Ginkgo  Generated from pipelines/1589998975 branch based on develop. Ginkgo version 1.10.0
A numerical linear algebra library targeting many-core architectures
The multigrid-preconditioned-solver-customized program

The customized multigrid preconditioned solver example..

This example depends on multigrid-preconditioned-solver.

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

This example shows how to customize the multigrid preconditioner.

In this example, we first read in a matrix from a file. The preconditioned CG solver is enhanced with a multigrid preconditioner. Several non-default options are used to create this preconditioner. The example features the generating time and runtime of the CG solver.

The commented program

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::ReferenceExecutor::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 as 1 and initial guess as 0

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

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<vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(initres);

copy b again

b->copy_from(host_b);

Prepare the stopping criteria

const gko::remove_complex<ValueType> tolerance = 1e-8;
auto iter_stop =
gko::share(gko::stop::Iteration::build().with_max_iters(100u).on(exec));
auto tol_stop = gko::share(gko::stop::ResidualNorm<ValueType>::build()
.with_baseline(gko::stop::mode::absolute)
.with_reduction_factor(tolerance)
.on(exec));
auto exact_tol_stop =
gko::share(gko::stop::ResidualNorm<ValueType>::build()
.with_baseline(gko::stop::mode::rhs_norm)
.with_reduction_factor(1e-14)
.on(exec));
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
gko::log::Convergence<ValueType>::create();
iter_stop->add_logger(logger);
tol_stop->add_logger(logger);

Now we customize some settings of the multigrid preconditioner. First we choose a smoother. Since the input matrix is spd, we use iterative refinement with two iterations and an Ic solver.

auto ic_gen = gko::share(
ic::build()
.with_factorization(gko::factorization::Ic<ValueType, int>::build())
.on(exec));
auto smoother_gen = gko::share(
gko::solver::build_smoother(ic_gen, 2u, static_cast<ValueType>(0.9)));

Use Pgm as the MultigridLevel factory.

auto mg_level_gen =
gko::share(pgm::build().with_deterministic(true).on(exec));

Next we select a CG solver for the coarsest level. Again, since the input matrix is known to be spd, and the Pgm restriction preserves this characteristic, we can safely choose the CG. We reuse the Ic factory here to generate an Ic preconditioner. It is important to solve until machine precision here to get a good convergence rate.

auto coarsest_gen = gko::share(cg::build()
.with_preconditioner(ic_gen)
.with_criteria(iter_stop, exact_tol_stop)
.on(exec));

Here we put the customized options together and create the multigrid factory.

std::shared_ptr<gko::LinOpFactory> multigrid_gen;
multigrid_gen =
mg::build()
.with_max_levels(10u)
.with_min_coarse_rows(32u)
.with_pre_smoother(smoother_gen)
.with_post_uses_pre(true)
.with_mg_level(mg_level_gen)
.with_coarsest_solver(coarsest_gen)
.with_default_initial_guess(gko::solver::initial_guess_mode::zero)
.with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
.on(exec);

Create solver factory

auto solver_gen = cg::build()
.with_criteria(iter_stop, tol_stop)
.with_preconditioner(multigrid_gen)
.on(exec);

Create solver

std::chrono::nanoseconds gen_time(0);
auto gen_tic = std::chrono::steady_clock::now();
auto solver = solver_gen->generate(A);
exec->synchronize();
auto gen_toc = std::chrono::steady_clock::now();
gen_time +=
std::chrono::duration_cast<std::chrono::nanoseconds>(gen_toc - gen_tic);

Solve system

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

Calculate residual

auto res = gko::initialize<vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(res);
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 << "CG iteration count: " << logger->get_num_iterations()
<< std::endl;
std::cout << "CG generation time [ms]: "
<< static_cast<double>(gen_time.count()) / 1000000.0 << std::endl;
std::cout << "CG execution time [ms]: "
<< static_cast<double>(time.count()) / 1000000.0 << std::endl;
std::cout << "CG execution time per iteration[ms]: "
<< static_cast<double>(time.count()) / 1000000.0 /
logger->get_num_iterations()
<< std::endl;
}

Results

This is the expected output:

Initial residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
25.9808
Final residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
5.81328e-09
CG iteration count: 12
CG generation time [ms]: 1.41642
CG execution time [ms]: 6.59244
CG execution time per iteration[ms]: 0.54937

