xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 331e053b67db45ac545b7af34250e835e8c780bf)

#include <../src/mat/impls/aij/seq/aij.h>
#include <../src/ksp/pc/impls/bddc/bddc.h>
#include <../src/ksp/pc/impls/bddc/bddcprivate.h>
#include <petscblaslapack.h>

static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y);
static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y);

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignMatMult_Private_Private"
PetscErrorCode PCBDDCBenignMatMult_Private_Private(Mat A, Vec x, Vec y, PetscBool transpose)
{
  PCBDDCBenignMatMult_ctx ctx;
  PetscErrorCode          ierr;
  PetscBool               apply_right,apply_left,reset_x;

  PetscFunctionBegin;
  ierr = MatShellGetContext(A,&ctx);CHKERRQ(ierr);
  if (transpose) {
    apply_right = ctx->apply_left;
    apply_left = ctx->apply_right;
  } else {
    apply_right = ctx->apply_right;
    apply_left = ctx->apply_left;
  }
  reset_x = PETSC_FALSE;
  if (apply_right) {
    const PetscScalar *ax;
    PetscInt          nl,i;

    ierr = VecGetLocalSize(x,&nl);CHKERRQ(ierr);
    ierr = VecGetArrayRead(x,&ax);CHKERRQ(ierr);
    ierr = PetscMemcpy(ctx->work,ax,nl*sizeof(PetscScalar));CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(x,&ax);CHKERRQ(ierr);
    for (i=0;i<ctx->benign_n;i++) {
      PetscScalar    sum,val;
      const PetscInt *idxs;
      PetscInt       nz,j;
      ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);CHKERRQ(ierr);
      ierr = ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);CHKERRQ(ierr);
      sum = 0.;
      if (ctx->apply_p0) {
        val = ctx->work[idxs[nz-1]];
        for (j=0;j<nz-1;j++) {
          sum += ctx->work[idxs[j]];
          ctx->work[idxs[j]] += val;
        }
      } else {
        for (j=0;j<nz-1;j++) {
          sum += ctx->work[idxs[j]];
        }
      }
      ctx->work[idxs[nz-1]] -= sum;
      ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);CHKERRQ(ierr);
    }
    ierr = VecPlaceArray(x,ctx->work);CHKERRQ(ierr);
    reset_x = PETSC_TRUE;
  }
  if (transpose) {
    ierr = MatMultTranspose(ctx->A,x,y);CHKERRQ(ierr);
  } else {
    ierr = MatMult(ctx->A,x,y);CHKERRQ(ierr);
  }
  if (reset_x) {
    ierr = VecResetArray(x);CHKERRQ(ierr);
  }
  if (apply_left) {
    PetscScalar *ay;
    PetscInt    i;

    ierr = VecGetArray(y,&ay);CHKERRQ(ierr);
    for (i=0;i<ctx->benign_n;i++) {
      PetscScalar    sum,val;
      const PetscInt *idxs;
      PetscInt       nz,j;
      ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);CHKERRQ(ierr);
      ierr = ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);CHKERRQ(ierr);
      val = -ay[idxs[nz-1]];
      if (ctx->apply_p0) {
        sum = 0.;
        for (j=0;j<nz-1;j++) {
          sum += ay[idxs[j]];
          ay[idxs[j]] += val;
        }
        ay[idxs[nz-1]] += sum;
      } else {
        for (j=0;j<nz-1;j++) {
          ay[idxs[j]] += val;
        }
        ay[idxs[nz-1]] = 0.;
      }
      ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(y,&ay);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignMatMultTranspose_Private"
PetscErrorCode PCBDDCBenignMatMultTranspose_Private(Mat A, Vec x, Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_TRUE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignMatMult_Private"
PetscErrorCode PCBDDCBenignMatMult_Private(Mat A, Vec x, Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_FALSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignShellMat"
PetscErrorCode PCBDDCBenignShellMat(PC pc, PetscBool restore)
{
  PC_IS                   *pcis = (PC_IS*)pc->data;
  PC_BDDC                 *pcbddc = (PC_BDDC*)pc->data;
  Mat_IS                  *matis = (Mat_IS*)pc->pmat->data;
  PCBDDCBenignMatMult_ctx ctx;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  if (!restore) {
    Mat                A,A_IB,A_BI;
    PetscScalar        *work;
    PCBDDCReuseSolvers reuse = pcbddc->sub_schurs->reuse_solver;

    if (!reuse) {
      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot setup shell matrices!");
    }

    /* local mat */
    ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
    ierr = MatSetSizes(A,pcis->n,pcis->n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = MatSetType(A,MATSHELL);CHKERRQ(ierr);
    ierr = MatShellSetOperation(A,MATOP_MULT,(void (*)(void))PCBDDCBenignMatMult_Private);CHKERRQ(ierr);
    ierr = MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCBenignMatMultTranspose_Private);CHKERRQ(ierr);
    ierr = PetscNew(&ctx);CHKERRQ(ierr);
    ierr = MatShellSetContext(A,ctx);CHKERRQ(ierr);
    ctx->apply_left = PETSC_TRUE;
    ctx->apply_right = PETSC_TRUE;
    ctx->apply_p0 = PETSC_TRUE;
    ctx->benign_n = pcbddc->benign_n;
    ctx->benign_zerodiag_subs = pcbddc->benign_zerodiag_subs;
    ctx->A = matis->A;
    ierr = PetscMalloc1(pcis->n,&work);CHKERRQ(ierr);
    ctx->work = work;
    ierr = MatSetUp(A);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    matis->A = A;

    /* A_IB */
    ierr = MatCreate(PETSC_COMM_SELF,&A_IB);CHKERRQ(ierr);
    ierr = MatSetSizes(A_IB,pcis->n-pcis->n_B,pcis->n_B,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = MatSetType(A_IB,MATSHELL);CHKERRQ(ierr);
    ierr = MatShellSetOperation(A_IB,MATOP_MULT,(void (*)(void))PCBDDCBenignMatMult_Private);CHKERRQ(ierr);
    ierr = MatShellSetOperation(A_IB,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCBenignMatMultTranspose_Private);CHKERRQ(ierr);
    ierr = PetscNew(&ctx);CHKERRQ(ierr);
    ierr = MatShellSetContext(A_IB,ctx);CHKERRQ(ierr);
    ctx->apply_left = PETSC_TRUE;
    ctx->apply_right = PETSC_FALSE;
    ctx->apply_p0 = PETSC_FALSE;
    ctx->benign_n = pcbddc->benign_n;
    ctx->benign_zerodiag_subs = reuse->benign_zerodiag_subs;
    ctx->A = pcis->A_IB;
    ctx->work = work;
    ierr = MatSetUp(A_IB);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(A_IB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(A_IB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    pcis->A_IB = A_IB;

    /* A_BI as A_IB^T */
    ierr = MatCreateTranspose(A_IB,&A_BI);CHKERRQ(ierr);
    pcbddc->benign_original_mat = pcis->A_BI;
    pcis->A_BI = A_BI;
  } else {
    ierr = MatShellGetContext(matis->A,&ctx);CHKERRQ(ierr);
    ierr = MatDestroy(&matis->A);CHKERRQ(ierr);
    matis->A = ctx->A;
    ierr = PetscFree(ctx);CHKERRQ(ierr);
    ierr = MatShellGetContext(pcis->A_IB,&ctx);CHKERRQ(ierr);
    ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
    pcis->A_IB = ctx->A;
    ierr = PetscFree(ctx->work);CHKERRQ(ierr);
    ierr = PetscFree(ctx);CHKERRQ(ierr);
    ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
    pcis->A_BI = pcbddc->benign_original_mat;
    pcbddc->benign_original_mat = NULL;
  }
  PetscFunctionReturn(0);
}

/* used just in bddc debug mode */
#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignProject"
PetscErrorCode PCBDDCBenignProject(PC pc, IS is1, IS is2, Mat *B)
{
  PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
  Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
  Mat            An;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatPtAP(matis->A,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&An);CHKERRQ(ierr);
  ierr = MatZeroRowsColumns(An,pcbddc->benign_n,pcbddc->benign_p0_lidx,1.0,NULL,NULL);CHKERRQ(ierr);
  if (is1) {
    ierr = MatGetSubMatrix(An,is1,is2,MAT_INITIAL_MATRIX,B);CHKERRQ(ierr);
    ierr = MatDestroy(&An);CHKERRQ(ierr);
  } else {
    *B = An;
  }
  PetscFunctionReturn(0);
}

/* TODO: add reuse flag */
#undef __FUNCT__
#define __FUNCT__ "MatSeqAIJCompress"
PetscErrorCode MatSeqAIJCompress(Mat A, Mat *B)
{
  Mat            Bt;
  PetscScalar    *a,*bdata;
  const PetscInt *ii,*ij;
  PetscInt       m,n,i,nnz,*bii,*bij;
  PetscBool      flg_row;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatGetSize(A,&n,&m);CHKERRQ(ierr);
  ierr = MatGetRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);CHKERRQ(ierr);
  ierr = MatSeqAIJGetArray(A,&a);CHKERRQ(ierr);
  nnz = n;
  for (i=0;i<ii[n];i++) {
    if (PetscLikely(PetscAbsScalar(a[i]) > PETSC_SMALL)) nnz++;
  }
  ierr = PetscMalloc1(n+1,&bii);CHKERRQ(ierr);
  ierr = PetscMalloc1(nnz,&bij);CHKERRQ(ierr);
  ierr = PetscMalloc1(nnz,&bdata);CHKERRQ(ierr);
  nnz = 0;
  bii[0] = 0;
  for (i=0;i<n;i++) {
    PetscInt j;
    for (j=ii[i];j<ii[i+1];j++) {
      PetscScalar entry = a[j];
      if (PetscLikely(PetscAbsScalar(entry) > PETSC_SMALL) || ij[j] == i) {
        bij[nnz] = ij[j];
        bdata[nnz] = entry;
        nnz++;
      }
    }
    bii[i+1] = nnz;
  }
  ierr = MatSeqAIJRestoreArray(A,&a);CHKERRQ(ierr);
  ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),n,m,bii,bij,bdata,&Bt);CHKERRQ(ierr);
  ierr = MatRestoreRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);CHKERRQ(ierr);
  {
    Mat_SeqAIJ *b = (Mat_SeqAIJ*)(Bt->data);
    b->free_a = PETSC_TRUE;
    b->free_ij = PETSC_TRUE;
  }
  *B = Bt;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDetectDisconnectedComponents"
PetscErrorCode MatDetectDisconnectedComponents(Mat A, PetscBool filter, PetscInt *ncc, IS* cc[])
{
  Mat                    B;
  IS                     is_dummy,*cc_n;
  ISLocalToGlobalMapping l2gmap_dummy;
  PCBDDCGraph            graph;
  PetscInt               i,n;
  PetscInt               *xadj,*adjncy;
  PetscInt               *xadj_filtered,*adjncy_filtered;
  PetscBool              flg_row,isseqaij;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  if (!A->rmap->N || !A->cmap->N) {
    *ncc = 0;
    *cc = NULL;
    PetscFunctionReturn(0);
  }
  ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
  if (!isseqaij && filter) {
    PetscBool isseqdense;

    ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&isseqdense);CHKERRQ(ierr);
    if (!isseqdense) {
      ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
    } else { /* TODO: rectangular case and LDA */
      PetscScalar *array;
      PetscReal   chop=1.e-6;

      ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
      ierr = MatDenseGetArray(B,&array);CHKERRQ(ierr);
      ierr = MatGetSize(B,&n,NULL);CHKERRQ(ierr);
      for (i=0;i<n;i++) {
        PetscInt j;
        for (j=i+1;j<n;j++) {
          PetscReal thresh = chop*(PetscAbsScalar(array[i*(n+1)])+PetscAbsScalar(array[j*(n+1)]));
          if (PetscAbsScalar(array[i*n+j]) < thresh) array[i*n+j] = 0.;
          if (PetscAbsScalar(array[j*n+i]) < thresh) array[j*n+i] = 0.;
        }
      }
      ierr = MatDenseRestoreArray(B,&array);CHKERRQ(ierr);
      ierr = MatConvert(B,MATSEQAIJ,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr);
    }
  } else {
    B = A;
  }
  ierr = MatGetRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);

  /* if filter is true, then removes entries lower than PETSC_SMALL in magnitude */
  if (filter) {
    PetscScalar *data;
    PetscInt    j,cum;

    ierr = PetscCalloc2(n+1,&xadj_filtered,xadj[n],&adjncy_filtered);CHKERRQ(ierr);
    ierr = MatSeqAIJGetArray(B,&data);CHKERRQ(ierr);
    cum = 0;
    for (i=0;i<n;i++) {
      PetscInt t;

      for (j=xadj[i];j<xadj[i+1];j++) {
        if (PetscUnlikely(PetscAbsScalar(data[j]) < PETSC_SMALL)) {
          continue;
        }
        adjncy_filtered[cum+xadj_filtered[i]++] = adjncy[j];
      }
      t = xadj_filtered[i];
      xadj_filtered[i] = cum;
      cum += t;
    }
    ierr = MatSeqAIJRestoreArray(B,&data);CHKERRQ(ierr);
  } else {
    xadj_filtered = NULL;
    adjncy_filtered = NULL;
  }

  /* compute local connected components using PCBDDCGraph */
  ierr = ISCreateStride(PETSC_COMM_SELF,n,0,1,&is_dummy);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingCreateIS(is_dummy,&l2gmap_dummy);CHKERRQ(ierr);
  ierr = ISDestroy(&is_dummy);CHKERRQ(ierr);
  ierr = PCBDDCGraphCreate(&graph);CHKERRQ(ierr);
  ierr = PCBDDCGraphInit(graph,l2gmap_dummy,n);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingDestroy(&l2gmap_dummy);CHKERRQ(ierr);
  if (xadj_filtered) {
    graph->xadj = xadj_filtered;
    graph->adjncy = adjncy_filtered;
  } else {
    graph->xadj = xadj;
    graph->adjncy = adjncy;
  }
  ierr = PCBDDCGraphSetUp(graph,1,NULL,NULL,0,NULL,NULL);CHKERRQ(ierr);
  ierr = PCBDDCGraphComputeConnectedComponents(graph);CHKERRQ(ierr);
  /* partial clean up */
  ierr = PetscFree2(xadj_filtered,adjncy_filtered);CHKERRQ(ierr);
  ierr = MatRestoreRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
  if (A != B) {
    ierr = MatDestroy(&B);CHKERRQ(ierr);
  }

  /* get back data */
  if (ncc) *ncc = graph->ncc;
  if (cc) {
    ierr = PetscMalloc1(graph->ncc,&cc_n);CHKERRQ(ierr);
    for (i=0;i<graph->ncc;i++) {
      ierr = ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],graph->queue+graph->cptr[i],PETSC_COPY_VALUES,&cc_n[i]);CHKERRQ(ierr);
    }
    *cc = cc_n;
  }
  /* clean up graph */
  graph->xadj = 0;
  graph->adjncy = 0;
  ierr = PCBDDCGraphDestroy(&graph);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignCheck"
PetscErrorCode PCBDDCBenignCheck(PC pc, IS zerodiag)
{
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  PC_IS*         pcis = (PC_IS*)(pc->data);
  IS             dirIS = NULL;
  PetscInt       i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);CHKERRQ(ierr);
  if (zerodiag) {
    Mat            A;
    Vec            vec3_N;
    PetscScalar    *vals;
    const PetscInt *idxs;
    PetscInt       nz,*count;

    /* p0 */
    ierr = VecSet(pcis->vec1_N,0.);CHKERRQ(ierr);
    ierr = PetscMalloc1(pcis->n,&vals);CHKERRQ(ierr);
    ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
    ierr = ISGetIndices(zerodiag,&idxs);CHKERRQ(ierr);
    for (i=0;i<nz;i++) vals[i] = 1.;
    ierr = VecSetValues(pcis->vec1_N,nz,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
    ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
    /* v_I */
    ierr = VecSetRandom(pcis->vec2_N,NULL);CHKERRQ(ierr);
    for (i=0;i<nz;i++) vals[i] = 0.;
    ierr = VecSetValues(pcis->vec2_N,nz,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
    ierr = ISRestoreIndices(zerodiag,&idxs);CHKERRQ(ierr);
    ierr = ISGetIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
    for (i=0;i<pcis->n_B;i++) vals[i] = 0.;
    ierr = VecSetValues(pcis->vec2_N,pcis->n_B,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
    ierr = ISRestoreIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
    if (dirIS) {
      PetscInt n;

      ierr = ISGetLocalSize(dirIS,&n);CHKERRQ(ierr);
      ierr = ISGetIndices(dirIS,&idxs);CHKERRQ(ierr);
      for (i=0;i<n;i++) vals[i] = 0.;
      ierr = VecSetValues(pcis->vec2_N,n,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
      ierr = ISRestoreIndices(dirIS,&idxs);CHKERRQ(ierr);
    }
    ierr = VecAssemblyBegin(pcis->vec2_N);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(pcis->vec2_N);CHKERRQ(ierr);
    ierr = VecDuplicate(pcis->vec1_N,&vec3_N);CHKERRQ(ierr);
    ierr = VecSet(vec3_N,0.);CHKERRQ(ierr);
    ierr = MatISGetLocalMat(pc->mat,&A);CHKERRQ(ierr);
    ierr = MatMult(A,pcis->vec1_N,vec3_N);CHKERRQ(ierr);
    ierr = VecDot(vec3_N,pcis->vec2_N,&vals[0]);CHKERRQ(ierr);
    if (PetscAbsScalar(vals[0]) > PETSC_SMALL) {
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Benign trick can not be applied! b(v_I,p_0) = %f (should be numerically 0.)",PetscAbsScalar(vals[0]));
    }
    ierr = PetscFree(vals);CHKERRQ(ierr);
    ierr = VecDestroy(&vec3_N);CHKERRQ(ierr);

    /* there should not be any pressure dofs lying on the interface */
    ierr = PetscCalloc1(pcis->n,&count);CHKERRQ(ierr);
    ierr = ISGetIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
    for (i=0;i<pcis->n_B;i++) count[idxs[i]]++;
    ierr = ISRestoreIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
    ierr = ISGetIndices(zerodiag,&idxs);CHKERRQ(ierr);
    for (i=0;i<nz;i++) {
      if (count[idxs[i]]) {
        SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Benign trick can not be applied! pressure dof %d is an interface dof",idxs[i]);
      }
    }
    ierr = ISRestoreIndices(zerodiag,&idxs);CHKERRQ(ierr);
    ierr = PetscFree(count);CHKERRQ(ierr);
  }
  ierr = ISDestroy(&dirIS);CHKERRQ(ierr);

  /* check PCBDDCBenignGetOrSetP0 */
  ierr = VecSetRandom(pcis->vec1_global,NULL);CHKERRQ(ierr);
  for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = -PetscGlobalRank-i;
  ierr = PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_FALSE);CHKERRQ(ierr);
  for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = 1;
  ierr = PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_TRUE);CHKERRQ(ierr);
  for (i=0;i<pcbddc->benign_n;i++) {
    if ((PetscInt)PetscRealPart(pcbddc->benign_p0[i]) != -PetscGlobalRank-i) {
      SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error testing PCBDDCBenignGetOrSetP0! Found %1.4e at %d instead of %1.4e\n",pcbddc->benign_p0[i],i,-PetscGlobalRank-i);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignDetectSaddlePoint"
PetscErrorCode PCBDDCBenignDetectSaddlePoint(PC pc, IS *zerodiaglocal)
{
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  IS             pressures,zerodiag,*zerodiag_subs;
  PetscInt       nz,n;
  PetscBool      sorted,have_null,has_null_pressures,recompute_zerodiag;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSFDestroy(&pcbddc->benign_sf);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->benign_original_mat);CHKERRQ(ierr);
  for (n=0;n<pcbddc->benign_n;n++) {
    ierr = ISDestroy(&pcbddc->benign_zerodiag_subs[n]);CHKERRQ(ierr);
  }
  ierr = PetscFree(pcbddc->benign_zerodiag_subs);CHKERRQ(ierr);
  pcbddc->benign_n = 0;
  /* if a local info on dofs is present, assumes the last field is represented by "pressures"
     otherwise, it uses only zerodiagonal dofs (ok if the pressure block is all zero; it could fail if it is not)
     Checks if all the pressure dofs in each subdomain have a zero diagonal
     If not, a change of basis on pressures is not needed
     since the local Schur complements are SPD
  */
  has_null_pressures = PETSC_TRUE;
  have_null = PETSC_TRUE;
  if (pcbddc->n_ISForDofsLocal) {
    PetscInt npl,*idxs,p = pcbddc->n_ISForDofsLocal-1;

    /* Dofs splitting for BDDC cannot have PETSC_COMM_SELF, so create a sequential IS */
    ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[p],&npl);CHKERRQ(ierr);
    ierr = ISGetIndices(pcbddc->ISForDofsLocal[p],(const PetscInt**)&idxs);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PETSC_COMM_SELF,npl,idxs,PETSC_COPY_VALUES,&pressures);CHKERRQ(ierr);
    ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[p],(const PetscInt**)&idxs);CHKERRQ(ierr);
    ierr = ISSorted(pressures,&sorted);CHKERRQ(ierr);
    if (!sorted) {
      ierr = ISSort(pressures);CHKERRQ(ierr);
    }
  } else {
    pressures = NULL;
  }
  /* pcis has not been setup yet, so get the local size from the subdomain matrix */
  ierr = MatGetLocalSize(pcbddc->local_mat,&n,NULL);CHKERRQ(ierr);
  ierr = MatFindZeroDiagonals(pcbddc->local_mat,&zerodiag);CHKERRQ(ierr);
  ierr = ISSorted(zerodiag,&sorted);CHKERRQ(ierr);
  if (!sorted) {
    ierr = ISSort(zerodiag);CHKERRQ(ierr);
  }
  ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
  if (!nz) {
    if (n) have_null = PETSC_FALSE;
    has_null_pressures = PETSC_FALSE;
    ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
  }
  recompute_zerodiag = PETSC_FALSE;
  /* in case disconnected subdomains info is present, split the pressures accordingly (otherwise the benign trick could fail) */
  zerodiag_subs = NULL;
  pcbddc->benign_n = 0;
  if (has_null_pressures) {
    IS       *subs;
    PetscInt nsubs,i;

    subs = pcbddc->local_subs;
    nsubs = pcbddc->n_local_subs;
    if (nsubs > 1) {
      ierr = PetscCalloc1(nsubs,&zerodiag_subs);CHKERRQ(ierr);
      for (i=0;i<nsubs;i++) {
        ISLocalToGlobalMapping l2g;
        IS                     t_zerodiag_subs;
        PetscInt               nl;

        ierr = ISLocalToGlobalMappingCreateIS(subs[i],&l2g);CHKERRQ(ierr);
        ierr = ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,zerodiag,&t_zerodiag_subs);CHKERRQ(ierr);
        ierr = ISGetLocalSize(t_zerodiag_subs,&nl);CHKERRQ(ierr);
        if (nl) {
          PetscBool valid = PETSC_TRUE;

          if (pressures) {
            IS t_pressure_subs;
            ierr = ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,pressures,&t_pressure_subs);CHKERRQ(ierr);
            ierr = ISEqual(t_pressure_subs,t_zerodiag_subs,&valid);CHKERRQ(ierr);
            ierr = ISDestroy(&t_pressure_subs);CHKERRQ(ierr);
          }
          if (valid) {
            ierr = ISLocalToGlobalMappingApplyIS(l2g,t_zerodiag_subs,&zerodiag_subs[pcbddc->benign_n]);CHKERRQ(ierr);
            pcbddc->benign_n++;
          } else {
            recompute_zerodiag = PETSC_TRUE;
          }
        }
        ierr = ISDestroy(&t_zerodiag_subs);CHKERRQ(ierr);
        ierr = ISLocalToGlobalMappingDestroy(&l2g);CHKERRQ(ierr);
      }
    } else { /* there's just one subdomain (or zero if they have not been detected */
      PetscBool valid = PETSC_TRUE;
      if (pressures) {
        ierr = ISEqual(pressures,zerodiag,&valid);CHKERRQ(ierr);
      }
      if (valid) {
        pcbddc->benign_n = 1;
        ierr = PetscMalloc1(pcbddc->benign_n,&zerodiag_subs);CHKERRQ(ierr);
        ierr = PetscObjectReference((PetscObject)zerodiag);CHKERRQ(ierr);
        zerodiag_subs[0] = zerodiag;
      }
    }
  }

  if (!pcbddc->benign_n) {
    ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
    recompute_zerodiag = PETSC_FALSE;
    has_null_pressures = PETSC_FALSE;
    have_null = PETSC_FALSE;
  }

  /* final check for null pressures */
  if (zerodiag && pressures) {
    PetscInt nz,np;
    ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
    ierr = ISGetLocalSize(pressures,&np);CHKERRQ(ierr);
    if (nz != np) have_null = PETSC_FALSE;
  }

  if (recompute_zerodiag) {
    ierr = ISDestroy(&zerodiag);CHKERRQ(ierr);
    if (pcbddc->benign_n == 1) {
      ierr = PetscObjectReference((PetscObject)zerodiag_subs[0]);CHKERRQ(ierr);
      zerodiag = zerodiag_subs[0];
    } else {
      PetscInt i,nzn,*new_idxs;

      nzn = 0;
      for (i=0;i<pcbddc->benign_n;i++) {
        PetscInt ns;
        ierr = ISGetLocalSize(zerodiag_subs[i],&ns);CHKERRQ(ierr);
        nzn += ns;
      }
      ierr = PetscMalloc1(nzn,&new_idxs);CHKERRQ(ierr);
      nzn = 0;
      for (i=0;i<pcbddc->benign_n;i++) {
        PetscInt ns,*idxs;
        ierr = ISGetLocalSize(zerodiag_subs[i],&ns);CHKERRQ(ierr);
        ierr = ISGetIndices(zerodiag_subs[i],(const PetscInt**)&idxs);CHKERRQ(ierr);
        ierr = PetscMemcpy(new_idxs+nzn,idxs,ns*sizeof(PetscInt));CHKERRQ(ierr);
        ierr = ISRestoreIndices(zerodiag_subs[i],(const PetscInt**)&idxs);CHKERRQ(ierr);
        nzn += ns;
      }
      ierr = PetscSortInt(nzn,new_idxs);CHKERRQ(ierr);
      ierr = ISCreateGeneral(PETSC_COMM_SELF,nzn,new_idxs,PETSC_OWN_POINTER,&zerodiag);CHKERRQ(ierr);
    }
    have_null = PETSC_FALSE;
  }

  if (has_null_pressures) {
    IS             zerodiagc;
    const PetscInt *idxs,*idxsc;
    PetscInt       i,s,*nnz;

    ierr = ISGetLocalSize(zerodiag,&nz);CHKERRQ(ierr);
    ierr = ISComplement(zerodiag,0,n,&zerodiagc);CHKERRQ(ierr);
    ierr = ISGetIndices(zerodiagc,&idxsc);CHKERRQ(ierr);
    /* local change of basis for pressures */
    ierr = MatDestroy(&pcbddc->benign_change);CHKERRQ(ierr);
    ierr = MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_change);CHKERRQ(ierr);
    ierr = MatSetType(pcbddc->benign_change,MATAIJ);CHKERRQ(ierr);
    ierr = MatSetSizes(pcbddc->benign_change,n,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = PetscMalloc1(n,&nnz);CHKERRQ(ierr);
    for (i=0;i<n-nz;i++) nnz[idxsc[i]] = 1; /* identity on velocities plus pressure dofs for non-singular subdomains */
    for (i=0;i<pcbddc->benign_n;i++) {
      PetscInt nzs,j;

      ierr = ISGetLocalSize(zerodiag_subs[i],&nzs);CHKERRQ(ierr);
      ierr = ISGetIndices(zerodiag_subs[i],&idxs);CHKERRQ(ierr);
      for (j=0;j<nzs-1;j++) nnz[idxs[j]] = 2; /* change on pressures */
      nnz[idxs[nzs-1]] = nzs; /* last local pressure dof in subdomain */
      ierr = ISRestoreIndices(zerodiag_subs[i],&idxs);CHKERRQ(ierr);
    }
    ierr = MatSeqAIJSetPreallocation(pcbddc->benign_change,0,nnz);CHKERRQ(ierr);
    ierr = PetscFree(nnz);CHKERRQ(ierr);
    /* set identity on velocities */
    for (i=0;i<n-nz;i++) {
      ierr = MatSetValue(pcbddc->benign_change,idxsc[i],idxsc[i],1.,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(zerodiagc,&idxsc);CHKERRQ(ierr);
    ierr = ISDestroy(&zerodiagc);CHKERRQ(ierr);
    ierr = PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);CHKERRQ(ierr);
    ierr = PetscMalloc3(pcbddc->benign_n,&pcbddc->benign_p0_lidx,pcbddc->benign_n,&pcbddc->benign_p0_gidx,pcbddc->benign_n,&pcbddc->benign_p0);CHKERRQ(ierr);
    /* set change on pressures */
    for (s=0;s<pcbddc->benign_n;s++) {
      PetscScalar *array;
      PetscInt    nzs;

      ierr = ISGetLocalSize(zerodiag_subs[s],&nzs);CHKERRQ(ierr);
      ierr = ISGetIndices(zerodiag_subs[s],&idxs);CHKERRQ(ierr);
      for (i=0;i<nzs-1;i++) {
        PetscScalar vals[2];
        PetscInt    cols[2];

        cols[0] = idxs[i];
        cols[1] = idxs[nzs-1];
        vals[0] = 1.;
        vals[1] = 1.;
        ierr = MatSetValues(pcbddc->benign_change,1,cols,2,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
      }
      ierr = PetscMalloc1(nzs,&array);CHKERRQ(ierr);
      for (i=0;i<nzs-1;i++) array[i] = -1.;
      array[nzs-1] = 1.;
      ierr = MatSetValues(pcbddc->benign_change,1,idxs+nzs-1,nzs,idxs,array,INSERT_VALUES);CHKERRQ(ierr);
      /* store local idxs for p0 */
      pcbddc->benign_p0_lidx[s] = idxs[nzs-1];
      ierr = ISRestoreIndices(zerodiag_subs[s],&idxs);CHKERRQ(ierr);
      ierr = PetscFree(array);CHKERRQ(ierr);
    }
    ierr = MatAssemblyBegin(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    /* project if needed */
    if (pcbddc->benign_change_explicit) {
      ierr = MatPtAP(pcbddc->local_mat,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&pcbddc->benign_original_mat);CHKERRQ(ierr);
      ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
      ierr = MatSeqAIJCompress(pcbddc->benign_original_mat,&pcbddc->local_mat);CHKERRQ(ierr);
      ierr = MatDestroy(&pcbddc->benign_original_mat);CHKERRQ(ierr);
    }
    /* store global idxs for p0 */
    ierr = ISLocalToGlobalMappingApply(pc->pmat->rmap->mapping,pcbddc->benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx);CHKERRQ(ierr);
  }
  pcbddc->benign_zerodiag_subs = zerodiag_subs;
  ierr = ISDestroy(&pressures);CHKERRQ(ierr);

