The simple solver with a custom logger example..
This example depends on simple-solver, simple-solver-logging, minimal-cuda-solver.
Introduction
The custom-logger example shows how Ginkgo's API can be leveraged to implement application-specific callbacks for Ginkgo's events. This is the most basic way of extending Ginkgo and a good first step for any application developer who wants to adapt Ginkgo to his specific needs.
Ginkgo's gko::log::Logger abstraction provides hooks to the events that happen during the library execution. These hooks concern any low-level event such as memory allocations, deallocations, copies and kernel launches up to high-level events such as linear operator applications and completion of solver iterations.
In this example, a simple logger is implemented to track the solver's recurrent residual norm and compute the true residual norm. At the end of the solver execution, a comparison table is shown on-screen.
About the example
Each example has the following sections:
-
Introduction:This gives an overview of the example and mentions any interesting aspects in the example that might help the reader.
-
The commented program: This section is intended for you to understand the details of the example so that you can play with it and understand Ginkgo and its features better.
-
Results: This section shows the results of the code when run. Though the results may not be completely the same, you can expect the behaviour to be similar.
-
The plain program: This is the complete code without any comments to have an complete overview of the code.
The commented program
return mtx->get_executor()->copy_val_to_host(mtx->get_const_values());
}
Utility function which computes the norm of a Ginkgo gko::matrix::Dense vector.
template <typename ValueType>
{
Get the executor of the vector
Initialize a result scalar containing the value 0.0.
auto b_norm =
gko::initialize<gko::matrix::Dense<gko::remove_complex<ValueType>>>(
{0.0}, exec);
Use the dense compute_norm2 function to compute the norm.
Use the other utility function to return the norm contained in b_norm
return get_first_element(b_norm.get());
}
Custom logger class which intercepts the residual norm scalar and solution vector in order to print a table of real vs recurrent (internal to the solvers) residual norms.
template <typename ValueType>
Output the logger's data in a table format
Print a header for the table
std::cout << "Recurrent vs true vs implicit residual norm:"
<< std::endl;
std::cout << '|' << std::setw(10) << "Iteration" << '|' << std::setw(25)
<< "Recurrent Residual Norm" << '|' << std::setw(25)
<< "True Residual Norm" << '|' << std::setw(25)
<< "Implicit Residual Norm" << '|' << std::endl;
Print a separation line. Note that for creating 10 characters std::setw() should be set to 11.
std::cout << '|' << std::setfill('-') << std::setw(11) << '|'
<< std::setw(26) << '|' << std::setw(26) << '|'
<< std::setw(26) << '|' << std::setfill(' ') << std::endl;
Print the data one by one in the form
std::cout << std::scientific;
for (std::size_t i = 0; i < iterations.size(); i++) {
std::cout << '|' << std::setw(10) << iterations[i] << '|'
<< std::setw(25) << recurrent_norms[i] << '|'
<< std::setw(25) << real_norms[i] << '|' << std::setw(25)
<< implicit_norms[i] << '|' << std::endl;
}
std::defaultfloat could be used here but some compilers do not support it properly, e.g. the Intel compiler
std::cout.unsetf(std::ios_base::floatfield);
Print a separation line
std::cout << '|' << std::setfill('-') << std::setw(11) << '|'
<< std::setw(26) << '|' << std::setw(26) << '|'
<< std::setw(26) << '|' << std::setfill(' ') << std::endl;
}
Customize the logging hook which is called everytime an iteration is completed
If the solver shares a residual norm, log its value
if (residual_norm) {
auto dense_norm = gko::as<gko_real_dense>(residual_norm);
Add the norm to the recurrent_norms vector
recurrent_norms.push_back(get_first_element(dense_norm));
Otherwise, use the recurrent residual vector
} else {
auto dense_residual = gko::as<gko_dense>(residual);
Compute the residual vector's norm
auto norm = compute_norm(dense_residual);
Add the computed norm to the recurrent_norms vector
recurrent_norms.push_back(norm);
}
If the solver shares the current solution vector
