/// Main program of uncertainty propagation of the ODE model parameters via intrusive spectral projection (ISP)
int main()
{
// Model parameters
Array1D<double> modelparams;
// Model parameter names
Array1D<string> modelparamnames;
// Auxiliary parameters: final time and time step of integration
Array1D<double> modelauxparams;
// Read the xml tree
RefPtr<XMLElement> xmlTree=readXMLTree("lorenz.in.xml");
// Read the model-specific input
readXMLModelInput(xmlTree,modelparams, modelparamnames, modelauxparams);
// Total nuber of input parameters
int fulldim=modelparams.XSize();
// Read the output preferences
dumpInfo* outPrint=new dumpInfo;
readXMLDumpInfo( xmlTree, &(outPrint->dumpInt), &(outPrint->fdumpInt), &(outPrint->dumpfile) );
// Output PC order
int order;
// PC type
string pcType;
// A 2d array (each row is an array of coefficients for the corresponding uncertain input parameter)
Array2D<double> allPCcoefs;
// The indices of the uncertain model parameters in the list of model parameters
Array1D<int> uncParamInd;
// Read the UQ-specific information from the xml tree
readXMLUncInput(xmlTree,allPCcoefs,uncParamInd , &order, &pcType);
// Stochastic dimensionality
int dim=uncParamInd.XSize();
// Instantiate a PC object for ISP computations
PCSet myPCSet("ISP",order,dim,pcType,0.0,1.0);
// The number of PC terms
const int nPCTerms = myPCSet.GetNumberPCTerms();
cout << "The number of PC terms in an expansion is " << nPCTerms << endl;
// Print the multiindices on screen
myPCSet.PrintMultiIndex();
// Initial time
double t0 = 0.0;
// Final time
double tf = modelauxparams(0);
// Time step
double dTym = modelauxparams(1);
// Number of steps
int nStep=(int) tf / dTym;
// Initial conditions of zero coverage (based on Makeev:2002)
Array1D<double> u(nPCTerms,0.e0);
Array1D<double> v(nPCTerms,0.e0);
Array1D<double> w(nPCTerms,0.e0);
Array1D<double> z(nPCTerms,0.e0);
// Array to hold the PC representation of the number 1
Array1D<double> one(nPCTerms,0.e0);
one(0)=1.0;
// The z-species is described as z=1-u-v-w
z=one;
myPCSet.SubtractInPlace(z,u);
myPCSet.SubtractInPlace(z,v);
myPCSet.SubtractInPlace(z,w);
// Right-hand sides
Array1D<double> dudt(nPCTerms,0.e0);
Array1D<double> dvdt(nPCTerms,0.e0);
Array1D<double> dwdt(nPCTerms,0.e0);
// Array of arrays to hold the input parameter PC representations in the output PC
// Each element is an array of coefficients for the corresponding input parameter, whether deterministic or uncertain
// The size of the array is the total number input parameters
Array1D< Array1D<double> > modelparamPCs(fulldim);
printf("\nInput parameter PC coefficients are given below\n");
for (int i=0; i<fulldim; i++){
printf("%s: ",modelparamnames(i).c_str());
modelparamPCs(i).Resize(nPCTerms,0.e0);
for (int j=0; j<nPCTerms; j++){
modelparamPCs(i)(j)=allPCcoefs(j,i);
printf(" %lg ",modelparamPCs(i)(j));
}
printf("\n");
}
printf("\n");
// Initial time and time step counter
int step=0;
double tym=t0;
// Work arrays for integration
Array1D<double> u_o(nPCTerms,0.e0);
Array1D<double> v_o(nPCTerms,0.e0);
Array1D<double> w_o(nPCTerms,0.e0);
Array1D<double> tmp_u(nPCTerms,0.e0);
Array1D<double> tmp_v(nPCTerms,0.e0);
Array1D<double> tmp_w(nPCTerms,0.e0);
// File to write the mean and stdev, name read from xml
FILE *f_dump,*modes_dump;
if(!(f_dump = fopen(outPrint->dumpfile.c_str(),"w"))){
printf("Could not open file '%s'\n",outPrint->dumpfile.c_str());
exit(1);
}
// File to dump the PC modes, name hardwired
string modes_dumpfile = "solution_ISP_modes.dat";
