ParallelMergeMesh.cpp

Go to the documentation of this file.

#include "moab/ParallelMergeMesh.hpp"
#include "moab/Core.hpp"
#include "moab/CartVect.hpp"
#include "moab/BoundBox.hpp"
#include "moab/Skinner.hpp"
#include "moab/MergeMesh.hpp"
#include "moab/CN.hpp"
#include <cfloat>
#include <algorithm>

#ifdef MOAB_HAVE_MPI
#include "moab_mpi.h"
#endif

namespace moab
{

// Constructor
/*Get Merge Data and tolerance*/
ParallelMergeMesh::ParallelMergeMesh( ParallelComm* pc, const double epsilon ) : myPcomm( pc ), myEps( epsilon )
{
    myMB = pc->get_moab();
    mySkinEnts.resize( 4 );
}

// Have a wrapper function on the actual merge to avoid memory leaks
// Merges elements within a proximity of epsilon
ErrorCode ParallelMergeMesh::merge( EntityHandle levelset, bool skip_local_merge, int dim )
{
    ErrorCode rval = PerformMerge( levelset, skip_local_merge, dim );MB_CHK_ERR( rval );
    CleanUp();
    return rval;
}

// Perform the merge
ErrorCode ParallelMergeMesh::PerformMerge( EntityHandle levelset, bool skip_local_merge, int dim )
{
    // Get the mesh dimension
    ErrorCode rval;
    if( dim < 0 )
    {
        rval = myMB->get_dimension( dim );MB_CHK_ERR( rval );
    }

    // Get the local skin elements
    rval = PopulateMySkinEnts( levelset, dim, skip_local_merge );
    // If there is only 1 proc, we can return now
    if( rval != MB_SUCCESS || myPcomm->size() == 1 ) { return rval; }

    // Determine the global bounding box
    double gbox[6];
    rval = GetGlobalBox( gbox );MB_CHK_ERR( rval );

    /* Assemble The Destination Tuples */
    // Get a list of tuples which contain (toProc, handle, x,y,z)
    myTup.initialize( 1, 0, 1, 3, mySkinEnts[0].size() );
    rval = PopulateMyTup( gbox );MB_CHK_ERR( rval );

    /* Gather-Scatter Tuple
       -tup comes out as (remoteProc,handle,x,y,z) */
    myCD.initialize( myPcomm->comm() );

    // 1 represents dynamic tuple, 0 represents index of the processor to send to
    myCD.gs_transfer( 1, myTup, 0 );

    /* Sort By X,Y,Z
       -Utilizes a custom quick sort incorporating epsilon*/
    SortTuplesByReal( myTup, myEps );

    // Initialize another tuple list for matches
    myMatches.initialize( 2, 0, 2, 0, mySkinEnts[0].size() );

    // ID the matching tuples
    rval = PopulateMyMatches();MB_CHK_ERR( rval );

    // We can free up the tuple myTup now
    myTup.reset();

    /*Gather-Scatter Again*/
    // 1 represents dynamic list, 0 represents proc index to send tuple to
    myCD.gs_transfer( 1, myMatches, 0 );
    // We can free up the crystal router now
    myCD.reset();

    // Sort the matches tuple list
    SortMyMatches();

    // Tag the shared elements
    rval = TagSharedElements( dim );MB_CHK_ERR( rval );

    // Free up the matches tuples
    myMatches.reset();
    return rval;
}

// Sets mySkinEnts with all of the skin entities on the processor
ErrorCode ParallelMergeMesh::PopulateMySkinEnts( const EntityHandle meshset, int dim, bool skip_local_merge )
{
    /*Merge Mesh Locally*/
    // Get all dim dimensional entities
    Range ents;
    ErrorCode rval = myMB->get_entities_by_dimension( meshset, dim, ents );MB_CHK_ERR( rval );

    if( ents.empty() && dim == 3 )
    {
        dim--;
        rval = myMB->get_entities_by_dimension( meshset, dim, ents );MB_CHK_ERR( rval );  // maybe dimension 2
    }

    // Merge Mesh Locally
    if( !skip_local_merge )
    {
        MergeMesh merger( myMB, false );
        merger.merge_entities( ents, myEps );
        // We can return if there is only 1 proc
        if( rval != MB_SUCCESS || myPcomm->size() == 1 ) { return rval; }

        // Rebuild the ents range
        ents.clear();
        rval = myMB->get_entities_by_dimension( meshset, dim, ents );MB_CHK_ERR( rval );
    }

