DistributedBoxCollection.cpp

/*

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*/
#include "DistributedBoxCollection.hpp"
#include "Exception.hpp"
#include "MathsCustomFunctions.hpp"
#include "Warnings.hpp"

// Static member for "fudge factor" is instantiated here
template<unsigned DIM>
const double DistributedBoxCollection<DIM>::msFudge = 5e-14;

template<unsigned DIM>
DistributedBoxCollection<DIM>::DistributedBoxCollection(double boxWidth, c_vector<double, 2*DIM> domainSize, bool isPeriodicInX, int localRows)
    : mBoxWidth(boxWidth),
      mIsPeriodicInX(isPeriodicInX),
      mAreLocalBoxesSet(false),
      mCalculateNodeNeighbours(true)
{
    // Periodicity only works in 2d and in serial.
    if (isPeriodicInX)
    {
        assert(DIM==2 && PetscTools::IsSequential());
    }

    // If the domain size is not 'divisible' (i.e. fmod(width, box_size) > 0.0) we swell the domain to enforce this.
    for (unsigned i=0; i<DIM; i++)
    {
        double r = fmod((domainSize[2*i+1]-domainSize[2*i]), boxWidth);
        if (r > 0.0)
        {
            domainSize[2*i+1] += boxWidth - r;
        }
    }

    mDomainSize = domainSize;

    // Calculate the number of boxes in each direction.
    mNumBoxesEachDirection = scalar_vector<unsigned>(DIM, 0u);

    for (unsigned i=0; i<DIM; i++)
    {
        double counter = mDomainSize(2*i);
        while (counter + msFudge < mDomainSize(2*i+1))
        {
            mNumBoxesEachDirection(i)++;
            counter += mBoxWidth;
        }
    }

    // Make sure there are enough boxes for the number of processes.
    if (mNumBoxesEachDirection(DIM-1) < PetscTools::GetNumProcs())
    {
        WARNING("There are more processes than convenient for the domain/mesh/box size.  The domain size has been swollen.")
        mDomainSize[2*DIM - 1] += (PetscTools::GetNumProcs() - mNumBoxesEachDirection(DIM-1))*mBoxWidth;
        mNumBoxesEachDirection(DIM-1) = PetscTools::GetNumProcs();
    }

    // Make a distributed vectory factory to split the rows of boxes between processes.
    mpDistributedBoxStackFactory = new DistributedVectorFactory(mNumBoxesEachDirection(DIM-1), localRows);

    // Calculate how many boxes in a row / face. A useful piece of data in the class.
    mNumBoxesInAFace = 1;
    for (unsigned i=1; i<DIM; i++)
    {
        mNumBoxesInAFace *= mNumBoxesEachDirection(i-1);
    }

    unsigned num_boxes = mNumBoxesInAFace * (mpDistributedBoxStackFactory->GetHigh() - mpDistributedBoxStackFactory->GetLow());

    mMinBoxIndex = mpDistributedBoxStackFactory->GetLow() * mNumBoxesInAFace;
    mMaxBoxIndex = mpDistributedBoxStackFactory->GetHigh() * mNumBoxesInAFace - 1;

    /*
     * The location of the Boxes doesn't matter as it isn't actually used so we don't bother to work it out.
     * The reason it isn't used is because this class works out which box a node lies in without refernece to actual
     * box locations, only their global index within the collection.
     */
    c_vector<double, 2*DIM> arbitrary_location;
    for (unsigned i=0; i<num_boxes; i++)
    {
        Box<DIM> new_box(arbitrary_location);
        mBoxes.push_back(new_box);

        unsigned global_index = mMinBoxIndex + i;
        mBoxesMapping[global_index] = mBoxes.size() - 1;
    }

    mNumBoxes = mNumBoxesInAFace * mNumBoxesEachDirection(DIM-1);
}

template<unsigned DIM>
DistributedBoxCollection<DIM>::~DistributedBoxCollection()
{
    delete mpDistributedBoxStackFactory;
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::EmptyBoxes()
{
    for (unsigned i=0; i<mBoxes.size(); i++)
    {
        mBoxes[i].ClearNodes();
    }
    for (unsigned i=0; i<mHaloBoxes.size(); i++)
    {
        mHaloBoxes[i].ClearNodes();
    }
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::SetupHaloBoxes()
{
    // Get top-most and bottom-most value of Distributed Box Stack.
    unsigned Hi = mpDistributedBoxStackFactory->GetHigh();
    unsigned Lo = mpDistributedBoxStackFactory->GetLow();

    // If I am not the top-most process, add halo structures to the right.
    if (!PetscTools::AmTopMost())
    {
        for (unsigned i=0; i < mNumBoxesInAFace; i++)
        {
            c_vector<double, 2*DIM> arbitrary_location; // See comment in constructor.
            Box<DIM> new_box(arbitrary_location);
            mHaloBoxes.push_back(new_box);

            unsigned global_index = Hi * mNumBoxesInAFace + i;
            mHaloBoxesMapping[global_index] = mHaloBoxes.size()-1;
            mHalosRight.push_back(global_index - mNumBoxesInAFace);
        }
    }

