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

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#include <flens/flens.cxx>
#include <iostream>

using namespace flens;
using namespace std;

int
main()
{
    typedef complex<double>             Complex;
    const Complex                       I(0,1);

    GeMatrix<FullStorage<Complex> >     A(3, 3);
    DenseVector<Array<Complex> >        b(3);

///
/// Setup the raw data.
///
    A = 2, I ,    0,
        0, 2, 1.+I ,
        0, 0,    3;

    b = 1,
        2,
        3;

///
/// $H$ is a symmetric matrix view constructed from the lower triangular
/// part of $A$.  Note that $H$ only references data from $A$.
///
    auto H = A.upper().hermitian();

    cout << "H = " << H << endl;
    cout << "b = " << b << endl;

///
/// Computes the Cholesky factorization $H = L L^T$ where $L$ is lower
/// triangular.  Matrix $H$ (i.e. the lower triangular part of $A$) gets
/// overwritten with $L$.
///
    int info = lapack::potrf(H);

    if (info!=0) {
        cerr << "H is singular" << endl;
        return info;
    }

///
/// Solve $L u = b$
///
    lapack::trs(NoTrans, A.lower(), b);

///
/// Solve $L^T x = u$
///
    lapack::trs(Trans, A.lower(), b);

    cout << "x = inv(H)*b = " << b << endl;

    return 0;
}