For a symmetric matrix A, A(:) (full "vectorization") contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n+1)/2 entries on and below the main diagonal. The half-vectorization, built as following with the package:
> A(itril(size(A))),
of a symmetric n×n matrix A is the n(n+1)/2 × 1 column vector obtained by "vectorizing" only the lower triangular part of A.
This package provides functions for conveniently indexing the triangular parts (both lower and upper) parst as well as the diagonals of the matrix.
It also provides the so called Duplication and Elimination matrices which is used to convert between full and half-vectorization of the matrix.
The output indices are useful for programmers who wish to manipulate directly the triangular parts without calling built-in functions such as TRIU, TRIL and DIAG |
