xref: /petsc/src/mat/impls/sell/seq/sell.c (revision c0aa6a63a7860d309a895cb4aa0f9e11e7859f3a)

/*
  Defines the basic matrix operations for the SELL matrix storage format.
*/
#include <../src/mat/impls/sell/seq/sell.h>  /*I   "petscmat.h"  I*/
#include <petscblaslapack.h>
#include <petsc/private/kernels/blocktranspose.h>
#if defined(PETSC_HAVE_IMMINTRIN_H) && (defined(__AVX512F__) || (defined(__AVX2__) && defined(__FMA__)) || defined(__AVX__)) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)

  #include <immintrin.h>

  #if !defined(_MM_SCALE_8)
  #define _MM_SCALE_8    8
  #endif

  #if defined(__AVX512F__)
  /* these do not work
   vec_idx  = _mm512_loadunpackhi_epi32(vec_idx,acolidx);
   vec_vals = _mm512_loadunpackhi_pd(vec_vals,aval);
  */
    #define AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y) \
    /* if the mask bit is set, copy from acolidx, otherwise from vec_idx */ \
    vec_idx  = _mm256_loadu_si256((__m256i const*)acolidx); \
    vec_vals = _mm512_loadu_pd(aval); \
    vec_x    = _mm512_i32gather_pd(vec_idx,x,_MM_SCALE_8); \
    vec_y    = _mm512_fmadd_pd(vec_x,vec_vals,vec_y)
  #elif defined(__AVX2__) && defined(__FMA__)
    #define AVX2_Mult_Private(vec_idx,vec_x,vec_vals,vec_y) \
    vec_vals = _mm256_loadu_pd(aval); \
    vec_idx  = _mm_loadu_si128((__m128i const*)acolidx); /* SSE2 */ \
    vec_x    = _mm256_i32gather_pd(x,vec_idx,_MM_SCALE_8); \
    vec_y    = _mm256_fmadd_pd(vec_x,vec_vals,vec_y)
  #endif
#endif  /* PETSC_HAVE_IMMINTRIN_H */

/*@C
 MatSeqSELLSetPreallocation - For good matrix assembly performance
 the user should preallocate the matrix storage by setting the parameter nz
 (or the array nnz).  By setting these parameters accurately, performance
 during matrix assembly can be increased significantly.

 Collective

 Input Parameters:
 +  B - The matrix
 .  nz - number of nonzeros per row (same for all rows)
 -  nnz - array containing the number of nonzeros in the various rows
 (possibly different for each row) or NULL

 Notes:
 If nnz is given then nz is ignored.

 Specify the preallocated storage with either nz or nnz (not both).
 Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
 allocation.  For large problems you MUST preallocate memory or you
 will get TERRIBLE performance, see the users' manual chapter on matrices.

 You can call MatGetInfo() to get information on how effective the preallocation was;
 for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
 You can also run with the option -info and look for messages with the string
 malloc in them to see if additional memory allocation was needed.

 Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
 entries or columns indices.

 The maximum number of nonzeos in any row should be as accurate as possible.
 If it is underestimated, you will get bad performance due to reallocation
 (MatSeqXSELLReallocateSELL).

 Level: intermediate

 .seealso: MatCreate(), MatCreateSELL(), MatSetValues(), MatGetInfo()

 @*/
PetscErrorCode MatSeqSELLSetPreallocation(Mat B,PetscInt rlenmax,const PetscInt rlen[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(B,MAT_CLASSID,1);
  PetscValidType(B,1);
  ierr = PetscTryMethod(B,"MatSeqSELLSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,rlenmax,rlen));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSeqSELLSetPreallocation_SeqSELL(Mat B,PetscInt maxallocrow,const PetscInt rlen[])
{
  Mat_SeqSELL    *b;
  PetscInt       i,j,totalslices;
  PetscBool      skipallocation=PETSC_FALSE,realalloc=PETSC_FALSE;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (maxallocrow >= 0 || rlen) realalloc = PETSC_TRUE;
  if (maxallocrow == MAT_SKIP_ALLOCATION) {
    skipallocation = PETSC_TRUE;
    maxallocrow    = 0;
  }

  ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);

  /* FIXME: if one preallocates more space than needed, the matrix does not shrink automatically, but for best performance it should */
  if (maxallocrow == PETSC_DEFAULT || maxallocrow == PETSC_DECIDE) maxallocrow = 5;
  if (maxallocrow < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"maxallocrow cannot be less than 0: value %" PetscInt_FMT,maxallocrow);
  if (rlen) {
    for (i=0; i<B->rmap->n; i++) {
      if (rlen[i] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"rlen cannot be less than 0: local row %" PetscInt_FMT " value %" PetscInt_FMT,i,rlen[i]);
      if (rlen[i] > B->cmap->n) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"rlen cannot be greater than row length: local row %" PetscInt_FMT " value %" PetscInt_FMT " rowlength %" PetscInt_FMT,i,rlen[i],B->cmap->n);
    }
  }

  B->preallocated = PETSC_TRUE;

  b = (Mat_SeqSELL*)B->data;

  totalslices = B->rmap->n/8+((B->rmap->n & 0x07)?1:0); /* ceil(n/8) */
  b->totalslices = totalslices;
  if (!skipallocation) {
    if (B->rmap->n & 0x07) {ierr = PetscInfo1(B,"Padding rows to the SEQSELL matrix because the number of rows is not the multiple of 8 (value %" PetscInt_FMT ")\n",B->rmap->n);CHKERRQ(ierr);}

    if (!b->sliidx) { /* sliidx gives the starting index of each slice, the last element is the total space allocated */
      ierr = PetscMalloc1(totalslices+1,&b->sliidx);CHKERRQ(ierr);
      ierr = PetscLogObjectMemory((PetscObject)B,(totalslices+1)*sizeof(PetscInt));CHKERRQ(ierr);
    }
    if (!rlen) { /* if rlen is not provided, allocate same space for all the slices */
      if (maxallocrow == PETSC_DEFAULT || maxallocrow == PETSC_DECIDE) maxallocrow = 10;
      else if (maxallocrow < 0) maxallocrow = 1;
      for (i=0; i<=totalslices; i++) b->sliidx[i] = i*8*maxallocrow;
    } else {
      maxallocrow = 0;
      b->sliidx[0] = 0;
      for (i=1; i<totalslices; i++) {
        b->sliidx[i] = 0;
        for (j=0;j<8;j++) {
          b->sliidx[i] = PetscMax(b->sliidx[i],rlen[8*(i-1)+j]);
        }
        maxallocrow = PetscMax(b->sliidx[i],maxallocrow);
        ierr = PetscIntSumError(b->sliidx[i-1],8*b->sliidx[i],&b->sliidx[i]);CHKERRQ(ierr);
      }
      /* last slice */
      b->sliidx[totalslices] = 0;
      for (j=(totalslices-1)*8;j<B->rmap->n;j++) b->sliidx[totalslices] = PetscMax(b->sliidx[totalslices],rlen[j]);
      maxallocrow = PetscMax(b->sliidx[totalslices],maxallocrow);
      b->sliidx[totalslices] = b->sliidx[totalslices-1] + 8*b->sliidx[totalslices];
    }

    /* allocate space for val, colidx, rlen */
    /* FIXME: should B's old memory be unlogged? */
    ierr = MatSeqXSELLFreeSELL(B,&b->val,&b->colidx);CHKERRQ(ierr);
    /* FIXME: assuming an element of the bit array takes 8 bits */
    ierr = PetscMalloc2(b->sliidx[totalslices],&b->val,b->sliidx[totalslices],&b->colidx);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)B,b->sliidx[totalslices]*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
    /* b->rlen will count nonzeros in each row so far. We dont copy rlen to b->rlen because the matrix has not been set. */
    ierr = PetscCalloc1(8*totalslices,&b->rlen);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)B,8*totalslices*sizeof(PetscInt));CHKERRQ(ierr);

    b->singlemalloc = PETSC_TRUE;
    b->free_val     = PETSC_TRUE;
    b->free_colidx  = PETSC_TRUE;
  } else {
    b->free_val    = PETSC_FALSE;
    b->free_colidx = PETSC_FALSE;
  }

  b->nz               = 0;
  b->maxallocrow      = maxallocrow;
  b->rlenmax          = maxallocrow;
  b->maxallocmat      = b->sliidx[totalslices];
  B->info.nz_unneeded = (double)b->maxallocmat;
  if (realalloc) {
    ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetRow_SeqSELL(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
{
  Mat_SeqSELL *a = (Mat_SeqSELL*)A->data;
  PetscInt    shift;

  PetscFunctionBegin;
  if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %" PetscInt_FMT " out of range",row);
  if (nz) *nz = a->rlen[row];
  shift = a->sliidx[row>>3]+(row&0x07);
  if (!a->getrowcols) {
    PetscErrorCode ierr;

    ierr = PetscMalloc2(a->rlenmax,&a->getrowcols,a->rlenmax,&a->getrowvals);CHKERRQ(ierr);
  }
  if (idx) {
    PetscInt j;
    for (j=0; j<a->rlen[row]; j++) a->getrowcols[j] = a->colidx[shift+8*j];
    *idx = a->getrowcols;
  }
  if (v) {
    PetscInt j;
    for (j=0; j<a->rlen[row]; j++) a->getrowvals[j] = a->val[shift+8*j];
    *v = a->getrowvals;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatRestoreRow_SeqSELL(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

