value_type
Stokhos::KL::OneDExponentialCovarianceFunction<value_type>::
bisection(const Func& func, const value_type& a, const value_type& b,
magnitude_type tol, int max_num_its)
{
value_type low, hi;
value_type fa = func.eval(a);
value_type fb = func.eval(b);
TEUCHOS_TEST_FOR_EXCEPTION(fa*fb > value_type(0.0), std::logic_error,
"Bounds [" << a << "," << b << "] must bracket the root!" << std::endl <<
"f(a) = " << fa << ", f(b) = " << fb << std::endl)
if (fa <= 0.0) {
low = a;
hi = b;
}
else {
low = b;
hi = a;
}
int nit = 0;
value_type u = low + (hi - low)/2.0;
value_type f = func.eval(u);
while ((Teuchos::ScalarTraits<value_type>::magnitude(hi - low) > 2.0*tol ||
Teuchos::ScalarTraits<value_type>::magnitude(f) > tol) &&
nit < max_num_its) {
//std::cout << "u = " << u << " f = " << f << std::endl;
if (f <= 0.0)
low = u;
else
hi = u;
u = low + (hi - low)/2.0;
f = func.eval(u);
++nit;
}
TEUCHOS_TEST_FOR_EXCEPTION(nit >= max_num_its, std::logic_error,
"Nonlinear solver did not converge!" << std::endl);
return u;
}
value_type
Stokhos::KL::OneDExponentialCovarianceFunction<value_type>::
newton(const Func& func, const value_type& a, const value_type& b,
magnitude_type tol, int max_num_its)
{
value_type u = (a+b)/2.0;
value_type f = func.eval(u);
int nit = 0;
while (Teuchos::ScalarTraits<value_type>::magnitude(f) > tol &&
nit < max_num_its) {
std::cout << "u = " << u << " f = " << f << std::endl;
value_type dfdu = func.deriv(u);
u -= f / dfdu;
f = func.eval(u);
++nit;
}
TEUCHOS_TEST_FOR_EXCEPTION(nit >= max_num_its, std::logic_error,
"Nonlinear solver did not converge!" << std::endl);
return u;
}
Lanczos_PCE_Setup(bool normalize, bool project) :
func()
{
rtol = 1e-8;
atol = 1e-12;
const OrdinalType d = 3;
const OrdinalType p = 5;
// Create product basis
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<OrdinalType,ValueType> > > bases(d);
for (OrdinalType i=0; i<d; i++)
bases[i] =
Teuchos::rcp(new Stokhos::LegendreBasis<OrdinalType,ValueType>(p));
basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<OrdinalType,ValueType>(bases));
// Create approximation
sz = basis->size();
Stokhos::OrthogPolyApprox<OrdinalType,ValueType> x(basis);
for (OrdinalType i=0; i<d; i++)
x.term(i, 1) = 1.0;
// Tensor product quadrature
Teuchos::RCP<const Stokhos::Quadrature<OrdinalType,ValueType> > quad =
Teuchos::rcp(new Stokhos::TensorProductQuadrature<OrdinalType,ValueType>(basis, 4*p));
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk =
basis->computeTripleProductTensor(basis->size());
// Quadrature expansion
exp = Teuchos::rcp(new Stokhos::QuadOrthogPolyExpansion<OrdinalType,ValueType>(basis, Cijk, quad));
// Compute PCE via quadrature expansion
u.reset(basis);
v.reset(basis);
func.eval(*exp, x, u);
exp->times(v,u,u);
// Compute Lanczos basis
st_bases.resize(1);
if (project) {
st_1d_proj_basis =
Teuchos::rcp(new Stokhos::LanczosProjPCEBasis<OrdinalType,ValueType>(
p, Teuchos::rcp(&u,false), Cijk, normalize));
st_bases[0] = st_1d_proj_basis;
}
else {
st_1d_basis =
Teuchos::rcp(new Stokhos::LanczosPCEBasis<OrdinalType,ValueType>(
p, Teuchos::rcp(&u,false), quad, normalize, false));
st_bases[0] = st_1d_basis;
}
st_basis =
Teuchos::rcp(new Stokhos::CompletePolynomialBasis<OrdinalType,ValueType>(st_bases, 1e-15));
st_sz = st_basis->size();
u_st.reset(st_basis);
v_st.reset(st_basis);
if (project) {
u_st[0] = st_1d_proj_basis->getNewCoeffs(0);
u_st[1] = st_1d_proj_basis->getNewCoeffs(1);
}
else {
u_st[0] = st_1d_basis->getNewCoeffs(0);
u_st[1] = st_1d_basis->getNewCoeffs(1);
}
// Tensor product quadrature
st_quad =
Teuchos::rcp(new Stokhos::TensorProductQuadrature<OrdinalType,ValueType>(st_basis));
// Triple product tensor
Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > st_Cijk =
st_basis->computeTripleProductTensor(st_basis->size());
// Quadrature expansion
Stokhos::QuadOrthogPolyExpansion<OrdinalType,ValueType> st_exp(st_basis,
st_Cijk,
st_quad);
st_exp.times(v_st, u_st, u_st);
}
