bool ExponentialMedium::sampleDistance(PathSampleGenerator &sampler, const Ray &ray,
MediumState &state, MediumSample &sample) const
{
if (state.bounce > _maxBounce)
return false;
float x = _falloffScale*(ray.pos() - _unitPoint).dot(_unitFalloffDirection);
float dx = _falloffScale*ray.dir().dot(_unitFalloffDirection);
float maxT = ray.farT();
if (_absorptionOnly) {
if (maxT == Ray::infinity() && dx <= 0.0f)
return false;
sample.t = maxT;
sample.weight = std::exp(-_sigmaT*densityIntegral(x, dx, ray.farT()));
sample.pdf = 1.0f;
sample.exited = true;
} else {
int component = sampler.nextDiscrete(3);
float sigmaTc = _sigmaT[component];
float xi = 1.0f - sampler.next1D();
float logXi = std::log(xi);
float t = inverseOpticalDepth(x, dx, sigmaTc, logXi);
sample.t = min(t, maxT);
sample.weight = std::exp(-_sigmaT*densityIntegral(x, dx, sample.t));
sample.exited = (t >= maxT);
if (sample.exited) {
sample.pdf = sample.weight.avg();
} else {
float rho = density(x, dx, sample.t);
sample.pdf = (rho*_sigmaT*sample.weight).avg();
sample.weight *= rho*_sigmaS;
}
sample.weight /= sample.pdf;
state.advance();
}
sample.p = ray.pos() + sample.t*ray.dir();
sample.phase = _phaseFunction.get();
return true;
}
int main()
{
FILE *planets,*results;
int i;
struct planet ss[9];
if((planets=fopen("planets.txt","r"))==NULL)
{
printf("Error loading planets.txt\n");
printf("Please press enter to continue");
getchar();
return(0);
}
if((results=fopen("results.txt","w"))==NULL)
{
printf("Error loading results.txt\n");
printf("Please press enter to continue");
getchar();
return(0);
}
for(i=0;i<9;i++)
{
fscanf(planets,"%s %lf %lf %lf",&ss[i].name,&ss[i].distance,&ss[i].mass,&ss[i].radius);
}
printf("Name Distance Mass Radius\n");
for(i=0;i<9;i++)
{
printf("%10s %g %g %g\n",ss[i].name,ss[i].distance,ss[i].mass,ss[i].radius);
}
for(i=0;i<9;i++)
{
fprintf(results,"%s %g %g\n",ss[i].name,ylength(&ss[i]),density(&ss[i]));
}
printf("Please press enter to continue");
getchar();
return(0);
}
doublereal WaterPropsIAPWS::psat(doublereal temperature, int waterState) {
doublereal densLiq = -1.0, densGas = -1.0, delGRT = 0.0;
doublereal dp, pcorr;
if (temperature >= T_c) {
densGas = density(temperature, P_c, WATER_SUPERCRIT);
setState_TR(temperature, densGas);
return P_c;
}
doublereal p = psat_est(temperature);
bool conv = false;
for (int i = 0; i < 30; i++) {
if (method == 1) {
corr(temperature, p, densLiq, densGas, delGRT);
doublereal delV = M_water * (1.0/densLiq - 1.0/densGas);
dp = - delGRT * Rgas * temperature / delV;
} else {
corr1(temperature, p, densLiq, densGas, pcorr);
dp = pcorr - p;
}
p += dp;
if ((method == 1) && delGRT < 1.0E-8) {
conv = true;
break;
} else {
if (fabs(dp/p) < 1.0E-9) {
conv = true;
break;
}
}
}
// Put the fluid in the desired end condition
if (waterState == WATER_LIQUID) {
setState_TR(temperature, densLiq);
} else if (waterState == WATER_GAS) {
setState_TR(temperature, densGas);
} else {
throw Cantera::CanteraError("WaterPropsIAPWS::psat",
"unknown water state input: " + Cantera::int2str(waterState));
}
return p;
}
bool AtmosphericMedium::sampleDistance(PathSampleGenerator &sampler, const Ray &ray,
MediumState &state, MediumSample &sample) const
{
if (state.bounce > _maxBounce)
return false;
Vec3f p = (ray.pos() - _center);
float t0 = p.dot(ray.dir());
float h = (p - t0*ray.dir()).length();
float maxT = ray.farT() + t0;
if (_absorptionOnly) {
sample.t = ray.farT();
sample.weight = std::exp(-_sigmaT*densityIntegral(h, t0, maxT));
sample.pdf = 1.0f;
sample.exited = true;
} else {
int component = sampler.nextDiscrete(3);
float sigmaTc = _sigmaT[component];
float xi = 1.0f - sampler.next1D();
float t = inverseOpticalDepth(h, t0, sigmaTc, xi);
sample.t = min(t, maxT);
sample.weight = std::exp(-_sigmaT*densityIntegral(h, t0, sample.t));
sample.exited = (t >= maxT);
if (sample.exited) {
sample.pdf = sample.weight.avg();
} else {
float rho = density(h, sample.t);
sample.pdf = (rho*_sigmaT*sample.weight).avg();
sample.weight *= rho*_sigmaS;
}
sample.weight /= sample.pdf;
sample.t -= t0;
state.advance();
}
sample.p = ray.pos() + sample.t*ray.dir();
sample.phase = _phaseFunction.get();
return true;
}
double l1Distance(const Kernel &rhs, long nr = 1000)
