Ginkgo: The ilu-preconditioned-solver program

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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(); }}};
gko::CudaExecutor::create
static std::shared_ptr< CudaExecutor > create(int device_id, std::shared_ptr< Executor > master, bool device_reset, allocation_mode alloc_mode=default_cuda_alloc_mode, CUstream_st *stream=nullptr)
Creates a new CudaExecutor.
gko::DpcppExecutor::create
static std::shared_ptr< DpcppExecutor > create(int device_id, std::shared_ptr< Executor > master, std::string device_type="all", dpcpp_queue_property property=dpcpp_queue_property::in_order)
Creates a new DpcppExecutor.
gko::HipExecutor::create
static std::shared_ptr< HipExecutor > create(int device_id, std::shared_ptr< Executor > master, bool device_reset, allocation_mode alloc_mode=default_hip_alloc_mode, CUstream_st *stream=nullptr)
Creates a new HipExecutor.
gko::OmpExecutor::create
static std::shared_ptr< OmpExecutor > create(std::shared_ptr< CpuAllocatorBase > alloc=std::make_shared< CpuAllocator >())
Creates a new OmpExecutor.
Definition executor.hpp:1396

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);
gko::read
std::unique_ptr< MatrixType > read(StreamType &&is, MatrixArgs &&... args)
Reads a matrix stored in matrix market format from an input stream.
Definition mtx_io.hpp:160
gko::share
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition utils_helper.hpp:224

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);
gko::preconditioner::Ilu
The Incomplete LU (ILU) preconditioner solves the equation for a given lower triangular matrix L,...
Definition ilu.hpp:117
gko::solver::UpperTrs
UpperTrs is the triangular solver which solves the system U x = b, when U is an upper triangular matr...
Definition triangular.hpp:237

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);
}
gko::initialize
std::unique_ptr< Matrix > initialize(size_type stride, std::initializer_list< typename Matrix::value_type > vals, std::shared_ptr< const Executor > exec, TArgs &&... create_args)
Creates and initializes a column-vector.
Definition dense.hpp:1593
gko::write
void write(StreamType &&os, MatrixPtrType &&matrix, layout_type layout=detail::mtx_io_traits< std::remove_cv_t< detail::pointee< MatrixPtrType > > >::default_layout)
Writes a matrix into an output stream in matrix market format.
Definition mtx_io.hpp:299

# 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);
}
gko::matrix::Csr
CSR is a matrix format which stores only the nonzero coefficients by compressing each row of the matr...
Definition csr.hpp:126
gko::matrix::Dense
Dense is a matrix format which explicitly stores all values of the matrix.
Definition dense.hpp:120
gko::solver::Gmres
GMRES or the generalized minimal residual method is an iterative type Krylov subspace method which is...
Definition gmres.hpp:75
gko::version_info::get
static const version_info & get()
Returns an instance of version_info.
Definition version.hpp:139
gko::one
constexpr T one()
Returns the multiplicative identity for T.
Definition math.hpp:654
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:264