xref: /petsc/src/mat/impls/baij/seq/baij2.c (revision efa12513287cff49a2b9648ae83199dcbfaad71a)
1 
2 #include <../src/mat/impls/baij/seq/baij.h>
3 #include <../src/mat/impls/dense/seq/dense.h>
4 #include <petsc/private/kernels/blockinvert.h>
5 #include <petscbt.h>
6 #include <petscblaslapack.h>
7 
8 #if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
9 #include <immintrin.h>
10 #endif
11 
12 PetscErrorCode MatIncreaseOverlap_SeqBAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
13 {
14   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
15   PetscErrorCode ierr;
16   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val,ival;
17   const PetscInt *idx;
18   PetscInt       start,end,*ai,*aj,bs,*nidx2;
19   PetscBT        table;
20 
21   PetscFunctionBegin;
22   m  = a->mbs;
23   ai = a->i;
24   aj = a->j;
25   bs = A->rmap->bs;
26 
27   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
28 
29   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
30   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
31   ierr = PetscMalloc1(A->rmap->N+1,&nidx2);CHKERRQ(ierr);
32 
33   for (i=0; i<is_max; i++) {
34     /* Initialise the two local arrays */
35     isz  = 0;
36     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
37 
38     /* Extract the indices, assume there can be duplicate entries */
39     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
40     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
41 
42     /* Enter these into the temp arrays i.e mark table[row], enter row into new index */
43     for (j=0; j<n; ++j) {
44       ival = idx[j]/bs; /* convert the indices into block indices */
45       if (ival>=m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"index greater than mat-dim");
46       if (!PetscBTLookupSet(table,ival)) nidx[isz++] = ival;
47     }
48     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
49     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
50 
51     k = 0;
52     for (j=0; j<ov; j++) { /* for each overlap*/
53       n = isz;
54       for (; k<n; k++) {  /* do only those rows in nidx[k], which are not done yet */
55         row   = nidx[k];
56         start = ai[row];
57         end   = ai[row+1];
58         for (l = start; l<end; l++) {
59           val = aj[l];
60           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
61         }
62       }
63     }
64     /* expand the Index Set */
65     for (j=0; j<isz; j++) {
66       for (k=0; k<bs; k++) nidx2[j*bs+k] = nidx[j]*bs+k;
67     }
68     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz*bs,nidx2,PETSC_COPY_VALUES,is+i);CHKERRQ(ierr);
69   }
70   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
71   ierr = PetscFree(nidx);CHKERRQ(ierr);
72   ierr = PetscFree(nidx2);CHKERRQ(ierr);
73   PetscFunctionReturn(0);
74 }
75 
76 PetscErrorCode MatCreateSubMatrix_SeqBAIJ_Private(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
77 {
78   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*c;
79   PetscErrorCode ierr;
80   PetscInt       *smap,i,k,kstart,kend,oldcols = a->nbs,*lens;
81   PetscInt       row,mat_i,*mat_j,tcol,*mat_ilen;
82   const PetscInt *irow,*icol;
83   PetscInt       nrows,ncols,*ssmap,bs=A->rmap->bs,bs2=a->bs2;
84   PetscInt       *aj = a->j,*ai = a->i;
85   MatScalar      *mat_a;
86   Mat            C;
87   PetscBool      flag;
88 
89   PetscFunctionBegin;
90   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
91   ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
92   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
93   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
94 
95   ierr  = PetscCalloc1(1+oldcols,&smap);CHKERRQ(ierr);
96   ssmap = smap;
97   ierr  = PetscMalloc1(1+nrows,&lens);CHKERRQ(ierr);
98   for (i=0; i<ncols; i++) smap[icol[i]] = i+1;
99   /* determine lens of each row */
100   for (i=0; i<nrows; i++) {
101     kstart  = ai[irow[i]];
102     kend    = kstart + a->ilen[irow[i]];
103     lens[i] = 0;
104     for (k=kstart; k<kend; k++) {
105       if (ssmap[aj[k]]) lens[i]++;
106     }
107   }
108   /* Create and fill new matrix */
109   if (scall == MAT_REUSE_MATRIX) {
110     c = (Mat_SeqBAIJ*)((*B)->data);
111 
112     if (c->mbs!=nrows || c->nbs!=ncols || (*B)->rmap->bs!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Submatrix wrong size");
113     ierr = PetscArraycmp(c->ilen,lens,c->mbs,&flag);CHKERRQ(ierr);
114     if (!flag) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
115     ierr = PetscArrayzero(c->ilen,c->mbs);CHKERRQ(ierr);
116     C    = *B;
117   } else {
118     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
119     ierr = MatSetSizes(C,nrows*bs,ncols*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
120     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
121     ierr = MatSeqBAIJSetPreallocation(C,bs,0,lens);CHKERRQ(ierr);
122   }
123   c = (Mat_SeqBAIJ*)(C->data);
124   for (i=0; i<nrows; i++) {
125     row      = irow[i];
126     kstart   = ai[row];
127     kend     = kstart + a->ilen[row];
128     mat_i    = c->i[i];
129     mat_j    = c->j + mat_i;
130     mat_a    = c->a + mat_i*bs2;
131     mat_ilen = c->ilen + i;
132     for (k=kstart; k<kend; k++) {
133       if ((tcol=ssmap[a->j[k]])) {
134         *mat_j++ = tcol - 1;
135         ierr     = PetscArraycpy(mat_a,a->a+k*bs2,bs2);CHKERRQ(ierr);
136         mat_a   += bs2;
137         (*mat_ilen)++;
138       }
139     }
140   }
141   /* sort */
142   {
143     MatScalar *work;
144     ierr = PetscMalloc1(bs2,&work);CHKERRQ(ierr);
145     for (i=0; i<nrows; i++) {
146       PetscInt ilen;
147       mat_i = c->i[i];
148       mat_j = c->j + mat_i;
149       mat_a = c->a + mat_i*bs2;
150       ilen  = c->ilen[i];
151       ierr  = PetscSortIntWithDataArray(ilen,mat_j,mat_a,bs2*sizeof(MatScalar),work);CHKERRQ(ierr);
152     }
153     ierr = PetscFree(work);CHKERRQ(ierr);
154   }
155 
156   /* Free work space */
157   ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
158   ierr = PetscFree(smap);CHKERRQ(ierr);
159   ierr = PetscFree(lens);CHKERRQ(ierr);
160   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
161   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
162 
163   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
164   *B   = C;
165   PetscFunctionReturn(0);
166 }
167 
168 PetscErrorCode MatCreateSubMatrix_SeqBAIJ(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
169 {
170   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
171   IS             is1,is2;
172   PetscErrorCode ierr;
173   PetscInt       *vary,*iary,nrows,ncols,i,bs=A->rmap->bs,count,maxmnbs,j;
174   const PetscInt *irow,*icol;
175 
176   PetscFunctionBegin;
177   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
178   ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
179   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
180   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
181 
182   /* Verify if the indices corespond to each element in a block
183    and form the IS with compressed IS */
184   maxmnbs = PetscMax(a->mbs,a->nbs);
185   ierr = PetscMalloc2(maxmnbs,&vary,maxmnbs,&iary);CHKERRQ(ierr);
186   ierr = PetscArrayzero(vary,a->mbs);CHKERRQ(ierr);
187   for (i=0; i<nrows; i++) vary[irow[i]/bs]++;
188   for (i=0; i<a->mbs; i++) {
189     if (vary[i]!=0 && vary[i]!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Index set does not match blocks");
190   }
191   count = 0;
192   for (i=0; i<nrows; i++) {
193     j = irow[i] / bs;
194     if ((vary[j]--)==bs) iary[count++] = j;
195   }
196   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,iary,PETSC_COPY_VALUES,&is1);CHKERRQ(ierr);
197 
198   ierr = PetscArrayzero(vary,a->nbs);CHKERRQ(ierr);
199   for (i=0; i<ncols; i++) vary[icol[i]/bs]++;
200   for (i=0; i<a->nbs; i++) {
201     if (vary[i]!=0 && vary[i]!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal error in PETSc");
202   }
203   count = 0;
204   for (i=0; i<ncols; i++) {
205     j = icol[i] / bs;
206     if ((vary[j]--)==bs) iary[count++] = j;
207   }
208   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,iary,PETSC_COPY_VALUES,&is2);CHKERRQ(ierr);
209   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
210   ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
211   ierr = PetscFree2(vary,iary);CHKERRQ(ierr);
212 
213   ierr = MatCreateSubMatrix_SeqBAIJ_Private(A,is1,is2,scall,B);CHKERRQ(ierr);
214   ierr = ISDestroy(&is1);CHKERRQ(ierr);
215   ierr = ISDestroy(&is2);CHKERRQ(ierr);
216   PetscFunctionReturn(0);
217 }
218 
219 PetscErrorCode MatDestroySubMatrix_SeqBAIJ(Mat C)
220 {
221   PetscErrorCode ierr;
222   Mat_SeqBAIJ    *c = (Mat_SeqBAIJ*)C->data;
223   Mat_SubSppt    *submatj = c->submatis1;
224 
225   PetscFunctionBegin;
226   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
227   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
228   PetscFunctionReturn(0);
229 }
230 
231 PetscErrorCode MatDestroySubMatrices_SeqBAIJ(PetscInt n,Mat *mat[])
232 {
233   PetscErrorCode ierr;
234   PetscInt       i;
235   Mat            C;
236   Mat_SeqBAIJ    *c;
237   Mat_SubSppt    *submatj;
238 
239   PetscFunctionBegin;
240   for (i=0; i<n; i++) {
241     C       = (*mat)[i];
242     c       = (Mat_SeqBAIJ*)C->data;
243     submatj = c->submatis1;
244     if (submatj) {
245       ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
246       ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
247       ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
248       ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
249       ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
250       ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
251     } else {
252       ierr = MatDestroy(&C);CHKERRQ(ierr);
253     }
254   }
255   ierr = PetscFree(*mat);CHKERRQ(ierr);
256   PetscFunctionReturn(0);
257 }
258 
259 PetscErrorCode MatCreateSubMatrices_SeqBAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
260 {
261   PetscErrorCode ierr;
262   PetscInt       i;
263 
264   PetscFunctionBegin;
265   if (scall == MAT_INITIAL_MATRIX) {
266     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
267   }
268 
269   for (i=0; i<n; i++) {
270     ierr = MatCreateSubMatrix_SeqBAIJ(A,irow[i],icol[i],scall,&(*B)[i]);CHKERRQ(ierr);
271   }
272   PetscFunctionReturn(0);
273 }
274 
275 /* -------------------------------------------------------*/
276 /* Should check that shapes of vectors and matrices match */
277 /* -------------------------------------------------------*/
278 
279 PetscErrorCode MatMult_SeqBAIJ_1(Mat A,Vec xx,Vec zz)
280 {
281   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
282   PetscScalar       *z,sum;
283   const PetscScalar *x;
284   const MatScalar   *v;
285   PetscErrorCode    ierr;
286   PetscInt          mbs,i,n;
287   const PetscInt    *idx,*ii,*ridx=NULL;
288   PetscBool         usecprow=a->compressedrow.use;
289 
290   PetscFunctionBegin;
291   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
292   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
293 
294   if (usecprow) {
295     mbs  = a->compressedrow.nrows;
296     ii   = a->compressedrow.i;
297     ridx = a->compressedrow.rindex;
298     ierr = PetscArrayzero(z,a->mbs);CHKERRQ(ierr);
299   } else {
300     mbs = a->mbs;
301     ii  = a->i;
302   }
303 
304   for (i=0; i<mbs; i++) {
305     n   = ii[1] - ii[0];
306     v   = a->a + ii[0];
307     idx = a->j + ii[0];
308     ii++;
309     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
310     PetscPrefetchBlock(v+1*n,1*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
311     sum = 0.0;
312     PetscSparseDensePlusDot(sum,x,v,idx,n);
313     if (usecprow) {
314       z[ridx[i]] = sum;
315     } else {
316       z[i]       = sum;
317     }
318   }
319   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
320   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
321   ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
322   PetscFunctionReturn(0);
323 }
324 
325 PetscErrorCode MatMult_SeqBAIJ_2(Mat A,Vec xx,Vec zz)
326 {
327   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
328   PetscScalar       *z = NULL,sum1,sum2,*zarray;
329   const PetscScalar *x,*xb;
330   PetscScalar       x1,x2;
331   const MatScalar   *v;
332   PetscErrorCode    ierr;
333   PetscInt          mbs,i,*idx,*ii,j,n,*ridx=NULL;
334   PetscBool         usecprow=a->compressedrow.use;
335 
336   PetscFunctionBegin;
337   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
338   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
339 
340   idx = a->j;
341   v   = a->a;
342   if (usecprow) {
343     mbs  = a->compressedrow.nrows;
344     ii   = a->compressedrow.i;
345     ridx = a->compressedrow.rindex;
