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mrpt-jk.cpp
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mrpt-jk.cpp
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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. See the enclosed file LICENSE for a copy or if
* that was not distributed with this file, You can obtain one at
* http://mozilla.org/MPL/2.0/.
*
* Copyright 2017 Max H. Gerlach
*
* */
/*
* multireweighthistosptjk.cpp
*
* Created on: Jul 25, 2011
* Author: gerlach
*/
// generalized for SDW DQMC (2015-02-06 - )
#include "mrpt-jk.h"
#include "tools.h"
#include "statistics.h"
#include "numerics.h"
using namespace std;
MultireweightHistosPTJK::MultireweightHistosPTJK(unsigned jkTotalBlocks, std::ostream& outStream)
: MultireweightHistosPT(outStream), blockCount(jkTotalBlocks) {
out << "Jackknifing: " << jkTotalBlocks << " blocks" << std::endl;
}
MultireweightHistosPTJK::~MultireweightHistosPTJK() {
}
void MultireweightHistosPTJK::setUpHistogramsHelperJK() {
lZ_bl.resize(boost::extents[blockCount][numReplicas]);
initArray(lZ_bl, LogVal(1.0));
H_bkm.resize(boost::extents[blockCount][numReplicas][binCount]);
initArray(H_bkm, 0);
g_bkm.resize(boost::extents[blockCount][numReplicas][binCount]);
initArray(g_bkm, 0);
H_blm.resize(boost::extents[blockCount][numReplicas][binCount]);
initArray(H_blm, 0);
N_bkl.resize(boost::extents[blockCount][numReplicas][numReplicas]);
initArray(N_bkl, 0);
H_bm.resize(boost::extents[blockCount][binCount]);
initArray(H_bm, 0);
lOmega_bm.resize(boost::extents[blockCount][binCount]);
initArray(lOmega_bm, LogVal(1.0));
}
void MultireweightHistosPTJK::setUpHistogramsJK(int binCount_) {
MultireweightHistosPT::setUpHistograms(binCount_); //whole data set
setUpHistogramsHelperJK();
}
void MultireweightHistosPTJK::setUpHistogramsIsingJK() {
MultireweightHistosPT::setUpHistogramsIsing(); //whole data set
setUpHistogramsHelperJK();
}
void MultireweightHistosPTJK::createHistogramsHelperJK() {
out << "Creating energy histograms etc., jackknife ready. minEnergyNormalized=" << minEnergyNormalized
<< " maxEnergyNormalized=" << maxEnergyNormalized
<< " binSize=" << binSize
<< " binCount=" << binCount << endl;
for (unsigned k = 0; k < numReplicas; ++k) {
unsigned N_k = (unsigned)energyTimeSeries[k]->size();
for (unsigned n = 0; n < N_k; ++n) {
//get bin number, correct due to rounding in cast:
int m = static_cast<int>(((*energyTimeSeries[k])[n] - minEnergyNormalized) / binSize);
//get cp index
int l = (*(cpiTimeSeries[k]))[n];
//update quantities over the whole data set:
(*m_kn[k])[n] = m;
N_kl[k][l] += 1;
++H_km[k][m];
++H_m[m]; //!!!
++H_lm[l][m]; //!!!
unsigned curBlock = (n * blockCount) / N_k; //integer division rounds down
for (signed b = 0; b < (signed)curBlock; ++b) {
N_bkl[b][k][l] += 1;
++H_bkm[b][k][m];
++H_bm[b][m]; //!!!
++H_blm[b][l][m]; //!!!
}
for (signed b = curBlock + 1; b < (signed)blockCount; ++b) {
N_bkl[b][k][l] += 1;
++H_bkm[b][k][m];
++H_bm[b][m]; //!!!
++H_blm[b][l][m]; //!!!
}
}
out << "." << flush;
}
//not needed any more
cpiTimeSeries.clear(); // destroyAll(cpiTimeSeries);
out << " done" << endl;
}
void MultireweightHistosPTJK::createHistogramsHelperDiscreteJK() {
out << "Creating energy histograms etc., jackknife ready. minEnergyNormalized=" << minEnergyNormalized
<< " maxEnergyNormalized=" << maxEnergyNormalized
<< " binSize=" << binSize
<< " binCount=" << binCount
<< " for originally discrete bins " << endl;
for (unsigned k = 0; k < numReplicas; ++k) {
unsigned N_k = (unsigned)energyTimeSeries[k]->size();
for (unsigned n = 0; n < N_k; ++n) {
//get bin number, correct due to rounding in cast:
// int m = static_cast<int>(((*energyTimeSeries[k])[n] - minEnergyNormalized) / binSize);
// int m = int(round(((*energyTimeSeries[k])[n] - minEnergyNormalized) / binSize));
int m = int(round(((*energyTimeSeries[k])[n] * systemSize - minEnergy) / deltaU));
//get cp index
int l = (*(cpiTimeSeries[k]))[n];
//update quantities over the whole data set:
(*m_kn[k])[n] = m;
N_kl[k][l] += 1;
++H_km[k][m];
++H_m[m]; //!!!
++H_lm[l][m]; //!!!
unsigned curBlock = (n * blockCount) / N_k; //integer division rounds down
for (signed b = 0; b < (signed)curBlock; ++b) {
N_bkl[b][k][l] += 1;
++H_bkm[b][k][m];
++H_bm[b][m]; //!!!