PetscErrorCode MatConvert_SeqSELL_SeqAIJ(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
{
  Mat            B;
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (reuse == MAT_REUSE_MATRIX) {
    B    = *newmat;
    ierr = MatZeroEntries(B);CHKERRQ(ierr);
  } else {
    ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
    ierr = MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
    ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
    ierr = MatSeqAIJSetPreallocation(B,0,a->rlen);CHKERRQ(ierr);
  }

  for (i=0; i<A->rmap->n; i++) {
    PetscInt    nz = 0,*cols = NULL;
    PetscScalar *vals = NULL;

    ierr = MatGetRow_SeqSELL(A,i,&nz,&cols,&vals);CHKERRQ(ierr);
    ierr = MatSetValues(B,1,&i,nz,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatRestoreRow_SeqSELL(A,i,&nz,&cols,&vals);CHKERRQ(ierr);
  }

  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  B->rmap->bs = A->rmap->bs;

  if (reuse == MAT_INPLACE_MATRIX) {
    ierr = MatHeaderReplace(A,&B);CHKERRQ(ierr);
  } else {
    *newmat = B;
  }
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/seq/aij.h>

PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat A,MatType newtype,MatReuse reuse,Mat *newmat)
{
  Mat               B;
  Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
  PetscInt          *ai=a->i,m=A->rmap->N,n=A->cmap->N,i,*rowlengths,row,ncols;
  const PetscInt    *cols;
  const PetscScalar *vals;
  PetscErrorCode    ierr;

  PetscFunctionBegin;

  if (reuse == MAT_REUSE_MATRIX) {
    B = *newmat;
  } else {
    /* Can we just use ilen? */
    ierr = PetscMalloc1(m,&rowlengths);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      rowlengths[i] = ai[i+1] - ai[i];
    }

    ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
    ierr = MatSetSizes(B,m,n,m,n);CHKERRQ(ierr);
    ierr = MatSetType(B,MATSEQSELL);CHKERRQ(ierr);
    ierr = MatSeqSELLSetPreallocation(B,0,rowlengths);CHKERRQ(ierr);
    ierr = PetscFree(rowlengths);CHKERRQ(ierr);
  }

  for (row=0; row<m; row++) {
    ierr = MatGetRow(A,row,&ncols,&cols,&vals);CHKERRQ(ierr);
    ierr = MatSetValues(B,1,&row,ncols,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatRestoreRow(A,row,&ncols,&cols,&vals);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  B->rmap->bs = A->rmap->bs;

  if (reuse == MAT_INPLACE_MATRIX) {
    ierr = MatHeaderReplace(A,&B);CHKERRQ(ierr);
  } else {
    *newmat = B;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatMult_SeqSELL(Mat A,Vec xx,Vec yy)
{
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  PetscScalar       *y;
  const PetscScalar *x;
  const MatScalar   *aval=a->val;
  PetscInt          totalslices=a->totalslices;
  const PetscInt    *acolidx=a->colidx;
  PetscInt          i,j;
  PetscErrorCode    ierr;
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  __m512d           vec_x,vec_y,vec_vals;
  __m256i           vec_idx;
  __mmask8          mask;
  __m512d           vec_x2,vec_y2,vec_vals2,vec_x3,vec_y3,vec_vals3,vec_x4,vec_y4,vec_vals4;
  __m256i           vec_idx2,vec_idx3,vec_idx4;
#elif defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  __m128i           vec_idx;
  __m256d           vec_x,vec_y,vec_y2,vec_vals;
  MatScalar         yval;
  PetscInt          r,rows_left,row,nnz_in_row;
#elif defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  __m128d           vec_x_tmp;
  __m256d           vec_x,vec_y,vec_y2,vec_vals;
  MatScalar         yval;
  PetscInt          r,rows_left,row,nnz_in_row;
#else
  PetscScalar       sum[8];
#endif

#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
#pragma disjoint(*x,*y,*aval)
#endif

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  for (i=0; i<totalslices; i++) { /* loop over slices */
    PetscPrefetchBlock(acolidx,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);
    PetscPrefetchBlock(aval,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);

    vec_y  = _mm512_setzero_pd();
    vec_y2 = _mm512_setzero_pd();
    vec_y3 = _mm512_setzero_pd();
    vec_y4 = _mm512_setzero_pd();

    j = a->sliidx[i]>>3; /* 8 bytes are read at each time, corresponding to a slice columnn */
    switch ((a->sliidx[i+1]-a->sliidx[i])/8 & 3) {
    case 3:
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx2,vec_x2,vec_vals2,vec_y2);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx3,vec_x3,vec_vals3,vec_y3);
      acolidx += 8; aval += 8;
      j += 3;
      break;
    case 2:
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx2,vec_x2,vec_vals2,vec_y2);
      acolidx += 8; aval += 8;
      j += 2;
      break;
    case 1:
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      j += 1;
      break;
    }
    #pragma novector
    for (; j<(a->sliidx[i+1]>>3); j+=4) {
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx2,vec_x2,vec_vals2,vec_y2);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx3,vec_x3,vec_vals3,vec_y3);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx4,vec_x4,vec_vals4,vec_y4);
      acolidx += 8; aval += 8;
    }

    vec_y = _mm512_add_pd(vec_y,vec_y2);
    vec_y = _mm512_add_pd(vec_y,vec_y3);
    vec_y = _mm512_add_pd(vec_y,vec_y4);
    if (i == totalslices-1 && A->rmap->n & 0x07) { /* if last slice has padding rows */
      mask = (__mmask8)(0xff >> (8-(A->rmap->n & 0x07)));
      _mm512_mask_storeu_pd(&y[8*i],mask,vec_y);
    } else {
      _mm512_storeu_pd(&y[8*i],vec_y);
    }
  }
#elif defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  for (i=0; i<totalslices; i++) { /* loop over full slices */
    PetscPrefetchBlock(acolidx,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);
    PetscPrefetchBlock(aval,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);

    /* last slice may have padding rows. Don't use vectorization. */
    if (i == totalslices-1 && (A->rmap->n & 0x07)) {
      rows_left = A->rmap->n - 8*i;
      for (r=0; r<rows_left; ++r) {
        yval = (MatScalar)0;
        row = 8*i + r;
        nnz_in_row = a->rlen[row];
        for (j=0; j<nnz_in_row; ++j) yval += aval[8*j+r] * x[acolidx[8*j+r]];
        y[row] = yval;
      }
      break;
    }

    vec_y  = _mm256_setzero_pd();
    vec_y2 = _mm256_setzero_pd();

    /* Process slice of height 8 (512 bits) via two subslices of height 4 (256 bits) via AVX */
    #pragma novector
    #pragma unroll(2)
    for (j=a->sliidx[i]; j<a->sliidx[i+1]; j+=8) {
      AVX2_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      aval += 4; acolidx += 4;
      AVX2_Mult_Private(vec_idx,vec_x,vec_vals,vec_y2);
      aval += 4; acolidx += 4;
    }

    _mm256_storeu_pd(y+i*8,vec_y);
    _mm256_storeu_pd(y+i*8+4,vec_y2);
  }
#elif defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  for (i=0; i<totalslices; i++) { /* loop over full slices */
    PetscPrefetchBlock(acolidx,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);
    PetscPrefetchBlock(aval,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);

    vec_y  = _mm256_setzero_pd();
    vec_y2 = _mm256_setzero_pd();

    /* last slice may have padding rows. Don't use vectorization. */
    if (i == totalslices-1 && (A->rmap->n & 0x07)) {
      rows_left = A->rmap->n - 8*i;
      for (r=0; r<rows_left; ++r) {
        yval = (MatScalar)0;
        row = 8*i + r;
        nnz_in_row = a->rlen[row];
        for (j=0; j<nnz_in_row; ++j) yval += aval[8*j + r] * x[acolidx[8*j + r]];
        y[row] = yval;
      }
      break;
    }

    /* Process slice of height 8 (512 bits) via two subslices of height 4 (256 bits) via AVX */
    #pragma novector
    #pragma unroll(2)
    for (j=a->sliidx[i]; j<a->sliidx[i+1]; j+=8) {
      vec_vals  = _mm256_loadu_pd(aval);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,0);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,1);
      vec_y     = _mm256_add_pd(_mm256_mul_pd(vec_x,vec_vals),vec_y);
      aval     += 4;

      vec_vals  = _mm256_loadu_pd(aval);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,0);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,1);
      vec_y2    = _mm256_add_pd(_mm256_mul_pd(vec_x,vec_vals),vec_y2);
      aval     += 4;
    }