    /*Get Skin
      -Get Range of all dimensional entities
      -skinEnts[i] is the skin entities of dimension i*/
    Skinner skinner( myMB );
    for( int skin_dim = dim; skin_dim >= 0; skin_dim-- )
    {
        rval = skinner.find_skin( meshset, ents, skin_dim, mySkinEnts[skin_dim] );MB_CHK_ERR( rval );
    }
    return MB_SUCCESS;
}

// Determine the global assembly box
ErrorCode ParallelMergeMesh::GetGlobalBox( double* gbox )
{
    ErrorCode rval;

    /*Get Bounding Box*/
    BoundBox box;
    if( mySkinEnts[0].size() != 0 )
    {
        rval = box.update( *myMB, mySkinEnts[0] );MB_CHK_ERR( rval );
    }

    // Invert the max
    box.bMax *= -1;

    /*Communicate to all processors*/
    MPI_Allreduce( (void*)&box, gbox, 6, MPI_DOUBLE, MPI_MIN, MPI_COMM_WORLD );

    /*Assemble Global Bounding Box*/
    // Flip the max back
    for( int i = 3; i < 6; i++ )
    {
        gbox[i] *= -1;
    }
    return MB_SUCCESS;
}

// Assemble the tuples with their processor destination
ErrorCode ParallelMergeMesh::PopulateMyTup( double* gbox )
{
    /*Figure out how do partition the global box*/
    double lengths[3];
    int parts[3];
    ErrorCode rval = PartitionGlobalBox( gbox, lengths, parts );MB_CHK_ERR( rval );

    /* Get Skin Coordinates, Vertices */
    double* x = new double[mySkinEnts[0].size()];
    double* y = new double[mySkinEnts[0].size()];
    double* z = new double[mySkinEnts[0].size()];
    rval      = myMB->get_coords( mySkinEnts[0], x, y, z );
    if( rval != MB_SUCCESS )
    {
        // Prevent Memory Leak
        delete[] x;
        delete[] y;
        delete[] z;
        return rval;
    }

    // Initialize variable to be used in the loops
    std::vector< int > toProcs;
    int xPart, yPart, zPart, xEps, yEps, zEps, baseProc;
    unsigned long long tup_i = 0, tup_ul = 0, tup_r = 0, count = 0;
    // These are boolean to determine if the vertex is on close enough to a given border
    bool xDup, yDup, zDup;
    bool canWrite = myTup.get_writeEnabled();
    if( !canWrite ) myTup.enableWriteAccess();
    // Go through each vertex
    for( Range::iterator it = mySkinEnts[0].begin(); it != mySkinEnts[0].end(); ++it )
    {
        xDup = false;
        yDup = false;
        zDup = false;
        // Figure out which x,y,z partition the element is in.
        xPart = static_cast< int >( floor( ( x[count] - gbox[0] ) / lengths[0] ) );
        xPart = ( xPart < parts[0] ? xPart : parts[0] - 1 );  // Make sure it stays within the bounds

        yPart = static_cast< int >( floor( ( y[count] - gbox[1] ) / lengths[1] ) );
        yPart = ( yPart < parts[1] ? yPart : parts[1] - 1 );  // Make sure it stays within the bounds

        zPart = static_cast< int >( floor( ( z[count] - gbox[2] ) / lengths[2] ) );
        zPart = ( zPart < parts[2] ? zPart : parts[2] - 1 );  // Make sure it stays within the bounds

        // Figure out the partition with the addition of Epsilon
        xEps = static_cast< int >( floor( ( x[count] - gbox[0] + myEps ) / lengths[0] ) );
        yEps = static_cast< int >( floor( ( y[count] - gbox[1] + myEps ) / lengths[1] ) );
        zEps = static_cast< int >( floor( ( z[count] - gbox[2] + myEps ) / lengths[2] ) );

        // Figure out if the vertex needs to be sent to multiple procs
        xDup = ( xPart != xEps && xEps < parts[0] );
        yDup = ( yPart != yEps && yEps < parts[1] );
        zDup = ( zPart != zEps && zEps < parts[2] );