{
double a,b,x;
a = min_ - 4.0*width_;
b = rhs.min_ - 4.0*rhs.width_;
double dm = (a < b ? a : b);
a = max_ + 4.0*width_;
b = rhs.max_ + 4.0*rhs.width_;
double dM = (a > b ? a : b);
double dD=(dM-dm)/(nr-1);
const function::Linear<double> lt(0, dm, nr-1, dM);
dM = 0.0;
for (long i=0; i<nr; ++i)
{
x = lt(i);
dM += fabs(density(x)-rhs.density(x))*dD;
}
return dM;
}
int MixtureFugacityTP::phaseState(bool checkState) const
{
int state = iState_;
if (checkState) {
double t = temperature();
double tcrit = critTemperature();
double rhocrit = critDensity();
if (t >= tcrit) {
return FLUID_SUPERCRIT;
}
double tmid = tcrit - 100.;
if (tmid < 0.0) {
tmid = tcrit / 2.0;
}
double pp = psatEst(tmid);
double mmw = meanMolecularWeight();
double molVolLiqTmid = liquidVolEst(tmid, pp);
double molVolGasTmid = GasConstant * tmid / (pp);
double densLiqTmid = mmw / molVolLiqTmid;
double densGasTmid = mmw / molVolGasTmid;
double densMidTmid = 0.5 * (densLiqTmid + densGasTmid);
doublereal rhoMid = rhocrit + (t - tcrit) * (rhocrit - densMidTmid) / (tcrit - tmid);
double rho = density();
int iStateGuess = FLUID_LIQUID_0;
if (rho < rhoMid) {
iStateGuess = FLUID_GAS;
}
double molarVol = mmw / rho;
double presCalc;
double dpdv = dpdVCalc(t, molarVol, presCalc);
if (dpdv < 0.0) {
state = iStateGuess;
} else {
state = FLUID_UNSTABLE;
}
}
return state;
}
void XZHydrostatic_Omega<EvalT, Traits>::
evaluateFields(typename Traits::EvalData workset)
{
#ifndef ALBANY_KOKKOS_UNDER_DEVELOPMENT
for (int cell=0; cell < workset.numCells; ++cell) {
for (int qp=0; qp < numQPs; ++qp) {
for (int level=0; level < numLevels; ++level) {
ScalarT sum = -0.5*divpivelx(cell,qp,level) * E.delta(level);
for (int j=0; j<level; ++j) sum -= divpivelx(cell,qp,j) * E.delta(j);
for (int dim=0; dim < numDims; ++dim) sum += Velocity(cell,qp,level,dim)*gradp(cell,qp,level,dim);
omega(cell,qp,level) = sum/(Cpstar(cell,qp,level)*density(cell,qp,level));
}
}
}
#else
Kokkos::parallel_for(XZHydrostatic_Omega_Policy(0,workset.numCells),*this);
cudaCheckError();
#endif
}
result_type result(Args const &args) const
{
if (this->is_dirty)
{
this->is_dirty = false;
std::size_t cnt = count(args);
range_type histogram = density(args);
typename range_type::iterator it = histogram.begin();
while (this->sum < 0.5 * cnt)
{
this->sum += it->second * cnt;
++it;
}
--it;
float_type over = numeric::average(this->sum - 0.5 * cnt, it->second * cnt);
this->median = it->first * over + (it + 1)->first * (1. - over);
}
return this->median;
}
double N_from_mu(Minimizer *min, Grid *potential, const Grid &constraint, double mu) {
Functional f = constrain(constraint, OfEffectivePotential(HS + IdealGas()
+ ChemicalPotential(mu)));
double Nnow = 0;
min->minimize(f, potential->description());
for (int i=0;i<numiters && min->improve_energy(false);i++) {
Grid density(potential->description(), EffectivePotentialToDensity()(1, potential->description(), *potential));
Nnow = density.sum()*potential->description().dvolume;
printf("Nnow is %g vs %g\n", Nnow, N);
fflush(stdout);
density.epsNativeSlice("papers/contact/figs/box.eps",
Cartesian(0,ymax+2,0), Cartesian(0,0,zmax+2),
Cartesian(0,-ymax/2-1,-zmax/2-1));
density.epsNativeSlice("papers/contact/figs/box-diagonal.eps",
Cartesian(xmax+2,0,zmax+2), Cartesian(0,ymax+2,0),
Cartesian(-xmax/2-1,-ymax/2-1,-zmax/2-1));
//sleep(3);
}
return Nnow;
}
doublereal SingleSpeciesTP::cv_mole() const
{
/*
* For single species, we go directory to the general Cp - Cv relation
*
* Cp = Cv + alpha**2 * V * T / beta
*
* where
* alpha = volume thermal expansion coefficient
* beta = isothermal compressibility
*/
doublereal cvbar = cp_mole();
doublereal alpha = thermalExpansionCoeff();
doublereal beta = isothermalCompressibility();
doublereal V = molecularWeight(0)/density();
doublereal T = temperature();
if (beta != 0.0) {
cvbar -= alpha * alpha * V * T / beta;
}
return cvbar;
}
void WaterSSTP::getEntropy_R_ref(doublereal* sr) const
{
doublereal p = pressure();
double T = temperature();
double dens = density();
int waterState = WATER_GAS;
double rc = m_sub.Rhocrit();
if (dens > rc) {
waterState = WATER_LIQUID;
}
doublereal dd = m_sub.density(T, OneAtm, waterState, dens);
if (dd <= 0.0) {
