dense2D<typename mtl::Collection
<typename mtl::Collection<VVector>::value_type
>::value_type, parameters<> >
inline orthogonalize_factors(VVector& v, tag::vector)
{
using ::mtl::two_norm;
using math::zero;
using mtl::size1D;
typedef typename mtl::Collection<VVector>::size_type Size;
typedef typename mtl::Collection<VVector>::value_type Vector;
typedef typename mtl::Collection<Vector>::value_type Scalar;
dense2D<Scalar, parameters<> > tau(size1D(v), size1D(v));
tau= zero(Scalar());
for (Size j= 0; j < size1D(v); ++j) {
for (Size i= 0; i < j; ++i) {
Scalar t= dot(entry1D(v, i), entry1D(v, j)) / tau[i][i];
tau[i][j]= t;
entry1D(v, j)-= t * entry1D(v, i);
}
tau[j][j]= dot(entry1D(v, j), entry1D(v, j));
}
return tau;
}
inline void orth(VVector& v, tag::vector)
{
typedef typename mtl::Collection<VVector>::size_type Size;
using mtl::size1D;
for (Size j= 0; j < size1D(v); ++j)
orth(v, j, tag::vector());
}
inline void orth(VVector& v, typename mtl::Collection<VVector>::size_type j, tag::vector)
{
using mtl::two_norm;
using mtl::size1D;
MTL_DEBUG_THROW_IF(j < 0 || j >= size1D(v), index_out_of_range());
typedef typename mtl::Collection<VVector>::size_type Size;
for (Size i= 0; i < j; ++i)
entry1D(v, j)-= dot(entry1D(v, i), entry1D(v, j)) * entry1D(v, i);
entry1D(v, j)/= two_norm(entry1D(v, j));
}