45 template <
typename ordinal_type,
typename value_type>
51 const Teuchos::ParameterList& params) :
53 name(
"Monomial Gram Schmidt PCE Basis")
55 this->
setup(max_p, pce, quad);
58 template <
typename ordinal_type,
typename value_type>
64 template <
typename ordinal_type,
typename value_type>
72 template <
typename ordinal_type,
typename value_type>
78 const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& A,
79 const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& F,
80 const Teuchos::Array<value_type>& weights,
82 Teuchos::Array<ordinal_type>& num_terms_,
83 Teuchos::SerialDenseMatrix<ordinal_type,value_type>& Qp_,
84 Teuchos::SerialDenseMatrix<ordinal_type,value_type>& Q_)
88 CPBUtils::compute_terms(max_p, this->d, max_sz, terms_, num_terms_);
110 nrm += B(i,
j)*B(i,
j)*weights[i];
120 Teuchos::Array<ordinal_type> piv(max_sz);
121 for (
int i=0; i<this->d+1; i++)
125 this->orthogonalization_method, threshold, this->verbose, B, weights,
130 Qp_.reshape(this->pce_sz, sz_);
133 tmp(i,
j) = Q_(i,
j)*weights[i];
135 Qp_.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, A, tmp, 0.0);
136 TEUCHOS_ASSERT(ret == 0);
KOKKOS_INLINE_FUNCTION PCE< Storage > sqrt(const PCE< Storage > &a)
KOKKOS_INLINE_FUNCTION PCE< Storage > pow(const PCE< Storage > &a, const PCE< Storage > &b)
virtual ordinal_type buildReducedBasis(ordinal_type max_p, value_type threshold, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &F, const Teuchos::Array< value_type > &weights, Teuchos::Array< Stokhos::MultiIndex< ordinal_type > > &terms_, Teuchos::Array< ordinal_type > &num_terms_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &Qp_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &Q_)
Build the reduced basis, parameterized by total order max_p.
Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product me...
Teuchos::SerialDenseMatrix< ordinal_type, value_type > SDM
MonomialGramSchmidtPCEBasis(ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, const Teuchos::ParameterList ¶ms=Teuchos::ParameterList())
Constructor.
void setup(ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad)
Abstract base class for quadrature methods.
virtual const std::string & getName() const
Return string name of basis.
virtual ~MonomialGramSchmidtPCEBasis()
Destructor.
Encapsulate various orthogonalization (ie QR) methods.