throw CanteraError("setPressure", "error");
}
m_sub.setState_TR(T, dd);
doublereal s = m_sub.entropy();
*sr = (s + SW_Offset)/ GasConstant;
dd = m_sub.density(T, p, waterState, dens);
}
void IonFlow::electricFieldMethod(const double* x, size_t j0, size_t j1)
{
for (size_t j = j0; j < j1; j++) {
double wtm = m_wtm[j];
double rho = density(j);
double dz = z(j+1) - z(j);
// mixture-average diffusion
double sum = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
m_flux(k,j) = m_wt[k]*(rho*m_diff[k+m_nsp*j]/wtm);
m_flux(k,j) *= (X(x,k,j) - X(x,k,j+1))/dz;
sum -= m_flux(k,j);
}
// ambipolar diffusion
double E_ambi = E(x,j);
for (size_t k : m_kCharge) {
double Yav = 0.5 * (Y(x,k,j) + Y(x,k,j+1));
double drift = rho * Yav * E_ambi
* m_speciesCharge[k] * m_mobility[k+m_nsp*j];
m_flux(k,j) += drift;
}
// correction flux
double sum_flux = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
sum_flux -= m_flux(k,j); // total net flux
}
double sum_ion = 0.0;
for (size_t k : m_kCharge) {
sum_ion += Y(x,k,j);
}
// The portion of correction for ions is taken off
for (size_t k : m_kNeutral) {
m_flux(k,j) += Y(x,k,j) / (1-sum_ion) * sum_flux;
}
}
}
// Calculate the modes of the density for the distribution
// and their associated errors
double
vpScale::MeanShift(vpColVector &error)
{
int n = error.getRows()/dimension;
vpColVector density(n);
vpColVector density_gradient(n);
vpColVector mean_shift(n);
int increment=1;
// choose smallest error as start point
int i=0;
while(error[i]<0 && error[i]<error[i+1])
i++;
// Do mean shift until no shift
while(increment >= 1 && i<n)
{
increment=0;
density[i] = KernelDensity(error, i);
density_gradient[i] = KernelDensityGradient(error, i);
mean_shift[i]=vpMath::sqr(bandwidth)*density_gradient[i]/((dimension+2)*density[i]);
double tmp_shift = mean_shift[i];
// Do mean shift
while(tmp_shift>0 && tmp_shift>error[i]-error[i+1])
{
i++;
increment++;
tmp_shift-=(error[i]-error[i-1]);
}
}
return error[i];
}
ShardDefinition::ShardDefinition(std::istream& input)
{
CsvTsv::InputColumn<size_t>
minPostings("MinPostings",
"Minimum number of postings for any document in shard.");
CsvTsv::InputColumn<double>
density("Density",
"Target density for RowTables in the shard.");
CsvTsv::CsvTableParser parser(input);
CsvTsv::TableReader reader(parser);
reader.DefineColumn(minPostings);
reader.DefineColumn(density);
reader.ReadPrologue();
while (!reader.AtEOF())
{
reader.ReadDataRow();
AddShard(minPostings, density);
}
reader.ReadEpilogue();
}
Real SodProblem::valueExact(Real t, const Point& p, int eq)
{
switch (eq) {
case 0:
return density(t, p);
break;
case 1:
return momentumX(t, p);
break;
case 2:
return momentumY(t, p);
break;
case 3:
return momentumZ(t, p);
case 4:
return energyTotal(t, p);
break;
default:
return 0.0;
mooseError("不可用的分量" << eq);
break;
}
}
void XZHydrostatic_GeoPotential<EvalT, Traits>::
evaluateFields(typename Traits::EvalData workset)
{
const Eta<EvalT> &E = Eta<EvalT>::self();
ScalarT sum;
for (int cell=0; cell < workset.numCells; ++cell) {
for (int node=0; node < numNodes; ++node) {
for (int level=0; level < numLevels; ++level) {
sum =
PhiSurf(cell,node) +
0.5 * Pi(cell,node,level) * E.delta(level) / density(cell,node,level);
for (int j=level+1; j < numLevels; ++j) sum += Pi(cell,node,j) * E.delta(j) / density(cell,node,j);
Phi(cell,node,level) = sum;
//std::cout <<"Inside GeoP, cell, node, PhiSurf(cell,node)="<<cell<<
//", "<<node<<", "<<PhiSurf(cell,node) <<std::endl;
}
}
}
}
void ShardDefinition::Write(std::ostream& output) const
{
CsvTsv::OutputColumn<size_t>
minPostings("MinPostings",
"Minimum number of postings for any document in shard.");
CsvTsv::OutputColumn<double>
density("Density",
"Target density for RowTables in the shard.");
CsvTsv::CsvTableFormatter formatter(output);
CsvTsv::TableWriter writer(formatter);
writer.DefineColumn(minPostings);
writer.DefineColumn(density);
writer.WritePrologue();
for (unsigned i = 0; i < m_shards.size(); ++i)
{
minPostings = m_shards[i].first;
density = m_shards[i].second;
writer.WriteDataRow();
}
writer.WriteEpilogue();
}
Real
RichardsDensityConstBulk::d2density(Real p) const
{
return density(p)/_bulk/_bulk;
}
/*
* Format a summary of the mixture state for output.