    _mm256_storeu_pd(y + i*8,     vec_y);
    _mm256_storeu_pd(y + i*8 + 4, vec_y2);
  }
#else
  for (i=0; i<totalslices; i++) { /* loop over slices */
    for (j=0; j<8; j++) sum[j] = 0.0;
    for (j=a->sliidx[i]; j<a->sliidx[i+1]; j+=8) {
      sum[0] += aval[j] * x[acolidx[j]];
      sum[1] += aval[j+1] * x[acolidx[j+1]];
      sum[2] += aval[j+2] * x[acolidx[j+2]];
      sum[3] += aval[j+3] * x[acolidx[j+3]];
      sum[4] += aval[j+4] * x[acolidx[j+4]];
      sum[5] += aval[j+5] * x[acolidx[j+5]];
      sum[6] += aval[j+6] * x[acolidx[j+6]];
      sum[7] += aval[j+7] * x[acolidx[j+7]];
    }
    if (i == totalslices-1 && (A->rmap->n & 0x07)) { /* if last slice has padding rows */
      for (j=0; j<(A->rmap->n & 0x07); j++) y[8*i+j] = sum[j];
    } else {
      for (j=0; j<8; j++) y[8*i+j] = sum[j];
    }
  }
#endif

  ierr = PetscLogFlops(2.0*a->nz-a->nonzerorowcnt);CHKERRQ(ierr); /* theoretical minimal FLOPs */
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
PetscErrorCode MatMultAdd_SeqSELL(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  PetscScalar       *y,*z;
  const PetscScalar *x;
  const MatScalar   *aval=a->val;
  PetscInt          totalslices=a->totalslices;
  const PetscInt    *acolidx=a->colidx;
  PetscInt          i,j;
  PetscErrorCode    ierr;
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  __m512d           vec_x,vec_y,vec_vals;
  __m256i           vec_idx;
  __mmask8          mask;
  __m512d           vec_x2,vec_y2,vec_vals2,vec_x3,vec_y3,vec_vals3,vec_x4,vec_y4,vec_vals4;
  __m256i           vec_idx2,vec_idx3,vec_idx4;
#elif defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  __m128d           vec_x_tmp;
  __m256d           vec_x,vec_y,vec_y2,vec_vals;
  MatScalar         yval;
  PetscInt          r,row,nnz_in_row;
#else
  PetscScalar       sum[8];
#endif

#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
#pragma disjoint(*x,*y,*aval)
#endif

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
#if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  for (i=0; i<totalslices; i++) { /* loop over slices */
    PetscPrefetchBlock(acolidx,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);
    PetscPrefetchBlock(aval,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);

    if (i == totalslices-1 && A->rmap->n & 0x07) { /* if last slice has padding rows */
      mask   = (__mmask8)(0xff >> (8-(A->rmap->n & 0x07)));
      vec_y  = _mm512_mask_loadu_pd(vec_y,mask,&y[8*i]);
    } else {
      vec_y  = _mm512_loadu_pd(&y[8*i]);
    }
    vec_y2 = _mm512_setzero_pd();
    vec_y3 = _mm512_setzero_pd();
    vec_y4 = _mm512_setzero_pd();

    j = a->sliidx[i]>>3; /* 8 bytes are read at each time, corresponding to a slice columnn */
    switch ((a->sliidx[i+1]-a->sliidx[i])/8 & 3) {
    case 3:
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx2,vec_x2,vec_vals2,vec_y2);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx3,vec_x3,vec_vals3,vec_y3);
      acolidx += 8; aval += 8;
      j += 3;
      break;
    case 2:
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx2,vec_x2,vec_vals2,vec_y2);
      acolidx += 8; aval += 8;
      j += 2;
      break;
    case 1:
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      j += 1;
      break;
    }
    #pragma novector
    for (; j<(a->sliidx[i+1]>>3); j+=4) {
      AVX512_Mult_Private(vec_idx,vec_x,vec_vals,vec_y);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx2,vec_x2,vec_vals2,vec_y2);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx3,vec_x3,vec_vals3,vec_y3);
      acolidx += 8; aval += 8;
      AVX512_Mult_Private(vec_idx4,vec_x4,vec_vals4,vec_y4);
      acolidx += 8; aval += 8;
    }

    vec_y = _mm512_add_pd(vec_y,vec_y2);
    vec_y = _mm512_add_pd(vec_y,vec_y3);
    vec_y = _mm512_add_pd(vec_y,vec_y4);
    if (i == totalslices-1 && A->rmap->n & 0x07) { /* if last slice has padding rows */
      _mm512_mask_storeu_pd(&z[8*i],mask,vec_y);
    } else {
      _mm512_storeu_pd(&z[8*i],vec_y);
    }
  }
#elif defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
  for (i=0; i<totalslices; i++) { /* loop over full slices */
    PetscPrefetchBlock(acolidx,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);
    PetscPrefetchBlock(aval,a->sliidx[i+1]-a->sliidx[i],0,PETSC_PREFETCH_HINT_T0);

    /* last slice may have padding rows. Don't use vectorization. */
    if (i == totalslices-1 && (A->rmap->n & 0x07)) {
      for (r=0; r<(A->rmap->n & 0x07); ++r) {
        row        = 8*i + r;
        yval       = (MatScalar)0.0;
        nnz_in_row = a->rlen[row];
        for (j=0; j<nnz_in_row; ++j) yval += aval[8*j+r] * x[acolidx[8*j+r]];
        z[row] = y[row] + yval;
      }
      break;
    }

    vec_y  = _mm256_loadu_pd(y+8*i);
    vec_y2 = _mm256_loadu_pd(y+8*i+4);

    /* Process slice of height 8 (512 bits) via two subslices of height 4 (256 bits) via AVX */
    for (j=a->sliidx[i]; j<a->sliidx[i+1]; j+=8) {
      vec_vals  = _mm256_loadu_pd(aval);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,0);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,1);
      vec_y     = _mm256_add_pd(_mm256_mul_pd(vec_x,vec_vals),vec_y);
      aval     += 4;

      vec_vals  = _mm256_loadu_pd(aval);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,0);
      vec_x_tmp = _mm_loadl_pd(vec_x_tmp, x + *acolidx++);
      vec_x_tmp = _mm_loadh_pd(vec_x_tmp, x + *acolidx++);
      vec_x     = _mm256_insertf128_pd(vec_x,vec_x_tmp,1);
      vec_y2    = _mm256_add_pd(_mm256_mul_pd(vec_x,vec_vals),vec_y2);
      aval     += 4;
    }

    _mm256_storeu_pd(z+i*8,vec_y);
    _mm256_storeu_pd(z+i*8+4,vec_y2);
  }
#else
  for (i=0; i<totalslices; i++) { /* loop over slices */
    for (j=0; j<8; j++) sum[j] = 0.0;
    for (j=a->sliidx[i]; j<a->sliidx[i+1]; j+=8) {
      sum[0] += aval[j] * x[acolidx[j]];
      sum[1] += aval[j+1] * x[acolidx[j+1]];
      sum[2] += aval[j+2] * x[acolidx[j+2]];
      sum[3] += aval[j+3] * x[acolidx[j+3]];
      sum[4] += aval[j+4] * x[acolidx[j+4]];
      sum[5] += aval[j+5] * x[acolidx[j+5]];
      sum[6] += aval[j+6] * x[acolidx[j+6]];
      sum[7] += aval[j+7] * x[acolidx[j+7]];
    }
    if (i == totalslices-1 && (A->rmap->n & 0x07)) {
      for (j=0; j<(A->rmap->n & 0x07); j++) z[8*i+j] = y[8*i+j] + sum[j];
    } else {
      for (j=0; j<8; j++) z[8*i+j] = y[8*i+j] + sum[j];
    }
  }
#endif

  ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqSELL(Mat A,Vec xx,Vec zz,Vec yy)
{
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  PetscScalar       *y;
  const PetscScalar *x;
  const MatScalar   *aval=a->val;
  const PetscInt    *acolidx=a->colidx;
  PetscInt          i,j,r,row,nnz_in_row,totalslices=a->totalslices;
  PetscErrorCode    ierr;

#if defined(PETSC_HAVE_PRAGMA_DISJOINT)
#pragma disjoint(*x,*y,*aval)
#endif

  PetscFunctionBegin;
  if (A->symmetric) {
    ierr = MatMultAdd_SeqSELL(A,xx,zz,yy);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (zz != yy) { ierr = VecCopy(zz,yy);CHKERRQ(ierr); }
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  for (i=0; i<a->totalslices; i++) { /* loop over slices */
    if (i == totalslices-1 && (A->rmap->n & 0x07)) {
      for (r=0; r<(A->rmap->n & 0x07); ++r) {
        row        = 8*i + r;
        nnz_in_row = a->rlen[row];
        for (j=0; j<nnz_in_row; ++j) y[acolidx[8*j+r]] += aval[8*j+r] * x[row];
      }
      break;
    }
    for (j=a->sliidx[i]; j<a->sliidx[i+1]; j+=8) {
      y[acolidx[j]]   += aval[j] * x[8*i];
      y[acolidx[j+1]] += aval[j+1] * x[8*i+1];
      y[acolidx[j+2]] += aval[j+2] * x[8*i+2];
      y[acolidx[j+3]] += aval[j+3] * x[8*i+3];
      y[acolidx[j+4]] += aval[j+4] * x[8*i+4];
      y[acolidx[j+5]] += aval[j+5] * x[8*i+5];
      y[acolidx[j+6]] += aval[j+6] * x[8*i+6];
      y[acolidx[j+7]] += aval[j+7] * x[8*i+7];
    }
  }
  ierr = PetscLogFlops(2.0*a->sliidx[a->totalslices]);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqSELL(Mat A,Vec xx,Vec yy)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (A->symmetric) {
    ierr = MatMult_SeqSELL(A,xx,yy);CHKERRQ(ierr);
  } else {
    ierr = VecSet(yy,0.0);CHKERRQ(ierr);
    ierr = MatMultTransposeAdd_SeqSELL(A,xx,yy,yy);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*
     Checks for missing diagonals
*/
PetscErrorCode MatMissingDiagonal_SeqSELL(Mat A,PetscBool  *missing,PetscInt *d)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       *diag,i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  *missing = PETSC_FALSE;
  if (A->rmap->n > 0 && !(a->colidx)) {
    *missing = PETSC_TRUE;
    if (d) *d = 0;
    ierr = PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n");CHKERRQ(ierr);
  } else {
    diag = a->diag;
    for (i=0; i<A->rmap->n; i++) {
      if (diag[i] == -1) {
        *missing = PETSC_TRUE;
        if (d) *d = i;
        ierr = PetscInfo1(A,"Matrix is missing diagonal number %" PetscInt_FMT "\n",i);CHKERRQ(ierr);
        break;
      }
    }
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatMarkDiagonal_SeqSELL(Mat A)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       i,j,m=A->rmap->n,shift;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!a->diag) {
    ierr         = PetscMalloc1(m,&a->diag);CHKERRQ(ierr);
    ierr         = PetscLogObjectMemory((PetscObject)A,m*sizeof(PetscInt));CHKERRQ(ierr);
    a->free_diag = PETSC_TRUE;
  }
  for (i=0; i<m; i++) { /* loop over rows */
    shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
    a->diag[i] = -1;
    for (j=0; j<a->rlen[i]; j++) {
      if (a->colidx[shift+j*8] == i) {
        a->diag[i] = shift+j*8;
        break;
      }
    }
  }
  PetscFunctionReturn(0);
}