346     ierr = PetscArrayzero(zarray,2*a->mbs);CHKERRQ(ierr);
347   } else {
348     mbs = a->mbs;
349     ii  = a->i;
350     z   = zarray;
351   }
352 
353   for (i=0; i<mbs; i++) {
354     n           = ii[1] - ii[0]; ii++;
355     sum1        = 0.0; sum2 = 0.0;
356     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
357     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
358     for (j=0; j<n; j++) {
359       xb    = x + 2*(*idx++); x1 = xb[0]; x2 = xb[1];
360       sum1 += v[0]*x1 + v[2]*x2;
361       sum2 += v[1]*x1 + v[3]*x2;
362       v    += 4;
363     }
364     if (usecprow) z = zarray + 2*ridx[i];
365     z[0] = sum1; z[1] = sum2;
366     if (!usecprow) z += 2;
367   }
368   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
369   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
370   ierr = PetscLogFlops(8.0*a->nz - 2.0*a->nonzerorowcnt);CHKERRQ(ierr);
371   PetscFunctionReturn(0);
372 }
373 
374 PetscErrorCode MatMult_SeqBAIJ_3(Mat A,Vec xx,Vec zz)
375 {
376   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
377   PetscScalar       *z = NULL,sum1,sum2,sum3,x1,x2,x3,*zarray;
378   const PetscScalar *x,*xb;
379   const MatScalar   *v;
380   PetscErrorCode    ierr;
381   PetscInt          mbs,i,*idx,*ii,j,n,*ridx=NULL;
382   PetscBool         usecprow=a->compressedrow.use;
383 
384 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
385 #pragma disjoint(*v,*z,*xb)
386 #endif
387 
388   PetscFunctionBegin;
389   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
390   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
391 
392   idx = a->j;
393   v   = a->a;
394   if (usecprow) {
395     mbs  = a->compressedrow.nrows;
396     ii   = a->compressedrow.i;
397     ridx = a->compressedrow.rindex;
398     ierr = PetscArrayzero(zarray,3*a->mbs);CHKERRQ(ierr);
399   } else {
400     mbs = a->mbs;
401     ii  = a->i;
402     z   = zarray;
403   }
404 
405   for (i=0; i<mbs; i++) {
406     n           = ii[1] - ii[0]; ii++;
407     sum1        = 0.0; sum2 = 0.0; sum3 = 0.0;
408     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
409     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
410     for (j=0; j<n; j++) {
411       xb = x + 3*(*idx++);
412       x1 = xb[0];
413       x2 = xb[1];
414       x3 = xb[2];
415 
416       sum1 += v[0]*x1 + v[3]*x2 + v[6]*x3;
417       sum2 += v[1]*x1 + v[4]*x2 + v[7]*x3;
418       sum3 += v[2]*x1 + v[5]*x2 + v[8]*x3;
419       v    += 9;
420     }
421     if (usecprow) z = zarray + 3*ridx[i];
422     z[0] = sum1; z[1] = sum2; z[2] = sum3;
423     if (!usecprow) z += 3;
424   }
425   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
426   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
427   ierr = PetscLogFlops(18.0*a->nz - 3.0*a->nonzerorowcnt);CHKERRQ(ierr);
428   PetscFunctionReturn(0);
429 }
430 
431 PetscErrorCode MatMult_SeqBAIJ_4(Mat A,Vec xx,Vec zz)
432 {
433   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
434   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,x1,x2,x3,x4,*zarray;
435   const PetscScalar *x,*xb;
436   const MatScalar   *v;
437   PetscErrorCode    ierr;
438   PetscInt          mbs,i,*idx,*ii,j,n,*ridx=NULL;
439   PetscBool         usecprow=a->compressedrow.use;
440 
441   PetscFunctionBegin;
442   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
443   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
444 
445   idx = a->j;
446   v   = a->a;
447   if (usecprow) {
448     mbs  = a->compressedrow.nrows;
449     ii   = a->compressedrow.i;
450     ridx = a->compressedrow.rindex;
451     ierr = PetscArrayzero(zarray,4*a->mbs);CHKERRQ(ierr);
452   } else {
453     mbs = a->mbs;
454     ii  = a->i;
455     z   = zarray;
456   }
457 
458   for (i=0; i<mbs; i++) {
459     n = ii[1] - ii[0];
460     ii++;
461     sum1 = 0.0;
462     sum2 = 0.0;
463     sum3 = 0.0;
464     sum4 = 0.0;
465 
466     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
467     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
468     for (j=0; j<n; j++) {
469       xb    = x + 4*(*idx++);
470       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
471       sum1 += v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
472       sum2 += v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
473       sum3 += v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
474       sum4 += v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
475       v    += 16;
476     }
477     if (usecprow) z = zarray + 4*ridx[i];
478     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4;
479     if (!usecprow) z += 4;
480   }
481   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
482   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
483   ierr = PetscLogFlops(32.0*a->nz - 4.0*a->nonzerorowcnt);CHKERRQ(ierr);
484   PetscFunctionReturn(0);
485 }
486 
487 PetscErrorCode MatMult_SeqBAIJ_5(Mat A,Vec xx,Vec zz)
488 {
489   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
490   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5,*zarray;
491   const PetscScalar *xb,*x;
492   const MatScalar   *v;
493   PetscErrorCode    ierr;
494   const PetscInt    *idx,*ii,*ridx=NULL;
495   PetscInt          mbs,i,j,n;
496   PetscBool         usecprow=a->compressedrow.use;
497 
498   PetscFunctionBegin;
499   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
500   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
501 
502   idx = a->j;
503   v   = a->a;
504   if (usecprow) {
505     mbs  = a->compressedrow.nrows;
506     ii   = a->compressedrow.i;
507     ridx = a->compressedrow.rindex;
508     ierr = PetscArrayzero(zarray,5*a->mbs);CHKERRQ(ierr);
509   } else {
510     mbs = a->mbs;
511     ii  = a->i;
512     z   = zarray;
513   }
514 
515   for (i=0; i<mbs; i++) {
516     n           = ii[1] - ii[0]; ii++;
517     sum1        = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0;
518     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
519     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
520     for (j=0; j<n; j++) {
521       xb    = x + 5*(*idx++);
522       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4];
523       sum1 += v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
524       sum2 += v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
525       sum3 += v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
526       sum4 += v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
527       sum5 += v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
528       v    += 25;
529     }
530     if (usecprow) z = zarray + 5*ridx[i];
531     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5;
532     if (!usecprow) z += 5;
533   }
534   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
535   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
536   ierr = PetscLogFlops(50.0*a->nz - 5.0*a->nonzerorowcnt);CHKERRQ(ierr);
537   PetscFunctionReturn(0);
538 }
539 
540 PetscErrorCode MatMult_SeqBAIJ_6(Mat A,Vec xx,Vec zz)
541 {
542   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
543   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6;
544   const PetscScalar *x,*xb;
545   PetscScalar       x1,x2,x3,x4,x5,x6,*zarray;
546   const MatScalar   *v;
547   PetscErrorCode    ierr;
548   PetscInt          mbs,i,*idx,*ii,j,n,*ridx=NULL;
549   PetscBool         usecprow=a->compressedrow.use;
550 
551   PetscFunctionBegin;
552   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
553   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
554 
555   idx = a->j;
556   v   = a->a;
557   if (usecprow) {
558     mbs  = a->compressedrow.nrows;
559     ii   = a->compressedrow.i;
560     ridx = a->compressedrow.rindex;
561     ierr = PetscArrayzero(zarray,6*a->mbs);CHKERRQ(ierr);
562   } else {
563     mbs = a->mbs;
564     ii  = a->i;
565     z   = zarray;
566   }
567 
568   for (i=0; i<mbs; i++) {
569     n  = ii[1] - ii[0];
570     ii++;
571     sum1 = 0.0;
572     sum2 = 0.0;
573     sum3 = 0.0;
574     sum4 = 0.0;
575     sum5 = 0.0;
576     sum6 = 0.0;
577 
578     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
579     PetscPrefetchBlock(v+36*n,36*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
580     for (j=0; j<n; j++) {
581       xb    = x + 6*(*idx++);
582       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5];
583       sum1 += v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
584       sum2 += v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
585       sum3 += v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
586       sum4 += v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
587       sum5 += v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
588       sum6 += v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
589       v    += 36;
590     }
591     if (usecprow) z = zarray + 6*ridx[i];
592     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6;
593     if (!usecprow) z += 6;
594   }
595 
596   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
597   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
598   ierr = PetscLogFlops(72.0*a->nz - 6.0*a->nonzerorowcnt);CHKERRQ(ierr);
599   PetscFunctionReturn(0);
600 }
601 
602 PetscErrorCode MatMult_SeqBAIJ_7(Mat A,Vec xx,Vec zz)
603 {
604   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
605   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7;
606   const PetscScalar *x,*xb;
607   PetscScalar       x1,x2,x3,x4,x5,x6,x7,*zarray;
608   const MatScalar   *v;
609   PetscErrorCode    ierr;
610   PetscInt          mbs,i,*idx,*ii,j,n,*ridx=NULL;
611   PetscBool         usecprow=a->compressedrow.use;
612 
613   PetscFunctionBegin;
614   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
615   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
616 
617   idx = a->j;
618   v   = a->a;
619   if (usecprow) {
620     mbs  = a->compressedrow.nrows;
621     ii   = a->compressedrow.i;
622     ridx = a->compressedrow.rindex;
623     ierr = PetscArrayzero(zarray,7*a->mbs);CHKERRQ(ierr);
624   } else {
625     mbs = a->mbs;
626     ii  = a->i;
627     z   = zarray;
628   }
629 
630   for (i=0; i<mbs; i++) {
631     n  = ii[1] - ii[0];
632     ii++;
633     sum1 = 0.0;
634     sum2 = 0.0;
635     sum3 = 0.0;
636     sum4 = 0.0;
637     sum5 = 0.0;
638     sum6 = 0.0;
639     sum7 = 0.0;
640 
641     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
642     PetscPrefetchBlock(v+49*n,49*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
643     for (j=0; j<n; j++) {
644       xb    = x + 7*(*idx++);
645       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5]; x7 = xb[6];
646       sum1 += v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
647       sum2 += v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
648       sum3 += v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
649       sum4 += v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
650       sum5 += v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
651       sum6 += v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
652       sum7 += v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
653       v    += 49;
654     }
655     if (usecprow) z = zarray + 7*ridx[i];
656     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
657     if (!usecprow) z += 7;
658   }
659 
660   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
661   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
662   ierr = PetscLogFlops(98.0*a->nz - 7.0*a->nonzerorowcnt);CHKERRQ(ierr);
663   PetscFunctionReturn(0);
664 }
665 
666 #if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
667 PetscErrorCode MatMult_SeqBAIJ_9_AVX2(Mat A,Vec xx,Vec zz)
668 {
669   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
670   PetscScalar    *z = NULL,*work,*workt,*zarray;
671   const PetscScalar *x,*xb;
672   const MatScalar   *v;
673   PetscErrorCode ierr;
674   PetscInt       mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2;
675   const PetscInt *idx,*ii,*ridx=NULL;
676   PetscInt       k;
677   PetscBool      usecprow=a->compressedrow.use;
678 
679   __m256d a0,a1,a2,a3,a4,a5;
680   __m256d w0,w1,w2,w3;
681   __m256d z0,z1,z2;
682   __m256i mask1 = _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL<<63);
683 
684   PetscFunctionBegin;
685   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
686   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
687 
688   idx = a->j;
689   v   = a->a;
690   if (usecprow) {
691     mbs  = a->compressedrow.nrows;
692     ii   = a->compressedrow.i;
693     ridx = a->compressedrow.rindex;
694     ierr = PetscArrayzero(zarray,bs*a->mbs);CHKERRQ(ierr);
695   } else {
696     mbs = a->mbs;
697     ii  = a->i;
698     z   = zarray;
699   }
700 
701   if (!a->mult_work) {