++H_blm[b][l][m]; //!!!
}
for (signed b = curBlock + 1; b < (signed)blockCount; ++b) {
N_bkl[b][k][l] += 1;
++H_bkm[b][k][m];
++H_bm[b][m]; //!!!
++H_blm[b][l][m]; //!!!
}
}
out << "." << flush;
}
//not needed any more
cpiTimeSeries.clear();
//destroyAll(cpiTimeSeries);
out << " done" << endl;
}
void MultireweightHistosPTJK::createHistograms(int binCount_) {
setUpHistogramsJK(binCount_);
createHistogramsHelperJK();
}
void MultireweightHistosPTJK::createHistogramsIsing() {
setUpHistogramsIsingJK();
createHistogramsHelperDiscreteJK();
}
MultireweightHistosPT::ResultsMap* MultireweightHistosPTJK::directNoReweighting() {
out << "Computing estimates from time series without any reweighting, jackknifed... "
<< flush;
ResultsMap* results = new ResultsMap;
//map (jk-block, cp-index) -> value
Double2Array meanEnergy_bl(boost::extents[blockCount][numReplicas]);
initArray(meanEnergy_bl, 0);
Double2Array meanEnergySquared_bl(boost::extents[blockCount][numReplicas]);
initArray(meanEnergySquared_bl, 0);
Double2Array meanObs_bl(boost::extents[blockCount][numReplicas]);
initArray(meanObs_bl, 0);
Double2Array meanObsSquared_bl(boost::extents[blockCount][numReplicas]);
initArray(meanObsSquared_bl, 0);
Double2Array meanObsToTheFourth_bl(boost::extents[blockCount][numReplicas]);
initArray(meanObsToTheFourth_bl, 0);
//calculate for each replica separately:
#pragma omp parallel for
for (signed k = 0; k < (signed)numReplicas; ++k) {
//arrays for this replica
Double2Array k_meanEnergy_bl(boost::extents[blockCount][numReplicas]);
initArray(k_meanEnergy_bl, 0);
Double2Array k_meanEnergySquared_bl(boost::extents[blockCount][numReplicas]);
initArray(k_meanEnergySquared_bl, 0);
Double2Array k_meanObs_bl(boost::extents[blockCount][numReplicas]);
initArray(k_meanObs_bl, 0);
Double2Array k_meanObsSquared_bl(boost::extents[blockCount][numReplicas]);
initArray(k_meanObsSquared_bl, 0);
Double2Array k_meanObsToTheFourth_bl(boost::extents[blockCount][numReplicas]);
initArray(k_meanObsToTheFourth_bl, 0);
unsigned N_k = (unsigned)energyTimeSeries[k]->size();
unsigned jkBlockSize = N_k / blockCount;
//sum up:
for (unsigned n = 0; n < N_k; ++n) {
int bi = (*cpiTimeSeries[k])[n];
double e = (*energyTimeSeries[k])[n];
double o = (*observableTimeSeries[k])[n];
const unsigned curBlock = n / jkBlockSize;
for (unsigned b = 0; b < blockCount; ++b) {
//TODO: optimize away this if: (two for loops -- should be
//done automatically anyway?)
if (b == curBlock) {
//leave out for this block
continue;
} else {
k_meanEnergy_bl[b][bi] += e;
k_meanEnergySquared_bl[b][bi] += e*e;
k_meanObs_bl[b][bi] += o;
k_meanObsSquared_bl[b][bi] += o*o;
k_meanObsToTheFourth_bl[b][bi] += o*o*o*o;
}
}
}
double samplesPerBlock = double(N_k - jkBlockSize)
/ double(numReplicas); //divisor: number of temperatures
//divide to form averages:
for (unsigned b = 0; b < blockCount; ++b) {
for (unsigned bi = 0; bi < numReplicas; ++bi) {
k_meanEnergy_bl[b][bi] /= samplesPerBlock;
k_meanEnergySquared_bl[b][bi] /= samplesPerBlock;
k_meanObs_bl[b][bi] /= samplesPerBlock;
k_meanObsSquared_bl[b][bi] /= samplesPerBlock;
k_meanObsToTheFourth_bl[b][bi] /= samplesPerBlock;
}
}
//average over replicas -- sum up everything from all replicas
#pragma omp critical
{
for (unsigned b = 0; b < blockCount; ++b) {
for (unsigned bi = 0; bi < numReplicas; ++bi) {
meanEnergy_bl[b][bi] += k_meanEnergy_bl[b][bi];
meanEnergySquared_bl[b][bi] += k_meanEnergySquared_bl[b][bi];
meanObs_bl[b][bi] += k_meanObs_bl[b][bi];
meanObsSquared_bl[b][bi] += k_meanObsSquared_bl[b][bi];
meanObsToTheFourth_bl[b][bi] +=
k_meanObsToTheFourth_bl[b][bi];
}
}
}
}
//average over replicas -- divide, compute quantities from higher moments
Double2Array heatCapacity_bl(boost::extents[blockCount][numReplicas]);
Double2Array suscObs_bl(boost::extents[blockCount][numReplicas]);
Double2Array suscPartObs_bl(boost::extents[blockCount][numReplicas]);
Double2Array binderObs_bl(boost::extents[blockCount][numReplicas]);
Double2Array binderRatioObs_bl(boost::extents[blockCount][numReplicas]);
for (unsigned b = 0; b < blockCount; ++b) {
for (unsigned bi = 0; bi < numReplicas; ++bi) {
double cp = controlParameterValues[bi];
meanEnergy_bl[b][bi] /= double(numReplicas);
meanEnergySquared_bl[b][bi] /= double(numReplicas);
meanObs_bl[b][bi] /= double(numReplicas);
meanObsSquared_bl[b][bi] /= double(numReplicas);
meanObsToTheFourth_bl[b][bi] /= double(numReplicas);
heatCapacity_bl[b][bi] = systemSize * cp*cp *
(meanEnergySquared_bl[b][bi] - pow(meanEnergy_bl[b][bi], 2));
suscPartObs_bl[b][bi] = systemSize * (meanObsSquared_bl[b][bi]);
suscObs_bl[b][bi] = systemSize *
(meanObsSquared_bl[b][bi] - pow(meanObs_bl[b][bi], 2));
binderObs_bl[b][bi] = 1.0 - (meanObsToTheFourth_bl[b][bi] /
(3 * pow(meanObsSquared_bl[b][bi], 2)));
binderRatioObs_bl[b][bi] = (meanObsToTheFourth_bl[b][bi] /
(pow(meanObsSquared_bl[b][bi], 2)));
}
}
//combine Jackknife blocks, for each cp...
