The preconditioned-solver program

The 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

The commented program

#include <ginkgo/ginkgo.hpp>


#include <fstream>
#include <iostream>
#include <string>


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

Some shortcuts

using vec = gko::matrix::Dense<>;
using mtx = gko::matrix::Csr<>;
using cg = gko::solver::Cg<>;
using bj = gko::preconditioner::Jacobi<>;

Print version information

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

Figure out where to run the code

std::shared_ptr<gko::Executor> exec;
if (argc == 1 || std::string(argv[1]) == "reference") {
    exec = gko::ReferenceExecutor::create();
} else if (argc == 2 && std::string(argv[1]) == "omp") {
    exec = gko::OmpExecutor::create();
} else if (argc == 2 && std::string(argv[1]) == "cuda" &&
           gko::CudaExecutor::get_num_devices() > 0) {
    exec = gko::CudaExecutor::create(0, gko::OmpExecutor::create());
} else {
    std::cerr << "Usage: " << argv[0] << " [executor]" << std::endl;
    std::exit(-1);
}

Read data

auto A = 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);

Create solver factory

auto solver_gen =
    cg::build()
        .with_criteria(
            gko::stop::Iteration::build().with_max_iters(20u).on(exec),
            gko::stop::ResidualNormReduction<>::build()
                .with_reduction_factor(1e-20)
                .on(exec))

Add preconditioner, these 2 lines are the only difference from the simple solver example

.with_preconditioner(bj::build().with_max_block_size(8u).on(exec))
.on(exec);

Create solver

auto solver = solver_gen->generate(A);

Solve system

solver->apply(lend(b), lend(x));

Print solution

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

Calculate residual

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

    std::cout << "Residual norm sqrt(r^T r): \n";
    write(std::cout, lend(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
9.08137e-16

Comments about programming and debugging

The plain program

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#include <ginkgo/ginkgo.hpp>


#include <fstream>
#include <iostream>
#include <string>


int main(int argc, char *argv[])
{
    using vec = gko::matrix::Dense<>;
    using mtx = gko::matrix::Csr<>;
    using cg = gko::solver::Cg<>;
    using bj = gko::preconditioner::Jacobi<>;

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

    std::shared_ptr<gko::Executor> exec;
    if (argc == 1 || std::string(argv[1]) == "reference") {
        exec = gko::ReferenceExecutor::create();
    } else if (argc == 2 && std::string(argv[1]) == "omp") {
        exec = gko::OmpExecutor::create();
    } else if (argc == 2 && std::string(argv[1]) == "cuda" &&
               gko::CudaExecutor::get_num_devices() > 0) {
        exec = gko::CudaExecutor::create(0, gko::OmpExecutor::create());
    } else {
        std::cerr << "Usage: " << argv[0] << " [executor]" << std::endl;
        std::exit(-1);
    }

    auto A = 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 solver_gen =
        cg::build()
            .with_criteria(
                gko::stop::Iteration::build().with_max_iters(20u).on(exec),
                gko::stop::ResidualNormReduction<>::build()
                    .with_reduction_factor(1e-20)
                    .on(exec))
            .with_preconditioner(bj::build().with_max_block_size(8u).on(exec))
            .on(exec);
    auto solver = solver_gen->generate(A);

    solver->apply(lend(b), lend(x));

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

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

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