The IR-ILU preconditioned solver example.
This example depends on ilu-preconditioned-solver, iterative-refinement.
Introduction
About the example
This example shows how to combine iterative refinement with the adaptive precision block-Jacobi preconditioner in order to approximately solve the triangular systems occurring in ILU preconditioning. Using an adaptive precision block-Jacobi preconditioner matrix as inner solver for the iterative refinement method is equivalent to doing adaptive precision block-Jacobi relaxation in the triangular solves. This example roughly approximates the triangular solves with five adaptive precision block-Jacobi sweeps with a maximum block size of 16.
This example is motivated by "Multiprecision block-Jacobi for Iterative
Triangular Solves" (Göbel, Anzt, Cojean, Flegar, Quintana-Ortí, Euro-Par 2020). The theory and a detailed analysis can be found there.
The commented program
#include <ginkgo/ginkgo.hpp>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <map>
#include <string>
int main(int argc, char* argv[])
{
Some shortcuts
using ValueType = double;
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
A block-Jacobi preconditioner is a block-diagonal linear operator, obtained by inverting the diagonal...
Definition jacobi.hpp:216
GMRES or the generalized minimal residual method is an iterative type Krylov subspace method which is...
Definition gmres.hpp:79
Iterative refinement (IR) is an iterative method that uses another coarse method to approximate the e...
Definition ir.hpp:112
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
Print version information
static const version_info & get()
Returns an instance of version_info.
Definition version.hpp:168
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";
const unsigned int sweeps = argc == 3 ? std::atoi(argv[2]) : 5u;
std::map<std::string, std::function<std::shared_ptr<gko::Executor>()>>
exec_map{
{"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:1373
executor where Ginkgo will perform the computation
const auto exec = exec_map.at(executor_string)();
Read data
constexpr T one()
Returns the multiplicative identity for T.
Definition math.hpp:803
detail::shared_type< OwningPointer > share(OwningPointer &&p)
Marks the object pointed to by p as shared.
Definition utils_helper.hpp:254
Create RHS and initial guess as 1
auto host_x = vec::create(exec->get_master(),
gko::dim<2>(num_rows, 1));
host_x->at(i, 0) = 1.;
}
std::size_t size_type
Integral type used for allocation quantities.
Definition types.hpp:120
detail::cloned_type< Pointer > clone(const Pointer &p)
Creates a unique clone of the object pointed to by p.
Definition utils_helper.hpp:203
A type representing the dimensions of a multidimensional object.
Definition dim.hpp:55
Generate incomplete factors using ParILU
auto par_ilu_fact =
ParILU is an incomplete LU factorization which is computed in parallel.
Definition par_ilu.hpp:97
Generate concrete factorization for input matrix
auto par_ilu =
gko::share(par_ilu_fact->generate(A));
Generate an iterative refinement factory to be used as a triangular solver in the preconditioner application. The generated method is equivalent to doing five block-Jacobi sweeps with a maximum block size of 16.
bj::build()
.with_max_block_size(16u)
.on(exec));
auto trisolve_factory =
ir::build()
.with_solver(bj_factory)
.with_criteria(gko::stop::Iteration::build().with_max_iters(sweeps))
.on(exec);
static constexpr precision_reduction autodetect() noexcept
Returns a special encoding which instructs the algorithm to automatically detect the best precision.
Definition types.hpp:347
Generate an ILU preconditioner factory by setting lower and upper triangular solver - in this case the previously defined iterative refinement method.
.on(exec);
The Incomplete LU (ILU) preconditioner solves the equation for a given lower triangular matrix L,...
Definition ilu.hpp:115
Use incomplete factors to generate ILU preconditioner
auto ilu_preconditioner =
gko::share(ilu_pre_factory->generate(par_ilu));
Create stopping criteria for Gmres
const RealValueType reduction_factor{1e-12};
gko::stop::Iteration::build().with_max_iters(1000u).on(exec));
.with_reduction_factor(reduction_factor)
.on(exec));
The ResidualNorm class is a stopping criterion which stops the iteration process when the actual resi...