for (unsigned bi = 0; bi < numReplicas; ++bi) {
double cp = controlParameterValues[bi];
//sum over jk blocks --> averages computed this way have reduced bias.
double jkSumEnergy = 0;
double jkSumHeatCapacity = 0;
double jkSumObs = 0;
double jkSumSuscPart = 0;
double jkSumSusc = 0;
double jkSumBinder = 0;
double jkSumBinderRatio = 0;
for (unsigned b = 0; b < blockCount; ++b) {
jkSumEnergy += meanEnergy_bl[b][bi];
jkSumHeatCapacity += heatCapacity_bl[b][bi];
jkSumObs += meanObs_bl[b][bi];
jkSumSuscPart += suscPartObs_bl[b][bi];
jkSumSusc += suscObs_bl[b][bi];
jkSumBinder += binderObs_bl[b][bi];
jkSumBinderRatio += binderRatioObs_bl[b][bi];
}
double resEnergy = jkSumEnergy / blockCount;
double resHeatCapacity = jkSumHeatCapacity / blockCount;
double resObs = jkSumObs / blockCount;
double resSuscPart = jkSumSuscPart / blockCount;
double resSusc = jkSumSusc / blockCount;
double resBinder = jkSumBinder / blockCount;
double resBinderRatio = jkSumBinderRatio / blockCount;
//error estimation
double sqDevEnergy = 0;
double sqDevHeatCapacity = 0;
double sqDevObs = 0;
double sqDevSuscPart = 0;
double sqDevSusc = 0;
double sqDevBinder = 0;
double sqDevBinderRatio = 0;
for (unsigned b = 0; b < blockCount; ++b) {
sqDevEnergy += pow(resEnergy - meanEnergy_bl[b][bi], 2);
sqDevHeatCapacity +=
pow(resHeatCapacity- heatCapacity_bl[b][bi], 2);
sqDevObs += pow(resObs - meanObs_bl[b][bi], 2);
sqDevSuscPart += pow(resSuscPart - suscPartObs_bl[b][bi], 2);
sqDevSusc += pow(resSusc - suscObs_bl[b][bi], 2);
sqDevBinder += pow(resBinder - binderObs_bl[b][bi], 2);
sqDevBinderRatio += pow(resBinderRatio - binderRatioObs_bl[b][bi], 2);
}
//set values and errors:
(*results)[cp] = ReweightingResult(resEnergy, sqrt(sqDevEnergy),
resHeatCapacity, sqrt(sqDevHeatCapacity),
resObs, sqrt(sqDevObs),
resSuscPart, sqrt(sqDevSuscPart),
resSusc, sqrt(sqDevSusc),
resBinder, sqrt(sqDevBinder),
resBinderRatio, sqrt(sqDevBinderRatio));
}
out << "done" << endl;
return results;
}
void MultireweightHistosPTJK::findDensityOfStatesNonIteratively() {
MultireweightHistosPT::findDensityOfStatesNonIteratively();
out << "Non-iterative estimate of the density of states, jackknife blocks... " << endl;
const double deltaU = binSize * systemSize;
for (int b = 0; b < (signed)blockCount; ++b) {
LogVal2Array x_lm(boost::extents[numReplicas][binCount - 1]); // <-> difference of microcanonical entropies at bins m, m+1
Double2Array w_lm(boost::extents[numReplicas][binCount - 1]); //weights at temperature l, energy bin m
vector<double> w_m(binCount - 1, 0); //sum_l { w_lm }
for (unsigned l = 0; l < numReplicas; ++l) {
double temperatureExponenet = +controlParameterValues[l] * deltaU;
for (unsigned m = 0; m < binCount - 1; ++m) {
double curHist = H_blm[b][l][m];
double nextHist = H_blm[b][l][m + 1];
if (curHist > 0 and nextHist > 0) {
x_lm[l][m] = (LogVal(nextHist * deltaU) / LogVal(curHist * deltaU)) * toLogValExp(temperatureExponenet);
w_lm[l][m] = curHist * nextHist / (curHist + nextHist);
w_m[m] += w_lm[l][m];
} else {
x_lm[l][m] = LogVal(); //very small
w_lm[l][m] = 0;
}
}
}
lOmega_bm[b][0] = LogVal(1.0);
for (unsigned m = 0; m < binCount - 1; ++m) {
