xref: /petsc/src/ksp/pc/impls/bddc/bddcscalingbasic.c (revision 5e5bbd0a99ea6ef6b187abb9b4a6405ccdf6db1e)

#include <petsc/private/pcbddcimpl.h>
#include <petsc/private/pcbddcprivateimpl.h>
#include <petscblaslapack.h>
#include <../src/mat/impls/dense/seq/dense.h>

/* prototypes for deluxe functions */
static PetscErrorCode PCBDDCScalingCreate_Deluxe(PC);
static PetscErrorCode PCBDDCScalingDestroy_Deluxe(PC);
static PetscErrorCode PCBDDCScalingSetUp_Deluxe(PC);
static PetscErrorCode PCBDDCScalingSetUp_Deluxe_Private(PC);
static PetscErrorCode PCBDDCScalingReset_Deluxe_Solvers(PCBDDCDeluxeScaling);

static PetscErrorCode PCBDDCMatTransposeMatSolve_SeqDense(Mat A,Mat B,Mat X)
{
  Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
  const PetscScalar *b;
  PetscScalar       *x;
  PetscInt          n;
  PetscBLASInt      nrhs,info,m;
  PetscBool         flg;

  PetscFunctionBegin;
  PetscCall(PetscBLASIntCast(A->rmap->n,&m));
  PetscCall(PetscObjectTypeCompareAny((PetscObject)B,&flg,MATSEQDENSE,MATMPIDENSE,NULL));
  PetscCheck(flg,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix B must be MATDENSE matrix");
  PetscCall(PetscObjectTypeCompareAny((PetscObject)X,&flg,MATSEQDENSE,MATMPIDENSE,NULL));
  PetscCheck(flg,PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix X must be MATDENSE matrix");

  PetscCall(MatGetSize(B,NULL,&n));
  PetscCall(PetscBLASIntCast(n,&nrhs));
  PetscCall(MatDenseGetArrayRead(B,&b));
  PetscCall(MatDenseGetArray(X,&x));
  PetscCall(PetscArraycpy(x,b,m*nrhs));
  PetscCall(MatDenseRestoreArrayRead(B,&b));

  if (A->factortype == MAT_FACTOR_LU) {
    PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&m,&nrhs,mat->v,&mat->lda,mat->pivots,x,&m,&info));
    PetscCheck(!info,PETSC_COMM_SELF,PETSC_ERR_LIB,"GETRS - Bad solve");
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only LU factor supported");

  PetscCall(MatDenseRestoreArray(X,&x));
  PetscCall(PetscLogFlops(nrhs*(2.0*m*m - m)));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingExtension_Basic(PC pc, Vec local_interface_vector, Vec global_vector)
{
  PC_IS*         pcis = (PC_IS*)pc->data;
  PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;

  PetscFunctionBegin;
  /* Apply partition of unity */
  PetscCall(VecPointwiseMult(pcbddc->work_scaling,pcis->D,local_interface_vector));
  PetscCall(VecSet(global_vector,0.0));
  PetscCall(VecScatterBegin(pcis->global_to_B,pcbddc->work_scaling,global_vector,ADD_VALUES,SCATTER_REVERSE));
  PetscCall(VecScatterEnd(pcis->global_to_B,pcbddc->work_scaling,global_vector,ADD_VALUES,SCATTER_REVERSE));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingExtension_Deluxe(PC pc, Vec x, Vec y)
{
  PC_IS*              pcis=(PC_IS*)pc->data;
  PC_BDDC*            pcbddc=(PC_BDDC*)pc->data;
  PCBDDCDeluxeScaling deluxe_ctx = pcbddc->deluxe_ctx;

