sympack_interf_impl.hpp

/*
   Copyright (c) 2012 The Regents of the University of California,
   through Lawrence Berkeley National Laboratory.  

Author: Mathias Jacquelin and Lin Lin

This file is part of PEXSI. All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

(1) Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
(2) Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
(3) Neither the name of the University of California, Lawrence Berkeley
National Laboratory, U.S. Dept. of Energy nor the names of its contributors may
be used to endorse or promote products derived from this software without
specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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You are under no obligation whatsoever to provide any bug fixes, patches, or
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("Enhancements") to anyone; however, if you choose to make your Enhancements
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 */
#ifndef _PEXSI_symPACK_INTERF_IMPL_HPP_
#define _PEXSI_symPACK_INTERF_IMPL_HPP_

// Interface with symPACK
#include "sympack.hpp"
//#include "sympack/sp_blas.hpp"

// Interface with PSelInv
#include "pexsi/pselinv.hpp"

// Interface with sparse matrix (CSC format)
#include "pexsi/sparse_matrix.hpp"
#include "pexsi/environment.hpp"
#include "pexsi/sparse_matrix.hpp"
#include "pexsi/NumMat.hpp"
#include "pexsi/NumVec.hpp"

// Interface with LAPACK
#include "pexsi/lapack.hpp"


#include <list>

namespace PEXSI{

template<typename T> void symPACKMatrixToSuperNode( 
    symPACK::symPACKMatrix<T>& SMat,
    SuperNodeType& super ){
  Int n = SMat.Size();

  symPACK::Ordering & Order = (symPACK::Ordering &)SMat.GetOrdering();
  const std::vector<Int>& SInvp = Order.invp;
  super.permInv.Resize( SInvp.size() );
  const std::vector<Int>& SPerm = Order.perm;
  super.perm.Resize( SPerm.size() );

  // perm
  for( Int i = 0; i < SPerm.size(); i++ ){
    super.permInv[i] = SPerm[i]-1;
  }

  // permInv
  for( Int i = 0; i < SInvp.size(); i++ ){
    super.perm[i] = SInvp[i]-1;
  }

  super.perm_r.Resize( n);
  for( Int i = 0; i < n; i++ ){
    super.perm_r[i] = i;
  }
  super.permInv_r = super.perm_r;


  std::vector<Int>& XSuper = SMat.GetSupernodalPartition();
  Int numSuper = XSuper.size() - 1;

  // superPtr
  IntNumVec& superPtr = super.superPtr;
  superPtr.Resize( numSuper + 1 );
  for( Int i = 0; i < numSuper + 1; i++ ){
    superPtr[i] = XSuper[i] - 1;
  }

  // superIdx
  IntNumVec& superIdx = super.superIdx;
  superIdx.Resize( n );
  const std::vector<Int>& superMember = SMat.GetSupMembership();
  for( Int i = 0; i < n; i++ ){
    superIdx(i) = superMember[i] - 1;
  }

  // etree
  const symPACK::ETree& etree = SMat.GetETree();
  super.etree.Resize(n);
  for( Int i = 0; i < etree.Size(); i++ ){
    super.etree[i] = etree.PostParent(i);
    if(super.etree[i]==0){
      super.etree[i]=n+1;
    }
    super.etree[i]-=1;
  }

}  // -----  end of symPACKMatrixToSuperNode ----- 



template<typename T> void symPACKMatrixToPMatrix( 
    symPACK::symPACKMatrix<T>& SMat,
    PMatrix<T>& PMat ){
  TIMER_START(symPACKtoPMatrix);
  // This routine assumes that the g, supernode and options of PMatrix
  // has been set outside this routine.