/*
  Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
*/
PetscErrorCode MatInvertDiagonal_SeqSELL(Mat A,PetscScalar omega,PetscScalar fshift)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*) A->data;
  PetscInt       i,*diag,m = A->rmap->n;
  MatScalar      *val = a->val;
  PetscScalar    *idiag,*mdiag;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (a->idiagvalid) PetscFunctionReturn(0);
  ierr = MatMarkDiagonal_SeqSELL(A);CHKERRQ(ierr);
  diag = a->diag;
  if (!a->idiag) {
    ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
    val  = a->val;
  }
  mdiag = a->mdiag;
  idiag = a->idiag;

  if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
    for (i=0; i<m; i++) {
      mdiag[i] = val[diag[i]];
      if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
        if (PetscRealPart(fshift)) {
          ierr = PetscInfo1(A,"Zero diagonal on row %" PetscInt_FMT "\n",i);CHKERRQ(ierr);
          A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
          A->factorerror_zeropivot_value = 0.0;
          A->factorerror_zeropivot_row   = i;
        } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %" PetscInt_FMT,i);
      }
      idiag[i] = 1.0/val[diag[i]];
    }
    ierr = PetscLogFlops(m);CHKERRQ(ierr);
  } else {
    for (i=0; i<m; i++) {
      mdiag[i] = val[diag[i]];
      idiag[i] = omega/(fshift + val[diag[i]]);
    }
    ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
  }
  a->idiagvalid = PETSC_TRUE;
  PetscFunctionReturn(0);
}

PetscErrorCode MatZeroEntries_SeqSELL(Mat A)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscArrayzero(a->val,a->sliidx[a->totalslices]);CHKERRQ(ierr);
  ierr = MatSeqSELLInvalidateDiagonal(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroy_SeqSELL(Mat A)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
#if defined(PETSC_USE_LOG)
  PetscLogObjectState((PetscObject)A,"Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT ", NZ=%" PetscInt_FMT,A->rmap->n,A->cmap->n,a->nz);
#endif
  ierr = MatSeqXSELLFreeSELL(A,&a->val,&a->colidx);CHKERRQ(ierr);
  ierr = ISDestroy(&a->row);CHKERRQ(ierr);
  ierr = ISDestroy(&a->col);CHKERRQ(ierr);
  ierr = PetscFree(a->diag);CHKERRQ(ierr);
  ierr = PetscFree(a->rlen);CHKERRQ(ierr);
  ierr = PetscFree(a->sliidx);CHKERRQ(ierr);
  ierr = PetscFree3(a->idiag,a->mdiag,a->ssor_work);CHKERRQ(ierr);
  ierr = PetscFree(a->solve_work);CHKERRQ(ierr);
  ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
  ierr = PetscFree(a->saved_values);CHKERRQ(ierr);
  ierr = PetscFree2(a->getrowcols,a->getrowvals);CHKERRQ(ierr);

  ierr = PetscFree(A->data);CHKERRQ(ierr);

  ierr = PetscObjectChangeTypeName((PetscObject)A,NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqSELLSetPreallocation_C",NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetOption_SeqSELL(Mat A,MatOption op,PetscBool flg)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  switch (op) {
  case MAT_ROW_ORIENTED:
    a->roworiented = flg;
    break;
  case MAT_KEEP_NONZERO_PATTERN:
    a->keepnonzeropattern = flg;
    break;
  case MAT_NEW_NONZERO_LOCATIONS:
    a->nonew = (flg ? 0 : 1);
    break;
  case MAT_NEW_NONZERO_LOCATION_ERR:
    a->nonew = (flg ? -1 : 0);
    break;
  case MAT_NEW_NONZERO_ALLOCATION_ERR:
    a->nonew = (flg ? -2 : 0);
    break;
  case MAT_UNUSED_NONZERO_LOCATION_ERR:
    a->nounused = (flg ? -1 : 0);
    break;
  case MAT_FORCE_DIAGONAL_ENTRIES:
  case MAT_IGNORE_OFF_PROC_ENTRIES:
  case MAT_USE_HASH_TABLE:
  case MAT_SORTED_FULL:
    ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
    break;
  case MAT_SPD:
  case MAT_SYMMETRIC:
  case MAT_STRUCTURALLY_SYMMETRIC:
  case MAT_HERMITIAN:
  case MAT_SYMMETRY_ETERNAL:
    /* These options are handled directly by MatSetOption() */
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetDiagonal_SeqSELL(Mat A,Vec v)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       i,j,n,shift;
  PetscScalar    *x,zero=0.0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
  if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");

  if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
    PetscInt *diag=a->diag;
    ierr = VecGetArray(v,&x);CHKERRQ(ierr);
    for (i=0; i<n; i++) x[i] = 1.0/a->val[diag[i]];
    ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = VecSet(v,zero);CHKERRQ(ierr);
  ierr = VecGetArray(v,&x);CHKERRQ(ierr);
  for (i=0; i<n; i++) { /* loop over rows */
    shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
    x[i] = 0;
    for (j=0; j<a->rlen[i]; j++) {
      if (a->colidx[shift+j*8] == i) {
        x[i] = a->val[shift+j*8];
        break;
      }
    }
  }
  ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDiagonalScale_SeqSELL(Mat A,Vec ll,Vec rr)
{
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  const PetscScalar *l,*r;
  PetscInt          i,j,m,n,row;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  if (ll) {
    /* The local size is used so that VecMPI can be passed to this routine
       by MatDiagonalScale_MPISELL */
    ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
    if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
    ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
    for (i=0; i<a->totalslices; i++) { /* loop over slices */
      if (i == a->totalslices-1 && (A->rmap->n & 0x07)) { /* if last slice has padding rows */
        for (j=a->sliidx[i],row=0; j<a->sliidx[i+1]; j++,row=((row+1)&0x07)) {
          if (row < (A->rmap->n & 0x07)) a->val[j] *= l[8*i+row];
        }
      } else {
        for (j=a->sliidx[i],row=0; j<a->sliidx[i+1]; j++,row=((row+1)&0x07)) {
          a->val[j] *= l[8*i+row];
        }
      }
    }
    ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
    ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
  }
  if (rr) {
    ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
    if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
    ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
    for (i=0; i<a->totalslices; i++) { /* loop over slices */
      if (i == a->totalslices-1 && (A->rmap->n & 0x07)) { /* if last slice has padding rows */
        for (j=a->sliidx[i],row=0; j<a->sliidx[i+1]; j++,row=((row+1)&0x07)) {
          if (row < (A->rmap->n & 0x07)) a->val[j] *= r[a->colidx[j]];
        }
      } else {
        for (j=a->sliidx[i]; j<a->sliidx[i+1]; j++) {
          a->val[j] *= r[a->colidx[j]];
        }
      }
    }
    ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
    ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
  }
  ierr = MatSeqSELLInvalidateDiagonal(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

extern PetscErrorCode MatSetValues_SeqSELL(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);

PetscErrorCode MatGetValues_SeqSELL(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
{
  Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;
  PetscInt    *cp,i,k,low,high,t,row,col,l;
  PetscInt    shift;
  MatScalar   *vp;