  /* determines if the coarse solver will be singular or not */
  ierr = MPI_Allreduce(&have_null,&pcbddc->benign_null,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
  *zerodiaglocal = zerodiag;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignGetOrSetP0"
PetscErrorCode PCBDDCBenignGetOrSetP0(PC pc, Vec v, PetscBool get)
{
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!pcbddc->benign_sf) {
    ierr = PetscSFCreate(PetscObjectComm((PetscObject)pc),&pcbddc->benign_sf);CHKERRQ(ierr);
    ierr = PetscSFSetGraphLayout(pcbddc->benign_sf,pc->pmat->rmap,pcbddc->benign_n,NULL,PETSC_OWN_POINTER,pcbddc->benign_p0_gidx);CHKERRQ(ierr);
  }
  if (get) { /* use SF to get values */
    PetscScalar *array;

    ierr = VecGetArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
  } else { /* use VecSetValues (not scalable, I should try to find a better solution (defining a new MPI_OP for reduction) */
    ierr = VecSetValues(v,pcbddc->benign_n,pcbddc->benign_p0_gidx,pcbddc->benign_p0,INSERT_VALUES);CHKERRQ(ierr);
    ierr = VecAssemblyBegin(v);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(v);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCBenignPopOrPushB0"
PetscErrorCode PCBDDCBenignPopOrPushB0(PC pc, PetscBool pop)
{
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* TODO: add error checking
    - avoid nested pop (or push) calls.
    - cannot push before pop.
    - cannot call this if pcbddc->local_mat is NULL
  */
  if (!pcbddc->benign_n) {
    PetscFunctionReturn(0);
  }
  if (pop) {
    if (pcbddc->benign_change_explicit) {
      IS       is_p0;
      MatReuse reuse;

      /* extract B_0 */
      reuse = MAT_INITIAL_MATRIX;
      if (pcbddc->benign_B0) {
        reuse = MAT_REUSE_MATRIX;
      }
      ierr = ISCreateGeneral(PETSC_COMM_SELF,pcbddc->benign_n,pcbddc->benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(pcbddc->local_mat,is_p0,NULL,reuse,&pcbddc->benign_B0);CHKERRQ(ierr);
      /* remove rows and cols from local problem */
      ierr = MatSetOption(pcbddc->local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);CHKERRQ(ierr);
      ierr = MatSetOption(pcbddc->local_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
      ierr = MatZeroRowsColumnsIS(pcbddc->local_mat,is_p0,1.0,NULL,NULL);CHKERRQ(ierr);
      ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
    } else {
      Mat_IS      *matis = (Mat_IS*)pc->pmat->data;
      PetscScalar *vals;
      PetscInt    i,n,*idxs_ins;

      ierr = VecGetLocalSize(matis->y,&n);CHKERRQ(ierr);
      ierr = PetscMalloc2(n,&idxs_ins,n,&vals);CHKERRQ(ierr);
      if (!pcbddc->benign_B0) {
        ierr = MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_B0);CHKERRQ(ierr);
        ierr = MatSetType(pcbddc->benign_B0,MATAIJ);CHKERRQ(ierr);
        ierr = MatSetSizes(pcbddc->benign_B0,pcbddc->benign_n,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
        if (!pcbddc->current_level) {
          /* this matrix is actually sparse: the nnz pattern is not known unless we do 2 sweeps of the next loop.
             Setting nnz=100 should be more than enough for the finest level */
          ierr = MatSeqAIJSetPreallocation(pcbddc->benign_B0,100,NULL);CHKERRQ(ierr);
        } else {
          PetscInt *nnz;
          ierr = PetscMalloc1(pcbddc->benign_n,&nnz);CHKERRQ(ierr);
          for (i=0;i<pcbddc->benign_n;i++) {
            ierr = ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nnz[i]);CHKERRQ(ierr);
            nnz[i] = n - nnz[i];
          }
          ierr = MatSeqAIJSetPreallocation(pcbddc->benign_B0,0,nnz);CHKERRQ(ierr);
          ierr = PetscFree(nnz);CHKERRQ(ierr);
        }
      }

      for (i=0;i<pcbddc->benign_n;i++) {
        PetscScalar *array;
        PetscInt    *idxs,j,nz,cum;

        ierr = VecSet(matis->x,0.);CHKERRQ(ierr);
        ierr = ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nz);CHKERRQ(ierr);
        ierr = ISGetIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);CHKERRQ(ierr);
        for (j=0;j<nz;j++) vals[j] = 1.;
        ierr = VecSetValues(matis->x,nz,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
        ierr = VecAssemblyBegin(matis->x);CHKERRQ(ierr);
        ierr = VecAssemblyEnd(matis->x);CHKERRQ(ierr);
        ierr = VecSet(matis->y,0.);CHKERRQ(ierr);
        ierr = MatMult(matis->A,matis->x,matis->y);CHKERRQ(ierr);
        ierr = VecGetArray(matis->y,&array);CHKERRQ(ierr);
        cum = 0;
        for (j=0;j<n;j++) {
          if (PetscUnlikely(PetscAbsReal(array[j]) > PETSC_SMALL)) {
            vals[cum] = array[j];
            idxs_ins[cum] = j;
            cum++;
          }
        }
        ierr = MatSetValues(pcbddc->benign_B0,1,&i,cum,idxs_ins,vals,INSERT_VALUES);CHKERRQ(ierr);
        ierr = VecRestoreArray(matis->y,&array);CHKERRQ(ierr);
        ierr = ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);CHKERRQ(ierr);
      }
      ierr = MatAssemblyBegin(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
      ierr = MatAssemblyEnd(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
      ierr = PetscFree2(idxs_ins,vals);CHKERRQ(ierr);
    }
  } else { /* push */
    if (pcbddc->benign_change_explicit) {
      PetscInt i;

      for (i=0;i<pcbddc->benign_n;i++) {
        PetscScalar *B0_vals;
        PetscInt    *B0_cols,B0_ncol;

        ierr = MatGetRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);CHKERRQ(ierr);
        ierr = MatSetValues(pcbddc->local_mat,1,pcbddc->benign_p0_lidx+i,B0_ncol,B0_cols,B0_vals,INSERT_VALUES);CHKERRQ(ierr);
        ierr = MatSetValues(pcbddc->local_mat,B0_ncol,B0_cols,1,pcbddc->benign_p0_lidx+i,B0_vals,INSERT_VALUES);CHKERRQ(ierr);
        ierr = MatSetValue(pcbddc->local_mat,pcbddc->benign_p0_lidx[i],pcbddc->benign_p0_lidx[i],0.0,INSERT_VALUES);CHKERRQ(ierr);
        ierr = MatRestoreRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);CHKERRQ(ierr);
      }
      ierr = MatAssemblyBegin(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
      ierr = MatAssemblyEnd(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    } else {
      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot push B0!\n");
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCAdaptiveSelection"
PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
{
  PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
  PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
  PetscBLASInt    B_dummyint,B_neigs,B_ierr,B_lwork;
  PetscBLASInt    *B_iwork,*B_ifail;
  PetscScalar     *work,lwork;
  PetscScalar     *St,*S,*eigv;
  PetscScalar     *Sarray,*Starray;
  PetscReal       *eigs,thresh;
  PetscInt        i,nmax,nmin,nv,cum,mss,cum2,cumarray,maxneigs;
  PetscBool       allocated_S_St;
#if defined(PETSC_USE_COMPLEX)
  PetscReal       *rwork;
#endif
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  if (!sub_schurs->schur_explicit) {
    SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS and/or MKL_CPARDISO");
  }

  if (sub_schurs->n_subs && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
    SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Adaptive selection not yet implemented for general matrix pencils (herm %d, posdef %d)\n",sub_schurs->is_hermitian,sub_schurs->is_posdef);
  }

  if (pcbddc->dbg_flag) {
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check adaptive selection of constraints\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  if (pcbddc->dbg_flag) {
    PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d cc %d (%d,%d).\n",PetscGlobalRank,sub_schurs->n_subs,sub_schurs->is_hermitian,sub_schurs->is_posdef);
  }

  /* max size of subsets */
  mss = 0;
  for (i=0;i<sub_schurs->n_subs;i++) {
    PetscInt subset_size;

    ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
    mss = PetscMax(mss,subset_size);
  }

  /* min/max and threshold */
  nmax = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
  nmin = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
  nmax = PetscMax(nmin,nmax);
  allocated_S_St = PETSC_FALSE;
  if (nmin) {
    allocated_S_St = PETSC_TRUE;
  }

  /* allocate lapack workspace */
  cum = cum2 = 0;
  maxneigs = 0;
  for (i=0;i<sub_schurs->n_subs;i++) {
    PetscInt n,subset_size;

    ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
    n = PetscMin(subset_size,nmax);
    cum += subset_size;
    cum2 += subset_size*n;
    maxneigs = PetscMax(maxneigs,n);
  }
  if (mss) {
    if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
      PetscBLASInt B_itype = 1;
      PetscBLASInt B_N = mss;
      PetscReal    zero = 0.0;
      PetscReal    eps = 0.0; /* dlamch? */

      B_lwork = -1;
      S = NULL;
      St = NULL;
      eigs = NULL;
      eigv = NULL;
      B_iwork = NULL;
      B_ifail = NULL;
#if defined(PETSC_USE_COMPLEX)
      rwork = NULL;
#endif
      thresh = 1.0;
      ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
      PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&zero,&thresh,&B_dummyint,&B_dummyint,&eps,&B_neigs,eigs,eigv,&B_N,&lwork,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
#else
      PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&zero,&thresh,&B_dummyint,&B_dummyint,&eps,&B_neigs,eigs,eigv,&B_N,&lwork,&B_lwork,B_iwork,B_ifail,&B_ierr));
#endif
      if (B_ierr != 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYGVX Lapack routine %d",(int)B_ierr);
      ierr = PetscFPTrapPop();CHKERRQ(ierr);
    } else {
        /* TODO */
    }
  } else {
    lwork = 0;
  }

  nv = 0;
  if (sub_schurs->is_vertices && pcbddc->use_vertices) { /* complement set of active subsets, each entry is a vertex (boundary made by active subsets, vertices and dirichlet dofs) */
    ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
  }
  ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
  if (allocated_S_St) {
    ierr = PetscMalloc2(mss*mss,&S,mss*mss,&St);CHKERRQ(ierr);
  }
  ierr = PetscMalloc5(mss*mss,&eigv,mss,&eigs,B_lwork,&work,5*mss,&B_iwork,mss,&B_ifail);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
  ierr = PetscMalloc1(7*mss,&rwork);CHKERRQ(ierr);
#endif
  ierr = PetscMalloc5(nv+sub_schurs->n_subs,&pcbddc->adaptive_constraints_n,
                      nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_idxs_ptr,
                      nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_data_ptr,
                      nv+cum,&pcbddc->adaptive_constraints_idxs,
                      nv+cum2,&pcbddc->adaptive_constraints_data);CHKERRQ(ierr);
  ierr = PetscMemzero(pcbddc->adaptive_constraints_n,(nv+sub_schurs->n_subs)*sizeof(PetscInt));CHKERRQ(ierr);

  maxneigs = 0;
  cum = cum2 = cumarray = 0;
  pcbddc->adaptive_constraints_idxs_ptr[0] = 0;
  pcbddc->adaptive_constraints_data_ptr[0] = 0;
  if (sub_schurs->is_vertices && pcbddc->use_vertices) {
    const PetscInt *idxs;

    ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
    for (cum=0;cum<nv;cum++) {
      pcbddc->adaptive_constraints_n[cum] = 1;
      pcbddc->adaptive_constraints_idxs[cum] = idxs[cum];
      pcbddc->adaptive_constraints_data[cum] = 1.0;
      pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum]+1;
      pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum]+1;
    }
    cum2 = cum;
    ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
  }

  if (mss) { /* multilevel */
    ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);CHKERRQ(ierr);
    ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);CHKERRQ(ierr);
  }

  thresh = pcbddc->adaptive_threshold;
  for (i=0;i<sub_schurs->n_subs;i++) {
    const PetscInt *idxs;
    PetscReal      infty = PETSC_MAX_REAL;
    PetscInt       j,subset_size,eigs_start = 0;
    PetscBLASInt   B_N;
    PetscBool      same_data = PETSC_FALSE;

    ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
    ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
    ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
    if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
      if (sub_schurs->is_hermitian) {
        PetscInt j,k;
        if (sub_schurs->n_subs == 1) { /* zeroing memory to use PetscMemcmp later */
          ierr = PetscMemzero(S,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
          ierr = PetscMemzero(St,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
        }
        for (j=0;j<subset_size;j++) {
          for (k=j;k<subset_size;k++) {
            S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
            St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
          }
        }
      } else {
        ierr = PetscMemcpy(S,Sarray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
        ierr = PetscMemcpy(St,Starray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
      }
    } else {
      S = Sarray + cumarray;
      St = Starray + cumarray;
    }

    /* see if we can save some work */
    if (sub_schurs->n_subs == 1) {
      ierr = PetscMemcmp(S,St,subset_size*subset_size*sizeof(PetscScalar),&same_data);CHKERRQ(ierr);
    }

    if (same_data) { /* there's no need of constraints here, deluxe scaling is enough */
      B_neigs = 0;
    } else {
      if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
        PetscBLASInt B_itype = 1;
        PetscBLASInt B_IL, B_IU;
        PetscReal    eps = -1.0; /* dlamch? */
        PetscInt     nmin_s;

        if (pcbddc->dbg_flag) {
          PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Computing for sub %d/%d %d %d.\n",i,sub_schurs->n_subs,subset_size,pcbddc->mat_graph->count[idxs[0]]);
        }

        ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
        if (thresh > 1.+PETSC_SMALL) {

          /* ask for eigenvalues larger than thresh */
#if defined(PETSC_USE_COMPLEX)
          PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
#else
          PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
#endif
        } else {
          B_IU = PetscMax(1,PetscMin(B_N,nmax));
          B_IL = 1;
#if defined(PETSC_USE_COMPLEX)
          PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
#else
          PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
#endif
        }
        ierr = PetscFPTrapPop();CHKERRQ(ierr);
        if (B_ierr) {
          if (B_ierr < 0 ) {
            SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
          } else if (B_ierr <= B_N) {
            SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
          } else {
            SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
          }
        }

        if (B_neigs > nmax) {
          if (pcbddc->dbg_flag) {
            PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, more than maximum required %d.\n",B_neigs,nmax);
          }
          eigs_start = B_neigs -nmax;
          B_neigs = nmax;
        }

        nmin_s = PetscMin(nmin,B_N);
        if (B_neigs < nmin_s) {
          PetscBLASInt B_neigs2;

          B_IU = B_N - B_neigs;
          B_IL = B_N - nmin_s + 1;
          if (pcbddc->dbg_flag) {
            PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, less than minimum required %d. Asking for %d to %d incl (fortran like)\n",B_neigs,nmin,B_IL,B_IU);
          }
          if (sub_schurs->is_hermitian) {
            PetscInt j;
            for (j=0;j<subset_size;j++) {
              ierr = PetscMemcpy(S+j*(subset_size+1),Sarray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));CHKERRQ(ierr);
            }
            for (j=0;j<subset_size;j++) {
              ierr = PetscMemcpy(St+j*(subset_size+1),Starray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));CHKERRQ(ierr);
            }
          } else {
            ierr = PetscMemcpy(S,Sarray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
            ierr = PetscMemcpy(St,Starray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
          }
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
          PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*subset_size,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
#else
          PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*subset_size,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
#endif
          ierr = PetscFPTrapPop();CHKERRQ(ierr);
          B_neigs += B_neigs2;
        }
        if (B_ierr) {
          if (B_ierr < 0 ) {
            SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
          } else if (B_ierr <= B_N) {
            SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
          } else {
            SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
          }
        }
        if (pcbddc->dbg_flag) {
          ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Got %d eigs\n",B_neigs);CHKERRQ(ierr);
          for (j=0;j<B_neigs;j++) {
            if (eigs[j] == 0.0) {
              ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     Inf\n");CHKERRQ(ierr);
            } else {
              ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",eigs[j+eigs_start]);CHKERRQ(ierr);
            }
          }
        }
      } else {
          /* TODO */
      }
    }
    maxneigs = PetscMax(B_neigs,maxneigs);
    pcbddc->adaptive_constraints_n[i+nv] = B_neigs;
    if (B_neigs) {
      ierr = PetscMemcpy(pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum],eigv+eigs_start*subset_size,B_neigs*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);

      if (pcbddc->dbg_flag > 1) {
        PetscInt ii;
        for (ii=0;ii<B_neigs;ii++) {
          ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector %d/%d (%d)\n",ii,B_neigs,B_N);CHKERRQ(ierr);
          for (j=0;j<B_N;j++) {
#if defined(PETSC_USE_COMPLEX)
            PetscReal r = PetscRealPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
            PetscReal c = PetscImaginaryPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
            ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);CHKERRQ(ierr);
#else
            ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);CHKERRQ(ierr);
#endif
          }
        }
      }
#if 0
      for (j=0;j<B_neigs;j++) {
        PetscBLASInt Blas_N,Blas_one = 1.0;
        PetscScalar norm;
        ierr = PetscBLASIntCast(subset_size,&Blas_N);CHKERRQ(ierr);
        PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum]+j*subset_size,
                                                   &Blas_one,pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum]+j*subset_size,&Blas_one));
        if (pcbddc->adaptive_constraints_data[cum2] > 0.0) {
          norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
        } else {
          norm = -1.0/PetscSqrtReal(PetscRealPart(norm));
        }
        PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum]+j*subset_size,&Blas_one));
      }
#endif
      ierr = PetscMemcpy(pcbddc->adaptive_constraints_idxs+pcbddc->adaptive_constraints_idxs_ptr[cum],idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
      pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + subset_size;
      pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum] + subset_size*B_neigs;
      cum++;
    }
    ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
    /* shift for next computation */
    cumarray += subset_size*subset_size;
  }
  if (pcbddc->dbg_flag) {
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  if (mss) {
    ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);CHKERRQ(ierr);
    ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);CHKERRQ(ierr);
    /* destroy matrices (junk) */
    ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
    ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
  }
  if (allocated_S_St) {
    ierr = PetscFree2(S,St);CHKERRQ(ierr);
  }
  ierr = PetscFree5(eigv,eigs,work,B_iwork,B_ifail);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
  ierr = PetscFree(rwork);CHKERRQ(ierr);
#endif
  if (pcbddc->dbg_flag) {
    PetscInt maxneigs_r;
    ierr = MPI_Allreduce(&maxneigs,&maxneigs_r,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of constraints per cc %d\n",maxneigs_r);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpSolvers"
PetscErrorCode PCBDDCSetUpSolvers(PC pc)
{
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  PetscScalar    *coarse_submat_vals;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* Setup local scatters R_to_B and (optionally) R_to_D */
  /* PCBDDCSetUpLocalWorkVectors should be called first! */
  ierr = PCBDDCSetUpLocalScatters(pc);CHKERRQ(ierr);

  /* Setup local neumann solver ksp_R */
  /* PCBDDCSetUpLocalScatters should be called first! */
  ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);

  /* Change global null space passed in by the user if change of basis has been requested */
  if (pcbddc->NullSpace && pcbddc->ChangeOfBasisMatrix) {
    ierr = PCBDDCNullSpaceAdaptGlobal(pc);CHKERRQ(ierr);
  }

  /*
     Setup local correction and local part of coarse basis.
     Gives back the dense local part of the coarse matrix in column major ordering
  */
  ierr = PCBDDCSetUpCorrection(pc,&coarse_submat_vals);CHKERRQ(ierr);

  /* Compute total number of coarse nodes and setup coarse solver */
  ierr = PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);CHKERRQ(ierr);

  /* free */
  ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCResetCustomization"
PetscErrorCode PCBDDCResetCustomization(PC pc)
{
  PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
  ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
  ierr = PCBDDCSetDofsSplitting(pc,0,NULL);CHKERRQ(ierr);
  ierr = PCBDDCSetDofsSplittingLocal(pc,0,NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCResetTopography"
PetscErrorCode PCBDDCResetTopography(PC pc)
{
  PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
  PetscInt       i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
  ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
  for (i=0;i<pcbddc->n_local_subs;i++) {
    ierr = ISDestroy(&pcbddc->local_subs[i]);CHKERRQ(ierr);
  }
  ierr = PetscFree(pcbddc->local_subs);CHKERRQ(ierr);
  ierr = PCBDDCSubSchursReset(pcbddc->sub_schurs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCResetSolvers"
PetscErrorCode PCBDDCResetSolvers(PC pc)
{
  PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
  if (pcbddc->coarse_phi_B) {
    PetscScalar *array;
    ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&array);CHKERRQ(ierr);
    ierr = PetscFree(array);CHKERRQ(ierr);
  }
  ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
  ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
  ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
  ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
  ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
  ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
  ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
  ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
  ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
  ierr = PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);CHKERRQ(ierr);
  ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
  ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->benign_change);CHKERRQ(ierr);
  ierr = VecDestroy(&pcbddc->benign_vec);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->benign_original_mat);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->benign_B0);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&pcbddc->benign_sf);CHKERRQ(ierr);
  if (pcbddc->benign_zerodiag_subs) {
    PetscInt i;
    for (i=0;i<pcbddc->benign_n;i++) {
      ierr = ISDestroy(&pcbddc->benign_zerodiag_subs[i]);CHKERRQ(ierr);
    }
    ierr = PetscFree(pcbddc->benign_zerodiag_subs);CHKERRQ(ierr);
  }
  ierr = PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpLocalWorkVectors"
PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
{
  PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
  PC_IS          *pcis = (PC_IS*)pc->data;
  VecType        impVecType;
  PetscInt       n_constraints,n_R,old_size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!pcbddc->ConstraintMatrix) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"BDDC Constraint matrix has not been created");
  }
  /* get sizes */
  n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - pcbddc->n_vertices;
  n_R = pcis->n - pcbddc->n_vertices;
  ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
  /* local work vectors (try to avoid unneeded work)*/
  /* R nodes */
  old_size = -1;
  if (pcbddc->vec1_R) {
    ierr = VecGetSize(pcbddc->vec1_R,&old_size);CHKERRQ(ierr);
  }
  if (n_R != old_size) {
    ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
    ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
    ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
    ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
    ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
    ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
  }
  /* local primal dofs */
  old_size = -1;
  if (pcbddc->vec1_P) {
    ierr = VecGetSize(pcbddc->vec1_P,&old_size);CHKERRQ(ierr);
  }
  if (pcbddc->local_primal_size != old_size) {
    ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
    ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
    ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);CHKERRQ(ierr);
    ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
  }
  /* local explicit constraints */
  old_size = -1;
  if (pcbddc->vec1_C) {
    ierr = VecGetSize(pcbddc->vec1_C,&old_size);CHKERRQ(ierr);
  }
  if (n_constraints && n_constraints != old_size) {
    ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
    ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
    ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
    ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpCorrection"
PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
{
  PetscErrorCode  ierr;
  /* pointers to pcis and pcbddc */
  PC_IS*          pcis = (PC_IS*)pc->data;
  PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
  PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
  /* submatrices of local problem */
  Mat             A_RV,A_VR,A_VV,local_auxmat2_R;
  /* submatrices of benign trick */
  Mat             B0_V = NULL;
  /* submatrices of local coarse problem */
  Mat             S_VV,S_CV,S_VC,S_CC;
  /* working matrices */
  Mat             C_CR;
  /* additional working stuff */
  PC              pc_R;
  Mat             F;
  PetscBool       isLU,isCHOL,isILU,need_benign_correction;

  PetscScalar     *coarse_submat_vals; /* TODO: use a PETSc matrix */
  PetscScalar     *work;
  PetscInt        *idx_V_B;
  PetscInt        lda_rhs,n,n_vertices,n_constraints,*p0_lidx_I;
  PetscInt        i,n_R,n_D,n_B;

  /* some shortcuts to scalars */
  PetscScalar     one=1.0,m_one=-1.0;

  PetscFunctionBegin;
  if (!pcbddc->symmetric_primal && pcbddc->benign_n) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Non-symmetric primal basis computation with benign trick not yet implemented");
  }

  /* Set Non-overlapping dimensions */
  n_vertices = pcbddc->n_vertices;
  n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - n_vertices;
  n_B = pcis->n_B;
  n_D = pcis->n - n_B;
  n_R = pcis->n - n_vertices;

  /* vertices in boundary numbering */
  ierr = PetscMalloc1(n_vertices,&idx_V_B);CHKERRQ(ierr);
  ierr = ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->local_primal_ref_node,&i,idx_V_B);CHKERRQ(ierr);
  if (i != n_vertices) {
    SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %d != %d\n",n_vertices,i);
  }

  /* Subdomain contribution (Non-overlapping) to coarse matrix  */
  ierr = PetscCalloc1(pcbddc->local_primal_size*pcbddc->local_primal_size,&coarse_submat_vals);CHKERRQ(ierr);
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_vertices,coarse_submat_vals,&S_VV);CHKERRQ(ierr);
  ierr = MatSeqDenseSetLDA(S_VV,pcbddc->local_primal_size);CHKERRQ(ierr);
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_vertices,coarse_submat_vals+n_vertices,&S_CV);CHKERRQ(ierr);
  ierr = MatSeqDenseSetLDA(S_CV,pcbddc->local_primal_size);CHKERRQ(ierr);
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_constraints,coarse_submat_vals+pcbddc->local_primal_size*n_vertices,&S_VC);CHKERRQ(ierr);
  ierr = MatSeqDenseSetLDA(S_VC,pcbddc->local_primal_size);CHKERRQ(ierr);
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_constraints,coarse_submat_vals+(pcbddc->local_primal_size+1)*n_vertices,&S_CC);CHKERRQ(ierr);
  ierr = MatSeqDenseSetLDA(S_CC,pcbddc->local_primal_size);CHKERRQ(ierr);