*/
void MolalityVPSSTP::reportCSV(std::ofstream& csvFile) const
{
csvFile.precision(3);
int tabS = 15;
int tabM = 30;
int tabL = 40;
try {
if (name() != "") {
csvFile << "\n"+name()+"\n\n";
}
csvFile << setw(tabL) << "temperature (K) =" << setw(tabS) << temperature() << endl;
csvFile << setw(tabL) << "pressure (Pa) =" << setw(tabS) << pressure() << endl;
csvFile << setw(tabL) << "density (kg/m^3) =" << setw(tabS) << density() << endl;
csvFile << setw(tabL) << "mean mol. weight (amu) =" << setw(tabS) << meanMolecularWeight() << endl;
csvFile << setw(tabL) << "potential (V) =" << setw(tabS) << electricPotential() << endl;
csvFile << endl;
csvFile << setw(tabL) << "enthalpy (J/kg) = " << setw(tabS) << enthalpy_mass() << setw(tabL) << "enthalpy (J/kmol) = " << setw(tabS) << enthalpy_mole() << endl;
csvFile << setw(tabL) << "internal E (J/kg) = " << setw(tabS) << intEnergy_mass() << setw(tabL) << "internal E (J/kmol) = " << setw(tabS) << intEnergy_mole() << endl;
csvFile << setw(tabL) << "entropy (J/kg) = " << setw(tabS) << entropy_mass() << setw(tabL) << "entropy (J/kmol) = " << setw(tabS) << entropy_mole() << endl;
csvFile << setw(tabL) << "Gibbs (J/kg) = " << setw(tabS) << gibbs_mass() << setw(tabL) << "Gibbs (J/kmol) = " << setw(tabS) << gibbs_mole() << endl;
csvFile << setw(tabL) << "heat capacity c_p (J/K/kg) = " << setw(tabS) << cp_mass() << setw(tabL) << "heat capacity c_p (J/K/kmol) = " << setw(tabS) << cp_mole() << endl;
csvFile << setw(tabL) << "heat capacity c_v (J/K/kg) = " << setw(tabS) << cv_mass() << setw(tabL) << "heat capacity c_v (J/K/kmol) = " << setw(tabS) << cv_mole() << endl;
csvFile.precision(8);
vector<std::string> pNames;
vector<vector_fp> data;
vector_fp temp(nSpecies());
getMoleFractions(&temp[0]);
pNames.push_back("X");
data.push_back(temp);
try {
getMolalities(&temp[0]);
pNames.push_back("Molal");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getChemPotentials(&temp[0]);
pNames.push_back("Chem. Pot. (J/kmol)");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getStandardChemPotentials(&temp[0]);
pNames.push_back("Chem. Pot. SS (J/kmol)");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getMolalityActivityCoefficients(&temp[0]);
pNames.push_back("Molal Act. Coeff.");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getActivities(&temp[0]);
pNames.push_back("Molal Activity");
data.push_back(temp);
size_t iHp = speciesIndex("H+");
if (iHp != npos) {
double pH = -log(temp[iHp]) / log(10.0);
csvFile << setw(tabL) << "pH = " << setw(tabS) << pH << endl;
}
} catch (CanteraError& err) {
err.save();
}
try {
getPartialMolarEnthalpies(&temp[0]);
pNames.push_back("Part. Mol Enthalpy (J/kmol)");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getPartialMolarEntropies(&temp[0]);
pNames.push_back("Part. Mol. Entropy (J/K/kmol)");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getPartialMolarIntEnergies(&temp[0]);
pNames.push_back("Part. Mol. Energy (J/kmol)");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getPartialMolarCp(&temp[0]);
pNames.push_back("Part. Mol. Cp (J/K/kmol");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
try {
getPartialMolarVolumes(&temp[0]);
pNames.push_back("Part. Mol. Cv (J/K/kmol)");
data.push_back(temp);
} catch (CanteraError& err) {
err.save();
}
csvFile << endl << setw(tabS) << "Species,";
for (size_t i = 0; i < pNames.size(); i++) {
csvFile << setw(tabM) << pNames[i] << ",";
}
csvFile << endl;
/*
csvFile.fill('-');
csvFile << setw(tabS+(tabM+1)*pNames.size()) << "-\n";
csvFile.fill(' ');
*/
for (size_t k = 0; k < nSpecies(); k++) {
csvFile << setw(tabS) << speciesName(k) + ",";
if (data[0][k] > SmallNumber) {
for (size_t i = 0; i < pNames.size(); i++) {
csvFile << setw(tabM) << data[i][k] << ",";
}
csvFile << endl;
} else {
for (size_t i = 0; i < pNames.size(); i++) {
csvFile << setw(tabM) << 0 << ",";
}
csvFile << endl;
}
}
} catch (CanteraError& err) {
err.save();
}
}
/**
* Format a summary of the mixture state for output.