702     k    = PetscMax(A->rmap->n,A->cmap->n);
703     ierr = PetscMalloc1(k+1,&a->mult_work);CHKERRQ(ierr);
704   }
705 
706   work = a->mult_work;
707   for (i=0; i<mbs; i++) {
708     n           = ii[1] - ii[0]; ii++;
709     workt       = work;
710     for (j=0; j<n; j++) {
711       xb = x + bs*(*idx++);
712       for (k=0; k<bs; k++) workt[k] = xb[k];
713       workt += bs;
714     }
715     if (usecprow) z = zarray + bs*ridx[i];
716 
717     z0 = _mm256_setzero_pd(); z1 = _mm256_setzero_pd(); z2 = _mm256_setzero_pd();
718 
719     for (j=0; j<n; j++) {
720       /* first column of a */
721       w0 = _mm256_set1_pd(work[j*9  ]);
722       a0 = _mm256_loadu_pd(&v[j*81  ]); z0 = _mm256_fmadd_pd(a0,w0,z0);
723       a1 = _mm256_loadu_pd(&v[j*81+4]); z1 = _mm256_fmadd_pd(a1,w0,z1);
724       a2 = _mm256_loadu_pd(&v[j*81+8]); z2 = _mm256_fmadd_pd(a2,w0,z2);
725 
726       /* second column of a */
727       w1 = _mm256_set1_pd(work[j*9+ 1]);
728       a0 = _mm256_loadu_pd(&v[j*81+ 9]); z0 = _mm256_fmadd_pd(a0,w1,z0);
729       a1 = _mm256_loadu_pd(&v[j*81+13]); z1 = _mm256_fmadd_pd(a1,w1,z1);
730       a2 = _mm256_loadu_pd(&v[j*81+17]); z2 = _mm256_fmadd_pd(a2,w1,z2);
731 
732       /* third column of a */
733       w2 = _mm256_set1_pd(work[j*9 +2]);
734       a3 = _mm256_loadu_pd(&v[j*81+18]); z0 = _mm256_fmadd_pd(a3,w2,z0);
735       a4 = _mm256_loadu_pd(&v[j*81+22]); z1 = _mm256_fmadd_pd(a4,w2,z1);
736       a5 = _mm256_loadu_pd(&v[j*81+26]); z2 = _mm256_fmadd_pd(a5,w2,z2);
737 
738       /* fourth column of a */
739       w3 = _mm256_set1_pd(work[j*9+ 3]);
740       a0 = _mm256_loadu_pd(&v[j*81+27]); z0 = _mm256_fmadd_pd(a0,w3,z0);
741       a1 = _mm256_loadu_pd(&v[j*81+31]); z1 = _mm256_fmadd_pd(a1,w3,z1);
742       a2 = _mm256_loadu_pd(&v[j*81+35]); z2 = _mm256_fmadd_pd(a2,w3,z2);
743 
744       /* fifth column of a */
745       w0 = _mm256_set1_pd(work[j*9+ 4]);
746       a3 = _mm256_loadu_pd(&v[j*81+36]); z0 = _mm256_fmadd_pd(a3,w0,z0);
747       a4 = _mm256_loadu_pd(&v[j*81+40]); z1 = _mm256_fmadd_pd(a4,w0,z1);
748       a5 = _mm256_loadu_pd(&v[j*81+44]); z2 = _mm256_fmadd_pd(a5,w0,z2);
749 
750       /* sixth column of a */
751       w1 = _mm256_set1_pd(work[j*9+ 5]);
752       a0 = _mm256_loadu_pd(&v[j*81+45]); z0 = _mm256_fmadd_pd(a0,w1,z0);
753       a1 = _mm256_loadu_pd(&v[j*81+49]); z1 = _mm256_fmadd_pd(a1,w1,z1);
754       a2 = _mm256_loadu_pd(&v[j*81+53]); z2 = _mm256_fmadd_pd(a2,w1,z2);
755 
756       /* seventh column of a */
757       w2 = _mm256_set1_pd(work[j*9+ 6]);
758       a0 = _mm256_loadu_pd(&v[j*81+54]); z0 = _mm256_fmadd_pd(a0,w2,z0);
759       a1 = _mm256_loadu_pd(&v[j*81+58]); z1 = _mm256_fmadd_pd(a1,w2,z1);
760       a2 = _mm256_loadu_pd(&v[j*81+62]); z2 = _mm256_fmadd_pd(a2,w2,z2);
761 
762       /* eigth column of a */
763       w3 = _mm256_set1_pd(work[j*9+ 7]);
764       a3 = _mm256_loadu_pd(&v[j*81+63]); z0 = _mm256_fmadd_pd(a3,w3,z0);
765       a4 = _mm256_loadu_pd(&v[j*81+67]); z1 = _mm256_fmadd_pd(a4,w3,z1);
766       a5 = _mm256_loadu_pd(&v[j*81+71]); z2 = _mm256_fmadd_pd(a5,w3,z2);
767 
768       /* ninth column of a */
769       w0 = _mm256_set1_pd(work[j*9+ 8]);
770       a0 = _mm256_loadu_pd(&v[j*81+72]); z0 = _mm256_fmadd_pd(a0,w0,z0);
771       a1 = _mm256_loadu_pd(&v[j*81+76]); z1 = _mm256_fmadd_pd(a1,w0,z1);
772       a2 = _mm256_maskload_pd(&v[j*81+80],mask1); z2 = _mm256_fmadd_pd(a2,w0,z2);
773     }
774 
775     _mm256_storeu_pd(&z[ 0], z0); _mm256_storeu_pd(&z[ 4], z1); _mm256_maskstore_pd(&z[8], mask1, z2);
776 
777     v += n*bs2;
778     if (!usecprow) z += bs;
779   }
780   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
781   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
782   ierr = PetscLogFlops(2.0*a->nz*bs2 - bs*a->nonzerorowcnt);CHKERRQ(ierr);
783   PetscFunctionReturn(0);
784 }
785 #endif
786 
787 PetscErrorCode MatMult_SeqBAIJ_11(Mat A,Vec xx,Vec zz)
788 {
789   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
790   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7,sum8,sum9,sum10,sum11;
791   const PetscScalar *x,*xb;
792   PetscScalar       *zarray,xv;
793   const MatScalar   *v;
794   PetscErrorCode    ierr;
795   const PetscInt    *ii,*ij=a->j,*idx;
796   PetscInt          mbs,i,j,k,n,*ridx=NULL;
797   PetscBool         usecprow=a->compressedrow.use;
798 
799   PetscFunctionBegin;
800   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
801   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
802 
803   v = a->a;
804   if (usecprow) {
805     mbs  = a->compressedrow.nrows;
806     ii   = a->compressedrow.i;
807     ridx = a->compressedrow.rindex;
808     ierr = PetscArrayzero(zarray,11*a->mbs);CHKERRQ(ierr);
809   } else {
810     mbs = a->mbs;
811     ii  = a->i;
812     z   = zarray;
813   }
814 
815   for (i=0; i<mbs; i++) {
816     n    = ii[i+1] - ii[i];
817     idx  = ij + ii[i];
818     sum1 = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0; sum6 = 0.0; sum7 = 0.0;
819     sum8 = 0.0; sum9 = 0.0; sum10 = 0.0; sum11 = 0.0;
820 
821     for (j=0; j<n; j++) {
822       xb = x + 11*(idx[j]);
823 
824       for (k=0; k<11; k++) {
825         xv     =  xb[k];
826         sum1  += v[0]*xv;
827         sum2  += v[1]*xv;
828         sum3  += v[2]*xv;
829         sum4  += v[3]*xv;
830         sum5  += v[4]*xv;
831         sum6  += v[5]*xv;
832         sum7  += v[6]*xv;
833         sum8  += v[7]*xv;
834         sum9  += v[8]*xv;
835         sum10 += v[9]*xv;
836         sum11 += v[10]*xv;
837         v     += 11;
838       }
839     }
840     if (usecprow) z = zarray + 11*ridx[i];
841     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
842     z[7] = sum8; z[8] = sum9; z[9] = sum10; z[10] = sum11;
843 
844     if (!usecprow) z += 11;
845   }
846 
847   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
848   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
849   ierr = PetscLogFlops(242.0*a->nz - 11.0*a->nonzerorowcnt);CHKERRQ(ierr);
850   PetscFunctionReturn(0);
851 }
852 
853 /* MatMult_SeqBAIJ_15 version 1: Columns in the block are accessed one at a time */
854 /* Default MatMult for block size 15 */
855 PetscErrorCode MatMult_SeqBAIJ_15_ver1(Mat A,Vec xx,Vec zz)
856 {
857   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
858   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7,sum8,sum9,sum10,sum11,sum12,sum13,sum14,sum15;
859   const PetscScalar *x,*xb;
860   PetscScalar       *zarray,xv;
861   const MatScalar   *v;
862   PetscErrorCode    ierr;
863   const PetscInt    *ii,*ij=a->j,*idx;
864   PetscInt          mbs,i,j,k,n,*ridx=NULL;
865   PetscBool         usecprow=a->compressedrow.use;
866 
867   PetscFunctionBegin;
868   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
869   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
870 
871   v = a->a;
872   if (usecprow) {
873     mbs  = a->compressedrow.nrows;
874     ii   = a->compressedrow.i;
875     ridx = a->compressedrow.rindex;
876     ierr = PetscArrayzero(zarray,15*a->mbs);CHKERRQ(ierr);
877   } else {
878     mbs = a->mbs;
879     ii  = a->i;
880     z   = zarray;
881   }
882 
883   for (i=0; i<mbs; i++) {
884     n    = ii[i+1] - ii[i];
885     idx  = ij + ii[i];
886     sum1 = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0; sum6 = 0.0; sum7 = 0.0;
887     sum8 = 0.0; sum9 = 0.0; sum10 = 0.0; sum11 = 0.0; sum12 = 0.0; sum13 = 0.0; sum14 = 0.0;sum15 = 0.0;
888 
889     for (j=0; j<n; j++) {
890       xb = x + 15*(idx[j]);
891 
892       for (k=0; k<15; k++) {
893         xv     =  xb[k];
894         sum1  += v[0]*xv;
895         sum2  += v[1]*xv;
896         sum3  += v[2]*xv;
897         sum4  += v[3]*xv;
898         sum5  += v[4]*xv;
899         sum6  += v[5]*xv;
900         sum7  += v[6]*xv;
901         sum8  += v[7]*xv;
902         sum9  += v[8]*xv;
903         sum10 += v[9]*xv;
904         sum11 += v[10]*xv;
905         sum12 += v[11]*xv;
906         sum13 += v[12]*xv;
907         sum14 += v[13]*xv;
908         sum15 += v[14]*xv;
909         v     += 15;
910       }
911     }
912     if (usecprow) z = zarray + 15*ridx[i];
913     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
914     z[7] = sum8; z[8] = sum9; z[9] = sum10; z[10] = sum11; z[11] = sum12; z[12] = sum13; z[13] = sum14;z[14] = sum15;
915 
916     if (!usecprow) z += 15;
917   }
918 
919   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
920   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
921   ierr = PetscLogFlops(450.0*a->nz - 15.0*a->nonzerorowcnt);CHKERRQ(ierr);
922   PetscFunctionReturn(0);
923 }
924 
925 /* MatMult_SeqBAIJ_15_ver2 : Columns in the block are accessed in sets of 4,4,4,3 */
926 PetscErrorCode MatMult_SeqBAIJ_15_ver2(Mat A,Vec xx,Vec zz)
927 {
928   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
929   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7,sum8,sum9,sum10,sum11,sum12,sum13,sum14,sum15;
930   const PetscScalar *x,*xb;
931   PetscScalar       x1,x2,x3,x4,*zarray;
932   const MatScalar   *v;
933   PetscErrorCode    ierr;
934   const PetscInt    *ii,*ij=a->j,*idx;
935   PetscInt          mbs,i,j,n,*ridx=NULL;
936   PetscBool         usecprow=a->compressedrow.use;
937 
938   PetscFunctionBegin;
939   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
940   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
941 
942   v = a->a;
943   if (usecprow) {
944     mbs  = a->compressedrow.nrows;
945     ii   = a->compressedrow.i;
946     ridx = a->compressedrow.rindex;
947     ierr = PetscArrayzero(zarray,15*a->mbs);CHKERRQ(ierr);
948   } else {
949     mbs = a->mbs;
950     ii  = a->i;
951     z   = zarray;
952   }
953 
954   for (i=0; i<mbs; i++) {
955     n    = ii[i+1] - ii[i];
956     idx  = ij + ii[i];
957     sum1 = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0; sum6 = 0.0; sum7 = 0.0;
958     sum8 = 0.0; sum9 = 0.0; sum10 = 0.0; sum11 = 0.0; sum12 = 0.0; sum13 = 0.0; sum14 = 0.0;sum15 = 0.0;
959 
960     for (j=0; j<n; j++) {
961       xb = x + 15*(idx[j]);
962       x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
963 
964       sum1  += v[0]*x1 + v[15]*x2 + v[30]*x3   + v[45]*x4;
965       sum2  += v[1]*x1 + v[16]*x2 + v[31]*x3   + v[46]*x4;
966       sum3  += v[2]*x1 + v[17]*x2 + v[32]*x3  + v[47]*x4;
967       sum4  += v[3]*x1 + v[18]*x2 + v[33]*x3  + v[48]*x4;
968       sum5  += v[4]*x1 + v[19]*x2 + v[34]*x3   + v[49]*x4;
969       sum6  += v[5]*x1 + v[20]*x2 + v[35]*x3   + v[50]*x4;
970       sum7  += v[6]*x1 + v[21]*x2 + v[36]*x3  + v[51]*x4;
971       sum8  += v[7]*x1 + v[22]*x2 + v[37]*x3  + v[52]*x4;
972       sum9  += v[8]*x1 + v[23]*x2 + v[38]*x3   + v[53]*x4;
973       sum10 += v[9]*x1 + v[24]*x2 + v[39]*x3   + v[54]*x4;
974       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3  + v[55]*x4;
975       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3  + v[56]*x4;
976       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3   + v[57]*x4;
977       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3   + v[58]*x4;
978       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3  + v[59]*x4;
979 
980       v += 60;
981 
982       x1 = xb[4]; x2 = xb[5]; x3 = xb[6]; x4 = xb[7];
983 
984       sum1  += v[0]*x1 + v[15]*x2 + v[30]*x3   + v[45]*x4;
985       sum2  += v[1]*x1 + v[16]*x2 + v[31]*x3   + v[46]*x4;
986       sum3  += v[2]*x1 + v[17]*x2 + v[32]*x3  + v[47]*x4;
987       sum4  += v[3]*x1 + v[18]*x2 + v[33]*x3  + v[48]*x4;
988       sum5  += v[4]*x1 + v[19]*x2 + v[34]*x3   + v[49]*x4;
989       sum6  += v[5]*x1 + v[20]*x2 + v[35]*x3   + v[50]*x4;
990       sum7  += v[6]*x1 + v[21]*x2 + v[36]*x3  + v[51]*x4;
991       sum8  += v[7]*x1 + v[22]*x2 + v[37]*x3  + v[52]*x4;
992       sum9  += v[8]*x1 + v[23]*x2 + v[38]*x3   + v[53]*x4;
993       sum10 += v[9]*x1 + v[24]*x2 + v[39]*x3   + v[54]*x4;
994       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3  + v[55]*x4;
995       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3  + v[56]*x4;
996       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3   + v[57]*x4;
997       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3   + v[58]*x4;
998       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3  + v[59]*x4;
999       v     += 60;
1000 
1001       x1     = xb[8]; x2 = xb[9]; x3 = xb[10]; x4 = xb[11];
1002       sum1  += v[0]*x1 + v[15]*x2 + v[30]*x3   + v[45]*x4;
1003       sum2  += v[1]*x1 + v[16]*x2 + v[31]*x3   + v[46]*x4;
1004       sum3  += v[2]*x1 + v[17]*x2 + v[32]*x3  + v[47]*x4;
1005       sum4  += v[3]*x1 + v[18]*x2 + v[33]*x3  + v[48]*x4;
1006       sum5  += v[4]*x1 + v[19]*x2 + v[34]*x3   + v[49]*x4;
1007       sum6  += v[5]*x1 + v[20]*x2 + v[35]*x3   + v[50]*x4;
1008       sum7  += v[6]*x1 + v[21]*x2 + v[36]*x3  + v[51]*x4;
1009       sum8  += v[7]*x1 + v[22]*x2 + v[37]*x3  + v[52]*x4;
