The ilu-preconditioned-solver program

The ILU-preconditioned solver example..

This example depends on simple-solver.

Table of contents
Introduction About the example The commented program	Results Comments about programming and debugging The plain program

Introduction

About the example

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

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<gko::solver::LowerTrs<ValueType, IndexType>,
                             gko::solver::UpperTrs<ValueType, IndexType>,
                             false>::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

Comments about programming and debugging

The plain program

#include <cstdlib>
#include <fstream>
#include <iostream>
#include <map>
#include <string>
 
#include <ginkgo/ginkgo.hpp>
 
 
int main(int argc, char* argv[])
{
    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>;
 
    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";
    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(); }}};
 
    const auto exec = exec_map.at(executor_string)();  // throws if not valid
 
    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);
 
    auto par_ilu_fact =
        gko::factorization::ParIlu<ValueType, IndexType>::build().on(exec);
    auto par_ilu = gko::share(par_ilu_fact->generate(A));
 
    auto ilu_pre_factory =
        gko::preconditioner::Ilu<gko::solver::LowerTrs<ValueType, IndexType>,
                                 gko::solver::UpperTrs<ValueType, IndexType>,
                                 false>::build()
            .on(exec);
 
    auto ilu_preconditioner = gko::share(ilu_pre_factory->generate(par_ilu));
 
    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);
 
    auto ilu_gmres = ilu_gmres_factory->generate(A);
 
    ilu_gmres->apply(b, x);
 
    std::cout << "Solution (x):\n";
    write(std::cout, x);
 
    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);
}