NodePartitioner.cpp

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*/
#include <cassert>
#include <algorithm>

#include "Exception.hpp"
#include "NodePartitioner.hpp"
#include "PetscMatTools.hpp"
#include "PetscTools.hpp"
#include "Timer.hpp"
#include "TrianglesMeshReader.hpp"
#include "Warnings.hpp"
#include "petscao.h"
#include "petscmat.h"

#include <parmetis.h>

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void NodePartitioner<ELEMENT_DIM, SPACE_DIM>::DumbPartitioning(AbstractMesh<ELEMENT_DIM, SPACE_DIM>& rMesh,
                                                               std::set<unsigned>& rNodesOwned)
{
    //Note that if there is not DistributedVectorFactory in the mesh, then a dumb partition based
    //on rMesh.GetNumNodes() is applied automatically.
    //If there is a DistributedVectorFactory then that one will be returned
    if (rMesh.GetDistributedVectorFactory()->GetProblemSize() != rMesh.GetNumNodes())
    {
        EXCEPTION("The distributed vector factory size in the mesh doesn't match the total number of nodes.");
    }

    for (unsigned node_index = rMesh.GetDistributedVectorFactory()->GetLow();
         node_index < rMesh.GetDistributedVectorFactory()->GetHigh();
         node_index++)
    {
         rNodesOwned.insert(node_index);
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void NodePartitioner<ELEMENT_DIM, SPACE_DIM>::PetscMatrixPartitioning(AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>& rMeshReader,
                                              std::vector<unsigned>& rNodePermutation,
                                              std::set<unsigned>& rNodesOwned,
                                              std::vector<unsigned>& rProcessorsOffset)
{
    assert(PetscTools::IsParallel());
    assert(ELEMENT_DIM==2 || ELEMENT_DIM==3);      // LCOV_EXCL_LINE // Metis works with triangles and tetras

    if (!PetscTools::HasParMetis()) //We must have ParMetis support compiled into Petsc
    {
        WARN_ONCE_ONLY("PETSc support for ParMetis is not installed.");      // LCOV_EXCL_LINE
    }

    unsigned num_nodes = rMeshReader.GetNumNodes();
    PetscInt num_procs = PetscTools::GetNumProcs();
    unsigned local_proc_index = PetscTools::GetMyRank();

    unsigned num_elements = rMeshReader.GetNumElements();
    unsigned num_local_elements = num_elements / num_procs;
    unsigned first_local_element = num_local_elements * local_proc_index;
    if (PetscTools::AmTopMost())
    {
        // Take the excess elements
        num_local_elements += num_elements - (num_local_elements * num_procs);
    }

    PetscTools::Barrier();
    Timer::Reset();

    /*
     * Create PETSc matrix which will have 1 for adjacent nodes.
     */
    Mat connectivity_matrix;
    PetscTools::SetupMat(connectivity_matrix, num_nodes, num_nodes, 54, PETSC_DECIDE, PETSC_DECIDE, false);

    if (!rMeshReader.IsFileFormatBinary())
    {
        // Advance the file pointer to the first element I own
        for (unsigned element_index = 0; element_index < first_local_element; element_index++)
        {
            rMeshReader.GetNextElementData();
        }
    }

    // In the loop below we assume that there exist edges between any pair of nodes in an element. This is
    // a reasonable assumption for triangles and tetrahedra. This won't be the case for quadratic simplices,
    // squares or hexahedra (or higher order elements), leading to slightly suboptimal partitions in these
    // cases.
    // We allow ELEMENT_DIM smaller than SPACE_DIM in case this is a 2D mesh in
    // a 3D space.
    assert(SPACE_DIM >= ELEMENT_DIM);

    for (unsigned element_index = 0; element_index < num_local_elements; element_index++)
    {
        ElementData element_data;

        if (rMeshReader.IsFileFormatBinary())
        {
            element_data = rMeshReader.GetElementData(first_local_element + element_index);
        }
        else
        {
            element_data = rMeshReader.GetNextElementData();
        }

        for (unsigned i=0; i<element_data.NodeIndices.size(); i++)
        {
            unsigned row = element_data.NodeIndices[i];
            for (unsigned j=0; j<i; j++)
            {
                unsigned col = element_data.NodeIndices[j];
                MatSetValue(connectivity_matrix, row, col, 1.0, INSERT_VALUES);
                MatSetValue(connectivity_matrix, col, row, 1.0, INSERT_VALUES);
            }
        }
    }
    PetscMatTools::Finalise(connectivity_matrix);

    PetscTools::Barrier();
    if (PetscTools::AmMaster())
    {
        Timer::PrintAndReset("Connectivity matrix assembly");
    }

    rMeshReader.Reset();