1010       sum9  += v[8]*x1 + v[23]*x2 + v[38]*x3   + v[53]*x4;
1011       sum10 += v[9]*x1 + v[24]*x2 + v[39]*x3   + v[54]*x4;
1012       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3  + v[55]*x4;
1013       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3  + v[56]*x4;
1014       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3   + v[57]*x4;
1015       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3   + v[58]*x4;
1016       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3  + v[59]*x4;
1017       v     += 60;
1018 
1019       x1     = xb[12]; x2 = xb[13]; x3 = xb[14];
1020       sum1  += v[0]*x1 + v[15]*x2 + v[30]*x3;
1021       sum2  += v[1]*x1 + v[16]*x2 + v[31]*x3;
1022       sum3  += v[2]*x1 + v[17]*x2 + v[32]*x3;
1023       sum4  += v[3]*x1 + v[18]*x2 + v[33]*x3;
1024       sum5  += v[4]*x1 + v[19]*x2 + v[34]*x3;
1025       sum6  += v[5]*x1 + v[20]*x2 + v[35]*x3;
1026       sum7  += v[6]*x1 + v[21]*x2 + v[36]*x3;
1027       sum8  += v[7]*x1 + v[22]*x2 + v[37]*x3;
1028       sum9  += v[8]*x1 + v[23]*x2 + v[38]*x3;
1029       sum10 += v[9]*x1 + v[24]*x2 + v[39]*x3;
1030       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3;
1031       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3;
1032       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3;
1033       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3;
1034       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3;
1035       v     += 45;
1036     }
1037     if (usecprow) z = zarray + 15*ridx[i];
1038     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
1039     z[7] = sum8; z[8] = sum9; z[9] = sum10; z[10] = sum11; z[11] = sum12; z[12] = sum13; z[13] = sum14;z[14] = sum15;
1040 
1041     if (!usecprow) z += 15;
1042   }
1043 
1044   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1045   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
1046   ierr = PetscLogFlops(450.0*a->nz - 15.0*a->nonzerorowcnt);CHKERRQ(ierr);
1047   PetscFunctionReturn(0);
1048 }
1049 
1050 /* MatMult_SeqBAIJ_15_ver3 : Columns in the block are accessed in sets of 8,7 */
1051 PetscErrorCode MatMult_SeqBAIJ_15_ver3(Mat A,Vec xx,Vec zz)
1052 {
1053   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1054   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7,sum8,sum9,sum10,sum11,sum12,sum13,sum14,sum15;
1055   const PetscScalar *x,*xb;
1056   PetscScalar       x1,x2,x3,x4,x5,x6,x7,x8,*zarray;
1057   const MatScalar   *v;
1058   PetscErrorCode    ierr;
1059   const PetscInt    *ii,*ij=a->j,*idx;
1060   PetscInt          mbs,i,j,n,*ridx=NULL;
1061   PetscBool         usecprow=a->compressedrow.use;
1062 
1063   PetscFunctionBegin;
1064   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1065   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
1066 
1067   v = a->a;
1068   if (usecprow) {
1069     mbs  = a->compressedrow.nrows;
1070     ii   = a->compressedrow.i;
1071     ridx = a->compressedrow.rindex;
1072     ierr = PetscArrayzero(zarray,15*a->mbs);CHKERRQ(ierr);
1073   } else {
1074     mbs = a->mbs;
1075     ii  = a->i;
1076     z   = zarray;
1077   }
1078 
1079   for (i=0; i<mbs; i++) {
1080     n    = ii[i+1] - ii[i];
1081     idx  = ij + ii[i];
1082     sum1 = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0; sum6 = 0.0; sum7 = 0.0;
1083     sum8 = 0.0; sum9 = 0.0; sum10 = 0.0; sum11 = 0.0; sum12 = 0.0; sum13 = 0.0; sum14 = 0.0;sum15 = 0.0;
1084 
1085     for (j=0; j<n; j++) {
1086       xb = x + 15*(idx[j]);
1087       x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5]; x7 = xb[6];
1088       x8 = xb[7];
1089 
1090       sum1  += v[0]*x1 + v[15]*x2  + v[30]*x3  + v[45]*x4 + v[60]*x5 + v[75]*x6 + v[90]*x7 + v[105]*x8;
1091       sum2  += v[1]*x1 + v[16]*x2  + v[31]*x3  + v[46]*x4 + v[61]*x5 + v[76]*x6 + v[91]*x7 + v[106]*x8;
1092       sum3  += v[2]*x1 + v[17]*x2  + v[32]*x3  + v[47]*x4 + v[62]*x5 + v[77]*x6 + v[92]*x7 + v[107]*x8;
1093       sum4  += v[3]*x1 + v[18]*x2 + v[33]*x3  + v[48]*x4 + v[63]*x5 + v[78]*x6 + v[93]*x7 + v[108]*x8;
1094       sum5  += v[4]*x1 + v[19]*x2 + v[34]*x3  + v[49]*x4 + v[64]*x5 + v[79]*x6 + v[94]*x7 + v[109]*x8;
1095       sum6  += v[5]*x1 + v[20]*x2 + v[35]*x3  + v[50]*x4 + v[65]*x5 + v[80]*x6 + v[95]*x7 + v[110]*x8;
1096       sum7  += v[6]*x1 + v[21]*x2 + v[36]*x3  + v[51]*x4 + v[66]*x5 + v[81]*x6 + v[96]*x7 + v[111]*x8;
1097       sum8  += v[7]*x1 + v[22]*x2  + v[37]*x3  + v[52]*x4 + v[67]*x5 + v[82]*x6 + v[97]*x7 + v[112]*x8;
1098       sum9  += v[8]*x1 + v[23]*x2  + v[38]*x3  + v[53]*x4 + v[68]*x5 + v[83]*x6 + v[98]*x7 + v[113]*x8;
1099       sum10 += v[9]*x1 + v[24]*x2  + v[39]*x3  + v[54]*x4 + v[69]*x5 + v[84]*x6 + v[99]*x7 + v[114]*x8;
1100       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3  + v[55]*x4 + v[70]*x5 + v[85]*x6 + v[100]*x7 + v[115]*x8;
1101       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3  + v[56]*x4 + v[71]*x5 + v[86]*x6 + v[101]*x7 + v[116]*x8;
1102       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3  + v[57]*x4 + v[72]*x5 + v[87]*x6 + v[102]*x7 + v[117]*x8;
1103       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3  + v[58]*x4 + v[73]*x5 + v[88]*x6 + v[103]*x7 + v[118]*x8;
1104       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3  + v[59]*x4 + v[74]*x5 + v[89]*x6 + v[104]*x7 + v[119]*x8;
1105       v     += 120;
1106 
1107       x1 = xb[8]; x2 = xb[9]; x3 = xb[10]; x4 = xb[11]; x5 = xb[12]; x6 = xb[13]; x7 = xb[14];
1108 
1109       sum1  += v[0]*x1 + v[15]*x2  + v[30]*x3  + v[45]*x4 + v[60]*x5 + v[75]*x6 + v[90]*x7;
1110       sum2  += v[1]*x1 + v[16]*x2  + v[31]*x3  + v[46]*x4 + v[61]*x5 + v[76]*x6 + v[91]*x7;
1111       sum3  += v[2]*x1 + v[17]*x2  + v[32]*x3  + v[47]*x4 + v[62]*x5 + v[77]*x6 + v[92]*x7;
1112       sum4  += v[3]*x1 + v[18]*x2 + v[33]*x3  + v[48]*x4 + v[63]*x5 + v[78]*x6 + v[93]*x7;
1113       sum5  += v[4]*x1 + v[19]*x2 + v[34]*x3  + v[49]*x4 + v[64]*x5 + v[79]*x6 + v[94]*x7;
1114       sum6  += v[5]*x1 + v[20]*x2 + v[35]*x3  + v[50]*x4 + v[65]*x5 + v[80]*x6 + v[95]*x7;
1115       sum7  += v[6]*x1 + v[21]*x2 + v[36]*x3  + v[51]*x4 + v[66]*x5 + v[81]*x6 + v[96]*x7;
1116       sum8  += v[7]*x1 + v[22]*x2  + v[37]*x3  + v[52]*x4 + v[67]*x5 + v[82]*x6 + v[97]*x7;
1117       sum9  += v[8]*x1 + v[23]*x2  + v[38]*x3  + v[53]*x4 + v[68]*x5 + v[83]*x6 + v[98]*x7;
1118       sum10 += v[9]*x1 + v[24]*x2  + v[39]*x3  + v[54]*x4 + v[69]*x5 + v[84]*x6 + v[99]*x7;
1119       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3  + v[55]*x4 + v[70]*x5 + v[85]*x6 + v[100]*x7;
1120       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3  + v[56]*x4 + v[71]*x5 + v[86]*x6 + v[101]*x7;
1121       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3  + v[57]*x4 + v[72]*x5 + v[87]*x6 + v[102]*x7;
1122       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3  + v[58]*x4 + v[73]*x5 + v[88]*x6 + v[103]*x7;
1123       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3  + v[59]*x4 + v[74]*x5 + v[89]*x6 + v[104]*x7;
1124       v     += 105;
1125     }
1126     if (usecprow) z = zarray + 15*ridx[i];
1127     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
1128     z[7] = sum8; z[8] = sum9; z[9] = sum10; z[10] = sum11; z[11] = sum12; z[12] = sum13; z[13] = sum14;z[14] = sum15;
1129 
1130     if (!usecprow) z += 15;
1131   }
1132 
1133   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1134   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
1135   ierr = PetscLogFlops(450.0*a->nz - 15.0*a->nonzerorowcnt);CHKERRQ(ierr);
1136   PetscFunctionReturn(0);
1137 }
1138 
1139 /* MatMult_SeqBAIJ_15_ver4 : All columns in the block are accessed at once */
1140 PetscErrorCode MatMult_SeqBAIJ_15_ver4(Mat A,Vec xx,Vec zz)
1141 {
1142   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1143   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7,sum8,sum9,sum10,sum11,sum12,sum13,sum14,sum15;
1144   const PetscScalar *x,*xb;
1145   PetscScalar       x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,*zarray;
1146   const MatScalar   *v;
1147   PetscErrorCode    ierr;
1148   const PetscInt    *ii,*ij=a->j,*idx;
1149   PetscInt          mbs,i,j,n,*ridx=NULL;
1150   PetscBool         usecprow=a->compressedrow.use;
1151 
1152   PetscFunctionBegin;
1153   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1154   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
1155 
1156   v = a->a;
1157   if (usecprow) {
1158     mbs  = a->compressedrow.nrows;
1159     ii   = a->compressedrow.i;
1160     ridx = a->compressedrow.rindex;
1161     ierr = PetscArrayzero(zarray,15*a->mbs);CHKERRQ(ierr);
1162   } else {
1163     mbs = a->mbs;
1164     ii  = a->i;
1165     z   = zarray;
1166   }
1167 
1168   for (i=0; i<mbs; i++) {
1169     n    = ii[i+1] - ii[i];
1170     idx  = ij + ii[i];
1171     sum1 = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0; sum6 = 0.0; sum7 = 0.0;
1172     sum8 = 0.0; sum9 = 0.0; sum10 = 0.0; sum11 = 0.0; sum12 = 0.0; sum13 = 0.0; sum14 = 0.0;sum15 = 0.0;
1173 
1174     for (j=0; j<n; j++) {
1175       xb = x + 15*(idx[j]);
1176       x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5]; x7 = xb[6];
1177       x8 = xb[7]; x9 = xb[8]; x10 = xb[9]; x11 = xb[10]; x12 = xb[11]; x13 = xb[12]; x14 = xb[13];x15 = xb[14];
1178 
1179       sum1  +=  v[0]*x1  + v[15]*x2 + v[30]*x3 + v[45]*x4 + v[60]*x5 + v[75]*x6 + v[90]*x7  + v[105]*x8 + v[120]*x9 + v[135]*x10 + v[150]*x11 + v[165]*x12 + v[180]*x13 + v[195]*x14 + v[210]*x15;
1180       sum2  +=  v[1]*x1  + v[16]*x2 + v[31]*x3 + v[46]*x4 + v[61]*x5 + v[76]*x6 + v[91]*x7  + v[106]*x8 + v[121]*x9 + v[136]*x10 + v[151]*x11 + v[166]*x12 + v[181]*x13 + v[196]*x14 + v[211]*x15;
1181       sum3  +=  v[2]*x1  + v[17]*x2 + v[32]*x3 + v[47]*x4 + v[62]*x5 + v[77]*x6 + v[92]*x7  + v[107]*x8 + v[122]*x9 + v[137]*x10 + v[152]*x11 + v[167]*x12 + v[182]*x13 + v[197]*x14 + v[212]*x15;
1182       sum4  +=  v[3]*x1  + v[18]*x2 + v[33]*x3 + v[48]*x4 + v[63]*x5 + v[78]*x6 + v[93]*x7  + v[108]*x8 + v[123]*x9 + v[138]*x10 + v[153]*x11 + v[168]*x12 + v[183]*x13 + v[198]*x14 + v[213]*x15;
1183       sum5  += v[4]*x1  + v[19]*x2 + v[34]*x3 + v[49]*x4 + v[64]*x5 + v[79]*x6 + v[94]*x7  + v[109]*x8 + v[124]*x9 + v[139]*x10 + v[154]*x11 + v[169]*x12 + v[184]*x13 + v[199]*x14 + v[214]*x15;
1184       sum6  += v[5]*x1  + v[20]*x2 + v[35]*x3 + v[50]*x4 + v[65]*x5 + v[80]*x6 + v[95]*x7  + v[110]*x8 + v[125]*x9 + v[140]*x10 + v[155]*x11 + v[170]*x12 + v[185]*x13 + v[200]*x14 + v[215]*x15;
1185       sum7  += v[6]*x1  + v[21]*x2 + v[36]*x3 + v[51]*x4 + v[66]*x5 + v[81]*x6 + v[96]*x7  + v[111]*x8 + v[126]*x9 + v[141]*x10 + v[156]*x11 + v[171]*x12 + v[186]*x13 + v[201]*x14 + v[216]*x15;
1186       sum8  += v[7]*x1  + v[22]*x2 + v[37]*x3 + v[52]*x4 + v[67]*x5 + v[82]*x6 + v[97]*x7  + v[112]*x8 + v[127]*x9 + v[142]*x10 + v[157]*x11 + v[172]*x12 + v[187]*x13 + v[202]*x14 + v[217]*x15;
1187       sum9  += v[8]*x1  + v[23]*x2 + v[38]*x3 + v[53]*x4 + v[68]*x5 + v[83]*x6 + v[98]*x7  + v[113]*x8 + v[128]*x9 + v[143]*x10 + v[158]*x11 + v[173]*x12 + v[188]*x13 + v[203]*x14 + v[218]*x15;
1188       sum10 += v[9]*x1  + v[24]*x2 + v[39]*x3 + v[54]*x4 + v[69]*x5 + v[84]*x6 + v[99]*x7  + v[114]*x8 + v[129]*x9 + v[144]*x10 + v[159]*x11 + v[174]*x12 + v[189]*x13 + v[204]*x14 + v[219]*x15;
1189       sum11 += v[10]*x1 + v[25]*x2 + v[40]*x3 + v[55]*x4 + v[70]*x5 + v[85]*x6 + v[100]*x7 + v[115]*x8 + v[130]*x9 + v[145]*x10 + v[160]*x11 + v[175]*x12 + v[190]*x13 + v[205]*x14 + v[220]*x15;
1190       sum12 += v[11]*x1 + v[26]*x2 + v[41]*x3 + v[56]*x4 + v[71]*x5 + v[86]*x6 + v[101]*x7 + v[116]*x8 + v[131]*x9 + v[146]*x10 + v[161]*x11 + v[176]*x12 + v[191]*x13 + v[206]*x14 + v[221]*x15;
1191       sum13 += v[12]*x1 + v[27]*x2 + v[42]*x3 + v[57]*x4 + v[72]*x5 + v[87]*x6 + v[102]*x7 + v[117]*x8 + v[132]*x9 + v[147]*x10 + v[162]*x11 + v[177]*x12 + v[192]*x13 + v[207]*x14 + v[222]*x15;
1192       sum14 += v[13]*x1 + v[28]*x2 + v[43]*x3 + v[58]*x4 + v[73]*x5 + v[88]*x6 + v[103]*x7 + v[118]*x8 + v[133]*x9 + v[148]*x10 + v[163]*x11 + v[178]*x12 + v[193]*x13 + v[208]*x14 + v[223]*x15;
1193       sum15 += v[14]*x1 + v[29]*x2 + v[44]*x3 + v[59]*x4 + v[74]*x5 + v[89]*x6 + v[104]*x7 + v[119]*x8 + v[134]*x9 + v[149]*x10 + v[164]*x11 + v[179]*x12 + v[194]*x13 + v[209]*x14 + v[224]*x15;
1194       v     += 225;
1195     }
1196     if (usecprow) z = zarray + 15*ridx[i];
1197     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
1198     z[7] = sum8; z[8] = sum9; z[9] = sum10; z[10] = sum11; z[11] = sum12; z[12] = sum13; z[13] = sum14;z[14] = sum15;
1199 
1200     if (!usecprow) z += 15;
1201   }
1202 
1203   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1204   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
1205   ierr = PetscLogFlops(450.0*a->nz - 15.0*a->nonzerorowcnt);CHKERRQ(ierr);