double ln_x_m = 0;
for (unsigned l = 0; l < numReplicas; ++l) {
if (w_m[m] > 0) ln_x_m += (w_lm[l][m] / w_m[m]) * x_lm[l][m].lnx;
}
lOmega_bm[b][m + 1].lnx = lOmega_bm[b][m].lnx + ln_x_m;
}
out << "." << flush;
}
out << "Done" << endl;
}
void MultireweightHistosPTJK::updateEffectiveCountsJK() {
//jackknife-blocked:
Heff_bm.resize(boost::extents[blockCount][binCount]);
initArray(Heff_bm, 0);
Neff_blm.resize(boost::extents[blockCount][numReplicas][binCount]);
initArray(Neff_blm, 0);
lHeff_bm.resize(boost::extents[blockCount][binCount]);
lNeff_blm.resize(boost::extents[blockCount][numReplicas][binCount]);
lPrecalc_blm.resize(boost::extents[blockCount][numReplicas][binCount]);
#pragma omp parallel for
for (signed b = 0; b < (signed)blockCount; ++b) {
for (unsigned k = 0; k < numReplicas; ++k) {
for (unsigned m = 0; m < binCount; ++m) {
Heff_bm[b][m] += double(H_bkm[b][k][m]) / g_km[k][m];
for (unsigned l = 0; l < numReplicas; ++l) {
Neff_blm[b][l][m] += double(N_bkl[b][k][l]) / g_km[k][m];
}
}
}
for (unsigned m = 0; m < binCount; ++m) {
lHeff_bm[b][m] = (Heff_bm[b][m] != 0 ? LogVal(Heff_bm[b][m]) : LogVal(LogVal::LogZero));
for (unsigned l = 0; l < numReplicas; ++l) {
lNeff_blm[b][l][m] = (Neff_blm[b][l][m] != 0 ? LogVal(Neff_blm[b][l][m]) : LogVal(LogVal::LogZero));
lPrecalc_blm[b][l][m] = lNeff_blm[b][l][m] * lBinSize * toLogValExp(-controlParameterValues[l] * U_m[m]); //for updateDensityOfStates
}
}
}
}
inline void MultireweightHistosPTJK::updateDensityOfStatesJK(unsigned b) {
//precalculated the part that does not depend on the estimates of the partition functions
//lPrecalc_blm[b][l][m] = lNeff_blm[b][l][m] * lBinSize * toLogValExp(-controlParameterValues[l] * U_m[m]);
for (int m = 0; m < (signed)binCount; ++m) {
lOmega_bm[b][m] = lHeff_bm[b][m];
LogVal denominator = lPrecalc_blm[b][0][m] / lZ_bl[b][0];
for (unsigned l = 1; l < numReplicas; ++l) {
denominator += lPrecalc_blm[b][l][m] / lZ_bl[b][l];
}
lOmega_bm[b][m] /= denominator;
}
}
void MultireweightHistosPTJK::findPartitionFunctionsAndDensityOfStates(double tolerance, int maxIterations) {
//iteration for whole data set:
MultireweightHistosPT::findPartitionFunctionsAndDensityOfStates(tolerance, maxIterations);
//jackknife data sets:
out << "Updating effective counts (JK)... " << flush;
updateEffectiveCountsJK();
out << "Done." << endl;
out << "Starting iteration to estimate density of states (jackknife), tolerance=" << tolerance << " maxIterations=" << maxIterations << endl;
#pragma omp parallel for
for (signed b = 0; b < (signed)blockCount; ++b) {
//starting value: result for the whole data set
for (unsigned l = 0; l < numReplicas; ++l) {
lZ_bl[b][l] = lZ_l[l];
}
updateDensityOfStatesJK(b);
boost::multi_array<LogVal, 1> lZ_l_lastIteration = lZ_bl[b];
int iterations = 0;
double deltaSquared = 0; //this is sum_l { ((Z_l - Z_l_old) / (Z_l)) ** 2 }, stop iteration once deltaSquared < tolerance ** 2
do {
++iterations;
deltaSquared = 0;
//update estimates of partition functions
lZ_bl[b][0] = lOmega_bm[b][0] * lBinSize * toLogValExp(-controlParameterValues[0] * U_m[0]);
for (unsigned m = 1; m < binCount; ++m) {