    // If I am not the bottom-most process, add halo structures to the left.
    if (!PetscTools::AmMaster())
    {
        for (unsigned i=0; i< mNumBoxesInAFace; i++)
        {
            c_vector<double, 2*DIM> arbitrary_location; // See comment in constructor.
            Box<DIM> new_box(arbitrary_location);
            mHaloBoxes.push_back(new_box);

            unsigned global_index = (Lo - 1) * mNumBoxesInAFace + i;
            mHaloBoxesMapping[global_index] = mHaloBoxes.size() - 1;

            mHalosLeft.push_back(global_index  + mNumBoxesInAFace);
        }
    }
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::UpdateHaloBoxes()
{
    mHaloNodesLeft.clear();
    for (unsigned i=0; i<mHalosLeft.size(); i++)
    {
        for (typename std::set<Node<DIM>* >::iterator iter=this->rGetBox(mHalosLeft[i]).rGetNodesContained().begin();
                iter!=this->rGetBox(mHalosLeft[i]).rGetNodesContained().end();
                iter++)
        {
            mHaloNodesLeft.push_back((*iter)->GetIndex());
        }
    }

    // Send right
    mHaloNodesRight.clear();
    for (unsigned i=0; i<mHalosRight.size(); i++)
    {
        for (typename std::set<Node<DIM>* >::iterator iter=this->rGetBox(mHalosRight[i]).rGetNodesContained().begin();
                iter!=this->rGetBox(mHalosRight[i]).rGetNodesContained().end();
                iter++)
        {
            mHaloNodesRight.push_back((*iter)->GetIndex());
        }
    }
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::GetNumLocalRows() const
{
    return mpDistributedBoxStackFactory->GetHigh() - mpDistributedBoxStackFactory->GetLow();
}

template<unsigned DIM>
bool DistributedBoxCollection<DIM>::GetBoxOwnership(unsigned globalIndex)
{
    return (!(globalIndex<mMinBoxIndex) && !(mMaxBoxIndex<globalIndex));
}

template<unsigned DIM>
bool DistributedBoxCollection<DIM>::GetHaloBoxOwnership(unsigned globalIndex)
{
    bool is_halo_right = ((globalIndex > mMaxBoxIndex) && !(globalIndex > mMaxBoxIndex + mNumBoxesInAFace));
    bool is_halo_left = ((globalIndex < mMinBoxIndex) && !(globalIndex < mMinBoxIndex - mNumBoxesInAFace));

    return (PetscTools::IsParallel() && (is_halo_right || is_halo_left));
}

template<unsigned DIM>
bool DistributedBoxCollection<DIM>::IsInteriorBox(unsigned globalIndex)
{
    bool is_on_boundary = !(globalIndex < mMaxBoxIndex - mNumBoxesInAFace) || (globalIndex < mMinBoxIndex + mNumBoxesInAFace);

    return (PetscTools::IsSequential() || !(is_on_boundary));
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::CalculateGlobalIndex(c_vector<unsigned, DIM> coordinateIndices)
{
    unsigned containing_box_index = 0;
    for (unsigned i=0; i<DIM; i++)
    {
        unsigned temp = 1;
        for (unsigned j=0; j<i; j++)
        {
            temp *= mNumBoxesEachDirection(j);
        }
        containing_box_index += temp*coordinateIndices[i];
    }

    return containing_box_index;
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::CalculateContainingBox(Node<DIM>* pNode)
{
    // Get the location of the node
    c_vector<double, DIM> location = pNode->rGetLocation();
    return CalculateContainingBox(location);
}


template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::CalculateContainingBox(c_vector<double, DIM>& rLocation)
{
    // The node must lie inside the boundary of the box collection
    for (unsigned i=0; i<DIM; i++)
    {
        if ( (rLocation[i] < mDomainSize(2*i)) || !(rLocation[i] < mDomainSize(2*i+1)) )
        {
            EXCEPTION("The point provided is outside all of the boxes");
        }
    }

    // Compute the containing box index in each dimension
    c_vector<unsigned, DIM> containing_box_indices = scalar_vector<unsigned>(DIM, 0u);
    for (unsigned i=0; i<DIM; i++)
    {
        double box_counter = mDomainSize(2*i);
        while (!((box_counter + mBoxWidth) > rLocation[i] + msFudge))
        {
            containing_box_indices[i]++;
            box_counter += mBoxWidth;
        }
    }

    // Use these to compute the index of the containing box
    unsigned containing_box_index = 0;
    for (unsigned i=0; i<DIM; i++)
    {
        unsigned temp = 1;
        for (unsigned j=0; j<i; j++)
        {
            temp *= mNumBoxesEachDirection(j);
        }
        containing_box_index += temp*containing_box_indices[i];
    }

