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Notes about the implementation

We rely heavily on polymorphism to make the library easy to extend in terms of functionality.

Hierarchical matrix

HMatrix follows a policy-based design (strategy pattern compile time variant), where the policies are

  • the type of compression
  • the type of admissible condition

The first policy is made explicit by the abstract class LowRankMatrix. This class defines the interface used by HMatrix, meaning that it has a function build that need to be implemented to define concrete compression. It allows adding new types of compression easily.

Note also that the Cluster is a shared resource with a shared pointer, so that it can be shared by several instances of HMatrix.

Low-rank matrix

LowRankMatrix is an Abstract Base Class (ABC) that makes explicit the interface used by HMatrix. The pure virtual function is

virtual void build(const VirtualGenerator<T> &A, const VirtualCluster &t, const double *const xt, const int *const tabt, const VirtualCluster &s, const double *const xs, const int *const tabs) = 0;

If you want to add another type of compression, you need to define a derived class from LowRankMatrix that implement such a function. In this function you need to populate the data of a LowRankMatrix.

Clustering

HMatrix needs cluster objects that follows the interface defined with VirtualCluster. In particular, Htool defines Cluster in cluster.hpp, which also follows a policy-based design. The policy is the type of clustering, for example PCA, which defines how the clusters are divided recursively. It needs to implement the following method:

void recursive_build(const double *const x, const double *const r, const int *const tab, const double *const g, int nb_sons, MPI_Comm comm, std::stack<Cluster<PCA> *> &s, std::stack<std::vector<int>> &n)