        // Add appropriate processors to the vector
        baseProc = xPart + yPart * parts[0] + zPart * parts[0] * parts[1];
        toProcs.push_back( baseProc );
        if( xDup )
        {
            toProcs.push_back( baseProc + 1 );  // Get partition to the right
        }
        if( yDup )
        {
            // Partition up 1
            toProcs.push_back( baseProc + parts[0] );
        }
        if( zDup )
        {
            // Partition above 1
            toProcs.push_back( baseProc + parts[0] * parts[1] );
        }
        if( xDup && yDup )
        {
            // Partition up 1 and right 1
            toProcs.push_back( baseProc + parts[0] + 1 );
        }
        if( xDup && zDup )
        {
            // Partition right 1 and above 1
            toProcs.push_back( baseProc + parts[0] * parts[1] + 1 );
        }
        if( yDup && zDup )
        {
            // Partition up 1 and above 1
            toProcs.push_back( baseProc + parts[0] * parts[1] + parts[0] );
        }
        if( xDup && yDup && zDup )
        {
            // Partition right 1, up 1, and above 1
            toProcs.push_back( baseProc + parts[0] * parts[1] + parts[0] + 1 );
        }
        // Grow the tuple list if necessary
        while( myTup.get_n() + toProcs.size() >= myTup.get_max() )
        {
            myTup.resize( myTup.get_max() ? myTup.get_max() + myTup.get_max() / 2 + 1 : 2 );
        }

        // Add each proc as a tuple
        for( std::vector< int >::iterator proc = toProcs.begin(); proc != toProcs.end(); ++proc )
        {
            myTup.vi_wr[tup_i++]   = *proc;
            myTup.vul_wr[tup_ul++] = *it;
            myTup.vr_wr[tup_r++]   = x[count];
            myTup.vr_wr[tup_r++]   = y[count];
            myTup.vr_wr[tup_r++]   = z[count];
            myTup.inc_n();
        }
        count++;
        toProcs.clear();
    }
    delete[] x;
    delete[] y;
    delete[] z;
    if( !canWrite ) myTup.disableWriteAccess();
    return MB_SUCCESS;
}

// Partition the global box by the number of procs
ErrorCode ParallelMergeMesh::PartitionGlobalBox( double* gbox, double* lengths, int* parts )
{
    // Determine the length of each side
    double xLen       = gbox[3] - gbox[0];
    double yLen       = gbox[4] - gbox[1];
    double zLen       = gbox[5] - gbox[2];
    unsigned numProcs = myPcomm->size();

    // Partition sides from the longest to shortest lengths
    // If x is the longest side
    if( xLen >= yLen && xLen >= zLen )
    {
        parts[0] = PartitionSide( xLen, yLen * zLen, numProcs, true );
        numProcs /= parts[0];
        // If y is second longest
        if( yLen >= zLen )
        {
            parts[1] = PartitionSide( yLen, zLen, numProcs, false );
            parts[2] = numProcs / parts[1];
        }
        // If z is the longer
        else
        {
            parts[2] = PartitionSide( zLen, yLen, numProcs, false );
            parts[1] = numProcs / parts[2];
        }
    }
    // If y is the longest side
    else if( yLen >= zLen )
    {
        parts[1] = PartitionSide( yLen, xLen * zLen, numProcs, true );
        numProcs /= parts[1];
        // If x is the second longest
        if( xLen >= zLen )
        {
            parts[0] = PartitionSide( xLen, zLen, numProcs, false );
            parts[2] = numProcs / parts[0];
        }
        // If z is the second longest
        else
        {
            parts[2] = PartitionSide( zLen, xLen, numProcs, false );
            parts[0] = numProcs / parts[2];
        }
    }
    // If z is the longest side
    else
    {
        parts[2] = PartitionSide( zLen, xLen * yLen, numProcs, true );
        numProcs /= parts[2];
        // If x is the second longest
        if( xLen >= yLen )
        {
            parts[0] = PartitionSide( xLen, yLen, numProcs, false );
            parts[1] = numProcs / parts[0];
        }
        // If y is the second longest
        else
        {
            parts[1] = PartitionSide( yLen, xLen, numProcs, false );
            parts[0] = numProcs / parts[1];
        }
    }

    // Divide up each side to give the lengths
    lengths[0] = xLen / (double)parts[0];
    lengths[1] = yLen / (double)parts[1];
    lengths[2] = zLen / (double)parts[2];
    return MB_SUCCESS;
}