  PetscFunctionBegin;
  PetscCall(VecSet(pcbddc->work_scaling,0.0));
  PetscCall(VecSet(y,0.0));
  if (deluxe_ctx->n_simple) { /* scale deluxe vertices using diagonal scaling */
    PetscInt          i;
    const PetscScalar *array_x,*array_D;
    PetscScalar       *array;
    PetscCall(VecGetArrayRead(x,&array_x));
    PetscCall(VecGetArrayRead(pcis->D,&array_D));
    PetscCall(VecGetArray(pcbddc->work_scaling,&array));
    for (i=0;i<deluxe_ctx->n_simple;i++) {
      array[deluxe_ctx->idx_simple_B[i]] = array_x[deluxe_ctx->idx_simple_B[i]]*array_D[deluxe_ctx->idx_simple_B[i]];
    }
    PetscCall(VecRestoreArray(pcbddc->work_scaling,&array));
    PetscCall(VecRestoreArrayRead(pcis->D,&array_D));
    PetscCall(VecRestoreArrayRead(x,&array_x));
  }
  /* sequential part : all problems and Schur applications collapsed into a single matrix vector multiplication or a matvec and a solve */
  if (deluxe_ctx->seq_mat) {
    PetscInt i;
    for (i=0;i<deluxe_ctx->seq_n;i++) {
      if (deluxe_ctx->change) {
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],x,deluxe_ctx->seq_work2[i],INSERT_VALUES,SCATTER_FORWARD));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],x,deluxe_ctx->seq_work2[i],INSERT_VALUES,SCATTER_FORWARD));
        if (deluxe_ctx->change_with_qr) {
          Mat change;

          PetscCall(KSPGetOperators(deluxe_ctx->change[i],&change,NULL));
          PetscCall(MatMultTranspose(change,deluxe_ctx->seq_work2[i],deluxe_ctx->seq_work1[i]));
        } else {
          PetscCall(KSPSolve(deluxe_ctx->change[i],deluxe_ctx->seq_work2[i],deluxe_ctx->seq_work1[i]));
        }
      } else {
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],x,deluxe_ctx->seq_work1[i],INSERT_VALUES,SCATTER_FORWARD));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],x,deluxe_ctx->seq_work1[i],INSERT_VALUES,SCATTER_FORWARD));
      }
      PetscCall(MatMultTranspose(deluxe_ctx->seq_mat[i],deluxe_ctx->seq_work1[i],deluxe_ctx->seq_work2[i]));
      if (deluxe_ctx->seq_mat_inv_sum[i]) {
        PetscScalar *x;

        PetscCall(VecGetArray(deluxe_ctx->seq_work2[i],&x));
        PetscCall(VecPlaceArray(deluxe_ctx->seq_work1[i],x));
        PetscCall(VecRestoreArray(deluxe_ctx->seq_work2[i],&x));
        PetscCall(MatSolveTranspose(deluxe_ctx->seq_mat_inv_sum[i],deluxe_ctx->seq_work1[i],deluxe_ctx->seq_work2[i]));
        PetscCall(VecResetArray(deluxe_ctx->seq_work1[i]));
      }
      if (deluxe_ctx->change) {
        Mat change;

        PetscCall(KSPGetOperators(deluxe_ctx->change[i],&change,NULL));
        PetscCall(MatMult(change,deluxe_ctx->seq_work2[i],deluxe_ctx->seq_work1[i]));
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work1[i],pcbddc->work_scaling,INSERT_VALUES,SCATTER_REVERSE));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work1[i],pcbddc->work_scaling,INSERT_VALUES,SCATTER_REVERSE));
      } else {
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work2[i],pcbddc->work_scaling,INSERT_VALUES,SCATTER_REVERSE));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work2[i],pcbddc->work_scaling,INSERT_VALUES,SCATTER_REVERSE));
      }
    }
  }
  /* put local boundary part in global vector */
  PetscCall(VecScatterBegin(pcis->global_to_B,pcbddc->work_scaling,y,ADD_VALUES,SCATTER_REVERSE));
  PetscCall(VecScatterEnd(pcis->global_to_B,pcbddc->work_scaling,y,ADD_VALUES,SCATTER_REVERSE));
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCScalingExtension(PC pc, Vec local_interface_vector, Vec global_vector)
{
  PC_BDDC        *pcbddc=(PC_BDDC*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidHeaderSpecific(local_interface_vector,VEC_CLASSID,2);
  PetscValidHeaderSpecific(global_vector,VEC_CLASSID,3);
  PetscCheck(local_interface_vector != pcbddc->work_scaling,PETSC_COMM_SELF,PETSC_ERR_SUP,"Local vector cannot be pcbddc->work_scaling!");
  PetscUseMethod(pc,"PCBDDCScalingExtension_C",(PC,Vec,Vec),(pc,local_interface_vector,global_vector));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingRestriction_Basic(PC pc, Vec global_vector, Vec local_interface_vector)
{
  PC_IS          *pcis = (PC_IS*)pc->data;