Definition residual_norm.hpp:138
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.
auto ilu_gmres_factory =
gmres::build()
.with_criteria(iter_stop, tol_stop)
.with_generated_preconditioner(ilu_preconditioner)
.on(exec);
Generate preconditioned solver for a specific target system
auto ilu_gmres = ilu_gmres_factory->generate(A);
Add logger
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
ilu_gmres->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
Warmup run
Solve system 100 times and take the average time.
std::chrono::nanoseconds time(0);
for (int i = 0; i < 100; i++) {
x->copy_from(clone_x);
auto tic = std::chrono::high_resolution_clock::now();
ilu_gmres->apply(b, x);
auto toc = std::chrono::high_resolution_clock::now();
time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);
}
std::cout << "Using " << sweeps << " block-Jacobi sweeps.\n";
Print solution
std::cout << "Solution (x):\n";
write(std::cout, x);
Get residual
std::cout << "GMRES iteration count: " << logger->get_num_iterations()
<< "\n";
std::cout << "GMRES execution time [ms]: "
<< static_cast<double>(time.count()) / 100000000.0 << "\n";
std::cout << "Residual norm sqrt(r^T r):\n";
write(std::cout, res);
}
Results
This is the expected output:
Using 5 block-Jacobi sweeps.
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
GMRES iteration count: 8
GMRES execution time [ms]: 0.377673
Residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
1.65303e-12
Comments about programming and debugging
The plain program
#include <ginkgo/ginkgo.hpp>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <map>
#include <string>
int main(int argc, char* argv[])
{
using ValueType = double;
using IndexType = int;
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";
const unsigned int sweeps = argc == 3 ? std::atoi(argv[2]) : 5u;
std::map<std::string, std::function<std::shared_ptr<gko::Executor>()>>
exec_map{
{"cuda",
[] {
}},
{"hip",
[] {
}},
{"dpcpp",
[] {
}},
{"reference", [] { return gko::ReferenceExecutor::create(); }}};
const auto exec = exec_map.at(executor_string)();
auto host_x = vec::create(exec->get_master(),
gko::dim<2>(num_rows, 1));
host_x->at(i, 0) = 1.;
}
auto par_ilu_fact =
auto par_ilu =
gko::share(par_ilu_fact->generate(A));
bj::build()
.with_max_block_size(16u)
.on(exec));
auto trisolve_factory =
ir::build()
.with_solver(bj_factory)
.with_criteria(gko::stop::Iteration::build().with_max_iters(sweeps))
.on(exec);
.on(exec);
auto ilu_preconditioner =
gko::share(ilu_pre_factory->generate(par_ilu));
const RealValueType reduction_factor{1e-12};
gko::stop::Iteration::build().with_max_iters(1000u).on(exec));
.with_reduction_factor(reduction_factor)
.on(exec));
auto ilu_gmres_factory =
gmres::build()
.with_criteria(iter_stop, tol_stop)
.with_generated_preconditioner(ilu_preconditioner)
.on(exec);
auto ilu_gmres = ilu_gmres_factory->generate(A);
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
ilu_gmres->add_logger(logger);
ilu_gmres->apply(b, x);
std::chrono::nanoseconds time(0);
for (int i = 0; i < 100; i++) {
x->copy_from(clone_x);
auto tic = std::chrono::high_resolution_clock::now();
ilu_gmres->apply(b, x);
auto toc = std::chrono::high_resolution_clock::now();
time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);
}
std::cout << "Using " << sweeps << " block-Jacobi sweeps.\n";
std::cout << "Solution (x):\n";
std::cout << "GMRES iteration count: " << logger->get_num_iterations()
<< "\n";
std::cout << "GMRES execution time [ms]: "
<< static_cast<double>(time.count()) / 100000000.0 << "\n";
std::cout << "Residual norm sqrt(r^T r):\n";
}
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