StandardPacked.jl

StandardPacked is a Julia package that wraps functions for storing symmetric matrices in their standard packed form, i.e., column-wise stacked upper or lower triangles. It also provides bindings for the corresponding LAPACK functions, which allow things such as eigendecompositions. Note that typically, the packed form requires a bit longer calculation times and is slightly more imprecise than the dense form; however, it requires less storage.

Additionally, this package also provides the scaled form of the packed storage, in which off-diagonal elements are scaled by a factor of $\sqrt2$. This kind of format is very often used as input to semidefinite solvers, as it has the advantage that the scalar product between the vectorizations of two packed matrices is the same as the Hilbert-Schmidt/Frobenius scalar product between the actual matrices.

Note that neither of those formats correspond to the rectangular full packed format. The latter has the same favorable scaling with respect to memory, but additionally a better layout for some linear algebra routines, making it almost as fast as the dense format. However, index access is a bit weird there and it is not in wide use; furthermore, there are far fewer LAPACK functions working with RFP. Consider RectangularFullPacked.jl instead.