  PetscFunctionBegin;
  PetscCall(VecScatterBegin(pcis->global_to_B,global_vector,local_interface_vector,INSERT_VALUES,SCATTER_FORWARD));
  PetscCall(VecScatterEnd(pcis->global_to_B,global_vector,local_interface_vector,INSERT_VALUES,SCATTER_FORWARD));
  /* Apply partition of unity */
  PetscCall(VecPointwiseMult(local_interface_vector,pcis->D,local_interface_vector));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingRestriction_Deluxe(PC pc, Vec x, Vec y)
{
  PC_IS*              pcis=(PC_IS*)pc->data;
  PC_BDDC*            pcbddc=(PC_BDDC*)pc->data;
  PCBDDCDeluxeScaling deluxe_ctx = pcbddc->deluxe_ctx;

  PetscFunctionBegin;
  /* get local boundary part of global vector */
  PetscCall(VecScatterBegin(pcis->global_to_B,x,y,INSERT_VALUES,SCATTER_FORWARD));
  PetscCall(VecScatterEnd(pcis->global_to_B,x,y,INSERT_VALUES,SCATTER_FORWARD));
  if (deluxe_ctx->n_simple) { /* scale deluxe vertices using diagonal scaling */
    PetscInt          i;
    PetscScalar       *array_y;
    const PetscScalar *array_D;
    PetscCall(VecGetArray(y,&array_y));
    PetscCall(VecGetArrayRead(pcis->D,&array_D));
    for (i=0;i<deluxe_ctx->n_simple;i++) {
      array_y[deluxe_ctx->idx_simple_B[i]] *= array_D[deluxe_ctx->idx_simple_B[i]];
    }
    PetscCall(VecRestoreArrayRead(pcis->D,&array_D));
    PetscCall(VecRestoreArray(y,&array_y));
  }
  /* sequential part : all problems and Schur applications collapsed into a single matrix vector multiplication or a matvec and a solve */
  if (deluxe_ctx->seq_mat) {
    PetscInt i;
    for (i=0;i<deluxe_ctx->seq_n;i++) {
      if (deluxe_ctx->change) {
        Mat change;

        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],y,deluxe_ctx->seq_work2[i],INSERT_VALUES,SCATTER_FORWARD));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],y,deluxe_ctx->seq_work2[i],INSERT_VALUES,SCATTER_FORWARD));
        PetscCall(KSPGetOperators(deluxe_ctx->change[i],&change,NULL));
        PetscCall(MatMultTranspose(change,deluxe_ctx->seq_work2[i],deluxe_ctx->seq_work1[i]));
      } else {
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],y,deluxe_ctx->seq_work1[i],INSERT_VALUES,SCATTER_FORWARD));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],y,deluxe_ctx->seq_work1[i],INSERT_VALUES,SCATTER_FORWARD));
      }
      if (deluxe_ctx->seq_mat_inv_sum[i]) {
        PetscScalar *x;

        PetscCall(VecGetArray(deluxe_ctx->seq_work1[i],&x));
        PetscCall(VecPlaceArray(deluxe_ctx->seq_work2[i],x));
        PetscCall(VecRestoreArray(deluxe_ctx->seq_work1[i],&x));
        PetscCall(MatSolve(deluxe_ctx->seq_mat_inv_sum[i],deluxe_ctx->seq_work1[i],deluxe_ctx->seq_work2[i]));
        PetscCall(VecResetArray(deluxe_ctx->seq_work2[i]));
      }
      PetscCall(MatMult(deluxe_ctx->seq_mat[i],deluxe_ctx->seq_work1[i],deluxe_ctx->seq_work2[i]));
      if (deluxe_ctx->change) {
        if (deluxe_ctx->change_with_qr) {
          Mat change;

