ILU Preconditioned Solver

The ILU-preconditioned solver example.

Kind: preconditioners
Builds on: simple-solver
Upstream source: examples/ilu-preconditioned-solver/ilu-preconditioned-solver.cpp in the Ginkgo repository.

Introduction

This example shows how to use incomplete factors generated via the ParILU algorithm to generate an incomplete factorization (ILU) preconditioner, how to specify the sparse triangular solves in the ILU preconditioner application, and how to generate an ILU-preconditioned solver and apply it to a specific problem.

The commented program

#include <cstdlib>
#include <fstream>
#include <iostream>
#include <map>
#include <string>

#include <ginkgo/ginkgo.hpp>


int main(int argc, char* argv[])
{

Some shortcuts

    using ValueType = double;
    using RealValueType = gko::remove_complex<ValueType>;
    using IndexType = int;

    using vec = gko::matrix::Dense<ValueType>;
    using real_vec = gko::matrix::Dense<RealValueType>;
    using mtx = gko::matrix::Csr<ValueType, IndexType>;
    using gmres = gko::solver::Gmres<ValueType>;

Print version information

    std::cout << gko::version_info::get() << std::endl;

    if (argc == 2 && (std::string(argv[1]) == "--help")) {
        std::cerr << "Usage: " << argv[0] << " [executor]" << std::endl;
        std::exit(-1);
    }

    const auto executor_string = argc >= 2 ? argv[1] : "reference";

Figure out where to run the code

    std::map<std::string, std::function<std::shared_ptr<gko::Executor>()>>
        exec_map{
            {"omp", [] { return gko::OmpExecutor::create(); }},
            {"cuda",
             [] {
                 return gko::CudaExecutor::create(0,
                                                  gko::OmpExecutor::create());
             }},
            {"hip",
             [] {
                 return gko::HipExecutor::create(0, gko::OmpExecutor::create());
             }},
            {"dpcpp",
             [] {
                 return gko::DpcppExecutor::create(0,
                                                   gko::OmpExecutor::create());
             }},
            {"reference", [] { return gko::ReferenceExecutor::create(); }}};

executor where Ginkgo will perform the computation

    const auto exec = exec_map.at(executor_string)();  // throws if not valid

Read data

    auto A = gko::share(gko::read<mtx>(std::ifstream("data/A.mtx"), exec));
    auto b = gko::read<vec>(std::ifstream("data/b.mtx"), exec);
    auto x = gko::read<vec>(std::ifstream("data/x0.mtx"), exec);

Generate incomplete factors using ParILU

    auto par_ilu_fact =
        gko::factorization::ParIlu<ValueType, IndexType>::build().on(exec);

Generate concrete factorization for input matrix

    auto par_ilu = gko::share(par_ilu_fact->generate(A));

Generate an ILU preconditioner factory by setting lower and upper triangular solver - in this case the exact triangular solves

    auto ilu_pre_factory =
        gko::preconditioner::Ilu<ValueType, false, IndexType>::build().on(exec);

Use incomplete factors to generate ILU preconditioner

    auto ilu_preconditioner = gko::share(ilu_pre_factory->generate(par_ilu));

Use preconditioner inside GMRES solver factory Generating a solver factory tied to a specific preconditioner makes sense if there are several very similar systems to solve, and the same solver+preconditioner combination is expected to be effective.

    const RealValueType reduction_factor{1e-7};
    auto ilu_gmres_factory =
        gmres::build()
            .with_criteria(gko::stop::Iteration::build().with_max_iters(1000u),
                           gko::stop::ResidualNorm<ValueType>::build()
                               .with_reduction_factor(reduction_factor))
            .with_generated_preconditioner(ilu_preconditioner)
            .on(exec);

Generate preconditioned solver for a specific target system

    auto ilu_gmres = ilu_gmres_factory->generate(A);

Solve system

    ilu_gmres->apply(b, x);

Print solution

    std::cout << "Solution (x):\n";
    write(std::cout, x);

Calculate residual

    auto one = gko::initialize<vec>({1.0}, exec);
    auto neg_one = gko::initialize<vec>({-1.0}, exec);
    auto res = gko::initialize<real_vec>({0.0}, exec);
    A->apply(one, x, neg_one, b);
    b->compute_norm2(res);

    std::cout << "Residual norm sqrt(r^T r):\n";
    write(std::cout, res);
}

Results

This is the expected output:

Solution (x):
%%MatrixMarket matrix array real general
19 1
0.252218
0.108645
0.0662811
0.0630433
0.0384088
0.0396536
0.0402648
0.0338935
0.0193098
0.0234653
0.0211499
0.0196413
0.0199151
0.0181674
0.0162722
0.0150714
0.0107016
0.0121141
0.0123025
Residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
1.46249e-08

The plain program