Extract the matrix from the solver
auto matrix = gko::as<gko::solver::detail::SolverBaseLinOp>(solver)
->get_system_matrix();
Store the matrix's executor
auto exec = matrix->get_executor();
Create a scalar containing the value 1.0
auto one = gko::initialize<gko_dense>({1.0}, exec);
Create a scalar containing the value -1.0
auto neg_one = gko::initialize<gko_dense>({-1.0}, exec);
Instantiate a temporary result variable
Compute the real residual vector by calling apply on the system matrix
matrix->apply(one, solution, neg_one, res);
Compute the norm of the residual vector and add it to the real_norms vector
real_norms.push_back(compute_norm(res.get()));
} else {
Add to the real_norms vector the value -1.0 if it could not be computed
real_norms.push_back(-1.0);
}
if (implicit_sq_residual_norm) {
auto dense_norm =
gko::as<gko_real_dense>(implicit_sq_residual_norm);
Add the norm to the implicit_norms vector
implicit_norms.push_back(std::sqrt(get_first_element(dense_norm)));
} else {
Add to the implicit_norms vector the value -1.0 if it could not be computed
implicit_norms.push_back(-1.0);
}
Add the current iteration number to the iterations vector
iterations.push_back(iteration);
}
Construct the logger
ResidualLogger()
:
gko::log::Logger(
gko::log::Logger::iteration_complete_mask)
{}
private:
Vector which stores all the recurrent residual norms
mutable std::vector<RealValueType> recurrent_norms{};
Vector which stores all the real residual norms
mutable std::vector<RealValueType> real_norms{};
Vector which stores all the implicit residual norms
mutable std::vector<RealValueType> implicit_norms{};
Vector which stores all the iteration numbers
mutable std::vector<std::size_t> iterations{};
};
int main(int argc, char* argv[])
{
Use some shortcuts. In Ginkgo, vectors are seen as a gko::matrix::Dense with one column/one row. The advantage of this concept is that using multiple vectors is a now a natural extension of adding columns/rows are necessary.
using ValueType = double;
using IndexType = int;
The gko::matrix::Csr class is used here, but any other matrix class such as gko::matrix::Coo, gko::matrix::Hybrid, gko::matrix::Ell or gko::matrix::Sellp could also be used.
The gko::solver::Cg is used here, but any other solver class can also be used.
Print the ginkgo version information.
Where do you want to run your solver ?
The gko::Executor class is one of the cornerstones of Ginkgo. Currently, we have support for an gko::OmpExecutor, which uses OpenMP multi-threading in most of its kernels, a gko::ReferenceExecutor, a single threaded specialization of the OpenMP executor and a gko::CudaExecutor which runs the code on a NVIDIA GPU if available.
- Note
- With the help of C++, you see that you only ever need to change the executor and all the other functions/ routines within Ginkgo should automatically work and run on the executor with any other changes.
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";
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(); }}};
executor where Ginkgo will perform the computation
const auto exec = exec_map.at(executor_string)();
Reading your data and transfer to the proper device.
Read the matrix, right hand side and the initial solution using the read function.
- Note
- Ginkgo uses C++ smart pointers to automatically manage memory. To this end, we use our own object ownership transfer functions that under the hood call the required smart pointer functions to manage object ownership. gko::share and gko::give are the functions that you would need to use.
auto A =
share(gko::read<mtx>(std::ifstream(
"data/A.mtx"), exec));
auto b = gko::read<vec>(std::ifstream("data/b.mtx"), exec);
auto x = gko::read<vec>(std::ifstream("data/x0.mtx"), exec);
const RealValueType reduction_factor = 1e-7;
Creating the solver
Generate the gko::solver factory. Ginkgo uses the concept of Factories to build solvers with certain properties. Observe the Fluent interface used here. Here a cg solver is generated with a stopping criteria of maximum iterations of 20 and a residual norm reduction of 1e-15. You also observe that the stopping criteria(gko::stop) are also generated from factories using their build methods. You need to specify the executors which each of the object needs to be built on.
