void qr<T>::output(array_2d<T>& x) const
{
if(x.rows() != m || x.columns() != n)
x.resize(idx(m, n));
lapack_interface<T>::call_lapack_geqrf(x, a);
}
void qr<T>::output(array_2d<T>& q, array_2d<T>& r) const
{
array<T> tau(min_nm);
if(r.rows() != m || r.columns() != n)
r.resize(idx(m, n));
lapack_interface<T>::call_lapack_geqrf(r, tau, a);
//Now construct Q
//Q should be a MxM matrix
if(q.rows() != m || q.columns() != m)
q.resize(idx(m, m));
if(n <= m) {
//Q can hold the MxN values of R needed by lapack's xORGQR routines
for(size_t i = 0; i < m; i++)
for(size_t j = 0; j < n; j++)
q[m*j + i] = r(i,j);
lapack_interface<T>::call_lapack_orgqr(q, tau);
} else {
//create a new array and do a copy since
//Q cannot hold the MxN values of R as needed by lapack's xORGQR routines
array_2d<T> temp_q(r(all(), size_range(0, m - 1)));
lapack_interface<T>::call_lapack_orgqr(temp_q, tau);
//copy the Q values from temp
for(size_t i = 0; i < m; i++)
for(size_t j = 0; j < m; j++)
q[m*j + i] = temp_q[m*j + i];
}
// R is upper triangular
for(size_t i = 0; i < m; i++)
for(size_t j = 0; j < n; j++)
if(i > j)
r(i,j) = 0;
}