          PetscCall(KSPGetOperators(deluxe_ctx->change[i],&change,NULL));
          PetscCall(MatMult(change,deluxe_ctx->seq_work2[i],deluxe_ctx->seq_work1[i]));
        } else {
          PetscCall(KSPSolveTranspose(deluxe_ctx->change[i],deluxe_ctx->seq_work2[i],deluxe_ctx->seq_work1[i]));
        }
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work1[i],y,INSERT_VALUES,SCATTER_REVERSE));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work1[i],y,INSERT_VALUES,SCATTER_REVERSE));
      } else {
        PetscCall(VecScatterBegin(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work2[i],y,INSERT_VALUES,SCATTER_REVERSE));
        PetscCall(VecScatterEnd(deluxe_ctx->seq_scctx[i],deluxe_ctx->seq_work2[i],y,INSERT_VALUES,SCATTER_REVERSE));
      }
    }
  }
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCScalingRestriction(PC pc, Vec global_vector, Vec local_interface_vector)
{
  PC_BDDC        *pcbddc=(PC_BDDC*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidHeaderSpecific(global_vector,VEC_CLASSID,2);
  PetscValidHeaderSpecific(local_interface_vector,VEC_CLASSID,3);
  PetscCheck(local_interface_vector != pcbddc->work_scaling,PETSC_COMM_SELF,PETSC_ERR_SUP,"Local vector cannot be pcbddc->work_scaling!");
  PetscUseMethod(pc,"PCBDDCScalingRestriction_C",(PC,Vec,Vec),(pc,global_vector,local_interface_vector));
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCScalingSetUp(PC pc)
{
  PC_IS*         pcis=(PC_IS*)pc->data;
  PC_BDDC*       pcbddc=(PC_BDDC*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscCall(PetscLogEventBegin(PC_BDDC_Scaling[pcbddc->current_level],pc,0,0,0));
  /* create work vector for the operator */
  PetscCall(VecDestroy(&pcbddc->work_scaling));
  PetscCall(VecDuplicate(pcis->vec1_B,&pcbddc->work_scaling));
  /* always rebuild pcis->D */
  if (pcis->use_stiffness_scaling) {
    PetscScalar *a;
    PetscInt    i,n;

    PetscCall(MatGetDiagonal(pcbddc->local_mat,pcis->vec1_N));
    PetscCall(VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->D,INSERT_VALUES,SCATTER_FORWARD));
    PetscCall(VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->D,INSERT_VALUES,SCATTER_FORWARD));
    PetscCall(VecAbs(pcis->D));
    PetscCall(VecGetLocalSize(pcis->D,&n));
    PetscCall(VecGetArray(pcis->D,&a));
    for (i=0;i<n;i++) if (PetscAbsScalar(a[i])<PETSC_SMALL) a[i] = 1.0;
    PetscCall(VecRestoreArray(pcis->D,&a));
  }
  PetscCall(VecSet(pcis->vec1_global,0.0));
  PetscCall(VecScatterBegin(pcis->global_to_B,pcis->D,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
  PetscCall(VecScatterEnd(pcis->global_to_B,pcis->D,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
  PetscCall(VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD));
  PetscCall(VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD));
  PetscCall(VecPointwiseDivide(pcis->D,pcis->D,pcis->vec1_B));
  /* now setup */
  if (pcbddc->use_deluxe_scaling) {
    if (!pcbddc->deluxe_ctx) {
      PetscCall(PCBDDCScalingCreate_Deluxe(pc));
    }
    PetscCall(PCBDDCScalingSetUp_Deluxe(pc));
    PetscCall(PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingRestriction_C",PCBDDCScalingRestriction_Deluxe));
    PetscCall(PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingExtension_C",PCBDDCScalingExtension_Deluxe));
  } else {
    PetscCall(PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingRestriction_C",PCBDDCScalingRestriction_Basic));
    PetscCall(PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingExtension_C",PCBDDCScalingExtension_Basic));
  }
  PetscCall(PetscLogEventEnd(PC_BDDC_Scaling[pcbddc->current_level],pc,0,0,0));