  /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
  ierr = KSPGetPC(pcbddc->ksp_R,&pc_R);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)pc_R,PCLU,&isLU);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)pc_R,PCILU,&isILU);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)pc_R,PCCHOLESKY,&isCHOL);CHKERRQ(ierr);
  lda_rhs = n_R;
  need_benign_correction = PETSC_FALSE;
  if (isLU || isILU || isCHOL) {
    ierr = PCFactorGetMatrix(pc_R,&F);CHKERRQ(ierr);
  } else if (sub_schurs->reuse_solver) {
    PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    MatFactorType      type;

    F = reuse_solver->F;
    ierr = MatGetFactorType(F,&type);CHKERRQ(ierr);
    if (type == MAT_FACTOR_CHOLESKY) isCHOL = PETSC_TRUE;
    ierr = MatGetSize(F,&lda_rhs,NULL);CHKERRQ(ierr);
    need_benign_correction = !!reuse_solver->benign_n;
  } else {
    F = NULL;
  }

  /* allocate workspace */
  n = 0;
  if (n_constraints) {
    n += lda_rhs*n_constraints;
  }
  if (n_vertices) {
    n = PetscMax(2*lda_rhs*n_vertices,n);
    n = PetscMax((lda_rhs+n_B)*n_vertices,n);
  }
  ierr = PetscMalloc1(n,&work);CHKERRQ(ierr);

  /* Precompute stuffs needed for preprocessing and application of BDDC*/
  if (n_constraints) {
    Mat         M1,M2,M3;
    Mat         auxmat;
    IS          is_aux;
    PetscScalar *array,*array2;

    ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
    ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);

    /* Extract constraints on R nodes: C_{CR}  */
    ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcis->is_B_local,MAT_INITIAL_MATRIX,&auxmat);CHKERRQ(ierr);

    /* Assemble         local_auxmat2_R =        (- A_{RR}^{-1} C^T_{CR}) needed by BDDC setup */
    /* Assemble pcbddc->local_auxmat2   = R_to_B (- A_{RR}^{-1} C^T_{CR}) needed by BDDC application */
    ierr = PetscMemzero(work,lda_rhs*n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
    for (i=0;i<n_constraints;i++) {
      const PetscScalar *row_cmat_values;
      const PetscInt    *row_cmat_indices;
      PetscInt          size_of_constraint,j;

      ierr = MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
      for (j=0;j<size_of_constraint;j++) {
        work[row_cmat_indices[j]+i*lda_rhs] = -row_cmat_values[j];
      }
      ierr = MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
    }
    ierr = MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,NULL,&local_auxmat2_R);CHKERRQ(ierr);
    if (F) {
      Mat B;

      ierr = MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&B);CHKERRQ(ierr);
      if (need_benign_correction) {
        PetscScalar        *marr;
        PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

        ierr = MatDenseGetArray(B,&marr);CHKERRQ(ierr);
        for (i=0;i<n_constraints;i++) {
          ierr = VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);CHKERRQ(ierr);
          ierr = PCBDDCReuseSolversChangeInterior(reuse_solver,pcbddc->vec1_R,NULL,PETSC_FALSE);CHKERRQ(ierr);
          ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
        }
        ierr = MatDenseRestoreArray(B,&marr);CHKERRQ(ierr);
      }
      ierr = MatMatSolve(F,B,local_auxmat2_R);CHKERRQ(ierr);
      if (need_benign_correction) {
        PetscScalar        *marr;
        PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

        ierr = MatDenseGetArray(local_auxmat2_R,&marr);CHKERRQ(ierr);
        for (i=0;i<n_constraints;i++) {
          ierr = VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);CHKERRQ(ierr);
          ierr = PCBDDCReuseSolversChangeInterior(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE);CHKERRQ(ierr);
          ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
        }
        ierr = MatDenseRestoreArray(local_auxmat2_R,&marr);CHKERRQ(ierr);
      }
      ierr = MatDestroy(&B);CHKERRQ(ierr);
    } else {
      PetscScalar *marr;

      ierr = MatDenseGetArray(local_auxmat2_R,&marr);CHKERRQ(ierr);
      for (i=0;i<n_constraints;i++) {
        ierr = VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);CHKERRQ(ierr);
        ierr = VecPlaceArray(pcbddc->vec2_R,marr+i*lda_rhs);CHKERRQ(ierr);
        ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
        ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
        ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
      }
      ierr = MatDenseRestoreArray(local_auxmat2_R,&marr);CHKERRQ(ierr);
    }
    if (!pcbddc->switch_static) {
      ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_constraints,NULL,&pcbddc->local_auxmat2);CHKERRQ(ierr);
      ierr = MatDenseGetArray(pcbddc->local_auxmat2,&array);CHKERRQ(ierr);
      ierr = MatDenseGetArray(local_auxmat2_R,&array2);CHKERRQ(ierr);
      for (i=0;i<n_constraints;i++) {
        ierr = VecPlaceArray(pcbddc->vec1_R,array2+i*lda_rhs);CHKERRQ(ierr);
        ierr = VecPlaceArray(pcis->vec1_B,array+i*n_B);CHKERRQ(ierr);
        ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);
        ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
      }
      ierr = MatDenseRestoreArray(local_auxmat2_R,&array2);CHKERRQ(ierr);
      ierr = MatDenseRestoreArray(pcbddc->local_auxmat2,&array);CHKERRQ(ierr);
      ierr = MatMatMult(auxmat,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);CHKERRQ(ierr);
    } else {
      if (lda_rhs != n_R) {
        IS dummy;

        ierr = ISCreateStride(PETSC_COMM_SELF,n_R,0,1,&dummy);CHKERRQ(ierr);
        ierr = MatGetSubMatrix(local_auxmat2_R,dummy,dummy,MAT_INITIAL_MATRIX,&pcbddc->local_auxmat2);CHKERRQ(ierr);
        ierr = ISDestroy(&dummy);CHKERRQ(ierr);
      } else {
        ierr = PetscObjectReference((PetscObject)local_auxmat2_R);CHKERRQ(ierr);
        pcbddc->local_auxmat2 = local_auxmat2_R;
      }
      ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);CHKERRQ(ierr);
    }
    ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
    /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1}  */
    ierr = MatScale(M3,m_one);CHKERRQ(ierr);
    ierr = MatDuplicate(M3,MAT_DO_NOT_COPY_VALUES,&M1);CHKERRQ(ierr);
    ierr = MatDuplicate(M3,MAT_DO_NOT_COPY_VALUES,&M2);CHKERRQ(ierr);
    if (isCHOL) {
      ierr = MatCholeskyFactor(M3,NULL,NULL);CHKERRQ(ierr);
    } else {
      ierr = MatLUFactor(M3,NULL,NULL,NULL);CHKERRQ(ierr);
    }
    ierr = VecSet(pcbddc->vec1_C,one);CHKERRQ(ierr);
    ierr = MatDiagonalSet(M2,pcbddc->vec1_C,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatMatSolve(M3,M2,M1);CHKERRQ(ierr);
    ierr = MatDestroy(&M2);CHKERRQ(ierr);
    ierr = MatDestroy(&M3);CHKERRQ(ierr);
    /* Assemble local_auxmat1 = S_CC*C_{CB} needed by BDDC application in KSP and in preproc */
    ierr = MatMatMult(M1,auxmat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
    ierr = MatDestroy(&auxmat);CHKERRQ(ierr);
    ierr = MatCopy(M1,S_CC,SAME_NONZERO_PATTERN);CHKERRQ(ierr); /* S_CC can have a different LDA, MatMatSolve doesn't support it */
    ierr = MatDestroy(&M1);CHKERRQ(ierr);
  }
  /* Get submatrices from subdomain matrix */
  if (pcbddc->benign_n) {
    IS        dummy;
    Mat       B0_R;
    PetscReal norm;

    ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&dummy);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pcbddc->benign_B0,dummy,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&B0_R);CHKERRQ(ierr);
    ierr = MatNorm(B0_R,NORM_INFINITY,&norm);CHKERRQ(ierr);
    if (norm > PETSC_SMALL) {
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Benign trick can not be applied! ||B0_R|| = %f (should be numerically 0.)",norm);
    }
    ierr = MatDestroy(&B0_R);CHKERRQ(ierr);
    ierr = ISDestroy(&dummy);CHKERRQ(ierr);
  }

  if (n_vertices) {
    IS is_aux;

    if (sub_schurs->reuse_solver) { /* is_R_local is not sorted, ISComplement doesn't like it */
      IS tis;

      ierr = ISDuplicate(pcbddc->is_R_local,&tis);CHKERRQ(ierr);
      ierr = ISSort(tis);CHKERRQ(ierr);
      ierr = ISComplement(tis,0,pcis->n,&is_aux);CHKERRQ(ierr);
      ierr = ISDestroy(&tis);CHKERRQ(ierr);
    } else {
      ierr = ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);CHKERRQ(ierr);
    }
    ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
    ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
    if (pcbddc->benign_n) {
      IS dummy;

      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&dummy);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(pcbddc->benign_B0,dummy,is_aux,MAT_INITIAL_MATRIX,&B0_V);CHKERRQ(ierr);
      ierr = ISDestroy(&dummy);CHKERRQ(ierr);
    }
    ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
  }

  /* Matrix of coarse basis functions (local) */
  if (pcbddc->coarse_phi_B) {
    PetscInt on_B,on_primal,on_D=n_D;
    if (pcbddc->coarse_phi_D) {
      ierr = MatGetSize(pcbddc->coarse_phi_D,&on_D,NULL);CHKERRQ(ierr);
    }
    ierr = MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);CHKERRQ(ierr);
    if (on_B != n_B || on_primal != pcbddc->local_primal_size || on_D != n_D) {
      PetscScalar *marray;

      ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&marray);CHKERRQ(ierr);
      ierr = PetscFree(marray);CHKERRQ(ierr);
      ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
      ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
      ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
      ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
    }
  }

  if (!pcbddc->coarse_phi_B) {
    PetscScalar *marray;

    n = n_B*pcbddc->local_primal_size;
    if (pcbddc->switch_static || pcbddc->dbg_flag) {
      n += n_D*pcbddc->local_primal_size;
    }
    if (!pcbddc->symmetric_primal) {
      n *= 2;
    }
    ierr = PetscCalloc1(n,&marray);CHKERRQ(ierr);
    ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marray,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
    n = n_B*pcbddc->local_primal_size;
    if (pcbddc->switch_static || pcbddc->dbg_flag) {
      ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
      n += n_D*pcbddc->local_primal_size;
    }
    if (!pcbddc->symmetric_primal) {
      ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_psi_B);CHKERRQ(ierr);
      if (pcbddc->switch_static || pcbddc->dbg_flag) {
        n = n_B*pcbddc->local_primal_size;
        ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_psi_D);CHKERRQ(ierr);
      }
    } else {
      ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);CHKERRQ(ierr);
      pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
      if (pcbddc->switch_static || pcbddc->dbg_flag) {
        ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);CHKERRQ(ierr);
        pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
      }
    }
  }

  /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
  p0_lidx_I = NULL;
  if (pcbddc->benign_n && (pcbddc->switch_static || pcbddc->dbg_flag)) {
    const PetscInt *idxs;

    ierr = ISGetIndices(pcis->is_I_local,&idxs);CHKERRQ(ierr);
    ierr = PetscMalloc1(pcbddc->benign_n,&p0_lidx_I);CHKERRQ(ierr);
    for (i=0;i<pcbddc->benign_n;i++) {
      ierr = PetscFindInt(pcbddc->benign_p0_lidx[i],pcis->n-pcis->n_B,idxs,&p0_lidx_I[i]);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(pcis->is_I_local,&idxs);CHKERRQ(ierr);
  }

  /* vertices */
  if (n_vertices) {

    ierr = MatConvert(A_VV,MATDENSE,MAT_REUSE_MATRIX,&A_VV);CHKERRQ(ierr);

    if (n_R) {
      Mat          A_RRmA_RV,A_RV_bcorr=NULL,S_VVt; /* S_VVt with LDA=N */
      PetscBLASInt B_N,B_one = 1;
      PetscScalar  *x,*y;
      PetscBool    isseqaij;

      ierr = MatScale(A_RV,m_one);CHKERRQ(ierr);
      if (need_benign_correction) {
        ISLocalToGlobalMapping RtoN;
        IS                     is_p0;
        PetscInt               *idxs_p0,n;

        ierr = PetscMalloc1(pcbddc->benign_n,&idxs_p0);CHKERRQ(ierr);
        ierr = ISLocalToGlobalMappingCreateIS(pcbddc->is_R_local,&RtoN);CHKERRQ(ierr);
        ierr = ISGlobalToLocalMappingApply(RtoN,IS_GTOLM_DROP,pcbddc->benign_n,pcbddc->benign_p0_lidx,&n,idxs_p0);CHKERRQ(ierr);
        if (n != pcbddc->benign_n) {
          SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in R numbering for benign p0! %d != %d\n",n,pcbddc->benign_n);
        }
        ierr = ISLocalToGlobalMappingDestroy(&RtoN);CHKERRQ(ierr);
        ierr = ISCreateGeneral(PETSC_COMM_SELF,n,idxs_p0,PETSC_OWN_POINTER,&is_p0);CHKERRQ(ierr);
        ierr = MatGetSubMatrix(A_RV,is_p0,NULL,MAT_INITIAL_MATRIX,&A_RV_bcorr);CHKERRQ(ierr);
        ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
      }

      if (lda_rhs == n_R) {
        ierr = MatConvert(A_RV,MATDENSE,MAT_REUSE_MATRIX,&A_RV);CHKERRQ(ierr);
      } else {
        PetscScalar    *av,*array;
        const PetscInt *xadj,*adjncy;
        PetscInt       n;
        PetscBool      flg_row;

        array = work+lda_rhs*n_vertices;
        ierr = PetscMemzero(array,lda_rhs*n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
        ierr = MatConvert(A_RV,MATSEQAIJ,MAT_REUSE_MATRIX,&A_RV);CHKERRQ(ierr);
        ierr = MatGetRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
        ierr = MatSeqAIJGetArray(A_RV,&av);CHKERRQ(ierr);
        for (i=0;i<n;i++) {
          PetscInt j;
          for (j=xadj[i];j<xadj[i+1];j++) array[lda_rhs*adjncy[j]+i] = av[j];
        }
        ierr = MatRestoreRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
        ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
        ierr = MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,array,&A_RV);CHKERRQ(ierr);
      }
      ierr = MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work,&A_RRmA_RV);CHKERRQ(ierr);
      if (F) {
        if (need_benign_correction) {
          PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
          PetscScalar        *marr;

          ierr = MatDenseGetArray(A_RV,&marr);CHKERRQ(ierr);
          /* need \Phi^T A_RV = (I+L)A_RV, L given by

                 | 0 0  0 | (V)
             L = | 0 0 -1 | (P-p0)
                 | 0 0 -1 | (p0)

          */
          for (i=0;i<reuse_solver->benign_n;i++) {
            const PetscScalar *vals;
            const PetscInt    *idxs,*idxs_zero;
            PetscInt          n,j,nz;

            ierr = ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);CHKERRQ(ierr);
            ierr = ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);CHKERRQ(ierr);
            ierr = MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);CHKERRQ(ierr);
            for (j=0;j<n;j++) {
              PetscScalar val = vals[j];
              PetscInt    k,col = idxs[j];
              for (k=0;k<nz;k++) marr[idxs_zero[k]+lda_rhs*col] -= val;
            }
            ierr = MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);CHKERRQ(ierr);
            ierr = ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);CHKERRQ(ierr);
          }
          /* need to correct the rhs */
          for (i=0;i<n_vertices;i++) {
            ierr = VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);CHKERRQ(ierr);
            ierr = PCBDDCReuseSolversChangeInterior(reuse_solver,pcbddc->vec1_R,NULL,PETSC_FALSE);CHKERRQ(ierr);
            ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
          }
          ierr = MatDenseRestoreArray(A_RV,&marr);CHKERRQ(ierr);
        }
        ierr = MatMatSolve(F,A_RV,A_RRmA_RV);CHKERRQ(ierr);
        /* need to correct the solution */
        if (need_benign_correction) {
          PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
          PetscScalar        *marr;

          ierr = MatDenseGetArray(A_RRmA_RV,&marr);CHKERRQ(ierr);
          for (i=0;i<n_vertices;i++) {
            ierr = VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);CHKERRQ(ierr);
            ierr = PCBDDCReuseSolversChangeInterior(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE);CHKERRQ(ierr);
            ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
          }
          ierr = MatDenseRestoreArray(A_RRmA_RV,&marr);CHKERRQ(ierr);
        }
      } else {
        ierr = MatDenseGetArray(A_RV,&y);CHKERRQ(ierr);
        for (i=0;i<n_vertices;i++) {
          ierr = VecPlaceArray(pcbddc->vec1_R,y+i*lda_rhs);CHKERRQ(ierr);
          ierr = VecPlaceArray(pcbddc->vec2_R,work+i*lda_rhs);CHKERRQ(ierr);
          ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
          ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
          ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
        }
        ierr = MatDenseRestoreArray(A_RV,&y);CHKERRQ(ierr);
      }
      ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
      /* S_VV and S_CV */
      if (n_constraints) {
        Mat B;

        ierr = PetscMemzero(work+lda_rhs*n_vertices,n_B*n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
        for (i=0;i<n_vertices;i++) {
          ierr = VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);CHKERRQ(ierr);
          ierr = VecPlaceArray(pcis->vec1_B,work+lda_rhs*n_vertices+i*n_B);CHKERRQ(ierr);
          ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
          ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);
          ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
        }
        ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_vertices,work+lda_rhs*n_vertices,&B);CHKERRQ(ierr);
        ierr = MatMatMult(pcbddc->local_auxmat1,B,MAT_REUSE_MATRIX,PETSC_DEFAULT,&S_CV);CHKERRQ(ierr);
        ierr = MatDestroy(&B);CHKERRQ(ierr);
        ierr = MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work+lda_rhs*n_vertices,&B);CHKERRQ(ierr);
        ierr = MatMatMult(local_auxmat2_R,S_CV,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);CHKERRQ(ierr);
        ierr = MatScale(S_CV,m_one);CHKERRQ(ierr);
        ierr = PetscBLASIntCast(lda_rhs*n_vertices,&B_N);CHKERRQ(ierr);
        PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,work+lda_rhs*n_vertices,&B_one,work,&B_one));
        ierr = MatDestroy(&B);CHKERRQ(ierr);
      }
      ierr = PetscObjectTypeCompare((PetscObject)A_VR,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
      if (!isseqaij) { /* MatMatMult with SEQ(S)BAIJ below will raise an error */
        ierr = MatConvert(A_VR,MATSEQAIJ,MAT_REUSE_MATRIX,&A_VR);CHKERRQ(ierr);
      }
      if (lda_rhs != n_R) {
        ierr = MatDestroy(&A_RRmA_RV);CHKERRQ(ierr);
        ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&A_RRmA_RV);CHKERRQ(ierr);
        ierr = MatSeqDenseSetLDA(A_RRmA_RV,lda_rhs);CHKERRQ(ierr);
      }
      ierr = MatMatMult(A_VR,A_RRmA_RV,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VVt);CHKERRQ(ierr);
      /* need A_VR * \Phi * A_RRmA_RV = A_VR * (I+L)^T * A_RRmA_RV, L given as before */
      if (need_benign_correction) {
        PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
        PetscScalar      *marr,*sums;

        ierr = PetscMalloc1(n_vertices,&sums);CHKERRQ(ierr);
        ierr = MatDenseGetArray(S_VVt,&marr);
        for (i=0;i<reuse_solver->benign_n;i++) {
          const PetscScalar *vals;
          const PetscInt    *idxs,*idxs_zero;
          PetscInt          n,j,nz;

          ierr = ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);CHKERRQ(ierr);
          ierr = ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);CHKERRQ(ierr);
          for (j=0;j<n_vertices;j++) {
            PetscInt k;
            sums[j] = 0.;
            for (k=0;k<nz;k++) sums[j] += work[idxs_zero[k]+j*lda_rhs];
          }
          ierr = MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);CHKERRQ(ierr);
          for (j=0;j<n;j++) {
            PetscScalar val = vals[j];
            PetscInt k;
            for (k=0;k<n_vertices;k++) {
              marr[idxs[j]+k*n_vertices] += val*sums[k];
            }
          }
          ierr = MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);CHKERRQ(ierr);
          ierr = ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);CHKERRQ(ierr);
        }
        ierr = PetscFree(sums);CHKERRQ(ierr);
        ierr = MatDenseRestoreArray(S_VVt,&marr);
        ierr = MatDestroy(&A_RV_bcorr);CHKERRQ(ierr);
      }
      ierr = MatDestroy(&A_RRmA_RV);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(n_vertices*n_vertices,&B_N);CHKERRQ(ierr);
      ierr = MatDenseGetArray(A_VV,&x);CHKERRQ(ierr);
      ierr = MatDenseGetArray(S_VVt,&y);CHKERRQ(ierr);
      PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,x,&B_one,y,&B_one));
      ierr = MatDenseRestoreArray(A_VV,&x);CHKERRQ(ierr);
      ierr = MatDenseRestoreArray(S_VVt,&y);CHKERRQ(ierr);
      ierr = MatCopy(S_VVt,S_VV,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
      ierr = MatDestroy(&S_VVt);CHKERRQ(ierr);
    } else {
      ierr = MatCopy(A_VV,S_VV,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
    }
    for (i=0;i<pcbddc->benign_n;i++) {
      const PetscScalar *vals;
      const PetscInt    *idxs;
      PetscInt          n,j,primal_idx;

      ierr = MatGetRow(B0_V,i,&n,&idxs,&vals);CHKERRQ(ierr);
      primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + i;
      for (j=0;j<n;j++) {
        coarse_submat_vals[primal_idx*pcbddc->local_primal_size+idxs[j]] = vals[j];
        coarse_submat_vals[idxs[j]*pcbddc->local_primal_size+primal_idx] = vals[j];
      }
      ierr = MatRestoreRow(B0_V,i,&n,&idxs,&vals);CHKERRQ(ierr);
    }
    ierr = MatDestroy(&A_VV);CHKERRQ(ierr);

    /* coarse basis functions */
    for (i=0;i<n_vertices;i++) {
      PetscScalar *y;

      ierr = VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);CHKERRQ(ierr);
      ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
      ierr = VecPlaceArray(pcis->vec1_B,y+n_B*i);CHKERRQ(ierr);
      ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      y[n_B*i+idx_V_B[i]] = 1.0;
      ierr = MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
      ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);

      if (pcbddc->switch_static || pcbddc->dbg_flag) {
        PetscInt j;

        ierr = MatDenseGetArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
        ierr = VecPlaceArray(pcis->vec1_D,y+n_D*i);CHKERRQ(ierr);
        ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecResetArray(pcis->vec1_D);CHKERRQ(ierr);
        for (j=0;j<pcbddc->benign_n;j++) y[n_D*i+p0_lidx_I[j]] = 0.0;
        ierr = MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
      }
      ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
    }
    /* if n_R == 0 the object is not destroyed */
    ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
  }

  if (n_constraints) {
    Mat B;

    ierr = MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&B);CHKERRQ(ierr);
    ierr = MatScale(S_CC,m_one);CHKERRQ(ierr);
    ierr = MatMatMult(local_auxmat2_R,S_CC,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);CHKERRQ(ierr);
    ierr = MatScale(S_CC,m_one);CHKERRQ(ierr);
    if (n_vertices) {
      if (isCHOL) { /* if we can solve the interior problem with cholesky, we should also be fine with transposing here */
        ierr = MatTranspose(S_CV,MAT_REUSE_MATRIX,&S_VC);CHKERRQ(ierr);
      } else {
        Mat S_VCt;

        if (lda_rhs != n_R) {
          ierr = MatDestroy(&B);CHKERRQ(ierr);
          ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&B);CHKERRQ(ierr);
          ierr = MatSeqDenseSetLDA(B,lda_rhs);CHKERRQ(ierr);
        }
        ierr = MatMatMult(A_VR,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VCt);CHKERRQ(ierr);
        ierr = MatCopy(S_VCt,S_VC,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
        ierr = MatDestroy(&S_VCt);CHKERRQ(ierr);
      }
    }
    ierr = MatDestroy(&B);CHKERRQ(ierr);
    /* coarse basis functions */
    for (i=0;i<n_constraints;i++) {
      PetscScalar *y;

      ierr = VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);CHKERRQ(ierr);
      ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
      ierr = VecPlaceArray(pcis->vec1_B,y+n_B*(i+n_vertices));CHKERRQ(ierr);
      ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
      ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);
      if (pcbddc->switch_static || pcbddc->dbg_flag) {
        PetscInt j;

        ierr = MatDenseGetArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
        ierr = VecPlaceArray(pcis->vec1_D,y+n_D*(i+n_vertices));CHKERRQ(ierr);
        ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecResetArray(pcis->vec1_D);CHKERRQ(ierr);
        for (j=0;j<pcbddc->benign_n;j++) y[n_D*i+p0_lidx_I[j]] = 0.0;
        ierr = MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
      }
      ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
    }
  }
  if (n_constraints) {
    ierr = MatDestroy(&local_auxmat2_R);CHKERRQ(ierr);
  }
  ierr = PetscFree(p0_lidx_I);CHKERRQ(ierr);
  ierr = MatDestroy(&B0_V);CHKERRQ(ierr);

  /* compute other basis functions for non-symmetric problems */
  if (!pcbddc->symmetric_primal) {
    Mat         B_V=NULL,B_C=NULL;
    PetscScalar *marray;

    if (n_constraints) {
      Mat S_CCT,C_CRT;

      ierr = MatTranspose(C_CR,MAT_INITIAL_MATRIX,&C_CRT);CHKERRQ(ierr);
      ierr = MatTranspose(S_CC,MAT_INITIAL_MATRIX,&S_CCT);CHKERRQ(ierr);
      ierr = MatMatMult(C_CRT,S_CCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_C);CHKERRQ(ierr);
      ierr = MatDestroy(&S_CCT);CHKERRQ(ierr);
      if (n_vertices) {
        Mat S_VCT;

        ierr = MatTranspose(S_VC,MAT_INITIAL_MATRIX,&S_VCT);CHKERRQ(ierr);
        ierr = MatMatMult(C_CRT,S_VCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_V);CHKERRQ(ierr);
        ierr = MatDestroy(&S_VCT);CHKERRQ(ierr);
      }
      ierr = MatDestroy(&C_CRT);CHKERRQ(ierr);
    }
    if (n_vertices && n_R) {
      PetscScalar    *av,*marray;
      const PetscInt *xadj,*adjncy;
      PetscInt       n;
      PetscBool      flg_row;

      /* B_V = B_V - A_VR^T */
      ierr = MatConvert(A_VR,MATSEQAIJ,MAT_REUSE_MATRIX,&A_VR);CHKERRQ(ierr);
      ierr = MatGetRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
      ierr = MatSeqAIJGetArray(A_VR,&av);CHKERRQ(ierr);
      ierr = MatDenseGetArray(B_V,&marray);CHKERRQ(ierr);
      for (i=0;i<n;i++) {
        PetscInt j;
        for (j=xadj[i];j<xadj[i+1];j++) marray[i*n_R + adjncy[j]] -= av[j];
      }
      ierr = MatDenseRestoreArray(B_V,&marray);CHKERRQ(ierr);
      ierr = MatRestoreRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
      ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
    }

