Home Browse Files
      1
      2
      3
      4
      5
      6
      7
      8
      9
     10
     11
     12
     13
     14
     15
     16
     17
     18
     19
     20
     21
     22
     23
     24
     25
     26
     27
     28
     29
     30
     31
     32
     33
     34
     35
     36
     37
     38
     39
     40
     41
     42
     43
     44
     45
     46
     47
     48
     49
     50
     51
     52
     53
     54
     55
     56
     57
     58
     59
     60
     61
     62
     63
     64
     65
     66
     67
     68
     69
#include <cxxstd/iostream.h>
#include <flens/flens.cxx>

using namespace std;
using namespace flens;

typedef double   T;

int
main()
{
    ///
    ///  Define some convenient typedefs for the matrix/vector types
    ///  of our system of linear equations.
    ///
    typedef SbMatrix<BandStorage<T> >           SymmetricBandMatrix;
    typedef DenseVector<Array<T> >              Vector;

    ///
    ///  We also need an extra vector type for the pivots.  The type of the
    ///  pivots is taken for the system matrix.
    ///
    typedef SymmetricBandMatrix::IndexType      IndexType;

    ///
    ///  Set up the baby problem ...
    ///
    const IndexType n = 4;

    ///
    ///  We allocate a symmetric band matrix with one off-diagonal.
    ///
    SymmetricBandMatrix     A(n, Upper, 1);

    Vector                  b(n);

    ///
    ///  We initialize the positiv definite $n \times n$ tridiagonal matrix.
    ///
    A.general().diag( 1) = -1;
    A.general().diag( 0) =  2;

    b =  1,
         2,
         3,
         4;

    cout << "A = " << A << endl;
    cout << "b = " << b << endl;

    ///
    /// We factorize $A$ with __lapack::pbtrf__
    ///
    /// :links: __lapack::pbtrf__ -> doc:flens/lapack/pb/pbtrf
    lapack::pbtrf(A);

    ///
    /// In the upper part of $A$ now the triangular factor $L^T$ is stored.
    ///
    cout << "L^T = " << A.general().upper() << endl;

    ///
    /// Solve it with __lapack::pbtrs__
    ///
    /// :links: __lapack::pbtrs__ -> doc:flens/lapack/pb/pbtrs
    lapack::pbtrs(A, b);

    cout << "x = " << b << endl;
}





































































































Home