  /* test */
  if (pcbddc->dbg_flag) {
    Mat         B0_B = NULL;
    Vec         B0_Bv = NULL, B0_Bv2 = NULL;
    Vec         vec2_global;
    PetscViewer viewer = pcbddc->dbg_viewer;
    PetscReal   error;

    /* extension -> from local to parallel */
    PetscCall(VecSet(pcis->vec1_global,0.0));
    PetscCall(VecSetRandom(pcis->vec1_B,NULL));
    PetscCall(VecScatterBegin(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
    PetscCall(VecScatterEnd(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
    PetscCall(VecDuplicate(pcis->vec1_global,&vec2_global));
    PetscCall(VecCopy(pcis->vec1_global,vec2_global));
    PetscCall(VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD));
    PetscCall(VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD));
    if (pcbddc->benign_n) {
      IS is_dummy;

      PetscCall(ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy));
      PetscCall(MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B));
      PetscCall(ISDestroy(&is_dummy));
      PetscCall(MatCreateVecs(B0_B,NULL,&B0_Bv));
      PetscCall(VecDuplicate(B0_Bv,&B0_Bv2));
      PetscCall(MatMult(B0_B,pcis->vec1_B,B0_Bv));
    }
    PetscCall(PCBDDCScalingExtension(pc,pcis->vec1_B,pcis->vec1_global));
    if (pcbddc->benign_saddle_point) {
      PetscReal errorl = 0.;
      PetscCall(VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD));
      PetscCall(VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD));
      if (pcbddc->benign_n) {
        PetscCall(MatMult(B0_B,pcis->vec1_B,B0_Bv2));
        PetscCall(VecAXPY(B0_Bv,-1.0,B0_Bv2));
        PetscCall(VecNorm(B0_Bv,NORM_INFINITY,&errorl));
      }
      PetscCallMPI(MPI_Allreduce(&errorl,&error,1,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)pc)));
      PetscCall(PetscViewerASCIIPrintf(viewer,"Error benign extension %1.14e\n",(double)error));
    }
    PetscCall(VecAXPY(pcis->vec1_global,-1.0,vec2_global));
    PetscCall(VecNorm(pcis->vec1_global,NORM_INFINITY,&error));
    PetscCall(PetscViewerASCIIPrintf(viewer,"Error scaling extension %1.14e\n",(double)error));
    PetscCall(VecDestroy(&vec2_global));

    /* restriction -> from parallel to local */
    PetscCall(VecSet(pcis->vec1_global,0.0));
    PetscCall(VecSetRandom(pcis->vec1_B,NULL));
    PetscCall(VecScatterBegin(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
    PetscCall(VecScatterEnd(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
    PetscCall(PCBDDCScalingRestriction(pc,pcis->vec1_global,pcis->vec1_B));
    PetscCall(VecScale(pcis->vec1_B,-1.0));
    PetscCall(VecScatterBegin(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
    PetscCall(VecScatterEnd(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE));
    PetscCall(VecNorm(pcis->vec1_global,NORM_INFINITY,&error));
    PetscCall(PetscViewerASCIIPrintf(viewer,"Error scaling restriction %1.14e\n",(double)error));
    PetscCall(MatDestroy(&B0_B));
    PetscCall(VecDestroy(&B0_Bv));
    PetscCall(VecDestroy(&B0_Bv2));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode PCBDDCScalingDestroy(PC pc)
{
  PC_BDDC*       pcbddc=(PC_BDDC*)pc->data;

  PetscFunctionBegin;
  if (pcbddc->deluxe_ctx) {
    PetscCall(PCBDDCScalingDestroy_Deluxe(pc));
  }
  PetscCall(VecDestroy(&pcbddc->work_scaling));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingRestriction_C",NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingExtension_C",NULL));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingCreate_Deluxe(PC pc)
{
  PC_BDDC*            pcbddc=(PC_BDDC*)pc->data;
  PCBDDCDeluxeScaling deluxe_ctx;

