Ginkgo Generated from branch based on master. Ginkgo version 1.7.0
A numerical linear algebra library targeting many-core architectures
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The mixed-multigrid-solver program

The mixed multigrid 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 mixed-precision multigrid solver.

In this example, we first read in a matrix from a file, then generate a right-hand side and an initial guess. The multigrid solver can mix different precision of MultigridLevel. The example features the generating time and runtime of the multigrid 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 MixedType = float;
using IndexType = int;
CSR is a matrix format which stores only the nonzero coefficients by compressing each row of the matr...
Definition csr.hpp:146
Dense is a matrix format which explicitly stores all values of the matrix.
Definition dense.hpp:136
Parallel graph match (Pgm) is the aggregate method introduced in the paper M.
Definition pgm.hpp:76
A block-Jacobi preconditioner is a block-diagonal linear operator, obtained by inverting the diagonal...
Definition jacobi.hpp:216
CG or the conjugate gradient method is an iterative type Krylov subspace method which is suitable for...
Definition cg.hpp:76
FCG or the flexible conjugate gradient method is an iterative type Krylov subspace method which is su...
Definition fcg.hpp:82
Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the e...
Definition ir.hpp:112
Multigrid methods have a hierarchy of many levels, whose corase level is a subset of the fine level,...
Definition multigrid.hpp:136

Print version information

std::cout << gko::version_info::get() << std::endl;
const auto executor_string = argc >= 2 ? argv[1] : "reference";
static const version_info & get()
Returns an instance of version_info.
Definition version.hpp:168

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",
[] {
}},
{"hip",
[] {
}},
{"dpcpp",
[] {
0, gko::ReferenceExecutor::create());
}},
{"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:1373

executor where Ginkgo will perform the computation

const auto exec = exec_map.at(executor_string)(); // throws if not valid
const int mixed_int = argc >= 3 ? std::atoi(argv[2]) : 1;
const bool use_mixed = mixed_int != 0; // nonzero uses mixed
std::cout << "Using mixed precision? " << use_mixed << std::endl;

Read data

auto A = share(gko::read<mtx>(std::ifstream("data/A.mtx"), exec));
constexpr T one()
Returns the multiplicative identity for T.
Definition math.hpp:803

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);
std::size_t size_type
Integral type used for allocation quantities.
Definition types.hpp:120
A type representing the dimensions of a multidimensional object.
Definition dim.hpp:55

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-12;
auto iter_stop =
gko::share(gko::stop::Iteration::build().with_max_iters(100u).on(exec));
.with_baseline(gko::stop::mode::absolute)
.with_reduction_factor(tolerance)
.on(exec));
The ResidualNorm class is a stopping criterion which stops the iteration process when the actual resi...
Definition residual_norm.hpp:138
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
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition utils_helper.hpp:254

Create smoother factory (ir with bj)

auto smoother_gen = gko::share(
ir::build()
.with_solver(bj::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<ValueType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
.on(exec));
auto smoother_gen2 = gko::share(
ir2::build()
.with_solver(bj2::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<MixedType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
.on(exec));

Create RestrictProlong factory

auto mg_level_gen =
gko::share(pgm::build().with_deterministic(true).on(exec));
auto mg_level_gen2 =
gko::share(pgm2::build().with_deterministic(true).on(exec));

Create CoarsesSolver factory

auto coarsest_solver_gen = gko::share(
ir::build()
.with_solver(bj::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<ValueType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(4u))
.on(exec));
auto coarsest_solver_gen2 = gko::share(
ir2::build()
.with_solver(bj2::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<MixedType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(4u))
.on(exec));

Create multigrid factory

std::shared_ptr<gko::LinOpFactory> multigrid_gen;
if (use_mixed) {
multigrid_gen =
mg::build()
.with_max_levels(10u)
.with_min_coarse_rows(2u)
.with_pre_smoother(smoother_gen, smoother_gen2)
.with_post_uses_pre(true)
.with_mg_level(mg_level_gen, mg_level_gen2)
.with_level_selector([](const gko::size_type level,
Definition lin_op.hpp:146

The first (index 0) level will use the first mg_level_gen, smoother_gen which are the factories with ValueType. The rest of levels (>= 1) will use the second (index 1) mg_level_gen2 and smoother_gen2 which use the MixedType. The rest of levels will use different type than the normal multigrid.