*/
std::string MolalityVPSSTP::report(bool show_thermo) const
{
char p[800];
string s = "";
try {
if (name() != "") {
sprintf(p, " \n %s:\n", name().c_str());
s += p;
}
sprintf(p, " \n temperature %12.6g K\n", temperature());
s += p;
sprintf(p, " pressure %12.6g Pa\n", pressure());
s += p;
sprintf(p, " density %12.6g kg/m^3\n", density());
s += p;
sprintf(p, " mean mol. weight %12.6g amu\n", meanMolecularWeight());
s += p;
doublereal phi = electricPotential();
sprintf(p, " potential %12.6g V\n", phi);
s += p;
size_t kk = nSpecies();
vector_fp x(kk);
vector_fp molal(kk);
vector_fp mu(kk);
vector_fp muss(kk);
vector_fp acMolal(kk);
vector_fp actMolal(kk);
getMoleFractions(&x[0]);
getMolalities(&molal[0]);
getChemPotentials(&mu[0]);
getStandardChemPotentials(&muss[0]);
getMolalityActivityCoefficients(&acMolal[0]);
getActivities(&actMolal[0]);
size_t iHp = speciesIndex("H+");
if (iHp != npos) {
double pH = -log(actMolal[iHp]) / log(10.0);
sprintf(p, " pH %12.4g \n", pH);
s += p;
}
if (show_thermo) {
sprintf(p, " \n");
s += p;
sprintf(p, " 1 kg 1 kmol\n");
s += p;
sprintf(p, " ----------- ------------\n");
s += p;
sprintf(p, " enthalpy %12.6g %12.4g J\n",
enthalpy_mass(), enthalpy_mole());
s += p;
sprintf(p, " internal energy %12.6g %12.4g J\n",
intEnergy_mass(), intEnergy_mole());
s += p;
sprintf(p, " entropy %12.6g %12.4g J/K\n",
entropy_mass(), entropy_mole());
s += p;
sprintf(p, " Gibbs function %12.6g %12.4g J\n",
gibbs_mass(), gibbs_mole());
s += p;
sprintf(p, " heat capacity c_p %12.6g %12.4g J/K\n",
cp_mass(), cp_mole());
s += p;
try {
sprintf(p, " heat capacity c_v %12.6g %12.4g J/K\n",
cv_mass(), cv_mole());
s += p;
} catch (CanteraError& err) {
err.save();
sprintf(p, " heat capacity c_v <not implemented> \n");
s += p;
}
}
sprintf(p, " \n");
s += p;
if (show_thermo) {
sprintf(p, " X "
" Molalities Chem.Pot. ChemPotSS ActCoeffMolal\n");
s += p;
sprintf(p, " "
" (J/kmol) (J/kmol) \n");
s += p;
sprintf(p, " ------------- "
" ------------ ------------ ------------ ------------\n");
s += p;
for (size_t k = 0; k < kk; k++) {
if (x[k] > SmallNumber) {
sprintf(p, "%18s %12.6g %12.6g %12.6g %12.6g %12.6g\n",
speciesName(k).c_str(), x[k], molal[k], mu[k], muss[k], acMolal[k]);
} else {
sprintf(p, "%18s %12.6g %12.6g N/A %12.6g %12.6g \n",
speciesName(k).c_str(), x[k], molal[k], muss[k], acMolal[k]);
}
s += p;
}
} else {
sprintf(p, " X"
"Molalities\n");
s += p;
sprintf(p, " -------------"
" ------------\n");
s += p;
for (size_t k = 0; k < kk; k++) {
sprintf(p, "%18s %12.6g %12.6g\n",
speciesName(k).c_str(), x[k], molal[k]);
s += p;
}
}
} catch (CanteraError& err) {
err.save();
}
return s;
}
void SingleSpeciesTP::getStandardVolumes(doublereal* vbar) const
{
vbar[0] = molecularWeight(0) / density();
}
void SingleSpeciesTP::getPartialMolarVolumes(doublereal* vbar) const
{
vbar[0] = molecularWeight(0) / density();
}
double run_walls(double eta, const char *name, Functional fhs, double teff) {
//printf("Filling fraction is %g with functional %s at temperature %g\n", eta, name, teff);
//fflush(stdout);
double kT = teff;
if (kT == 0) kT = 1;
Functional f = OfEffectivePotential(fhs);
const double zmax = width + 2*spacing;
Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint, f);
// We reuse the potential, which should give us a better starting
// guess on each calculation.
static Grid *potential = 0;
if (strcmp(name, "hard") == 0) {
// start over for each potential
delete potential;
potential = 0;
}
if (!potential) {
potential = new Grid(gd);
*potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
*potential = -kT*potential->cwise().log();
}
// FIXME below I use the HS energy because of issues with the actual
// functional.
