Packed storage matrix

A packed storage matrix, also known as packed matrix, is a term used in programming for representing an $m\times n$ 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:

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

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