First Steps

The term general matrix refers to a matrix that is not necessarily square or symmetric. Further, full storage denotes that all \(mn\) elements of a \(m \times n\) matrix get stored.

FLENS realizes this matrix type in class GeMatrix.
For the full storage scheme there are three classes
- FullStorage,
- FullStorageView and
- ConstFullStorageView.
The different storage schemes are used for providing matrix views (see below) and ensure const correctness. In short one can say View means that no memory gets allocated and Const that only read-access is granted.

For dense vectors FLENS defines the

class DenseVector and
corresponding storage schemes
- Array,
- ArrayView and
- ConstArrayView.

In a first example we allocate and initialize a general matrix and play around with it.

Example Code

flens/examples/tut01-page01-example.cc

#include <flens/flens.cxx>

#include <iostream>

using namespace flens;

using namespace std;

int

main()

{

    typedef GeMatrix<FullStorage<double, ColMajor> >  GEMatrix;

    GEMatrix A(4,4);

    A = 1, 2, 3,  4,

        5, 6, 7,  8,

        9, 8, 7,  6,

        5, 4, 3, 20;

    cout << "A = " << A << endl;

    cout << "Dim. of A: " << A.numRows() << " x " << A.numCols() << endl;

    cout << endl;

    cout << "Row indices: " << A.firstRow() << ".." << A.lastRow() << endl;

    cout << endl;

    cout << "Col indices: " << A.firstCol() << ".." << A.lastCol() << endl;

    cout << endl;

    A(3,2) = 42;

    cout << "changed element: A(3,2) = " << A(3,2) << endl;

    cout << endl;

    cout << "A = " << A << endl;

    A = 42;

    cout << "A = " << A << endl;

    return 0;

}

Comments on Example Code

We simply include everything of FLENS

#include <flens/flens.cxx>

#include <iostream>

Typedef for a general matrix with elements of type double. Internally elements are stored in column major order.

typedef GeMatrix<FullStorage<double, ColMajor> > GEMatrix;

Matrix A gets dynamically allocated and then initialized.

    GEMatrix A(4,4);

    A = 1, 2, 3,  4,

        5, 6, 7,  8,

        9, 8, 7,  6,

        5, 4, 3, 20;

Print the matrix content using output streams:

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

We print some information about matrix dimensions and index ranges. You will see that by default in FLENS indices start at 1 (like in Fortran):

    cout << "Dim. of A: " << A.numRows() << " x " << A.numCols() << endl;

    cout << endl;

    cout << "Row indices: " << A.firstRow() << ".." << A.lastRow() << endl;

    cout << endl;

    cout << "Col indices: " << A.firstCol() << ".." << A.lastCol() << endl;

    cout << endl;

Also for element access (write) we provide a Fortran-Style interface:

A(3,2) = 42;

The same for read access:

cout << "changed element: A(3,2) = " << A(3,2) << endl;

You also can fill the whole matrix with a new value:

A = 42;

Compile and Run

$shell> cd flens/examples                                                       
$shell> g++ -Wall -std=c++11 -I../.. tut01-page01-example.cc                    
$shell> ./a.out                                                                 
A = 
            1             2             3             4 
            5             6             7             8 
            9             8             7             6 
            5             4             3            20 
Dim. of A: 4 x 4
Row indices: 1..4
Col indices: 1..4
changed element: A(3,2) = 42
A = 
            1             2             3             4 
            5             6             7             8 
            9            42             7             6 
            5             4             3            20 
A = 
           42            42            42            42 
           42            42            42            42 
           42            42            42            42 
           42            42            42            42