  Int mpirank, mpisize;
  const GridType *g = PMat.Grid();

  // FIXME Check PMatrix and symPACKMatrix has the same communicator
  MPI_Comm comm = g->comm;
  MPI_Comm colComm = g->colComm;
  MPI_Comm rowComm = g->rowComm;
  MPI_Comm_size(comm, &mpisize); 
  MPI_Comm_rank(comm, &mpirank);

  Int nprow = g->numProcRow, npcol = g->numProcCol;

  Int mpirow = mpirank / npcol;  
  Int mpicol = mpirank % npcol;

  Int n = SMat.Size();
  PMat.ColBlockIdx().clear();
  PMat.RowBlockIdx().clear();
  PMat.ColBlockIdx().resize( PMat.NumLocalBlockCol() );
  PMat.RowBlockIdx().resize( PMat.NumLocalBlockRow() );

  const IntNumVec& superIdx = PMat.SuperNode()->superIdx;
#if ( _DEBUGlevel_ >= 1 )
  statusOFS << "superIdx = " << superIdx << std::endl;
#endif


  // for loop over all supernodes
  //
  //   if the current processor owns the supernode (the ownership is block
  //   cyclic)
  //     serialize the information
  //     broadcast the information to all processors
  //   elseif 
  //     receive the information from the processor owning the
  //     supernode, and save the information in a deserialized buffer
  //   endif
  //
  //   (Local operation from now)
  //   if the current processor owns the correct processor column
  //     for loop over the local blocks
  //       for loop over each row
  //         if the current row number belong to the current processor
  //           add the row index to a vector for LBuf
  //         endif
  //       endfor
  //     endfor
  //
  //     Allocate the sign of LBuf for saving the nonzero values
  //     Convert the format of rowind
  //
  //     for loop over the local blocks
  //       for loop over each row
  //         if the current row number belong to the current processor
  //           Append the nonzero values to nzval
  //         endif
  //       endfor
  //     endfor
  //   endif
  //
  //   discard the temporary information in the buffer for all
  //   processors
  //
  // endfor
  //
  // Perform SendToCrossDiagonal to fill the U part.
  //
  // Remark:
  //   1.  The communiation is performed in a supernode-by-supernode
  //   way.  This may not be very fast.  A first improvement is to
  //   broadcast all local supernodes at once and then do local
  //   post-processing.
  symPACK::Mapping * mapping = (symPACK::Mapping*)SMat.GetMapping();

  Int numSuper = PMat.NumSuper();


#if 1
  symPACK::Icomm snodeIcomm;
  std::vector<char> buffer;
  for( Int iSuper = 0; iSuper < numSuper; iSuper++ ){
    symPACK::SuperNode<T> * snode;

    Int iOwner = mapping->Map(iSuper,iSuper);

    if( mpirank == iOwner ){
      // Get the local supernode
      Int iSuperLocal = SMat.snodeLocalIndex(iSuper+1);
      //symPACK::SuperNode<T>& snodetmp = SMat.GetLocalSupernode(iSuperLocal-1);
      symPACK::SuperNode<T>* snodetmp = SMat.snodeLocal(iSuper+1); 
#if ( _DEBUGlevel_ >= 1 )
      statusOFS << "iSuper = " << iSuper << ", iSuperLocal = " <<
        iSuperLocal << ", id = " << snodetmp->Id() << ", size = " << 
        snodetmp->Size() << ", #Block = " << snodetmp->NZBlockCnt() <<
        std::endl;
      //    statusOFS << "snode (before bcast) = " << *snodetmp << std::endl;
#endif
      // Serialize the information in the current supernode
      snodetmp->Serialize( snodeIcomm);
      Int msgSize = snodeIcomm.size();
#if ( _DEBUGlevel_ >= 1 )
      statusOFS << "msgSize = " << msgSize << std::endl;
#endif

