lapack-geqp3.cc (flens/examples/lapack-geqp3.cc)

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#include <cxxstd/iostream.h>

#include <flens/flens.cxx>

using namespace std;

using namespace flens;

int

main()

{

    typedef GeMatrix<FullStorage<double> >   GeMatrix;

    typedef typename GeMatrix::IndexType     IndexType;

    typedef DenseVector<Array<IndexType> >   IndexVector;

    typedef DenseVector<Array<double> >      DenseVector;

    GeMatrix        A(4,4);

    IndexVector     jPiv;

    DenseVector     tau;

    DenseVector     b(4);

    //DenseVector   work;

    A =  2,   3,  -1,   0,

        -6,  -5,   0,   2,

         2,  -5,   6,  -6,

         4,   6,   2,  -3;

    b = 20,

       -33,

       -43,

        49;

    cout << "A = " << A << endl;

    cout << "b = " << b << endl;

///

/// Compute the factorization $AP = QR$.  As vector `jPiv` has initially length

/// zero it gets internally resized to length $n$ and initialized with Zero.

/// This means that *all columns are free columns*.  Also note that the

/// workspace gets created implicitly and temporarily.  So you might not want

/// to do this inside a loop.

///

    lapack::qp3(A, jPiv, tau);

    //lapack::qp3(A, jPiv, tau, work);

///

/// Compute $\tilde{b} = Q^H b$. Vector $b$ gets overwritten with $\tilde{b}$.

///

    lapack::ormqr(Left, Trans, A, tau, b);

    //lapack::ormqr(Left, Trans, A, tau, b, work);

///

/// Solve $R u = \tilde{b}$.  Vector $b$ gets overwritten with $u =P^T x$.

///

    blas::sv(NoTrans, A.upper(), b);

///

/// Compute $x = Pu$.  Note that we need an extra vector here!

///

    DenseVector     x(4);

    for (IndexType i=1; i<=x.length(); ++i) {

        x(jPiv(i)) = b(i);

    }

    cout << "x = " << x << endl;

///

/// Output some additional information:

///

    cout << "jPiv = " << jPiv << endl;

}