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 IndexType = int;
using vec = gko::matrix::Dense<ValueType>;
using mtx = gko::matrix::Csr<ValueType, IndexType>;
using cg = gko::solver::Cg<ValueType>;
using ir = gko::solver::Ir<ValueType>;
using mg = gko::solver::Multigrid;
using ic = gko::preconditioner::Ic<gko::solver::LowerTrs<ValueType>>;
using pgm = gko::multigrid::Pgm<ValueType, IndexType>;
std::cout << gko::version_info::get() << std::endl;
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::ReferenceExecutor::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 = vec::create(exec->get_master(), gko::dim<2>(size, 1));
auto host_b = vec::create(exec->get_master(), gko::dim<2>(size, 1));
for (auto i = 0; i < size; i++) {
host_x->at(i, 0) = 0.;
host_b->at(i, 0) = 1.;
}
auto x = vec::create(exec);
auto b = vec::create(exec);
x->copy_from(host_x);
b->copy_from(host_b);
auto one = gko::initialize<vec>({1.0}, exec);
auto neg_one = gko::initialize<vec>({-1.0}, exec);
auto initres = gko::initialize<vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(initres);
b->copy_from(host_b);
const gko::remove_complex<ValueType> tolerance = 1e-8;
auto iter_stop =
gko::share(gko::stop::Iteration::build().with_max_iters(100u).on(exec));
auto tol_stop = gko::share(gko::stop::ResidualNorm<ValueType>::build()
.with_baseline(gko::stop::mode::absolute)
.with_reduction_factor(tolerance)
.on(exec));
auto exact_tol_stop =
gko::share(gko::stop::ResidualNorm<ValueType>::build()
.with_baseline(gko::stop::mode::rhs_norm)
.with_reduction_factor(1e-14)
.on(exec));
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
gko::log::Convergence<ValueType>::create();
iter_stop->add_logger(logger);
tol_stop->add_logger(logger);
auto ic_gen = gko::share(
ic::build()
.with_factorization(gko::factorization::Ic<ValueType, int>::build())
.on(exec));
auto smoother_gen = gko::share(
gko::solver::build_smoother(ic_gen, 2u, static_cast<ValueType>(0.9)));
auto mg_level_gen =
gko::share(pgm::build().with_deterministic(true).on(exec));
auto coarsest_gen = gko::share(cg::build()
.with_preconditioner(ic_gen)
.with_criteria(iter_stop, exact_tol_stop)
.on(exec));
std::shared_ptr<gko::LinOpFactory> multigrid_gen;
multigrid_gen =
mg::build()
.with_max_levels(10u)
.with_min_coarse_rows(32u)
.with_pre_smoother(smoother_gen)
.with_post_uses_pre(true)
.with_mg_level(mg_level_gen)
.with_coarsest_solver(coarsest_gen)
.with_default_initial_guess(gko::solver::initial_guess_mode::zero)
.with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
.on(exec);
auto solver_gen = cg::build()
.with_criteria(iter_stop, tol_stop)
.with_preconditioner(multigrid_gen)
.on(exec);
std::chrono::nanoseconds gen_time(0);
auto gen_tic = std::chrono::steady_clock::now();
auto solver = solver_gen->generate(A);
exec->synchronize();
auto gen_toc = std::chrono::steady_clock::now();
gen_time +=
std::chrono::duration_cast<std::chrono::nanoseconds>(gen_toc - gen_tic);
exec->synchronize();
std::chrono::nanoseconds time(0);
auto tic = std::chrono::steady_clock::now();
solver->apply(b, x);
exec->synchronize();
auto toc = std::chrono::steady_clock::now();
time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);
auto res = gko::initialize<vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(res);
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 << "CG iteration count: " << logger->get_num_iterations()
<< std::endl;
std::cout << "CG generation time [ms]: "
<< static_cast<double>(gen_time.count()) / 1000000.0 << std::endl;
std::cout << "CG execution time [ms]: "
<< static_cast<double>(time.count()) / 1000000.0 << std::endl;
std::cout << "CG execution time per iteration[ms]: "
<< static_cast<double>(time.count()) / 1000000.0 /
logger->get_num_iterations()
<< 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:28
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:73
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:19
gko::solver::Ir
Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the e...
Definition: ir.hpp:81
gko::factorization::Ic
Represents an incomplete Cholesky factorization (IC(0)) of a sparse matrix.
Definition: ic.hpp:45
gko::size_type
std::size_t size_type
Integral type used for allocation quantities.
Definition: types.hpp:89
gko::preconditioner::Ic
The Incomplete Cholesky (IC) preconditioner solves the equation for a given lower triangular matrix ...
Definition: ic.hpp:113
gko::solver::Multigrid
Multigrid methods have a hierarchy of many levels, whose corase level is a subset of the fine level,...
Definition: multigrid.hpp:107
gko::solver::initial_guess_mode::zero
the input is zero
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:139
gko::stop::ResidualNorm
The ResidualNorm class is a stopping criterion which stops the iteration process when the actual resi...
Definition: residual_norm.hpp:113
gko::multigrid::Pgm
Parallel graph match (Pgm) is the aggregate method introduced in the paper M.
Definition: matrix.hpp:38
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:48
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:295
gko::share
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition: utils_helper.hpp:224
gko::solver::build_smoother
auto build_smoother(std::shared_ptr< const LinOpFactory > factory, size_type iteration=1, ValueType relaxation_factor=0.9)
build_smoother gives a shortcut to build a smoother by IR(Richardson) with limited stop criterion(ite...
Definition: ir.hpp:302
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:1396
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:260
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:869
gko::one
constexpr T one()
Returns the multiplicative identity for T.
Definition: math.hpp:630
Generated by   doxygen 1.8.16