void operator()(MatrixT& A, VectorT& b, VectorT& x)
{
row_normalize_system(A, b);
//
// Determine the linear solver kernel and forward to an internal solve method
// which determines the preconditioner and actually calls the solver backend
//
if(solver_id_ == viennafvm::linsolv::viennacl::solver_ids::bicgstab)
{
// std::cout << "using solver: bicgstab .. " << std::endl;
::viennacl::linalg::bicgstab_tag solver_tag(break_tolerance_, max_iterations_);
solve_intern(A, b, x, solver_tag);
}
else
if(solver_id_ == viennafvm::linsolv::viennacl::solver_ids::gmres)
{
// std::cout << "using solver: gmres .. " << std::endl;
::viennacl::linalg::gmres_tag solver_tag(break_tolerance_, max_iterations_);
solve_intern(A, b, x, solver_tag);
}
else
if(solver_id_ == viennafvm::linsolv::viennacl::solver_ids::cg)
{
// std::cout << "using solver: cg .. " << std::endl;
::viennacl::linalg::cg_tag solver_tag(break_tolerance_, max_iterations_);
solve_intern(A, b, x, solver_tag);
}
else
{
std::cerr << "[ERROR] ViennaFVM::LinearSolver: solver not supported .. " << std::endl;
}
}
VectorType solve(MatrixType const & system_matrix,
VectorType const & rhs,
viennashe::solvers::linear_solver_config const & config,
viennashe::solvers::serial_linear_solver_tag
)
{
typedef typename VectorType::value_type NumericT;
//
// Step 1: Convert data to ViennaCL types:
//
viennacl::compressed_matrix<NumericT> A(system_matrix.size1(), system_matrix.size2());
viennacl::vector<NumericT> b(system_matrix.size1());
viennacl::fast_copy(&(rhs[0]), &(rhs[0]) + rhs.size(), b.begin());
detail::copy(system_matrix, A);
//
// Step 2: Setup preconditioner and run solver
//
log::info<log_linear_solver>() << "* solve(): Computing preconditioner (single-threaded)... " << std::endl;
//viennacl::linalg::ilut_tag precond_tag(config.ilut_entries(),
// config.ilut_drop_tolerance());
viennacl::linalg::ilu0_tag precond_tag;
viennacl::linalg::ilu0_precond<viennacl::compressed_matrix<NumericT> > preconditioner(A, precond_tag);
log::info<log_linear_solver>() << "* solve(): Solving system (single-threaded)... " << std::endl;
viennacl::linalg::bicgstab_tag solver_tag(config.tolerance(), config.max_iters());
//log::debug<log_linear_solver>() << "Compressed matrix: " << system_matrix << std::endl;
//log::debug<log_linear_solver>() << "Compressed rhs: " << rhs << std::endl;
viennacl::vector<NumericT> vcl_result = viennacl::linalg::solve(A,
b,
solver_tag,
preconditioner);
//log::debug<log_linear_solver>() << "Number of iterations (ILUT): " << solver_tag.iters() << std::endl;
//
// Step 3: Convert data back:
//
VectorType result(vcl_result.size());
viennacl::fast_copy(vcl_result.begin(), vcl_result.end(), &(result[0]));
viennashe::util::check_vector_for_valid_entries(result);
//
// As a check, compute residual:
//
log::info<log_linear_solver>() << "* solve(): residual: "
<< viennacl::linalg::norm_2(viennacl::linalg::prod(A, vcl_result) - b) / viennacl::linalg::norm_2(b)
<< " after " << solver_tag.iters() << " iterations." << std::endl;
//log::debug<log_linear_solver>() << "SHE result (compressed): " << compressed_result << std::endl;
return result;
}
/**
* The main steps in this tutorial are the following:
* - Setup the systems
* - Run solvers without preconditioner and with ILUT preconditioner for comparison
* - Run solver with SPAI preconditioner on CPU
* - Run solver with SPAI preconditioner on GPU
* - Run solver with factored SPAI preconditioner on CPU
* - Run solver with factored SPAI preconditioner on GPU
*
**/
int main (int, const char **)
{
typedef float ScalarType;
typedef boost::numeric::ublas::compressed_matrix<ScalarType> MatrixType;
typedef boost::numeric::ublas::vector<ScalarType> VectorType;
typedef viennacl::compressed_matrix<ScalarType> GPUMatrixType;
typedef viennacl::vector<ScalarType> GPUVectorType;
/**
* If you have multiple OpenCL-capable devices in your system, we pick the second device for this tutorial.