      // Communicate the supernode
      MPI_Bcast( &msgSize, 1, MPI_INT, mpirank, comm );
      MPI_Bcast( snodeIcomm.front(), msgSize, MPI_CHAR, mpirank, comm );
      // Copy the data from buffer to snode
      //symPACK::Deserialize( snodeIcomm.front(), snode );

      snode = SMat.CreateSuperNode(SMat.GetOptions().decomposition,snodeIcomm.front(),msgSize,-1);
      snode->InitIdxToBlk();
    } // if owning the supernode
    else{
      // Receive the supernode
      Int rootRank = iOwner;
      Int msgSize;
      MPI_Bcast( &msgSize, 1, MPI_INT, rootRank, comm );
      buffer.resize(msgSize);
      MPI_Bcast( &buffer[0], msgSize, MPI_CHAR, rootRank, comm );
      //symPACK::Deserialize( &buffer[0], snode );

      snode = SMat.CreateSuperNode(SMat.GetOptions().decomposition,&buffer[0],msgSize,-1);
      snode->InitIdxToBlk();
    } // if not owning the supernode but is in the receiving column

#if ( _DEBUGlevel_ >= 1 )
    statusOFS << "All communication is finished." << std::endl;
#endif

    // Local operation from now
    if( mpicol == ( iSuper % npcol ) ){
      Int jb = iSuper / npcol;
      std::vector<LBlock<T> >& Lcol = PMat.L(jb);
      std::set<Int> blkSet;
      Int superSize = snode->Size();

      // Count the number of blocks in the supernode belonging to this
      // processor
      for( Int blkidx = 0; blkidx < snode->NZBlockCnt(); blkidx++ ){
        symPACK::NZBlockDesc desc = snode->GetNZBlockDesc( blkidx );
        Int nrows = snode->NRows(blkidx);
        Int firstRow = desc.GIndex - 1;
        Int lastRow = firstRow + nrows - 1;
#if ( _DEBUGlevel_ >= 1 )
        statusOFS << "firstRow = " << firstRow << ", lastRow = " << lastRow << std::endl;
#endif
        for( Int i = superIdx(firstRow); i <= superIdx(lastRow); i++ ){
          if( mpirow == ( i % nprow ) ){
            blkSet.insert( i );
          } // if the current processor is in the right processor row
        }
      } // for ( blkidx )

      Int numBlkLocal = blkSet.size();
      std::vector<Int> blkVec;
      blkVec.insert( blkVec.end(), blkSet.begin(), blkSet.end() );
      Lcol.resize( blkVec.size() );

      // Allocate the nonzero rows and nzvals 
#if ( _DEBUGlevel_ >= 1 )
      statusOFS << "Lcol.size = " << Lcol.size() << std::endl;
      statusOFS << "blkSet.size = " << blkSet.size() << std::endl;
      statusOFS << "blkVec = " << blkVec << std::endl;
#endif

      std::vector<std::vector<Int> > rowsBlk( Lcol.size() );
      std::vector<std::vector<T> > nzvalBlk( Lcol.size() );

      for( Int blkidx = 0; blkidx < snode->NZBlockCnt(); blkidx++ ){
        symPACK::NZBlockDesc desc = snode->GetNZBlockDesc( blkidx );
        Int nrows = snode->NRows(blkidx);
        Int firstRow = desc.GIndex - 1;
        Int lastRow = firstRow + nrows - 1;
        T* nzval = snode->GetNZval( desc.Offset );
        std::vector<Int>::iterator vi;
        Int pos;
        for( Int i = firstRow; i <= lastRow; i++ ){
          vi = find( blkVec.begin(), blkVec.end(), superIdx(i) );
          if( vi != blkVec.end() ){
            pos = vi - blkVec.begin();
            rowsBlk[pos].push_back(i);
            nzvalBlk[pos].insert(
                nzvalBlk[pos].end(),
                nzval, nzval + superSize ); 
          }
          nzval += superSize;
        }
      } // for ( blkidx )

