int main(int argc, char **argv)
{
try {
const int d = 7;
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(1);
bases[0] = Teuchos::rcp(new Stokhos::HermiteBasis<int,double>(d));
Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
Teuchos::RCP<Teuchos::SerialDenseMatrix<int,double> > Bij =
basis->computeDerivDoubleProductTensor();
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk =
basis->computeTripleProductTensor(basis->size());
Teuchos::RCP<Stokhos::Dense3Tensor<int,double> > Dijk =
basis->computeDerivTripleProductTensor(Bij, Cijk);
Stokhos::DerivOrthogPolyExpansion<int,double> expn(basis, Bij, Cijk, Dijk);
Stokhos::OrthogPolyApprox<int,double> u(basis),v(basis),w(basis);
u[0] = 1.0;
u[1] = 0.4;
u[2] = 0.06;
u[3] = 0.002;
expn.log(v,u);
expn.times(w,v,v);
expn.plusEqual(w,1.0);
expn.divide(v,1.0,w);
expn.sinh(w,v);
std::cout << "u (orthogonal basis) = " << u << std::endl;
std::cout.precision(12);
std::cout << "w (orthogonal basis) = " << w << std::endl;
}
catch (std::exception& e) {
std::cout << e.what() << std::endl;
}
}
int decstat()
{
if(T[nt++].t==13)
{
stmtflag[no]=1;
if(T[nt++].t==20)
{
if(expn())
{
if(T[nt++].t==21)
{
if(stmt())
{
if(dprime())
return 1;
else
return 0;
}
else
return 0;
}
else
{
strcpy(miss,")");
return 0;
}
}
else
return 0;
}
else
{
strcpy(miss,"(");
return 0;
}
}
else
{
nt--;
return 0;
}
}
int assstat()
{
if(T[nt++].t==50)
{
stmtflag[no]=1;
if(T[nt++].t==28)
{
if(expn())
return 1;
else
return 0;
}
else
{
strcpy(miss,"=");
return 0;
}
}
else
{
nt--;
return 0;
}
}
int main(int argc, char **argv)
{
try {
// Basis of dimension 3, order 5
const int d = 3;
const int p = 5;
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(d);
for (int i=0; i<d; i++) {
bases[i] = Teuchos::rcp(new Stokhos::HermiteBasis<int,double>(p));
}
Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
// Quadrature method
Teuchos::RCP<const Stokhos::Quadrature<int,double> > quad =
Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(basis));
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk =
basis->computeTripleProductTensor(basis->size());
// Expansion method
Stokhos::QuadOrthogPolyExpansion<int,double> expn(basis, Cijk, quad);
// Polynomial expansions
Stokhos::OrthogPolyApprox<int,double> u(basis), v(basis), w(basis);
u.term(0,0) = 1.0;
for (int i=0; i<d; i++) {
u.term(i,1) = 0.4 / d;
u.term(i,2) = 0.06 / d;
u.term(i,3) = 0.002 / d;
}
// Compute expansion
expn.log(v,u);
expn.times(w,v,v);
expn.plusEqual(w,1.0);
expn.divide(v,1.0,w);
// Print u and v
std::cout << "v = 1.0 / (log(u)^2 + 1):" << std::endl;
std::cout << "\tu = ";
u.print(std::cout);
std::cout << "\tv = ";
v.print(std::cout);
// Compute moments
double mean = v.mean();
double std_dev = v.standard_deviation();
// Evaluate PCE and function at a point = 0.25 in each dimension
Teuchos::Array<double> pt(d);
for (int i=0; i<d; i++)
pt[i] = 0.25;
double up = u.evaluate(pt);
