi))) * 180.0 / pi;
cout << boldOn << greenOn << underlineOn << "Cone of Uncertainty:" << resetFormats << greenOn << " " << coneAngle << "\u00B0"
<< '\n'
<< resetFormats;
cout << "--------------------------------------------\n";
}
void Directionality::OffsetTheta()
{
// We measure theta from the z-axis down to the neutrino vector
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
theta[dataset] = 90 - theta[dataset];
}
thetaTrue = 90 + thetaTrue;
}
void Directionality::PrintAngles()
{
cout << boldOn << cyanOn << "Final Angles!\n" << resetFormats;
cout << "--------------------------------------------\n";
for (int dataset = Data; dataset < DatasetSize; dataset++)
{
float phiErrorTemp, thetaErrorTemp;
if (dataset == Sim || dataset == SimUnbiased || dataset == PerfSim || dataset == PerfSimUnbiased || ANGLES_STATISTICS)
{
phiErrorTemp = phiError[dataset];
thetaErrorTemp = thetaError[dataset];
}
else
{
phiErrorTemp = phiErrorSystematics[dataset];