lZ_bl[b][0] += lOmega_bm[b][m] * lBinSize * toLogValExp(-controlParameterValues[0] * U_m[m]);
}
for (int l = 1; l < (signed)numReplicas; ++l) {
lZ_l_lastIteration[l] = lZ_bl[b][l]; //store old value
lZ_bl[b][l] = lOmega_bm[b][0] * lBinSize * toLogValExp(-controlParameterValues[l] * U_m[0]);
for (unsigned m = 1; m < binCount; ++m) {
lZ_bl[b][l] += lOmega_bm[b][m] * lBinSize * toLogValExp(-controlParameterValues[l] * U_m[m]);
}
lZ_bl[b][l] /= lZ_bl[b][0]; //normalize
deltaSquared += pow(expm1(lZ_bl[b][l].lnx - lZ_l_lastIteration[l].lnx), 2); //gauge change from last iteration
}
lZ_bl[b][0].lnx = 0; //sets to 1 (normalize)
// if (iterations % 10 == 0) {
// out << "block " << b << ", Iteration " << iterations << ", deltaSquared=" << deltaSquared << endl;
// }
updateDensityOfStatesJK(b);
} while (iterations < maxIterations and deltaSquared >= tolerance * tolerance);
out << "block " << b << ": Iterations: " << iterations << " deltaSquared: " << deltaSquared << endl;
}
out << "Done." << endl;
}
void MultireweightHistosPTJK::saveLogDensityOfStates(const std::string& filename) {
//determine error
vector<double> omegaError_m(binCount);
for (unsigned m = 0; m < binCount; ++m) {
double avg_lOmega_bm_lnx = 0;
for (unsigned b = 0; b < blockCount; ++b) {
avg_lOmega_bm_lnx += lOmega_bm[b][m].lnx;
}
avg_lOmega_bm_lnx /= blockCount;
double sqDev = 0;
for (unsigned b = 0; b < blockCount; ++b) {
// sqDev += pow(lOmega_m[m].lnx - lOmega_bm[b][m].lnx, 2);
sqDev += pow(avg_lOmega_bm_lnx - lOmega_bm[b][m].lnx, 2);
}
omegaError_m[m] = sqrt((double(blockCount - 1) / blockCount) * sqDev);
}
ofstream output(filename.c_str());
output.precision(15);
output.setf(std::ios::scientific, std::ios::floatfield);
output << "## logarithm of density of states, mrpt estimation\n"
<< "## energy (normalized)\t ln(d.o.s.)\t error (jk)"
<< endl;
for (unsigned m = 0; m < binCount; ++m) {
output << U_m[m] / systemSize
<< "\t" << lOmega_m[m] / lOmega_m[binCount / 2]
<< "\t" << omegaError_m[m]
<< '\n';
}
}
void MultireweightHistosPTJK::saveLogDensityOfStatesIsing(const std::string& filename) {
//determine error
vector<double> omegaError_m(binCount);
for (unsigned m = 0; m < binCount; ++m) {
double avg_lOmega_bm_lnx = 0;
for (unsigned b = 0; b < blockCount; ++b) {
avg_lOmega_bm_lnx += lOmega_bm[b][m].lnx;
}
avg_lOmega_bm_lnx /= blockCount;
double sqDev = 0;
for (unsigned b = 0; b < blockCount; ++b) {
// sqDev += pow(lOmega_m[m].lnx - lOmega_bm[b][m].lnx, 2);
sqDev += pow(avg_lOmega_bm_lnx - lOmega_bm[b][m].lnx, 2);
}
omegaError_m[m] = sqrt((double(blockCount - 1) / blockCount) * sqDev);
}
ofstream output(filename.c_str());
output.precision(15);
output.setf(std::ios::scientific, std::ios::floatfield);
output << "## logarithm of density of states, mrpt estimation\n"
<< "## ln(d.o.s.) normalized to ln(2) for the lowest energy entry\n"
<< "## energy (normalized)\t ln(d.o.s.)\t error (jk)"
<< endl;
LogVal norm = lOmega_m[0] / LogVal(2);
//Normierung ist additiv im Logarithmus -- Fehler des
//logarithmierten Werts bleibt also gleich
//Normierung ist nur dann korrekt und stimmig mit Beale,
//wenn U[0] == -2 * systemSize
//d.h., wenn Grundzustand wirklich erreicht!