    // This index must be less than the total number of boxes
    assert(containing_box_index < mNumBoxes);

    return containing_box_index;
}

template<unsigned DIM>
c_vector<unsigned, DIM> DistributedBoxCollection<DIM>::CalculateCoordinateIndices(unsigned globalIndex)
{
    c_vector<unsigned, DIM> indices;

    switch(DIM)
    {
        case 1:
        {
            indices[0]=globalIndex;
            break;
        }
        case 2:
        {
            unsigned remainder=globalIndex % mNumBoxesEachDirection(0);
            indices[0]=remainder;
            indices[1]=(unsigned)(globalIndex/mNumBoxesEachDirection(0));
            break;
        }

        case 3:
        {
            unsigned remainder1=globalIndex % (mNumBoxesEachDirection(0)*mNumBoxesEachDirection(1));
            unsigned remainder2=remainder1 % mNumBoxesEachDirection(0);
            indices[0]=remainder2;
            indices[1]=((globalIndex-indices[0])/mNumBoxesEachDirection(0))%mNumBoxesEachDirection(1);
            indices[2]=((globalIndex-indices[0]-mNumBoxesEachDirection(0)*indices[1])/(mNumBoxesEachDirection(0)*mNumBoxesEachDirection(1)));
            break;
        }
        default:
        {
            NEVER_REACHED;
        }
    }

    return indices;
}

template<unsigned DIM>
Box<DIM>& DistributedBoxCollection<DIM>::rGetBox(unsigned boxIndex)
{
    assert(!(boxIndex<mMinBoxIndex) && !(mMaxBoxIndex<boxIndex));
    return mBoxes[boxIndex-mMinBoxIndex];
}

template<unsigned DIM>
Box<DIM>& DistributedBoxCollection<DIM>::rGetHaloBox(unsigned boxIndex)
{
    assert(GetHaloBoxOwnership(boxIndex));

    unsigned local_index = mHaloBoxesMapping.find(boxIndex)->second;

    return mHaloBoxes[local_index];
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::GetNumBoxes()
{
    return mNumBoxes;
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::GetNumLocalBoxes()
{
    return mBoxes.size();
}

template<unsigned DIM>
c_vector<double, 2*DIM> DistributedBoxCollection<DIM>::rGetDomainSize() const
{
    return mDomainSize;
}

template<unsigned DIM>
bool DistributedBoxCollection<DIM>::GetAreLocalBoxesSet() const
{
    return mAreLocalBoxesSet;
}

template<unsigned DIM>
double DistributedBoxCollection<DIM>::GetBoxWidth() const
{
    return mBoxWidth;
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::GetNumRowsOfBoxes() const
{
    return mpDistributedBoxStackFactory->GetHigh() - mpDistributedBoxStackFactory->GetLow();
}

template<unsigned DIM>
int DistributedBoxCollection<DIM>::LoadBalance(std::vector<int> localDistribution)
{
    MPI_Status status;

    int proc_right = (PetscTools::AmTopMost()) ? MPI_PROC_NULL : (int)PetscTools::GetMyRank() + 1;
    int proc_left = (PetscTools::AmMaster()) ? MPI_PROC_NULL : (int)PetscTools::GetMyRank() - 1;

    // A variable that will return the new number of rows.
    int new_rows = localDistribution.size();

    unsigned rows_on_left_process = 0;
    std::vector<int> node_distr_on_left_process;

    unsigned num_local_rows = localDistribution.size();

    MPI_Send(&num_local_rows, 1, MPI_UNSIGNED, proc_right, 123, PETSC_COMM_WORLD);
    MPI_Recv(&rows_on_left_process, 1, MPI_UNSIGNED, proc_left, 123, PETSC_COMM_WORLD, &status);

    node_distr_on_left_process.resize(rows_on_left_process > 0 ? rows_on_left_process : 1);

    MPI_Send(&localDistribution[0], num_local_rows, MPI_INT, proc_right, 123, PETSC_COMM_WORLD);
    MPI_Recv(&node_distr_on_left_process[0], rows_on_left_process, MPI_INT, proc_left, 123, PETSC_COMM_WORLD, &status);

    int local_load = 0;
    for (unsigned i=0; i<localDistribution.size(); i++)
    {
        local_load += localDistribution[i];
    }
    int load_on_left_proc = 0;
    for (unsigned i=0; i<node_distr_on_left_process.size(); i++)
    {
        load_on_left_proc += node_distr_on_left_process[i];
    }

    if (!PetscTools::AmMaster())
    {
        // Calculate (Difference in load with a shift) - (Difference in current loads) for a move left and right of the boundary
        // This code uses integer arithmetic in order to avoid the rounding errors associated with doubles
        int local_to_left_sq = (local_load - load_on_left_proc) * (local_load - load_on_left_proc);
        int delta_left =  ( (local_load + node_distr_on_left_process[node_distr_on_left_process.size() - 1]) - (load_on_left_proc - node_distr_on_left_process[node_distr_on_left_process.size() - 1]) );
        delta_left = delta_left*delta_left - local_to_left_sq;

        int delta_right = ( (local_load - localDistribution[0]) - (load_on_left_proc + localDistribution[0]));
        delta_right = delta_right*delta_right - local_to_left_sq;

        // If a delta is negative we should accept that change. If both are negative choose the largest change.
        int local_change = 0;
        bool move_left = (!(delta_left > 0) && (node_distr_on_left_process.size() > 1));
        if (move_left)
        {
            local_change = 1;
        }

        bool move_right = !(delta_right > 0) && (localDistribution.size() > 2);
        if (move_right)
        {
            local_change = -1;
        }

        if (move_left && move_right)
        {
            local_change = (fabs((double)delta_right) > fabs((double)delta_left)) ? -1 : 1;
        }

        // Update the number of local rows.
        new_rows += local_change;

        // Send the result of the calculation back to the left processes.
        MPI_Send(&local_change, 1, MPI_INT, proc_left, 123, PETSC_COMM_WORLD);
    }