// Partition a side based on the length ratios
int ParallelMergeMesh::PartitionSide( double sideLen, double restLen, unsigned numProcs, bool altRatio )
{
    // If theres only 1 processor, then just return 1
    if( numProcs == 1 ) { return 1; }
    // Initialize with the ratio of 1 proc
    double ratio    = -DBL_MAX;
    unsigned factor = 1;
    // We need to be able to save the last ratio and factor (for comparison)
    double oldRatio  = ratio;
    double oldFactor = 1;

    // This is the ratio were shooting for
    double goalRatio = sideLen / restLen;

    // Calculate the divisor and numerator power
    // This avoid if statements in the loop and is useful since both calculations are similar
    double divisor, p;
    if( altRatio )
    {
        divisor = (double)numProcs * sideLen;
        p       = 3;
    }
    else
    {
        divisor = (double)numProcs;
        p       = 2;
    }

    // Find each possible factor
    for( unsigned i = 2; i <= numProcs / 2; i++ )
    {
        // If it is a factor...
        if( numProcs % i == 0 )
        {
            // We need to save the past factor
            oldRatio  = ratio;
            oldFactor = factor;
            // There are 2 different ways to calculate the ratio:
            // Comparing 1 side to 2 sides: (i*i*i)/(numProcs*x)
            // Justification:  We have a ratio x:y:z (side Lengths) == a:b:c (procs).  So a=kx,
            // b=ky, c=kz. Also, abc=n (numProcs) => bc = n/a.  Also, a=kx => k=a/x => 1/k=x/a And so
            // x/(yz) == (kx)/(kyz) == (kx)/(kykz(1/k)) == a/(bc(x/a)) == a/((n/a)(x/a)) == a^3/(nx).
            // Comparing 1 side to 1 side: (i*i)/numprocs
            // Justification: i/(n/i) == i^2/n
            ratio  = pow( (double)i, p ) / divisor;
            factor = i;
            // Once we have passed the goal ratio, we can break since we'll only move away from the
            // goal ratio
            if( ratio >= goalRatio ) { break; }
        }
    }
    // If we haven't reached the goal ratio yet, check out factor = numProcs
    if( ratio < goalRatio )
    {
        oldRatio  = ratio;
        oldFactor = factor;
        factor    = numProcs;
        ratio     = pow( (double)numProcs, p ) / divisor;
    }

    // Figure out if our oldRatio is better than ratio
    if( fabs( ratio - goalRatio ) > fabs( oldRatio - goalRatio ) ) { factor = oldFactor; }
    // Return our findings
    return factor;
}

// Id the tuples that are matching
ErrorCode ParallelMergeMesh::PopulateMyMatches()
{
    // Counters for accessing tuples more efficiently
    unsigned long i = 0, mat_i = 0, mat_ul = 0, j = 0, tup_r = 0;
    double eps2 = myEps * myEps;

    uint tup_mi, tup_ml, tup_mul, tup_mr;
    myTup.getTupleSize( tup_mi, tup_ml, tup_mul, tup_mr );

    bool canWrite = myMatches.get_writeEnabled();
    if( !canWrite ) myMatches.enableWriteAccess();

    while( ( i + 1 ) < myTup.get_n() )
    {
        // Proximity Comparison
        double xi = myTup.vr_rd[tup_r], yi = myTup.vr_rd[tup_r + 1], zi = myTup.vr_rd[tup_r + 2];

        bool done = false;
        while( !done )
        {
            j++;
            tup_r += tup_mr;
            if( j >= myTup.get_n() ) { break; }
            CartVect cv( myTup.vr_rd[tup_r] - xi, myTup.vr_rd[tup_r + 1] - yi, myTup.vr_rd[tup_r + 2] - zi );
            if( cv.length_squared() > eps2 ) { done = true; }
        }
        // Allocate the tuple list before adding matches
        while( myMatches.get_n() + ( j - i ) * ( j - i - 1 ) >= myMatches.get_max() )
        {
            myMatches.resize( myMatches.get_max() ? myMatches.get_max() + myMatches.get_max() / 2 + 1 : 2 );
        }