const double approx_energy = fhs(kT, eta/(4*M_PI/3))*dw*dw*width;
const double precision = fabs(approx_energy*1e-5);
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, kT,
potential,
QuadraticLineMinimizer));
took("Setting up the variables");
for (int i=0;min.improve_energy(false) && i<100;i++) {
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(kT, gd, *potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, eta);
z_plot(plotname, Grid(gd, 4*M_PI*density/3));
free(plotname);
{
GridDescription gdj = density.description();
double sep = gdj.dz*gdj.Lat.a3().norm();
int div = gdj.Nz;
int mid = int (div/2.0);
double Ntot_per_A = 0;
double mydist = 0;
for (int j=0; j<mid; j++){
Ntot_per_A += density(0,0,j)*sep;
mydist += sep;
}
double Extra_per_A = Ntot_per_A - eta/(4.0/3.0*M_PI)*width/2;
FILE *fout = fopen("papers/fuzzy-fmt/figs/wallsfillingfracInfo.txt", "a");
fprintf(fout, "walls%s-%04.2f.dat - If you want to match the bulk filling fraction of figs/walls%s-%04.2f.dat, than the number of extra spheres per area to add is %04.10f. So you'll want to multiply %04.2f by your cavity volume and divide by (4/3)pi. Then add %04.10f times the Area of your cavity to this number\n",
name, eta, name, eta, Extra_per_A, eta, Extra_per_A);
int wallslen = 20;
double Extra_spheres = (eta*wallslen*wallslen*wallslen/(4*M_PI/3) + Extra_per_A*wallslen*wallslen);
fprintf (fout, "For filling fraction %04.02f and walls of length %d you'll want to use %.0f spheres.\n\n", eta, wallslen, Extra_spheres);
fclose(fout);
}
{
//double peak = peak_memory()/1024.0/1024;
//double current = current_memory()/1024.0/1024;
//printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
took("Plotting stuff");
printf("density %g gives ff %g for eta = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, eta, teff);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
doublereal Phase::molarDensity() const
{
return density()/meanMolecularWeight();
}
void TGaussianMixture::expectation_maximization(const double *x, const double *w_n, unsigned int N, unsigned int iterations) {
double *p_kn = new double[nclusters*N];
// Determine total weight
double sum_w = 0.;
for(unsigned int n=0; n<N; n++) { sum_w += w_n[n]; }
// Choose means randomly from given points
unsigned int *index = new unsigned int[nclusters];
bool repeated_index;
for(unsigned int k=0; k<nclusters; k++) {
repeated_index = true;
while(repeated_index) {
index[k] = gsl_rng_uniform_int(r, N);
repeated_index = false;
for(unsigned int i=0; i<k; i++) {
if(index[i] == index[k]) { repeated_index = true; break; }
}
}
for(unsigned int i=0; i<ndim; i++) { mu[k*ndim + i] = x[index[k]*ndim + i]; }
}
delete[] index;
// Assign points to nearest cluster center
double sum, tmp, min_dist;
unsigned int nearest_cluster;
for(unsigned int n=0; n<N; n++) {
// Find nearest cluster center
min_dist = inf_replacement;
for(unsigned int k=0; k<nclusters; k++) {
sum = 0.;
for(unsigned int i=0; i<ndim; i++) {
tmp = x[n*ndim + i] - mu[k*ndim + i];
sum += tmp*tmp;
}
if(sum < min_dist) {
min_dist = sum;
nearest_cluster = k;
}
}
for(unsigned int k=0; k<nclusters; k++) { p_kn[n*nclusters + k] = 0.; }
p_kn[n*nclusters + nearest_cluster] = 1.;
w[nearest_cluster] += w_n[n];
}
sum = 0.;
for(unsigned int k=0; k<nclusters; k++) { sum += w[k]; }
for(unsigned int k=0; k<nclusters; k++) { w[k] /= sum; }
// Iterate
for(unsigned int count=0; count<=iterations; count++) {
// Assign probability for each point to be in each cluster
if(count != 0) {
density(x, N, p_kn);
for(unsigned int n=0; n<N; n++) {
// Normalize probability for point to be in some cluster to unity
sum = 0.;
for(unsigned int k=0; k<nclusters; k++) { sum += p_kn[n*nclusters + k]; }
for(unsigned int k=0; k<nclusters; k++) { p_kn[n*nclusters + k] /= sum; }
}
}
// Determine cluster properties from members
if(count != 0) {
for(unsigned int k=0; k<nclusters; k++) { // Strength of Gaussian
w[k] = 0.;
for(unsigned int n=0; n<N; n++) {
w[k] += w_n[n] * p_kn[n*nclusters + k];
}
w[k] /= sum_w;
}
}
for(unsigned int k=0; k<nclusters; k++) { // Mean of Gaussian
for(unsigned int j=0; j<ndim; j++) {
mu[k*ndim + j] = 0.;
for(unsigned int n=0; n<N; n++) {
mu[k*ndim + j] += w_n[n] * p_kn[n*nclusters + k] * x[n*ndim + j] / w[k];
}
mu[k*ndim + j] /= sum_w;
}
}
for(unsigned int k=0; k<nclusters; k++) { // Covariance
for(unsigned int i=0; i<ndim; i++) {
for(unsigned int j=i; j<ndim; j++) {
sum = 0.;
tmp = 0.;
for(unsigned int n=0; n<N; n++) {
sum += p_kn[n*nclusters + k] * w_n[n] * (x[n*ndim + i] - mu[k*ndim + i]) * (x[n*ndim + j] - mu[k*ndim + j]);
tmp += w_n[n] * p_kn[n*nclusters + k];
}
sum /= tmp;
if(i == j) {
gsl_matrix_set(cov[k], i, j, 1.01*sum + 0.01);
} else {
gsl_matrix_set(cov[k], i, j, sum);
gsl_matrix_set(cov[k], j, i, sum);
}
}
}
}
invert_covariance();
/*std::cout << "Iteration #" << count << std::endl;
std::cout << "=======================================" << std::endl;
for(unsigned int k=0; k<nclusters; k++) {
std::cout << "Cluster #" << k+1 << std::endl;
std::cout << "w = " << w[k] << std::endl;
std::cout << "mu =";
for(unsigned int i=0; i<ndim; i++) {
std::cout << " " << mu[k*ndim + i];
}
std::cout << std::endl;
std::cout << "Covariance:" << std::endl;
for(unsigned int i=0; i<ndim; i++) {
for(unsigned int j=0; j<ndim; j++) {
std::cout << " " << gsl_matrix_get(cov[k], i, j);
}
std::cout << std::endl;
}
std::cout << std::endl;
}*/
//w_k = np.einsum('n,kn->k', w, p_kn) / N
//mu = np.einsum('k,n,kn,nj->kj', 1./w_k, w, p_kn, x) / N
//for j in xrange(k):
// Delta[j] = x - mu[j]
//cov = np.einsum('kn,n,kni,knj->kij', p_kn, w, Delta, Delta)
//cov = np.einsum('kij,k->kij', cov, 1./np.sum(p_kn, axis=1))
}
// Find the vector sqrt_cov s.t. sqrt_cov sqrt_cov^T = cov.