    // Receive changes from right hand process.
    int remote_change = 0;
    MPI_Recv(&remote_change, 1, MPI_INT, proc_right, 123, PETSC_COMM_WORLD, &status);

    // Update based on change or right/top boundary
    new_rows -= remote_change;

    return new_rows;
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::SetupLocalBoxesHalfOnly()
{
    if (mAreLocalBoxesSet)
    {
        EXCEPTION("Local Boxes Are Already Set");
    }
    else
    {
        switch (DIM)
        {
            case 1:
            {
                // We only need to look for neighbours in the current and successive boxes plus some others for halos
                mLocalBoxes.clear();

                // Iterate over the global box indices
                for (unsigned global_index = mMinBoxIndex; global_index<mMaxBoxIndex+1; global_index++)
                {
                    std::set<unsigned> local_boxes;

                    // Insert the current box
                    local_boxes.insert(global_index);

                    // Set some bools to find out where we are
                    bool right = (global_index==mNumBoxesEachDirection(0)-1);
                    bool left = (global_index == 0);
                    bool proc_left = (global_index == mpDistributedBoxStackFactory->GetLow());

                    // If we're not at the right-most box, then insert the box to the right
                    if (!right)
                    {
                        local_boxes.insert(global_index+1);
                    }
                    // If we're on a left process boundary and not on process 0, insert the (halo) box to the left
                    if (proc_left && !left)
                    {
                        local_boxes.insert(global_index-1);
                    }

                    mLocalBoxes.push_back(local_boxes);
                }
                break;
            }
            case 2:
            {
                // We only need to look for neighbours in the current box and half the neighbouring boxes plus some others for halos
                mLocalBoxes.clear();

                for (unsigned global_index = mMinBoxIndex; global_index<mMaxBoxIndex+1; global_index++)
                {
                    std::set<unsigned> local_boxes;

                    // Set up bools to find out where we are
                    bool left = (global_index%mNumBoxesEachDirection(0) == 0);
                    bool right = (global_index%mNumBoxesEachDirection(0) == mNumBoxesEachDirection(0)-1);
                    bool top = !(global_index < mNumBoxesEachDirection(0)*mNumBoxesEachDirection(1) - mNumBoxesEachDirection(0));
                    bool bottom = (global_index < mNumBoxesEachDirection(0));
                    bool bottom_proc = (CalculateCoordinateIndices(global_index)[1] == mpDistributedBoxStackFactory->GetLow());

                    // Insert the current box
                    local_boxes.insert(global_index);

                    // If we're on the bottom of the process boundary, but not the bottom of the domain add boxes below
                    if(!bottom && bottom_proc)
                    {
                        local_boxes.insert(global_index - mNumBoxesEachDirection(0));
                        if(!left)
                        {
                            local_boxes.insert(global_index - mNumBoxesEachDirection(0) - 1);
                        }
                        if(!right)
                        {
                            local_boxes.insert(global_index - mNumBoxesEachDirection(0) + 1);
                        }
                    }

                    // If we're not at the top of the domain insert boxes above
                    if(!top)
                    {
                        local_boxes.insert(global_index + mNumBoxesEachDirection(0));

                        if(!right)
                        {
                            local_boxes.insert(global_index + mNumBoxesEachDirection(0) + 1);
                        }
                        if(!left)
                        {
                            local_boxes.insert(global_index + mNumBoxesEachDirection(0) - 1);
                        }
                        else if ( (global_index % mNumBoxesEachDirection(0) == 0) && (mIsPeriodicInX) ) // If we're on the left edge but its periodic include the box on the far right and up one.
                        {
                            local_boxes.insert(global_index +  2 * mNumBoxesEachDirection(0) - 1);
                        }
                    }

                    // If we're not on the far right hand side inseryt box to the right
                    if(!right)
                    {
                        local_boxes.insert(global_index + 1);
                    }
                    // If we're on the right edge but it's periodic include the box on the far left of the domain
                    else if ( (global_index % mNumBoxesEachDirection(0) == mNumBoxesEachDirection(0)-1) && (mIsPeriodicInX) )
                    {
                        local_boxes.insert(global_index - mNumBoxesEachDirection(0) + 1);
                        // If we're also not on the top-most row, then insert the box above- on the far left of the domain
                        if (global_index < mBoxes.size() - mNumBoxesEachDirection(0))
                        {
                            local_boxes.insert(global_index + 1);
                        }
                    }

                    mLocalBoxes.push_back(local_boxes);
                }
                break;
            }
            case 3:
            {
                // We only need to look for neighbours in the current box and half the neighbouring boxes plus some others for halos
                mLocalBoxes.clear();
                unsigned num_boxes_xy = mNumBoxesEachDirection(0)*mNumBoxesEachDirection(1);


                for (unsigned global_index = mMinBoxIndex; global_index<mMaxBoxIndex+1; global_index++)
                {
                    std::set<unsigned> local_boxes;