for (unsigned m = 0; m < binCount; ++m) {
output << U_m[m] / systemSize
<< "\t" << lOmega_m[m] / norm
<< "\t" << omegaError_m[m]
<< '\n';
}
}
ReweightingResult MultireweightHistosPTJK::reweightJackknifeInternal(
double targetControlParameter, unsigned jkBlock,
const DoubleSeriesCollection& w_kn) {
//everything normalized by system volume:
double meanEnergy = 0;
double meanEnergySquared = 0;
double meanObservable = 0;
double meanObservableSquared = 0;
double meanObservableToTheFourth = 0;
for (int k = 0; k < (signed)numReplicas; ++k) {
unsigned N_k = (unsigned)energyTimeSeries[k]->size();
unsigned jkBlockSize = N_k / blockCount;
for (unsigned n = 0; n < N_k; ++n) {
const unsigned curBlock = n / jkBlockSize;
if (curBlock == jkBlock) {
n += jkBlockSize;
continue;
} else {
double e = (*energyTimeSeries[k])[n];
double o = (*observableTimeSeries[k])[n];
meanEnergy += e * (*w_kn[k])[n];
meanEnergySquared += e*e * (*w_kn[k])[n];
meanObservable += o * (*w_kn[k])[n];
meanObservableSquared += o*o * (*w_kn[k])[n];
meanObservableToTheFourth += o*o*o*o * (*w_kn[k])[n];
}
}
}
double heatCapacity = systemSize * targetControlParameter * targetControlParameter
* (meanEnergySquared - pow(meanEnergy, 2));
double suscObservable = systemSize * (meanObservableSquared - pow(meanObservable, 2));
double binderObservable = 1.0 - (meanObservableToTheFourth / (3 * pow(meanObservableSquared, 2)));
double binderRatioObservable = meanObservableToTheFourth / pow(meanObservableSquared, 2);
double suscPartObservable = systemSize * meanObservableSquared;
return ReweightingResult(meanEnergy, heatCapacity, meanObservable,
suscPartObservable, suscObservable, binderObservable, binderRatioObservable);
}
void MultireweightHistosPTJK::reweight1stMomentInternalJK(const DoubleSeriesCollection& timeSeries, const DoubleSeriesCollection& w_kn, unsigned jkBlock, double& firstMoment) {
double first = 0;
for (int k = 0; k < (signed)numReplicas; ++k) {
unsigned N_k = (unsigned)timeSeries[k]->size();
unsigned jkBlockSize = N_k / blockCount;
for (unsigned n = 0; n < N_k; ++n) {
const unsigned curBlock = n / jkBlockSize;
if (curBlock == jkBlock) {
n += jkBlockSize;
continue;
} else {
double v = (*timeSeries[k])[n];
first += v * (*w_kn[k])[n];
}
}
}
firstMoment = first;
}
void MultireweightHistosPTJK::reweight2ndMomentInternalJK(const DoubleSeriesCollection& timeSeries, const DoubleSeriesCollection& w_kn, unsigned jkBlock, double& secondMoment) {
double second = 0;
for (int k = 0; k < (signed)numReplicas; ++k) {
unsigned N_k = (unsigned)timeSeries[k]->size();
unsigned jkBlockSize = N_k / blockCount;
for (unsigned n = 0; n < N_k; ++n) {
const unsigned curBlock = n / jkBlockSize;
if (curBlock == jkBlock) {
n += jkBlockSize;
continue;
} else {
double v = (*timeSeries[k])[n];
second += v*v * (*w_kn[k])[n];
}
}
}
secondMoment = second;
}
void MultireweightHistosPTJK::reweight1stMoment2ndMomentInternalJK(
const DoubleSeriesCollection& timeSeries,
const DoubleSeriesCollection& w_kn, unsigned jkBlock,
double& firstMoment, double& secondMoment) {
double first = 0;
double second = 0;
for (int k = 0; k < (signed)numReplicas; ++k) {
unsigned N_k = (unsigned)timeSeries[k]->size();
unsigned jkBlockSize = N_k / blockCount;
for (unsigned n = 0; n < N_k; ++n) {
const unsigned curBlock = n / jkBlockSize;
if (curBlock == jkBlock) {
n += jkBlockSize;
continue;
} else {
double v = (*timeSeries[k])[n];
first += v * (*w_kn[k])[n];
second += v*v * (*w_kn[k])[n];
}
}
}
firstMoment = first;
secondMoment = second;
}
void MultireweightHistosPTJK::reweight2ndMoment4thMomentInternalJK(
const DoubleSeriesCollection& timeSeries,
const DoubleSeriesCollection& w_kn, unsigned jkBlock,
double& secondMoment, double& fourthMoment) {
double second = 0;
double fourth = 0;
for (int k = 0; k < (signed)numReplicas; ++k) {
unsigned N_k = (unsigned)timeSeries[k]->size();
unsigned jkBlockSize = N_k / blockCount;
for (unsigned n = 0; n < N_k; ++n) {
const unsigned curBlock = n / jkBlockSize;
if (curBlock == jkBlock) {
n += jkBlockSize;
continue;
} else {
double v = (*timeSeries[k])[n];
second += v*v * (*w_kn[k])[n];
fourth += v*v*v*v * (*w_kn[k])[n];
}
}
}
fourthMoment = fourth;
secondMoment = second;
}
double MultireweightHistosPTJK::reweightEnergyJK(double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double result = 0;
reweight1stMomentInternalJK(energyTimeSeries, w_kn, jkBlock, result);
//destroyAll(w_kn);
return result;
}
double MultireweightHistosPTJK::reweightSpecificHeatJK(double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double firstMoment = 0;
double secondMoment = 0;
reweight1stMoment2ndMomentInternalJK(energyTimeSeries, w_kn, jkBlock, firstMoment, secondMoment);
double result = systemSize * pow(targetControlParameter, 2) *
(secondMoment - pow(firstMoment, 2));;
//destroyAll(w_kn);
return result;