    PetscInt connectivity_matrix_lo;
    PetscInt connectivity_matrix_hi;
    MatGetOwnershipRange(connectivity_matrix, &connectivity_matrix_lo, &connectivity_matrix_hi);

    unsigned num_local_nodes = connectivity_matrix_hi - connectivity_matrix_lo;

    /* PETSc MatCreateMPIAdj and parMETIS rely on adjacency arrays
     * Named here:      xadj            adjncy
     * parMETIS name:   xadj            adjncy    (see S4.2 in parMETIS manual)
     * PETSc name:      i               j         (see MatCreateMPIAdj in PETSc manual)
     *
     * The adjacency information of all nodes is listed in the main array, adjncy.  Since each node
     * has a variable number of adjacent nodes, the array xadj is used to store the index (in adjncy) where
     * this information starts.  Since xadj[i] is the start of node i's information, xadj[i+1] marks the end.
     *
     *
     */
    MatInfo matrix_info;
    MatGetInfo(connectivity_matrix, MAT_LOCAL, &matrix_info);
    unsigned local_num_nz = (unsigned) matrix_info.nz_used;

    size_t size = (num_local_nodes+1)*sizeof(PetscInt);
    void* ptr;
    PetscMalloc(size, &ptr);
    PetscInt* xadj = (PetscInt*) ptr;
    size = local_num_nz*sizeof(PetscInt);
    PetscMalloc(size, &ptr);
    PetscInt* adjncy = (PetscInt*) ptr;

    PetscInt row_num_nz;
    const PetscInt* column_indices;

    xadj[0]=0;
    for (PetscInt row_global_index=connectivity_matrix_lo; row_global_index<connectivity_matrix_hi; row_global_index++)
    {
        MatGetRow(connectivity_matrix, row_global_index, &row_num_nz, &column_indices, PETSC_NULL);

        unsigned row_local_index = row_global_index - connectivity_matrix_lo;
        xadj[row_local_index+1] = xadj[row_local_index] + row_num_nz;
        for (PetscInt col_index=0; col_index<row_num_nz; col_index++)
        {
           adjncy[xadj[row_local_index] + col_index] =  column_indices[col_index];
        }

        MatRestoreRow(connectivity_matrix, row_global_index, &row_num_nz,&column_indices, PETSC_NULL);
    }

    PetscTools::Destroy(connectivity_matrix);

    // Convert to an adjacency matrix
    Mat adj_matrix;
    MatCreateMPIAdj(PETSC_COMM_WORLD, num_local_nodes, num_nodes, xadj, adjncy, PETSC_NULL, &adj_matrix);

    PetscTools::Barrier();
    if (PetscTools::AmMaster())
    {
        Timer::PrintAndReset("Adjacency matrix creation");
    }

    // Get PETSc to call ParMETIS
    MatPartitioning part;
    MatPartitioningCreate(PETSC_COMM_WORLD, &part);
    MatPartitioningSetAdjacency(part, adj_matrix);
    MatPartitioningSetFromOptions(part);
    IS new_process_numbers;

    MatPartitioningApply(part, &new_process_numbers);
    MatPartitioningDestroy(PETSC_DESTROY_PARAM(part));

    PetscTools::Destroy(adj_matrix);

    PetscTools::Barrier();
    if (PetscTools::AmMaster())
    {
        Timer::PrintAndReset("PETSc-ParMETIS call");
    }

    // Figure out who owns what - processor offsets
    PetscInt* num_nodes_per_process = new PetscInt[num_procs];
#if (PETSC_VERSION_MAJOR == 3) //PETSc 3.x.x
    ISPartitioningCount(new_process_numbers, num_procs, num_nodes_per_process);
#else
    ISPartitioningCount(new_process_numbers, num_nodes_per_process);
#endif

    rProcessorsOffset.resize(num_procs);
    rProcessorsOffset[0] = 0;
    for (PetscInt i=1; i<num_procs; i++)
    {
        rProcessorsOffset[i] = rProcessorsOffset[i-1] + num_nodes_per_process[i-1];
    }
    unsigned my_num_nodes = num_nodes_per_process[local_proc_index];
    delete[] num_nodes_per_process;

    // Figure out who owns what - new node numbering
    IS new_global_node_indices;
    ISPartitioningToNumbering(new_process_numbers, &new_global_node_indices);

    // Index sets only give local information, we want global
    AO ordering;
    AOCreateBasicIS(new_global_node_indices, PETSC_NULL /* natural ordering */, &ordering);