return level >= 1 ? 1 : 0;
})
.with_coarsest_solver(coarsest_solver_gen2)
.with_criteria(iter_stop, tol_stop)
.on(exec);
} else {
multigrid_gen = mg::build()
.with_max_levels(10u)
.with_min_coarse_rows(2u)
.with_pre_smoother(smoother_gen)
.with_post_uses_pre(true)
.with_mg_level(mg_level_gen)
.with_coarsest_solver(coarsest_solver_gen)
.with_criteria(iter_stop, tol_stop)
.on(exec);
}
std::chrono::nanoseconds gen_time(0);
auto gen_tic = std::chrono::steady_clock::now();

auto solver = solver_gen->generate(A);

auto solver = multigrid_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);

Add logger

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:106

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 explicitly, because the residual is not available inside of the multigrid solver

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 << "Multigrid iteration count: "
<< logger->get_num_iterations() << std::endl;
std::cout << "Multigrid generation time [ms]: "
<< static_cast<double>(gen_time.count()) / 1000000.0 << std::endl;
std::cout << "Multigrid execution time [ms]: "
<< static_cast<double>(time.count()) / 1000000.0 << std::endl;
std::cout << "Multigrid 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
4.3589
Final residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
6.31088e-14
Multigrid iteration count: 9
Multigrid generation time [ms]: 3.35361
Multigrid execution time [ms]: 10.048
Multigrid execution time per iteration[ms]: 1.11644

Comments about programming and debugging

The plain program

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HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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******************************<GINKGO LICENSE>*******************************/
#include <ginkgo/ginkgo.hpp>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <string>
int main(int argc, char* argv[])
{
using ValueType = double;
using MixedType = float;
using IndexType = int;
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",
[] {
}},
{"hip",
[] {
}},
{"dpcpp",
[] {
0, gko::ReferenceExecutor::create());
}},
{"reference", [] { return gko::ReferenceExecutor::create(); }}};
const auto exec = exec_map.at(executor_string)(); // throws if not valid
const int mixed_int = argc >= 3 ? std::atoi(argv[2]) : 1;
const bool use_mixed = mixed_int != 0; // nonzero uses mixed
std::cout << "Using mixed precision? " << use_mixed << std::endl;
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-12;
auto iter_stop =
gko::share(gko::stop::Iteration::build().with_max_iters(100u).on(exec));
.with_baseline(gko::stop::mode::absolute)
.with_reduction_factor(tolerance)
.on(exec));
auto smoother_gen = gko::share(
ir::build()
.with_solver(bj::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<ValueType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
.on(exec));
auto smoother_gen2 = gko::share(
ir2::build()
.with_solver(bj2::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<MixedType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
.on(exec));
auto mg_level_gen =
gko::share(pgm::build().with_deterministic(true).on(exec));
auto mg_level_gen2 =
gko::share(pgm2::build().with_deterministic(true).on(exec));
auto coarsest_solver_gen = gko::share(
ir::build()
.with_solver(bj::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<ValueType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(4u))
.on(exec));
auto coarsest_solver_gen2 = gko::share(
ir2::build()
.with_solver(bj2::build().with_max_block_size(1u))
.with_relaxation_factor(static_cast<MixedType>(0.9))
.with_criteria(gko::stop::Iteration::build().with_max_iters(4u))
.on(exec));
std::shared_ptr<gko::LinOpFactory> multigrid_gen;
if (use_mixed) {
multigrid_gen =
mg::build()
.with_max_levels(10u)
.with_min_coarse_rows(2u)
.with_pre_smoother(smoother_gen, smoother_gen2)
.with_post_uses_pre(true)
.with_mg_level(mg_level_gen, mg_level_gen2)
.with_level_selector([](const gko::size_type level,
return level >= 1 ? 1 : 0;
})
.with_coarsest_solver(coarsest_solver_gen2)
.with_criteria(iter_stop, tol_stop)
.on(exec);
} else {
multigrid_gen = mg::build()
.with_max_levels(10u)
.with_min_coarse_rows(2u)
.with_pre_smoother(smoother_gen)
.with_post_uses_pre(true)
.with_mg_level(mg_level_gen)
.with_coarsest_solver(coarsest_solver_gen)
.with_criteria(iter_stop, tol_stop)
.on(exec);
}
std::chrono::nanoseconds gen_time(0);
auto gen_tic = std::chrono::steady_clock::now();
auto solver = multigrid_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);
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);
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 << "Multigrid iteration count: "
<< logger->get_num_iterations() << std::endl;
std::cout << "Multigrid generation time [ms]: "
<< static_cast<double>(gen_time.count()) / 1000000.0 << std::endl;
std::cout << "Multigrid execution time [ms]: "
<< static_cast<double>(time.count()) / 1000000.0 << std::endl;
std::cout << "Multigrid execution time per iteration[ms]: "
<< static_cast<double>(time.count()) / 1000000.0 /
logger->get_num_iterations()
<< std::endl;
}
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