auto solver_gen =
cg::build()
.with_criteria(gko::stop::Iteration::build().with_max_iters(20u),
.with_reduction_factor(reduction_factor))
.on(exec);
Instantiate a ResidualLogger logger.
auto logger = std::make_shared<ResidualLogger<ValueType>>();
Add the previously created logger to the solver factory. The logger will be automatically propagated to all solvers created from this factory.
solver_gen->add_logger(logger);
Generate the solver from the matrix. The solver factory built in the previous step takes a "matrix"(a gko::LinOp to be more general) as an input. In this case we provide it with a full matrix that we previously read, but as the solver only effectively uses the apply() method within the provided "matrix" object, you can effectively create a gko::LinOp class with your own apply implementation to accomplish more tasks. We will see an example of how this can be done in the custom-matrix-format example
auto solver = solver_gen->generate(A);
Finally, solve the system. The solver, being a gko::LinOp, can be applied to a right hand side, b to obtain the solution, x.
Print the solution to the command line.
std::cout << "Solution (x):\n";
Print the table of the residuals obtained from the logger
To measure if your solution has actually converged, you can measure the error of the solution. one, neg_one are objects that represent the numbers which allow for a uniform interface when computing on any device. To compute the residual, all you need to do is call the apply method, which in this case is an spmv and equivalent to the LAPACK z_spmv routine. Finally, you compute the euclidean 2-norm with the compute_norm2 function.
auto one = gko::initialize<vec>({1.0}, exec);
auto neg_one = gko::initialize<vec>({-1.0}, exec);
auto res = gko::initialize<real_vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(res);
std::cout << "Residual norm sqrt(r^T r):\n";
}
Results
The following is the expected result:
Solution (x):
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
Recurrent vs true vs implicit residual norm:
| Iteration| Recurrent Residual Norm| True Residual Norm| Implicit Residual Norm|
|----------|-------------------------|-------------------------|-------------------------|
| 0| 4.358899e+00| 4.358899e+00| 4.358899e+00|
| 1| 2.304548e+00| 2.304548e+00| 2.304548e+00|
| 2| 1.467706e+00| 1.467706e+00| 1.467706e+00|
| 3| 9.848751e-01| 9.848751e-01| 9.848751e-01|
| 4| 7.418330e-01| 7.418330e-01| 7.418330e-01|
| 5| 5.136231e-01| 5.136231e-01| 5.136231e-01|
| 6| 3.841650e-01| 3.841650e-01| 3.841650e-01|
| 7| 3.164394e-01| 3.164394e-01| 3.164394e-01|
| 8| 2.277088e-01| 2.277088e-01| 2.277088e-01|
| 9| 1.703121e-01| 1.703121e-01| 1.703121e-01|
| 10| 9.737220e-02| 9.737220e-02| 9.737220e-02|
| 11| 6.168306e-02| 6.168306e-02| 6.168306e-02|
| 12| 4.541231e-02| 4.541231e-02| 4.541231e-02|
| 13| 3.195304e-02| 3.195304e-02| 3.195304e-02|
| 14| 1.616058e-02| 1.616058e-02| 1.616058e-02|
| 15| 6.570152e-03| 6.570152e-03| 6.570152e-03|
| 16| 2.643669e-03| 2.643669e-03| 2.643669e-03|
| 17| 8.588089e-04| 8.588089e-04| 8.588089e-04|
| 18| 2.864613e-04| 2.864613e-04| 2.864613e-04|
| 19| 1.641952e-15| 2.107881e-15| 1.641952e-15|
|----------|-------------------------|-------------------------|-------------------------|
Residual norm sqrt(r^T r):
1 1
2.10788e-15
Comments about programming and debugging
The plain program
#include <ginkgo/ginkgo.hpp>
#include <fstream>