**/
#ifdef VIENNACL_WITH_OPENCL
// Optional: Customize OpenCL backend
viennacl::ocl::platform pf = viennacl::ocl::get_platforms()[0];
std::vector<viennacl::ocl::device> const & devices = pf.devices();
// Optional: Set first device to first context:
viennacl::ocl::setup_context(0, devices[0]);
// Optional: Set second device for second context (use the same device for the second context if only one device available):
if (devices.size() > 1)
viennacl::ocl::setup_context(1, devices[1]);
else
viennacl::ocl::setup_context(1, devices[0]);
std::cout << viennacl::ocl::current_device().info() << std::endl;
viennacl::context ctx(viennacl::ocl::get_context(1));
#else
viennacl::context ctx;
#endif
/**
* Create uBLAS-based sparse matrix and read system matrix from file
**/
MatrixType M;
if (!viennacl::io::read_matrix_market_file(M, "../examples/testdata/mat65k.mtx"))
{
std::cerr<<"ERROR: Could not read matrix file " << std::endl;
exit(EXIT_FAILURE);
}
std::cout << "Size of matrix: " << M.size1() << std::endl;
std::cout << "Avg. Entries per row: " << double(M.nnz()) / static_cast<double>(M.size1()) << std::endl;
/**
* Use a constant load vector for simplicity
**/
VectorType rhs(M.size2());
for (std::size_t i=0; i<rhs.size(); ++i)
rhs(i) = ScalarType(1);
/**
* Create the ViennaCL matrix and vector and initialize with uBLAS data:
**/
GPUMatrixType gpu_M(M.size1(), M.size2(), ctx);
GPUVectorType gpu_rhs(M.size1(), ctx);
viennacl::copy(M, gpu_M);
viennacl::copy(rhs, gpu_rhs);
/**
* <h2>Solver Runs</h2>
* We use a relative tolerance of \f$ 10^{-10} \f$ with a maximum of 50 iterations for each use case.
* Usually more than 50 solver iterations are required for convergence, but this choice ensures shorter execution times and suffices for this tutorial.
**/
viennacl::linalg::bicgstab_tag solver_tag(1e-10, 50); //for simplicity and reasonably short execution times we use only 50 iterations here
/**
* The first reference is to use no preconditioner (CPU and GPU):
**/
std::cout << "--- Reference 1: Pure BiCGStab on CPU ---" << std::endl;
VectorType result = viennacl::linalg::solve(M, rhs, solver_tag);
std::cout << " * Solver iterations: " << solver_tag.iters() << std::endl;
VectorType residual = viennacl::linalg::prod(M, result) - rhs;
std::cout << " * Rel. Residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(rhs) << std::endl;
std::cout << "--- Reference 2: Pure BiCGStab on GPU ---" << std::endl;
GPUVectorType gpu_result = viennacl::linalg::solve(gpu_M, gpu_rhs, solver_tag);
std::cout << " * Solver iterations: " << solver_tag.iters() << std::endl;
GPUVectorType gpu_residual = viennacl::linalg::prod(gpu_M, gpu_result);
gpu_residual -= gpu_rhs;
std::cout << " * Rel. Residual: " << viennacl::linalg::norm_2(gpu_residual) / viennacl::linalg::norm_2(gpu_rhs) << std::endl;
/**
* The second reference is a standard ILUT preconditioner (only CPU):
**/
std::cout << "--- Reference 2: BiCGStab with ILUT on CPU ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::ilut_precond<MatrixType> ilut(M, viennacl::linalg::ilut_tag());
std::cout << " * Iterative solver run..." << std::endl;
run_solver(M, rhs, solver_tag, ilut);
/**
* <h2>Step 1: SPAI with CPU</h2>
**/
std::cout << "--- Test 1: CPU-based SPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::spai_precond<MatrixType> spai_cpu(M, viennacl::linalg::spai_tag(1e-3, 3, 5e-2));
std::cout << " * Iterative solver run..." << std::endl;
run_solver(M, rhs, solver_tag, spai_cpu);
/**
* <h2>Step 2: FSPAI with CPU</h2>
**/
std::cout << "--- Test 2: CPU-based FSPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::fspai_precond<MatrixType> fspai_cpu(M, viennacl::linalg::fspai_tag());
std::cout << " * Iterative solver run..." << std::endl;
run_solver(M, rhs, solver_tag, fspai_cpu);
/**
* <h2>Step 3: SPAI with GPU</h2>
**/
std::cout << "--- Test 3: GPU-based SPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::spai_precond<GPUMatrixType> spai_gpu(gpu_M, viennacl::linalg::spai_tag(1e-3, 3, 5e-2));
std::cout << " * Iterative solver run..." << std::endl;
run_solver(gpu_M, gpu_rhs, solver_tag, spai_gpu);
/**
* <h2>Step 4: FSPAI with GPU</h2>
**/
std::cout << "--- Test 4: GPU-based FSPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::fspai_precond<GPUMatrixType> fspai_gpu(gpu_M, viennacl::linalg::fspai_tag());
std::cout << " * Iterative solver run..." << std::endl;
run_solver(gpu_M, gpu_rhs, solver_tag, fspai_gpu);
/**
* That's it! Print success message and exit.