    // The locally owned range under the new numbering
    PetscInt* local_range = new PetscInt[my_num_nodes];
    for (unsigned i=0; i<my_num_nodes; i++)
    {
        local_range[i] = rProcessorsOffset[local_proc_index] + i;
    }
    AOApplicationToPetsc(ordering, my_num_nodes, local_range);
    //AOView(ordering, PETSC_VIEWER_STDOUT_WORLD);

    // Fill in rNodesOwned
    rNodesOwned.insert(local_range, local_range + my_num_nodes);
    delete[] local_range;

    // Once we know the offsets we can compute the permutation vector
    PetscInt* global_range = new PetscInt[num_nodes];
    for (unsigned i=0; i<num_nodes; i++)
    {
        global_range[i] = i;
    }
    AOPetscToApplication(ordering, num_nodes, global_range);

    rNodePermutation.resize(num_nodes);
    std::copy(global_range, global_range+num_nodes, rNodePermutation.begin());
    delete[] global_range;

    AODestroy(PETSC_DESTROY_PARAM(ordering));
    ISDestroy(PETSC_DESTROY_PARAM(new_process_numbers));
    ISDestroy(PETSC_DESTROY_PARAM(new_global_node_indices));

    PetscTools::Barrier();
    if (PetscTools::AmMaster())
    {
        Timer::PrintAndReset("PETSc-ParMETIS output manipulation");
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void NodePartitioner<ELEMENT_DIM, SPACE_DIM>::GeometricPartitioning(AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>& rMeshReader,
                                    std::vector<unsigned>& rNodePermutation,
                                    std::set<unsigned>& rNodesOwned,
                                    std::vector<unsigned>& rProcessorsOffset,
                                    ChasteCuboid<SPACE_DIM>* pRegion)
{
    PetscTools::Barrier();

    unsigned num_nodes =  rMeshReader.GetNumNodes();

    // Work out where each node should lie.
    std::vector<unsigned> node_ownership(num_nodes, 0);
    std::vector<unsigned> node_index_ownership(num_nodes, UNSIGNED_UNSET);

    for (unsigned node=0; node < num_nodes; node++)
    {
        std::vector<double> location = rMeshReader.GetNextNode();

        // Make sure it is the correct size
        assert(location.size() == SPACE_DIM);

        // Establish whether it lies in the domain. ChasteCuboid::DoesContain is
        // insufficient for this as it treats all boundaries as open.
        const ChastePoint<SPACE_DIM>& lower = pRegion->rGetLowerCorner();
        const ChastePoint<SPACE_DIM>& upper = pRegion->rGetUpperCorner();

        bool does_contain = true;

        for (unsigned d=0; d<SPACE_DIM; d++)
        {
            bool boundary_check;
            boundary_check = ((location[d] > lower[d]) || sqrt((location[d]-lower[d])*(location[d]-lower[d])) < DBL_EPSILON);
            does_contain = (does_contain && boundary_check && (location[d] < upper[d]));
        }

        if (does_contain)
        {
            node_ownership[node] = 1;
            rNodesOwned.insert(node);
            node_index_ownership[node] = PetscTools::GetMyRank();
        }
    }

    // Make sure each node will be owned by exactly on process
    std::vector<unsigned> global_ownership(num_nodes, 0);
    std::vector<unsigned> global_index_ownership(num_nodes, UNSIGNED_UNSET);

    MPI_Allreduce(&node_ownership[0], &global_ownership[0], num_nodes, MPI_UNSIGNED, MPI_LXOR, PETSC_COMM_WORLD);
    for (unsigned i=0; i<num_nodes; i++)
    {
        if (global_ownership[i] == 0)
        {
            EXCEPTION("A node is either not in geometric region, or the regions are not disjoint.");
        }
    }

    // Create the permutation and offset vectors.
    MPI_Allreduce(&node_index_ownership[0], &global_index_ownership[0], num_nodes, MPI_UNSIGNED, MPI_MIN, PETSC_COMM_WORLD);

    for (unsigned proc=0; proc<PetscTools::GetNumProcs(); proc++)
    {
        rProcessorsOffset.push_back(rNodePermutation.size());
        for (unsigned node=0; node<num_nodes; node++)
        {
            if (global_index_ownership[node] == proc)
            {
                rNodePermutation.push_back(node);
            }
        }
    }
    assert(rNodePermutation.size() == num_nodes);
}

// Explicit instantiation
template class NodePartitioner<1,1>;
template class NodePartitioner<1,2>;
template class NodePartitioner<1,3>;
template class NodePartitioner<2,2>;
template class NodePartitioner<2,3>;
template class NodePartitioner<3,3>;