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#include <vector>
#include <iostream>
#include <amgcl/backend/builtin.hpp>
#include <amgcl/adapter/crs_tuple.hpp>
#include <amgcl/coarsening/rigid_body_modes.hpp>
#include <amgcl/mpi/distributed_matrix.hpp>
#include <amgcl/mpi/make_solver.hpp>
#include <amgcl/mpi/amg.hpp>
#include <amgcl/mpi/coarsening/smoothed_aggregation.hpp>
#include <amgcl/mpi/relaxation/spai0.hpp>
#include <amgcl/mpi/solver/cg.hpp>
#include <amgcl/io/binary.hpp>
#include <amgcl/profiler.hpp>
#if defined(AMGCL_HAVE_PARMETIS)
# include <amgcl/mpi/partition/parmetis.hpp>
#elif defined(AMGCL_HAVE_SCOTCH)
# include <amgcl/mpi/partition/ptscotch.hpp>
#endif
int main(int argc, char *argv[]) {
// The command line should contain the matrix, the RHS, and the coordinate files:
if (argc < 4) {
std::cerr << "Usage: " << argv[0] << " <A.bin> <b.bin> <coo.bin>" << std::endl;
return 1;
}
amgcl::mpi::init mpi(&argc, &argv);
amgcl::mpi::communicator world(MPI_COMM_WORLD);
// The profiler:
amgcl::profiler<> prof("Nullspace");
// Read the system matrix, the RHS, and the coordinates:
prof.tic("read");
// Get the global size of the matrix:
ptrdiff_t rows = amgcl::io::crs_size<ptrdiff_t>(argv[1]);
// Split the matrix into approximately equal chunks of rows, and
// make sure each chunk size is divisible by 3.
ptrdiff_t chunk = (rows + world.size - 1) / world.size;
if (chunk % 3) chunk += 3 - chunk % 3;
ptrdiff_t row_beg = std::min(rows, chunk * world.rank);
ptrdiff_t row_end = std::min(rows, row_beg + chunk);
chunk = row_end - row_beg;
// Read our part of the system matrix, the RHS and the coordinates.
std::vector<ptrdiff_t> ptr, col;
std::vector<double> val, rhs, coo;
amgcl::io::read_crs(argv[1], rows, ptr, col, val, row_beg, row_end);
ptrdiff_t n, m;
amgcl::io::read_dense(argv[2], n, m, rhs, row_beg, row_end);
amgcl::precondition(n == rows && m == 1, "The RHS file has wrong dimensions");
amgcl::io::read_dense(argv[3], n, m, coo, row_beg / 3, row_end / 3);
amgcl::precondition(n * 3 == rows && m == 3, "The coordinate file has wrong dimensions");
prof.toc("read");
if (world.rank == 0) {
std::cout
<< "Matrix " << argv[1] << ": " << rows << "x" << rows << std::endl
<< "RHS " << argv[2] << ": " << rows << "x1" << std::endl
<< "Coords " << argv[3] << ": " << rows / 3 << "x3" << std::endl;
}
// Declare the backends and the solver type
typedef amgcl::backend::builtin<double> SBackend; // the solver backend
typedef amgcl::backend::builtin<float> PBackend; // the preconditioner backend
typedef amgcl::mpi::make_solver<
amgcl::mpi::amg<
PBackend,
amgcl::mpi::coarsening::smoothed_aggregation<PBackend>,
amgcl::mpi::relaxation::spai0<PBackend>
>,
amgcl::mpi::solver::cg<PBackend>
> Solver;
// The distributed matrix
auto A = std::make_shared<amgcl::mpi::distributed_matrix<SBackend>>(
world, std::tie(chunk, ptr, col, val));
// Partition the matrix, the RHS vector, and the coordinates.
// If neither ParMETIS not PT-SCOTCH are not available,
// just keep the current naive partitioning.
#if defined(AMGCL_HAVE_PARMETIS) || defined(AMGCL_HAVE_SCOTCH)
# if defined(AMGCL_HAVE_PARMETIS)
typedef amgcl::mpi::partition::parmetis<SBackend> Partition;
# elif defined(AMGCL_HAVE_SCOTCH)
typedef amgcl::mpi::partition::ptscotch<SBackend> Partition;
# endif
if (world.size > 1) {
auto t = prof.scoped_tic("partition");
Partition part;
// part(A) returns the distributed permutation matrix.
// Keep the DOFs belonging to the same grid nodes together
// (use block-wise partitioning with block size 3).
auto P = part(*A, 3);
auto R = transpose(*P);
// Reorder the matrix:
A = product(*R, *product(*A, *P));
// Reorder the RHS vector and the coordinates:
R->move_to_backend();
std::vector<double> new_rhs(R->loc_rows());
std::vector<double> new_coo(R->loc_rows());
amgcl::backend::spmv(1, *R, rhs, 0, new_rhs);
amgcl::backend::spmv(1, *R, coo, 0, new_coo);
rhs.swap(new_rhs);
coo.swap(new_coo);
// Update the number of the local rows
// (it may have changed as a result of permutation).
chunk = A->loc_rows();
}
#endif
// Solver parameters:
Solver::params prm;
prm.solver.maxiter = 500;
prm.precond.coarsening.aggr.eps_strong = 0;
// Convert the coordinates to the rigid body modes.
// The function returns the number of near null-space vectors
// (3 in 2D case, 6 in 3D case) and writes the vectors to the
// std::vector<double> specified as the last argument:
prm.precond.coarsening.aggr.nullspace.cols = amgcl::coarsening::rigid_body_modes(
3, coo, prm.precond.coarsening.aggr.nullspace.B);
// Initialize the solver with the system matrix.
prof.tic("setup");
Solver solve(world, A, prm);
prof.toc("setup");
// Show the mini-report on the constructed solver:
if (world.rank == 0) std::cout << solve << std::endl;
// Solve the system with the zero initial approximation:
int iters;
double error;
std::vector<double> x(chunk, 0.0);
prof.tic("solve");
std::tie(iters, error) = solve(*A, rhs, x);
prof.toc("solve");
// Output the number of iterations, the relative error,
// and the profiling data:
if (world.rank == 0) {
std::cout
<< "Iters: " << iters << std::endl
<< "Error: " << error << std::endl
<< prof << std::endl;
}
}
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