Ginkgo Generated from branch based on main. Ginkgo version 1.10.0
A numerical linear algebra library targeting many-core architectures
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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

}
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",
[] {
}},
{"hip",
[] {
}},
{"dpcpp",
[] {
}},
{"reference", [] { return gko::ReferenceExecutor::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.
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.
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.
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 = share(gko::read<mtx>(std::ifstream("data/A.mtx"), exec));
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:159

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);
static std::unique_ptr< Dense > create(std::shared_ptr< const Executor > exec, const dim< 2 > &size={}, size_type stride=0)
Creates an uninitialized Dense matrix of the specified size.
std::size_t size_type
Integral type used for allocation quantities.
Definition types.hpp:90
detail::cloned_type< Pointer > clone(const Pointer &p)
Creates a unique clone of the object pointed to by p.
Definition utils_helper.hpp:173
A type representing the dimensions of a multidimensional object.
Definition dim.hpp:26

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);
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:1574

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 =
solver->add_logger(logger);
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:73

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);
std::decay_t< T > * as(U *obj)
Performs polymorphic type conversion.
Definition utils_helper.hpp:307

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

#include <fstream>
#include <iomanip>
#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;
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",
[] {
}},
{"hip",
[] {
}},
{"dpcpp",
[] {
}},
{"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 =
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;
}
CSR is a matrix format which stores only the nonzero coefficients by compressing each row of the matr...
Definition csr.hpp:126
Dense is a matrix format which explicitly stores all values of the matrix.
Definition dense.hpp:120
CG or the conjugate gradient method is an iterative type Krylov subspace method which is suitable for...
Definition cg.hpp:50
Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the e...
Definition ir.hpp:85
static const version_info & get()
Returns an instance of version_info.
Definition version.hpp:139
@ solver
Solver events.
Definition profiler_hook.hpp:34
constexpr T one()
Returns the multiplicative identity for T.
Definition math.hpp:654
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
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:295
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition utils_helper.hpp:224