  PetscFunctionBegin;
  for (k=0; k<m; k++) { /* loop over requested rows */
    row = im[k];
    if (row<0) continue;
    if (PetscUnlikelyDebug(row >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,row,A->rmap->n-1);
    shift = a->sliidx[row>>3]+(row&0x07); /* starting index of the row */
    cp = a->colidx+shift; /* pointer to the row */
    vp = a->val+shift; /* pointer to the row */
    for (l=0; l<n; l++) { /* loop over requested columns */
      col = in[l];
      if (col<0) continue;
      if (PetscUnlikelyDebug(col >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: row %" PetscInt_FMT " max %" PetscInt_FMT,col,A->cmap->n-1);
      high = a->rlen[row]; low = 0; /* assume unsorted */
      while (high-low > 5) {
        t = (low+high)/2;
        if (*(cp+t*8) > col) high = t;
        else low = t;
      }
      for (i=low; i<high; i++) {
        if (*(cp+8*i) > col) break;
        if (*(cp+8*i) == col) {
          *v++ = *(vp+8*i);
          goto finished;
        }
      }
      *v++ = 0.0;
    finished:;
    }
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatView_SeqSELL_ASCII(Mat A,PetscViewer viewer)
{
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  PetscInt          i,j,m=A->rmap->n,shift;
  const char        *name;
  PetscViewerFormat format;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
  if (format == PETSC_VIEWER_ASCII_MATLAB) {
    PetscInt nofinalvalue = 0;
    /*
    if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-1))) {
      nofinalvalue = 1;
    }
    */
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %" PetscInt_FMT " %" PetscInt_FMT " \n",m,A->cmap->n);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %" PetscInt_FMT " \n",a->nz);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
    ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",4);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
#else
    ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%" PetscInt_FMT ",3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
#endif
    ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);

    for (i=0; i<m; i++) {
      shift = a->sliidx[i>>3]+(i&0x07);
      for (j=0; j<a->rlen[i]; j++) {
#if defined(PETSC_USE_COMPLEX)
        ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n",i+1,a->colidx[shift+8*j]+1,(double)PetscRealPart(a->val[shift+8*j]),(double)PetscImaginaryPart(a->val[shift+8*j]));CHKERRQ(ierr);
#else
        ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",i+1,a->colidx[shift+8*j]+1,(double)a->val[shift+8*j]);CHKERRQ(ierr);
#endif
      }
    }
    /*
    if (nofinalvalue) {
#if defined(PETSC_USE_COMPLEX)
      ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n",m,A->cmap->n,0.,0.);CHKERRQ(ierr);
#else
      ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n",m,A->cmap->n,0.0);CHKERRQ(ierr);
#endif
    }
    */
    ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
  } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO) {
    PetscFunctionReturn(0);
  } else if (format == PETSC_VIEWER_ASCII_COMMON) {
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      ierr = PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i);CHKERRQ(ierr);
      shift = a->sliidx[i>>3]+(i&0x07);
      for (j=0; j<a->rlen[i]; j++) {
#if defined(PETSC_USE_COMPLEX)
        if (PetscImaginaryPart(a->val[shift+8*j]) > 0.0 && PetscRealPart(a->val[shift+8*j]) != 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->colidx[shift+8*j],(double)PetscRealPart(a->val[shift+8*j]),(double)PetscImaginaryPart(a->val[shift+8*j]));CHKERRQ(ierr);
        } else if (PetscImaginaryPart(a->val[shift+8*j]) < 0.0 && PetscRealPart(a->val[shift+8*j]) != 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->colidx[shift+8*j],(double)PetscRealPart(a->val[shift+8*j]),(double)-PetscImaginaryPart(a->val[shift+8*j]));CHKERRQ(ierr);
        } else if (PetscRealPart(a->val[shift+8*j]) != 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[shift+8*j],(double)PetscRealPart(a->val[shift+8*j]));CHKERRQ(ierr);
        }
#else
        if (a->val[shift+8*j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[shift+8*j],(double)a->val[shift+8*j]);CHKERRQ(ierr);}
#endif
      }
      ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
    }
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
  } else if (format == PETSC_VIEWER_ASCII_DENSE) {
    PetscInt    cnt=0,jcnt;
    PetscScalar value;
#if defined(PETSC_USE_COMPLEX)
    PetscBool   realonly=PETSC_TRUE;
    for (i=0; i<a->sliidx[a->totalslices]; i++) {
      if (PetscImaginaryPart(a->val[i]) != 0.0) {
        realonly = PETSC_FALSE;
        break;
      }
    }
#endif

    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      jcnt = 0;
      shift = a->sliidx[i>>3]+(i&0x07);
      for (j=0; j<A->cmap->n; j++) {
        if (jcnt < a->rlen[i] && j == a->colidx[shift+8*j]) {
          value = a->val[cnt++];
          jcnt++;
        } else {
          value = 0.0;
        }
#if defined(PETSC_USE_COMPLEX)
        if (realonly) {
          ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)PetscRealPart(value));CHKERRQ(ierr);
        } else {
          ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",(double)PetscRealPart(value),(double)PetscImaginaryPart(value));CHKERRQ(ierr);
        }
#else
        ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)value);CHKERRQ(ierr);
#endif
      }
      ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
    }
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
  } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
    PetscInt fshift=1;
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
    ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate complex general\n");CHKERRQ(ierr);
#else
    ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate real general\n");CHKERRQ(ierr);
#endif
    ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", m, A->cmap->n, a->nz);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      shift = a->sliidx[i>>3]+(i&0x07);
      for (j=0; j<a->rlen[i]; j++) {
#if defined(PETSC_USE_COMPLEX)
        ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %g %g\n",i+fshift,a->colidx[shift+8*j]+fshift,(double)PetscRealPart(a->val[shift+8*j]),(double)PetscImaginaryPart(a->val[shift+8*j]));CHKERRQ(ierr);
#else
        ierr = PetscViewerASCIIPrintf(viewer,"%" PetscInt_FMT " %" PetscInt_FMT " %g\n",i+fshift,a->colidx[shift+8*j]+fshift,(double)a->val[shift+8*j]);CHKERRQ(ierr);
#endif
      }
    }
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
  } else if (format == PETSC_VIEWER_NATIVE) {
    for (i=0; i<a->totalslices; i++) { /* loop over slices */
      PetscInt row;
      ierr = PetscViewerASCIIPrintf(viewer,"slice %" PetscInt_FMT ": %" PetscInt_FMT " %" PetscInt_FMT "\n",i,a->sliidx[i],a->sliidx[i+1]);CHKERRQ(ierr);
      for (j=a->sliidx[i],row=0; j<a->sliidx[i+1]; j++,row=((row+1)&0x07)) {
#if defined(PETSC_USE_COMPLEX)
        if (PetscImaginaryPart(a->val[j]) > 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer,"  %" PetscInt_FMT " %" PetscInt_FMT " %g + %g i\n",8*i+row,a->colidx[j],(double)PetscRealPart(a->val[j]),(double)PetscImaginaryPart(a->val[j]));CHKERRQ(ierr);
        } else if (PetscImaginaryPart(a->val[j]) < 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer,"  %" PetscInt_FMT " %" PetscInt_FMT " %g - %g i\n",8*i+row,a->colidx[j],(double)PetscRealPart(a->val[j]),-(double)PetscImaginaryPart(a->val[j]));CHKERRQ(ierr);
        } else {
          ierr = PetscViewerASCIIPrintf(viewer,"  %" PetscInt_FMT " %" PetscInt_FMT " %g\n",8*i+row,a->colidx[j],(double)PetscRealPart(a->val[j]));CHKERRQ(ierr);
        }
#else
        ierr = PetscViewerASCIIPrintf(viewer,"  %" PetscInt_FMT " %" PetscInt_FMT " %g\n",8*i+row,a->colidx[j],(double)a->val[j]);CHKERRQ(ierr);
#endif
      }
    }
  } else {
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
    if (A->factortype) {
      for (i=0; i<m; i++) {
        shift = a->sliidx[i>>3]+(i&0x07);
        ierr = PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i);CHKERRQ(ierr);
        /* L part */
        for (j=shift; j<a->diag[i]; j+=8) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->val[shift+8*j]) > 0.0) {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->colidx[j],(double)PetscRealPart(a->val[j]),(double)PetscImaginaryPart(a->val[j]));CHKERRQ(ierr);
          } else if (PetscImaginaryPart(a->val[shift+8*j]) < 0.0) {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->colidx[j],(double)PetscRealPart(a->val[j]),(double)(-PetscImaginaryPart(a->val[j])));CHKERRQ(ierr);
          } else {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[j],(double)PetscRealPart(a->val[j]));CHKERRQ(ierr);
          }
#else
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[j],(double)a->val[j]);CHKERRQ(ierr);
#endif
        }
        /* diagonal */
        j = a->diag[i];
#if defined(PETSC_USE_COMPLEX)
        if (PetscImaginaryPart(a->val[j]) > 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->colidx[j],(double)PetscRealPart(1.0/a->val[j]),(double)PetscImaginaryPart(1.0/a->val[j]));CHKERRQ(ierr);
        } else if (PetscImaginaryPart(a->val[j]) < 0.0) {
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->colidx[j],(double)PetscRealPart(1.0/a->val[j]),(double)(-PetscImaginaryPart(1.0/a->val[j])));CHKERRQ(ierr);
        } else {
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[j],(double)PetscRealPart(1.0/a->val[j]));CHKERRQ(ierr);
        }
#else
        ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[j],(double)(1.0/a->val[j]));CHKERRQ(ierr);
#endif

        /* U part */
        for (j=a->diag[i]+1; j<shift+8*a->rlen[i]; j+=8) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->val[j]) > 0.0) {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->colidx[j],(double)PetscRealPart(a->val[j]),(double)PetscImaginaryPart(a->val[j]));CHKERRQ(ierr);
          } else if (PetscImaginaryPart(a->val[j]) < 0.0) {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->colidx[j],(double)PetscRealPart(a->val[j]),(double)(-PetscImaginaryPart(a->val[j])));CHKERRQ(ierr);
          } else {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[j],(double)PetscRealPart(a->val[j]));CHKERRQ(ierr);
          }
#else
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[j],(double)a->val[j]);CHKERRQ(ierr);
#endif
        }
        ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
      }
    } else {
      for (i=0; i<m; i++) {
        shift = a->sliidx[i>>3]+(i&0x07);
        ierr = PetscViewerASCIIPrintf(viewer,"row %" PetscInt_FMT ":",i);CHKERRQ(ierr);
        for (j=0; j<a->rlen[i]; j++) {
#if defined(PETSC_USE_COMPLEX)
          if (PetscImaginaryPart(a->val[j]) > 0.0) {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g + %g i)",a->colidx[shift+8*j],(double)PetscRealPart(a->val[shift+8*j]),(double)PetscImaginaryPart(a->val[shift+8*j]));CHKERRQ(ierr);
          } else if (PetscImaginaryPart(a->val[j]) < 0.0) {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g - %g i)",a->colidx[shift+8*j],(double)PetscRealPart(a->val[shift+8*j]),(double)-PetscImaginaryPart(a->val[shift+8*j]));CHKERRQ(ierr);
          } else {
            ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[shift+8*j],(double)PetscRealPart(a->val[shift+8*j]));CHKERRQ(ierr);
          }
#else
          ierr = PetscViewerASCIIPrintf(viewer," (%" PetscInt_FMT ", %g) ",a->colidx[shift+8*j],(double)a->val[shift+8*j]);CHKERRQ(ierr);
#endif
        }
        ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
      }
    }
    ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
  }
  ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#include <petscdraw.h>
PetscErrorCode MatView_SeqSELL_Draw_Zoom(PetscDraw draw,void *Aa)
{
  Mat               A=(Mat)Aa;
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  PetscInt          i,j,m=A->rmap->n,shift;
  int               color;
  PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r;
  PetscViewer       viewer;
  PetscViewerFormat format;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
  ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
  ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);