                    // Set some bools to find out where we are
                    bool top = !(global_index % num_boxes_xy < num_boxes_xy - mNumBoxesEachDirection(0));
                    bool bottom = (global_index % num_boxes_xy < mNumBoxesEachDirection(0));
                    bool left = (global_index % mNumBoxesEachDirection(0) == 0);
                    bool right = (global_index % mNumBoxesEachDirection(0) == mNumBoxesEachDirection(0) - 1);
                    bool front = (global_index < num_boxes_xy);
                    bool back = !(global_index < num_boxes_xy*mNumBoxesEachDirection(2) - num_boxes_xy);
                    bool proc_front = (CalculateCoordinateIndices(global_index)[2] == mpDistributedBoxStackFactory->GetLow());
                    bool proc_back = (CalculateCoordinateIndices(global_index)[2] == mpDistributedBoxStackFactory->GetHigh()-1);

                    // Insert the current box
                    local_boxes.insert(global_index);

                    // If we're not on the front face, add appropriate boxes on the closer face
                    if(!front)
                    {
                        // If we're not on the top of the domain
                        if(!top)
                        {
                            local_boxes.insert( global_index - num_boxes_xy + mNumBoxesEachDirection(0) );
                            if(!left)
                            {
                                local_boxes.insert( global_index - num_boxes_xy + mNumBoxesEachDirection(0) - 1);
                            }
                            if(!right)
                            {
                                local_boxes.insert( global_index - num_boxes_xy + mNumBoxesEachDirection(0) + 1);
                            }
                        }
                        if(!right)
                        {
                            local_boxes.insert( global_index - num_boxes_xy + 1);
                        }

                        // If we are on the front of the process we have to add extra boxes as they are halos.
                        if(proc_front)
                        {
                            local_boxes.insert( global_index - num_boxes_xy );

                            if(!left)
                            {
                                local_boxes.insert( global_index - num_boxes_xy - 1);
                            }
                            if(!bottom)
                            {
                                local_boxes.insert( global_index - num_boxes_xy - mNumBoxesEachDirection(0));

                                if(!left)
                                {
                                    local_boxes.insert( global_index - num_boxes_xy - mNumBoxesEachDirection(0) - 1);
                                }
                                if(!right)
                                {
                                    local_boxes.insert( global_index - num_boxes_xy - mNumBoxesEachDirection(0) + 1);
                                }
                            }

                        }
                    }
                    if(!right)
                    {
                        local_boxes.insert( global_index + 1);
                    }
                    // If we're not on the very top add boxes above
                    if(!top)
                    {
                        local_boxes.insert( global_index + mNumBoxesEachDirection(0));

                        if(!right)
                        {
                            local_boxes.insert( global_index + mNumBoxesEachDirection(0) + 1);
                        }
                        if(!left)
                        {
                            local_boxes.insert( global_index + mNumBoxesEachDirection(0) - 1);
                        }
                    }

                    // If we're not on the back add boxes behind
                    if(!back)
                    {
                        local_boxes.insert(global_index + num_boxes_xy);

                        if(!right)
                        {
                            local_boxes.insert(global_index + num_boxes_xy + 1);
                        }
                        if(!top)
                        {
                            local_boxes.insert(global_index + num_boxes_xy + mNumBoxesEachDirection(0));
                            if(!right)
                            {
                                local_boxes.insert(global_index + num_boxes_xy + mNumBoxesEachDirection(0) + 1);
                            }
                            if(!left)
                            {
                                local_boxes.insert(global_index + num_boxes_xy + mNumBoxesEachDirection(0) - 1);
                            }
                        }
                        // If we are on the back proc we should make sure we get everything in the face further back
                        if(proc_back)
                        {
                            if(!left)
                            {
                                local_boxes.insert(global_index + num_boxes_xy - 1);
                            }
                            if(!bottom)
                            {
                                local_boxes.insert(global_index + num_boxes_xy - mNumBoxesEachDirection(0));

                                if(!left)
                                {
                                    local_boxes.insert(global_index + num_boxes_xy - mNumBoxesEachDirection(0) - 1);
                                }
                                if(!right)
                                {
                                    local_boxes.insert(global_index + num_boxes_xy - mNumBoxesEachDirection(0) + 1);
                                }
                            }
                        }
                    }
                    mLocalBoxes.push_back(local_boxes);
                }

                break;
            }
            default:
                NEVER_REACHED;
        }
        mAreLocalBoxesSet=true;
    }
}



template<unsigned DIM>
void DistributedBoxCollection<DIM>::SetupAllLocalBoxes()
{
    mAreLocalBoxesSet = true;
    switch (DIM)
    {
        case 1:
        {
            for (unsigned i=mMinBoxIndex; i<mMaxBoxIndex+1; i++)
            {
                std::set<unsigned> local_boxes;

                local_boxes.insert(i);

                // add the two neighbours
                if (i!=0)
                {
                    local_boxes.insert(i-1);
                }
                if (i+1 != mNumBoxesEachDirection(0))
                {
                    local_boxes.insert(i+1);
                }

                mLocalBoxes.push_back(local_boxes);
            }
            break;
        }
        case 2:
        {
            mLocalBoxes.clear();

            unsigned M = mNumBoxesEachDirection(0);
            unsigned N = mNumBoxesEachDirection(1);

            std::vector<bool> is_xmin(N*M); // far left
            std::vector<bool> is_xmax(N*M); // far right
            std::vector<bool> is_ymin(N*M); // bottom
            std::vector<bool> is_ymax(N*M); // top

            for (unsigned i=0; i<M*N; i++)
            {
                is_xmin[i] = (i%M==0);
                is_xmax[i] = ((i+1)%M==0);
                is_ymin[i] = (i%(M*N)<M);
                is_ymax[i] = (i%(M*N)>=(N-1)*M);
            }

            for (unsigned i=mMinBoxIndex; i<mMaxBoxIndex+1; i++)
            {
                std::set<unsigned> local_boxes;

                local_boxes.insert(i);

