Ginkgo  Generated from pipelines/224724463 branch based on develop. Ginkgo version 1.3.0 A numerical linear algebra library targeting many-core architectures
The ilu-preconditioned-solver program

The ILU-preconditioned solver example..

This example depends on simple-solver.

1. Introduction
2. The commented program

# 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 <ginkgo/ginkgo.hpp>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <map>
#include <string>
int main(int argc, char *argv[])
{

Some shortcuts

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

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",
[] {
true);
}},
{"hip",
[] {
true);
}},
{"dpcpp",
[] {
}},
{"reference", [] { return gko::ReferenceExecutor::create(); }}};

executor where Ginkgo will perform the computation

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

Generate incomplete factors using ParILU

auto par_ilu_fact =

Generate concrete factorization for input matrix

auto par_ilu = 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 =
false>::build()
.on(exec);

Use incomplete factors to generate ILU preconditioner

auto ilu_preconditioner = ilu_pre_factory->generate(gko::share(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).on(exec),
.with_reduction_factor(reduction_factor)
.on(exec))
.with_generated_preconditioner(gko::share(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(gko::lend(b), gko::lend(x));

Print solution

std::cout << "Solution (x):\n";
write(std::cout, gko::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<real_vec>({0.0}, exec);
A->apply(gko::lend(one), gko::lend(x), gko::lend(neg_one), gko::lend(b));
b->compute_norm2(gko::lend(res));
std::cout << "Residual norm sqrt(r^T r):\n";
write(std::cout, gko::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
1.46249e-08

# The plain program

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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include <ginkgo/ginkgo.hpp>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <map>
#include <string>
int main(int argc, char *argv[])
{
using ValueType = double;
using RealValueType = gko::remove_complex<ValueType>;
using IndexType = int;
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",
[] {
true);
}},
{"hip",
[] {
true);
}},
{"dpcpp",
[] {
}},
{"reference", [] { return gko::ReferenceExecutor::create(); }}};
const auto exec = exec_map.at(executor_string)(); // throws if not valid
auto par_ilu_fact =
auto par_ilu = par_ilu_fact->generate(A);
auto ilu_pre_factory =
false>::build()
.on(exec);
auto ilu_preconditioner = ilu_pre_factory->generate(gko::share(par_ilu));
const RealValueType reduction_factor{1e-7};
auto ilu_gmres_factory =
gmres::build()
.with_criteria(
gko::stop::Iteration::build().with_max_iters(1000u).on(exec),
.with_reduction_factor(reduction_factor)
.on(exec))
.with_generated_preconditioner(gko::share(ilu_preconditioner))
.on(exec);
auto ilu_gmres = ilu_gmres_factory->generate(A);
ilu_gmres->apply(gko::lend(b), gko::lend(x));
std::cout << "Solution (x):\n";
write(std::cout, gko::lend(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(gko::lend(one), gko::lend(x), gko::lend(neg_one), gko::lend(b));
b->compute_norm2(gko::lend(res));
std::cout << "Residual norm sqrt(r^T r):\n";
write(std::cout, gko::lend(res));
}
gko::matrix::Csr
CSR is a matrix format which stores only the nonzero coefficients by compressing each row of the matr...
Definition: coo.hpp:51
gko::real
constexpr std::enable_if_t<!is_complex_s< T >::value, T > real(const T &x)
Returns the real part of the object.
Definition: math.hpp:817
gko::HipExecutor::create
static std::shared_ptr< HipExecutor > create(int device_id, std::shared_ptr< Executor > master, bool device_reset=false)
Creates a new HipExecutor.
gko::layout_type::array
The matrix should be written as dense matrix in column-major order.
gko::matrix::Dense
Dense is a matrix format which explicitly stores all values of the matrix.
Definition: coo.hpp:55
gko::CudaExecutor::create
static std::shared_ptr< CudaExecutor > create(int device_id, std::shared_ptr< Executor > master, bool device_reset=false)
Creates a new CudaExecutor.
gko::OmpExecutor::create
static std::shared_ptr< OmpExecutor > create()
Creates a new OmpExecutor.
Definition: executor.hpp:909
gko::stop::ResidualNormReduction
The ResidualNormReduction class is a stopping criterion which stops the iteration process when the re...
Definition: residual_norm.hpp:113
gko::solver::Gmres
GMRES or the generalized minimal residual method is an iterative type Krylov subspace method which is...
Definition: gmres.hpp:72
gko::write
void write(StreamType &&os, MatrixType *matrix, layout_type layout=layout_type::array)
Reads a matrix stored in matrix market format from an input stream.
Definition: mtx_io.hpp:134
gko::version_info::get
static const version_info & get()
Returns an instance of version_info.
Definition: version.hpp:168
gko::lend
std::enable_if< detail::have_ownership_s< Pointer >::value, detail::pointee< Pointer > * >::type lend(const Pointer &p)
Returns a non-owning (plain) pointer to the object pointed to by p.
Definition: utils.hpp:253
gko::DpcppExecutor::create
static std::shared_ptr< DpcppExecutor > create(int device_id, std::shared_ptr< Executor > master, std::string device_type="all")
Creates a new DpcppExecutor.
gko::share
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition: utils.hpp:210
gko::factorization::ParIlu
ParILU is an incomplete LU factorization which is computed in parallel.
Definition: par_ilu.hpp:95
gko::solver::UpperTrs
UpperTrs is the triangular solver which solves the system U x = b, when U is an upper triangular matr...
Definition: lower_trs.hpp:62
gko::remove_complex
typename detail::remove_complex_s< T >::type remove_complex
Obtain the type which removed the complex of complex/scalar type or the template parameter of class b...
Definition: math.hpp:344
gko::one
constexpr T one()
Returns the multiplicative identity for T.
Definition: math.hpp:742
gko::preconditioner::Ilu
The Incomplete LU (ILU) preconditioner solves the equation for a given lower triangular matrix L,...
Definition: ilu.hpp:113