  /* loop over matrix elements drawing boxes */

  if (format != PETSC_VIEWER_DRAW_CONTOUR) {
    ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
    /* Blue for negative, Cyan for zero and  Red for positive */
    color = PETSC_DRAW_BLUE;
    for (i=0; i<m; i++) {
      shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
      y_l = m - i - 1.0; y_r = y_l + 1.0;
      for (j=0; j<a->rlen[i]; j++) {
        x_l = a->colidx[shift+j*8]; x_r = x_l + 1.0;
        if (PetscRealPart(a->val[shift+8*j]) >=  0.) continue;
        ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
      }
    }
    color = PETSC_DRAW_CYAN;
    for (i=0; i<m; i++) {
      shift = a->sliidx[i>>3]+(i&0x07);
      y_l = m - i - 1.0; y_r = y_l + 1.0;
      for (j=0; j<a->rlen[i]; j++) {
        x_l = a->colidx[shift+j*8]; x_r = x_l + 1.0;
        if (a->val[shift+8*j] !=  0.) continue;
        ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
      }
    }
    color = PETSC_DRAW_RED;
    for (i=0; i<m; i++) {
      shift = a->sliidx[i>>3]+(i&0x07);
      y_l = m - i - 1.0; y_r = y_l + 1.0;
      for (j=0; j<a->rlen[i]; j++) {
        x_l = a->colidx[shift+j*8]; x_r = x_l + 1.0;
        if (PetscRealPart(a->val[shift+8*j]) <=  0.) continue;
        ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
      }
    }
    ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
  } else {
    /* use contour shading to indicate magnitude of values */
    /* first determine max of all nonzero values */
    PetscReal minv=0.0,maxv=0.0;
    PetscInt  count=0;
    PetscDraw popup;
    for (i=0; i<a->sliidx[a->totalslices]; i++) {
      if (PetscAbsScalar(a->val[i]) > maxv) maxv = PetscAbsScalar(a->val[i]);
    }
    if (minv >= maxv) maxv = minv + PETSC_SMALL;
    ierr = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
    ierr = PetscDrawScalePopup(popup,minv,maxv);CHKERRQ(ierr);

    ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      shift = a->sliidx[i>>3]+(i&0x07);
      y_l = m - i - 1.0;
      y_r = y_l + 1.0;
      for (j=0; j<a->rlen[i]; j++) {
        x_l = a->colidx[shift+j*8];
        x_r = x_l + 1.0;
        color = PetscDrawRealToColor(PetscAbsScalar(a->val[count]),minv,maxv);
        ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
        count++;
      }
    }
    ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#include <petscdraw.h>
PetscErrorCode MatView_SeqSELL_Draw(Mat A,PetscViewer viewer)
{
  PetscDraw      draw;
  PetscReal      xr,yr,xl,yl,h,w;
  PetscBool      isnull;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
  ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
  if (isnull) PetscFunctionReturn(0);

  xr   = A->cmap->n; yr  = A->rmap->n; h = yr/10.0; w = xr/10.0;
  xr  += w;          yr += h;         xl = -w;     yl = -h;
  ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
  ierr = PetscDrawZoom(draw,MatView_SeqSELL_Draw_Zoom,A);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
  ierr = PetscDrawSave(draw);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatView_SeqSELL(Mat A,PetscViewer viewer)
{
  PetscBool      iascii,isbinary,isdraw;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
  if (iascii) {
    ierr = MatView_SeqSELL_ASCII(A,viewer);CHKERRQ(ierr);
  } else if (isbinary) {
    /* ierr = MatView_SeqSELL_Binary(A,viewer);CHKERRQ(ierr); */
  } else if (isdraw) {
    ierr = MatView_SeqSELL_Draw(A,viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatAssemblyEnd_SeqSELL(Mat A,MatAssemblyType mode)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       i,shift,row_in_slice,row,nrow,*cp,lastcol,j,k;
  MatScalar      *vp;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
  /* To do: compress out the unused elements */
  ierr = MatMarkDiagonal_SeqSELL(A);CHKERRQ(ierr);
  ierr = PetscInfo6(A,"Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; storage space: %" PetscInt_FMT " allocated %" PetscInt_FMT " used (%" PetscInt_FMT " nonzeros+%" PetscInt_FMT " paddedzeros)\n",A->rmap->n,A->cmap->n,a->maxallocmat,a->sliidx[a->totalslices],a->nz,a->sliidx[a->totalslices]-a->nz);CHKERRQ(ierr);
  ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %" PetscInt_FMT "\n",a->reallocs);CHKERRQ(ierr);
  ierr = PetscInfo1(A,"Maximum nonzeros in any row is %" PetscInt_FMT "\n",a->rlenmax);CHKERRQ(ierr);
  /* Set unused slots for column indices to last valid column index. Set unused slots for values to zero. This allows for a use of unmasked intrinsics -> higher performance */
  for (i=0; i<a->totalslices; ++i) {
    shift = a->sliidx[i];    /* starting index of the slice */
    cp    = a->colidx+shift; /* pointer to the column indices of the slice */
    vp    = a->val+shift;    /* pointer to the nonzero values of the slice */
    for (row_in_slice=0; row_in_slice<8; ++row_in_slice) { /* loop over rows in the slice */
      row  = 8*i + row_in_slice;
      nrow = a->rlen[row]; /* number of nonzeros in row */
      /*
        Search for the nearest nonzero. Normally setting the index to zero may cause extra communication.
        But if the entire slice are empty, it is fine to use 0 since the index will not be loaded.
      */
      lastcol = 0;
      if (nrow>0) { /* nonempty row */
        lastcol = cp[8*(nrow-1)+row_in_slice]; /* use the index from the last nonzero at current row */
      } else if (!row_in_slice) { /* first row of the currect slice is empty */
        for (j=1;j<8;j++) {
          if (a->rlen[8*i+j]) {
            lastcol = cp[j];
            break;
          }
        }
      } else {
        if (a->sliidx[i+1] != shift) lastcol = cp[row_in_slice-1]; /* use the index from the previous row */
      }

      for (k=nrow; k<(a->sliidx[i+1]-shift)/8; ++k) {
        cp[8*k+row_in_slice] = lastcol;
        vp[8*k+row_in_slice] = (MatScalar)0;
      }
    }
  }

  A->info.mallocs += a->reallocs;
  a->reallocs      = 0;

  ierr = MatSeqSELLInvalidateDiagonal(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatGetInfo_SeqSELL(Mat A,MatInfoType flag,MatInfo *info)
{
  Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;

  PetscFunctionBegin;
  info->block_size   = 1.0;
  info->nz_allocated = a->maxallocmat;
  info->nz_used      = a->sliidx[a->totalslices]; /* include padding zeros */
  info->nz_unneeded  = (a->maxallocmat-a->sliidx[a->totalslices]);
  info->assemblies   = A->num_ass;
  info->mallocs      = A->info.mallocs;
  info->memory       = ((PetscObject)A)->mem;
  if (A->factortype) {
    info->fill_ratio_given  = A->info.fill_ratio_given;
    info->fill_ratio_needed = A->info.fill_ratio_needed;
    info->factor_mallocs    = A->info.factor_mallocs;
  } else {
    info->fill_ratio_given  = 0;
    info->fill_ratio_needed = 0;
    info->factor_mallocs    = 0;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetValues_SeqSELL(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       shift,i,k,l,low,high,t,ii,row,col,nrow;
  PetscInt       *cp,nonew=a->nonew,lastcol=-1;
  MatScalar      *vp,value;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  for (k=0; k<m; k++) { /* loop over added rows */
    row = im[k];
    if (row < 0) continue;
    if (PetscUnlikelyDebug(row >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT,row,A->rmap->n-1);
    shift = a->sliidx[row>>3]+(row&0x07); /* starting index of the row */
    cp    = a->colidx+shift; /* pointer to the row */
    vp    = a->val+shift; /* pointer to the row */
    nrow  = a->rlen[row];
    low   = 0;
    high  = nrow;

    for (l=0; l<n; l++) { /* loop over added columns */
      col = in[l];
      if (col<0) continue;
      if (PetscUnlikelyDebug(col >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Col too large: row %" PetscInt_FMT " max %" PetscInt_FMT,col,A->cmap->n-1);
      if (a->roworiented) {
        value = v[l+k*n];
      } else {
        value = v[k+l*m];
      }
      if ((value == 0.0 && a->ignorezeroentries) && (is == ADD_VALUES)) continue;