                // add the box to the left
                if (!is_xmin[i])
                {
                    local_boxes.insert(i-1);
                }
                else // Add Periodic Box if needed
                {
                    if(mIsPeriodicInX)
                    {
                        local_boxes.insert(i+M-1);
                    }
                }

                // add the box to the right
                if (!is_xmax[i])
                {
                    local_boxes.insert(i+1);
                }
                else // Add Periodic Box if needed
                {
                    if(mIsPeriodicInX)
                    {
                        local_boxes.insert(i-M+1);
                    }
                }

                // add the one below
                if (!is_ymin[i])
                {
                    local_boxes.insert(i-M);
                }

                // add the one above
                if (!is_ymax[i])
                {
                    local_boxes.insert(i+M);
                }

                // add the four corner boxes

                if ( (!is_xmin[i]) && (!is_ymin[i]) )
                {
                    local_boxes.insert(i-1-M);
                }
                if ( (!is_xmin[i]) && (!is_ymax[i]) )
                {
                    local_boxes.insert(i-1+M);
                }
                if ( (!is_xmax[i]) && (!is_ymin[i]) )
                {
                    local_boxes.insert(i+1-M);
                }
                if ( (!is_xmax[i]) && (!is_ymax[i]) )
                {
                    local_boxes.insert(i+1+M);
                }

                // Add Periodic Corner Boxes if needed
                if(mIsPeriodicInX)
                {
                    if( (is_xmin[i]) && (!is_ymin[i]) )
                    {
                        local_boxes.insert(i-1);
                    }
                    if ( (is_xmin[i]) && (!is_ymax[i]) )
                    {
                        local_boxes.insert(i-1+2*M);
                    }
                    if ( (is_xmax[i]) && (!is_ymin[i]) )
                    {
                        local_boxes.insert(i+1-2*M);
                    }
                    if ( (is_xmax[i]) && (!is_ymax[i]) )
                    {
                        local_boxes.insert(i+1);
                    }
                }

                mLocalBoxes.push_back(local_boxes);
            }
            break;
        }
        case 3:
        {
            mLocalBoxes.clear();

            unsigned M = mNumBoxesEachDirection(0);
            unsigned N = mNumBoxesEachDirection(1);
            unsigned P = mNumBoxesEachDirection(2);

            std::vector<bool> is_xmin(N*M*P); // far left
            std::vector<bool> is_xmax(N*M*P); // far right
            std::vector<bool> is_ymin(N*M*P); // nearest
            std::vector<bool> is_ymax(N*M*P); // furthest
            std::vector<bool> is_zmin(N*M*P); // bottom layer
            std::vector<bool> is_zmax(N*M*P); // top layer

            for (unsigned i=0; i<M*N*P; i++)
            {
                is_xmin[i] = (i%M==0);
                is_xmax[i] = ((i+1)%M==0);
                is_ymin[i] = (i%(M*N)<M);
                is_ymax[i] = (i%(M*N)>=(N-1)*M);
                is_zmin[i] = (i<M*N);
                is_zmax[i] = (i>=M*N*(P-1));
            }

            for (unsigned i=mMinBoxIndex; i<mMaxBoxIndex+1; i++)
            {
                std::set<unsigned> local_boxes;

                // add itself as a local box
                local_boxes.insert(i);

                // now add all 26 other neighbours.....

                // add the box left
                if (!is_xmin[i])
                {
                    local_boxes.insert(i-1);

                    // plus some others towards the left
                    if (!is_ymin[i])
                    {
                        local_boxes.insert(i-1-M);
                    }

                    if (!is_ymax[i])
                    {
                        local_boxes.insert(i-1+M);
                    }

                    if (!is_zmin[i])
                    {
                        local_boxes.insert(i-1-M*N);
                    }

                    if (!is_zmax[i])
                    {
                        local_boxes.insert(i-1+M*N);
                    }
                }

                // add the box to the right
                if (!is_xmax[i])
                {
                    local_boxes.insert(i+1);

                    // plus some others towards the right
                    if (!is_ymin[i])
                    {
                        local_boxes.insert(i+1-M);
                    }

                    if (!is_ymax[i])
                    {
                        local_boxes.insert(i+1+M);
                    }

                    if (!is_zmin[i])
                    {
                        local_boxes.insert(i+1-M*N);
                    }

                    if (!is_zmax[i])
                    {
                        local_boxes.insert(i+1+M*N);
                    }
                }

                // add the boxes next along the y axis
                if (!is_ymin[i])
                {
                    local_boxes.insert(i-M);

                    // and more in this plane
                    if (!is_zmin[i])
                    {
                        local_boxes.insert(i-M-M*N);
                    }

                    if (!is_zmax[i])
                    {
                        local_boxes.insert(i-M+M*N);
                    }
                }

                // add the boxes next along the y axis
                if (!is_ymax[i])
                {
                    local_boxes.insert(i+M);