if(!(modes_dump = fopen(modes_dumpfile.c_str(),"w"))){
printf("Could not open file '%s'\n",modes_dumpfile.c_str());
exit(1);
}
// write time, u, v, w (all modes) to file
WriteModesToFilePtr(tym, u.GetArrayPointer(), v.GetArrayPointer(), w.GetArrayPointer(), nPCTerms, modes_dump);
// Write out initial step
// Get standard deviations
double uStDv = myPCSet.StDv(u);
double vStDv = myPCSet.StDv(v);
double wStDv = myPCSet.StDv(w);
// write u, v, w (mean and standard deviation) to file
WriteMeanStdDevToFilePtr(tym, u(0), v(0), w(0), uStDv, vStDv, wStDv, f_dump);
// write u, v, w (mean and standard deviation) to screen
WriteMeanStdDevToStdOut(step, tym, u(0), v(0), w(0), uStDv, vStDv, wStDv);
// Forward run
while(tym < tf) {
// Integrate with 2nd order Runge Kutta
// Save solution at current time step
myPCSet.Copy(u_o,u);
myPCSet.Copy(v_o,v);
myPCSet.Copy(w_o,w);
// Compute right hand sides
GetRHS(myPCSet,modelparamPCs(0).GetArrayPointer(),modelparamPCs(1).GetArrayPointer(),modelparamPCs(2).GetArrayPointer(),u.GetArrayPointer(),v.GetArrayPointer(),w.GetArrayPointer(),dudt.GetArrayPointer(),dvdt.GetArrayPointer(),dwdt.GetArrayPointer());
// Advance u, v, w to mid-point
myPCSet.Multiply(dudt,0.5*dTym,tmp_u); // 0.5*dTym*dudt
myPCSet.Multiply(dvdt,0.5*dTym,tmp_v); // 0.5*dTym*dvdt
myPCSet.Multiply(dwdt,0.5*dTym,tmp_w); // 0.5*dTym*dwdt
myPCSet.Add(u_o,tmp_u,u); // u = u_o + 0.5*dTym*dudt
myPCSet.Add(v_o,tmp_v,v); // v = v_o + 0.5*dTym*dvdt
myPCSet.Add(w_o,tmp_w,w); // w = w_o + 0.5*dTym*dwdt
// Compute z = 1 - u - v - w
z=one;
myPCSet.SubtractInPlace(z,u);
myPCSet.SubtractInPlace(z,v);
myPCSet.SubtractInPlace(z,w);
// Compute right hand sides
GetRHS(myPCSet,modelparamPCs(0).GetArrayPointer(),modelparamPCs(1).GetArrayPointer(),modelparamPCs(2).GetArrayPointer(),u.GetArrayPointer(),v.GetArrayPointer(),w.GetArrayPointer(),dudt.GetArrayPointer(),dvdt.GetArrayPointer(),dwdt.GetArrayPointer());
// Advance u, v, w to next time step
myPCSet.Multiply(dudt,dTym,tmp_u); // dTym*dudt
myPCSet.Multiply(dvdt,dTym,tmp_v); // dTym*dvdt
myPCSet.Multiply(dwdt,dTym,tmp_w); // dTym*dwdt
myPCSet.Add(u_o,tmp_u,u); // u = u_o + dTym*dudt
myPCSet.Add(v_o,tmp_v,v); // v = v_o + dTym*dvdt
myPCSet.Add(w_o,tmp_w,w); // w = w_o + dTym*dwdt
// Compute z = 1 - u - v - w
z=one;
myPCSet.SubtractInPlace(z,u);
myPCSet.SubtractInPlace(z,v);
myPCSet.SubtractInPlace(z,w);
// Advance time and step counter
tym += dTym;
step+=1;
// write time, u, v, w (all modes) to file
if(step % outPrint->fdumpInt == 0){
WriteModesToFilePtr(tym, u.GetArrayPointer(), v.GetArrayPointer(), w.GetArrayPointer(), nPCTerms, modes_dump);
}
// Get standard deviations
uStDv = myPCSet.StDv(u);
vStDv = myPCSet.StDv(v);
wStDv = myPCSet.StDv(w);
// write u, v, w (mean and standard deviation) to file
if(step % outPrint->fdumpInt == 0){
WriteMeanStdDevToFilePtr(tym, u(0), v(0), w(0), uStDv, vStDv, wStDv, f_dump);
}
// write u, v, w (mean and standard deviation) to screen
if(step % outPrint->dumpInt == 0){
WriteMeanStdDevToStdOut(step, tym, u(0), v(0), w(0), uStDv, vStDv, wStDv);
}
}
// Close output file
if(fclose(f_dump)){
printf("Could not close file '%s'\n",outPrint->dumpfile.c_str());
exit(1);
}
// Close output file
if(fclose(modes_dump)){
printf("Could not close file '%s'\n",modes_dumpfile.c_str());
exit(1);
}
return 0;
}
int main(int ac, char** av)
{
if (ac != 2) error_macro("expecting 1 argument: CMAKE_BINARY_DIR")
std::string
dir = string(av[1]) + "/paper_GMD_2015/fig_a/",
h5 = dir + "out_lgrngn",
svg = dir + "out_lgrngn_spec.svg";
Gnuplot gp;
int off = 2; // TODO!!!