    /* currently there's no support for MatTransposeMatSolve(F,B,X) */
    ierr = MatDenseGetArray(B_V,&marray);CHKERRQ(ierr);
    for (i=0;i<n_vertices;i++) {
      ierr = VecPlaceArray(pcbddc->vec1_R,marray+i*n_R);CHKERRQ(ierr);
      ierr = VecPlaceArray(pcbddc->vec2_R,work+i*n_R);CHKERRQ(ierr);
      ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
      ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
      ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
    }
    ierr = MatDenseRestoreArray(B_V,&marray);CHKERRQ(ierr);
    ierr = MatDenseGetArray(B_C,&marray);CHKERRQ(ierr);
    for (i=n_vertices;i<n_constraints+n_vertices;i++) {
      ierr = VecPlaceArray(pcbddc->vec1_R,marray+(i-n_vertices)*n_R);CHKERRQ(ierr);
      ierr = VecPlaceArray(pcbddc->vec2_R,work+i*n_R);CHKERRQ(ierr);
      ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
      ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
      ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
    }
    ierr = MatDenseRestoreArray(B_C,&marray);CHKERRQ(ierr);
    /* coarse basis functions */
    for (i=0;i<pcbddc->local_primal_size;i++) {
      PetscScalar *y;

      ierr = VecPlaceArray(pcbddc->vec1_R,work+i*n_R);CHKERRQ(ierr);
      ierr = MatDenseGetArray(pcbddc->coarse_psi_B,&y);CHKERRQ(ierr);
      ierr = VecPlaceArray(pcis->vec1_B,y+n_B*i);CHKERRQ(ierr);
      ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      if (i<n_vertices) {
        y[n_B*i+idx_V_B[i]] = 1.0;
      }
      ierr = MatDenseRestoreArray(pcbddc->coarse_psi_B,&y);CHKERRQ(ierr);
      ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);

      if (pcbddc->switch_static || pcbddc->dbg_flag) {
        ierr = MatDenseGetArray(pcbddc->coarse_psi_D,&y);CHKERRQ(ierr);
        ierr = VecPlaceArray(pcis->vec1_D,y+n_D*i);CHKERRQ(ierr);
        ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
        ierr = VecResetArray(pcis->vec1_D);CHKERRQ(ierr);
        ierr = MatDenseRestoreArray(pcbddc->coarse_psi_D,&y);CHKERRQ(ierr);
      }
      ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
    }
    ierr = MatDestroy(&B_V);CHKERRQ(ierr);
    ierr = MatDestroy(&B_C);CHKERRQ(ierr);
  }
  /* free memory */
  ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
  ierr = MatDestroy(&S_VV);CHKERRQ(ierr);
  ierr = MatDestroy(&S_CV);CHKERRQ(ierr);
  ierr = MatDestroy(&S_VC);CHKERRQ(ierr);
  ierr = MatDestroy(&S_CC);CHKERRQ(ierr);
  ierr = PetscFree(work);CHKERRQ(ierr);
  if (n_vertices) {
    ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
  }
  if (n_constraints) {
    ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
  }
  /* Checking coarse_sub_mat and coarse basis functios */
  /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
  /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
  if (pcbddc->dbg_flag) {
    Mat         coarse_sub_mat;
    Mat         AUXMAT,TM1,TM2,TM3,TM4;
    Mat         coarse_phi_D,coarse_phi_B;
    Mat         coarse_psi_D,coarse_psi_B;
    Mat         A_II,A_BB,A_IB,A_BI;
    Mat         C_B,CPHI;
    IS          is_dummy;
    Vec         mones;
    MatType     checkmattype=MATSEQAIJ;
    PetscReal   real_value;

    if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
      Mat A;
      ierr = PCBDDCBenignProject(pc,NULL,NULL,&A);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(A,pcis->is_I_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(A,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(A,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(A,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
      ierr = MatDestroy(&A);CHKERRQ(ierr);
    } else {
      ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
      ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
      ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
      ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
    }
    ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
    ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
    if (!pcbddc->symmetric_primal) {
      ierr = MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);CHKERRQ(ierr);
      ierr = MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);CHKERRQ(ierr);
    }
    ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);

    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat computation (symmetric %d)\n",pcbddc->symmetric_primal);CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    if (!pcbddc->symmetric_primal) {
      ierr = MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
      ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
      ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
      ierr = MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
      ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
      ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
      ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
      ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
      ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
      ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
      ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
      ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
    } else {
      ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
      ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
      ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
      ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
      ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
      ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
      ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
      ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
    }
    ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
    ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
    ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
    ierr = MatConvert(TM1,MATSEQDENSE,MAT_REUSE_MATRIX,&TM1);CHKERRQ(ierr);
    if (pcbddc->benign_n) {
      Mat         B0_I,B0_B,B0_BPHI,B0_IPHI;
      PetscScalar *data,*data2;
      PetscInt    j;

      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
      ierr = MatGetSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_I_local,MAT_INITIAL_MATRIX,&B0_I);
      ierr = MatMatMult(B0_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);CHKERRQ(ierr);
      ierr = MatConvert(B0_BPHI,MATSEQDENSE,MAT_REUSE_MATRIX,&B0_BPHI);CHKERRQ(ierr);
      ierr = MatDenseGetArray(TM1,&data);CHKERRQ(ierr);
      ierr = MatDenseGetArray(B0_BPHI,&data2);CHKERRQ(ierr);
      for (j=0;j<pcbddc->benign_n;j++) {
        PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
        for (i=0;i<pcbddc->local_primal_size;i++) {
          data[primal_idx*pcbddc->local_primal_size+i] += data2[i*pcbddc->benign_n+j];
          data[i*pcbddc->local_primal_size+primal_idx] += data2[i*pcbddc->benign_n+j];
        }
      }
      ierr = MatDenseRestoreArray(TM1,&data);CHKERRQ(ierr);
      ierr = MatDenseRestoreArray(B0_BPHI,&data2);CHKERRQ(ierr);
      ierr = MatDestroy(&B0_B);CHKERRQ(ierr);
      ierr = ISDestroy(&is_dummy);CHKERRQ(ierr);
      ierr = MatDestroy(&B0_BPHI);CHKERRQ(ierr);
      ierr = MatMatMult(B0_I,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&B0_IPHI);CHKERRQ(ierr);
      ierr = MatDestroy(&B0_I);CHKERRQ(ierr);
      ierr = MatNorm(B0_IPHI,NORM_FROBENIUS,&real_value);CHKERRQ(ierr);
      ierr = MatDestroy(&B0_IPHI);CHKERRQ(ierr);
    }
#if 0
  {
    PetscViewer viewer;
    char filename[256];
    sprintf(filename,"details_local_coarse_mat%d_level%d.m",PetscGlobalRank,pcbddc->current_level);
    ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
    ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject)coarse_sub_mat,"computed");CHKERRQ(ierr);
    ierr = MatView(coarse_sub_mat,viewer);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject)TM1,"projected");CHKERRQ(ierr);
    ierr = MatView(TM1,viewer);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject)pcbddc->coarse_phi_B,"phi_B");CHKERRQ(ierr);
    ierr = MatView(pcbddc->coarse_phi_B,viewer);CHKERRQ(ierr);
    if (pcbddc->coarse_phi_D) {
      ierr = PetscObjectSetName((PetscObject)pcbddc->coarse_phi_D,"phi_D");CHKERRQ(ierr);
      ierr = MatView(pcbddc->coarse_phi_D,viewer);CHKERRQ(ierr);
    }
    if (pcbddc->coarse_psi_B) {
      ierr = PetscObjectSetName((PetscObject)pcbddc->coarse_psi_B,"psi_B");CHKERRQ(ierr);
      ierr = MatView(pcbddc->coarse_psi_B,viewer);CHKERRQ(ierr);
    }
    if (pcbddc->coarse_phi_B) {
      ierr = PetscObjectSetName((PetscObject)pcbddc->coarse_psi_D,"psi_D");CHKERRQ(ierr);
      ierr = MatView(pcbddc->coarse_psi_D,viewer);CHKERRQ(ierr);
    }
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
  }
#endif
    ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
    ierr = MatNorm(TM1,NORM_FROBENIUS,&real_value);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d          matrix error % 1.14e\n",PetscGlobalRank,real_value);CHKERRQ(ierr);

    /* check constraints */
    if (!pcbddc->benign_n) { /* TODO: add benign case */
      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size,0,1,&is_dummy);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);
      ierr = MatMatMult(C_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&CPHI);CHKERRQ(ierr);
      ierr = MatCreateVecs(CPHI,&mones,NULL);CHKERRQ(ierr);
      ierr = VecSet(mones,-1.0);CHKERRQ(ierr);
      ierr = MatDiagonalSet(CPHI,mones,ADD_VALUES);CHKERRQ(ierr);
      ierr = MatNorm(CPHI,NORM_FROBENIUS,&real_value);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d phi constraints error % 1.14e\n",PetscGlobalRank,real_value);CHKERRQ(ierr);
      if (!pcbddc->symmetric_primal) {
        ierr = MatMatMult(C_B,coarse_psi_B,MAT_REUSE_MATRIX,1.0,&CPHI);CHKERRQ(ierr);
        ierr = VecSet(mones,-1.0);CHKERRQ(ierr);
        ierr = MatDiagonalSet(CPHI,mones,ADD_VALUES);CHKERRQ(ierr);
        ierr = MatNorm(CPHI,NORM_FROBENIUS,&real_value);CHKERRQ(ierr);
        ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d psi constraints error % 1.14e\n",PetscGlobalRank,real_value);CHKERRQ(ierr);
      }
      ierr = MatDestroy(&C_B);CHKERRQ(ierr);
      ierr = MatDestroy(&CPHI);CHKERRQ(ierr);
      ierr = ISDestroy(&is_dummy);CHKERRQ(ierr);
      ierr = VecDestroy(&mones);CHKERRQ(ierr);
    }
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = MatDestroy(&A_II);CHKERRQ(ierr);
    ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
    ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
    ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
    ierr = MatDestroy(&TM1);CHKERRQ(ierr);
    ierr = MatDestroy(&TM2);CHKERRQ(ierr);
    ierr = MatDestroy(&TM3);CHKERRQ(ierr);
    ierr = MatDestroy(&TM4);CHKERRQ(ierr);
    ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
    ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
    if (!pcbddc->symmetric_primal) {
      ierr = MatDestroy(&coarse_psi_D);CHKERRQ(ierr);
      ierr = MatDestroy(&coarse_psi_B);CHKERRQ(ierr);
    }
    ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
  }
  /* get back data */
  *coarse_submat_vals_n = coarse_submat_vals;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSubMatrixUnsorted"
PetscErrorCode MatGetSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat* B)
{
  Mat            *work_mat;
  IS             isrow_s,iscol_s;
  PetscBool      rsorted,csorted;
  PetscInt       rsize,*idxs_perm_r,csize,*idxs_perm_c;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = ISSorted(isrow,&rsorted);CHKERRQ(ierr);
  ierr = ISSorted(iscol,&csorted);CHKERRQ(ierr);
  ierr = ISGetLocalSize(isrow,&rsize);CHKERRQ(ierr);
  ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);

  if (!rsorted) {
    const PetscInt *idxs;
    PetscInt *idxs_sorted,i;

    ierr = PetscMalloc1(rsize,&idxs_perm_r);CHKERRQ(ierr);
    ierr = PetscMalloc1(rsize,&idxs_sorted);CHKERRQ(ierr);
    for (i=0;i<rsize;i++) {
      idxs_perm_r[i] = i;
    }
    ierr = ISGetIndices(isrow,&idxs);CHKERRQ(ierr);
    ierr = PetscSortIntWithPermutation(rsize,idxs,idxs_perm_r);CHKERRQ(ierr);
    for (i=0;i<rsize;i++) {
      idxs_sorted[i] = idxs[idxs_perm_r[i]];
    }
    ierr = ISRestoreIndices(isrow,&idxs);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_sorted,PETSC_OWN_POINTER,&isrow_s);CHKERRQ(ierr);
  } else {
    ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
    isrow_s = isrow;
  }

  if (!csorted) {
    if (isrow == iscol) {
      ierr = PetscObjectReference((PetscObject)isrow_s);CHKERRQ(ierr);
      iscol_s = isrow_s;
    } else {
      const PetscInt *idxs;
      PetscInt *idxs_sorted,i;

      ierr = PetscMalloc1(csize,&idxs_perm_c);CHKERRQ(ierr);
      ierr = PetscMalloc1(csize,&idxs_sorted);CHKERRQ(ierr);
      for (i=0;i<csize;i++) {
        idxs_perm_c[i] = i;
      }
      ierr = ISGetIndices(iscol,&idxs);CHKERRQ(ierr);
      ierr = PetscSortIntWithPermutation(csize,idxs,idxs_perm_c);CHKERRQ(ierr);
      for (i=0;i<csize;i++) {
        idxs_sorted[i] = idxs[idxs_perm_c[i]];
      }
      ierr = ISRestoreIndices(iscol,&idxs);CHKERRQ(ierr);
      ierr = ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_sorted,PETSC_OWN_POINTER,&iscol_s);CHKERRQ(ierr);
    }
  } else {
    ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
    iscol_s = iscol;
  }

  ierr = MatGetSubMatrices(A,1,&isrow_s,&iscol_s,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);

  if (!rsorted || !csorted) {
    Mat      new_mat;
    IS       is_perm_r,is_perm_c;

    if (!rsorted) {
      PetscInt *idxs_r,i;
      ierr = PetscMalloc1(rsize,&idxs_r);CHKERRQ(ierr);
      for (i=0;i<rsize;i++) {
        idxs_r[idxs_perm_r[i]] = i;
      }
      ierr = PetscFree(idxs_perm_r);CHKERRQ(ierr);
      ierr = ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_r,PETSC_OWN_POINTER,&is_perm_r);CHKERRQ(ierr);
    } else {
      ierr = ISCreateStride(PETSC_COMM_SELF,rsize,0,1,&is_perm_r);CHKERRQ(ierr);
    }
    ierr = ISSetPermutation(is_perm_r);CHKERRQ(ierr);

    if (!csorted) {
      if (isrow_s == iscol_s) {
        ierr = PetscObjectReference((PetscObject)is_perm_r);CHKERRQ(ierr);
        is_perm_c = is_perm_r;
      } else {
        PetscInt *idxs_c,i;
        ierr = PetscMalloc1(csize,&idxs_c);CHKERRQ(ierr);
        for (i=0;i<csize;i++) {
          idxs_c[idxs_perm_c[i]] = i;
        }
        ierr = PetscFree(idxs_perm_c);CHKERRQ(ierr);
        ierr = ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_c,PETSC_OWN_POINTER,&is_perm_c);CHKERRQ(ierr);
      }
    } else {
      ierr = ISCreateStride(PETSC_COMM_SELF,csize,0,1,&is_perm_c);CHKERRQ(ierr);
    }
    ierr = ISSetPermutation(is_perm_c);CHKERRQ(ierr);

    ierr = MatPermute(work_mat[0],is_perm_r,is_perm_c,&new_mat);CHKERRQ(ierr);
    ierr = MatDestroy(&work_mat[0]);CHKERRQ(ierr);
    work_mat[0] = new_mat;
    ierr = ISDestroy(&is_perm_r);CHKERRQ(ierr);
    ierr = ISDestroy(&is_perm_c);CHKERRQ(ierr);
  }

  ierr = PetscObjectReference((PetscObject)work_mat[0]);CHKERRQ(ierr);
  *B = work_mat[0];
  ierr = MatDestroyMatrices(1,&work_mat);CHKERRQ(ierr);
  ierr = ISDestroy(&isrow_s);CHKERRQ(ierr);
  ierr = ISDestroy(&iscol_s);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCComputeLocalMatrix"
PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
{
  Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  Mat            new_mat;
  IS             is_local,is_global;
  PetscInt       local_size;
  PetscBool      isseqaij;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
  ierr = MatGetSize(matis->A,&local_size,NULL);CHKERRQ(ierr);
  ierr = ISCreateStride(PetscObjectComm((PetscObject)matis->A),local_size,0,1,&is_local);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingApplyIS(pc->pmat->rmap->mapping,is_local,&is_global);CHKERRQ(ierr);
  ierr = ISDestroy(&is_local);CHKERRQ(ierr);
  ierr = MatGetSubMatrixUnsorted(ChangeOfBasisMatrix,is_global,is_global,&new_mat);CHKERRQ(ierr);
  ierr = ISDestroy(&is_global);CHKERRQ(ierr);

  /* check */
  if (pcbddc->dbg_flag) {
    Vec       x,x_change;
    PetscReal error;

    ierr = MatCreateVecs(ChangeOfBasisMatrix,&x,&x_change);CHKERRQ(ierr);
    ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
    ierr = MatMult(ChangeOfBasisMatrix,x,x_change);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = MatMult(new_mat,matis->x,matis->y);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
    ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on N: %1.6e\n",error);CHKERRQ(ierr);
    ierr = VecDestroy(&x);CHKERRQ(ierr);
    ierr = VecDestroy(&x_change);CHKERRQ(ierr);
  }

  /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
  ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
  if (isseqaij) {
    Mat M;

    ierr = MatPtAP(matis->A,new_mat,MAT_INITIAL_MATRIX,2.0,&M);CHKERRQ(ierr);
    ierr = MatSeqAIJCompress(M,&pcbddc->local_mat);CHKERRQ(ierr);
    ierr = MatDestroy(&M);CHKERRQ(ierr);
  } else {
    Mat work_mat,M;

    ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
    ierr = MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&M);CHKERRQ(ierr);
    ierr = MatSeqAIJCompress(M,&pcbddc->local_mat);CHKERRQ(ierr);
    ierr = MatDestroy(&M);CHKERRQ(ierr);
    ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
  }
  if (matis->A->symmetric_set) {
    ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
    ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);CHKERRQ(ierr);
#endif
  }
  /*
  ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
  ierr = MatView(new_mat,(PetscViewer)0);CHKERRQ(ierr);
  */
  ierr = MatDestroy(&new_mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpLocalScatters"
PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
{
  PC_IS*          pcis = (PC_IS*)(pc->data);
  PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
  PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
  PetscInt        *idx_R_local=NULL;
  PetscInt        n_vertices,i,j,n_R,n_D,n_B;
  PetscInt        vbs,bs;
  PetscBT         bitmask=NULL;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  /*
    No need to setup local scatters if
      - primal space is unchanged
        AND
      - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
        AND
      - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
  */
  if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
    PetscFunctionReturn(0);
  }
  /* destroy old objects */
  ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
  /* Set Non-overlapping dimensions */
  n_B = pcis->n_B;
  n_D = pcis->n - n_B;
  n_vertices = pcbddc->n_vertices;

  /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */

  /* create auxiliary bitmask and allocate workspace */
  if (!sub_schurs->reuse_solver) {
    ierr = PetscMalloc1(pcis->n-n_vertices,&idx_R_local);CHKERRQ(ierr);
    ierr = PetscBTCreate(pcis->n,&bitmask);CHKERRQ(ierr);
    for (i=0;i<n_vertices;i++) {
      ierr = PetscBTSet(bitmask,pcbddc->local_primal_ref_node[i]);CHKERRQ(ierr);
    }

    for (i=0, n_R=0; i<pcis->n; i++) {
      if (!PetscBTLookup(bitmask,i)) {
        idx_R_local[n_R++] = i;
      }
    }
  } else { /* A different ordering (already computed) is present if we are reusing the Schur solver */
    PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    ierr = ISGetIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
    ierr = ISGetLocalSize(reuse_solver->is_R,&n_R);CHKERRQ(ierr);
  }

  /* Block code */
  vbs = 1;
  ierr = MatGetBlockSize(pcbddc->local_mat,&bs);CHKERRQ(ierr);
  if (bs>1 && !(n_vertices%bs)) {
    PetscBool is_blocked = PETSC_TRUE;
    PetscInt  *vary;
    if (!sub_schurs->reuse_solver) {
      ierr = PetscMalloc1(pcis->n/bs,&vary);CHKERRQ(ierr);
      ierr = PetscMemzero(vary,pcis->n/bs*sizeof(PetscInt));CHKERRQ(ierr);
      /* Verify that the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
      /* it is ok to check this way since local_primal_ref_node are always sorted by local numbering and idx_R_local is obtained as a complement */
      for (i=0; i<n_vertices; i++) vary[pcbddc->local_primal_ref_node[i]/bs]++;
      for (i=0; i<pcis->n/bs; i++) {
        if (vary[i]!=0 && vary[i]!=bs) {
          is_blocked = PETSC_FALSE;
          break;
        }
      }
      ierr = PetscFree(vary);CHKERRQ(ierr);
    } else {
      /* Verify directly the R set */
      for (i=0; i<n_R/bs; i++) {
        PetscInt j,node=idx_R_local[bs*i];
        for (j=1; j<bs; j++) {
          if (node != idx_R_local[bs*i+j]-j) {
            is_blocked = PETSC_FALSE;
            break;
          }
        }
      }
    }
    if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
      vbs = bs;
      for (i=0;i<n_R/vbs;i++) {
        idx_R_local[i] = idx_R_local[vbs*i]/vbs;
      }
    }
  }
  ierr = ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);CHKERRQ(ierr);
  if (sub_schurs->reuse_solver) {
    PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    ierr = ISRestoreIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
    ierr = ISDestroy(&reuse_solver->is_R);CHKERRQ(ierr);
    ierr = PetscObjectReference((PetscObject)pcbddc->is_R_local);CHKERRQ(ierr);
    reuse_solver->is_R = pcbddc->is_R_local;
  } else {
    ierr = PetscFree(idx_R_local);CHKERRQ(ierr);
  }

  /* print some info if requested */
  if (pcbddc->dbg_flag) {
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"r_size = %d, v_size = %d, constraints = %d, local_primal_size = %d\n",n_R,n_vertices,pcbddc->local_primal_size-n_vertices-pcbddc->benign_n,pcbddc->local_primal_size);CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
  if (!sub_schurs->reuse_solver) {
    IS       is_aux1,is_aux2;
    PetscInt *aux_array1,*aux_array2,*is_indices,*idx_R_local;

    ierr = ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
    ierr = PetscMalloc1(pcis->n_B-n_vertices,&aux_array1);CHKERRQ(ierr);
    ierr = PetscMalloc1(pcis->n_B-n_vertices,&aux_array2);CHKERRQ(ierr);
    ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
    for (i=0; i<n_D; i++) {
      ierr = PetscBTSet(bitmask,is_indices[i]);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
    for (i=0, j=0; i<n_R; i++) {
      if (!PetscBTLookup(bitmask,idx_R_local[i])) {
        aux_array1[j++] = i;
      }
    }
    ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
    ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
    for (i=0, j=0; i<n_B; i++) {
      if (!PetscBTLookup(bitmask,is_indices[i])) {
        aux_array2[j++] = i;
      }
    }
    ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
    ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
    ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
    ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);

    if (pcbddc->switch_static || pcbddc->dbg_flag) {
      ierr = PetscMalloc1(n_D,&aux_array1);CHKERRQ(ierr);
      for (i=0, j=0; i<n_R; i++) {
        if (PetscBTLookup(bitmask,idx_R_local[i])) {
          aux_array1[j++] = i;
        }
      }
      ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
      ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
      ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
    }
    ierr = PetscBTDestroy(&bitmask);CHKERRQ(ierr);
    ierr = ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
  } else {
    PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    IS                 tis;
    PetscInt           schur_size;

    ierr = ISGetLocalSize(reuse_solver->is_B,&schur_size);CHKERRQ(ierr);
    ierr = ISCreateStride(PETSC_COMM_SELF,schur_size,n_D,1,&tis);CHKERRQ(ierr);
    ierr = VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_B,reuse_solver->is_B,&pcbddc->R_to_B);CHKERRQ(ierr);
    ierr = ISDestroy(&tis);CHKERRQ(ierr);
    if (pcbddc->switch_static || pcbddc->dbg_flag) {
      ierr = ISCreateStride(PETSC_COMM_SELF,n_D,0,1,&tis);CHKERRQ(ierr);
      ierr = VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
      ierr = ISDestroy(&tis);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpLocalSolvers"
PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
{
  PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
  PC_IS          *pcis = (PC_IS*)pc->data;
  PC             pc_temp;
  Mat            A_RR;
  MatReuse       reuse;
  PetscScalar    m_one = -1.0;
  PetscReal      value;
  PetscInt       n_D,n_R;
  PetscBool      use_exact,use_exact_reduced,issbaij;
  PetscErrorCode ierr;
  /* prefixes stuff */
  char           dir_prefix[256],neu_prefix[256],str_level[16];
  size_t         len;

  PetscFunctionBegin;

  /* compute prefixes */
  ierr = PetscStrcpy(dir_prefix,"");CHKERRQ(ierr);
  ierr = PetscStrcpy(neu_prefix,"");CHKERRQ(ierr);
  if (!pcbddc->current_level) {
    ierr = PetscStrcpy(dir_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
    ierr = PetscStrcpy(neu_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
    ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
    ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
  } else {
    ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
    sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
    ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
    len -= 15; /* remove "pc_bddc_coarse_" */
    if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
    if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
    ierr = PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
    ierr = PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
    ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
    ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
    ierr = PetscStrcat(dir_prefix,str_level);CHKERRQ(ierr);
    ierr = PetscStrcat(neu_prefix,str_level);CHKERRQ(ierr);
  }

  /* DIRICHLET PROBLEM */
  if (dirichlet) {
    PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    if (pcbddc->benign_n && !pcbddc->benign_change_explicit && pcbddc->dbg_flag) {
      Mat    A_IIn;

      ierr = PCBDDCBenignProject(pc,pcis->is_I_local,pcis->is_I_local,&A_IIn);CHKERRQ(ierr);
      ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
      pcis->A_II = A_IIn;
    }
    if (pcbddc->local_mat->symmetric_set) {
      ierr = MatSetOption(pcis->A_II,MAT_SYMMETRIC,pcbddc->local_mat->symmetric_set);CHKERRQ(ierr);
    }
    /* Matrix for Dirichlet problem is pcis->A_II */
    n_D = pcis->n - pcis->n_B;
    if (!pcbddc->ksp_D) { /* create object if not yet build */
      ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
      ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
      /* default */
      ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
      ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);CHKERRQ(ierr);
      ierr = PetscObjectTypeCompare((PetscObject)pcis->A_II,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
      ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
      if (issbaij) {
        ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
      } else {
        ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
      }
      /* Allow user's customization */
      ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
      ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
    }
    ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
    if (sub_schurs->reuse_solver) {
      PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

      ierr = KSPSetPC(pcbddc->ksp_D,reuse_solver->interior_solver);CHKERRQ(ierr);
    }
    /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
    if (!n_D) {
      ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
      ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
    }
    /* Set Up KSP for Dirichlet problem of BDDC */
    ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
    /* set ksp_D into pcis data */
    ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
    ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
    pcis->ksp_D = pcbddc->ksp_D;
  }

  /* NEUMANN PROBLEM */
  A_RR = 0;
  if (neumann) {
    PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    PetscInt        ibs,mbs;
    PetscBool       issbaij;
    Mat_IS*         matis = (Mat_IS*)pc->pmat->data;
    /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
    ierr = ISGetSize(pcbddc->is_R_local,&n_R);CHKERRQ(ierr);
    if (pcbddc->ksp_R) { /* already created ksp */
      PetscInt nn_R;
      ierr = KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);CHKERRQ(ierr);
      ierr = PetscObjectReference((PetscObject)A_RR);CHKERRQ(ierr);
      ierr = MatGetSize(A_RR,&nn_R,NULL);CHKERRQ(ierr);
      if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
        ierr = KSPReset(pcbddc->ksp_R);CHKERRQ(ierr);
        ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
        reuse = MAT_INITIAL_MATRIX;
      } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
        if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
          ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
          reuse = MAT_INITIAL_MATRIX;
        } else { /* safe to reuse the matrix */
          reuse = MAT_REUSE_MATRIX;
        }
      }
      /* last check */
      if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
        ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
        reuse = MAT_INITIAL_MATRIX;
      }
    } else { /* first time, so we need to create the matrix */
      reuse = MAT_INITIAL_MATRIX;
    }
    /* extract A_RR */
    ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
    ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
    ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
    if (ibs != mbs) { /* need to convert to SEQAIJ to extract any submatrix with is_R_local */
      if (matis->A == pcbddc->local_mat) {
        ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
        ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);CHKERRQ(ierr);
      } else {
        ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_REUSE_MATRIX,&pcbddc->local_mat);CHKERRQ(ierr);
      }
    } else if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
      if (matis->A == pcbddc->local_mat) {
        ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
        ierr = MatConvert(matis->A,MATSEQBAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);CHKERRQ(ierr);
      } else {
        ierr = MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_REUSE_MATRIX,&pcbddc->local_mat);CHKERRQ(ierr);
      }
    }
    ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
    if (pcbddc->local_mat->symmetric_set) {
      ierr = MatSetOption(A_RR,MAT_SYMMETRIC,pcbddc->local_mat->symmetric_set);CHKERRQ(ierr);
    }
    if (pcbddc->benign_n && !pcbddc->benign_change_explicit && pcbddc->dbg_flag) {
      Mat A_RRn;
      ierr = PCBDDCBenignProject(pc,pcbddc->is_R_local,pcbddc->is_R_local,&A_RRn);CHKERRQ(ierr);
      ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
      A_RR = A_RRn;
    }
    if (!pcbddc->ksp_R) { /* create object if not present */
      ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
      ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
      /* default */
      ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
      ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);CHKERRQ(ierr);
      ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
      ierr = PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
      if (issbaij) {
        ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
      } else {
        ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
      }
      /* Allow user's customization */
      ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
      ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
    }
    /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
    if (!n_R) {
      ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
      ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
    }
    /* Reuse solver if it is present */
    if (sub_schurs->reuse_solver) {
      PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

      ierr = KSPSetPC(pcbddc->ksp_R,reuse_solver->correction_solver);CHKERRQ(ierr);
    }
    ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);CHKERRQ(ierr);
    /* Set Up KSP for Neumann problem of BDDC */
    ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
  }
  /* free Neumann problem's matrix */
  ierr = MatDestroy(&A_RR);CHKERRQ(ierr);