        // We now know that tuples [i to j) exclusive match.
        // If n tuples match, n*(n-1) match tuples will be made
        // tuples are of the form (proc1,proc2,handle1,handle2)
        if( i + 1 < j )
        {
            int kproc           = i * tup_mi;
            unsigned long khand = i * tup_mul;
            for( unsigned long k = i; k < j; k++ )
            {
                int lproc           = kproc + tup_mi;
                unsigned long lhand = khand + tup_mul;
                for( unsigned long l = k + 1; l < j; l++ )
                {
                    myMatches.vi_wr[mat_i++]   = myTup.vi_rd[kproc];   // proc1
                    myMatches.vi_wr[mat_i++]   = myTup.vi_rd[lproc];   // proc2
                    myMatches.vul_wr[mat_ul++] = myTup.vul_rd[khand];  // handle1
                    myMatches.vul_wr[mat_ul++] = myTup.vul_rd[lhand];  // handle2
                    myMatches.inc_n();

                    myMatches.vi_wr[mat_i++]   = myTup.vi_rd[lproc];   // proc1
                    myMatches.vi_wr[mat_i++]   = myTup.vi_rd[kproc];   // proc2
                    myMatches.vul_wr[mat_ul++] = myTup.vul_rd[lhand];  // handle1
                    myMatches.vul_wr[mat_ul++] = myTup.vul_rd[khand];  // handle2
                    myMatches.inc_n();
                    lproc += tup_mi;
                    lhand += tup_mul;
                }
                kproc += tup_mi;
                khand += tup_mul;
            }  // End for(int k...
        }
        i = j;
    }  // End while(i+1<tup.n)

    if( !canWrite ) myMatches.disableWriteAccess();
    return MB_SUCCESS;
}

// Sort the matching tuples so that vertices can be tagged accurately
ErrorCode ParallelMergeMesh::SortMyMatches()
{
    TupleList::buffer buf( mySkinEnts[0].size() );
    // Sorts are necessary to check for doubles
    // Sort by remote handle
    myMatches.sort( 3, &buf );
    // Sort by matching proc
    myMatches.sort( 1, &buf );
    // Sort by local handle
    myMatches.sort( 2, &buf );
    buf.reset();
    return MB_SUCCESS;
}

// Tag the shared elements using existing PComm functionality
ErrorCode ParallelMergeMesh::TagSharedElements( int dim )
{
    // Manipulate the matches list to tag vertices and entities
    // Set up proc ents
    Range proc_ents;
    ErrorCode rval;

    // get the entities in the partition sets
    for( Range::iterator rit = myPcomm->partitionSets.begin(); rit != myPcomm->partitionSets.end(); ++rit )
    {
        Range tmp_ents;
        rval = myMB->get_entities_by_handle( *rit, tmp_ents, true );
        if( MB_SUCCESS != rval ) { return rval; }
        proc_ents.merge( tmp_ents );
    }
    if( myMB->dimension_from_handle( *proc_ents.rbegin() ) != myMB->dimension_from_handle( *proc_ents.begin() ) )
    {
        Range::iterator lower = proc_ents.lower_bound( CN::TypeDimensionMap[0].first ),
                        upper = proc_ents.upper_bound( CN::TypeDimensionMap[dim - 1].second );
        proc_ents.erase( lower, upper );
    }

    // This vector doesn't appear to be used but its in resolve_shared_ents
    int maxp = -1;
    std::vector< int > sharing_procs( MAX_SHARING_PROCS );
    std::fill( sharing_procs.begin(), sharing_procs.end(), maxp );

    // get ents shared by 1 or n procs
    std::map< std::vector< int >, std::vector< EntityHandle > > proc_nranges;
    Range proc_verts;
    rval = myMB->get_adjacencies( proc_ents, 0, false, proc_verts, Interface::UNION );
    if( rval != MB_SUCCESS ) { return rval; }

    rval = myPcomm->tag_shared_verts( myMatches, proc_nranges, proc_verts );
    if( rval != MB_SUCCESS ) { return rval; }

    // get entities shared by 1 or n procs
    rval = myPcomm->get_proc_nvecs( dim, dim - 1, &mySkinEnts[0], proc_nranges );
    if( rval != MB_SUCCESS ) { return rval; }

    // create the sets for each interface; store them as tags on
    // the interface instance
    Range iface_sets;
    rval = myPcomm->create_interface_sets( proc_nranges );
    if( rval != MB_SUCCESS ) { return rval; }
    // establish comm procs and buffers for them
    std::set< unsigned int > procs;
    rval = myPcomm->get_interface_procs( procs, true );
    if( rval != MB_SUCCESS ) { return rval; }

    // resolve shared entity remote handles; implemented in ghost cell exchange
    // code because it's so similar
    rval = myPcomm->exchange_ghost_cells( -1, -1, 0, true, true );
    if( rval != MB_SUCCESS ) { return rval; }
    // now build parent/child links for interface sets
    rval = myPcomm->create_iface_pc_links();
    return rval;
}