      // Save the information to Lcol
      for ( Int iblk = 0; iblk < Lcol.size(); iblk++ ){
        std::vector<Int>& rows = rowsBlk[iblk];
        std::vector<T>& nzval = nzvalBlk[iblk];
        LBlock<T>& LB = Lcol[iblk];
        LB.blockIdx = blkVec[iblk];
        LB.numRow = rows.size();
        LB.numCol = superSize;
        LB.rows = IntNumVec( LB.numRow, true, &rows[0] );
        if( LB.numRow * LB.numCol != nzval.size() ){
          std::ostringstream msg;
          msg << "message size does not match for the blockIdx " << LB.blockIdx << std::endl
            << "LB.numRow * LB.numCol = " << LB.numRow * LB.numCol << std::endl
            << "nzval.size            = " << nzval.size() << std::endl;
          ErrorHandling( msg.str().c_str() );
        }
        // Convert the row major format to column major format
        Transpose( NumMat<T>( LB.numCol, LB.numRow, true,
              &nzval[0] ), LB.nzval );
      }
    } // if the current processor is in the right processor column

    // Set the MPI Barrier
    delete snode;
    MPI_Barrier( comm );
  }
#else
  std::vector<symPACK::SuperNode<T> * > & localSnodes = SMat.GetLocalSupernodes();
  std::vector<int> sizes(mpisize,0);

  //first do the counting
  for(Int supidx = 0; supidx < localSnodes.size(); supidx++){
    symPACK::SuperNode<T> * curSnode = localSnodes[supidx];
    Int ksup = curSnode->Id();
    Int superSize = curSnode->Size();

    std::vector<bool> isSent(mpisize,false);

    //find where this supernode is supposed to go
    Int destCol = ksup % npcol;
    for( Int blkidx = 0; blkidx < snode->NZBlockCnt(); blkidx++ ){
      symPACK::NZBlockDesc desc = snode->GetNZBlockDesc( blkidx );
      Int nrows = snode->NRows(blkidx);
      Int firstRow = desc.GIndex - 1;
      Int lastRow = firstRow + nrows - 1;

      for( Int i = firstRow; i <= lastRow; i++ ){
        Int isup = superIdx[i];
        Int destRow = isup % nprow;
        Int pnum = destRow*npcol + destCol;

        if(!isSent[pnum]){
          //Supernode index and number of rows
          sizes[pNum]+=sizeof(Int)+sizeof(Int);
          isSent[pnum] = true;
        }

        //add one row + the index
        sizes[pNum]+=sizeof(Int)+superSize*sizeof(T);
      }
    } // for ( blkidx )


    //compute the displacement and total buffersize required
    std::vector<int> displs(mpisize+1,0);
    displs[0]=0;
    std::partial_sum(sizes.begin(),sizes.end(),displs.begin()+1);

    int total_send_size = displs.back();
    symPACK::Icomm * IsendPtr = new symPACK::Icomm(total_send_size,MPI_REQUEST_NULL);


#endif

  PMatrixLtoU( PMat );


  //Fill ColBlockIdx and RowBlockIdx
  for( Int jb = 0; jb < PMat.NumLocalBlockCol(); jb++ ){
    Int bnum = GBj( jb, g );
    if( bnum >= numSuper ) continue;
    std::vector<LBlock<T> >& Lcol = PMat.L(jb);
    for( Int iblk = 0; iblk < Lcol.size(); iblk++ ){
      LBlock<T>& LB = Lcol[iblk];
      PMat.ColBlockIdx(jb).push_back(LB.blockIdx);
      Int LBi = LB.blockIdx / g->numProcRow; 
      PMat.RowBlockIdx( LBi ).push_back( bnum );
    }
  }

  for( Int ib = 0; ib < PMat.NumLocalBlockRow(); ib++ ){
    Int bnum = GBi( ib, g );
    if( bnum >= numSuper ) continue;
    std::vector<UBlock<T> >& Urow = PMat.U(ib);
    for(Int jblk = 0; jblk < Urow.size(); jblk++ ){
      UBlock<T> & UB = Urow[jblk];
      PMat.RowBlockIdx(ib).push_back(UB.blockIdx);
      Int LBj = UB.blockIdx / g->numProcCol; 
      PMat.ColBlockIdx( LBj ).push_back( bnum );
    }
  }