                    // and more in this plane
                    if (!is_zmin[i])
                    {
                        local_boxes.insert(i+M-M*N);
                    }

                    if (!is_zmax[i])
                    {
                        local_boxes.insert(i+M+M*N);
                    }
                }

                // add the box directly above
                if (!is_zmin[i])
                {
                    local_boxes.insert(i-N*M);
                }

                // add the box directly below
                if (!is_zmax[i])
                {
                    local_boxes.insert(i+N*M);
                }

                // finally, the 8 corners are left

                if ( (!is_xmin[i]) && (!is_ymin[i]) && (!is_zmin[i]) )
                {
                    local_boxes.insert(i-1-M-M*N);
                }

                if ( (!is_xmin[i]) && (!is_ymin[i]) && (!is_zmax[i]) )
                {
                    local_boxes.insert(i-1-M+M*N);
                }

                if ( (!is_xmin[i]) && (!is_ymax[i]) && (!is_zmin[i]) )
                {
                    local_boxes.insert(i-1+M-M*N);
                }

                if ( (!is_xmin[i]) && (!is_ymax[i]) && (!is_zmax[i]) )
                {
                    local_boxes.insert(i-1+M+M*N);
                }

                if ( (!is_xmax[i]) && (!is_ymin[i]) && (!is_zmin[i]) )
                {
                    local_boxes.insert(i+1-M-M*N);
                }

                if ( (!is_xmax[i]) && (!is_ymin[i]) && (!is_zmax[i]) )
                {
                    local_boxes.insert(i+1-M+M*N);
                }

                if ( (!is_xmax[i]) && (!is_ymax[i]) && (!is_zmin[i]) )
                {
                    local_boxes.insert(i+1+M-M*N);
                }

                if ( (!is_xmax[i]) && (!is_ymax[i]) && (!is_zmax[i]) )
                {
                    local_boxes.insert(i+1+M+M*N);
                }

                mLocalBoxes.push_back(local_boxes);
            }
            break;
        }
        default:
            NEVER_REACHED;
    }
}

template<unsigned DIM>
std::set<unsigned> DistributedBoxCollection<DIM>::GetLocalBoxes(unsigned boxIndex)
{
    // Make sure the box is locally owned
    assert(!(boxIndex < mMinBoxIndex) && !(mMaxBoxIndex<boxIndex));
    return mLocalBoxes[boxIndex-mMinBoxIndex];
}

template<unsigned DIM>
bool DistributedBoxCollection<DIM>::IsOwned(Node<DIM>* pNode)
{
    unsigned index = CalculateContainingBox(pNode);

    return GetBoxOwnership(index);
}

template<unsigned DIM>
bool DistributedBoxCollection<DIM>::IsOwned(c_vector<double, DIM>& location)
{
    unsigned index = CalculateContainingBox(location);

    return GetBoxOwnership(index);
}

template<unsigned DIM>
unsigned DistributedBoxCollection<DIM>::GetProcessOwningNode(Node<DIM>* pNode)
{
    unsigned box_index = CalculateContainingBox(pNode);
    unsigned containing_process = PetscTools::GetMyRank();

    if (box_index > mMaxBoxIndex)
    {
        containing_process++;
    }
    else if (box_index < mMinBoxIndex)
    {
        containing_process--;
    }

    return containing_process;
}

template<unsigned DIM>
std::vector<unsigned>& DistributedBoxCollection<DIM>::rGetHaloNodesRight()
{
    return mHaloNodesRight;
}

template<unsigned DIM>
std::vector<unsigned>& DistributedBoxCollection<DIM>::rGetHaloNodesLeft()
{
    return mHaloNodesLeft;
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::SetCalculateNodeNeighbours(bool calculateNodeNeighbours)
{
    mCalculateNodeNeighbours = calculateNodeNeighbours;
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::CalculateNodePairs(std::vector<Node<DIM>*>& rNodes, std::vector<std::pair<Node<DIM>*, Node<DIM>*> >& rNodePairs, std::map<unsigned, std::set<unsigned> >& rNodeNeighbours)
{
    rNodePairs.clear();
    rNodeNeighbours.clear();

    // Create an empty neighbours set for each node
    for (unsigned i=0; i<rNodes.size(); i++)
    {
        unsigned node_index = rNodes[i]->GetIndex();

        // Get the box containing this node
        unsigned box_index = CalculateContainingBox(rNodes[i]);

        if (GetBoxOwnership(box_index))
        {
            rNodeNeighbours[node_index] = std::set<unsigned>();
        }
    }

    for (std::map<unsigned, unsigned>::iterator map_iter = mBoxesMapping.begin();
            map_iter != mBoxesMapping.end();
            ++map_iter)
    {
        // Get the box global index
        unsigned box_index = map_iter->first;

        AddPairsFromBox(box_index, rNodePairs, rNodeNeighbours);
    }
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::CalculateInteriorNodePairs(std::vector<Node<DIM>*>& rNodes, std::vector<std::pair<Node<DIM>*, Node<DIM>*> >& rNodePairs, std::map<unsigned, std::set<unsigned> >& rNodeNeighbours)
{
    rNodePairs.clear();
    rNodeNeighbours.clear();