1206   PetscFunctionReturn(0);
1207 }
1208 
1209 /*
1210     This will not work with MatScalar == float because it calls the BLAS
1211 */
1212 PetscErrorCode MatMult_SeqBAIJ_N(Mat A,Vec xx,Vec zz)
1213 {
1214   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1215   PetscScalar       *z = NULL,*work,*workt,*zarray;
1216   const PetscScalar *x,*xb;
1217   const MatScalar   *v;
1218   PetscErrorCode    ierr;
1219   PetscInt          mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2;
1220   const PetscInt    *idx,*ii,*ridx=NULL;
1221   PetscInt          ncols,k;
1222   PetscBool         usecprow=a->compressedrow.use;
1223 
1224   PetscFunctionBegin;
1225   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1226   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
1227 
1228   idx = a->j;
1229   v   = a->a;
1230   if (usecprow) {
1231     mbs  = a->compressedrow.nrows;
1232     ii   = a->compressedrow.i;
1233     ridx = a->compressedrow.rindex;
1234     ierr = PetscArrayzero(zarray,bs*a->mbs);CHKERRQ(ierr);
1235   } else {
1236     mbs = a->mbs;
1237     ii  = a->i;
1238     z   = zarray;
1239   }
1240 
1241   if (!a->mult_work) {
1242     k    = PetscMax(A->rmap->n,A->cmap->n);
1243     ierr = PetscMalloc1(k+1,&a->mult_work);CHKERRQ(ierr);
1244   }
1245   work = a->mult_work;
1246   for (i=0; i<mbs; i++) {
1247     n           = ii[1] - ii[0]; ii++;
1248     ncols       = n*bs;
1249     workt       = work;
1250     for (j=0; j<n; j++) {
1251       xb = x + bs*(*idx++);
1252       for (k=0; k<bs; k++) workt[k] = xb[k];
1253       workt += bs;
1254     }
1255     if (usecprow) z = zarray + bs*ridx[i];
1256     PetscKernel_w_gets_Ar_times_v(bs,ncols,work,v,z);
1257     v += n*bs2;
1258     if (!usecprow) z += bs;
1259   }
1260   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1261   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
1262   ierr = PetscLogFlops(2.0*a->nz*bs2 - bs*a->nonzerorowcnt);CHKERRQ(ierr);
1263   PetscFunctionReturn(0);
1264 }
1265 
1266 PetscErrorCode MatMultAdd_SeqBAIJ_1(Mat A,Vec xx,Vec yy,Vec zz)
1267 {
1268   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1269   const PetscScalar *x;
1270   PetscScalar       *y,*z,sum;
1271   const MatScalar   *v;
1272   PetscErrorCode    ierr;
1273   PetscInt          mbs=a->mbs,i,n,*ridx=NULL;
1274   const PetscInt    *idx,*ii;
1275   PetscBool         usecprow=a->compressedrow.use;
1276 
1277   PetscFunctionBegin;
1278   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1279   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1280 
1281   idx = a->j;
1282   v   = a->a;
1283   if (usecprow) {
1284     if (zz != yy) {
1285       ierr = PetscArraycpy(z,y,mbs);CHKERRQ(ierr);
1286     }
1287     mbs  = a->compressedrow.nrows;
1288     ii   = a->compressedrow.i;
1289     ridx = a->compressedrow.rindex;
1290   } else {
1291     ii = a->i;
1292   }
1293 
1294   for (i=0; i<mbs; i++) {
1295     n = ii[1] - ii[0];
1296     ii++;
1297     if (!usecprow) {
1298       sum         = y[i];
1299     } else {
1300       sum = y[ridx[i]];
1301     }
1302     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
1303     PetscPrefetchBlock(v+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
1304     PetscSparseDensePlusDot(sum,x,v,idx,n);
1305     v   += n;
1306     idx += n;
1307     if (usecprow) {
1308       z[ridx[i]] = sum;
1309     } else {
1310       z[i] = sum;
1311     }
1312   }
1313   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1314   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1315   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1316   PetscFunctionReturn(0);
1317 }
1318 
1319 PetscErrorCode MatMultAdd_SeqBAIJ_2(Mat A,Vec xx,Vec yy,Vec zz)
1320 {
1321   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1322   PetscScalar       *y = NULL,*z = NULL,sum1,sum2;
1323   const PetscScalar *x,*xb;
1324   PetscScalar       x1,x2,*yarray,*zarray;
1325   const MatScalar   *v;
1326   PetscErrorCode    ierr;
1327   PetscInt          mbs = a->mbs,i,n,j;
1328   const PetscInt    *idx,*ii,*ridx = NULL;
1329   PetscBool         usecprow = a->compressedrow.use;
1330 
1331   PetscFunctionBegin;
1332   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1333   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1334 
1335   idx = a->j;
1336   v   = a->a;
1337   if (usecprow) {
1338     if (zz != yy) {
1339       ierr = PetscArraycpy(zarray,yarray,2*mbs);CHKERRQ(ierr);
1340     }
1341     mbs  = a->compressedrow.nrows;
1342     ii   = a->compressedrow.i;
1343     ridx = a->compressedrow.rindex;
1344   } else {
1345     ii = a->i;
1346     y  = yarray;
1347     z  = zarray;
1348   }
1349 
1350   for (i=0; i<mbs; i++) {
1351     n = ii[1] - ii[0]; ii++;
1352     if (usecprow) {
1353       z = zarray + 2*ridx[i];
1354       y = yarray + 2*ridx[i];
1355     }
1356     sum1 = y[0]; sum2 = y[1];
1357     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
1358     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1359     for (j=0; j<n; j++) {
1360       xb = x + 2*(*idx++);
1361       x1 = xb[0];
1362       x2 = xb[1];
1363 
1364       sum1 += v[0]*x1 + v[2]*x2;
1365       sum2 += v[1]*x1 + v[3]*x2;
1366       v    += 4;
1367     }
1368     z[0] = sum1; z[1] = sum2;
1369     if (!usecprow) {
1370       z += 2; y += 2;
1371     }
1372   }
1373   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1374   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1375   ierr = PetscLogFlops(4.0*a->nz);CHKERRQ(ierr);
1376   PetscFunctionReturn(0);
1377 }
1378 
1379 PetscErrorCode MatMultAdd_SeqBAIJ_3(Mat A,Vec xx,Vec yy,Vec zz)
1380 {
1381   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1382   PetscScalar       *y = NULL,*z = NULL,sum1,sum2,sum3,x1,x2,x3,*yarray,*zarray;
1383   const PetscScalar *x,*xb;
1384   const MatScalar   *v;
1385   PetscErrorCode    ierr;
1386   PetscInt          mbs = a->mbs,i,j,n;
1387   const PetscInt    *idx,*ii,*ridx = NULL;
1388   PetscBool         usecprow = a->compressedrow.use;
1389 
1390   PetscFunctionBegin;
1391   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1392   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1393 
1394   idx = a->j;
1395   v   = a->a;
1396   if (usecprow) {
1397     if (zz != yy) {
1398       ierr = PetscArraycpy(zarray,yarray,3*mbs);CHKERRQ(ierr);
1399     }
1400     mbs  = a->compressedrow.nrows;
1401     ii   = a->compressedrow.i;
1402     ridx = a->compressedrow.rindex;
1403   } else {
1404     ii = a->i;
1405     y  = yarray;
1406     z  = zarray;
1407   }
1408 
1409   for (i=0; i<mbs; i++) {
1410     n = ii[1] - ii[0]; ii++;
1411     if (usecprow) {
1412       z = zarray + 3*ridx[i];
1413       y = yarray + 3*ridx[i];
1414     }
1415     sum1 = y[0]; sum2 = y[1]; sum3 = y[2];
1416     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
1417     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1418     for (j=0; j<n; j++) {
1419       xb    = x + 3*(*idx++); x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
1420       sum1 += v[0]*x1 + v[3]*x2 + v[6]*x3;
1421       sum2 += v[1]*x1 + v[4]*x2 + v[7]*x3;
1422       sum3 += v[2]*x1 + v[5]*x2 + v[8]*x3;
1423       v    += 9;
1424     }
1425     z[0] = sum1; z[1] = sum2; z[2] = sum3;
1426     if (!usecprow) {
1427       z += 3; y += 3;
1428     }
1429   }
1430   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1431   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1432   ierr = PetscLogFlops(18.0*a->nz);CHKERRQ(ierr);
1433   PetscFunctionReturn(0);
1434 }
1435 
1436 PetscErrorCode MatMultAdd_SeqBAIJ_4(Mat A,Vec xx,Vec yy,Vec zz)
1437 {
1438   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1439   PetscScalar       *y = NULL,*z = NULL,sum1,sum2,sum3,sum4,x1,x2,x3,x4,*yarray,*zarray;
1440   const PetscScalar *x,*xb;
1441   const MatScalar   *v;
1442   PetscErrorCode    ierr;
1443   PetscInt          mbs = a->mbs,i,j,n;
1444   const PetscInt    *idx,*ii,*ridx=NULL;
1445   PetscBool         usecprow=a->compressedrow.use;
1446 
1447   PetscFunctionBegin;
1448   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1449   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1450 
1451   idx = a->j;
1452   v   = a->a;
1453   if (usecprow) {
1454     if (zz != yy) {
1455       ierr = PetscArraycpy(zarray,yarray,4*mbs);CHKERRQ(ierr);
1456     }
1457     mbs  = a->compressedrow.nrows;
1458     ii   = a->compressedrow.i;
1459     ridx = a->compressedrow.rindex;
1460   } else {
1461     ii = a->i;
1462     y  = yarray;
1463     z  = zarray;
1464   }
1465 
1466   for (i=0; i<mbs; i++) {
1467     n = ii[1] - ii[0]; ii++;
1468     if (usecprow) {
1469       z = zarray + 4*ridx[i];
1470       y = yarray + 4*ridx[i];
1471     }
1472     sum1 = y[0]; sum2 = y[1]; sum3 = y[2]; sum4 = y[3];
1473     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
1474     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1475     for (j=0; j<n; j++) {
1476       xb    = x + 4*(*idx++);
1477       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
1478       sum1 += v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1479       sum2 += v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1480       sum3 += v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1481       sum4 += v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1482       v    += 16;
1483     }
1484     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4;
1485     if (!usecprow) {
1486       z += 4; y += 4;
1487     }
1488   }
1489   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1490   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1491   ierr = PetscLogFlops(32.0*a->nz);CHKERRQ(ierr);
1492   PetscFunctionReturn(0);
1493 }
1494 
1495 PetscErrorCode MatMultAdd_SeqBAIJ_5(Mat A,Vec xx,Vec yy,Vec zz)
1496 {
1497   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1498   PetscScalar       *y = NULL,*z = NULL,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1499   const PetscScalar *x,*xb;
1500   PetscScalar       *yarray,*zarray;
1501   const MatScalar   *v;
1502   PetscErrorCode    ierr;
1503   PetscInt          mbs = a->mbs,i,j,n;
1504   const PetscInt    *idx,*ii,*ridx = NULL;
1505   PetscBool         usecprow=a->compressedrow.use;
1506 
1507   PetscFunctionBegin;
1508   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1509   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1510 
1511   idx = a->j;
1512   v   = a->a;
1513   if (usecprow) {
1514     if (zz != yy) {
1515       ierr = PetscArraycpy(zarray,yarray,5*mbs);CHKERRQ(ierr);
1516     }
1517     mbs  = a->compressedrow.nrows;
1518     ii   = a->compressedrow.i;
1519     ridx = a->compressedrow.rindex;
1520   } else {
1521     ii = a->i;
1522     y  = yarray;
1523     z  = zarray;
1524   }
1525 
1526   for (i=0; i<mbs; i++) {
1527     n = ii[1] - ii[0]; ii++;
1528     if (usecprow) {
1529       z = zarray + 5*ridx[i];
1530       y = yarray + 5*ridx[i];
1531     }
1532     sum1 = y[0]; sum2 = y[1]; sum3 = y[2]; sum4 = y[3]; sum5 = y[4];
1533     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
1534     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1535     for (j=0; j<n; j++) {
1536       xb    = x + 5*(*idx++);
1537       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4];
1538       sum1 += v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
1539       sum2 += v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
1540       sum3 += v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
1541       sum4 += v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
1542       sum5 += v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
1543       v    += 25;
1544     }
1545     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5;
1546     if (!usecprow) {
1547       z += 5; y += 5;
1548     }
1549   }
1550   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1551   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1552   ierr = PetscLogFlops(50.0*a->nz);CHKERRQ(ierr);
1553   PetscFunctionReturn(0);
1554 }
1555 
1556 PetscErrorCode MatMultAdd_SeqBAIJ_6(Mat A,Vec xx,Vec yy,Vec zz)
1557 {
1558   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1559   PetscScalar       *y = NULL,*z = NULL,sum1,sum2,sum3,sum4,sum5,sum6;
1560   const PetscScalar *x,*xb;
1561   PetscScalar       x1,x2,x3,x4,x5,x6,*yarray,*zarray;
1562   const MatScalar   *v;
1563   PetscErrorCode    ierr;
1564   PetscInt          mbs = a->mbs,i,j,n;
1565   const PetscInt    *idx,*ii,*ridx=NULL;
1566   PetscBool         usecprow=a->compressedrow.use;
1567 
1568   PetscFunctionBegin;
1569   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1570   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1571 
1572   idx = a->j;
1573   v   = a->a;