  for( Int ib = 0; ib < PMat.NumLocalBlockRow(); ib++ ){
    std::sort(PMat.RowBlockIdx(ib).begin(),PMat.RowBlockIdx(ib).end(),std::less<Int>());
  }
  for( Int jb = 0; jb < PMat.NumLocalBlockCol(); jb++ ){
    std::sort(PMat.ColBlockIdx(jb).begin(),PMat.ColBlockIdx(jb).end(),std::less<Int>());
  }

  const SuperNodeType* super = PMat.SuperNode();
  for( Int ksup = 0; ksup < numSuper; ksup++ ){
    Int pcol = ( ksup % npcol );
    Int prow = ( ksup % nprow );
    if( mpirow == prow ){
      NumMat<T> DiagBuf;
      DiagBuf.Resize(SuperSize( ksup, super ), SuperSize( ksup, super ));
      if( mpicol == pcol ){
        Int jb = ksup / npcol;
        std::vector<LBlock<T> >& Lcol = PMat.L(jb);
        LBlock<T>& LB = Lcol[0];
        for(Int row = 0; row<LB.nzval.m(); row++){
          for(Int col = row+1; col<LB.nzval.n(); col++){
            //LB.nzval(row,col) = T(std::conj(LB.nzval(col,row))) * LB.nzval(row,row);
            LB.nzval(row,col) = (LB.nzval(col,row)) * LB.nzval(row,row);
          }
        } 
        DiagBuf = LB.nzval;
      }
    }
  }
  TIMER_STOP(symPACKtoPMatrix);
}  // -----  end of symPACKMatrixToPMatrix ----- 

template<typename T> void PMatrixLtoU( PMatrix<T>& PMat )
{
  TIMER_START(PMatrixLtoU);

  //Send L to U
  Int mpirank, mpisize;
  const GridType *g = PMat.Grid();

  // FIXME Check PMatrix and symPACKMatrix has the same communicator
  MPI_Comm comm = g->comm;
  MPI_Comm colComm = g->colComm;
  MPI_Comm rowComm = g->rowComm;
  MPI_Comm_size(comm, &mpisize); 
  MPI_Comm_rank(comm, &mpirank);

  Int nprow = g->numProcRow, npcol = g->numProcCol;
  Int mpirow = mpirank / npcol;  
  Int mpicol = mpirank % npcol;

  Int numSuper = PMat.NumSuper();
  for( Int ksup = 0; ksup < numSuper; ksup++ ){
#if ( _DEBUGlevel_ >= 1 )
    statusOFS<<"----------------------- "<< ksup<<std::endl;
#endif
    //If I'm in the supernodal column
    std::vector<Int> all_proc_list;
    std::vector<Int> all_blocks_cnt;
    std::vector<Int> sizes;
    std::vector<Int> displs;

    std::vector<Int> sender_proc;
    std::vector<std::list<LBlock<T> * > > blocks_to_receiver;

    std::vector<Int> receiver_proc;
    //If I'm in the supernodal column
    if( mpicol == ( ksup % npcol ) ){
      Int jb = ksup / npcol;
      std::vector<LBlock<T> >& Lcol = PMat.L(jb);
      Int root = (ksup % nprow);
      //compute the list of receiving processors based on my local structure
      std::set<Int> proc_set;
      blocks_to_receiver.resize(npcol);
      Int startBlk = mpirow==root?1:0;
      for ( Int iblk = startBlk; iblk < Lcol.size(); iblk++ ){
        LBlock<T>& LB = Lcol[iblk];
        //column of the target processor
        Int snode_idx = LB.blockIdx;
        Int tgt_pcol =  snode_idx % npcol;
        blocks_to_receiver[tgt_pcol].push_back(&LB);
        proc_set.insert(tgt_pcol);
      }
      //Insert the set into the vector to be able to send it
      receiver_proc.insert(receiver_proc.begin(),proc_set.begin(),proc_set.end());