for(unsigned int k=0; k<nclusters; k++) {
sqrt_matrix(cov[k], sqrt_cov[k], esv, eival, eivec, sqrt_eival);
}
// Cleanup
delete[] p_kn;
}
void WaterSSTP::setTemperature(const doublereal temp)
{
Phase::setTemperature(temp);
m_sub.setState_TR(temp, density());
}
void Phase::saveState(size_t lenstate, doublereal* state) const
{
state[0] = temperature();
state[1] = density();
getMassFractions(state + 2);
}
std::string ThermoPhase::report(bool show_thermo, doublereal threshold) const
{
fmt::MemoryWriter b;
try {
if (name() != "") {
b.write("\n {}:\n", name());
}
b.write("\n");
b.write(" temperature {:12.6g} K\n", temperature());
b.write(" pressure {:12.6g} Pa\n", pressure());
b.write(" density {:12.6g} kg/m^3\n", density());
b.write(" mean mol. weight {:12.6g} amu\n", meanMolecularWeight());
doublereal phi = electricPotential();
if (phi != 0.0) {
b.write(" potential {:12.6g} V\n", phi);
}
if (show_thermo) {
b.write("\n");
b.write(" 1 kg 1 kmol\n");
b.write(" ----------- ------------\n");
b.write(" enthalpy {:12.5g} {:12.4g} J\n",
enthalpy_mass(), enthalpy_mole());
b.write(" internal energy {:12.5g} {:12.4g} J\n",
intEnergy_mass(), intEnergy_mole());
b.write(" entropy {:12.5g} {:12.4g} J/K\n",
entropy_mass(), entropy_mole());
b.write(" Gibbs function {:12.5g} {:12.4g} J\n",
gibbs_mass(), gibbs_mole());
b.write(" heat capacity c_p {:12.5g} {:12.4g} J/K\n",
cp_mass(), cp_mole());
try {
b.write(" heat capacity c_v {:12.5g} {:12.4g} J/K\n",
cv_mass(), cv_mole());
} catch (NotImplementedError&) {
b.write(" heat capacity c_v <not implemented> \n");
}
}
vector_fp x(m_kk);
vector_fp y(m_kk);
vector_fp mu(m_kk);
getMoleFractions(&x[0]);
getMassFractions(&y[0]);
getChemPotentials(&mu[0]);
int nMinor = 0;
doublereal xMinor = 0.0;
doublereal yMinor = 0.0;
b.write("\n");
if (show_thermo) {
b.write(" X "
" Y Chem. Pot. / RT\n");
b.write(" ------------- "
"------------ ------------\n");
for (size_t k = 0; k < m_kk; k++) {
if (abs(x[k]) >= threshold) {
if (abs(x[k]) > SmallNumber) {
b.write("{:>18s} {:12.6g} {:12.6g} {:12.6g}\n",
speciesName(k), x[k], y[k], mu[k]/RT());
} else {
b.write("{:>18s} {:12.6g} {:12.6g}\n",
speciesName(k), x[k], y[k]);
}
} else {
nMinor++;
xMinor += x[k];
yMinor += y[k];
}
}
} else {
b.write(" X Y\n");
b.write(" ------------- ------------\n");
for (size_t k = 0; k < m_kk; k++) {
if (abs(x[k]) >= threshold) {
b.write("{:>18s} {:12.6g} {:12.6g}\n",
speciesName(k), x[k], y[k]);
} else {
nMinor++;
xMinor += x[k];
yMinor += y[k];
}
}
}
if (nMinor) {
b.write(" [{:+5d} minor] {:12.6g} {:12.6g}\n",
nMinor, xMinor, yMinor);
}
} catch (CanteraError& err) {
return b.str() + err.what();
}
return b.str();
}
void MetalSHEelectrons::getParameters(int& n, doublereal* const c) const
{
n = 1;
c[0] = density();
}
void run_with_eta(double eta, const char *name, Functional fhs) {
// Generates a data file for the pair distribution function, for filling fraction eta
// and distance of first sphere from wall of z0. Data saved in a table such that the
// columns are x values and rows are z1 values.
printf("Now starting run_with_eta with eta = %g name = %s\n",
eta, name);
Functional f = OfEffectivePotential(fhs + IdealGas());
double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
f = OfEffectivePotential(fhs + IdealGas()
+ ChemicalPotential(mu));
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width));
GridDescription gd(lat, dx);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinsphere);
f = constrain(constraint, f);
potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
potential = -potential.cwise().log();
const double approx_energy = (fhs + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*uipow(width,3);
const double precision = fabs(approx_energy*1e-10);
//printf("Minimizing to %g absolute precision...\n", precision);
{ // Put mimizer in block so as to free it when we finish minimizing to save memory.