      /* search in this row for the specified colmun, i indicates the column to be set */
      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high-low > 5) {
        t = (low+high)/2;
        if (*(cp+t*8) > col) high = t;
        else low = t;
      }
      for (i=low; i<high; i++) {
        if (*(cp+i*8) > col) break;
        if (*(cp+i*8) == col) {
          if (is == ADD_VALUES) *(vp+i*8) += value;
          else *(vp+i*8) = value;
          low = i + 1;
          goto noinsert;
        }
      }
      if (value == 0.0 && a->ignorezeroentries) goto noinsert;
      if (nonew == 1) goto noinsert;
      if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%" PetscInt_FMT ", %" PetscInt_FMT ") in the matrix", row, col);
      /* If the current row length exceeds the slice width (e.g. nrow==slice_width), allocate a new space, otherwise do nothing */
      MatSeqXSELLReallocateSELL(A,A->rmap->n,1,nrow,a->sliidx,row/8,row,col,a->colidx,a->val,cp,vp,nonew,MatScalar);
      /* add the new nonzero to the high position, shift the remaining elements in current row to the right by one slot */
      for (ii=nrow-1; ii>=i; ii--) {
        *(cp+(ii+1)*8) = *(cp+ii*8);
        *(vp+(ii+1)*8) = *(vp+ii*8);
      }
      a->rlen[row]++;
      *(cp+i*8) = col;
      *(vp+i*8) = value;
      a->nz++;
      A->nonzerostate++;
      low = i+1; high++; nrow++;
noinsert:;
    }
    a->rlen[row] = nrow;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatCopy_SeqSELL(Mat A,Mat B,MatStructure str)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* If the two matrices have the same copy implementation, use fast copy. */
  if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
    Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;
    Mat_SeqSELL *b=(Mat_SeqSELL*)B->data;

    if (a->sliidx[a->totalslices] != b->sliidx[b->totalslices]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Number of nonzeros in two matrices are different");
    ierr = PetscArraycpy(b->val,a->val,a->sliidx[a->totalslices]);CHKERRQ(ierr);
  } else {
    ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetUp_SeqSELL(Mat A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSeqSELLSetPreallocation(A,PETSC_DEFAULT,NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSeqSELLGetArray_SeqSELL(Mat A,PetscScalar *array[])
{
  Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;

  PetscFunctionBegin;
  *array = a->val;
  PetscFunctionReturn(0);
}

PetscErrorCode MatSeqSELLRestoreArray_SeqSELL(Mat A,PetscScalar *array[])
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

PetscErrorCode MatRealPart_SeqSELL(Mat A)
{
  Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;
  PetscInt    i;
  MatScalar   *aval=a->val;

  PetscFunctionBegin;
  for (i=0; i<a->sliidx[a->totalslices]; i++) aval[i]=PetscRealPart(aval[i]);
  PetscFunctionReturn(0);
}

PetscErrorCode MatImaginaryPart_SeqSELL(Mat A)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)A->data;
  PetscInt       i;
  MatScalar      *aval=a->val;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  for (i=0; i<a->sliidx[a->totalslices]; i++) aval[i] = PetscImaginaryPart(aval[i]);
  ierr = MatSeqSELLInvalidateDiagonal(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatScale_SeqSELL(Mat inA,PetscScalar alpha)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)inA->data;
  MatScalar      *aval=a->val;
  PetscScalar    oalpha=alpha;
  PetscBLASInt   one=1,size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscBLASIntCast(a->sliidx[a->totalslices],&size);CHKERRQ(ierr);
  PetscStackCallBLAS("BLASscal",BLASscal_(&size,&oalpha,aval,&one));
  ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
  ierr = MatSeqSELLInvalidateDiagonal(inA);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatShift_SeqSELL(Mat Y,PetscScalar a)
{
  Mat_SeqSELL    *y=(Mat_SeqSELL*)Y->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!Y->preallocated || !y->nz) {
    ierr = MatSeqSELLSetPreallocation(Y,1,NULL);CHKERRQ(ierr);
  }
  ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSOR_SeqSELL(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
  Mat_SeqSELL       *a=(Mat_SeqSELL*)A->data;
  PetscScalar       *x,sum,*t;
  const MatScalar   *idiag=NULL,*mdiag;
  const PetscScalar *b,*xb;
  PetscInt          n,m=A->rmap->n,i,j,shift;
  const PetscInt    *diag;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  its = its*lits;

  if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
  if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqSELL(A,omega,fshift);CHKERRQ(ierr);}
  a->fshift = fshift;
  a->omega  = omega;

  diag  = a->diag;
  t     = a->ssor_work;
  idiag = a->idiag;
  mdiag = a->mdiag;

  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
  /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
  if (flag == SOR_APPLY_UPPER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_UPPER is not implemented");
  if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
  if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");

  if (flag & SOR_ZERO_INITIAL_GUESS) {
    if ((flag & SOR_FORWARD_SWEEP) || (flag & SOR_LOCAL_FORWARD_SWEEP)) {
      for (i=0; i<m; i++) {
        shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
        sum   = b[i];
        n     = (diag[i]-shift)/8;
        for (j=0; j<n; j++) sum -= a->val[shift+j*8]*x[a->colidx[shift+j*8]];
        t[i]  = sum;
        x[i]  = sum*idiag[i];
      }
      xb   = t;
      ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
    } else xb = b;
    if ((flag & SOR_BACKWARD_SWEEP) || (flag & SOR_LOCAL_BACKWARD_SWEEP)) {
      for (i=m-1; i>=0; i--) {
        shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
        sum   = xb[i];
        n     = a->rlen[i]-(diag[i]-shift)/8-1;
        for (j=1; j<=n; j++) sum -= a->val[diag[i]+j*8]*x[a->colidx[diag[i]+j*8]];
        if (xb == b) {
          x[i] = sum*idiag[i];
        } else {
          x[i] = (1.-omega)*x[i]+sum*idiag[i];  /* omega in idiag */
        }
      }
      ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
    }
    its--;
  }
  while (its--) {
    if ((flag & SOR_FORWARD_SWEEP) || (flag & SOR_LOCAL_FORWARD_SWEEP)) {
      for (i=0; i<m; i++) {
        /* lower */
        shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
        sum   = b[i];
        n     = (diag[i]-shift)/8;
        for (j=0; j<n; j++) sum -= a->val[shift+j*8]*x[a->colidx[shift+j*8]];
        t[i]  = sum;             /* save application of the lower-triangular part */
        /* upper */
        n     = a->rlen[i]-(diag[i]-shift)/8-1;
        for (j=1; j<=n; j++) sum -= a->val[diag[i]+j*8]*x[a->colidx[diag[i]+j*8]];
        x[i]  = (1.-omega)*x[i]+sum*idiag[i];  /* omega in idiag */
      }
      xb   = t;
      ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
    } else xb = b;
    if ((flag & SOR_BACKWARD_SWEEP) || (flag & SOR_LOCAL_BACKWARD_SWEEP)) {
      for (i=m-1; i>=0; i--) {
        shift = a->sliidx[i>>3]+(i&0x07); /* starting index of the row i */
        sum = xb[i];
        if (xb == b) {
          /* whole matrix (no checkpointing available) */
          n     = a->rlen[i];
          for (j=0; j<n; j++) sum -= a->val[shift+j*8]*x[a->colidx[shift+j*8]];
          x[i] = (1.-omega)*x[i]+(sum+mdiag[i]*x[i])*idiag[i];
        } else { /* lower-triangular part has been saved, so only apply upper-triangular */
          n     = a->rlen[i]-(diag[i]-shift)/8-1;
          for (j=1; j<=n; j++) sum -= a->val[diag[i]+j*8]*x[a->colidx[diag[i]+j*8]];
          x[i]  = (1.-omega)*x[i]+sum*idiag[i];  /* omega in idiag */
        }
      }
      if (xb == b) {
        ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
      } else {
        ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
      }
    }
  }
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------*/
static struct _MatOps MatOps_Values = {MatSetValues_SeqSELL,
                                       MatGetRow_SeqSELL,
                                       MatRestoreRow_SeqSELL,
                                       MatMult_SeqSELL,
                               /* 4*/  MatMultAdd_SeqSELL,
                                       MatMultTranspose_SeqSELL,
                                       MatMultTransposeAdd_SeqSELL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 10*/ NULL,
                                       NULL,
                                       NULL,
                                       MatSOR_SeqSELL,
                                       NULL,
                               /* 15*/ MatGetInfo_SeqSELL,
                                       MatEqual_SeqSELL,
                                       MatGetDiagonal_SeqSELL,
                                       MatDiagonalScale_SeqSELL,
                                       NULL,
                               /* 20*/ NULL,
                                       MatAssemblyEnd_SeqSELL,
                                       MatSetOption_SeqSELL,
                                       MatZeroEntries_SeqSELL,
                               /* 24*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 29*/ MatSetUp_SeqSELL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 34*/ MatDuplicate_SeqSELL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 39*/ NULL,
                                       NULL,
                                       NULL,
                                       MatGetValues_SeqSELL,
                                       MatCopy_SeqSELL,
                               /* 44*/ NULL,
                                       MatScale_SeqSELL,
                                       MatShift_SeqSELL,
                                       NULL,
                                       NULL,
                               /* 49*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 54*/ MatFDColoringCreate_SeqXAIJ,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 59*/ NULL,
                                       MatDestroy_SeqSELL,
                                       MatView_SeqSELL,
                                       NULL,
                                       NULL,
                               /* 64*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 69*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 74*/ NULL,
                                       MatFDColoringApply_AIJ, /* reuse the FDColoring function for AIJ */
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 79*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 84*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 89*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 94*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /* 99*/ NULL,
                                       NULL,
                                       NULL,
                                       MatConjugate_SeqSELL,
                                       NULL,
                               /*104*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /*109*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       MatMissingDiagonal_SeqSELL,
                               /*114*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /*119*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /*124*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /*129*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /*134*/ NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                                       NULL,
                               /*139*/ NULL,
                                       NULL,
                                       NULL,
                                       MatFDColoringSetUp_SeqXAIJ,
                                       NULL,
                               /*144*/ NULL
};