  PetscFunctionBegin;
  PetscCall(PetscNew(&deluxe_ctx));
  pcbddc->deluxe_ctx = deluxe_ctx;
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingDestroy_Deluxe(PC pc)
{
  PC_BDDC*            pcbddc=(PC_BDDC*)pc->data;

  PetscFunctionBegin;
  PetscCall(PCBDDCScalingReset_Deluxe_Solvers(pcbddc->deluxe_ctx));
  PetscCall(PetscFree(pcbddc->deluxe_ctx));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingReset_Deluxe_Solvers(PCBDDCDeluxeScaling deluxe_ctx)
{
  PetscInt       i;

  PetscFunctionBegin;
  PetscCall(PetscFree(deluxe_ctx->idx_simple_B));
  deluxe_ctx->n_simple = 0;
  for (i=0;i<deluxe_ctx->seq_n;i++) {
    PetscCall(VecScatterDestroy(&deluxe_ctx->seq_scctx[i]));
    PetscCall(VecDestroy(&deluxe_ctx->seq_work1[i]));
    PetscCall(VecDestroy(&deluxe_ctx->seq_work2[i]));
    PetscCall(MatDestroy(&deluxe_ctx->seq_mat[i]));
    PetscCall(MatDestroy(&deluxe_ctx->seq_mat_inv_sum[i]));
  }
  PetscCall(PetscFree5(deluxe_ctx->seq_scctx,deluxe_ctx->seq_work1,deluxe_ctx->seq_work2,deluxe_ctx->seq_mat,deluxe_ctx->seq_mat_inv_sum));
  PetscCall(PetscFree(deluxe_ctx->workspace));
  deluxe_ctx->seq_n = 0;
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingSetUp_Deluxe(PC pc)
{
  PC_IS               *pcis=(PC_IS*)pc->data;
  PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
  PCBDDCDeluxeScaling deluxe_ctx=pcbddc->deluxe_ctx;
  PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;

  PetscFunctionBegin;
  /* reset data structures if the topology has changed */
  if (pcbddc->recompute_topography) {
    PetscCall(PCBDDCScalingReset_Deluxe_Solvers(deluxe_ctx));
  }

  /* Compute data structures to solve sequential problems */
  PetscCall(PCBDDCScalingSetUp_Deluxe_Private(pc));

  /* diagonal scaling on interface dofs not contained in cc */
  if (sub_schurs->is_vertices || sub_schurs->is_dir) {
    PetscInt n_com,n_dir;
    n_com = 0;
    if (sub_schurs->is_vertices) {
      PetscCall(ISGetLocalSize(sub_schurs->is_vertices,&n_com));
    }
    n_dir = 0;
    if (sub_schurs->is_dir) {
      PetscCall(ISGetLocalSize(sub_schurs->is_dir,&n_dir));
    }
    if (!deluxe_ctx->n_simple) {
      deluxe_ctx->n_simple = n_dir + n_com;
      PetscCall(PetscMalloc1(deluxe_ctx->n_simple,&deluxe_ctx->idx_simple_B));
      if (sub_schurs->is_vertices) {
        PetscInt       nmap;
        const PetscInt *idxs;

        PetscCall(ISGetIndices(sub_schurs->is_vertices,&idxs));
        PetscCall(ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_com,idxs,&nmap,deluxe_ctx->idx_simple_B));
        PetscCheck(nmap == n_com,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error when mapping simply scaled dofs (is_vertices)! %" PetscInt_FMT " != %" PetscInt_FMT,nmap,n_com);
        PetscCall(ISRestoreIndices(sub_schurs->is_vertices,&idxs));
      }
      if (sub_schurs->is_dir) {
        PetscInt       nmap;
        const PetscInt *idxs;