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, 1,
&potential,
QuadraticLineMinimizer));
for (int i=0;min.improve_energy(true) && i<100;i++) {
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
took("Doing the minimization");
}
Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
Grid gsigma(gd, gSigmaA(1.0)(1, gd, density));
Grid nA(gd, ShellConvolve(2)(1, density)/(4*M_PI*4));
Grid n3(gd, StepConvolve(1)(1, density));
Grid nbar_sokolowski(gd, StepConvolve(1.6)(1, density));
nbar_sokolowski /= (4.0/3.0*M_PI*ipow(1.6, 3));
// Create the walls directory if it doesn't exist.
if (mkdir("papers/pair-correlation/figs/walls", 0777) != 0 && errno != EEXIST) {
// We failed to create the directory, and it doesn't exist.
printf("Failed to create papers/pair-correlation/figs/walls: %s",
strerror(errno));
exit(1); // fail immediately with error code
}
// here you choose the values of z0 to use
// dx is the resolution at which we compute the density.
char *plotname = new char[4096];
for (double z0 = 2.1; z0 < 4.5; z0 += 2.1) {
// For each z0, we now pick one of our methods for computing the
// pair distribution function:
for (int version = 0; version < numplots; version++) {
sprintf(plotname,
"papers/pair-correlation/figs/triplet%s-%s-%04.2f-%1.2f.dat",
name, fun[version], eta, z0);
FILE *out = fopen(plotname,"w");
FILE *xfile = fopen("papers/pair-correlation/figs/triplet-x.dat","w");
FILE *zfile = fopen("papers/pair-correlation/figs/triplet-z.dat","w");
// the +1 for z0 and z1 are to shift the plot over, so that a sphere touching the wall
// is at z = 0, to match with the monte carlo data
const Cartesian r0(0,0,z0);
for (double x = 0; x < 4; x += dx) {
for (double z1 = -4; z1 <= 9; z1 += dx) {
const Cartesian r1(x,0,z1);
double g2 = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out, "%g\t", g3);
fprintf(xfile, "%g\t", x);
fprintf(zfile, "%g\t", z1);
}
fprintf(out, "\n");
fprintf(xfile, "\n");
fprintf(zfile, "\n");
}
fclose(out);
fclose(xfile);
fclose(zfile);
}
}
delete[] plotname;
took("Dumping the triplet dist plots");
const double ds = 0.01; // step size to use in path plots, FIXME increase for publication!
const double delta = .1; //this is the value of radius of the
//particle as it moves around the contact
//sphere on its path
char *plotname_path = new char[4096];
for (int version = 0; version < numplots; version++) {
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet%s-path-%s-%04.2f.dat",
name, fun[version], eta);
FILE *out_path = fopen(plotname_path, "w");
if (!out_path) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-back-contact-%s-%04.2f.dat",
fun[version], eta);
FILE *out_back = fopen(plotname_path, "w");
if (!out_back) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
fprintf(out_path, "# unused\tg3\tz\tx\n");
fprintf(out_back, "# unused\tg3\tz\tx\n");
const Cartesian r0(0,0, 2.0+delta);
const double max_theta = M_PI*2.0/3;
for (double z = 7; z >= 2*(2.0 + delta); z-=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double z = -7; z <= -(2.0 + delta); z+=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
const double dtheta = ds/2;
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, (2.0+delta)*(1+cos(theta)));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0,-(2.0+delta)*cos(theta));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double x = (2.0+delta)*sqrt(3)/2; x<=6; x+=ds){
const Cartesian r1(x, 0, 1.0+delta/2);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
fclose(out_path);
fclose(out_back);
}
for (int version = 0; version < numplots; version++) {
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-path-inbetween-%s-%04.2f.dat",
fun[version], eta);
FILE *out_path = fopen(plotname_path, "w");
if (!out_path) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-back-inbetween-%s-%04.2f.dat",
fun[version], eta);
FILE *out_back = fopen(plotname_path, "w");
if (!out_back) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
fprintf(out_path, "# unused\tg3\tz\tx\n");
fprintf(out_back, "# unused\tg3\tz\tx\n");
const Cartesian r0(0,0, 4.0+2*delta);
const double max_theta = M_PI;
for (double z = 11; z >= 3*(2.0 + delta); z-=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double z = -10; z <= -(2.0 + delta); z+=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
const double dtheta = ds/2;
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, (2.0+delta)*(2+cos(theta)));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, -(2.0+delta)*cos(theta));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double x = 0; x>=-6; x-=ds){
const Cartesian r1(x, 0, 2.0+delta);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
fclose(out_path);
fclose(out_back);
}
delete[] plotname_path;
}