// Make sure to free up any allocated data
// Need to avoid a double free
void ParallelMergeMesh::CleanUp()
{
    // The reset operation is now safe and avoids a double free()
    myMatches.reset();
    myTup.reset();
    myCD.reset();
}

// Simple quick  sort to real
void ParallelMergeMesh::SortTuplesByReal( TupleList& tup, double eps )
{
    bool canWrite = tup.get_writeEnabled();
    if( !canWrite ) tup.enableWriteAccess();

    uint mi, ml, mul, mr;
    tup.getTupleSize( mi, ml, mul, mr );
    PerformRealSort( tup, 0, tup.get_n(), eps, mr );

    if( !canWrite ) tup.disableWriteAccess();
}

// Swap around tuples
void ParallelMergeMesh::SwapTuples( TupleList& tup, unsigned long a, unsigned long b )
{
    if( a == b ) return;

    uint mi, ml, mul, mr;
    tup.getTupleSize( mi, ml, mul, mr );

    // Swap mi
    unsigned long a_val = a * mi, b_val = b * mi;
    for( unsigned long i = 0; i < mi; i++ )
    {
        sint t           = tup.vi_rd[a_val];
        tup.vi_wr[a_val] = tup.vi_rd[b_val];
        tup.vi_wr[b_val] = t;
        a_val++;
        b_val++;
    }
    // Swap ml
    a_val = a * ml;
    b_val = b * ml;
    for( unsigned long i = 0; i < ml; i++ )
    {
        slong t          = tup.vl_rd[a_val];
        tup.vl_wr[a_val] = tup.vl_rd[b_val];
        tup.vl_wr[b_val] = t;
        a_val++;
        b_val++;
    }
    // Swap mul
    a_val = a * mul;
    b_val = b * mul;
    for( unsigned long i = 0; i < mul; i++ )
    {
        Ulong t           = tup.vul_rd[a_val];
        tup.vul_wr[a_val] = tup.vul_rd[b_val];
        tup.vul_wr[b_val] = t;
        a_val++;
        b_val++;
    }
    // Swap mr
    a_val = a * mr;
    b_val = b * mr;
    for( unsigned long i = 0; i < mr; i++ )
    {
        realType t       = tup.vr_rd[a_val];
        tup.vr_wr[a_val] = tup.vr_rd[b_val];
        tup.vr_wr[b_val] = t;
        a_val++;
        b_val++;
    }
}

// Perform the sorting of a tuple by real
// To sort an entire tuple_list, call (tup,0,tup.n,epsilon)
void ParallelMergeMesh::PerformRealSort( TupleList& tup, unsigned long left, unsigned long right, double eps,
                                         uint tup_mr )
{
    // If list size is only 1 or 0 return
    if( left + 1 >= right ) { return; }
    unsigned long swap = left, tup_l = left * tup_mr, tup_t = tup_l + tup_mr;

    // Swap the median with the left position for a (hopefully) better split
    SwapTuples( tup, left, ( left + right ) / 2 );

    // Partition the data
    for( unsigned long t = left + 1; t < right; t++ )
    {
        // If the left value(pivot) is greater than t_val, swap it into swap
        if( TupleGreaterThan( tup, tup_l, tup_t, eps, tup_mr ) )
        {
            swap++;
            SwapTuples( tup, swap, t );
        }
        tup_t += tup_mr;
    }

    // Swap so that position swap is in the correct position
    SwapTuples( tup, left, swap );

    // Sort left and right of swap
    PerformRealSort( tup, left, swap, eps, tup_mr );
    PerformRealSort( tup, swap + 1, right, eps, tup_mr );
}

// Note, this takes the actual tup.vr[] index (aka i*tup.mr)
bool ParallelMergeMesh::TupleGreaterThan( TupleList& tup, unsigned long vrI, unsigned long vrJ, double eps,
                                          uint tup_mr )
{
    unsigned check = 0;
    while( check < tup_mr )
    {
        // If the values are the same
        if( fabs( tup.vr_rd[vrI + check] - tup.vr_rd[vrJ + check] ) <= eps )
        {
            check++;
            continue;
        }
        // If I greater than J
        else if( tup.vr_rd[vrI + check] > tup.vr_rd[vrJ + check] )
        {
            return true;
        }
        // If J greater than I
        else
        {
            return false;
        }
    }
    // All Values are the same
    return false;
}

}  // End namespace moab