Advanced usage

Installation

Htool is a C++11 header library, you need to download it, using for example

git clone https://github.com/htool-ddm/htool

and you need to include the header files contained in include/htool. Note that Htool requires

• a MPI implementation, to perform communications on parallel computing architectures,

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

And optionally

• LAPACK, to perform SVD compression,

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

Required inputs

At the very least, Htool requires a geometry and a function to generate the coefficients of the matrix you wish to compress. More precisely,

• the geometry is a matrix of size \(d\times N\), where \(N\) is the number of points and \(d\) the geometric dimension, stored in a column-major array,

• the function generating the coefficients is passed to Htool using the interface htool::VirtualGenerator.

Here is an example where we define the interaction between to set of points target_points and source_points with \(\kappa (x,y)=e^{-|x-y|}\):

class MyMatrix : public VirtualGenerator<double> {
 const vector<double> & target_points;
 const vector<double> & source_points;
 int dimension;

 public:
 MyMatrix(int dimension0, int nr, int nc, const vector<double> &p10, const  vector<double> &p20) : VirtualGenerator(nr, nc), target_points (target_points_0), source_points(source_points_0), dimension(dimension0) {}

 void copy_submatrix(int M, int N, const int *const rows, const int *const  cols, double *ptr) const override {
  for (int j = 0; j < M; j++) {
   for (int k = 0; k < N; k++) {
    double norm2=0;
    for (int p = 0; p < dimension; p++) {
     norm2+= (target_points[p+dimension*row[j]]-source_points[p+dimension*cols[k]])*(target_points[p+dimension*row[j]]-source_points[p+dimension*cols[k]]);
    }
    ptr[j + M * k] = exp(-sqrt(norm2));
   }
  }
 }
};

Note

Htool does not have any a priori information on the kernel, so it is up to the user to optimize the computations in htool::VirtualGenerator::copy_submatrix.

Build a HMatrix

Use a HMatrix

Full example

Solvers