      //Now do a gatherv on the root
      mpi::Gatherv(receiver_proc,all_proc_list,sizes,displs,root, colComm);

      //Do a gatherv of the local blocks to each processors
      std::vector<Int> blocks_cnt(receiver_proc.size());
      for(Int j = 0; j< receiver_proc.size();++j){
        Int pcol = receiver_proc[j];
        std::list<LBlock<T> *> & blocks = blocks_to_receiver[pcol];
        blocks_cnt[j] = blocks.size();
      }
      mpi::Gatherv(blocks_cnt,all_blocks_cnt,root, colComm);

      //On the root, convert from a sender array to a receiver array
      if(mpirow == root){

        //sender_proc[i] contains the set of sender to processor column i
        std::vector<std::set<Int> > sender_procs(npcol);
        std::vector<Int> urow_sizes(npcol,0);      
        for(Int prow = 0; prow < nprow; ++prow){
          Int * recv_list = &all_proc_list[displs[prow]];
          Int * recv_blocks = &all_blocks_cnt[displs[prow]];
          Int size = sizes[prow];
          for(Int i = 0; i<size;++i){
            Int pcol = recv_list[i];
            sender_procs[pcol].insert(prow);
            Int ucol_contrib = recv_blocks[i];
            urow_sizes[pcol]+=ucol_contrib;
          }
        }
        //now prepare the data structures for a scatterv along the rows
        all_blocks_cnt = urow_sizes;
        all_proc_list.clear();
        sizes.resize(npcol);
        displs.resize(npcol);
        Int totalsize = 0;
        for(Int pcol = 0; pcol < npcol; ++pcol){
          sizes[pcol] = sender_procs[pcol].size()*sizeof(Int);
          displs[pcol] = totalsize;
          totalsize += sizes[pcol];
        }
        //put the senders in the all_proc_list_array
        all_proc_list.reserve(totalsize / sizeof(Int) );
        for(Int pcol = 0; pcol < npcol; ++pcol){
          all_proc_list.insert(all_proc_list.end(),sender_procs[pcol].begin(),sender_procs[pcol].end());
        }

      }
    }

    //If I'm in the supernodal row
    if( mpirow == ( ksup % nprow ) ){
      Int root = (ksup % npcol);
      //scatter the sizes
      Int localSize = 0;
      MPI_Scatter(mpicol==root?&sizes[0]:NULL,sizeof(Int),MPI_BYTE,
          &localSize,sizeof(Int),MPI_BYTE, root, rowComm);
      sender_proc.resize(localSize / sizeof(Int));
      //Now do the scatterv; 
      MPI_Scatterv(mpicol==root?&all_proc_list[0]:NULL,
                    mpicol==root?&sizes[0]:NULL,
                      mpicol==root?&displs[0]:NULL,MPI_BYTE,
                        &sender_proc[0],localSize,MPI_BYTE, root, rowComm);

      Int urowSize = 0;
      MPI_Scatter(mpicol==root?&all_blocks_cnt[0]:NULL,sizeof(Int),MPI_BYTE,
          &urowSize,sizeof(Int),MPI_BYTE, root, rowComm);
      //Resize Urow
      Int ib = ksup / nprow;
      std::vector<UBlock<T> >& Urow = PMat.U(ib);
      Urow.resize(urowSize);


      //At this point we have both a sender AND a receiver list
      //and Urows are resized
    }

