A packed storage matrix, also known as packed matrix, is a term used in programming for representing an matrix. It is a more compact way than an m-by-n rectangular array by exploiting a special structure of the matrix.
Typical examples of matrices that can take advantage of packed storage include:
- symmetric or hermitian matrix
- Triangular matrix
- Banded matrix.
Code examples (Fortran)
Both of the following storage schemes are used extensively in BLAS and LAPACK.
An example of packed storage for hermitian matrix:
complex:: A(n,n) ! a hermitian matrix complex:: AP(n*(n+1)/2) ! packed storage for A ! the lower triangle of A is stored column-by-column in AP. ! unpacking the matrix AP to A do j=1,n k = j*(j-1)/2 A(1:j,j) = AP(1+k:j+k) A(j,1:j-1) = conjg(AP(1+k:j-1+k)) end do
An example of packed storage for banded matrix:
real:: A(m,n) ! a banded matrix with kl subdiagonals and ku superdiagonals real:: AP(-kl:ku,n) ! packed storage for A ! the band of A is stored column-by-column in AP. Some elements of AP are unused. ! unpacking the matrix AP to A do j=1,n forall(i=max(1,j-kl):min(m,j+ku)) A(i,j) = AP(i-j,j) end do print *,AP(0,:) ! the diagonal