}
double MultireweightHistosPTJK::reweightObservableJK(double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double result = 0;
reweight1stMomentInternalJK(observableTimeSeries, w_kn, jkBlock, result);
//destroyAll(w_kn);
return result;
}
double MultireweightHistosPTJK::reweightObservableSusceptibilityPartJK(double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double secondMoment = 0;
reweight2ndMomentInternalJK(observableTimeSeries, w_kn, jkBlock, secondMoment);
double result = systemSize * secondMoment;
//destroyAll(w_kn);
return result;
}
double MultireweightHistosPTJK::reweightObservableSusceptibilityJK(
double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double firstMoment = 0;
double secondMoment = 0;
reweight1stMoment2ndMomentInternalJK(observableTimeSeries, w_kn, jkBlock, firstMoment, secondMoment);
double result = systemSize * (secondMoment - pow(firstMoment, 2));;
// destroyAll(w_kn);
return result;
}
double MultireweightHistosPTJK::reweightObservableBinderJK(double targetControlParameter,
unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double secondMoment = 0;
double fourthMoment = 0;
reweight2ndMoment4thMomentInternalJK(observableTimeSeries, w_kn, jkBlock,
secondMoment, fourthMoment);
double result = 1.0 - (fourthMoment / (3 * pow(secondMoment, 2)));
// destroyAll(w_kn);
return result;
}
void MultireweightHistosPTJK::reweightObservableSecondFourthMomentJK(
double& outSecondMoment, double& outFourthMoment,
double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
reweight2ndMoment4thMomentInternalJK(observableTimeSeries, w_kn, jkBlock,
outSecondMoment, outFourthMoment);
}
double MultireweightHistosPTJK::reweightObservableBinderRatioJK(
double targetControlParameter, unsigned jkBlock) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, jkBlock);
double secondMoment = 0;
double fourthMoment = 0;
reweight2ndMoment4thMomentInternalJK(observableTimeSeries, w_kn, jkBlock,
secondMoment, fourthMoment);
double result = (fourthMoment / (pow(secondMoment, 2)));
// destroyAll(w_kn);
return result;
}
MultireweightHistosPTJK::DoubleSeriesCollection MultireweightHistosPTJK::computeWeightsJK(double targetControlParameter, unsigned jkBlock) {
// out << "Computing weights w_kn at cp=" << targetControlParameter << ", jackknife block:" << jkBlock << endl;
vector<LogVal> arguments(binCount);
arguments[0] = lOmega_bm[jkBlock][0] * toLogValExp(-targetControlParameter * U_m[0]);
LogVal normalization = arguments[0];
for (unsigned m = 1; m < binCount; ++m) {
arguments[m] = lOmega_bm[jkBlock][m] * toLogValExp(-targetControlParameter * U_m[m]);
normalization += arguments[m];
}
//normalize arguments, calculate weight corresponding to bin
vector<double> weightFromBin(binCount);
for (unsigned m = 0; m < binCount; ++m) {
if (H_bm[jkBlock][m] == 0) {
weightFromBin[m] = 0;
} else {
arguments[m] /= normalization;
weightFromBin[m] = toDouble(arguments[m]) / double(H_bm[jkBlock][m]);
}
}
DoubleSeriesCollection w_kn(numReplicas);
//calculate weight for each sample
for (int k = 0; k < (signed)numReplicas; ++k) {
unsigned N_k = (unsigned)m_kn[k]->size();
w_kn[k].reset(new vector<double>(N_k));
unsigned jkBlockSize = N_k / blockCount;
for (unsigned n = 0; n < N_k; ++n) {
unsigned curBlock = (n * blockCount) / N_k;
if (curBlock == jkBlock) {
n += jkBlockSize;
continue;
} else {
unsigned m = (*m_kn[k])[n];
(*w_kn[k])[n] = weightFromBin[m];
}
}
}
return w_kn;
}
ReweightingResult MultireweightHistosPTJK::reweight(double targetControlParameter) {
out << "Jackknife estimation of energy and " << observable << " moments at cp=" << targetControlParameter << endl;
//jackknifed dataset:
vector<double> jkEnergy_b(blockCount);
vector<double> jkHeatCapacity_b(blockCount);
vector<double> jkObs_b(blockCount);
vector<double> jkSuscPart_b(blockCount);
vector<double> jkSusc_b(blockCount);
vector<double> jkBinder_b(blockCount);
vector<double> jkBinderRatio_b(blockCount);
#pragma omp parallel for
for (signed b = 0; b < (signed)blockCount; ++b) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, b);
ReweightingResult results =
reweightJackknifeInternal(targetControlParameter, b, w_kn);
jkEnergy_b[b] = results.energyAvg;
jkHeatCapacity_b[b] = results.heatCapacity;
jkObs_b[b] = results.obsAvg;
jkSuscPart_b[b] = results.obsSuscPart;
jkSusc_b[b] = results.obsSusc;
jkBinder_b[b] = results.obsBinder;
jkBinderRatio_b[b] = results.obsBinderRatio;
// destroyAll(w_kn);
out << '#' << flush;
}
//Jackknife for error and average (--> bias correction)
ReweightingResult totalResult;
jackknife(totalResult.energyAvg, totalResult.energyError, jkEnergy_b);
jackknife(totalResult.heatCapacity, totalResult.heatCapacityError,
jkHeatCapacity_b);
jackknife(totalResult.obsAvg, totalResult.obsError, jkObs_b);
jackknife(totalResult.obsSuscPart, totalResult.obsSuscPartError, jkSuscPart_b);
