It All Starts With a General Matrix
In this session we introduce matrix types
Like the GeMatrix type these matrix types use a full storage scheme for storing their elements. Often you start we a GeMatrix and then create triangular views or symmetric views. Such an task often arises in the implementation of numerical algorithms. For example, in FLENS-LAPACK this is a often used feature of FLENS.
Example Code
We setup some general matrix and then create triangular and symmetric matric views that reference the upper or lower part.
#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;
auto U = A.upper();
cout << "U = " << U << endl;
auto SU = U.symmetric();
cout << "SU = " << SU << endl;
auto SL = A.lower().symmetric();
cout << "SL = " << SL << endl;
auto L = A.lowerUnit();
cout << "L = " << L << endl;
return 0;
}
Comments on Example Code
U is a triangular matrix referencing the upper triangular part.
cout << "U = " << U << endl;
SU is a symmetric matrix. The upper triangular part of SU is referencing U (which in turn references the upper part of A).
cout << "SU = " << SU << endl;
SL is a symmetric matrix. The lower triangular part of SL is referencing the lower part of A).
cout << "SL = " << SL << endl;
L is a unit triangular matrix referencing the lower part of A. The term “unit” denotes that elements on the diagonal are assumed to be one.
cout << "L = " << L << endl;
Compile and Run
$shell> cd flens/examples $shell> g++ -Wall -std=c++11 -I../.. tut03-page01-example.cc $shell> ./a.out A = 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 20 U = 1 2 3 4 0 6 7 8 0 0 7 6 0 0 0 20 SU = 1 2 3 4 2 6 7 8 3 7 7 6 4 8 6 20 SL = 1 5 9 5 5 6 8 4 9 8 7 3 5 4 3 20 L = 1 0 0 0 5 1 0 0 9 8 1 0 5 4 3 1