lapack-complex-ungqr.cc (flens/examples/lapack-complex-ungqr.cc)

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#include <cxxstd/iostream.h>

#include <flens/flens.cxx>

using namespace std;

using namespace flens;

int

main()

{

    typedef complex<double>             Complex;

    const Complex                       I(0,1);

    GeMatrix<FullStorage<Complex> >     A(4,4), Q;

    DenseVector<Array<Complex> >        b(4);

    DenseVector<Array<Complex> >        tau;

    //DenseVector<Array<Complex> >      work;

    A =  2,   3,  -1,   0,

        -6,  -5,   0,   2,

         2,  -5,   6,  -6,

         4,   6,   2,  -3;

    A *= I;

    b = 20,

       -33,

       -43,

        49;

    b *= I;

    cout << "A = " << A << endl;

    cout << "b = " << b << endl;

///

/// Compute the factorization $A = QR$.  Note that the workspace gets created

/// implicitly and temporarily.  So you might not want to do this inside a loop.

///

    lapack::qrf(A, tau);

    //lapack::qrf(A, tau, work);

///

/// Explicitly setup $Q$.

///

    Q = A;

    lapack::ungqr(Q, tau);

    //lapack::orgqr(Q, tau, work);

    cout << "Q = " << Q << endl;

///

/// Compute $\tilde{b} = Q^T b$.

///

    DenseVector<Array<Complex> >  x;

    x = conjTrans(Q)*b;

///

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

///

    const auto R = A.upper();

    blas::sv(NoTrans, R, x);

    cout << "x = " << x << endl;

}