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// Thyra: Interfaces and Support for Abstract Numerical Algorithms
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#ifndef THYRA_SILLY_MODIFIED_GRAM_SHMIDT_HPP
#define THYRA_SILLY_MODIFIED_GRAM_SHMIDT_HPP
#include "Thyra_MultiVectorBase.hpp"
#include "Thyra_MultiVectorStdOps.hpp"
#include "Thyra_VectorStdOps.hpp"
#include "Thyra_DetachedMultiVectorView.hpp"
namespace Thyra {
/** \brief Silly little implementation of the modified Gram-Schmidt algorithm
* to compute a QR factorization A=Q*R of a multi-vector A.
*
* \param V [in/out] On input, V contains the columns of A to compute the QR
* factorization. On output, V contains the columns of Q.
*
* \param R [out] On output, contains the upper triangular matrix R.
*
* \ingroup Thyra_Op_Vec_examples_cg_grp
*/
template<class Scalar>
void sillyModifiedGramSchmidt(
const Ptr<MultiVectorBase<Scalar> > &V,
const Ptr<RCP<MultiVectorBase<Scalar> > > &R_out
)
{
typedef Teuchos::ScalarTraits<Scalar> ST; using Teuchos::as;
const int n = V->domain()->dim();
*R_out = createMembers(V->domain(), V->domain());
DetachedMultiVectorView<Scalar> R(*(*R_out));
for (int k = 0; k < n; ++k) {
R(k,k) = norm(*V->col(k));
Vt_S(V->col(k).ptr(), ST::one()/R(k,k));
for (int j = k+1; j < n; ++j) {
R(k,j) = scalarProd(*V->col(k), *V->col(j));
Vp_StV(V->col(j).ptr(), -R(k,j), *V->col(k));
}
}
} // end sillyModifiedGramSchmidt
} // namespace Thyra
#endif // THYRA_SILLY_MODIFIED_GRAM_SHMIDT_HPP
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