**/
std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;
return EXIT_SUCCESS;
}
int main (int argc, const char * argv[])
{
typedef float ScalarType;
typedef boost::numeric::ublas::compressed_matrix<ScalarType> MatrixType;
typedef boost::numeric::ublas::vector<ScalarType> VectorType;
typedef viennacl::compressed_matrix<ScalarType> GPUMatrixType;
typedef viennacl::vector<ScalarType> GPUVectorType;
MatrixType M;
//
// Read system matrix from file
//
#ifdef _MSC_VER
if (!viennacl::io::read_matrix_market_file(M, "../../examples/testdata/mat65k.mtx"))
#else
if (!viennacl::io::read_matrix_market_file(M, "../examples/testdata/mat65k.mtx"))
#endif
{
std::cerr<<"ERROR: Could not read matrix file " << std::endl;
exit(EXIT_FAILURE);
}
std::cout << "Size of matrix: " << M.size1() << std::endl;
std::cout << "Avg. Entries per row: " << M.nnz() / static_cast<double>(M.size1()) << std::endl;
//
// Use uniform load vector:
//
VectorType rhs(M.size2());
for (size_t i=0; i<rhs.size(); ++i)
rhs(i) = 1;
GPUMatrixType gpu_M(M.size1(), M.size2());
GPUVectorType gpu_rhs(M.size1());
viennacl::copy(M, gpu_M);
viennacl::copy(rhs, gpu_rhs);
///////////////////////////////// Tests to follow /////////////////////////////
viennacl::linalg::bicgstab_tag solver_tag(1e-10, 50); //for simplicity and reasonably short execution times we use only 50 iterations here
//
// Reference: No preconditioner:
//
std::cout << "--- Reference 1: Pure BiCGStab on CPU ---" << std::endl;
VectorType result = viennacl::linalg::solve(M, rhs, solver_tag);
std::cout << " * Solver iterations: " << solver_tag.iters() << std::endl;
VectorType residual = viennacl::linalg::prod(M, result) - rhs;
std::cout << " * Rel. Residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(rhs) << std::endl;
std::cout << "--- Reference 2: Pure BiCGStab on GPU ---" << std::endl;
GPUVectorType gpu_result = viennacl::linalg::solve(gpu_M, gpu_rhs, solver_tag);
std::cout << " * Solver iterations: " << solver_tag.iters() << std::endl;
GPUVectorType gpu_residual = viennacl::linalg::prod(gpu_M, gpu_result) - gpu_rhs;
std::cout << " * Rel. Residual: " << viennacl::linalg::norm_2(gpu_residual) / viennacl::linalg::norm_2(gpu_rhs) << std::endl;
//
// Reference: ILUT preconditioner:
//
std::cout << "--- Reference 2: BiCGStab with ILUT on CPU ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::ilut_precond<MatrixType> ilut(M, viennacl::linalg::ilut_tag());
std::cout << " * Iterative solver run..." << std::endl;
run_solver(M, rhs, solver_tag, ilut);
//
// Test 1: SPAI with CPU:
//
std::cout << "--- Test 1: CPU-based SPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::spai_precond<MatrixType> spai_cpu(M, viennacl::linalg::spai_tag(1e-3, 3, 5e-2));
std::cout << " * Iterative solver run..." << std::endl;
run_solver(M, rhs, solver_tag, spai_cpu);
//
// Test 2: FSPAI with CPU:
//
std::cout << "--- Test 2: CPU-based FSPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::fspai_precond<MatrixType> fspai_cpu(M, viennacl::linalg::fspai_tag());
std::cout << " * Iterative solver run..." << std::endl;
run_solver(M, rhs, solver_tag, fspai_cpu);
//
// Test 3: SPAI with GPU:
//
std::cout << "--- Test 3: GPU-based SPAI ---" << std::endl;
std::cout << " * Preconditioner setup..." << std::endl;
viennacl::linalg::spai_precond<GPUMatrixType> spai_gpu(gpu_M, viennacl::linalg::spai_tag(1e-3, 3, 5e-2));
std::cout << " * Iterative solver run..." << std::endl;
run_solver(gpu_M, gpu_rhs, solver_tag, spai_gpu);
return EXIT_SUCCESS;
}