Ginkgo  Generated from pipelines/1068515030 branch based on master. Ginkgo version 1.7.0
A numerical linear algebra library targeting many-core architectures
The iterative-refinement program

The iterative refinement solver example..

This example depends on simple-solver.

Table of contents
  1. Introduction
  2. The commented program
  1. Results
  2. The plain program

This example shows how to use the iterative refinement solver.

In this example, we first read in a matrix from file, then generate a right-hand side and an initial guess. An inaccurate CG solver is used as the inner solver to an iterative refinement (IR) method which solves a linear system. The example features the iteration count and runtime of the IR solver.

The commented program

#include <ginkgo/ginkgo.hpp>
#include <fstream>
#include <iomanip>
#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;
using vec = gko::matrix::Dense<ValueType>;
using real_vec = gko::matrix::Dense<RealValueType>;
using mtx = gko::matrix::Csr<ValueType, IndexType>;
using cg = gko::solver::Cg<ValueType>;
using ir = gko::solver::Ir<ValueType>;

Print version information

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

Figure out where to run the code

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(); }}};

executor where Ginkgo will perform the computation

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

Read data

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

Create RHS and initial guess as 1

gko::size_type size = A->get_size()[0];
auto host_x = gko::matrix::Dense<ValueType>::create(exec->get_master(),
gko::dim<2>(size, 1));
for (auto i = 0; i < size; i++) {
host_x->at(i, 0) = 1.;
}
auto x = gko::clone(exec, host_x);
auto b = gko::clone(exec, host_x);

Calculate initial residual by overwriting b

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

copy b again

b->copy_from(host_x);

Create solver factory

gko::size_type max_iters = 10000u;
RealValueType outer_reduction_factor{1e-12};
RealValueType inner_reduction_factor{1e-2};
auto solver_gen =
ir::build()
.with_solver(cg::build().with_criteria(
gko::stop::ResidualNorm<ValueType>::build()
.with_reduction_factor(inner_reduction_factor)))
.with_criteria(
gko::stop::Iteration::build().with_max_iters(max_iters),
gko::stop::ResidualNorm<ValueType>::build()
.with_reduction_factor(outer_reduction_factor))
.on(exec);

Create solver

auto solver = solver_gen->generate(A);
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
gko::log::Convergence<ValueType>::create();
solver->add_logger(logger);

Solve system

exec->synchronize();
std::chrono::nanoseconds time(0);
auto tic = std::chrono::steady_clock::now();
solver->apply(b, x);
auto toc = std::chrono::steady_clock::now();
time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);

Get residual

auto res = gko::as<real_vec>(logger->get_residual_norm());
std::cout << "Initial residual norm sqrt(r^T r):\n";
write(std::cout, initres);
std::cout << "Final residual norm sqrt(r^T r):\n";
write(std::cout, res);

Print solver statistics

std::cout << "IR iteration count: " << logger->get_num_iterations()
<< std::endl;
std::cout << "IR execution time [ms]: "
<< static_cast<double>(time.count()) / 1000000.0 << std::endl;
}

Results

This is the expected output:

Initial residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
194.679
Final residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
4.23821e-11
IR iteration count: 24
IR execution time [ms]: 0.794962

Comments about programming and debugging

The plain program

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#include <ginkgo/ginkgo.hpp>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <string>
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 cg = gko::solver::Cg<ValueType>;
using ir = gko::solver::Ir<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 = share(gko::read<mtx>(std::ifstream("data/A.mtx"), exec));
gko::size_type size = A->get_size()[0];
auto host_x = gko::matrix::Dense<ValueType>::create(exec->get_master(),
gko::dim<2>(size, 1));
for (auto i = 0; i < size; i++) {
host_x->at(i, 0) = 1.;
}
auto x = gko::clone(exec, host_x);
auto b = gko::clone(exec, host_x);
auto one = gko::initialize<vec>({1.0}, exec);
auto neg_one = gko::initialize<vec>({-1.0}, exec);
auto initres = gko::initialize<real_vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(initres);
b->copy_from(host_x);
gko::size_type max_iters = 10000u;
RealValueType outer_reduction_factor{1e-12};
RealValueType inner_reduction_factor{1e-2};
auto solver_gen =
ir::build()
.with_solver(cg::build().with_criteria(
gko::stop::ResidualNorm<ValueType>::build()
.with_reduction_factor(inner_reduction_factor)))
.with_criteria(
gko::stop::Iteration::build().with_max_iters(max_iters),
gko::stop::ResidualNorm<ValueType>::build()
.with_reduction_factor(outer_reduction_factor))
.on(exec);
auto solver = solver_gen->generate(A);
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
gko::log::Convergence<ValueType>::create();
solver->add_logger(logger);
exec->synchronize();
std::chrono::nanoseconds time(0);
auto tic = std::chrono::steady_clock::now();
solver->apply(b, x);
auto toc = std::chrono::steady_clock::now();
time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);
auto res = gko::as<real_vec>(logger->get_residual_norm());
std::cout << "Initial residual norm sqrt(r^T r):\n";
write(std::cout, initres);
std::cout << "Final residual norm sqrt(r^T r):\n";
write(std::cout, res);
std::cout << "IR iteration count: " << logger->get_num_iterations()
<< std::endl;
std::cout << "IR execution time [ms]: "
<< static_cast<double>(time.count()) / 1000000.0 << std::endl;
}
gko::matrix::Csr
CSR is a matrix format which stores only the nonzero coefficients by compressing each row of the matr...
Definition: matrix.hpp:54
gko::log::profile_event_category::solver
Solver events.
gko::log::Convergence::create
static std::unique_ptr< Convergence > create(std::shared_ptr< const Executor >, const mask_type &enabled_events=Logger::criterion_events_mask|Logger::iteration_complete_mask)
Creates a convergence logger.
Definition: convergence.hpp:106
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: dense_cache.hpp:48
gko::solver::Ir
Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the e...
Definition: ir.hpp:108
gko::size_type
std::size_t size_type
Integral type used for allocation quantities.
Definition: types.hpp:120
gko::matrix::Dense::at
value_type & at(size_type row, size_type col) noexcept
Returns a single element of the matrix.
Definition: dense.hpp:897
gko::clone
detail::cloned_type< Pointer > clone(const Pointer &p)
Creates a unique clone of the object pointed to by p.
Definition: utils_helper.hpp:203
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::version_info::get
static const version_info & get()
Returns an instance of version_info.
Definition: version.hpp:168
gko::stop::ResidualNorm
The ResidualNorm class is a stopping criterion which stops the iteration process when the actual resi...
Definition: residual_norm.hpp:138
gko::dim< 2 >
gko::solver::Cg
CG or the conjugate gradient method is an iterative type Krylov subspace method which is suitable for...
Definition: cg.hpp:74
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:324
gko::share
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition: utils_helper.hpp:254
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::OmpExecutor::create
static std::shared_ptr< OmpExecutor > create(std::shared_ptr< CpuAllocatorBase > alloc=std::make_shared< CpuAllocator >())
Creates a new OmpExecutor.
Definition: executor.hpp:1373
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:354
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::real
constexpr auto real(const T &x)
Returns the real part of the object.
Definition: math.hpp:1041
gko::one
constexpr T one()
Returns the multiplicative identity for T.
Definition: math.hpp:803
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