Packed storage matrix


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:
Both of the following storage schemes are used extensively in BLAS and LAPACK.
An example of packed storage for hermitian matrix:

complex:: A ! a hermitian matrix
complex:: AP ! 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*/2
 A = AP
 A = conjg
end do

An example of packed storage for banded matrix:

real:: A ! a banded matrix with kl subdiagonals and ku superdiagonals
real:: AP ! 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:min) A = AP
end do
print *,AP ! the diagonal