PetscErrorCode MatStoreValues_SeqSELL(Mat mat)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)mat->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!a->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");

  /* allocate space for values if not already there */
  if (!a->saved_values) {
    ierr = PetscMalloc1(a->sliidx[a->totalslices]+1,&a->saved_values);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)mat,(a->sliidx[a->totalslices]+1)*sizeof(PetscScalar));CHKERRQ(ierr);
  }

  /* copy values over */
  ierr = PetscArraycpy(a->saved_values,a->val,a->sliidx[a->totalslices]);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatRetrieveValues_SeqSELL(Mat mat)
{
  Mat_SeqSELL    *a=(Mat_SeqSELL*)mat->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!a->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
  if (!a->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
  ierr = PetscArraycpy(a->val,a->saved_values,a->sliidx[a->totalslices]);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
 MatSeqSELLRestoreArray - returns access to the array where the data for a MATSEQSELL matrix is stored obtained by MatSeqSELLGetArray()

 Not Collective

 Input Parameters:
 .  mat - a MATSEQSELL matrix
 .  array - pointer to the data

 Level: intermediate

 .seealso: MatSeqSELLGetArray(), MatSeqSELLRestoreArrayF90()
 @*/
PetscErrorCode MatSeqSELLRestoreArray(Mat A,PetscScalar **array)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscUseMethod(A,"MatSeqSELLRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_EXTERN PetscErrorCode MatCreate_SeqSELL(Mat B)
{
  Mat_SeqSELL    *b;
  PetscMPIInt    size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRMPI(ierr);
  if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");

  ierr = PetscNewLog(B,&b);CHKERRQ(ierr);

  B->data = (void*)b;

  ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);

  b->row                = NULL;
  b->col                = NULL;
  b->icol               = NULL;
  b->reallocs           = 0;
  b->ignorezeroentries  = PETSC_FALSE;
  b->roworiented        = PETSC_TRUE;
  b->nonew              = 0;
  b->diag               = NULL;
  b->solve_work         = NULL;
  B->spptr              = NULL;
  b->saved_values       = NULL;
  b->idiag              = NULL;
  b->mdiag              = NULL;
  b->ssor_work          = NULL;
  b->omega              = 1.0;
  b->fshift             = 0.0;
  b->idiagvalid         = PETSC_FALSE;
  b->keepnonzeropattern = PETSC_FALSE;

  ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQSELL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqSELLGetArray_C",MatSeqSELLGetArray_SeqSELL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqSELLRestoreArray_C",MatSeqSELLRestoreArray_SeqSELL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqSELL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqSELL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqSELLSetPreallocation_C",MatSeqSELLSetPreallocation_SeqSELL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqsell_seqaij_C",MatConvert_SeqSELL_SeqAIJ);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
 Given a matrix generated with MatGetFactor() duplicates all the information in A into B
 */
PetscErrorCode MatDuplicateNoCreate_SeqSELL(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
{
  Mat_SeqSELL    *c,*a=(Mat_SeqSELL*)A->data;
  PetscInt       i,m=A->rmap->n;
  PetscInt       totalslices=a->totalslices;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  c = (Mat_SeqSELL*)C->data;

  C->factortype = A->factortype;
  c->row        = NULL;
  c->col        = NULL;
  c->icol       = NULL;
  c->reallocs   = 0;

  C->assembled = PETSC_TRUE;

  ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
  ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);

  ierr = PetscMalloc1(8*totalslices,&c->rlen);CHKERRQ(ierr);
  ierr = PetscLogObjectMemory((PetscObject)C,m*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscMalloc1(totalslices+1,&c->sliidx);CHKERRQ(ierr);
  ierr = PetscLogObjectMemory((PetscObject)C, (totalslices+1)*sizeof(PetscInt));CHKERRQ(ierr);

  for (i=0; i<m; i++) c->rlen[i] = a->rlen[i];
  for (i=0; i<totalslices+1; i++) c->sliidx[i] = a->sliidx[i];

  /* allocate the matrix space */
  if (mallocmatspace) {
    ierr = PetscMalloc2(a->maxallocmat,&c->val,a->maxallocmat,&c->colidx);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)C,a->maxallocmat*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);

    c->singlemalloc = PETSC_TRUE;

    if (m > 0) {
      ierr = PetscArraycpy(c->colidx,a->colidx,a->maxallocmat);CHKERRQ(ierr);
      if (cpvalues == MAT_COPY_VALUES) {
        ierr = PetscArraycpy(c->val,a->val,a->maxallocmat);CHKERRQ(ierr);
      } else {
        ierr = PetscArrayzero(c->val,a->maxallocmat);CHKERRQ(ierr);
      }
    }
  }

  c->ignorezeroentries = a->ignorezeroentries;
  c->roworiented       = a->roworiented;
  c->nonew             = a->nonew;
  if (a->diag) {
    ierr = PetscMalloc1(m,&c->diag);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)C,m*sizeof(PetscInt));CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      c->diag[i] = a->diag[i];
    }
  } else c->diag = NULL;

  c->solve_work         = NULL;
  c->saved_values       = NULL;
  c->idiag              = NULL;
  c->ssor_work          = NULL;
  c->keepnonzeropattern = a->keepnonzeropattern;
  c->free_val           = PETSC_TRUE;
  c->free_colidx        = PETSC_TRUE;

  c->maxallocmat  = a->maxallocmat;
  c->maxallocrow  = a->maxallocrow;
  c->rlenmax      = a->rlenmax;
  c->nz           = a->nz;
  C->preallocated = PETSC_TRUE;

  c->nonzerorowcnt = a->nonzerorowcnt;
  C->nonzerostate  = A->nonzerostate;

  ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDuplicate_SeqSELL(Mat A,MatDuplicateOption cpvalues,Mat *B)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
  ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
  if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
    ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
  }
  ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
  ierr = MatDuplicateNoCreate_SeqSELL(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
 MatCreateSeqSELL - Creates a sparse matrix in SELL format.

 Collective

 Input Parameters:
+  comm - MPI communicator, set to PETSC_COMM_SELF
.  m - number of rows
.  n - number of columns
.  rlenmax - maximum number of nonzeros in a row
-  rlen - array containing the number of nonzeros in the various rows
 (possibly different for each row) or NULL

 Output Parameter:
.  A - the matrix

 It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
 MatXXXXSetPreallocation() paradigm instead of this routine directly.
 [MatXXXXSetPreallocation() is, for example, MatSeqSELLSetPreallocation]

 Notes:
 If nnz is given then nz is ignored

 Specify the preallocated storage with either rlenmax or rlen (not both).
 Set rlenmax=PETSC_DEFAULT and rlen=NULL for PETSc to control dynamic memory
 allocation.  For large problems you MUST preallocate memory or you
 will get TERRIBLE performance, see the users' manual chapter on matrices.

 Level: intermediate

 .seealso: MatCreate(), MatCreateSELL(), MatSetValues()

 @*/
PetscErrorCode MatCreateSeqSELL(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt maxallocrow,const PetscInt rlen[],Mat *A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCreate(comm,A);CHKERRQ(ierr);
  ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
  ierr = MatSetType(*A,MATSEQSELL);CHKERRQ(ierr);
  ierr = MatSeqSELLSetPreallocation_SeqSELL(*A,maxallocrow,rlen);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatEqual_SeqSELL(Mat A,Mat B,PetscBool * flg)
{
  Mat_SeqSELL     *a=(Mat_SeqSELL*)A->data,*b=(Mat_SeqSELL*)B->data;
  PetscInt       totalslices=a->totalslices;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* If the  matrix dimensions are not equal,or no of nonzeros */
  if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz) || (a->rlenmax != b->rlenmax)) {
    *flg = PETSC_FALSE;
    PetscFunctionReturn(0);
  }
  /* if the a->colidx are the same */
  ierr = PetscArraycmp(a->colidx,b->colidx,a->sliidx[totalslices],flg);CHKERRQ(ierr);
  if (!*flg) PetscFunctionReturn(0);
  /* if a->val are the same */
  ierr = PetscArraycmp(a->val,b->val,a->sliidx[totalslices],flg);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSeqSELLInvalidateDiagonal(Mat A)
{
  Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;

  PetscFunctionBegin;
  a->idiagvalid  = PETSC_FALSE;
  PetscFunctionReturn(0);
}

PetscErrorCode MatConjugate_SeqSELL(Mat A)
{
#if defined(PETSC_USE_COMPLEX)
  Mat_SeqSELL *a=(Mat_SeqSELL*)A->data;
  PetscInt    i;
  PetscScalar *val = a->val;

  PetscFunctionBegin;
  for (i=0; i<a->sliidx[a->totalslices]; i++) {
    val[i] = PetscConj(val[i]);
  }
#else
  PetscFunctionBegin;
#endif
  PetscFunctionReturn(0);
}