    
    //Communicate this supernode
    //If I'm a sender
    if( mpicol == ( ksup % npcol ) ){
      std::vector<Int> mask( LBlockMask::TOTAL_NUMBER, 1 );
      //for each target col
      for(Int tpcol = 0; tpcol < npcol; tpcol++){
        //dont send to the root first because it can be a sender too !
        Int pcol = (mpicol+1+tpcol) % npcol;
        Int pnum = (ksup % nprow)*npcol + pcol;
        if(pnum!=mpirank){
          //Serialize everything in the blocks_to_receiver list
          std::list<LBlock<T> *> & blocks = blocks_to_receiver[pcol];
          if(blocks.size()>0){
            std::stringstream sstm;
            Int numLBlocks = blocks.size();
#if ( _DEBUGlevel_ >= 1 )
            statusOFS<<"Sending "<<numLBlocks<<" LBlocks"<<std::endl;
#endif
            serialize( numLBlocks , sstm, NO_MASK);
            typename std::list<LBlock<T> *>::iterator it;
            for(it = blocks.begin(); 
                it!=blocks.end();++it){
              LBlock<T> & LB = *(*it);
#if ( _DEBUGlevel_ >= 1 )
              statusOFS<<"Sent LB: "<<LB<<std::endl;
#endif
              serialize(LB, sstm,mask);
            }


            mpi::Send(sstm, pnum, PMat.IdxToTag(ksup,PMatrix<T>::SELINV_TAG_L_SIZE),
                PMat.IdxToTag(ksup,PMatrix<T>::SELINV_TAG_L_CONTENT), comm);
          }
        }
      }
    }

    //If I'm a receiver 
    if( mpirow == ( ksup % nprow ) ){
      std::vector<Int> mask( LBlockMask::TOTAL_NUMBER, 1 );
      Int ib = ksup / nprow;
      std::vector<UBlock<T> >& Urow = PMat.U(ib);

      //for each target row
      Int idx = 0;
      for(Int i = 0; i < sender_proc.size(); ++i){
        Int prow = sender_proc[i];
        Int pnum = (prow)*npcol + (ksup % npcol);
        if(pnum != mpirank){
          std::stringstream sstm;
          mpi::Recv(sstm,MPI_ANY_SOURCE,PMat.IdxToTag(ksup,PMatrix<T>::SELINV_TAG_L_SIZE),
              PMat.IdxToTag(ksup,PMatrix<T>::SELINV_TAG_L_CONTENT), comm);

          //now deserialize and put everything in U
          Int numLBlocks = 0;
          deserialize(numLBlocks, sstm, NO_MASK);
#if ( _DEBUGlevel_ >= 1 )
          statusOFS<<"Receiving "<<numLBlocks<<" LBlocks"<<std::endl;
#endif
          for(Int i = 0; i<numLBlocks;++i){
            LBlock<T> LB;
            deserialize(LB, sstm, mask);

#if ( _DEBUGlevel_ >= 1 )
            statusOFS<<"Received LB: "<<LB<<std::endl;
#endif
            //put this LBlock in the appropriate UBlock
            UBlock<T> & UB = Urow[idx];

            UB.blockIdx = LB.blockIdx;
            UB.numCol = LB.numRow;
            UB.numRow = LB.numCol;
            UB.cols = LB.rows;
            Transpose(LB.nzval,UB.nzval);
            ++idx; 
          }
        }
        else{
          Int pcol = mpicol ;
          //do the copy locally
          Int ib = ksup / nprow;
          std::vector<UBlock<T> >& Urow = PMat.U(ib);
          //Serialize everything in the blocks_to_receiver list
          std::list<LBlock<T> *> & blocks = blocks_to_receiver[pcol];
          if(blocks.size()>0){
            typename std::list<LBlock<T> *>::iterator it;
            for(it = blocks.begin(); 
                it!=blocks.end();++it){
              LBlock<T> & LB = *(*it);
              UBlock<T> & UB = Urow[idx];

              UB.blockIdx = LB.blockIdx;
              UB.numCol = LB.numRow;
              UB.numRow = LB.numCol;
              UB.cols = LB.rows;
              Transpose(LB.nzval,UB.nzval);
              ++idx; 
            }
          }
        }


      }
    }
  }

  TIMER_STOP(PMatrixLtoU);
}  // -----  end of PMatrixLToU ----- 


}


#endif //_PEXSI_symPACK_INTERF_IMPL_HPP_