The preconditioned solver example.
This example depends on preconditioned-solver.
This example shows how to use the adaptive precision block-Jacobi preconditioner.
In this example, we first read in a matrix from file, then generate a right-hand side and an initial guess. The preconditioned CG solver is enhanced with a block-Jacobi preconditioner that optimizes the storage format for the distinct inverted diagonal blocks to the numerical requirements. The example features the iteration count and runtime of the CG solver.
The commented program
const auto executor_string = argc >= 2 ? argv[1] : "reference";
Figure out where to run the code
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:1396
executor where Ginkgo will perform the computation
const auto exec = exec_map.at(executor_string)();
Read data
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
auto host_x = vec::create(exec->get_master(),
gko::dim<2>(size, 1));
for (auto i = 0; i < size; i++) {
host_x->at(i, 0) = 1.;
}
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
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
Create solver factory
const RealValueType reduction_factor = 1e-7;
auto solver_gen =
cg::build()
.with_criteria(gko::stop::Iteration::build().with_max_iters(10000u),
gko::stop::ResidualNorm<ValueType>::build()
.with_reduction_factor(reduction_factor))
Add preconditioner, these 2 lines are the only difference from the simple solver example
.with_preconditioner(
bj::build().with_max_block_size(16u).with_storage_optimization(
.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:314
Create solver
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
solver_gen->add_logger(logger);
auto solver = solver_gen->generate(A);
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
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 << "Implicit residual norm squared (r^2):\n";
write(std::cout, impl_res);
std::decay_t< T > * as(U *obj)
Performs polymorphic type conversion.
Definition utils_helper.hpp:307
Print solver statistics
std::cout << "CG iteration count: " << logger->get_num_iterations()
<< std::endl;
std::cout << "CG 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
5.69384e-06
Implicit residual norm squared (r^2):
%%MatrixMarket matrix array real general
1 1
1.27043e-15
CG iteration count: 5
CG execution time [ms]: 0.080041
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;
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{
{"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>(size, 1));
for (auto i = 0; i < size; i++) {
host_x->at(i, 0) = 1.;
}
A->apply(one, x, neg_one, b);
b->compute_norm2(initres);
b->copy_from(host_x);
const RealValueType reduction_factor = 1e-7;
auto solver_gen =
cg::build()
.with_criteria(gko::stop::Iteration::build().with_max_iters(10000u),
gko::stop::ResidualNorm<ValueType>::build()
.with_reduction_factor(reduction_factor))
.with_preconditioner(
bj::build().with_max_block_size(16u).with_storage_optimization(
.on(exec);
std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
solver_gen->add_logger(logger);
auto solver = solver_gen->generate(A);
exec->synchronize();
std::chrono::nanoseconds time(0);
auto tic = std::chrono::steady_clock::now();
auto toc = std::chrono::steady_clock::now();
time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);
std::cout << "Initial residual norm sqrt(r^T r):\n";
write(std::cout, initres);
std::cout << "Final residual norm sqrt(r^T r):\n";
std::cout << "Implicit residual norm squared (r^2):\n";
write(std::cout, impl_res);
std::cout << "CG iteration count: " << logger->get_num_iterations()
<< std::endl;
std::cout << "CG 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
A block-Jacobi preconditioner is a block-diagonal linear operator, obtained by inverting the diagonal...
Definition jacobi.hpp:190
CG or the conjugate gradient method is an iterative type Krylov subspace method which is suitable for...
Definition cg.hpp:50
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