jackknife(totalResult.obsSusc, totalResult.obsSuscError, jkSusc_b);
jackknife(totalResult.obsBinder, totalResult.obsBinderError, jkBinder_b);
jackknife(totalResult.obsBinderRatio, totalResult.obsBinderRatioError, jkBinderRatio_b);
out << " Done." << endl;
return totalResult;
}
ReweightedMomentsJK MultireweightHistosPTJK::reweightObservableMoments(
double targetControlParameter) {
out << "Jackknife estimation of " << observable << " moments at cp=" << targetControlParameter << endl;
std::vector<double> jkBlocks_o(blockCount, 0);
std::vector<double> jkBlocks_o2(blockCount, 0);
std::vector<double> jkBlocks_o4(blockCount, 0);
#pragma omp parallel for
for (signed b = 0; b < (signed)blockCount; ++b) {
DoubleSeriesCollection w_kn = computeWeightsJK(targetControlParameter, b);
double firstMoment = 0;
double secondMoment = 0;
double fourthMoment = 0;
reweight1stMomentInternalJK(observableTimeSeries, w_kn, b, firstMoment);
reweight2ndMoment4thMomentInternalJK(observableTimeSeries, w_kn, b, secondMoment, fourthMoment);
jkBlocks_o[b] = firstMoment;
jkBlocks_o2[b] = secondMoment;
jkBlocks_o4[b] = fourthMoment;
out << '#' << flush;
}
double mean_o = 0;
double mean_o2 = 0;
double mean_o4 = 0;
double err_o = 0; // errors: currently not passed out of this function
double err_o2 = 0;
double err_o4 = 0;
jackknife(mean_o, err_o, jkBlocks_o);
jackknife(mean_o2, err_o2, jkBlocks_o2);
jackknife(mean_o4, err_o4, jkBlocks_o4);
out << " Done." << endl;
return ReweightedMomentsJK(mean_o, mean_o2, mean_o4,
jkBlocks_o, jkBlocks_o2, jkBlocks_o4);
}
HistogramDouble* MultireweightHistosPTJK::reweightEnergyHistogram(double targetControlParameter) {
out << "Jackknife estimation of energy histogram at cp=" << targetControlParameter << ", " << binCount << " bins... " << endl;
//helper array:
vector<LogVal> arguments(binCount);
//histogram from whole data set
vector<double> histo_m(binCount);
arguments[0] = lOmega_m[0] * toLogValExp(-targetControlParameter * U_m[0]);
LogVal normalization = arguments[0];
for (unsigned m = 1; m < binCount; ++m) {
arguments[m] = lOmega_m[m] * toLogValExp(-targetControlParameter * U_m[m]);
normalization += arguments[m];
}
for (unsigned m = 0; m < binCount; ++m) {
arguments[m] /= normalization;
histo_m[m] = toDouble(arguments[m]);
}
//histograms created from jacknifed sub-sets
Double2Array histo_bm(boost::extents[blockCount][binCount]);
initArray(histo_bm, 0);
#pragma omp parallel for
for (signed b = 0; b < (signed)blockCount; ++ b) {
vector<LogVal> args(binCount);
args[0] = lOmega_bm[b][0] * toLogValExp(-targetControlParameter * U_m[0]);
LogVal normalization = args[0];
for (unsigned m = 1; m < binCount; ++m) {
args[m] = lOmega_bm[b][m] * toLogValExp(-targetControlParameter * U_m[m]);
normalization += args[m];
}
for (unsigned m = 0; m < binCount; ++m) {
args[m] /= normalization;
histo_bm[b][m] = toDouble(args[m]);
}
}
//error estimation
vector<double> sqDev(binCount, 0);
for (unsigned b = 0; b < blockCount; ++b) {
for (unsigned m = 0; m < binCount; ++m) {
sqDev[m] += pow(histo_bm[b][m] - histo_m[m], 2);
}
}
vector<double> errors(binCount);
double factor = double(blockCount - 1) / double(blockCount);
for (unsigned m = 0; m < binCount; ++m) {
errors[m] = sqrt(factor * sqDev[m]);
}
//prepare instance of nice histogram class to return
HistogramDouble* result = new HistogramDouble;
result->assignVector(histo_m,
minEnergyNormalized, maxEnergyNormalized, targetControlParameter, systemN);
result->assignErrorBarVector(errors);
result->headerLines +=
"## MRPT reweighted histogram of normalized energy\n";
result->updateMeta();
return result;
}
HistogramDouble* MultireweightHistosPTJK::reweightObservableHistogram(double targetControlParameter, unsigned obsBinCount) {
out << "Jackknife estimation of " << observable << " histogram at cp=" << targetControlParameter << ", " << obsBinCount << " bins... " << endl;
//histogram created from the whole data-set
vector<double> obsHisto(obsBinCount, 0.0);
DoubleSeriesCollection total_w_kn = computeWeights(targetControlParameter);
MultireweightHistosPT::reweightObservableHistogramInternal(targetControlParameter, obsBinCount, total_w_kn, obsHisto);
// destroyAll(total_w_kn);
HistogramDouble* result = new HistogramDouble;
result->assignVector(obsHisto, minObservableNormalized, maxObservableNormalized, targetControlParameter, systemN);
result->headerLines += "## MRPT reweighted histogram of normalized " + observable + "\n";
result->updateMeta();
const double SMALL = 1e-10; //to fit maxObservableNormalized into the highest bin
double obsBinSize = (maxObservableNormalized - minObservableNormalized + SMALL) / obsBinCount;
Double2Array obsHisto_bm(boost::extents[blockCount][obsBinCount]);
initArray(obsHisto_bm, 0);
#pragma omp parallel for
for (signed b = 0; b < (signed)blockCount; ++ b) {