float ymin = .4 * .01, ymax = .9 * 10000;
const int at = 9000;
gp << "set term svg dynamic enhanced fsize 15 size 900, 1500 \n";
gp << "set output '" << svg << "'\n";
gp << "set logscale xy\n";
gp << "set xrange [.002:100]\n";
gp << "set yrange [" << ymin << ":" << ymax << "]\n";
gp << "set ylabel '[mg^{-1} μm^{-1}]'\n"; // TODO: add textual description (PDF?)
gp << "set grid\n";
gp << "set nokey\n";
// FSSP range
gp << "set arrow from .5," << ymin << " to .5," << ymax << " nohead\n";
gp << "set arrow from 25," << ymin << " to 25," << ymax << " nohead\n";
gp << "set xlabel offset 0,1.5 'particle radius [μm]'\n";
gp << "set key samplen 1.2\n";
gp << "set xtics rotate by 65 right (.01, .1, 1, 10, 100) \n";
// TODO: use dashed lines to allow printing in black and white... same in image plots
assert(focus.first.size() == focus.second.size());
gp << "set multiplot layout " << focus.first.size() << ",2 columnsfirst upwards\n";
// focus to the gridbox from where the size distribution is plotted
char lbl = 'i';
for (auto &fcs : std::set<std::set<std::pair<int,int>>>({focus.first, focus.second}))
{
for (auto it = fcs.begin(); it != fcs.end(); ++it)
{
const int &x = it->first, &y = it->second;
gp << "set label 1 '(" << lbl << ")' at graph -.15, 1.02 font ',20'\n";
//gp << "set title 'x=" << x << " y=" << y << "'\n";
std::map<float, float> focus_d;
std::map<float, float> focus_w;
//info on the number and location of histogram edges
vector<quantity<si::length>> left_edges_rd = bins_dry();
int nsd = left_edges_rd.size() - 1;
vector<quantity<si::length>> left_edges_rw = bins_wet();
int nsw = left_edges_rw.size() - 1;
for (int i = 0; i < nsd; ++i)
{
const string name = "rd_rng" + zeropad(i) + "_mom0";
blitz::Array<float, 2> tmp_d(1e-6 * h5load(h5, name, at));
focus_d[left_edges_rd[i] / 1e-6 / si::metres] = sum(tmp_d(
blitz::Range(x-1, x+1),
blitz::Range(y-1, y+1)
))
/ 9 // mean over 9 gridpoints
/ ((left_edges_rd[i+1] - left_edges_rd[i]) / 1e-6 / si::metres); // per micrometre
}
for (int i = 0; i < nsw; ++i)
{
const string name = "rw_rng" + zeropad(i + off) + "_mom0";
blitz::Array<float, 2> tmp_w(1e-6 * h5load(h5, name, at));
focus_w[left_edges_rw[i] / 1e-6 / si::metres] = sum(tmp_w(
blitz::Range(x-1, x+1),
blitz::Range(y-1, y+1)
))
/ 9
/ ((left_edges_rw[i+1] - left_edges_rw[i]) / 1e-6 / si::metres); // per micrometre
}
notice_macro("setting-up plot parameters");
gp << "plot"
<< "'-' with histeps title 'wet radius' lw 3 lc rgb 'blue',"
<< "'-' with histeps title 'dry radius' lw 1 lc rgb 'red' " << endl;
gp.send(focus_w);
gp.send(focus_d);
lbl -= 2;
}
lbl = 'j';
}
}