  /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
  if (pcbddc->NullSpace || pcbddc->dbg_flag) {
    if (pcbddc->dbg_flag) {
      ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
    }
    if (dirichlet) { /* Dirichlet */
      ierr = VecSetRandom(pcis->vec1_D,NULL);CHKERRQ(ierr);
      ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
      ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);CHKERRQ(ierr);
      ierr = VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);CHKERRQ(ierr);
      ierr = VecNorm(pcis->vec1_D,NORM_INFINITY,&value);CHKERRQ(ierr);
      /* need to be adapted? */
      use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
      ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
      ierr = PCBDDCSetUseExactDirichlet(pc,use_exact_reduced);CHKERRQ(ierr);
      /* print info */
      if (pcbddc->dbg_flag) {
        ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);CHKERRQ(ierr);
        ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      }
      if (pcbddc->NullSpace && !use_exact_reduced && !pcbddc->switch_static) {
        ierr = PCBDDCNullSpaceAssembleCorrection(pc,PETSC_TRUE,pcis->is_I_local);CHKERRQ(ierr);
      }
    }
    if (neumann) { /* Neumann */
      ierr = KSPGetOperators(pcbddc->ksp_R,&A_RR,NULL);CHKERRQ(ierr);
      ierr = VecSetRandom(pcbddc->vec1_R,NULL);CHKERRQ(ierr);
      ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
      ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
      ierr = VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);CHKERRQ(ierr);
      ierr = VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);CHKERRQ(ierr);
      /* need to be adapted? */
      use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
      ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
      /* print info */
      if (pcbddc->dbg_flag) {
        ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);CHKERRQ(ierr);
        ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      }
      if (pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
        ierr = PCBDDCNullSpaceAssembleCorrection(pc,PETSC_FALSE,pcbddc->is_R_local);CHKERRQ(ierr);
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSolveSubstructureCorrection"
static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec inout_B, Vec inout_D, PetscBool applytranspose)
{
  PetscErrorCode  ierr;
  PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
  PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

  PetscFunctionBegin;
  if (!sub_schurs->reuse_solver) {
    ierr = VecSet(pcbddc->vec1_R,0.);CHKERRQ(ierr);
  }
  if (!pcbddc->switch_static) {
    if (applytranspose && pcbddc->local_auxmat1) {
      ierr = MatMultTranspose(pcbddc->local_auxmat2,inout_B,pcbddc->vec1_C);CHKERRQ(ierr);
      ierr = MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);CHKERRQ(ierr);
    }
    if (!sub_schurs->reuse_solver) {
      ierr = VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    } else {
      PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

      ierr = VecScatterBegin(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    }
  } else {
    ierr = VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    if (applytranspose && pcbddc->local_auxmat1) {
      ierr = MatMultTranspose(pcbddc->local_auxmat2,pcbddc->vec1_R,pcbddc->vec1_C);CHKERRQ(ierr);
      ierr = MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);CHKERRQ(ierr);
      ierr = VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    }
  }
  if (!sub_schurs->reuse_solver) {
    if (applytranspose) {
      ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
    } else {
      ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
    }
  } else {
    PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    if (applytranspose) {
      ierr = MatFactorSolveSchurComplementTranspose(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);CHKERRQ(ierr);
    } else {
      ierr = MatFactorSolveSchurComplement(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);CHKERRQ(ierr);
    }
  }
  ierr = VecSet(inout_B,0.);CHKERRQ(ierr);
  if (!pcbddc->switch_static) {
    if (!sub_schurs->reuse_solver) {
      ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    } else {
      PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

      ierr = VecScatterBegin(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = VecScatterEnd(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    }
    if (!applytranspose && pcbddc->local_auxmat1) {
      ierr = MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);CHKERRQ(ierr);
      ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,inout_B,inout_B);CHKERRQ(ierr);
    }
  } else {
    ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    if (!applytranspose && pcbddc->local_auxmat1) {
      ierr = MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);CHKERRQ(ierr);
      ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
    }
    ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
#undef __FUNCT__
#define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
{
  PetscErrorCode ierr;
  PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
  PC_IS*            pcis = (PC_IS*)  (pc->data);
  const PetscScalar zero = 0.0;

  PetscFunctionBegin;
  /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
  if (applytranspose) {
    ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
    if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
  } else {
    ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
    if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
  }

  /* add p0 to the last value of vec1_P holding the coarse dof relative to p0 */
  if (pcbddc->benign_n) {
    PetscScalar *array;
    PetscInt    j;

    ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
    for (j=0;j<pcbddc->benign_n;j++) array[pcbddc->local_primal_size-pcbddc->benign_n+j] += pcbddc->benign_p0[j];
    ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
  }

  /* start communications from local primal nodes to rhs of coarse solver */
  ierr = VecSet(pcbddc->coarse_vec,zero);CHKERRQ(ierr);
  ierr = PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);

  /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
  /* TODO remove null space when doing multilevel */
  if (pcbddc->coarse_ksp) {
    Mat coarse_mat;
    Vec rhs,sol;
    MatNullSpace nullsp;

    ierr = KSPGetRhs(pcbddc->coarse_ksp,&rhs);CHKERRQ(ierr);
    ierr = KSPGetSolution(pcbddc->coarse_ksp,&sol);CHKERRQ(ierr);
    ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
    ierr = MatGetNullSpace(coarse_mat,&nullsp);CHKERRQ(ierr);
    if (nullsp) {
      ierr = MatNullSpaceRemove(nullsp,rhs);CHKERRQ(ierr);
    }
    if (applytranspose) {
      ierr = KSPSolveTranspose(pcbddc->coarse_ksp,rhs,sol);CHKERRQ(ierr);
    } else {
      ierr = KSPSolve(pcbddc->coarse_ksp,rhs,sol);CHKERRQ(ierr);
    }
    if (nullsp) {
      ierr = MatNullSpaceRemove(nullsp,sol);CHKERRQ(ierr);
    }
  }

  /* Local solution on R nodes */
  if (pcis->n) { /* in/out pcbddc->vec1_B,pcbddc->vec1_D */
    ierr = PCBDDCSolveSubstructureCorrection(pc,pcis->vec1_B,pcis->vec1_D,applytranspose);CHKERRQ(ierr);
  }

  /* communications from coarse sol to local primal nodes */
  ierr = PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
  ierr = PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);

  /* Sum contributions from two levels */
  if (applytranspose) {
    ierr = MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
    if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
  } else {
    ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
    if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
  }
  /* store p0 */
  if (pcbddc->benign_n) {
    PetscScalar *array;
    PetscInt    j;

    ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
    for (j=0;j<pcbddc->benign_n;j++) pcbddc->benign_p0[j] = array[pcbddc->local_primal_size-pcbddc->benign_n+j];
    ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
{
  PetscErrorCode ierr;
  PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
  PetscScalar    *array;
  Vec            from,to;

  PetscFunctionBegin;
  if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
    from = pcbddc->coarse_vec;
    to = pcbddc->vec1_P;
    if (pcbddc->coarse_ksp) { /* get array from coarse processes */
      Vec tvec;

      ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
      ierr = VecResetArray(tvec);CHKERRQ(ierr);
      ierr = KSPGetSolution(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
      ierr = VecGetArray(tvec,&array);CHKERRQ(ierr);
      ierr = VecPlaceArray(from,array);CHKERRQ(ierr);
      ierr = VecRestoreArray(tvec,&array);CHKERRQ(ierr);
    }
  } else { /* from local to global -> put data in coarse right hand side */
    from = pcbddc->vec1_P;
    to = pcbddc->coarse_vec;
  }
  ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
{
  PetscErrorCode ierr;
  PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
  PetscScalar    *array;
  Vec            from,to;

  PetscFunctionBegin;
  if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
    from = pcbddc->coarse_vec;
    to = pcbddc->vec1_P;
  } else { /* from local to global -> put data in coarse right hand side */
    from = pcbddc->vec1_P;
    to = pcbddc->coarse_vec;
  }
  ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
  if (smode == SCATTER_FORWARD) {
    if (pcbddc->coarse_ksp) { /* get array from coarse processes */
      Vec tvec;

      ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
      ierr = VecGetArray(to,&array);CHKERRQ(ierr);
      ierr = VecPlaceArray(tvec,array);CHKERRQ(ierr);
      ierr = VecRestoreArray(to,&array);CHKERRQ(ierr);
    }
  } else {
    if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
     ierr = VecResetArray(from);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

/* uncomment for testing purposes */
/* #define PETSC_MISSING_LAPACK_GESVD 1 */
#undef __FUNCT__
#define __FUNCT__ "PCBDDCConstraintsSetUp"
PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
{
  PetscErrorCode    ierr;
  PC_IS*            pcis = (PC_IS*)(pc->data);
  PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
  Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
  /* one and zero */
  PetscScalar       one=1.0,zero=0.0;
  /* space to store constraints and their local indices */
  PetscScalar       *constraints_data;
  PetscInt          *constraints_idxs,*constraints_idxs_B;
  PetscInt          *constraints_idxs_ptr,*constraints_data_ptr;
  PetscInt          *constraints_n;
  /* iterators */
  PetscInt          i,j,k,total_counts,total_counts_cc,cum;
  /* BLAS integers */
  PetscBLASInt      lwork,lierr;
  PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
  PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
  /* reuse */
  PetscInt          olocal_primal_size,olocal_primal_size_cc;
  PetscInt          *olocal_primal_ref_node,*olocal_primal_ref_mult;
  /* change of basis */
  PetscBool         qr_needed;
  PetscBT           change_basis,qr_needed_idx;
  /* auxiliary stuff */
  PetscInt          *nnz,*is_indices;
  PetscInt          ncc;
  /* some quantities */
  PetscInt          n_vertices,total_primal_vertices,valid_constraints;
  PetscInt          size_of_constraint,max_size_of_constraint=0,max_constraints,temp_constraints;

  PetscFunctionBegin;
  /* Destroy Mat objects computed previously */
  ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
  ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
  /* save info on constraints from previous setup (if any) */
  olocal_primal_size = pcbddc->local_primal_size;
  olocal_primal_size_cc = pcbddc->local_primal_size_cc;
  ierr = PetscMalloc2(olocal_primal_size_cc,&olocal_primal_ref_node,olocal_primal_size_cc,&olocal_primal_ref_mult);CHKERRQ(ierr);
  ierr = PetscMemcpy(olocal_primal_ref_node,pcbddc->local_primal_ref_node,olocal_primal_size_cc*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscMemcpy(olocal_primal_ref_mult,pcbddc->local_primal_ref_mult,olocal_primal_size_cc*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);CHKERRQ(ierr);
  ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);

  /* print some info */
  if (pcbddc->dbg_flag) {
    IS       vertices;
    PetscInt nv,nedges,nfaces;
    ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&nfaces,NULL,&nedges,NULL,&vertices);CHKERRQ(ierr);
    ierr = ISGetSize(vertices,&nv);CHKERRQ(ierr);
    ierr = ISDestroy(&vertices);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%d)\n",PetscGlobalRank,nv,pcbddc->use_vertices);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%d)\n",PetscGlobalRank,nedges,pcbddc->use_edges);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%d)\n",PetscGlobalRank,nfaces,pcbddc->use_faces);CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  if (!pcbddc->adaptive_selection) {
    IS           ISForVertices,*ISForFaces,*ISForEdges;
    MatNullSpace nearnullsp;
    const Vec    *nearnullvecs;
    Vec          *localnearnullsp;
    PetscScalar  *array;
    PetscInt     n_ISForFaces,n_ISForEdges,nnsp_size;
    PetscBool    nnsp_has_cnst;
    /* LAPACK working arrays for SVD or POD */
    PetscBool    skip_lapack,boolforchange;
    PetscScalar  *work;
    PetscReal    *singular_vals;
#if defined(PETSC_USE_COMPLEX)
    PetscReal    *rwork;
#endif
#if defined(PETSC_MISSING_LAPACK_GESVD)
    PetscScalar  *temp_basis,*correlation_mat;
#else
    PetscBLASInt dummy_int=1;
    PetscScalar  dummy_scalar=1.;
#endif

    /* Get index sets for faces, edges and vertices from graph */
    ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);CHKERRQ(ierr);
    /* free unneeded index sets */
    if (!pcbddc->use_vertices) {
      ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
    }
    if (!pcbddc->use_edges) {
      for (i=0;i<n_ISForEdges;i++) {
        ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
      }
      ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
      n_ISForEdges = 0;
    }
    if (!pcbddc->use_faces) {
      for (i=0;i<n_ISForFaces;i++) {
        ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
      }
      ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
      n_ISForFaces = 0;
    }

#if defined(PETSC_USE_DEBUG)
    /* HACK: when solving singular problems not using vertices, a change of basis is mandatory.
       Also use_change_of_basis should be consistent among processors */
    if (pcbddc->NullSpace) {
      PetscBool tbool[2],gbool[2];

      if (!ISForVertices && !pcbddc->user_ChangeOfBasisMatrix) {
        pcbddc->use_change_of_basis = PETSC_TRUE;
        if (!ISForEdges) {
          pcbddc->use_change_on_faces = PETSC_TRUE;
        }
      }
      tbool[0] = pcbddc->use_change_of_basis;
      tbool[1] = pcbddc->use_change_on_faces;
      ierr = MPI_Allreduce(tbool,gbool,2,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
      pcbddc->use_change_of_basis = gbool[0];
      pcbddc->use_change_on_faces = gbool[1];
    }
#endif

    /* check if near null space is attached to global mat */
    ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
    if (nearnullsp) {
      ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
      /* remove any stored info */
      ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
      ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
      /* store information for BDDC solver reuse */
      ierr = PetscObjectReference((PetscObject)nearnullsp);CHKERRQ(ierr);
      pcbddc->onearnullspace = nearnullsp;
      ierr = PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);CHKERRQ(ierr);
      for (i=0;i<nnsp_size;i++) {
        ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);CHKERRQ(ierr);
      }
    } else { /* if near null space is not provided BDDC uses constants by default */
      nnsp_size = 0;
      nnsp_has_cnst = PETSC_TRUE;
    }
    /* get max number of constraints on a single cc */
    max_constraints = nnsp_size;
    if (nnsp_has_cnst) max_constraints++;

    /*
         Evaluate maximum storage size needed by the procedure
         - Indices for connected component i stored at "constraints_idxs + constraints_idxs_ptr[i]"
         - Values for constraints on connected component i stored at "constraints_data + constraints_data_ptr[i]"
         There can be multiple constraints per connected component
                                                                                                                                                           */
    n_vertices = 0;
    if (ISForVertices) {
      ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
    }
    ncc = n_vertices+n_ISForFaces+n_ISForEdges;
    ierr = PetscMalloc3(ncc+1,&constraints_idxs_ptr,ncc+1,&constraints_data_ptr,ncc,&constraints_n);CHKERRQ(ierr);

    total_counts = n_ISForFaces+n_ISForEdges;
    total_counts *= max_constraints;
    total_counts += n_vertices;
    ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);

    total_counts = 0;
    max_size_of_constraint = 0;
    for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
      IS used_is;
      if (i<n_ISForEdges) {
        used_is = ISForEdges[i];
      } else {
        used_is = ISForFaces[i-n_ISForEdges];
      }
      ierr = ISGetSize(used_is,&j);CHKERRQ(ierr);
      total_counts += j;
      max_size_of_constraint = PetscMax(j,max_size_of_constraint);
    }
    ierr = PetscMalloc3(total_counts*max_constraints+n_vertices,&constraints_data,total_counts+n_vertices,&constraints_idxs,total_counts+n_vertices,&constraints_idxs_B);CHKERRQ(ierr);

    /* get local part of global near null space vectors */
    ierr = PetscMalloc1(nnsp_size,&localnearnullsp);CHKERRQ(ierr);
    for (k=0;k<nnsp_size;k++) {
      ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
      ierr = VecScatterBegin(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    }

    /* whether or not to skip lapack calls */
    skip_lapack = PETSC_TRUE;
    if (n_ISForFaces+n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;

    /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
    if (!skip_lapack) {
      PetscScalar temp_work;

#if defined(PETSC_MISSING_LAPACK_GESVD)
      /* Proper Orthogonal Decomposition (POD) using the snapshot method */
      ierr = PetscMalloc1(max_constraints*max_constraints,&correlation_mat);CHKERRQ(ierr);
      ierr = PetscMalloc1(max_constraints,&singular_vals);CHKERRQ(ierr);
      ierr = PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
      ierr = PetscMalloc1(3*max_constraints,&rwork);CHKERRQ(ierr);
#endif
      /* now we evaluate the optimal workspace using query with lwork=-1 */
      ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
      lwork = -1;
      ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
      PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
#else
      PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
#endif
      ierr = PetscFPTrapPop();CHKERRQ(ierr);
      if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
#else /* on missing GESVD */
      /* SVD */
      PetscInt max_n,min_n;
      max_n = max_size_of_constraint;
      min_n = max_constraints;
      if (max_size_of_constraint < max_constraints) {
        min_n = max_size_of_constraint;
        max_n = max_constraints;
      }
      ierr = PetscMalloc1(min_n,&singular_vals);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
      ierr = PetscMalloc1(5*min_n,&rwork);CHKERRQ(ierr);
#endif
      /* now we evaluate the optimal workspace using query with lwork=-1 */
      lwork = -1;
      ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
      ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
      PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&constraints_data[0],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr));
#else
      PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&constraints_data[0],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr));
#endif
      ierr = PetscFPTrapPop();CHKERRQ(ierr);
      if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
#endif /* on missing GESVD */
      /* Allocate optimal workspace */
      ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
      ierr = PetscMalloc1(lwork,&work);CHKERRQ(ierr);
    }
    /* Now we can loop on constraining sets */
    total_counts = 0;
    constraints_idxs_ptr[0] = 0;
    constraints_data_ptr[0] = 0;
    /* vertices */
    if (n_vertices) {
      ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
      ierr = PetscMemcpy(constraints_idxs,is_indices,n_vertices*sizeof(PetscInt));CHKERRQ(ierr);
      for (i=0;i<n_vertices;i++) {
        constraints_n[total_counts] = 1;
        constraints_data[total_counts] = 1.0;
        constraints_idxs_ptr[total_counts+1] = constraints_idxs_ptr[total_counts]+1;
        constraints_data_ptr[total_counts+1] = constraints_data_ptr[total_counts]+1;
        total_counts++;
      }
      ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
      n_vertices = total_counts;
    }

    /* edges and faces */
    total_counts_cc = total_counts;
    for (ncc=0;ncc<n_ISForEdges+n_ISForFaces;ncc++) {
      IS        used_is;
      PetscBool idxs_copied = PETSC_FALSE;

      if (ncc<n_ISForEdges) {
        used_is = ISForEdges[ncc];
        boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
      } else {
        used_is = ISForFaces[ncc-n_ISForEdges];
        boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
      }
      temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */

      ierr = ISGetSize(used_is,&size_of_constraint);CHKERRQ(ierr);
      ierr = ISGetIndices(used_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
      /* change of basis should not be performed on local periodic nodes */
      if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
      if (nnsp_has_cnst) {
        PetscScalar quad_value;

        ierr = PetscMemcpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
        idxs_copied = PETSC_TRUE;

        if (!pcbddc->use_nnsp_true) {
          quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
        } else {
          quad_value = 1.0;
        }
        for (j=0;j<size_of_constraint;j++) {
          constraints_data[constraints_data_ptr[total_counts_cc]+j] = quad_value;
        }
        temp_constraints++;
        total_counts++;
      }
      for (k=0;k<nnsp_size;k++) {
        PetscReal real_value;
        PetscScalar *ptr_to_data;

        ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
        ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]+temp_constraints*size_of_constraint];
        for (j=0;j<size_of_constraint;j++) {
          ptr_to_data[j] = array[is_indices[j]];
        }
        ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
        /* check if array is null on the connected component */
        ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
        PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,ptr_to_data,&Blas_one));
        if (real_value > 0.0) { /* keep indices and values */
          temp_constraints++;
          total_counts++;
          if (!idxs_copied) {
            ierr = PetscMemcpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
            idxs_copied = PETSC_TRUE;
          }
        }
      }
      ierr = ISRestoreIndices(used_is,(const PetscInt**)&is_indices);CHKERRQ(ierr);
      valid_constraints = temp_constraints;
      if (!pcbddc->use_nnsp_true && temp_constraints) {
        if (temp_constraints == 1) { /* just normalize the constraint */
          PetscScalar norm,*ptr_to_data;

          ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
          PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,ptr_to_data,&Blas_one,ptr_to_data,&Blas_one));
          norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
          PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,ptr_to_data,&Blas_one));
        } else { /* perform SVD */
          PetscReal   tol = 1.0e-8; /* tolerance for retaining eigenmodes */
          PetscScalar *ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];

#if defined(PETSC_MISSING_LAPACK_GESVD)
          /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
             POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
             -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
                the constraints basis will differ (by a complex factor with absolute value equal to 1)
                from that computed using LAPACKgesvd
             -> This is due to a different computation of eigenvectors in LAPACKheev
             -> The quality of the POD-computed basis will be the same */
          ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
          /* Store upper triangular part of correlation matrix */
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
          for (j=0;j<temp_constraints;j++) {
            for (k=0;k<j+1;k++) {
              PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k] = BLASdot_(&Blas_N,ptr_to_data+k*size_of_constraint,&Blas_one,ptr_to_data+j*size_of_constraint,&Blas_one));
            }
          }
          /* compute eigenvalues and eigenvectors of correlation matrix */
          ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
          PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
#else
          PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
#endif
          ierr = PetscFPTrapPop();CHKERRQ(ierr);
          if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
          /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
          j = 0;
          while (j < temp_constraints && singular_vals[j] < tol) j++;
          total_counts = total_counts-j;
          valid_constraints = temp_constraints-j;
          /* scale and copy POD basis into used quadrature memory */
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
          if (j<temp_constraints) {
            PetscInt ii;
            for (k=j;k<temp_constraints;k++) singular_vals[k] = 1.0/PetscSqrtReal(singular_vals[k]);
            ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
            PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,ptr_to_data,&Blas_LDA,correlation_mat,&Blas_LDB,&zero,temp_basis,&Blas_LDC));
            ierr = PetscFPTrapPop();CHKERRQ(ierr);
            for (k=0;k<temp_constraints-j;k++) {
              for (ii=0;ii<size_of_constraint;ii++) {
                ptr_to_data[k*size_of_constraint+ii] = singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
              }
            }
          }
#else  /* on missing GESVD */
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
          PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,ptr_to_data,&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr));
#else
          PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,ptr_to_data,&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr));
#endif
          if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
          ierr = PetscFPTrapPop();CHKERRQ(ierr);
          /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
          k = temp_constraints;
          if (k > size_of_constraint) k = size_of_constraint;
          j = 0;
          while (j < k && singular_vals[k-j-1] < tol) j++;
          valid_constraints = k-j;
          total_counts = total_counts-temp_constraints+valid_constraints;
#endif /* on missing GESVD */
        }
      }
      /* update pointers information */
      if (valid_constraints) {
        constraints_n[total_counts_cc] = valid_constraints;
        constraints_idxs_ptr[total_counts_cc+1] = constraints_idxs_ptr[total_counts_cc]+size_of_constraint;
        constraints_data_ptr[total_counts_cc+1] = constraints_data_ptr[total_counts_cc]+size_of_constraint*valid_constraints;
        /* set change_of_basis flag */
        if (boolforchange) {
          PetscBTSet(change_basis,total_counts_cc);
        }
        total_counts_cc++;
      }
    }
    /* free workspace */
    if (!skip_lapack) {
      ierr = PetscFree(work);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
      ierr = PetscFree(rwork);CHKERRQ(ierr);
#endif
      ierr = PetscFree(singular_vals);CHKERRQ(ierr);
#if defined(PETSC_MISSING_LAPACK_GESVD)
      ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
      ierr = PetscFree(temp_basis);CHKERRQ(ierr);
#endif
    }
    for (k=0;k<nnsp_size;k++) {
      ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
    }
    ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
    /* free index sets of faces, edges and vertices */
    for (i=0;i<n_ISForFaces;i++) {
      ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
    }
    if (n_ISForFaces) {
      ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
    }
    for (i=0;i<n_ISForEdges;i++) {
      ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
    }
    if (n_ISForEdges) {
      ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
    }
    ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
  } else {
    PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

    total_counts = 0;
    n_vertices = 0;
    if (sub_schurs->is_vertices && pcbddc->use_vertices) {
      ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);CHKERRQ(ierr);
    }
    max_constraints = 0;
    total_counts_cc = 0;
    for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
      total_counts += pcbddc->adaptive_constraints_n[i];
      if (pcbddc->adaptive_constraints_n[i]) total_counts_cc++;
      max_constraints = PetscMax(max_constraints,pcbddc->adaptive_constraints_n[i]);
    }
    constraints_idxs_ptr = pcbddc->adaptive_constraints_idxs_ptr;
    constraints_data_ptr = pcbddc->adaptive_constraints_data_ptr;
    constraints_idxs = pcbddc->adaptive_constraints_idxs;
    constraints_data = pcbddc->adaptive_constraints_data;
    /* constraints_n differs from pcbddc->adaptive_constraints_n */
    ierr = PetscMalloc1(total_counts_cc,&constraints_n);CHKERRQ(ierr);
    total_counts_cc = 0;
    for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
      if (pcbddc->adaptive_constraints_n[i]) {
        constraints_n[total_counts_cc++] = pcbddc->adaptive_constraints_n[i];
      }
    }
#if 0
    printf("Found %d totals (%d)\n",total_counts_cc,total_counts);
    for (i=0;i<total_counts_cc;i++) {
      printf("const %d, start %d",i,constraints_idxs_ptr[i]);
      printf(" end %d:\n",constraints_idxs_ptr[i+1]);
      for (j=constraints_idxs_ptr[i];j<constraints_idxs_ptr[i+1];j++) {
        printf(" %d",constraints_idxs[j]);
      }
      printf("\n");
      printf("number of cc: %d\n",constraints_n[i]);
    }
    for (i=0;i<n_vertices;i++) {
      PetscPrintf(PETSC_COMM_SELF,"[%d] vertex %d, n %d\n",PetscGlobalRank,i,pcbddc->adaptive_constraints_n[i]);
    }
    for (i=0;i<sub_schurs->n_subs;i++) {
      PetscPrintf(PETSC_COMM_SELF,"[%d] sub %d, edge %d, n %d\n",PetscGlobalRank,i,(PetscBool)PetscBTLookup(sub_schurs->is_edge,i),pcbddc->adaptive_constraints_n[i+n_vertices]);
    }
#endif

    max_size_of_constraint = 0;
    for (i=0;i<total_counts_cc;i++) max_size_of_constraint = PetscMax(max_size_of_constraint,constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i]);
    ierr = PetscMalloc1(constraints_idxs_ptr[total_counts_cc],&constraints_idxs_B);CHKERRQ(ierr);
    /* Change of basis */
    ierr = PetscBTCreate(total_counts_cc,&change_basis);CHKERRQ(ierr);
    if (pcbddc->use_change_of_basis) {
      for (i=0;i<sub_schurs->n_subs;i++) {
        if (PetscBTLookup(sub_schurs->is_edge,i) || pcbddc->use_change_on_faces) {
          ierr = PetscBTSet(change_basis,i+n_vertices);CHKERRQ(ierr);
        }
      }
    }
  }
  pcbddc->local_primal_size = total_counts;
  ierr = PetscMalloc1(pcbddc->local_primal_size+pcbddc->benign_n,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);

  /* map constraints_idxs in boundary numbering */
  ierr = ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,constraints_idxs_ptr[total_counts_cc],constraints_idxs,&i,constraints_idxs_B);CHKERRQ(ierr);
  if (i != constraints_idxs_ptr[total_counts_cc]) {
    SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %d != %d\n",constraints_idxs_ptr[total_counts_cc],i);
  }

  /* Create constraint matrix */
  ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
  ierr = MatSetType(pcbddc->ConstraintMatrix,MATAIJ);CHKERRQ(ierr);
  ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);