        PetscCall(ISGetIndices(sub_schurs->is_dir,&idxs));
        PetscCall(ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_dir,idxs,&nmap,deluxe_ctx->idx_simple_B+n_com));
        PetscCheck(nmap == n_dir,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error when mapping simply scaled dofs (sub_schurs->is_dir)! %" PetscInt_FMT " != %" PetscInt_FMT,nmap,n_dir);
        PetscCall(ISRestoreIndices(sub_schurs->is_dir,&idxs));
      }
      PetscCall(PetscSortInt(deluxe_ctx->n_simple,deluxe_ctx->idx_simple_B));
    } else {
      PetscCheck(deluxe_ctx->n_simple == n_dir + n_com,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of simply scaled dofs %" PetscInt_FMT " is different from the previous one computed %" PetscInt_FMT,n_dir + n_com,deluxe_ctx->n_simple);
    }
  } else {
    deluxe_ctx->n_simple = 0;
    deluxe_ctx->idx_simple_B = NULL;
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode PCBDDCScalingSetUp_Deluxe_Private(PC pc)
{
  PC_BDDC                *pcbddc=(PC_BDDC*)pc->data;
  PCBDDCDeluxeScaling    deluxe_ctx=pcbddc->deluxe_ctx;
  PCBDDCSubSchurs        sub_schurs = pcbddc->sub_schurs;
  PetscScalar            *matdata,*matdata2;
  PetscInt               i,max_subset_size,cum,cum2;
  const PetscInt         *idxs;
  PetscBool              newsetup = PETSC_FALSE;

  PetscFunctionBegin;
  PetscCheck(sub_schurs,PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Missing PCBDDCSubSchurs");
  if (!sub_schurs->n_subs) PetscFunctionReturn(0);

  /* Allocate arrays for subproblems */
  if (!deluxe_ctx->seq_n) {
    deluxe_ctx->seq_n = sub_schurs->n_subs;
    PetscCall(PetscCalloc5(deluxe_ctx->seq_n,&deluxe_ctx->seq_scctx,deluxe_ctx->seq_n,&deluxe_ctx->seq_work1,deluxe_ctx->seq_n,&deluxe_ctx->seq_work2,deluxe_ctx->seq_n,&deluxe_ctx->seq_mat,deluxe_ctx->seq_n,&deluxe_ctx->seq_mat_inv_sum));
    newsetup = PETSC_TRUE;
  } else PetscCheck(deluxe_ctx->seq_n == sub_schurs->n_subs,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of deluxe subproblems %" PetscInt_FMT " is different from the sub_schurs %" PetscInt_FMT,deluxe_ctx->seq_n,sub_schurs->n_subs);

  /* the change of basis is just a reference to sub_schurs->change (if any) */
  deluxe_ctx->change         = sub_schurs->change;
  deluxe_ctx->change_with_qr = sub_schurs->change_with_qr;

  /* Create objects for deluxe */
  max_subset_size = 0;
  for (i=0;i<sub_schurs->n_subs;i++) {
    PetscInt subset_size;
    PetscCall(ISGetLocalSize(sub_schurs->is_subs[i],&subset_size));
    max_subset_size = PetscMax(subset_size,max_subset_size);
  }
  if (newsetup) {
    PetscCall(PetscMalloc1(2*max_subset_size,&deluxe_ctx->workspace));
  }
  cum = cum2 = 0;
  PetscCall(ISGetIndices(sub_schurs->is_Ej_all,&idxs));
  PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all,&matdata));
  PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&matdata2));
  for (i=0;i<deluxe_ctx->seq_n;i++) {
    PetscInt     subset_size;

    PetscCall(ISGetLocalSize(sub_schurs->is_subs[i],&subset_size));
    if (newsetup) {
      IS  sub;
      /* work vectors */
      PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,deluxe_ctx->workspace,&deluxe_ctx->seq_work1[i]));
      PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,deluxe_ctx->workspace+subset_size,&deluxe_ctx->seq_work2[i]));

      /* scatters */
      PetscCall(ISCreateGeneral(PETSC_COMM_SELF,subset_size,idxs+cum,PETSC_COPY_VALUES,&sub));
      PetscCall(VecScatterCreate(pcbddc->work_scaling,sub,deluxe_ctx->seq_work1[i],NULL,&deluxe_ctx->seq_scctx[i]));
      PetscCall(ISDestroy(&sub));
    }