1574   if (usecprow) {
1575     if (zz != yy) {
1576       ierr = PetscArraycpy(zarray,yarray,6*mbs);CHKERRQ(ierr);
1577     }
1578     mbs  = a->compressedrow.nrows;
1579     ii   = a->compressedrow.i;
1580     ridx = a->compressedrow.rindex;
1581   } else {
1582     ii = a->i;
1583     y  = yarray;
1584     z  = zarray;
1585   }
1586 
1587   for (i=0; i<mbs; i++) {
1588     n = ii[1] - ii[0]; ii++;
1589     if (usecprow) {
1590       z = zarray + 6*ridx[i];
1591       y = yarray + 6*ridx[i];
1592     }
1593     sum1 = y[0]; sum2 = y[1]; sum3 = y[2]; sum4 = y[3]; sum5 = y[4]; sum6 = y[5];
1594     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
1595     PetscPrefetchBlock(v+36*n,36*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1596     for (j=0; j<n; j++) {
1597       xb    = x + 6*(*idx++);
1598       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5];
1599       sum1 += v[0]*x1 + v[6]*x2  + v[12]*x3  + v[18]*x4 + v[24]*x5 + v[30]*x6;
1600       sum2 += v[1]*x1 + v[7]*x2  + v[13]*x3  + v[19]*x4 + v[25]*x5 + v[31]*x6;
1601       sum3 += v[2]*x1 + v[8]*x2  + v[14]*x3  + v[20]*x4 + v[26]*x5 + v[32]*x6;
1602       sum4 += v[3]*x1 + v[9]*x2  + v[15]*x3  + v[21]*x4 + v[27]*x5 + v[33]*x6;
1603       sum5 += v[4]*x1 + v[10]*x2 + v[16]*x3  + v[22]*x4 + v[28]*x5 + v[34]*x6;
1604       sum6 += v[5]*x1 + v[11]*x2 + v[17]*x3  + v[23]*x4 + v[29]*x5 + v[35]*x6;
1605       v    += 36;
1606     }
1607     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6;
1608     if (!usecprow) {
1609       z += 6; y += 6;
1610     }
1611   }
1612   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1613   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1614   ierr = PetscLogFlops(72.0*a->nz);CHKERRQ(ierr);
1615   PetscFunctionReturn(0);
1616 }
1617 
1618 PetscErrorCode MatMultAdd_SeqBAIJ_7(Mat A,Vec xx,Vec yy,Vec zz)
1619 {
1620   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1621   PetscScalar       *y = NULL,*z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7;
1622   const PetscScalar *x,*xb;
1623   PetscScalar       x1,x2,x3,x4,x5,x6,x7,*yarray,*zarray;
1624   const MatScalar   *v;
1625   PetscErrorCode    ierr;
1626   PetscInt          mbs = a->mbs,i,j,n;
1627   const PetscInt    *idx,*ii,*ridx = NULL;
1628   PetscBool         usecprow=a->compressedrow.use;
1629 
1630   PetscFunctionBegin;
1631   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1632   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1633 
1634   idx = a->j;
1635   v   = a->a;
1636   if (usecprow) {
1637     if (zz != yy) {
1638       ierr = PetscArraycpy(zarray,yarray,7*mbs);CHKERRQ(ierr);
1639     }
1640     mbs  = a->compressedrow.nrows;
1641     ii   = a->compressedrow.i;
1642     ridx = a->compressedrow.rindex;
1643   } else {
1644     ii = a->i;
1645     y  = yarray;
1646     z  = zarray;
1647   }
1648 
1649   for (i=0; i<mbs; i++) {
1650     n = ii[1] - ii[0]; ii++;
1651     if (usecprow) {
1652       z = zarray + 7*ridx[i];
1653       y = yarray + 7*ridx[i];
1654     }
1655     sum1 = y[0]; sum2 = y[1]; sum3 = y[2]; sum4 = y[3]; sum5 = y[4]; sum6 = y[5]; sum7 = y[6];
1656     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
1657     PetscPrefetchBlock(v+49*n,49*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1658     for (j=0; j<n; j++) {
1659       xb    = x + 7*(*idx++);
1660       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5]; x7 = xb[6];
1661       sum1 += v[0]*x1 + v[7]*x2  + v[14]*x3  + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1662       sum2 += v[1]*x1 + v[8]*x2  + v[15]*x3  + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1663       sum3 += v[2]*x1 + v[9]*x2  + v[16]*x3  + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1664       sum4 += v[3]*x1 + v[10]*x2 + v[17]*x3  + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1665       sum5 += v[4]*x1 + v[11]*x2 + v[18]*x3  + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1666       sum6 += v[5]*x1 + v[12]*x2 + v[19]*x3  + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1667       sum7 += v[6]*x1 + v[13]*x2 + v[20]*x3  + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1668       v    += 49;
1669     }
1670     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
1671     if (!usecprow) {
1672       z += 7; y += 7;
1673     }
1674   }
1675   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1676   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1677   ierr = PetscLogFlops(98.0*a->nz);CHKERRQ(ierr);
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
1682 PetscErrorCode MatMultAdd_SeqBAIJ_9_AVX2(Mat A,Vec xx,Vec yy,Vec zz)
1683 {
1684   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
1685   PetscScalar    *z = NULL,*work,*workt,*zarray;
1686   const PetscScalar *x,*xb;
1687   const MatScalar   *v;
1688   PetscErrorCode ierr;
1689   PetscInt       mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2;
1690   PetscInt       k;
1691   PetscBool      usecprow=a->compressedrow.use;
1692   const PetscInt *idx,*ii,*ridx=NULL;
1693 
1694   __m256d a0,a1,a2,a3,a4,a5;
1695   __m256d w0,w1,w2,w3;
1696   __m256d z0,z1,z2;
1697   __m256i mask1 = _mm256_set_epi64x(0LL, 0LL, 0LL, 1LL<<63);
1698 
1699   PetscFunctionBegin;
1700   ierr = VecCopy(yy,zz);CHKERRQ(ierr);
1701   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1702   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
1703 
1704   idx = a->j;
1705   v   = a->a;
1706   if (usecprow) {
1707     mbs  = a->compressedrow.nrows;
1708     ii   = a->compressedrow.i;
1709     ridx = a->compressedrow.rindex;
1710   } else {
1711     mbs = a->mbs;
1712     ii  = a->i;
1713     z   = zarray;
1714   }
1715 
1716   if (!a->mult_work) {
1717     k    = PetscMax(A->rmap->n,A->cmap->n);
1718     ierr = PetscMalloc1(k+1,&a->mult_work);CHKERRQ(ierr);
1719   }
1720 
1721   work = a->mult_work;
1722   for (i=0; i<mbs; i++) {
1723     n           = ii[1] - ii[0]; ii++;
1724     workt       = work;
1725     for (j=0; j<n; j++) {
1726       xb = x + bs*(*idx++);
1727       for (k=0; k<bs; k++) workt[k] = xb[k];
1728       workt += bs;
1729     }
1730     if (usecprow) z = zarray + bs*ridx[i];
1731 
1732     z0 = _mm256_loadu_pd(&z[ 0]); z1 = _mm256_loadu_pd(&z[ 4]); z2 = _mm256_set1_pd(z[ 8]);
1733 
1734     for (j=0; j<n; j++) {
1735       /* first column of a */
1736       w0 = _mm256_set1_pd(work[j*9  ]);
1737       a0 = _mm256_loadu_pd(&v[j*81  ]); z0 = _mm256_fmadd_pd(a0,w0,z0);
1738       a1 = _mm256_loadu_pd(&v[j*81+4]); z1 = _mm256_fmadd_pd(a1,w0,z1);
1739       a2 = _mm256_loadu_pd(&v[j*81+8]); z2 = _mm256_fmadd_pd(a2,w0,z2);
1740 
1741       /* second column of a */
1742       w1 = _mm256_set1_pd(work[j*9+ 1]);
1743       a0 = _mm256_loadu_pd(&v[j*81+ 9]); z0 = _mm256_fmadd_pd(a0,w1,z0);
1744       a1 = _mm256_loadu_pd(&v[j*81+13]); z1 = _mm256_fmadd_pd(a1,w1,z1);
1745       a2 = _mm256_loadu_pd(&v[j*81+17]); z2 = _mm256_fmadd_pd(a2,w1,z2);
1746 
1747       /* third column of a */
1748       w2 = _mm256_set1_pd(work[j*9+ 2]);
1749       a3 = _mm256_loadu_pd(&v[j*81+18]); z0 = _mm256_fmadd_pd(a3,w2,z0);
1750       a4 = _mm256_loadu_pd(&v[j*81+22]); z1 = _mm256_fmadd_pd(a4,w2,z1);
1751       a5 = _mm256_loadu_pd(&v[j*81+26]); z2 = _mm256_fmadd_pd(a5,w2,z2);
1752 
1753       /* fourth column of a */
1754       w3 = _mm256_set1_pd(work[j*9+ 3]);
1755       a0 = _mm256_loadu_pd(&v[j*81+27]); z0 = _mm256_fmadd_pd(a0,w3,z0);
1756       a1 = _mm256_loadu_pd(&v[j*81+31]); z1 = _mm256_fmadd_pd(a1,w3,z1);
1757       a2 = _mm256_loadu_pd(&v[j*81+35]); z2 = _mm256_fmadd_pd(a2,w3,z2);
1758 
1759       /* fifth column of a */
1760       w0 = _mm256_set1_pd(work[j*9+ 4]);
1761       a3 = _mm256_loadu_pd(&v[j*81+36]); z0 = _mm256_fmadd_pd(a3,w0,z0);
1762       a4 = _mm256_loadu_pd(&v[j*81+40]); z1 = _mm256_fmadd_pd(a4,w0,z1);
1763       a5 = _mm256_loadu_pd(&v[j*81+44]); z2 = _mm256_fmadd_pd(a5,w0,z2);
1764 
1765       /* sixth column of a */
1766       w1 = _mm256_set1_pd(work[j*9+ 5]);
1767       a0 = _mm256_loadu_pd(&v[j*81+45]); z0 = _mm256_fmadd_pd(a0,w1,z0);
1768       a1 = _mm256_loadu_pd(&v[j*81+49]); z1 = _mm256_fmadd_pd(a1,w1,z1);
1769       a2 = _mm256_loadu_pd(&v[j*81+53]); z2 = _mm256_fmadd_pd(a2,w1,z2);
1770 
1771       /* seventh column of a */
1772       w2 = _mm256_set1_pd(work[j*9+ 6]);
1773       a0 = _mm256_loadu_pd(&v[j*81+54]); z0 = _mm256_fmadd_pd(a0,w2,z0);
1774       a1 = _mm256_loadu_pd(&v[j*81+58]); z1 = _mm256_fmadd_pd(a1,w2,z1);
1775       a2 = _mm256_loadu_pd(&v[j*81+62]); z2 = _mm256_fmadd_pd(a2,w2,z2);
1776 
1777       /* eigth column of a */
1778       w3 = _mm256_set1_pd(work[j*9+ 7]);
1779       a3 = _mm256_loadu_pd(&v[j*81+63]); z0 = _mm256_fmadd_pd(a3,w3,z0);
1780       a4 = _mm256_loadu_pd(&v[j*81+67]); z1 = _mm256_fmadd_pd(a4,w3,z1);
1781       a5 = _mm256_loadu_pd(&v[j*81+71]); z2 = _mm256_fmadd_pd(a5,w3,z2);
1782 
1783       /* ninth column of a */
1784       w0 = _mm256_set1_pd(work[j*9+ 8]);
1785       a0 = _mm256_loadu_pd(&v[j*81+72]); z0 = _mm256_fmadd_pd(a0,w0,z0);
1786       a1 = _mm256_loadu_pd(&v[j*81+76]); z1 = _mm256_fmadd_pd(a1,w0,z1);
1787       a2 = _mm256_maskload_pd(&v[j*81+80],mask1); z2 = _mm256_fmadd_pd(a2,w0,z2);
1788     }
1789 
1790     _mm256_storeu_pd(&z[ 0], z0); _mm256_storeu_pd(&z[ 4], z1); _mm256_maskstore_pd(&z[8], mask1, z2);
1791 
1792     v += n*bs2;
1793     if (!usecprow) z += bs;
1794   }
1795   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1796   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
1797   ierr = PetscLogFlops(162.0*a->nz);CHKERRQ(ierr);
1798   PetscFunctionReturn(0);
1799 }
1800 #endif
1801 
1802 PetscErrorCode MatMultAdd_SeqBAIJ_11(Mat A,Vec xx,Vec yy,Vec zz)
1803 {
1804   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1805   PetscScalar       *y = NULL,*z = NULL,sum1,sum2,sum3,sum4,sum5,sum6,sum7,sum8,sum9,sum10,sum11;
1806   const PetscScalar *x,*xb;
1807   PetscScalar       x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,*yarray,*zarray;
1808   const MatScalar   *v;
1809   PetscErrorCode    ierr;
1810   PetscInt          mbs = a->mbs,i,j,n;
1811   const PetscInt    *idx,*ii,*ridx = NULL;
1812   PetscBool         usecprow=a->compressedrow.use;
1813 
1814   PetscFunctionBegin;
1815   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1816   ierr = VecGetArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1817 
1818   idx = a->j;
1819   v   = a->a;
1820   if (usecprow) {
1821     if (zz != yy) {
1822       ierr = PetscArraycpy(zarray,yarray,7*mbs);CHKERRQ(ierr);
1823     }
1824     mbs  = a->compressedrow.nrows;
1825     ii   = a->compressedrow.i;
1826     ridx = a->compressedrow.rindex;
1827   } else {
1828     ii = a->i;
1829     y  = yarray;
1830     z  = zarray;
1831   }
1832 
1833   for (i=0; i<mbs; i++) {
1834     n = ii[1] - ii[0]; ii++;
1835     if (usecprow) {
1836       z = zarray + 11*ridx[i];
1837       y = yarray + 11*ridx[i];
1838     }
1839     sum1 = y[0]; sum2 = y[1]; sum3 = y[2]; sum4 = y[3]; sum5 = y[4]; sum6 = y[5]; sum7 = y[6];
1840     sum8 = y[7]; sum9 = y[8]; sum10 = y[9]; sum11 = y[10];
1841     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);     /* Indices for the next row (assumes same size as this one) */
1842     PetscPrefetchBlock(v+121*n,121*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1843     for (j=0; j<n; j++) {
1844       xb    = x + 11*(*idx++);
1845       x1    = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5 = xb[4]; x6 = xb[5]; x7 = xb[6];x8 = xb[7]; x9 = xb[8]; x10 = xb[9]; x11 = xb[10];
1846       sum1 += v[  0]*x1 + v[  11]*x2  + v[2*11]*x3  + v[3*11]*x4 + v[4*11]*x5 + v[5*11]*x6 + v[6*11]*x7+ v[7*11]*x8 + v[8*11]*x9  + v[9*11]*x10  + v[10*11]*x11;
1847       sum2 += v[1+0]*x1 + v[1+11]*x2  + v[1+2*11]*x3  + v[1+3*11]*x4 + v[1+4*11]*x5 + v[1+5*11]*x6 + v[1+6*11]*x7+ v[1+7*11]*x8 + v[1+8*11]*x9  + v[1+9*11]*x10  + v[1+10*11]*x11;
1848       sum3 += v[2+0]*x1 + v[2+11]*x2  + v[2+2*11]*x3  + v[2+3*11]*x4 + v[2+4*11]*x5 + v[2+5*11]*x6 + v[2+6*11]*x7+ v[2+7*11]*x8 + v[2+8*11]*x9  + v[2+9*11]*x10  + v[2+10*11]*x11;
1849       sum4 += v[3+0]*x1 + v[3+11]*x2  + v[3+2*11]*x3  + v[3+3*11]*x4 + v[3+4*11]*x5 + v[3+5*11]*x6 + v[3+6*11]*x7+ v[3+7*11]*x8 + v[3+8*11]*x9  + v[3+9*11]*x10  + v[3+10*11]*x11;
1850       sum5 += v[4+0]*x1 + v[4+11]*x2  + v[4+2*11]*x3  + v[4+3*11]*x4 + v[4+4*11]*x5 + v[4+5*11]*x6 + v[4+6*11]*x7+ v[4+7*11]*x8 + v[4+8*11]*x9  + v[4+9*11]*x10  + v[4+10*11]*x11;
1851       sum6 += v[5+0]*x1 + v[5+11]*x2  + v[5+2*11]*x3  + v[5+3*11]*x4 + v[5+4*11]*x5 + v[5+5*11]*x6 + v[5+6*11]*x7+ v[5+7*11]*x8 + v[5+8*11]*x9  + v[5+9*11]*x10  + v[5+10*11]*x11;
1852       sum7 += v[6+0]*x1 + v[6+11]*x2  + v[6+2*11]*x3  + v[6+3*11]*x4 + v[6+4*11]*x5 + v[6+5*11]*x6 + v[6+6*11]*x7+ v[6+7*11]*x8 + v[6+8*11]*x9  + v[6+9*11]*x10  + v[6+10*11]*x11;