  /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
  /* determine if a QR strategy is needed for change of basis */
  qr_needed = PETSC_FALSE;
  ierr = PetscBTCreate(total_counts_cc,&qr_needed_idx);CHKERRQ(ierr);
  total_primal_vertices=0;
  pcbddc->local_primal_size_cc = 0;
  for (i=0;i<total_counts_cc;i++) {
    size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    if (size_of_constraint == 1) {
      pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]];
      pcbddc->local_primal_size_cc += 1;
    } else if (PetscBTLookup(change_basis,i)) {
      for (k=0;k<constraints_n[i];k++) {
        pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]+k];
      }
      pcbddc->local_primal_size_cc += constraints_n[i];
      if (constraints_n[i] > 1 || pcbddc->use_qr_single || pcbddc->faster_deluxe) {
        PetscBTSet(qr_needed_idx,i);
        qr_needed = PETSC_TRUE;
      }
    } else {
      pcbddc->local_primal_size_cc += 1;
    }
  }
  /* note that the local variable n_vertices used below stores the number of pointwise constraints */
  pcbddc->n_vertices = total_primal_vertices;
  /* permute indices in order to have a sorted set of vertices */
  ierr = PetscSortInt(total_primal_vertices,pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);

  ierr = PetscMalloc2(pcbddc->local_primal_size_cc+pcbddc->benign_n,&pcbddc->local_primal_ref_node,pcbddc->local_primal_size_cc+pcbddc->benign_n,&pcbddc->local_primal_ref_mult);CHKERRQ(ierr);
  ierr = PetscMemcpy(pcbddc->local_primal_ref_node,pcbddc->primal_indices_local_idxs,total_primal_vertices*sizeof(PetscInt));CHKERRQ(ierr);
  for (i=0;i<total_primal_vertices;i++) pcbddc->local_primal_ref_mult[i] = 1;

  /* nonzero structure of constraint matrix */
  /* and get reference dof for local constraints */
  ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
  for (i=0;i<total_primal_vertices;i++) nnz[i] = 1;

  j = total_primal_vertices;
  total_counts = total_primal_vertices;
  cum = total_primal_vertices;
  for (i=n_vertices;i<total_counts_cc;i++) {
    if (!PetscBTLookup(change_basis,i)) {
      pcbddc->local_primal_ref_node[cum] = constraints_idxs[constraints_idxs_ptr[i]];
      pcbddc->local_primal_ref_mult[cum] = constraints_n[i];
      cum++;
      size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
      for (k=0;k<constraints_n[i];k++) {
        pcbddc->primal_indices_local_idxs[total_counts++] = constraints_idxs[constraints_idxs_ptr[i]+k];
        nnz[j+k] = size_of_constraint;
      }
      j += constraints_n[i];
    }
  }
  ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
  ierr = PetscFree(nnz);CHKERRQ(ierr);

  /* set values in constraint matrix */
  for (i=0;i<total_primal_vertices;i++) {
    ierr = MatSetValue(pcbddc->ConstraintMatrix,i,pcbddc->local_primal_ref_node[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
  }
  total_counts = total_primal_vertices;
  for (i=n_vertices;i<total_counts_cc;i++) {
    if (!PetscBTLookup(change_basis,i)) {
      PetscInt *cols;

      size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
      cols = constraints_idxs+constraints_idxs_ptr[i];
      for (k=0;k<constraints_n[i];k++) {
        PetscInt    row = total_counts+k;
        PetscScalar *vals;

        vals = constraints_data+constraints_data_ptr[i]+k*size_of_constraint;
        ierr = MatSetValues(pcbddc->ConstraintMatrix,1,&row,size_of_constraint,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
      }
      total_counts += constraints_n[i];
    }
  }
  /* assembling */
  ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /*
  ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
  ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
  */
  /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
  if (pcbddc->use_change_of_basis) {
    /* dual and primal dofs on a single cc */
    PetscInt     dual_dofs,primal_dofs;
    /* working stuff for GEQRF */
    PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
    PetscBLASInt lqr_work;
    /* working stuff for UNGQR */
    PetscScalar  *gqr_work,lgqr_work_t;
    PetscBLASInt lgqr_work;
    /* working stuff for TRTRS */
    PetscScalar  *trs_rhs;
    PetscBLASInt Blas_NRHS;
    /* pointers for values insertion into change of basis matrix */
    PetscInt     *start_rows,*start_cols;
    PetscScalar  *start_vals;
    /* working stuff for values insertion */
    PetscBT      is_primal;
    PetscInt     *aux_primal_numbering_B;
    /* matrix sizes */
    PetscInt     global_size,local_size;
    /* temporary change of basis */
    Mat          localChangeOfBasisMatrix;
    /* extra space for debugging */
    PetscScalar  *dbg_work;

    /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
    ierr = MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);CHKERRQ(ierr);
    ierr = MatSetType(localChangeOfBasisMatrix,MATAIJ);CHKERRQ(ierr);
    ierr = MatSetSizes(localChangeOfBasisMatrix,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
    /* nonzeros for local mat */
    ierr = PetscMalloc1(pcis->n,&nnz);CHKERRQ(ierr);
    for (i=0;i<pcis->n;i++) nnz[i]=1;
    for (i=n_vertices;i<total_counts_cc;i++) {
      if (PetscBTLookup(change_basis,i)) {
        size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
        if (PetscBTLookup(qr_needed_idx,i)) {
          for (j=0;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = size_of_constraint;
        } else {
          nnz[constraints_idxs[constraints_idxs_ptr[i]]] = size_of_constraint;
          for (j=1;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = 2;
        }
      }
    }
    ierr = MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
    ierr = PetscFree(nnz);CHKERRQ(ierr);
    /* Set initial identity in the matrix */
    for (i=0;i<pcis->n;i++) {
      ierr = MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
    }

    if (pcbddc->dbg_flag) {
      ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
    }


    /* Now we loop on the constraints which need a change of basis */
    /*
       Change of basis matrix is evaluated similarly to the FIRST APPROACH in
       Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)

       Basic blocks of change of basis matrix T computed by

          - Using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)

            | 1        0   ...        0         s_1/S |
            | 0        1   ...        0         s_2/S |
            |              ...                        |
            | 0        ...            1     s_{n-1}/S |
            | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |

            with S = \sum_{i=1}^n s_i^2
            NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
                  in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering

          - QR decomposition of constraints otherwise
    */
    if (qr_needed) {
      /* space to store Q */
      ierr = PetscMalloc1(max_size_of_constraint*max_size_of_constraint,&qr_basis);CHKERRQ(ierr);
      /* first we issue queries for optimal work */
      ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
      lqr_work = -1;
      PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
      if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
      ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
      ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
      lgqr_work = -1;
      ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
      ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
      if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
      PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
      if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
      ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
      ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
      /* array to store scaling factors for reflectors */
      ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
      /* array to store rhs and solution of triangular solver */
      ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
      /* allocating workspace for check */
      if (pcbddc->dbg_flag) {
        ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&dbg_work);CHKERRQ(ierr);
      }
    }
    /* array to store whether a node is primal or not */
    ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
    ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
    ierr = ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,pcbddc->local_primal_ref_node,&i,aux_primal_numbering_B);CHKERRQ(ierr);
    if (i != total_primal_vertices) {
      SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
    }
    for (i=0;i<total_primal_vertices;i++) {
      ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
    }
    ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);

    /* loop on constraints and see whether or not they need a change of basis and compute it */
    for (total_counts=n_vertices;total_counts<total_counts_cc;total_counts++) {
      size_of_constraint = constraints_idxs_ptr[total_counts+1]-constraints_idxs_ptr[total_counts];
      if (PetscBTLookup(change_basis,total_counts)) {
        /* get constraint info */
        primal_dofs = constraints_n[total_counts];
        dual_dofs = size_of_constraint-primal_dofs;

        if (pcbddc->dbg_flag) {
          ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %d: %d need a change of basis (size %d)\n",total_counts,primal_dofs,size_of_constraint);CHKERRQ(ierr);
        }

        if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */

          /* copy quadrature constraints for change of basis check */
          if (pcbddc->dbg_flag) {
            ierr = PetscMemcpy(dbg_work,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
          }
          /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
          ierr = PetscMemcpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);

          /* compute QR decomposition of constraints */
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
          PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
          if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
          ierr = PetscFPTrapPop();CHKERRQ(ierr);

          /* explictly compute R^-T */
          ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
          for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
          ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
          PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
          if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
          ierr = PetscFPTrapPop();CHKERRQ(ierr);

          /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
          PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
          if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
          ierr = PetscFPTrapPop();CHKERRQ(ierr);

          /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
             i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
             where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
          ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
          ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
          PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&zero,constraints_data+constraints_data_ptr[total_counts],&Blas_LDC));
          ierr = PetscFPTrapPop();CHKERRQ(ierr);
          ierr = PetscMemcpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);

          /* insert values in change of basis matrix respecting global ordering of new primal dofs */
          start_rows = &constraints_idxs[constraints_idxs_ptr[total_counts]];
          /* insert cols for primal dofs */
          for (j=0;j<primal_dofs;j++) {
            start_vals = &qr_basis[j*size_of_constraint];
            start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+j];
            ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
          }
          /* insert cols for dual dofs */
          for (j=0,k=0;j<dual_dofs;k++) {
            if (!PetscBTLookup(is_primal,constraints_idxs_B[constraints_idxs_ptr[total_counts]+k])) {
              start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
              start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+k];
              ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
              j++;
            }
          }

          /* check change of basis */
          if (pcbddc->dbg_flag) {
            PetscInt   ii,jj;
            PetscBool valid_qr=PETSC_TRUE;
            ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
            ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
            ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
            ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
            ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
            ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
            ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
            PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&Blas_M,&Blas_N,&Blas_K,&one,dbg_work,&Blas_LDA,qr_basis,&Blas_LDB,&zero,&dbg_work[size_of_constraint*primal_dofs],&Blas_LDC));
            ierr = PetscFPTrapPop();CHKERRQ(ierr);
            for (jj=0;jj<size_of_constraint;jj++) {
              for (ii=0;ii<primal_dofs;ii++) {
                if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
                if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
              }
            }
            if (!valid_qr) {
              ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
              for (jj=0;jj<size_of_constraint;jj++) {
                for (ii=0;ii<primal_dofs;ii++) {
                  if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
                    PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not orthogonal to constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
                  }
                  if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
                    PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not unitary w.r.t constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
                  }
                }
              }
            } else {
              ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
            }
          }
        } else { /* simple transformation block */
          PetscInt    row,col;
          PetscScalar val,norm;

          ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
          PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,constraints_data+constraints_data_ptr[total_counts],&Blas_one,constraints_data+constraints_data_ptr[total_counts],&Blas_one));
          for (j=0;j<size_of_constraint;j++) {
            PetscInt row_B = constraints_idxs_B[constraints_idxs_ptr[total_counts]+j];
            row = constraints_idxs[constraints_idxs_ptr[total_counts]+j];
            if (!PetscBTLookup(is_primal,row_B)) {
              col = constraints_idxs[constraints_idxs_ptr[total_counts]];
              ierr = MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
              ierr = MatSetValue(localChangeOfBasisMatrix,row,col,constraints_data[constraints_data_ptr[total_counts]+j]/norm,INSERT_VALUES);CHKERRQ(ierr);
            } else {
              for (k=0;k<size_of_constraint;k++) {
                col = constraints_idxs[constraints_idxs_ptr[total_counts]+k];
                if (row != col) {
                  val = -constraints_data[constraints_data_ptr[total_counts]+k]/constraints_data[constraints_data_ptr[total_counts]];
                } else {
                  val = constraints_data[constraints_data_ptr[total_counts]]/norm;
                }
                ierr = MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
              }
            }
          }
          if (pcbddc->dbg_flag) {
            ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
          }
        }
      } else {
        if (pcbddc->dbg_flag) {
          ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d does not need a change of basis (size %d)\n",total_counts,size_of_constraint);CHKERRQ(ierr);
        }
      }
    }

    /* free workspace */
    if (qr_needed) {
      if (pcbddc->dbg_flag) {
        ierr = PetscFree(dbg_work);CHKERRQ(ierr);
      }
      ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
      ierr = PetscFree(qr_tau);CHKERRQ(ierr);
      ierr = PetscFree(qr_work);CHKERRQ(ierr);
      ierr = PetscFree(gqr_work);CHKERRQ(ierr);
      ierr = PetscFree(qr_basis);CHKERRQ(ierr);
    }
    ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

    /* assembling of global change of variable */
    {
      Mat      tmat;
      PetscInt bs;

      ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
      ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
      ierr = MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&tmat);CHKERRQ(ierr);
      ierr = MatISSetLocalMat(tmat,localChangeOfBasisMatrix);CHKERRQ(ierr);
      ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
      ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);CHKERRQ(ierr);
      ierr = MatGetBlockSize(pc->pmat,&bs);CHKERRQ(ierr);
      ierr = MatSetBlockSize(pcbddc->ChangeOfBasisMatrix,bs);CHKERRQ(ierr);
      ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
      ierr = MatISSetMPIXAIJPreallocation_Private(tmat,pcbddc->ChangeOfBasisMatrix,PETSC_TRUE);CHKERRQ(ierr);
      ierr = MatISGetMPIXAIJ(tmat,MAT_REUSE_MATRIX,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
      ierr = MatDestroy(&tmat);CHKERRQ(ierr);
      ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
      ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
      ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = VecReciprocal(pcis->vec1_global);CHKERRQ(ierr);
      ierr = MatDiagonalScale(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,NULL);CHKERRQ(ierr);
    }
    /* check */
    if (pcbddc->dbg_flag) {
      PetscReal error;
      Vec       x,x_change;

      ierr = VecDuplicate(pcis->vec1_global,&x);CHKERRQ(ierr);
      ierr = VecDuplicate(pcis->vec1_global,&x_change);CHKERRQ(ierr);
      ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
      ierr = VecCopy(x,pcis->vec1_global);CHKERRQ(ierr);
      ierr = VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
      ierr = MatMult(localChangeOfBasisMatrix,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
      ierr = VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
      ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);CHKERRQ(ierr);
      ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
      ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
      ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change: %1.6e\n",error);CHKERRQ(ierr);
      ierr = VecDestroy(&x);CHKERRQ(ierr);
      ierr = VecDestroy(&x_change);CHKERRQ(ierr);
    }

    /* adapt sub_schurs computed (if any) */
    if (pcbddc->use_deluxe_scaling) {
      PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;
      if (sub_schurs->S_Ej_all) {
        Mat                    S_new,tmat;
        ISLocalToGlobalMapping NtoSall;
        IS                     is_all_N,is_V,is_V_Sall;
        const PetscScalar      *array;
        const PetscInt         *idxs_V,*idxs_all;
        PetscInt               i,n_V;

        ierr = ISLocalToGlobalMappingApplyIS(pcis->BtoNmap,sub_schurs->is_Ej_all,&is_all_N);CHKERRQ(ierr);
        ierr = MatGetSubMatrix(localChangeOfBasisMatrix,is_all_N,is_all_N,MAT_INITIAL_MATRIX,&tmat);CHKERRQ(ierr);
        ierr = ISCreateGeneral(PETSC_COMM_SELF,pcbddc->n_vertices,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&is_V);CHKERRQ(ierr);
        ierr = ISLocalToGlobalMappingCreateIS(is_all_N,&NtoSall);CHKERRQ(ierr);
        ierr = ISGlobalToLocalMappingApplyIS(NtoSall,IS_GTOLM_DROP,is_V,&is_V_Sall);CHKERRQ(ierr);
        ierr = ISLocalToGlobalMappingDestroy(&NtoSall);CHKERRQ(ierr);
        ierr = ISDestroy(&is_all_N);CHKERRQ(ierr);
        ierr = ISDestroy(&is_V);CHKERRQ(ierr);
        ierr = MatPtAP(sub_schurs->S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);CHKERRQ(ierr);
        ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
        ierr = PetscObjectReference((PetscObject)S_new);CHKERRQ(ierr);
        ierr = MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);CHKERRQ(ierr);
        ierr = ISGetLocalSize(is_V_Sall,&n_V);CHKERRQ(ierr);
        ierr = ISGetIndices(is_V_Sall,&idxs_V);CHKERRQ(ierr);
        ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs_all);CHKERRQ(ierr);
        ierr = VecGetArrayRead(pcis->D,&array);CHKERRQ(ierr);
        for (i=0;i<n_V;i++) {
          PetscScalar val;
          PetscInt    idx;

          idx = idxs_V[i];
          val = array[idxs_all[idxs_V[i]]];
          ierr = MatSetValue(S_new,idx,idx,val,INSERT_VALUES);CHKERRQ(ierr);
        }
        ierr = MatAssemblyBegin(S_new,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
        ierr = MatAssemblyEnd(S_new,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
        sub_schurs->S_Ej_all = S_new;
        ierr = MatDestroy(&S_new);CHKERRQ(ierr);
        if (sub_schurs->sum_S_Ej_all) {
          ierr = MatPtAP(sub_schurs->sum_S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);CHKERRQ(ierr);
          ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
          ierr = PetscObjectReference((PetscObject)S_new);CHKERRQ(ierr);
          ierr = MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);CHKERRQ(ierr);
          sub_schurs->sum_S_Ej_all = S_new;
          ierr = MatDestroy(&S_new);CHKERRQ(ierr);
        }
        ierr = VecRestoreArrayRead(pcis->D,&array);CHKERRQ(ierr);
        ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs_all);CHKERRQ(ierr);
        ierr = ISRestoreIndices(is_V_Sall,&idxs_V);CHKERRQ(ierr);
        ierr = MatDestroy(&tmat);CHKERRQ(ierr);
        ierr = ISDestroy(&is_V_Sall);CHKERRQ(ierr);
      }
    }
    ierr = MatDestroy(&localChangeOfBasisMatrix);CHKERRQ(ierr);
  } else if (pcbddc->user_ChangeOfBasisMatrix) {
    ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
    pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
  }

  /* set up change of basis context */
  if (pcbddc->ChangeOfBasisMatrix) {
    PCBDDCChange_ctx change_ctx;

    if (!pcbddc->new_global_mat) {
      PetscInt global_size,local_size;

      ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
      ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
      ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->new_global_mat);CHKERRQ(ierr);
      ierr = MatSetSizes(pcbddc->new_global_mat,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
      ierr = MatSetType(pcbddc->new_global_mat,MATSHELL);CHKERRQ(ierr);
      ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT,(void (*)(void))PCBDDCMatMult_Private);CHKERRQ(ierr);
      ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCMatMultTranspose_Private);CHKERRQ(ierr);
      ierr = PetscNew(&change_ctx);CHKERRQ(ierr);
      ierr = MatShellSetContext(pcbddc->new_global_mat,change_ctx);CHKERRQ(ierr);
    } else {
      ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
      ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
      ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
    }
    if (!pcbddc->user_ChangeOfBasisMatrix) {
      ierr = PetscObjectReference((PetscObject)pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
      change_ctx->global_change = pcbddc->ChangeOfBasisMatrix;
    } else {
      ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
      change_ctx->global_change = pcbddc->user_ChangeOfBasisMatrix;
    }
    ierr = VecDuplicateVecs(pcis->vec1_global,2,&change_ctx->work);CHKERRQ(ierr);
    ierr = MatSetUp(pcbddc->new_global_mat);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  } else {
    ierr = MatDestroy(&pcbddc->new_global_mat);CHKERRQ(ierr);
  }

  /* add pressure dofs to set of primal nodes for numbering purposes */
  for (i=0;i<pcbddc->benign_n;i++) {
    pcbddc->local_primal_ref_node[pcbddc->local_primal_size_cc] = pcbddc->benign_p0_lidx[i];
    pcbddc->primal_indices_local_idxs[pcbddc->local_primal_size] = pcbddc->benign_p0_lidx[i];
    pcbddc->local_primal_ref_mult[pcbddc->local_primal_size_cc] = 1;
    pcbddc->local_primal_size_cc++;
    pcbddc->local_primal_size++;
  }

  /* check if a new primal space has been introduced (also take into account benign trick) */
  pcbddc->new_primal_space_local = PETSC_TRUE;
  if (olocal_primal_size == pcbddc->local_primal_size) {
    ierr = PetscMemcmp(pcbddc->local_primal_ref_node,olocal_primal_ref_node,olocal_primal_size_cc*sizeof(PetscInt),&pcbddc->new_primal_space_local);CHKERRQ(ierr);
    pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
    if (!pcbddc->new_primal_space_local) {
      ierr = PetscMemcmp(pcbddc->local_primal_ref_mult,olocal_primal_ref_mult,olocal_primal_size_cc*sizeof(PetscInt),&pcbddc->new_primal_space_local);CHKERRQ(ierr);
      pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
    }
  }
  ierr = PetscFree2(olocal_primal_ref_node,olocal_primal_ref_mult);CHKERRQ(ierr);
  /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
  ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);

  /* flush dbg viewer */
  if (pcbddc->dbg_flag) {
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  /* free workspace */
  ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
  ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
  if (!pcbddc->adaptive_selection) {
    ierr = PetscFree3(constraints_idxs_ptr,constraints_data_ptr,constraints_n);CHKERRQ(ierr);
    ierr = PetscFree3(constraints_data,constraints_idxs,constraints_idxs_B);CHKERRQ(ierr);
  } else {
    ierr = PetscFree5(pcbddc->adaptive_constraints_n,
                      pcbddc->adaptive_constraints_idxs_ptr,
                      pcbddc->adaptive_constraints_data_ptr,
                      pcbddc->adaptive_constraints_idxs,
                      pcbddc->adaptive_constraints_data);CHKERRQ(ierr);
    ierr = PetscFree(constraints_n);CHKERRQ(ierr);
    ierr = PetscFree(constraints_idxs_B);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCAnalyzeInterface"
PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
{
  PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
  PC_IS       *pcis = (PC_IS*)pc->data;
  Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
  PetscInt    ierr,i,vertex_size,N;
  PetscViewer viewer=pcbddc->dbg_viewer;

  PetscFunctionBegin;
  /* Reset previously computed graph */
  ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
  /* Init local Graph struct */
  ierr = MatGetSize(pc->pmat,&N,NULL);CHKERRQ(ierr);
  ierr = PCBDDCGraphInit(pcbddc->mat_graph,pcis->mapping,N);CHKERRQ(ierr);

  /* Check validity of the csr graph passed in by the user */
  if (pcbddc->mat_graph->nvtxs_csr && pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
    SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid size of local CSR graph! Found %d, expected %d\n",pcbddc->mat_graph->nvtxs_csr,pcbddc->mat_graph->nvtxs);
  }

  /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
  if ( (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) && pcbddc->use_local_adj) {
    PetscInt  *xadj,*adjncy;
    PetscInt  nvtxs;
    PetscBool flg_row=PETSC_FALSE;

    ierr = MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
    if (flg_row) {
      ierr = PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
      pcbddc->computed_rowadj = PETSC_TRUE;
    }
    ierr = MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
  }
  if (pcbddc->dbg_flag) {
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
  vertex_size = 1;
  if (pcbddc->user_provided_isfordofs) {
    if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
      ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
      for (i=0;i<pcbddc->n_ISForDofs;i++) {
        ierr = PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
        ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
      }
      pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
      pcbddc->n_ISForDofs = 0;
      ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
    }
    /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
    ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
  } else {
    if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
      ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
      ierr = PetscMalloc1(pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
      for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
        ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
      }
    }
  }

  /* Setup of Graph */
  if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
    ierr = PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
  }
  if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
    ierr = PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
  }
  if (!pcbddc->user_primal_vertices_local && pcbddc->user_primal_vertices) { /* need to convert from global to local */
    ierr = PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->user_primal_vertices,&pcbddc->user_primal_vertices_local);CHKERRQ(ierr);
  }
  ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices_local);CHKERRQ(ierr);

  /* attach info on disconnected subdomains if present */
  if (pcbddc->n_local_subs) {
    PetscInt *local_subs;

    ierr = PetscMalloc1(N,&local_subs);CHKERRQ(ierr);
    for (i=0;i<pcbddc->n_local_subs;i++) {
      const PetscInt *idxs;
      PetscInt       nl,j;

      ierr = ISGetLocalSize(pcbddc->local_subs[i],&nl);CHKERRQ(ierr);
      ierr = ISGetIndices(pcbddc->local_subs[i],&idxs);CHKERRQ(ierr);
      for (j=0;j<nl;j++) {
        local_subs[idxs[j]] = i;
      }
      ierr = ISRestoreIndices(pcbddc->local_subs[i],&idxs);CHKERRQ(ierr);
    }
    pcbddc->mat_graph->n_local_subs = pcbddc->n_local_subs;
    pcbddc->mat_graph->local_subs = local_subs;
  }

  /* Graph's connected components analysis */
  ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);

  /* print some info to stdout */
  if (pcbddc->dbg_flag) {
    ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);CHKERRQ(ierr);
  }

  /* mark topography has done */
  pcbddc->recompute_topography = PETSC_FALSE;
  PetscFunctionReturn(0);
}

/* given an index sets possibly with holes, renumbers the indexes removing the holes */
#undef __FUNCT__
#define __FUNCT__ "PCBDDCSubsetNumbering"
PetscErrorCode PCBDDCSubsetNumbering(IS subset, IS subset_mult, PetscInt *N_n, IS *subset_n)
{
  PetscSF        sf;
  PetscLayout    map;
  const PetscInt *idxs;
  PetscInt       *leaf_data,*root_data,*gidxs;
  PetscInt       N,n,i,lbounds[2],gbounds[2],Nl;
  PetscInt       n_n,nlocals,start,first_index;
  PetscMPIInt    commsize;
  PetscBool      first_found;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = ISGetLocalSize(subset,&n);CHKERRQ(ierr);
  if (subset_mult) {
    PetscCheckSameComm(subset,1,subset_mult,2);
    ierr = ISGetLocalSize(subset,&i);CHKERRQ(ierr);
    if (i != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Local subset and multiplicity sizes don't match! %d != %d",n,i);
  }
  /* create workspace layout for computing global indices of subset */
  ierr = ISGetIndices(subset,&idxs);CHKERRQ(ierr);
  lbounds[0] = lbounds[1] = 0;
  for (i=0;i<n;i++) {
    if (idxs[i] < lbounds[0]) lbounds[0] = idxs[i];
    else if (idxs[i] > lbounds[1]) lbounds[1] = idxs[i];
  }
  lbounds[0] = -lbounds[0];
  ierr = MPI_Allreduce(lbounds,gbounds,2,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)subset));CHKERRQ(ierr);
  gbounds[0] = -gbounds[0];
  N = gbounds[1] - gbounds[0] + 1;
  ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)subset),&map);CHKERRQ(ierr);
  ierr = PetscLayoutSetBlockSize(map,1);CHKERRQ(ierr);
  ierr = PetscLayoutSetSize(map,N);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(map);CHKERRQ(ierr);
  ierr = PetscLayoutGetLocalSize(map,&Nl);CHKERRQ(ierr);

  /* create sf : leaf_data == multiplicity of indexes, root data == global index in layout */
  ierr = PetscMalloc2(n,&leaf_data,Nl,&root_data);CHKERRQ(ierr);
  if (subset_mult) {
    const PetscInt* idxs_mult;

    ierr = ISGetIndices(subset_mult,&idxs_mult);CHKERRQ(ierr);
    ierr = PetscMemcpy(leaf_data,idxs_mult,n*sizeof(PetscInt));CHKERRQ(ierr);
    ierr = ISRestoreIndices(subset_mult,&idxs_mult);CHKERRQ(ierr);
  } else {
    for (i=0;i<n;i++) leaf_data[i] = 1;
  }
  /* local size of new subset */
  n_n = 0;
  for (i=0;i<n;i++) n_n += leaf_data[i];

  /* global indexes in layout */
  ierr = PetscMalloc1(n_n,&gidxs);CHKERRQ(ierr); /* allocating possibly extra space in gidxs which will be used later */
  for (i=0;i<n;i++) gidxs[i] = idxs[i] - gbounds[0];
  ierr = ISRestoreIndices(subset,&idxs);CHKERRQ(ierr);
  ierr = PetscSFCreate(PetscObjectComm((PetscObject)subset),&sf);CHKERRQ(ierr);
  ierr = PetscSFSetGraphLayout(sf,map,n,NULL,PETSC_COPY_VALUES,gidxs);CHKERRQ(ierr);
  ierr = PetscLayoutDestroy(&map);CHKERRQ(ierr);