    /* S_E_j */
    PetscCall(MatDestroy(&deluxe_ctx->seq_mat[i]));
    PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,matdata+cum2,&deluxe_ctx->seq_mat[i]));

    /* \sum_k S^k_E_j */
    PetscCall(MatDestroy(&deluxe_ctx->seq_mat_inv_sum[i]));
    PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,matdata2+cum2,&deluxe_ctx->seq_mat_inv_sum[i]));
    PetscCall(MatSetOption(deluxe_ctx->seq_mat_inv_sum[i],MAT_SPD,sub_schurs->is_posdef));
    PetscCall(MatSetOption(deluxe_ctx->seq_mat_inv_sum[i],MAT_HERMITIAN,sub_schurs->is_hermitian));
    if (sub_schurs->is_hermitian) {
      PetscCall(MatCholeskyFactor(deluxe_ctx->seq_mat_inv_sum[i],NULL,NULL));
    } else {
      PetscCall(MatLUFactor(deluxe_ctx->seq_mat_inv_sum[i],NULL,NULL,NULL));
    }
    if (pcbddc->deluxe_singlemat) {
      Mat X,Y;
      if (!sub_schurs->is_hermitian) {
        PetscCall(MatTranspose(deluxe_ctx->seq_mat[i],MAT_INITIAL_MATRIX,&X));
      } else {
        PetscCall(PetscObjectReference((PetscObject)deluxe_ctx->seq_mat[i]));
        X    = deluxe_ctx->seq_mat[i];
      }
      PetscCall(MatDuplicate(X,MAT_DO_NOT_COPY_VALUES,&Y));
      if (!sub_schurs->is_hermitian) {
        PetscCall(PCBDDCMatTransposeMatSolve_SeqDense(deluxe_ctx->seq_mat_inv_sum[i],X,Y));
      } else {
        PetscCall(MatMatSolve(deluxe_ctx->seq_mat_inv_sum[i],X,Y));
      }

      PetscCall(MatDestroy(&deluxe_ctx->seq_mat_inv_sum[i]));
      PetscCall(MatDestroy(&deluxe_ctx->seq_mat[i]));
      PetscCall(MatDestroy(&X));
      if (deluxe_ctx->change) {
        Mat C,CY;
        PetscCheck(deluxe_ctx->change_with_qr,PETSC_COMM_SELF,PETSC_ERR_SUP,"Only QR based change of basis");
        PetscCall(KSPGetOperators(deluxe_ctx->change[i],&C,NULL));
        PetscCall(MatMatMult(C,Y,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&CY));
        PetscCall(MatMatTransposeMult(CY,C,MAT_REUSE_MATRIX,PETSC_DEFAULT,&Y));
        PetscCall(MatDestroy(&CY));
        PetscCall(MatProductClear(Y)); /* clear internal matproduct structure of Y since CY is destroyed */
      }
      PetscCall(MatTranspose(Y,MAT_INPLACE_MATRIX,&Y));
      deluxe_ctx->seq_mat[i] = Y;
    }
    cum += subset_size;
    cum2 += subset_size*subset_size;
  }
  PetscCall(ISRestoreIndices(sub_schurs->is_Ej_all,&idxs));
  PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&matdata));
  PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&matdata2));
  if (pcbddc->deluxe_singlemat) {
    deluxe_ctx->change         = NULL;
    deluxe_ctx->change_with_qr = PETSC_FALSE;
  }

  if (deluxe_ctx->change && !deluxe_ctx->change_with_qr) {
    for (i=0;i<deluxe_ctx->seq_n;i++) {
      if (newsetup) {
        PC pc;

        PetscCall(KSPGetPC(deluxe_ctx->change[i],&pc));
        PetscCall(PCSetType(pc,PCLU));
        PetscCall(KSPSetFromOptions(deluxe_ctx->change[i]));
      }
      PetscCall(KSPSetUp(deluxe_ctx->change[i]));
    }
  }
  PetscFunctionReturn(0);
}