#include <map>
#include <iomanip>
#include <ios>
#include <iostream>
#include <string>
#include <vector>
template <typename ValueType>
{
}
template <typename ValueType>
{
auto b_norm =
gko::initialize<gko::matrix::Dense<gko::remove_complex<ValueType>>>(
{0.0}, exec);
return get_first_element(b_norm.get());
}
template <typename ValueType>
{
std::cout << "Recurrent vs true vs implicit residual norm:"
<< std::endl;
std::cout << '|' << std::setw(10) << "Iteration" << '|' << std::setw(25)
<< "Recurrent Residual Norm" << '|' << std::setw(25)
<< "True Residual Norm" << '|' << std::setw(25)
<< "Implicit Residual Norm" << '|' << std::endl;
std::cout << '|' << std::setfill('-') << std::setw(11) << '|'
<< std::setw(26) << '|' << std::setw(26) << '|'
<< std::setw(26) << '|' << std::setfill(' ') << std::endl;
std::cout << std::scientific;
for (std::size_t i = 0; i < iterations.size(); i++) {
std::cout << '|' << std::setw(10) << iterations[i] << '|'
<< std::setw(25) << recurrent_norms[i] << '|'
<< std::setw(25) << real_norms[i] << '|' << std::setw(25)
<< implicit_norms[i] << '|' << std::endl;
}
std::cout.unsetf(std::ios_base::floatfield);
std::cout << '|' << std::setfill('-') << std::setw(11) << '|'
<< std::setw(26) << '|' << std::setw(26) << '|'
<< std::setw(26) << '|' << std::setfill(' ') << std::endl;
}
bool) const override
{
if (residual_norm) {
auto dense_norm = gko::as<gko_real_dense>(residual_norm);
recurrent_norms.push_back(get_first_element(dense_norm));
} else {
auto dense_residual = gko::as<gko_dense>(residual);
auto norm = compute_norm(dense_residual);
recurrent_norms.push_back(norm);
}
if (solution) {
auto matrix = gko::as<gko::solver::detail::SolverBaseLinOp>(solver)
->get_system_matrix();
auto exec = matrix->get_executor();
auto one = gko::initialize<gko_dense>({1.0}, exec);
auto neg_one = gko::initialize<gko_dense>({-1.0}, exec);
matrix->apply(one, solution, neg_one, res);
real_norms.push_back(compute_norm(res.get()));
} else {
real_norms.push_back(-1.0);
}
if (implicit_sq_residual_norm) {
auto dense_norm =
gko::as<gko_real_dense>(implicit_sq_residual_norm);
implicit_norms.push_back(std::sqrt(get_first_element(dense_norm)));
} else {
implicit_norms.push_back(-1.0);
}
iterations.push_back(iteration);
}
ResidualLogger()
:
gko::log::Logger(
gko::log::Logger::iteration_complete_mask)
{}
private:
mutable std::vector<RealValueType> recurrent_norms{};
mutable std::vector<RealValueType> real_norms{};
mutable std::vector<RealValueType> implicit_norms{};
mutable std::vector<std::size_t> iterations{};
};
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 A =
share(gko::read<mtx>(std::ifstream(
"data/A.mtx"), exec));
auto b = gko::read<vec>(std::ifstream("data/b.mtx"), exec);
auto x = gko::read<vec>(std::ifstream("data/x0.mtx"), exec);
const RealValueType reduction_factor = 1e-7;
auto solver_gen =
cg::build()
.with_criteria(gko::stop::Iteration::build().with_max_iters(20u),
.with_reduction_factor(reduction_factor))
.on(exec);
auto logger = std::make_shared<ResidualLogger<ValueType>>();
solver_gen->add_logger(logger);
auto solver = solver_gen->generate(A);
std::cout << "Solution (x):\n";
logger->write();
auto one = gko::initialize<vec>({1.0}, exec);
auto neg_one = gko::initialize<vec>({-1.0}, exec);
auto res = gko::initialize<real_vec>({0.0}, exec);
A->apply(one, x, neg_one, b);
b->compute_norm2(res);
std::cout << "Residual norm sqrt(r^T r):\n";
}
1.8.16