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What is Htool?

Htool is an implementation of hierarchical matrices (cf. this reference or this one), it was written to test Domain Decomposition Methods (DDM) applied to Boundary Element Method (BEM). It provides:

  • routines to build hierarchical matrix structures (cluster trees, block trees, low-rank matrices and block matrices),
  • parallel matrix-vector and matrix-matrix product using MPI and OpenMP,
  • preconditioning techniques using domain decomposition methods,
  • the possibility to use Htool with any generator of coefficients (e.g., your own BEM library),
  • an interface with HPDDM for iterative solvers,
  • and several utility functions to display information about matrix structures and timing.

It is now used in FreeFEM starting from version 4.5, and we developed a Python interface using pybind11.

How to use Htool?


Htool is a header-only library written in C++11 with MPI and OpenMP, but it can be used without the latter if needed. Then, to use Htool, it requires:

  • BLAS, to perform algebraic operations (dense matrix-matrix or matrix-vector operations).

And if you want, it needs:

  • LAPACK, to perform SVD compression,
  • HPDDM and its dependencies (BLAS, LAPACK) to use iterative solvers and DDM preconditioners.


Since Htool is a header-only library, you can just include in your code the include folder of this repository. You can also use the following command to install the include folder in the one of your system to make it more widely available: in the root of this repository on your system, you can do:

mkdir build
cd build
cmake ..
cmake --build . --config Release --target install -- -j $(nproc)

Note that you can modify the install prefix using cmake .. -DCMAKE_INSTALL_PREFIX:PATH=your/install/path instead of the third line.

Embedding Htool in your code

We mostly refer to smallest_example.cpp and in the examples folder to see how to use Htool.

A function that generates the coefficients must be provided to Htool. To do so, a structure inheriting from IMatrix<T> must be defined with a method called T get_coef(const int& i, const int& j) const, where T is the type of your coefficients. This method will return the coefficient (i,j) of the considered problem. A method get_submatrix can also be defined to provide a more efficient way to build a sub-block of the matrix. An example of such interface is given in test_hmat_partialACA.hpp or BemTool (see bemtool/miscellaneous/htool_wrap.hpp). This new structure and the geometry will be used to define an object HMatrix.

A new type of compressor can also be added by defining a structure inheriting from LowRankMatrix with a method called build which populates the data members needed (see partialACA.hpp).

Python interface

See this repository.

Who is behind Htool?

If you need help or have questions regarding Htool, feel free to contact Pierre Marchand and Pierre-Henri Tournier.


University of Bath, United Kingdom
ANR NonlocalDD, (grant ANR-15-CE23-0017-01), France
Inria Paris, France
Laboratoire Jacques-Louis Lions Paris, France


Matthieu Ancellin
Xavier Claeys
Pierre Jolivet
Frédéric Nataf

ANR NonlocalDD