  /* reduce from leaves to roots */
  ierr = PetscMemzero(root_data,Nl*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscSFReduceBegin(sf,MPIU_INT,leaf_data,root_data,MPI_MAX);CHKERRQ(ierr);
  ierr = PetscSFReduceEnd(sf,MPIU_INT,leaf_data,root_data,MPI_MAX);CHKERRQ(ierr);

  /* count indexes in local part of layout */
  nlocals = 0;
  first_index = -1;
  first_found = PETSC_FALSE;
  for (i=0;i<Nl;i++) {
    if (!first_found && root_data[i]) {
      first_found = PETSC_TRUE;
      first_index = i;
    }
    nlocals += root_data[i];
  }

  /* cumulative of number of indexes and size of subset without holes */
#if defined(PETSC_HAVE_MPI_EXSCAN)
  start = 0;
  ierr = MPI_Exscan(&nlocals,&start,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)subset));CHKERRQ(ierr);
#else
  ierr = MPI_Scan(&nlocals,&start,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)subset));CHKERRQ(ierr);
  start = start-nlocals;
#endif

  if (N_n) { /* compute total size of new subset if requested */
    *N_n = start + nlocals;
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)subset),&commsize);CHKERRQ(ierr);
    ierr = MPI_Bcast(N_n,1,MPIU_INT,commsize-1,PetscObjectComm((PetscObject)subset));CHKERRQ(ierr);
  }

  /* adapt root data with cumulative */
  if (first_found) {
    PetscInt old_index;

    root_data[first_index] += start;
    old_index = first_index;
    for (i=first_index+1;i<Nl;i++) {
      if (root_data[i]) {
        root_data[i] += root_data[old_index];
        old_index = i;
      }
    }
  }

  /* from roots to leaves */
  ierr = PetscSFBcastBegin(sf,MPIU_INT,root_data,leaf_data);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(sf,MPIU_INT,root_data,leaf_data);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);

  /* create new IS with global indexes without holes */
  if (subset_mult) {
    const PetscInt* idxs_mult;
    PetscInt        cum;

    cum = 0;
    ierr = ISGetIndices(subset_mult,&idxs_mult);CHKERRQ(ierr);
    for (i=0;i<n;i++) {
      PetscInt j;
      for (j=0;j<idxs_mult[i];j++) gidxs[cum++] = leaf_data[i] - idxs_mult[i] + j;
    }
    ierr = ISRestoreIndices(subset_mult,&idxs_mult);CHKERRQ(ierr);
  } else {
    for (i=0;i<n;i++) {
      gidxs[i] = leaf_data[i]-1;
    }
  }
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)subset),n_n,gidxs,PETSC_OWN_POINTER,subset_n);CHKERRQ(ierr);
  ierr = PetscFree2(leaf_data,root_data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCOrthonormalizeVecs"
PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
{
  PetscInt       i,j;
  PetscScalar    *alphas;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* this implements stabilized Gram-Schmidt */
  ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
  for (i=0;i<n;i++) {
    ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
    if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
    for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
  }
  ierr = PetscFree(alphas);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatISGetSubassemblingPattern"
PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscInt redprocs, IS* is_sends)
{
  IS             ranks_send_to;
  PetscInt       n_neighs,*neighs,*n_shared,**shared;
  PetscMPIInt    size,rank,color;
  PetscInt       *xadj,*adjncy;
  PetscInt       *adjncy_wgt,*v_wgt,*ranks_send_to_idx;
  PetscInt       i,local_size,threshold=0;
  PetscBool      use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
  PetscSubcomm   subcomm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);

  /* Get info on mapping */
  ierr = ISLocalToGlobalMappingGetSize(mat->rmap->mapping,&local_size);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingGetInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);

  /* build local CSR graph of subdomains' connectivity */
  ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
  xadj[0] = 0;
  xadj[1] = PetscMax(n_neighs-1,0);
  ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
  ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);

  if (threshold) {
    PetscInt xadj_count = 0;
    for (i=1;i<n_neighs;i++) {
      if (n_shared[i] > threshold) {
        adjncy[xadj_count] = neighs[i];
        adjncy_wgt[xadj_count] = n_shared[i];
        xadj_count++;
      }
    }
    xadj[1] = xadj_count;
  } else {
    if (xadj[1]) {
      ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
      ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
    }
  }
  ierr = ISLocalToGlobalMappingRestoreInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
  if (use_square) {
    for (i=0;i<xadj[1];i++) {
      adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
    }
  }
  ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);

  ierr = PetscMalloc1(1,&ranks_send_to_idx);CHKERRQ(ierr);

  /*
    Restrict work on active processes only.
  */
  ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
  ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
  ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
  ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
  if (color) {
    ierr = PetscFree(xadj);CHKERRQ(ierr);
    ierr = PetscFree(adjncy);CHKERRQ(ierr);
    ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
  } else {
    Mat             subdomain_adj;
    IS              new_ranks,new_ranks_contig;
    MatPartitioning partitioner;
    PetscInt        prank,rstart=0,rend=0;
    PetscInt        *is_indices,*oldranks;
    PetscBool       aggregate;

    ierr = MPI_Comm_size(PetscSubcommChild(subcomm),&size);CHKERRQ(ierr);
    ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
    prank = rank;
    ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,PetscSubcommChild(subcomm));CHKERRQ(ierr);
    /*
    for (i=0;i<size;i++) {
      PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
    }
    */
    for (i=0;i<xadj[1];i++) {
      ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
    }
    ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
    aggregate = ((redprocs > 0 && redprocs < size) ? PETSC_TRUE : PETSC_FALSE);
    if (aggregate) {
      PetscInt    lrows,row,ncols,*cols;
      PetscMPIInt nrank;
      PetscScalar *vals;

      ierr = MPI_Comm_rank(PetscSubcommChild(subcomm),&nrank);CHKERRQ(ierr);
      lrows = 0;
      if (nrank<redprocs) {
        lrows = size/redprocs;
        if (nrank<size%redprocs) lrows++;
      }
      ierr = MatCreateAIJ(PetscSubcommChild(subcomm),lrows,lrows,size,size,50,NULL,50,NULL,&subdomain_adj);CHKERRQ(ierr);
      ierr = MatGetOwnershipRange(subdomain_adj,&rstart,&rend);CHKERRQ(ierr);
      ierr = MatSetOption(subdomain_adj,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
      ierr = MatSetOption(subdomain_adj,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
      row = nrank;
      ncols = xadj[1]-xadj[0];
      cols = adjncy;
      ierr = PetscMalloc1(ncols,&vals);CHKERRQ(ierr);
      for (i=0;i<ncols;i++) vals[i] = adjncy_wgt[i];
      ierr = MatSetValues(subdomain_adj,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatAssemblyBegin(subdomain_adj,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
      ierr = MatAssemblyEnd(subdomain_adj,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
      ierr = PetscFree(xadj);CHKERRQ(ierr);
      ierr = PetscFree(adjncy);CHKERRQ(ierr);
      ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
      ierr = PetscFree(vals);CHKERRQ(ierr);
    } else {
      ierr = MatCreateMPIAdj(PetscSubcommChild(subcomm),1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
    }
    /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */

    /* Partition */
    ierr = MatPartitioningCreate(PetscSubcommChild(subcomm),&partitioner);CHKERRQ(ierr);
    ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
    if (use_vwgt) {
      ierr = PetscMalloc1(1,&v_wgt);CHKERRQ(ierr);
      v_wgt[0] = local_size;
      ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
    }
    n_subdomains = PetscMin((PetscInt)size,n_subdomains);
    ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
    ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
    ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
    /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */

    /* renumber new_ranks to avoid "holes" in new set of processors */
    ierr = PCBDDCSubsetNumbering(new_ranks,NULL,NULL,&new_ranks_contig);CHKERRQ(ierr);
    ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
    ierr = ISGetIndices(new_ranks_contig,(const PetscInt**)&is_indices);CHKERRQ(ierr);
    if (!redprocs) {
      ranks_send_to_idx[0] = oldranks[is_indices[0]];
    } else {
      PetscInt    idxs[1];
      PetscMPIInt tag;
      MPI_Request *reqs;

      ierr = PetscObjectGetNewTag((PetscObject)subdomain_adj,&tag);CHKERRQ(ierr);
      ierr = PetscMalloc1(rend-rstart,&reqs);CHKERRQ(ierr);
      for (i=rstart;i<rend;i++) {
        ierr = MPI_Isend(is_indices+i-rstart,1,MPIU_INT,i,tag,PetscSubcommChild(subcomm),&reqs[i-rstart]);CHKERRQ(ierr);
      }
      ierr = MPI_Recv(idxs,1,MPIU_INT,MPI_ANY_SOURCE,tag,PetscSubcommChild(subcomm),MPI_STATUS_IGNORE);CHKERRQ(ierr);
      ierr = MPI_Waitall(rend-rstart,reqs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
      ierr = PetscFree(reqs);CHKERRQ(ierr);
      ranks_send_to_idx[0] = oldranks[idxs[0]];
    }
    ierr = ISRestoreIndices(new_ranks_contig,(const PetscInt**)&is_indices);CHKERRQ(ierr);
    /* clean up */
    ierr = PetscFree(oldranks);CHKERRQ(ierr);
    ierr = ISDestroy(&new_ranks_contig);CHKERRQ(ierr);
    ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
    ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
  }
  ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);

  /* assemble parallel IS for sends */
  i = 1;
  if (color) i=0;
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
  /* get back IS */
  *is_sends = ranks_send_to;
  PetscFunctionReturn(0);
}

typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;

#undef __FUNCT__
#define __FUNCT__ "MatISSubassemble"
PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, PetscBool restrict_full, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
{
  Mat                    local_mat;
  IS                     is_sends_internal;
  PetscInt               rows,cols,new_local_rows;
  PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
  PetscBool              ismatis,isdense,newisdense,destroy_mat;
  ISLocalToGlobalMapping l2gmap;
  PetscInt*              l2gmap_indices;
  const PetscInt*        is_indices;
  MatType                new_local_type;
  /* buffers */
  PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
  PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
  PetscInt               *recv_buffer_idxs_local;
  PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
  /* MPI */
  MPI_Comm               comm,comm_n;
  PetscSubcomm           subcomm;
  PetscMPIInt            n_sends,n_recvs,commsize;
  PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
  PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
  PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
  MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
  MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  /* TODO: add missing checks */
  PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
  PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
  PetscValidLogicalCollectiveEnum(mat,reuse,5);
  PetscValidLogicalCollectiveInt(mat,nis,7);
  ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
  if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
  ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
  if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
  ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
  if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
  if (reuse == MAT_REUSE_MATRIX && *mat_n) {
    PetscInt mrows,mcols,mnrows,mncols;
    ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
    if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
    ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
    ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
    if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
    if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
  }
  ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
  PetscValidLogicalCollectiveInt(mat,bs,0);
  /* prepare IS for sending if not provided */
  if (!is_sends) {
    if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
    ierr = MatISGetSubassemblingPattern(mat,n_subdomains,0,&is_sends_internal);CHKERRQ(ierr);
  } else {
    ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
    is_sends_internal = is_sends;
  }

  /* get comm */
  ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);

  /* compute number of sends */
  ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
  ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);

  /* compute number of receives */
  ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
  ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
  ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
  ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
  for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
  ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
  ierr = PetscFree(iflags);CHKERRQ(ierr);

  /* restrict comm if requested */
  subcomm = 0;
  destroy_mat = PETSC_FALSE;
  if (restrict_comm) {
    PetscMPIInt color,subcommsize;

    color = 0;
    if (restrict_full) {
      if (!n_recvs) color = 1; /* processes not receiving anything will not partecipate in new comm (full restriction) */
    } else {
      if (!n_recvs && n_sends) color = 1; /* just those processes that are sending but not receiving anything will not partecipate in new comm */
    }
    ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
    subcommsize = commsize - subcommsize;
    /* check if reuse has been requested */
    if (reuse == MAT_REUSE_MATRIX) {
      if (*mat_n) {
        PetscMPIInt subcommsize2;
        ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
        if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
        comm_n = PetscObjectComm((PetscObject)*mat_n);
      } else {
        comm_n = PETSC_COMM_SELF;
      }
    } else { /* MAT_INITIAL_MATRIX */
      PetscMPIInt rank;

      ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
      ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
      ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
      ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
      comm_n = PetscSubcommChild(subcomm);
    }
    /* flag to destroy *mat_n if not significative */
    if (color) destroy_mat = PETSC_TRUE;
  } else {
    comm_n = comm;
  }

  /* prepare send/receive buffers */
  ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
  ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
  ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
  ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
  if (nis) {
    ierr = PetscCalloc1(commsize,&ilengths_idxs_is);CHKERRQ(ierr);
  }

  /* Get data from local matrices */
  if (!isdense) {
    SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
    /* TODO: See below some guidelines on how to prepare the local buffers */
    /*
       send_buffer_vals should contain the raw values of the local matrix
       send_buffer_idxs should contain:
       - MatType_PRIVATE type
       - PetscInt        size_of_l2gmap
       - PetscInt        global_row_indices[size_of_l2gmap]
       - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
    */
  } else {
    ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingGetSize(mat->rmap->mapping,&i);CHKERRQ(ierr);
    ierr = PetscMalloc1(i+2,&send_buffer_idxs);CHKERRQ(ierr);
    send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
    send_buffer_idxs[1] = i;
    ierr = ISLocalToGlobalMappingGetIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
    ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingRestoreIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
    ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
    for (i=0;i<n_sends;i++) {
      ilengths_vals[is_indices[i]] = len*len;
      ilengths_idxs[is_indices[i]] = len+2;
    }
  }
  ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
  /* additional is (if any) */
  if (nis) {
    PetscMPIInt psum;
    PetscInt j;
    for (j=0,psum=0;j<nis;j++) {
      PetscInt plen;
      ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
      ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
      psum += len+1; /* indices + lenght */
    }
    ierr = PetscMalloc1(psum,&send_buffer_idxs_is);CHKERRQ(ierr);
    for (j=0,psum=0;j<nis;j++) {
      PetscInt plen;
      const PetscInt *is_array_idxs;
      ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
      send_buffer_idxs_is[psum] = plen;
      ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
      ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
      ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
      psum += plen+1; /* indices + lenght */
    }
    for (i=0;i<n_sends;i++) {
      ilengths_idxs_is[is_indices[i]] = psum;
    }
    ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
  }

  buf_size_idxs = 0;
  buf_size_vals = 0;
  buf_size_idxs_is = 0;
  for (i=0;i<n_recvs;i++) {
    buf_size_idxs += (PetscInt)olengths_idxs[i];
    buf_size_vals += (PetscInt)olengths_vals[i];
    if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
  }
  ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
  ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
  ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);

  /* get new tags for clean communications */
  ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
  ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
  ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);

  /* allocate for requests */
  ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
  ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
  ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
  ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
  ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
  ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);

  /* communications */
  ptr_idxs = recv_buffer_idxs;
  ptr_vals = recv_buffer_vals;
  ptr_idxs_is = recv_buffer_idxs_is;
  for (i=0;i<n_recvs;i++) {
    source_dest = onodes[i];
    ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
    ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
    ptr_idxs += olengths_idxs[i];
    ptr_vals += olengths_vals[i];
    if (nis) {
      ierr = MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);CHKERRQ(ierr);
      ptr_idxs_is += olengths_idxs_is[i];
    }
  }
  for (i=0;i<n_sends;i++) {
    ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
    ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
    ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
    if (nis) {
      ierr = MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);CHKERRQ(ierr);
    }
  }
  ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
  ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);

  /* assemble new l2g map */
  ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
  ptr_idxs = recv_buffer_idxs;
  new_local_rows = 0;
  for (i=0;i<n_recvs;i++) {
    new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
    ptr_idxs += olengths_idxs[i];
  }
  ierr = PetscMalloc1(new_local_rows,&l2gmap_indices);CHKERRQ(ierr);
  ptr_idxs = recv_buffer_idxs;
  new_local_rows = 0;
  for (i=0;i<n_recvs;i++) {
    ierr = PetscMemcpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
    new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
    ptr_idxs += olengths_idxs[i];
  }
  ierr = PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
  ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);

  /* infer new local matrix type from received local matrices type */
  /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
  /* it also assumes that if the block size is set, than it is the same among all local matrices (see checks at the beginning of the function) */
  if (n_recvs) {
    MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
    ptr_idxs = recv_buffer_idxs;
    for (i=0;i<n_recvs;i++) {
      if ((PetscInt)new_local_type_private != *ptr_idxs) {
        new_local_type_private = MATAIJ_PRIVATE;
        break;
      }
      ptr_idxs += olengths_idxs[i];
    }
    switch (new_local_type_private) {
      case MATDENSE_PRIVATE:
        if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
          new_local_type = MATSEQAIJ;
          bs = 1;
        } else { /* if I receive only 1 dense matrix */
          new_local_type = MATSEQDENSE;
          bs = 1;
        }
        break;
      case MATAIJ_PRIVATE:
        new_local_type = MATSEQAIJ;
        bs = 1;
        break;
      case MATBAIJ_PRIVATE:
        new_local_type = MATSEQBAIJ;
        break;
      case MATSBAIJ_PRIVATE:
        new_local_type = MATSEQSBAIJ;
        break;
      default:
        SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,__FUNCT__);
        break;
    }
  } else { /* by default, new_local_type is seqdense */
    new_local_type = MATSEQDENSE;
    bs = 1;
  }

  /* create MATIS object if needed */
  if (reuse == MAT_INITIAL_MATRIX) {
    ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
    ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,NULL,mat_n);CHKERRQ(ierr);
  } else {
    /* it also destroys the local matrices */
    ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
  }
  ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
  ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);

  ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);

  /* Global to local map of received indices */
  ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local);CHKERRQ(ierr); /* needed for values insertion */
  ierr = ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);

  /* restore attributes -> type of incoming data and its size */
  buf_size_idxs = 0;
  for (i=0;i<n_recvs;i++) {
    recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
    recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
    buf_size_idxs += (PetscInt)olengths_idxs[i];
  }
  ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);

  /* set preallocation */
  ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);CHKERRQ(ierr);
  if (!newisdense) {
    PetscInt *new_local_nnz=0;

    ptr_vals = recv_buffer_vals;
    ptr_idxs = recv_buffer_idxs_local;
    if (n_recvs) {
      ierr = PetscCalloc1(new_local_rows,&new_local_nnz);CHKERRQ(ierr);
    }
    for (i=0;i<n_recvs;i++) {
      PetscInt j;
      if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
        for (j=0;j<*(ptr_idxs+1);j++) {
          new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
        }
      } else {
        /* TODO */
      }
      ptr_idxs += olengths_idxs[i];
    }
    if (new_local_nnz) {
      for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
      ierr = MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);CHKERRQ(ierr);
      for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
      ierr = MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
      for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
      ierr = MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
    } else {
      ierr = MatSetUp(local_mat);CHKERRQ(ierr);
    }
    ierr = PetscFree(new_local_nnz);CHKERRQ(ierr);
  } else {
    ierr = MatSetUp(local_mat);CHKERRQ(ierr);
  }

  /* set values */
  ptr_vals = recv_buffer_vals;
  ptr_idxs = recv_buffer_idxs_local;
  for (i=0;i<n_recvs;i++) {
    if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
      ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
      ierr = MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
      ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
      ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
      ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
    } else {
      /* TODO */
    }
    ptr_idxs += olengths_idxs[i];
    ptr_vals += olengths_vals[i];
  }
  ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
  ierr = PetscFree(recv_buffer_idxs_local);CHKERRQ(ierr);

#if 0
  if (!restrict_comm) { /* check */
    Vec       lvec,rvec;
    PetscReal infty_error;

    ierr = MatCreateVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
    ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
    ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
    ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
    ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
    ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
    ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
    ierr = VecDestroy(&rvec);CHKERRQ(ierr);
    ierr = VecDestroy(&lvec);CHKERRQ(ierr);
  }
#endif

  /* assemble new additional is (if any) */
  if (nis) {
    PetscInt **temp_idxs,*count_is,j,psum;

    ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
    ierr = PetscCalloc1(nis,&count_is);CHKERRQ(ierr);
    ptr_idxs = recv_buffer_idxs_is;
    psum = 0;
    for (i=0;i<n_recvs;i++) {
      for (j=0;j<nis;j++) {
        PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
        count_is[j] += plen; /* increment counting of buffer for j-th IS */
        psum += plen;
        ptr_idxs += plen+1; /* shift pointer to received data */
      }
    }
    ierr = PetscMalloc1(nis,&temp_idxs);CHKERRQ(ierr);
    ierr = PetscMalloc1(psum,&temp_idxs[0]);CHKERRQ(ierr);
    for (i=1;i<nis;i++) {
      temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
    }
    ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
    ptr_idxs = recv_buffer_idxs_is;
    for (i=0;i<n_recvs;i++) {
      for (j=0;j<nis;j++) {
        PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
        ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
        count_is[j] += plen; /* increment starting point of buffer for j-th IS */
        ptr_idxs += plen+1; /* shift pointer to received data */
      }
    }
    for (i=0;i<nis;i++) {
      ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
      ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
      ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
    }
    ierr = PetscFree(count_is);CHKERRQ(ierr);
    ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
    ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
  }
  /* free workspace */
  ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
  ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
  ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
  ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
  if (isdense) {
    ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
    ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
  } else {
    /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
  }
  if (nis) {
    ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
    ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
  }
  ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
  ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
  ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
  ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
  ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
  ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
  ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
  ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
  ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
  ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
  ierr = PetscFree(onodes);CHKERRQ(ierr);
  if (nis) {
    ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
    ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
    ierr = PetscFree(onodes_is);CHKERRQ(ierr);
  }
  ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
  if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
    ierr = MatDestroy(mat_n);CHKERRQ(ierr);
    for (i=0;i<nis;i++) {
      ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
    }
    *mat_n = NULL;
  }
  PetscFunctionReturn(0);
}

/* temporary hack into ksp private data structure */
#include <petsc/private/kspimpl.h>

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpCoarseSolver"
PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
{
  PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
  PC_IS                  *pcis = (PC_IS*)pc->data;
  Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
  MatNullSpace           CoarseNullSpace=NULL;
  ISLocalToGlobalMapping coarse_islg;
  IS                     coarse_is,*isarray;
  PetscInt               i,im_active=-1,active_procs=-1;
  PetscInt               nis,nisdofs,nisneu,nisvert;
  PC                     pc_temp;
  PCType                 coarse_pc_type;
  KSPType                coarse_ksp_type;
  PetscBool              multilevel_requested,multilevel_allowed;
  PetscBool              isredundant,isbddc,isnn,coarse_reuse;
  Mat                    t_coarse_mat_is;
  PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
  PetscMPIInt            all_procs;
  PetscBool              csin_ml,csin_ds,csin,csin_type_simple,redist;
  PetscBool              compute_vecs = PETSC_FALSE;
  PetscScalar            *array;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  /* Assign global numbering to coarse dofs */
  if (pcbddc->new_primal_space || pcbddc->coarse_size == -1) { /* a new primal space is present or it is the first initialization, so recompute global numbering */
    PetscInt ocoarse_size;
    compute_vecs = PETSC_TRUE;
    ocoarse_size = pcbddc->coarse_size;
    ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
    ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
    /* see if we can avoid some work */
    if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
      /* if the coarse size is different or we are using adaptive selection, better to not reuse the coarse matrix */
      if (ocoarse_size != pcbddc->coarse_size || pcbddc->adaptive_selection) {
        PC        pc;
        PetscBool isbddc;

        /* temporary workaround since PCBDDC does not have a reset method so far */
        ierr = KSPGetPC(pcbddc->coarse_ksp,&pc);CHKERRQ(ierr);
        ierr = PetscObjectTypeCompare((PetscObject)pc,PCBDDC,&isbddc);CHKERRQ(ierr);
        if (isbddc) {
          ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
        } else {
          ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
        }
        coarse_reuse = PETSC_FALSE;
      } else { /* we can safely reuse already computed coarse matrix */
        coarse_reuse = PETSC_TRUE;
      }
    } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
      coarse_reuse = PETSC_FALSE;
    }
    /* reset any subassembling information */
    ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
    ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
  } else { /* primal space is unchanged, so we can reuse coarse matrix */
    coarse_reuse = PETSC_TRUE;
  }

  /* count "active" (i.e. with positive local size) and "void" processes */
  im_active = !!(pcis->n);
  ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
  void_procs = all_procs-active_procs;
  csin_type_simple = PETSC_TRUE;
  redist = PETSC_FALSE;
  if (pcbddc->current_level && void_procs) {
    csin_ml = PETSC_TRUE;
    ncoarse_ml = void_procs;
    /* it has no sense to redistribute on a set of processors larger than the number of active processes */
    if (pcbddc->redistribute_coarse > 0 && pcbddc->redistribute_coarse < active_procs) {
      csin_ds = PETSC_TRUE;
      ncoarse_ds = pcbddc->redistribute_coarse;
      redist = PETSC_TRUE;
    } else {
      csin_ds = PETSC_TRUE;
      ncoarse_ds = active_procs;
      redist = PETSC_TRUE;
    }
  } else {
    csin_ml = PETSC_FALSE;
    ncoarse_ml = all_procs;
    if (void_procs) {
      csin_ds = PETSC_TRUE;
      ncoarse_ds = void_procs;
      csin_type_simple = PETSC_FALSE;
    } else {
      if (pcbddc->redistribute_coarse > 0 && pcbddc->redistribute_coarse < all_procs) {
        csin_ds = PETSC_TRUE;
        ncoarse_ds = pcbddc->redistribute_coarse;
        redist = PETSC_TRUE;
      } else {
        csin_ds = PETSC_FALSE;
        ncoarse_ds = all_procs;
      }
    }
  }

  /*
    test if we can go multilevel: three conditions must be satisfied:
    - we have not exceeded the number of levels requested
    - we can actually subassemble the active processes
    - we can find a suitable number of MPI processes where we can place the subassembled problem
  */
  multilevel_allowed = PETSC_FALSE;
  multilevel_requested = PETSC_FALSE;
  if (pcbddc->current_level < pcbddc->max_levels) {
    multilevel_requested = PETSC_TRUE;
    if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
      multilevel_allowed = PETSC_FALSE;
    } else {
      multilevel_allowed = PETSC_TRUE;
    }
  }
  /* determine number of process partecipating to coarse solver */
  if (multilevel_allowed) {
    ncoarse = ncoarse_ml;
    csin = csin_ml;
    redist = PETSC_FALSE;
  } else {
    ncoarse = ncoarse_ds;
    csin = csin_ds;
  }

  /* creates temporary l2gmap and IS for coarse indexes */
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);

  /* creates temporary MATIS object for coarse matrix */
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,NULL,&coarse_submat_dense);CHKERRQ(ierr);
  ierr = MatDenseGetArray(coarse_submat_dense,&array);CHKERRQ(ierr);
  ierr = PetscMemcpy(array,coarse_submat_vals,sizeof(*coarse_submat_vals)*pcbddc->local_primal_size*pcbddc->local_primal_size);CHKERRQ(ierr);
  ierr = MatDenseRestoreArray(coarse_submat_dense,&array);CHKERRQ(ierr);
  ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,NULL,&t_coarse_mat_is);CHKERRQ(ierr);
  ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);

  /* compute dofs splitting and neumann boundaries for coarse dofs */
  if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal || (pcbddc->benign_saddle_point && pcbddc->user_primal_vertices_local))) { /* protects from unneded computations */
    PetscInt               *tidxs,*tidxs2,nout,tsize,i;
    const PetscInt         *idxs;
    ISLocalToGlobalMapping tmap;

    /* create map between primal indices (in local representative ordering) and local primal numbering */
    ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
    /* allocate space for temporary storage */
    ierr = PetscMalloc1(pcbddc->local_primal_size,&tidxs);CHKERRQ(ierr);
    ierr = PetscMalloc1(pcbddc->local_primal_size,&tidxs2);CHKERRQ(ierr);
    /* allocate for IS array */
    nisdofs = pcbddc->n_ISForDofsLocal;
    nisneu = !!pcbddc->NeumannBoundariesLocal;
    nisvert = 0;
    if (pcbddc->benign_saddle_point && pcbddc->user_primal_vertices_local) {
      nisvert = 1;
    }
    nis = nisdofs + nisneu + nisvert;
    ierr = PetscMalloc1(nis,&isarray);CHKERRQ(ierr);
    /* dofs splitting */
    for (i=0;i<nisdofs;i++) {
      /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
      ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
      ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
      ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
      ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
      ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
      ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
      /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
    }
    /* neumann boundaries */
    if (pcbddc->NeumannBoundariesLocal) {
      /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
      ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
      ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
      ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
      ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
      ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
      ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
      /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
    }
    /* primal vertices (benign) */
    if (pcbddc->benign_saddle_point && pcbddc->user_primal_vertices_local) {
      ierr = ISGetLocalSize(pcbddc->user_primal_vertices_local,&tsize);CHKERRQ(ierr);
      ierr = ISGetIndices(pcbddc->user_primal_vertices_local,&idxs);CHKERRQ(ierr);
      ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
      ierr = ISRestoreIndices(pcbddc->user_primal_vertices_local,&idxs);CHKERRQ(ierr);
      ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
      ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nis-1]);CHKERRQ(ierr);
    }
    /* free memory */
    ierr = PetscFree(tidxs);CHKERRQ(ierr);
    ierr = PetscFree(tidxs2);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
  } else {
    nis = 0;
    nisdofs = 0;
    nisneu = 0;
    nisvert = 0;
    isarray = NULL;
  }
  /* destroy no longer needed map */
  ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);

