Examples of usage for hodlr-toolbox
These pages provide a list of possible usages for the hm-toolbox. Some examples apply both to the HSS and HODLR storage, some others are only given for one of the two; note that the functionalities are largely equivalent between the formats, so the steps in one format can usually be repeated in the other with no changes.
A notable exception is in the 'handle' constructor, which uses Adaptive Cross Approximation for the HODLR format, and randomized sampling in the HSS one. The latter also requires a fast matrix vector multiplication, which the former doesn't.
This difference can often be overcome relying on the conversion between the formats provided by the HM2HSS and HSS2HM functions.
- Computing the matrix exponential showcases the functions EXPM implemented in the toolbox; we see that in certain cases hierarchical formats can be superior to sparse approximation for the matrix exponential, despite the guaranteed exponential decay of the entries far from the diagonal.