ezp

ezp is a lightweight C++ wrapper for selected distributed solvers for linear systems.

Features

1. easy to use interface
2. drop-in header-only library
3. standalone solver binaries that can be invoked by various callers
4. random tested implementation

The following solvers are implemented.

availability	type of matrix	operation	solver	package
✅	general (partial pivoting)	simple	PxGESV	ScaLAPACK
✅	general (partial pivoting)	expert	PxGESVX	ScaLAPACK
✅	symmetric/Hermitian positive definite	simple	PxPOSV	ScaLAPACK
✅	symmetric/Hermitian positive definite	expert	PxPOSVX	ScaLAPACK
✅	general band (partial pivoting)	simple	PxGBSV	ScaLAPACK
✅	general band (no pivoting)	simple	PxDBSV	ScaLAPACK
✅	symmetric/Hermitian positive definite band	simple	PxPBSV	ScaLAPACK
✅	sparse (one- or zero-indexing CSR format)	direct	PARDISO	MKL
✅	sparse (one-indexing COO format)	direct	MUMPS	MUMPS
✅	sparse (zero-indexing CSR format)	iterative	Lis	Lis

Important

• Use branch master for development and testing.
• Use branch lite-lib for integration into other projects.

Dependency

The ezp library requires C++ 20 compatible compiler. The following drivers are needed.

1. an implementation of LAPACK and BLAS, such as OpenBLAS, MKL, etc.
2. an implementation of ScaLAPACK
3. an implementation of MPI, such as OpenMPI, MPICH, etc.

Example

It is assumed that the root node (rank 0) prepares the left hand side $$A$$ and right hand side $$B$$. The solvers distribute the matrices to available processes and solve the system, return the solution back to the master node.

The solvers are designed in such a way that all BLACS and ScaLAPACK details are hidden. One shall prepare the matrices (on the root node) and call the solver. The following is a typical example. It highly resembles the sequential version of how one would typically solve a linear system.

The following is a working example.

#include <ezp/pgesv.hpp>
#include <iomanip>
#include <iostream>

using namespace ezp;

int main() {
    // get the current blacs environment
    const auto rank = get_env<int>().rank();

    constexpr auto N = 6, NRHS = 2;

    // storage for the matrices A and B
    std::vector<double> A, B;

    if(0 == rank) {
        // the matrices are only initialized on the root process
        A.resize(N * N, 0.);
        B.resize(N * NRHS, 1.);

        // helper functor to convert 2D indices to 1D indices
        // it's likely the matrices are provided by some other subsystem
        const auto IDX = par_dgesv<int>::indexer{N};

        for(auto I = 0; I < N; ++I) A[IDX(I, I)] = static_cast<double>(I);
    }

    // create a parallel solver
    // it takes the number of rows and columns of the process grid as arguments
    // or let the library automatically determine as follows
    // need to wrap the data in full_mat objects
    // it requires the number of rows and columns of the matrix, and a pointer to the data
    // on non-root processes, the data pointer is nullptr as the vector is empty
    // par_dgesv<int>().solve(full_mat{N, N, A.data()}, full_mat{N, NRHS, B.data()});
    par_dgesv<int>().solve({N, N, A.data()}, {N, NRHS, B.data()});

    if(0 == rank) {
        std::cout << std::setprecision(10) << "Solution:\n";
        for(auto i = 0; i < B.size(); ++i) std::cout << B[i] << '\n';
    }

    return 0;
}