double vp = 1.0/(std::log(up)*std::log(up)+1.0);
double vp2 = v.evaluate(pt);
// Print results
std::cout << "\tv mean = " << mean << std::endl;
std::cout << "\tv std. dev. = " << std_dev << std::endl;
std::cout << "\tv(0.25) (true) = " << vp << std::endl;
std::cout << "\tv(0.25) (pce) = " << vp2 << std::endl;
// Check the answer
if (std::abs(vp - vp2) < 1e-2)
std::cout << "\nExample Passed!" << std::endl;
}
catch (std::exception& e) {
std::cout << e.what() << std::endl;
}
}
void deom::rem_sch (cx_cube& dtotal, const cx_cube& total, const double t) {
const int nsav = nddo;
dtotal.slices(0,nddo-1).zeros();
for (int iado=0; iado<nsav; ++iado) {
const cx_mat& ado = total.slice(iado);
if (iado==0 || is_valid (ado)) {
string key = keys(iado);
const int tier = maps[key].tier;
const cx_double gams = maps[key].gams;
dtotal.slice(iado) += -deom_ci*(ham1*ado-ado*ham1)-gams*ado;
for (int m=0; m<nmod; ++m) {
qddo.slice(m) = qmd1.slice(m)*ado;
ddoq.slice(m) = ado*qmd1.slice(m);
dtotal.slice(iado) -= delt_res(m)*(
qmd1.slice(m)*(qddo.slice(m)-ddoq.slice(m))
-(qddo.slice(m)-ddoq.slice(m))*qmd1.slice(m));
}
if (tier < lmax) {
for (int mp=0; mp<nind; ++mp) {
const int m = mp/nper;
const int p = mp%nper;
const int n = key[mp]-'0';
const cx_double sn = -deom_ci*sqrt((n+1)/coef_abs(m,p));
const cx_double cl = sn*coef_lft(m,p);
const cx_double cr = sn*coef_rht(m,p);
key[mp] = static_cast<char>(key[mp]+1);
const auto &xp = maps.emplace(key,hnod(nddo,tier+1,gams+expn(mp)));
if (!xp.second) {
int loc = xp.first->second.rank;
dtotal.slice(loc) += cl*qddo.slice(m)-cr*ddoq.slice(m);
} else {
keys(nddo) = key;
dtotal.slice(nddo) = cl*qddo.slice(m)-cr*ddoq.slice(m);
nddo += 1;
}
key[mp] = static_cast<char>(key[mp]-1);
}
}
if (iado > 0) {
for (int mp=0; mp<nind; ++mp) {
const int m = mp/nper;
const int p = mp%nper;
const int n = key[mp]-'0';
if (n > 0) {
key[mp] = static_cast<char>(key[mp]-1);
const cx_double sn = -deom_ci*sqrt(n*coef_abs(m,p));
const auto &xp = maps.emplace(key,hnod(nddo,tier-1,gams-expn(mp)));
if (!xp.second) {
int loc = xp.first->second.rank;
dtotal.slice(loc) += sn*(qddo.slice(m)-ddoq.slice(m));
} else {
keys(nddo) = key;
dtotal.slice(nddo) = sn*(qddo.slice(m)-ddoq.slice(m));
nddo += 1;
}
key[mp] = static_cast<char>(key[mp]+1);
}
}
}
}
}
}
int loopstat()
{
if(T[nt++].t==15)
{
stmtflag[no]=1;
if(T[nt++].t==20)
{
if(expn())
{
if(T[nt++].t==21)
{
if(stmt())
return 1;
else
return 0;
}
else
{
strcpy(miss,")");
return 0;
}
}
else
return 0;
}
else
{
strcpy(miss,"(");
return 0;
}
}
else
{
nt--;
if(T[nt++].t==16)
{
stmtflag[no]=1;
if(T[nt++].t==20)
{
if(assstat())
{
if(T[nt++].t==27)
{
if(expn())
{
if(T[nt++].t==27)
{
if(assstat())
{
if(T[nt++].t==21)
{
if(stmt())
return 1;
}
else
{
strcpy(miss,")");
return 0;
}
}
}
else
{
if(stmtflag[no]==0)
strcpy(miss,";");
return 0;
}
}
}
strcpy(miss,";");
return 0;
}
}
else
{
if(stmtflag[no]==1)
strcpy(miss,"(");
return 0;
}
}
else
{
nt--;
return 0;
}
}
}
