static std::ptrdiff_t invoke( const fortran_int_t n, VectorX& x,
real_type& est, fortran_int_t& kase, minimal_workspace ) {
namespace bindings = ::boost::numeric::bindings;
bindings::detail::array< real_type > tmp_v( min_size_v( n ) );
bindings::detail::array<
fortran_int_t > tmp_isgn( min_size_isgn( n ) );
return invoke( n, x, est, kase, workspace( tmp_v, tmp_isgn ) );
}
void Hamiltonian::set_v(boost::python::list v_) {
/**
Update Hamiltonian velocities (all are real-valued scalars -the components of Python list) - Python-friendly
\param[in] v The vector of real-valued velocities to be used for Hamiltonian calculations.
The velocities are only needed for vibronic Hamiltonian (adiabatic representation) calculations.
Otherwise, they are not used.
Only status_adi is set to 0, so only adiabatic Hamiltonian is recomputed.
For future: in fact, we only need to update the vibronic Hamiltonian, so we still may save a lot, when adiabatic
calculations imply electronic structure calculations
*/
int sz = boost::python::len(v_);
vector<double> tmp_v(sz,0.0);
for(int i=0; i<sz; i++) {
tmp_v[i] = boost::python::extract<double>(v_[i]);
}
set_v(tmp_v);
}
/// 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;
}
void ndarr<T>::broadcast_rec(int shape_n){
vector<T> tmp_v(v);
shape.insert(shape.begin(), shape_n);
for (int i=0; i<shape_n-1; i++)
v.insert(v.end(), tmp_v.begin(), tmp_v.end());
}