    // Create an empty neighbours set for each node
    for (unsigned i=0; i<rNodes.size(); i++)
    {
        unsigned node_index = rNodes[i]->GetIndex();

        // Get the box containing this node
        unsigned box_index = CalculateContainingBox(rNodes[i]);

        if (GetBoxOwnership(box_index))
        {
            rNodeNeighbours[node_index] = std::set<unsigned>();
        }
    }

    for (std::map<unsigned, unsigned>::iterator map_iter = mBoxesMapping.begin();
            map_iter != mBoxesMapping.end();
            ++map_iter)
    {
        // Get the box global index
        unsigned box_index = map_iter->first;

        if (IsInteriorBox(box_index))
        {
            AddPairsFromBox(box_index, rNodePairs, rNodeNeighbours);
        }
    }
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::CalculateBoundaryNodePairs(std::vector<Node<DIM>*>& rNodes, std::vector<std::pair<Node<DIM>*, Node<DIM>*> >& rNodePairs, std::map<unsigned, std::set<unsigned> >& rNodeNeighbours)
{
    for (std::map<unsigned, unsigned>::iterator map_iter = mBoxesMapping.begin();
            map_iter != mBoxesMapping.end();
            ++map_iter)
    {
        // Get the box global index
        unsigned box_index = map_iter->first;

        if (!IsInteriorBox(box_index))
        {
            AddPairsFromBox(box_index, rNodePairs, rNodeNeighbours);
        }
    }
}

template<unsigned DIM>
void DistributedBoxCollection<DIM>::AddPairsFromBox(unsigned boxIndex, std::vector<std::pair<Node<DIM>*, Node<DIM>*> >& rNodePairs, std::map<unsigned, std::set<unsigned> >& rNodeNeighbours)
{
    // Get the box
    Box<DIM> box = rGetBox(boxIndex);

    // Get the set of nodes in this box
    std::set< Node<DIM>* >& r_contained_nodes = box.rGetNodesContained();

    // Get the local boxes to this box
    std::set<unsigned> local_boxes_indices = GetLocalBoxes(boxIndex);

    // Loop over all the local boxes
    for (std::set<unsigned>::iterator box_iter = local_boxes_indices.begin();
         box_iter != local_boxes_indices.end();
         box_iter++)
    {
        Box<DIM>* p_neighbour_box;

        // Establish whether box is locally owned or halo.
        if (GetBoxOwnership(*box_iter))
        {
            p_neighbour_box = &mBoxes[mBoxesMapping[*box_iter]];
        }
        else // Assume it is a halo.
        {
            p_neighbour_box = &mHaloBoxes[mHaloBoxesMapping[*box_iter]];
        }
        assert(p_neighbour_box);

        // Get the set of nodes contained in this box
        std::set< Node<DIM>* >& r_contained_neighbour_nodes = p_neighbour_box->rGetNodesContained();

        // Loop over these nodes
        for (typename std::set<Node<DIM>*>::iterator neighbour_node_iter = r_contained_neighbour_nodes.begin();
             neighbour_node_iter != r_contained_neighbour_nodes.end();
             ++neighbour_node_iter)
        {
            // Get the index of the other node
            unsigned other_node_index = (*neighbour_node_iter)->GetIndex();

            // Loop over nodes in this box
            for (typename std::set<Node<DIM>*>::iterator node_iter = r_contained_nodes.begin();
                 node_iter != r_contained_nodes.end();
                 ++node_iter)
            {
                unsigned node_index = (*node_iter)->GetIndex();

                // If we're in the same box, then take care not to store the node pair twice
                if (*box_iter == boxIndex)
                {
                    if (other_node_index > node_index)
                    {
                        rNodePairs.push_back(std::pair<Node<DIM>*, Node<DIM>*>((*node_iter), (*neighbour_node_iter)));
                        if (mCalculateNodeNeighbours)
                        {
                            rNodeNeighbours[node_index].insert(other_node_index);
                            rNodeNeighbours[other_node_index].insert(node_index);
                        }
                    }
                }
                else
                {
                    rNodePairs.push_back(std::pair<Node<DIM>*, Node<DIM>*>((*node_iter), (*neighbour_node_iter)));
                    if (mCalculateNodeNeighbours)
                    {
                        rNodeNeighbours[node_index].insert(other_node_index);
                        rNodeNeighbours[other_node_index].insert(node_index);
                    }
                }

            }
        }
    }
}

template<unsigned DIM>
std::vector<int> DistributedBoxCollection<DIM>::CalculateNumberOfNodesInEachStrip()
{
    std::vector<int> cell_numbers(mpDistributedBoxStackFactory->GetHigh() - mpDistributedBoxStackFactory->GetLow(), 0);

    for (std::map<unsigned, unsigned>::iterator iter = mBoxesMapping.begin();
            iter != mBoxesMapping.end();
            ++iter)
    {
        c_vector<unsigned, DIM> coords = CalculateCoordinateIndices(iter->first);
        unsigned location_in_vector = coords[DIM-1]-mpDistributedBoxStackFactory->GetLow();

        cell_numbers[location_in_vector] += mBoxes[iter->second].rGetNodesContained().size();
    }

    return cell_numbers;
}

// Explicit instantiation

template class DistributedBoxCollection<1>;
template class DistributedBoxCollection<2>;
template class DistributedBoxCollection<3>;