  /* restrict on coarse candidates (if needed) */
  coarse_mat_is = NULL;
  if (csin) {
    if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
      if (redist) {
        PetscMPIInt rank;
        PetscInt    spc,n_spc_p1,dest[1],destsize;

        ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
        spc = active_procs/ncoarse;
        n_spc_p1 = active_procs%ncoarse;
        if (im_active) {
          destsize = 1;
          if (rank > n_spc_p1*(spc+1)-1) {
            dest[0] = n_spc_p1+(rank-(n_spc_p1*(spc+1)))/spc;
          } else {
            dest[0] = rank/(spc+1);
          }
        } else {
          destsize = 0;
        }
        ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),destsize,dest,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
      } else if (csin_type_simple) {
        PetscMPIInt rank;
        PetscInt    issize,isidx;

        ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
        if (im_active) {
          issize = 1;
          isidx = (PetscInt)rank;
        } else {
          issize = 0;
          isidx = -1;
        }
        ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
      } else { /* get a suitable subassembling pattern from MATIS code */
        ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
      }

      /* we need to shift on coarse candidates either if we are not redistributing or we are redistributing and we have enough void processes */
      if (!redist || ncoarse <= void_procs) {
        PetscInt ncoarse_cand,tissize,*nisindices;
        PetscInt *coarse_candidates;
        const PetscInt* tisindices;

        /* get coarse candidates' ranks in pc communicator */
        ierr = PetscMalloc1(all_procs,&coarse_candidates);CHKERRQ(ierr);
        ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
        for (i=0,ncoarse_cand=0;i<all_procs;i++) {
          if (!coarse_candidates[i]) {
            coarse_candidates[ncoarse_cand++]=i;
          }
        }
        if (ncoarse_cand < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",ncoarse_cand,ncoarse);


        if (pcbddc->dbg_flag) {
          ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
          ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
          ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
          ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
          for (i=0;i<ncoarse_cand;i++) {
            ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
          }
          ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
          ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
        }
        /* shift the pattern on coarse candidates */
        ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
        ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
        ierr = PetscMalloc1(tissize,&nisindices);CHKERRQ(ierr);
        for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
        ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
        ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
        ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
      }
      if (pcbddc->dbg_flag) {
        ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
        ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
        ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      }
    }
    /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
    if (multilevel_allowed) { /* we need to keep tracking of void processes for future placements */
      ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,PETSC_FALSE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
    } else { /* this is the last level, so use just receiving processes in subcomm */
      ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
    }
  } else {
    if (pcbddc->dbg_flag) {
      ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
      ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    }
    ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
    coarse_mat_is = t_coarse_mat_is;
  }

  /* create local to global scatters for coarse problem */
  if (compute_vecs) {
    PetscInt lrows;
    ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
    if (coarse_mat_is) {
      ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
    } else {
      lrows = 0;
    }
    ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
    ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
    ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
    ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
  }
  ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
  ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);

  /* set defaults for coarse KSP and PC */
  if (multilevel_allowed) {
    coarse_ksp_type = KSPRICHARDSON;
    coarse_pc_type = PCBDDC;
  } else {
    coarse_ksp_type = KSPPREONLY;
    coarse_pc_type = PCREDUNDANT;
  }

  /* print some info if requested */
  if (pcbddc->dbg_flag) {
    if (!multilevel_allowed) {
      ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
      if (multilevel_requested) {
        ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Not enough active processes on level %d (active processes %d, coarsening ratio %d)\n",pcbddc->current_level,active_procs,pcbddc->coarsening_ratio);CHKERRQ(ierr);
      } else if (pcbddc->max_levels) {
        ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
      }
      ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    }
  }

  /* create the coarse KSP object only once with defaults */
  if (coarse_mat_is) {
    MatReuse coarse_mat_reuse;
    PetscViewer dbg_viewer = NULL;
    if (pcbddc->dbg_flag) {
      dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
      ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
    }
    if (!pcbddc->coarse_ksp) {
      char prefix[256],str_level[16];
      size_t len;
      ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
      ierr = KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);CHKERRQ(ierr);
      ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
      ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
      ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
      ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
      ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
      ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
      ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
      /* prefix */
      ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
      ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
      if (!pcbddc->current_level) {
        ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
        ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
      } else {
        ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
        if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
        if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
        ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
        sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
        ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
      }
      ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
      /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
      ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
      ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
      ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
      /* allow user customization */
      ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
    }
    /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
    ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
    if (nisdofs) {
      ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
      for (i=0;i<nisdofs;i++) {
        ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
      }
    }
    if (nisneu) {
      ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
      ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
    }
    if (nisvert) {
      ierr = PCBDDCSetPrimalVerticesIS(pc_temp,isarray[nis-1]);CHKERRQ(ierr);
      ierr = ISDestroy(&isarray[nis-1]);CHKERRQ(ierr);
    }

    /* get some info after set from options */
    ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
    ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
    ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
    if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
      ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
      isbddc = PETSC_FALSE;
    }
    ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
    if (isredundant) {
      KSP inner_ksp;
      PC  inner_pc;
      ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
      ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
      ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
    }

    /* assemble coarse matrix */
    if (coarse_reuse) {
      ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
      ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
      coarse_mat_reuse = MAT_REUSE_MATRIX;
    } else {
      coarse_mat_reuse = MAT_INITIAL_MATRIX;
    }
    if (isbddc || isnn) {
      if (isbddc) { /* currently there's no API for this */
        PC_BDDC* pcbddc = (PC_BDDC*)pc_temp->data;
        pcbddc->detect_disconnected = PETSC_TRUE;
      }
      if (pcbddc->coarsening_ratio > 1) {
        if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
          ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
          if (pcbddc->dbg_flag) {
            ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
            ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
            ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
            ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
          }
        }
        ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
      } else {
        ierr = PetscObjectReference((PetscObject)coarse_mat_is);CHKERRQ(ierr);
        coarse_mat = coarse_mat_is;
      }
    } else {
      ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
    }
    ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);

    /* propagate symmetry info of coarse matrix */
    ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
    if (pc->pmat->symmetric_set) {
      ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pc->pmat->symmetric);CHKERRQ(ierr);
    }
    if (pc->pmat->hermitian_set) {
      ierr = MatSetOption(coarse_mat,MAT_HERMITIAN,pc->pmat->hermitian);CHKERRQ(ierr);
    }
    if (pc->pmat->spd_set) {
      ierr = MatSetOption(coarse_mat,MAT_SPD,pc->pmat->spd);CHKERRQ(ierr);
    }
    /* set operators */
    ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
    if (pcbddc->dbg_flag) {
      ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
    }
  } else { /* processes non partecipating to coarse solver (if any) */
    coarse_mat = 0;
  }
  ierr = PetscFree(isarray);CHKERRQ(ierr);
#if 0
  {
    PetscViewer viewer;
    char filename[256];
    sprintf(filename,"coarse_mat_level%d.m",pcbddc->current_level);
    ierr = PetscViewerASCIIOpen(PetscObjectComm((PetscObject)coarse_mat),filename,&viewer);CHKERRQ(ierr);
    ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
    ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
  }
#endif

  /* Compute coarse null space (special handling by BDDC only) */
#if 0
  if (pcbddc->NullSpace) {
    ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
  }
#endif
  /* hack */
  if (pcbddc->coarse_ksp) {
    Vec crhs,csol;

    ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
    ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
    if (!csol) {
      ierr = MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
    }
    if (!crhs) {
      ierr = MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
    }
  }

  /* compute null space for coarse solver if the benign trick has been requested */
  if (pcbddc->benign_null) {

    ierr = VecSet(pcbddc->vec1_P,0.);CHKERRQ(ierr);
    for (i=0;i<pcbddc->benign_n;i++) {
      ierr = VecSetValue(pcbddc->vec1_P,pcbddc->local_primal_size-pcbddc->benign_n+i,1.0,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    if (coarse_mat) {
      Vec         nullv;
      PetscScalar *array,*array2;
      PetscInt    nl;

      ierr = MatCreateVecs(coarse_mat,&nullv,NULL);CHKERRQ(ierr);
      ierr = VecGetLocalSize(nullv,&nl);CHKERRQ(ierr);
      ierr = VecGetArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);CHKERRQ(ierr);
      ierr = VecGetArray(nullv,&array2);CHKERRQ(ierr);
      ierr = PetscMemcpy(array2,array,nl*sizeof(*array));CHKERRQ(ierr);
      ierr = VecRestoreArray(nullv,&array2);CHKERRQ(ierr);
      ierr = VecRestoreArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);CHKERRQ(ierr);
      ierr = VecNormalize(nullv,NULL);CHKERRQ(ierr);
      ierr = MatNullSpaceCreate(PetscObjectComm((PetscObject)coarse_mat),PETSC_FALSE,1,&nullv,&CoarseNullSpace);CHKERRQ(ierr);
      ierr = VecDestroy(&nullv);CHKERRQ(ierr);
    }
  }

  if (pcbddc->coarse_ksp) {
    PetscBool ispreonly;

    if (CoarseNullSpace) {
      PetscBool isnull;
      ierr = MatNullSpaceTest(CoarseNullSpace,coarse_mat,&isnull);CHKERRQ(ierr);
      if (0) {
        if (isbddc && !pcbddc->benign_saddle_point) {
          ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
        } else {
          ierr = MatSetNullSpace(coarse_mat,CoarseNullSpace);CHKERRQ(ierr);
        }
      } else {
        ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
      }
    }
    /* setup coarse ksp */
    ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
    /* Check coarse problem if in debug mode or if solving with an iterative method */
    ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
    if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
      KSP       check_ksp;
      KSPType   check_ksp_type;
      PC        check_pc;
      Vec       check_vec,coarse_vec;
      PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
      PetscInt  its;
      PetscBool compute_eigs;
      PetscReal *eigs_r,*eigs_c;
      PetscInt  neigs;
      const char *prefix;

      /* Create ksp object suitable for estimation of extreme eigenvalues */
      ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
      ierr = KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);CHKERRQ(ierr);
      ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
      ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
      if (ispreonly) {
        check_ksp_type = KSPPREONLY;
        compute_eigs = PETSC_FALSE;
      } else {
        check_ksp_type = KSPGMRES;
        compute_eigs = PETSC_TRUE;
      }
      ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
      ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
      ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
      ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
      ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
      ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
      ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
      ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
      ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
      ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
      ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
      /* create random vec */
      ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
      ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
      ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
      if (CoarseNullSpace) {
        ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
      }
      ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
      /* solve coarse problem */
      ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
      if (CoarseNullSpace) {
        ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
      }
      /* set eigenvalue estimation if preonly has not been requested */
      if (compute_eigs) {
        ierr = PetscMalloc1(pcbddc->coarse_size+1,&eigs_r);CHKERRQ(ierr);
        ierr = PetscMalloc1(pcbddc->coarse_size+1,&eigs_c);CHKERRQ(ierr);
        ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
        lambda_max = eigs_r[neigs-1];
        lambda_min = eigs_r[0];
        if (pcbddc->use_coarse_estimates) {
          if (lambda_max>lambda_min) {
            ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
            ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
          }
        }
      }

      /* check coarse problem residual error */
      if (pcbddc->dbg_flag) {
        PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
        ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
        ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
        ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
        ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
        ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
        ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (use estimates %d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
        ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
        ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
        if (CoarseNullSpace) {
          ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem is singular\n");CHKERRQ(ierr);
        }
        if (compute_eigs) {
          PetscReal lambda_max_s,lambda_min_s;
          ierr = KSPGetType(check_ksp,&check_ksp_type);CHKERRQ(ierr);
          ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
          ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
          ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem eigenvalues (estimated with %d iterations of %s): %1.6e %1.6e (%1.6e %1.6e)\n",its,check_ksp_type,lambda_min,lambda_max,lambda_min_s,lambda_max_s);CHKERRQ(ierr);
          for (i=0;i<neigs;i++) {
            ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
          }
        }
        ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
        ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
      }
      ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
      if (compute_eigs) {
        ierr = PetscFree(eigs_r);CHKERRQ(ierr);
        ierr = PetscFree(eigs_c);CHKERRQ(ierr);
      }
    }
  }
  /* print additional info */
  if (pcbddc->dbg_flag) {
    /* waits until all processes reaches this point */
    ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
  }

  /* free memory */
  ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
  ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCComputePrimalNumbering"
PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
{
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
  PC_IS*         pcis = (PC_IS*)pc->data;
  Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
  IS             subset,subset_mult,subset_n;
  PetscInt       local_size,coarse_size=0;
  PetscInt       *local_primal_indices=NULL;
  const PetscInt *t_local_primal_indices;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* Compute global number of coarse dofs */
  if (pcbddc->local_primal_size && !pcbddc->local_primal_ref_node) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"BDDC ConstraintsSetUp should be called first");
  }
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&subset_n);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingApplyIS(pcis->mapping,subset_n,&subset);CHKERRQ(ierr);
  ierr = ISDestroy(&subset_n);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_mult,PETSC_COPY_VALUES,&subset_mult);CHKERRQ(ierr);
  ierr = PCBDDCSubsetNumbering(subset,subset_mult,&coarse_size,&subset_n);CHKERRQ(ierr);
  ierr = ISDestroy(&subset);CHKERRQ(ierr);
  ierr = ISDestroy(&subset_mult);CHKERRQ(ierr);
  ierr = ISGetLocalSize(subset_n,&local_size);CHKERRQ(ierr);
  if (local_size != pcbddc->local_primal_size) {
    SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid number of local primal indices computed %d != %d",local_size,pcbddc->local_primal_size);
  }
  ierr = PetscMalloc1(local_size,&local_primal_indices);CHKERRQ(ierr);
  ierr = ISGetIndices(subset_n,&t_local_primal_indices);CHKERRQ(ierr);
  ierr = PetscMemcpy(local_primal_indices,t_local_primal_indices,local_size*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = ISRestoreIndices(subset_n,&t_local_primal_indices);CHKERRQ(ierr);
  ierr = ISDestroy(&subset_n);CHKERRQ(ierr);

  /* check numbering */
  if (pcbddc->dbg_flag) {
    PetscScalar coarsesum,*array,*array2;
    PetscInt    i;
    PetscBool   set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;

    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
    /* counter */
    ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
    ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
    for (i=0;i<pcbddc->local_primal_size;i++) {
      ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
    ierr = VecGetArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
    for (i=0;i<pcis->n;i++) {
      if (array[i] != 0.0 && array[i] != array2[i]) {
        PetscInt owned = (PetscInt)PetscRealPart(array[i]);
        PetscInt neigh = (PetscInt)PetscRealPart(array2[i]);
        set_error = PETSC_TRUE;
        ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a %d processes instead of %d!\n",PetscGlobalRank,i,owned,neigh);CHKERRQ(ierr);
      }
    }
    ierr = VecRestoreArray(pcis->vec2_N,&array2);CHKERRQ(ierr);
    ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    for (i=0;i<pcis->n;i++) {
      if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
    }
    ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
    ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
    ierr = VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
    if (pcbddc->dbg_flag > 1 || set_error_reduced) {
      PetscInt *gidxs;

      ierr = PetscMalloc1(pcbddc->local_primal_size,&gidxs);CHKERRQ(ierr);
      ierr = ISLocalToGlobalMappingApply(pcis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,gidxs);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
      ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
      for (i=0;i<pcbddc->local_primal_size;i++) {
        ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d,%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i],gidxs[i]);CHKERRQ(ierr);
      }
      ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
      ierr = PetscFree(gidxs);CHKERRQ(ierr);
    }
    ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);CHKERRQ(ierr);
    if (set_error_reduced) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
  }
  /* ierr = PetscPrintf(PetscObjectComm((PetscObject)pc),"Size of coarse problem is %d\n",coarse_size);CHKERRQ(ierr); */
  /* get back data */
  *coarse_size_n = coarse_size;
  *local_primal_indices_n = local_primal_indices;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCGlobalToLocal"
PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
{
  IS             localis_t;
  PetscInt       i,lsize,*idxs,n;
  PetscScalar    *vals;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* get indices in local ordering exploiting local to global map */
  ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
  ierr = PetscMalloc1(lsize,&vals);CHKERRQ(ierr);
  for (i=0;i<lsize;i++) vals[i] = 1.0;
  ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
  ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
  ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
  if (idxs) { /* multilevel guard */
    ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
  ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
  ierr = PetscFree(vals);CHKERRQ(ierr);
  ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
  /* now compute set in local ordering */
  ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
  ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
  for (i=0,lsize=0;i<n;i++) {
    if (PetscRealPart(vals[i]) > 0.5) {
      lsize++;
    }
  }
  ierr = PetscMalloc1(lsize,&idxs);CHKERRQ(ierr);
  for (i=0,lsize=0;i<n;i++) {
    if (PetscRealPart(vals[i]) > 0.5) {
      idxs[lsize++] = i;
    }
  }
  ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
  *localis = localis_t;
  PetscFunctionReturn(0);
}

/* the next two functions will be called in KSPMatMult if a change of basis has been requested */
#undef __FUNCT__
#define __FUNCT__ "PCBDDCMatMult_Private"
static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y)
{
  PCBDDCChange_ctx change_ctx;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
  ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
  ierr = MatMult(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
  ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCMatMultTranspose_Private"
static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y)
{
  PCBDDCChange_ctx change_ctx;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
  ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
  ierr = MatMultTranspose(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
  ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCSetUpSubSchurs"
PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
{
  PC_IS               *pcis=(PC_IS*)pc->data;
  PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
  PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
  Mat                 S_j;
  PetscInt            *used_xadj,*used_adjncy;
  PetscBool           free_used_adj;
  PetscErrorCode      ierr;

  PetscFunctionBegin;
  /* decide the adjacency to be used for determining internal problems for local schur on subsets */
  free_used_adj = PETSC_FALSE;
  if (pcbddc->sub_schurs_layers == -1) {
    used_xadj = NULL;
    used_adjncy = NULL;
  } else {
    if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
      used_xadj = pcbddc->mat_graph->xadj;
      used_adjncy = pcbddc->mat_graph->adjncy;
    } else if (pcbddc->computed_rowadj) {
      used_xadj = pcbddc->mat_graph->xadj;
      used_adjncy = pcbddc->mat_graph->adjncy;
    } else {
      PetscBool      flg_row=PETSC_FALSE;
      const PetscInt *xadj,*adjncy;
      PetscInt       nvtxs;

      ierr = MatGetRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
      if (flg_row) {
        ierr = PetscMalloc2(nvtxs+1,&used_xadj,xadj[nvtxs],&used_adjncy);CHKERRQ(ierr);
        ierr = PetscMemcpy(used_xadj,xadj,(nvtxs+1)*sizeof(*xadj));CHKERRQ(ierr);
        ierr = PetscMemcpy(used_adjncy,adjncy,(xadj[nvtxs])*sizeof(*adjncy));CHKERRQ(ierr);
        free_used_adj = PETSC_TRUE;
      } else {
        pcbddc->sub_schurs_layers = -1;
        used_xadj = NULL;
        used_adjncy = NULL;
      }
      ierr = MatRestoreRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
    }
  }

  /* setup sub_schurs data */
  ierr = MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);CHKERRQ(ierr);
  if (!sub_schurs->schur_explicit) {
    /* pcbddc->ksp_D up to date only if not using MatFactor with Schur complement support */
    ierr = MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);CHKERRQ(ierr);
    ierr = PCBDDCSubSchursSetUp(sub_schurs,NULL,S_j,PETSC_FALSE,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,pcbddc->faster_deluxe,pcbddc->adaptive_selection,PETSC_FALSE,PETSC_FALSE,0,NULL,NULL);CHKERRQ(ierr);
  } else {
    PetscBool reuse_solvers = (PetscBool)!pcbddc->use_change_of_basis;
    PetscBool isseqaij;
    PetscInt  benign_n;

    if (!pcbddc->use_vertices && reuse_solvers) {
      PetscInt n_vertices;

      ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);CHKERRQ(ierr);
      reuse_solvers = (PetscBool)!n_vertices;
    }
    ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
    if (!isseqaij) {
      Mat_IS* matis = (Mat_IS*)pc->pmat->data;
      if (matis->A == pcbddc->local_mat) {
        ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
        ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);CHKERRQ(ierr);
      } else {
        ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_REUSE_MATRIX,&pcbddc->local_mat);CHKERRQ(ierr);
      }
    }
    if (!pcbddc->benign_change_explicit) {
      benign_n = pcbddc->benign_n;
    } else {
      benign_n = 0;
    }
    ierr = PCBDDCSubSchursSetUp(sub_schurs,pcbddc->local_mat,S_j,pcbddc->sub_schurs_exact_schur,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,pcbddc->faster_deluxe,pcbddc->adaptive_selection,reuse_solvers,pcbddc->benign_saddle_point,benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_zerodiag_subs);CHKERRQ(ierr);
  }
  ierr = MatDestroy(&S_j);CHKERRQ(ierr);

  /* free adjacency */
  if (free_used_adj) {
    ierr = PetscFree2(used_xadj,used_adjncy);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCInitSubSchurs"
PetscErrorCode PCBDDCInitSubSchurs(PC pc)
{
  PC_IS               *pcis=(PC_IS*)pc->data;
  PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
  PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
  PCBDDCGraph         graph;
  PetscErrorCode      ierr;

  PetscFunctionBegin;
  /* attach interface graph for determining subsets */
  if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
    IS       verticesIS,verticescomm;
    PetscInt vsize,*idxs;

    ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);CHKERRQ(ierr);
    ierr = ISGetSize(verticesIS,&vsize);CHKERRQ(ierr);
    ierr = ISGetIndices(verticesIS,(const PetscInt**)&idxs);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),vsize,idxs,PETSC_COPY_VALUES,&verticescomm);CHKERRQ(ierr);
    ierr = ISRestoreIndices(verticesIS,(const PetscInt**)&idxs);CHKERRQ(ierr);
    ierr = ISDestroy(&verticesIS);CHKERRQ(ierr);
    ierr = PCBDDCGraphCreate(&graph);CHKERRQ(ierr);
    ierr = PCBDDCGraphInit(graph,pcbddc->mat_graph->l2gmap,pcbddc->mat_graph->nvtxs_global);CHKERRQ(ierr);
    ierr = PCBDDCGraphSetUp(graph,0,NULL,pcbddc->DirichletBoundariesLocal,0,NULL,verticescomm);CHKERRQ(ierr);
    ierr = ISDestroy(&verticescomm);CHKERRQ(ierr);
    ierr = PCBDDCGraphComputeConnectedComponents(graph);CHKERRQ(ierr);
/*
    if (pcbddc->dbg_flag) {
      ierr = PCBDDCGraphASCIIView(graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);CHKERRQ(ierr);
    }
*/
  } else {
    graph = pcbddc->mat_graph;
  }

  /* sub_schurs init */
  ierr = PCBDDCSubSchursInit(sub_schurs,pcis->is_I_local,pcis->is_B_local,graph,pcis->BtoNmap);CHKERRQ(ierr);

  /* free graph struct */
  if (pcbddc->sub_schurs_rebuild) {
    ierr = PCBDDCGraphDestroy(&graph);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCBDDCCheckOperator"
PetscErrorCode PCBDDCCheckOperator(PC pc)
{
  PC_IS               *pcis=(PC_IS*)pc->data;
  PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
  PetscErrorCode      ierr;

  PetscFunctionBegin;
  if (pcbddc->n_vertices == pcbddc->local_primal_size) {
    IS             zerodiag = NULL;
    Mat            S_j,B0_B=NULL;
    Vec            dummy_vec=NULL,vec_check_B,vec_scale_P;
    PetscScalar    *p0_check,*array,*array2;
    PetscReal      norm;
    PetscInt       i;

    /* B0 and B0_B */
    if (zerodiag) {
      IS       dummy;

      ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&dummy);CHKERRQ(ierr);
      ierr = MatGetSubMatrix(pcbddc->benign_B0,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);CHKERRQ(ierr);
      ierr = MatCreateVecs(B0_B,NULL,&dummy_vec);CHKERRQ(ierr);
      ierr = ISDestroy(&dummy);CHKERRQ(ierr);
    }
    /* I need a primal vector to scale primal nodes since BDDC sums contibutions */
    ierr = VecDuplicate(pcbddc->vec1_P,&vec_scale_P);CHKERRQ(ierr);
    ierr = VecSet(pcbddc->vec1_P,1.0);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecReciprocal(vec_scale_P);CHKERRQ(ierr);
    /* S_j */
    ierr = MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);CHKERRQ(ierr);
    ierr = MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);CHKERRQ(ierr);

    /* mimic vector in \widetilde{W}_\Gamma */
    ierr = VecSetRandom(pcis->vec1_N,NULL);CHKERRQ(ierr);
    /* continuous in primal space */
    ierr = VecSetRandom(pcbddc->coarse_vec,NULL);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
    ierr = PetscCalloc1(pcbddc->benign_n,&p0_check);CHKERRQ(ierr);
    for (i=0;i<pcbddc->benign_n;i++) p0_check[i] = array[pcbddc->local_primal_size-pcbddc->benign_n+i];
    ierr = VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);CHKERRQ(ierr);
    ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
    ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecDuplicate(pcis->vec2_B,&vec_check_B);CHKERRQ(ierr);
    ierr = VecCopy(pcis->vec2_B,vec_check_B);CHKERRQ(ierr);

    /* assemble rhs for coarse problem */
    /* widetilde{S}_\Gamma w_\Gamma + \widetilde{B0}^T_B p0 */
    /* local with Schur */
    ierr = MatMult(S_j,pcis->vec2_B,pcis->vec1_B);CHKERRQ(ierr);
    if (zerodiag) {
      ierr = VecGetArray(dummy_vec,&array);CHKERRQ(ierr);
      for (i=0;i<pcbddc->benign_n;i++) array[i] = p0_check[i];
      ierr = VecRestoreArray(dummy_vec,&array);CHKERRQ(ierr);
      ierr = MatMultTransposeAdd(B0_B,dummy_vec,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
    }
    /* sum on primal nodes the local contributions */
    ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
    ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
    for (i=0;i<pcbddc->local_primal_size;i++) array2[i] = array[pcbddc->local_primal_ref_node[i]];
    ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
    ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
    ierr = VecSet(pcbddc->coarse_vec,0.);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
    ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
    /* scale primal nodes (BDDC sums contibutions) */
    ierr = VecPointwiseMult(pcbddc->vec1_P,vec_scale_P,pcbddc->vec1_P);CHKERRQ(ierr);
    ierr = VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);CHKERRQ(ierr);
    ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
    ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
    ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    /* global: \widetilde{B0}_B w_\Gamma */
    if (zerodiag) {
      ierr = MatMult(B0_B,pcis->vec2_B,dummy_vec);CHKERRQ(ierr);
      ierr = VecGetArray(dummy_vec,&array);CHKERRQ(ierr);
      for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = array[i];
      ierr = VecRestoreArray(dummy_vec,&array);CHKERRQ(ierr);
    }
    /* BDDC */
    ierr = VecSet(pcis->vec1_D,0.);CHKERRQ(ierr);
    ierr = PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);CHKERRQ(ierr);

    ierr = VecCopy(pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
    ierr = VecAXPY(pcis->vec1_B,-1.0,vec_check_B);CHKERRQ(ierr);
    ierr = VecNorm(pcis->vec1_B,NORM_INFINITY,&norm);CHKERRQ(ierr);
    PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC local error is %1.4e\n",PetscGlobalRank,norm);
    for (i=0;i<pcbddc->benign_n;i++) {
      PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC p0[%d] error is %1.4e\n",PetscGlobalRank,i,PetscAbsScalar(pcbddc->benign_p0[i]-p0_check[i]));
    }
    ierr = PetscFree(p0_check);CHKERRQ(ierr);
    ierr = VecDestroy(&vec_scale_P);CHKERRQ(ierr);
    ierr = VecDestroy(&vec_check_B);CHKERRQ(ierr);
    ierr = VecDestroy(&dummy_vec);CHKERRQ(ierr);
    ierr = MatDestroy(&S_j);CHKERRQ(ierr);
    ierr = MatDestroy(&B0_B);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}