double predcorr( double t, double I ) // Predictor Correcotr Method
{
double I_p, I_i1; // I_p: estimated value of current
// I_i1: new value of current at next time step
I_p = I + h * dydx( t, I ); // Predictor Formula
I_i1 = I + 0.5 * h * ( dydx( t, I ) + dydx( t + h, I_p ) ); // Corrector Formula
I_i1 = I_i1+1;
return I_i1;
}
double WaveformUtilities::Eccentricity_rDot(const std::vector<double>& t, const std::vector<double>& rDot,
const double r0, const double Omega0, double& DeltarDot, double& DeltaPhiDot) {
//// Do the fit to the model:
//// rDot(t) = vbar0 + arbar0*t + Br*cos(omegar*t+phir)
//// First fit to rDotDot to find phase, frequency, and amplitude
std::vector<double> rDotDot = dydx(rDot, t);
std::vector<double> aDotDotGuesses(3);
aDotDotGuesses[0] = 0.5*(max(rDotDot)-min(rDotDot));
aDotDotGuesses[1] = Omega0;
aDotDotGuesses[2] = 0.0;
std::vector<double> rDotDotMinusAvg = rDotDot-avg(rDotDot);
std::vector<double> TrivialSigmas(t.size(), 1.0);
Eccentricity_rDotDotFit e_dd;
FitNonlinear<Eccentricity_rDotDotFit> rDotDotFit(t, rDotDotMinusAvg, TrivialSigmas, aDotDotGuesses, e_dd, 1.e-8);
rDotDotFit.hold(0, aDotDotGuesses[0]);
rDotDotFit.hold(1, aDotDotGuesses[1]);
rDotDotFit.fit();
rDotDotFit.free(1);
rDotDotFit.fit();
rDotDotFit.free(0);
rDotDotFit.fit();
//// Next fit to rDot to find all parameters
std::vector<double> aDotGuesses(5);
aDotGuesses[0] = avg(rDot);
aDotGuesses[1] = avg(rDotDot);
aDotGuesses[2] = rDotDotFit.a[0] / rDotDotFit.a[1];
aDotGuesses[3] = rDotDotFit.a[1];
aDotGuesses[4] = rDotDotFit.a[2];
Eccentricity_rDotFit e_d;
FitNonlinear<Eccentricity_rDotFit> rDotFit(t, rDot, TrivialSigmas, aDotGuesses, e_d, 1.e-8);
rDotFit.fit();
//// Adjust the parameters
//double& vbar0 = rDotFit.a[0];
//double& arbar0 = rDotFit.a[1];
double& Br = rDotFit.a[2];
double& omegar = rDotFit.a[3];
double& phir = rDotFit.a[4];
DeltarDot = -Br * cos(phir); // Eq. (71) of arXiv:1012.1549
DeltaPhiDot = Br * omegar * sin(phir) / (2* r0 * Omega0); // Eq. (73) of arXiv:1012.1549
//// Return the measured eccentricity
return -Br / (r0 * omegar);
}
/////////////////////////////////////////////////
// Epidemiological modeling and model fitting
void TEpidemModel::RunModel(const TFltV& StartValV, const double& StartT, const double& StopT, const int& NSteps, TVec<TFltV>& OutValV) {
TFltV ValV(StartValV), dydx(StartValV.Len()), ValV2(StartValV.Len());
OutValV.Clr(false);
for (int v = 0; v < StartValV.Len(); v++) {
OutValV.Add();
OutValV[v].Clr(false);
OutValV[v].Add(StartValV[v]);
}
const double h = (StopT-StartT) / NSteps;
double x = StartT;
for (int k = 0; k < NSteps; k++) {
GetDerivs(x, ValV, dydx);
RungeKutta(ValV, dydx, x, h, ValV2);
for (int v = 0; v < ValV2.Len(); v++) {
double X = ValV2[v];
if (X < 0 || _isnan(X) || !_finite(X)) { X = 0; }
OutValV[v].Add(X);
}
ValV = ValV2;
x += h;
}
}
void TEpidemModel::RunEuler(const TFltV& StartValV, const double& StartT, const double& StopT, const int& NSteps, TVec<TFltV>& OutValV) {
const double h = (StopT-StartT) / NSteps;
TFltV ValV(StartValV), dydx(StartValV.Len()), ValV2(StartValV.Len());
for (int v = 0; v < StartValV.Len(); v++) {
OutValV.Add();
OutValV[v].Clr(false);
OutValV[v].Add(StartValV[v]);
}
OutValV.Add(); // x values
OutValV.Last().Add(StartT);
for (double x = StartT; x <= StopT; x += h) {
GetDerivs(x, ValV, dydx);
for (int v = 0; v < ValV.Len(); v++) {
ValV[v] += h*dydx[v];
OutValV[v].Add(ValV[v]);
}
OutValV.Last().Add(x+h);
}
for (int v = 1; v < OutValV.Len(); v++) {
IAssert(OutValV[v].Len()==OutValV[v-1].Len());
}
}
// run the model internally with 10 times greater resolution
void TEpidemModel::RunModel10(const TFltV& StartValV, const double& StartT, const double& StopT, const int& NSteps, TVec<TFltV>& OutValV) {
TFltV ValV(StartValV), dydx(StartValV.Len()), ValV2(StartValV.Len());
OutValV.Clr(false);
for (int v = 0; v < StartValV.Len(); v++) {
OutValV.Add();
OutValV[v].Clr(false);
OutValV[v].Add(StartValV[v]);
}
const double h = (StopT-StartT) / (10*NSteps);
double x = StartT;
for (int k = 0; k < 10*NSteps; k++) {
GetDerivs(x, ValV, dydx);
RungeKutta(ValV, dydx, x, h, ValV2);
// take values at only every 10th step
if (k % 10 == 0) {
for (int v = 0; v < ValV2.Len(); v++) {
OutValV[v].Add(ValV2[v]); }
}
ValV = ValV2;
x += h;
}
}
