The triangular shape is a special case of the banded shape. There
are four kinds of triangular matrices in MTL, based on the
Uplo argument:
| Uplo type | Sub | Super |
| upper | 0 | N - 1 |
| unit_upper | -1 | N - 1 |
| lower | M - 1 | 0 |
| unit_lower | M - 1 | -1 |
The following is an example of a triangle<upper> shaped
matrix:
[ 1 2 3 4 5 ]
[ 0 6 7 8 9 ]
[ 0 0 10 11 12 ]
[ 0 0 0 13 14 ]
[ 0 0 0 0 15 ]
The next example is of a triangle<unit_lower>
matrix. The main diagonal is not stored, since it consists of
all ones. The MTL algorithms recognize when a matrix is ``unit''
and perform a slightly different operation to take this into
account. The ones will not show up in an iteration of the
matrix, and access to the A(i,i) element of a unit lower/upper
matrix is an error.
[ 1 0 0 0 0 ]
[ 1 1 0 0 0 ]
[ 2 3 1 0 0 ]
[ 4 5 6 1 0 ]
[ 7 8 9 10 1 ]
Here are a couple examples of creating some triangular matrix types:
typedef matrix < double,
triangle,
banded<>,
column_major >::type UpperTriangle;
typedef matrix < double,
triangle,
packed<>,
row_major >::type UnitLowerTriangle;
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