1853       sum8 += v[7+0]*x1 + v[7+11]*x2  + v[7+2*11]*x3  + v[7+3*11]*x4 + v[7+4*11]*x5 + v[7+5*11]*x6 + v[7+6*11]*x7+ v[7+7*11]*x8 + v[7+8*11]*x9  + v[7+9*11]*x10  + v[7+10*11]*x11;
1854       sum9 += v[8+0]*x1 + v[8+11]*x2  + v[8+2*11]*x3  + v[8+3*11]*x4 + v[8+4*11]*x5 + v[8+5*11]*x6 + v[8+6*11]*x7+ v[8+7*11]*x8 + v[8+8*11]*x9  + v[8+9*11]*x10  + v[8+10*11]*x11;
1855       sum10 += v[9+0]*x1 + v[9+11]*x2  + v[9+2*11]*x3  + v[9+3*11]*x4 + v[9+4*11]*x5 + v[9+5*11]*x6 + v[9+6*11]*x7+ v[9+7*11]*x8 + v[9+8*11]*x9  + v[9+9*11]*x10  + v[9+10*11]*x11;
1856       sum11 += v[10+0]*x1 + v[10+11]*x2  + v[10+2*11]*x3  + v[10+3*11]*x4 + v[10+4*11]*x5 + v[10+5*11]*x6 + v[10+6*11]*x7+ v[10+7*11]*x8 + v[10+8*11]*x9  + v[10+9*11]*x10  + v[10+10*11]*x11;
1857       v    += 121;
1858     }
1859     z[0] = sum1; z[1] = sum2; z[2] = sum3; z[3] = sum4; z[4] = sum5; z[5] = sum6; z[6] = sum7;
1860     z[7] = sum6; z[8] = sum7; z[9] = sum8; z[10] = sum9; z[11] = sum10;
1861     if (!usecprow) {
1862       z += 11; y += 11;
1863     }
1864   }
1865   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1866   ierr = VecRestoreArrayPair(yy,zz,&yarray,&zarray);CHKERRQ(ierr);
1867   ierr = PetscLogFlops(242.0*a->nz);CHKERRQ(ierr);
1868   PetscFunctionReturn(0);
1869 }
1870 
1871 PetscErrorCode MatMultAdd_SeqBAIJ_N(Mat A,Vec xx,Vec yy,Vec zz)
1872 {
1873   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1874   PetscScalar       *z = NULL,*work,*workt,*zarray;
1875   const PetscScalar *x,*xb;
1876   const MatScalar   *v;
1877   PetscErrorCode    ierr;
1878   PetscInt          mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2;
1879   PetscInt          ncols,k;
1880   const PetscInt    *ridx = NULL,*idx,*ii;
1881   PetscBool         usecprow = a->compressedrow.use;
1882 
1883   PetscFunctionBegin;
1884   ierr = VecCopy(yy,zz);CHKERRQ(ierr);
1885   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1886   ierr = VecGetArray(zz,&zarray);CHKERRQ(ierr);
1887 
1888   idx = a->j;
1889   v   = a->a;
1890   if (usecprow) {
1891     mbs  = a->compressedrow.nrows;
1892     ii   = a->compressedrow.i;
1893     ridx = a->compressedrow.rindex;
1894   } else {
1895     mbs = a->mbs;
1896     ii  = a->i;
1897     z   = zarray;
1898   }
1899 
1900   if (!a->mult_work) {
1901     k    = PetscMax(A->rmap->n,A->cmap->n);
1902     ierr = PetscMalloc1(k+1,&a->mult_work);CHKERRQ(ierr);
1903   }
1904   work = a->mult_work;
1905   for (i=0; i<mbs; i++) {
1906     n     = ii[1] - ii[0]; ii++;
1907     ncols = n*bs;
1908     workt = work;
1909     for (j=0; j<n; j++) {
1910       xb = x + bs*(*idx++);
1911       for (k=0; k<bs; k++) workt[k] = xb[k];
1912       workt += bs;
1913     }
1914     if (usecprow) z = zarray + bs*ridx[i];
1915     PetscKernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);
1916     v += n*bs2;
1917     if (!usecprow) z += bs;
1918   }
1919   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1920   ierr = VecRestoreArray(zz,&zarray);CHKERRQ(ierr);
1921   ierr = PetscLogFlops(2.0*a->nz*bs2);CHKERRQ(ierr);
1922   PetscFunctionReturn(0);
1923 }
1924 
1925 PetscErrorCode MatMultHermitianTranspose_SeqBAIJ(Mat A,Vec xx,Vec zz)
1926 {
1927   PetscScalar    zero = 0.0;
1928   PetscErrorCode ierr;
1929 
1930   PetscFunctionBegin;
1931   ierr = VecSet(zz,zero);CHKERRQ(ierr);
1932   ierr = MatMultHermitianTransposeAdd_SeqBAIJ(A,xx,zz,zz);CHKERRQ(ierr);
1933   PetscFunctionReturn(0);
1934 }
1935 
1936 PetscErrorCode MatMultTranspose_SeqBAIJ(Mat A,Vec xx,Vec zz)
1937 {
1938   PetscScalar    zero = 0.0;
1939   PetscErrorCode ierr;
1940 
1941   PetscFunctionBegin;
1942   ierr = VecSet(zz,zero);CHKERRQ(ierr);
1943   ierr = MatMultTransposeAdd_SeqBAIJ(A,xx,zz,zz);CHKERRQ(ierr);
1944   PetscFunctionReturn(0);
1945 }
1946 
1947 PetscErrorCode MatMultHermitianTransposeAdd_SeqBAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1948 {
1949   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
1950   PetscScalar       *z,x1,x2,x3,x4,x5;
1951   const PetscScalar *x,*xb = NULL;
1952   const MatScalar   *v;
1953   PetscErrorCode    ierr;
1954   PetscInt          mbs,i,rval,bs=A->rmap->bs,j,n;
1955   const PetscInt    *idx,*ii,*ib,*ridx = NULL;
1956   Mat_CompressedRow cprow = a->compressedrow;
1957   PetscBool         usecprow = cprow.use;
1958 
1959   PetscFunctionBegin;
1960   if (yy != zz) { ierr = VecCopy(yy,zz);CHKERRQ(ierr); }
1961   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1962   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
1963 
1964   idx = a->j;
1965   v   = a->a;
1966   if (usecprow) {
1967     mbs  = cprow.nrows;
1968     ii   = cprow.i;
1969     ridx = cprow.rindex;
1970   } else {
1971     mbs=a->mbs;
1972     ii = a->i;
1973     xb = x;
1974   }
1975 
1976   switch (bs) {
1977   case 1:
1978     for (i=0; i<mbs; i++) {
1979       if (usecprow) xb = x + ridx[i];
1980       x1 = xb[0];
1981       ib = idx + ii[0];
1982       n  = ii[1] - ii[0]; ii++;
1983       for (j=0; j<n; j++) {
1984         rval     = ib[j];
1985         z[rval] += PetscConj(*v) * x1;
1986         v++;
1987       }
1988       if (!usecprow) xb++;
1989     }
1990     break;
1991   case 2:
1992     for (i=0; i<mbs; i++) {
1993       if (usecprow) xb = x + 2*ridx[i];
1994       x1 = xb[0]; x2 = xb[1];
1995       ib = idx + ii[0];
1996       n  = ii[1] - ii[0]; ii++;
1997       for (j=0; j<n; j++) {
1998         rval       = ib[j]*2;
1999         z[rval++] += PetscConj(v[0])*x1 + PetscConj(v[1])*x2;
2000         z[rval++] += PetscConj(v[2])*x1 + PetscConj(v[3])*x2;
2001         v         += 4;
2002       }
2003       if (!usecprow) xb += 2;
2004     }
2005     break;
2006   case 3:
2007     for (i=0; i<mbs; i++) {
2008       if (usecprow) xb = x + 3*ridx[i];
2009       x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
2010       ib = idx + ii[0];
2011       n  = ii[1] - ii[0]; ii++;
2012       for (j=0; j<n; j++) {
2013         rval       = ib[j]*3;
2014         z[rval++] += PetscConj(v[0])*x1 + PetscConj(v[1])*x2 + PetscConj(v[2])*x3;
2015         z[rval++] += PetscConj(v[3])*x1 + PetscConj(v[4])*x2 + PetscConj(v[5])*x3;
2016         z[rval++] += PetscConj(v[6])*x1 + PetscConj(v[7])*x2 + PetscConj(v[8])*x3;
2017         v         += 9;
2018       }
2019       if (!usecprow) xb += 3;
2020     }
2021     break;
2022   case 4:
2023     for (i=0; i<mbs; i++) {
2024       if (usecprow) xb = x + 4*ridx[i];
2025       x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
2026       ib = idx + ii[0];
2027       n  = ii[1] - ii[0]; ii++;
2028       for (j=0; j<n; j++) {
2029         rval       = ib[j]*4;
2030         z[rval++] +=  PetscConj(v[0])*x1 + PetscConj(v[1])*x2  + PetscConj(v[2])*x3  + PetscConj(v[3])*x4;
2031         z[rval++] +=  PetscConj(v[4])*x1 + PetscConj(v[5])*x2  + PetscConj(v[6])*x3  + PetscConj(v[7])*x4;
2032         z[rval++] +=  PetscConj(v[8])*x1 + PetscConj(v[9])*x2  + PetscConj(v[10])*x3 + PetscConj(v[11])*x4;
2033         z[rval++] += PetscConj(v[12])*x1 + PetscConj(v[13])*x2 + PetscConj(v[14])*x3 + PetscConj(v[15])*x4;
2034         v         += 16;
2035       }
2036       if (!usecprow) xb += 4;
2037     }
2038     break;
2039   case 5:
2040     for (i=0; i<mbs; i++) {
2041       if (usecprow) xb = x + 5*ridx[i];
2042       x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
2043       x4 = xb[3]; x5 = xb[4];
2044       ib = idx + ii[0];
2045       n  = ii[1] - ii[0]; ii++;
2046       for (j=0; j<n; j++) {
2047         rval       = ib[j]*5;
2048         z[rval++] +=  PetscConj(v[0])*x1 +  PetscConj(v[1])*x2 +  PetscConj(v[2])*x3 +  PetscConj(v[3])*x4 +  PetscConj(v[4])*x5;
2049         z[rval++] +=  PetscConj(v[5])*x1 +  PetscConj(v[6])*x2 +  PetscConj(v[7])*x3 +  PetscConj(v[8])*x4 +  PetscConj(v[9])*x5;
2050         z[rval++] += PetscConj(v[10])*x1 + PetscConj(v[11])*x2 + PetscConj(v[12])*x3 + PetscConj(v[13])*x4 + PetscConj(v[14])*x5;
2051         z[rval++] += PetscConj(v[15])*x1 + PetscConj(v[16])*x2 + PetscConj(v[17])*x3 + PetscConj(v[18])*x4 + PetscConj(v[19])*x5;
2052         z[rval++] += PetscConj(v[20])*x1 + PetscConj(v[21])*x2 + PetscConj(v[22])*x3 + PetscConj(v[23])*x4 + PetscConj(v[24])*x5;
2053         v         += 25;
2054       }
2055       if (!usecprow) xb += 5;
2056     }
2057     break;
2058   default: /* block sizes larger than 5 by 5 are handled by BLAS */
2059     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"block size larger than 5 is not supported yet");
2060 #if 0
2061     {
2062       PetscInt          ncols,k,bs2=a->bs2;
2063       PetscScalar       *work,*workt,zb;
2064       const PetscScalar *xtmp;
2065       if (!a->mult_work) {
2066         k    = PetscMax(A->rmap->n,A->cmap->n);
2067         ierr = PetscMalloc1(k+1,&a->mult_work);CHKERRQ(ierr);
2068       }
2069       work = a->mult_work;
2070       xtmp = x;
2071       for (i=0; i<mbs; i++) {
2072         n     = ii[1] - ii[0]; ii++;
2073         ncols = n*bs;
2074         ierr  = PetscArrayzero(work,ncols);CHKERRQ(ierr);
2075         if (usecprow) xtmp = x + bs*ridx[i];
2076         PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,xtmp,v,work);
2077         v += n*bs2;
2078         if (!usecprow) xtmp += bs;
2079         workt = work;
2080         for (j=0; j<n; j++) {
2081           zb = z + bs*(*idx++);
2082           for (k=0; k<bs; k++) zb[k] += workt[k] ;
2083           workt += bs;
2084         }
2085       }
2086     }
2087 #endif
2088   }
2089   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
2090   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
2091   ierr = PetscLogFlops(2.0*a->nz*a->bs2);CHKERRQ(ierr);
2092   PetscFunctionReturn(0);
2093 }
2094 
2095 PetscErrorCode MatMultTransposeAdd_SeqBAIJ(Mat A,Vec xx,Vec yy,Vec zz)
2096 {
2097   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2098   PetscScalar       *zb,*z,x1,x2,x3,x4,x5;
2099   const PetscScalar *x,*xb = NULL;
2100   const MatScalar   *v;
2101   PetscErrorCode    ierr;
2102   PetscInt          mbs,i,rval,bs=A->rmap->bs,j,n,bs2=a->bs2;
2103   const PetscInt    *idx,*ii,*ib,*ridx = NULL;
2104   Mat_CompressedRow cprow   = a->compressedrow;
2105   PetscBool         usecprow=cprow.use;
2106 
2107   PetscFunctionBegin;
2108   if (yy != zz) { ierr = VecCopy(yy,zz);CHKERRQ(ierr); }
2109   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
2110   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
2111 
2112   idx = a->j;
2113   v   = a->a;
2114   if (usecprow) {
2115     mbs  = cprow.nrows;
2116     ii   = cprow.i;
2117     ridx = cprow.rindex;
2118   } else {
2119     mbs=a->mbs;
2120     ii = a->i;
2121     xb = x;
2122   }
2123 
2124   switch (bs) {
2125   case 1:
2126     for (i=0; i<mbs; i++) {
2127       if (usecprow) xb = x + ridx[i];
2128       x1 = xb[0];
2129       ib = idx + ii[0];
2130       n  = ii[1] - ii[0]; ii++;
2131       for (j=0; j<n; j++) {
2132         rval     = ib[j];
2133         z[rval] += *v * x1;
2134         v++;
2135       }
2136       if (!usecprow) xb++;
2137     }
2138     break;
2139   case 2:
2140     for (i=0; i<mbs; i++) {
2141       if (usecprow) xb = x + 2*ridx[i];
2142       x1 = xb[0]; x2 = xb[1];
2143       ib = idx + ii[0];
2144       n  = ii[1] - ii[0]; ii++;
2145       for (j=0; j<n; j++) {
2146         rval       = ib[j]*2;
2147         z[rval++] += v[0]*x1 + v[1]*x2;
2148         z[rval++] += v[2]*x1 + v[3]*x2;
2149         v         += 4;
2150       }
2151       if (!usecprow) xb += 2;
2152     }
2153     break;
2154   case 3:
2155     for (i=0; i<mbs; i++) {
2156       if (usecprow) xb = x + 3*ridx[i];
2157       x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
2158       ib = idx + ii[0];
2159       n  = ii[1] - ii[0]; ii++;
2160       for (j=0; j<n; j++) {
2161         rval       = ib[j]*3;
2162         z[rval++] += v[0]*x1 + v[1]*x2 + v[2]*x3;
2163         z[rval++] += v[3]*x1 + v[4]*x2 + v[5]*x3;
2164         z[rval++] += v[6]*x1 + v[7]*x2 + v[8]*x3;
2165         v         += 9;
2166       }
2167       if (!usecprow) xb += 3;
2168     }
2169     break;
2170   case 4:
2171     for (i=0; i<mbs; i++) {
2172       if (usecprow) xb = x + 4*ridx[i];
2173       x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
2174       ib = idx + ii[0];
2175       n  = ii[1] - ii[0]; ii++;
2176       for (j=0; j<n; j++) {
2177         rval       = ib[j]*4;
2178         z[rval++] +=  v[0]*x1 +  v[1]*x2 +  v[2]*x3 +  v[3]*x4;
2179         z[rval++] +=  v[4]*x1 +  v[5]*x2 +  v[6]*x3 +  v[7]*x4;
2180         z[rval++] +=  v[8]*x1 +  v[9]*x2 + v[10]*x3 + v[11]*x4;
2181         z[rval++] += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
2182         v         += 16;
2183       }
2184       if (!usecprow) xb += 4;
2185     }
2186     break;
2187   case 5:
2188     for (i=0; i<mbs; i++) {
2189       if (usecprow) xb = x + 5*ridx[i];
2190       x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
2191       x4 = xb[3]; x5 = xb[4];
2192       ib = idx + ii[0];
2193       n  = ii[1] - ii[0]; ii++;
2194       for (j=0; j<n; j++) {
2195         rval       = ib[j]*5;
2196         z[rval++] +=  v[0]*x1 +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5;
2197         z[rval++] +=  v[5]*x1 +  v[6]*x2 +  v[7]*x3 +  v[8]*x4 +  v[9]*x5;
2198         z[rval++] += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5;
2199         z[rval++] += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5;
2200         z[rval++] += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5;
2201         v         += 25;
2202       }
2203       if (!usecprow) xb += 5;
2204     }
2205     break;
2206   default: {      /* block sizes larger then 5 by 5 are handled by BLAS */
2207     PetscInt          ncols,k;
2208     PetscScalar       *work,*workt;
2209     const PetscScalar *xtmp;
2210     if (!a->mult_work) {
2211       k    = PetscMax(A->rmap->n,A->cmap->n);
2212       ierr = PetscMalloc1(k+1,&a->mult_work);CHKERRQ(ierr);
2213     }
2214     work = a->mult_work;
2215     xtmp = x;
2216     for (i=0; i<mbs; i++) {
2217       n     = ii[1] - ii[0]; ii++;
2218       ncols = n*bs;
2219       ierr  = PetscArrayzero(work,ncols);CHKERRQ(ierr);
2220       if (usecprow) xtmp = x + bs*ridx[i];
2221       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,xtmp,v,work);
2222       v += n*bs2;
2223       if (!usecprow) xtmp += bs;
2224       workt = work;
2225       for (j=0; j<n; j++) {
2226         zb = z + bs*(*idx++);
2227         for (k=0; k<bs; k++) zb[k] += workt[k];
2228         workt += bs;
2229       }
2230     }
2231     }
2232   }
2233   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
2234   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
2235   ierr = PetscLogFlops(2.0*a->nz*a->bs2);CHKERRQ(ierr);
2236   PetscFunctionReturn(0);
2237 }
2238 
2239 PetscErrorCode MatScale_SeqBAIJ(Mat inA,PetscScalar alpha)
2240 {
2241   Mat_SeqBAIJ    *a      = (Mat_SeqBAIJ*)inA->data;
2242   PetscInt       totalnz = a->bs2*a->nz;
2243   PetscScalar    oalpha  = alpha;
2244   PetscErrorCode ierr;
2245   PetscBLASInt   one = 1,tnz;
2246 
2247   PetscFunctionBegin;
2248   ierr = PetscBLASIntCast(totalnz,&tnz);CHKERRQ(ierr);
2249   PetscStackCallBLAS("BLASscal",BLASscal_(&tnz,&oalpha,a->a,&one));
2250   ierr = PetscLogFlops(totalnz);CHKERRQ(ierr);
2251   PetscFunctionReturn(0);
2252 }
2253 
2254 PetscErrorCode MatNorm_SeqBAIJ(Mat A,NormType type,PetscReal *norm)
2255 {
2256   PetscErrorCode ierr;
2257   Mat_SeqBAIJ    *a  = (Mat_SeqBAIJ*)A->data;
2258   MatScalar      *v  = a->a;
2259   PetscReal      sum = 0.0;
2260   PetscInt       i,j,k,bs=A->rmap->bs,nz=a->nz,bs2=a->bs2,k1;
2261 
2262   PetscFunctionBegin;
2263   if (type == NORM_FROBENIUS) {
2264 #if defined(PETSC_USE_REAL___FP16)
2265     PetscBLASInt one = 1,cnt = bs2*nz;
2266     PetscStackCallBLAS("BLASnrm2",*norm = BLASnrm2_(&cnt,v,&one));
2267 #else
2268     for (i=0; i<bs2*nz; i++) {
2269       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2270     }
2271 #endif
2272     *norm = PetscSqrtReal(sum);
2273     ierr = PetscLogFlops(2.0*bs2*nz);CHKERRQ(ierr);
2274   } else if (type == NORM_1) { /* maximum column sum */
2275     PetscReal *tmp;
2276     PetscInt  *bcol = a->j;
2277     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2278     for (i=0; i<nz; i++) {
2279       for (j=0; j<bs; j++) {
2280         k1 = bs*(*bcol) + j; /* column index */
2281         for (k=0; k<bs; k++) {
2282           tmp[k1] += PetscAbsScalar(*v); v++;
2283         }
2284       }
2285       bcol++;
2286     }
2287     *norm = 0.0;
2288     for (j=0; j<A->cmap->n; j++) {
2289       if (tmp[j] > *norm) *norm = tmp[j];
2290     }
2291     ierr = PetscFree(tmp);CHKERRQ(ierr);
2292     ierr = PetscLogFlops(PetscMax(bs2*nz-1,0));CHKERRQ(ierr);
2293   } else if (type == NORM_INFINITY) { /* maximum row sum */
2294     *norm = 0.0;
2295     for (k=0; k<bs; k++) {
2296       for (j=0; j<a->mbs; j++) {
2297         v   = a->a + bs2*a->i[j] + k;
2298         sum = 0.0;
2299         for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2300           for (k1=0; k1<bs; k1++) {
2301             sum += PetscAbsScalar(*v);
2302             v   += bs;
2303           }
2304         }
2305         if (sum > *norm) *norm = sum;
2306       }
2307     }
2308     ierr = PetscLogFlops(PetscMax(bs2*nz-1,0));CHKERRQ(ierr);
2309   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for this norm yet");
2310   PetscFunctionReturn(0);
2311 }
2312 
2313 
2314 PetscErrorCode MatEqual_SeqBAIJ(Mat A,Mat B,PetscBool * flg)
2315 {
2316   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)B->data;
2317   PetscErrorCode ierr;
2318 
2319   PetscFunctionBegin;
2320   /* If the  matrix/block dimensions are not equal, or no of nonzeros or shift */
2321   if ((A->rmap->N != B->rmap->N) || (A->cmap->n != B->cmap->n) || (A->rmap->bs != B->rmap->bs)|| (a->nz != b->nz)) {
2322     *flg = PETSC_FALSE;
2323     PetscFunctionReturn(0);
2324   }
2325 
2326   /* if the a->i are the same */
2327   ierr = PetscArraycmp(a->i,b->i,a->mbs+1,flg);CHKERRQ(ierr);
2328   if (!*flg) PetscFunctionReturn(0);
2329 
2330   /* if a->j are the same */
2331   ierr = PetscArraycmp(a->j,b->j,a->nz,flg);CHKERRQ(ierr);
2332   if (!*flg) PetscFunctionReturn(0);
2333 
2334   /* if a->a are the same */
2335   ierr = PetscArraycmp(a->a,b->a,(a->nz)*(A->rmap->bs)*(B->rmap->bs),flg);CHKERRQ(ierr);
2336   PetscFunctionReturn(0);
2337 
2338 }
2339 
2340 PetscErrorCode MatGetDiagonal_SeqBAIJ(Mat A,Vec v)
2341 {
2342   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
2343   PetscErrorCode ierr;
2344   PetscInt       i,j,k,n,row,bs,*ai,*aj,ambs,bs2;
2345   PetscScalar    *x,zero = 0.0;
2346   MatScalar      *aa,*aa_j;
2347 
2348   PetscFunctionBegin;
2349   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2350   bs   = A->rmap->bs;
2351   aa   = a->a;
2352   ai   = a->i;
2353   aj   = a->j;
2354   ambs = a->mbs;
2355   bs2  = a->bs2;
2356 
2357   ierr = VecSet(v,zero);CHKERRQ(ierr);
2358   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2359   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2360   if (n != A->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2361   for (i=0; i<ambs; i++) {
2362     for (j=ai[i]; j<ai[i+1]; j++) {
2363       if (aj[j] == i) {
2364         row  = i*bs;
2365         aa_j = aa+j*bs2;
2366         for (k=0; k<bs2; k+=(bs+1),row++) x[row] = aa_j[k];
2367         break;
2368       }
2369     }
2370   }
2371   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2372   PetscFunctionReturn(0);
2373 }
2374 
2375 PetscErrorCode MatDiagonalScale_SeqBAIJ(Mat A,Vec ll,Vec rr)
2376 {
2377   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2378   const PetscScalar *l,*r,*li,*ri;
2379   PetscScalar       x;
2380   MatScalar         *aa, *v;
2381   PetscErrorCode    ierr;
2382   PetscInt          i,j,k,lm,rn,M,m,n,mbs,tmp,bs,bs2,iai;
2383   const PetscInt    *ai,*aj;
2384 
2385   PetscFunctionBegin;
2386   ai  = a->i;
2387   aj  = a->j;
2388   aa  = a->a;
2389   m   = A->rmap->n;
2390   n   = A->cmap->n;
2391   bs  = A->rmap->bs;
2392   mbs = a->mbs;
2393   bs2 = a->bs2;
2394   if (ll) {
2395     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
2396     ierr = VecGetLocalSize(ll,&lm);CHKERRQ(ierr);
2397     if (lm != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2398     for (i=0; i<mbs; i++) { /* for each block row */
2399       M  = ai[i+1] - ai[i];
2400       li = l + i*bs;
2401       v  = aa + bs2*ai[i];
2402       for (j=0; j<M; j++) { /* for each block */
2403         for (k=0; k<bs2; k++) {
2404           (*v++) *= li[k%bs];
2405         }
2406       }
2407     }
2408     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
2409     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2410   }
2411 
2412   if (rr) {
2413     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
2414     ierr = VecGetLocalSize(rr,&rn);CHKERRQ(ierr);
2415     if (rn != n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2416     for (i=0; i<mbs; i++) { /* for each block row */
2417       iai = ai[i];
2418       M   = ai[i+1] - iai;
2419       v   = aa + bs2*iai;
2420       for (j=0; j<M; j++) { /* for each block */
2421         ri = r + bs*aj[iai+j];
2422         for (k=0; k<bs; k++) {
2423           x = ri[k];
2424           for (tmp=0; tmp<bs; tmp++) v[tmp] *= x;
2425           v += bs;
2426         }
2427       }
2428     }
2429     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
2430     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2431   }
2432   PetscFunctionReturn(0);
2433 }
2434 
2435 
2436 PetscErrorCode MatGetInfo_SeqBAIJ(Mat A,MatInfoType flag,MatInfo *info)
2437 {
2438   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data;
2439 
2440   PetscFunctionBegin;
2441   info->block_size   = a->bs2;
2442   info->nz_allocated = a->bs2*a->maxnz;
2443   info->nz_used      = a->bs2*a->nz;
2444   info->nz_unneeded  = info->nz_allocated - info->nz_used;
2445   info->assemblies   = A->num_ass;
2446   info->mallocs      = A->info.mallocs;
2447   info->memory       = ((PetscObject)A)->mem;
2448   if (A->factortype) {
2449     info->fill_ratio_given  = A->info.fill_ratio_given;
2450     info->fill_ratio_needed = A->info.fill_ratio_needed;
2451     info->factor_mallocs    = A->info.factor_mallocs;
2452   } else {
2453     info->fill_ratio_given  = 0;
2454     info->fill_ratio_needed = 0;
2455     info->factor_mallocs    = 0;
2456   }
2457   PetscFunctionReturn(0);
2458 }
2459 
2460 PetscErrorCode MatZeroEntries_SeqBAIJ(Mat A)
2461 {
2462   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data;
2463   PetscErrorCode ierr;
2464 
2465   PetscFunctionBegin;
2466   ierr = PetscArrayzero(a->a,a->bs2*a->i[a->mbs]);CHKERRQ(ierr);
2467   PetscFunctionReturn(0);
2468 }
2469 
2470 PetscErrorCode MatMatMultSymbolic_SeqBAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat C)
2471 {
2472   PetscErrorCode ierr;
2473 
2474   PetscFunctionBegin;
2475   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
2476   C->ops->matmultnumeric = MatMatMultNumeric_SeqBAIJ_SeqDense;
2477   PetscFunctionReturn(0);
2478 }
2479 
2480 PetscErrorCode MatMatMult_SeqBAIJ_1_Private(Mat A,PetscScalar* b,PetscInt bm,PetscScalar* c,PetscInt cm,PetscInt cn)
2481 {
2482   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2483   PetscScalar       *z = NULL,sum1;
2484   const PetscScalar *xb;
2485   PetscScalar       x1;
2486   const MatScalar   *v,*vv;
2487   PetscInt          mbs,i,*idx,*ii,j,*jj,n,k,*ridx=NULL;
2488   PetscBool         usecprow=a->compressedrow.use;
2489 
2490   PetscFunctionBegin;
2491   idx = a->j;
2492   v   = a->a;
2493   if (usecprow) {
2494     mbs  = a->compressedrow.nrows;
2495     ii   = a->compressedrow.i;
2496     ridx = a->compressedrow.rindex;
2497   } else {
2498     mbs = a->mbs;
2499     ii  = a->i;
2500     z   = c;
2501   }
2502 
2503   for (i=0; i<mbs; i++) {
2504     n           = ii[1] - ii[0]; ii++;
2505     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
2506     PetscPrefetchBlock(v+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
2507     if (usecprow) z = c + ridx[i];
2508     jj = idx;
2509     vv = v;
2510     for (k=0; k<cn; k++) {
2511       idx = jj;
2512       v = vv;
2513       sum1    = 0.0;
2514       for (j=0; j<n; j++) {
2515         xb    = b + (*idx++); x1 = xb[0+k*bm];
2516         sum1 += v[0]*x1;
2517         v    += 1;
2518       }
2519       z[0+k*cm] = sum1;
2520     }
2521     if (!usecprow) z += 1;
2522   }
2523   PetscFunctionReturn(0);
2524 }
2525 
2526 PetscErrorCode MatMatMult_SeqBAIJ_2_Private(Mat A,PetscScalar* b,PetscInt bm,PetscScalar* c,PetscInt cm,PetscInt cn)
2527 {
2528   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2529   PetscScalar       *z = NULL,sum1,sum2;
2530   const PetscScalar *xb;
2531   PetscScalar       x1,x2;
2532   const MatScalar   *v,*vv;
2533   PetscInt          mbs,i,*idx,*ii,j,*jj,n,k,*ridx=NULL;
2534   PetscBool         usecprow=a->compressedrow.use;
2535 
2536   PetscFunctionBegin;
2537   idx = a->j;
2538   v   = a->a;
2539   if (usecprow) {
2540     mbs  = a->compressedrow.nrows;
2541     ii   = a->compressedrow.i;
2542     ridx = a->compressedrow.rindex;
2543   } else {
2544     mbs = a->mbs;
2545     ii  = a->i;
2546     z   = c;
2547   }
2548 
2549   for (i=0; i<mbs; i++) {
2550     n           = ii[1] - ii[0]; ii++;
2551     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
2552     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
2553     if (usecprow) z = c + 2*ridx[i];
2554     jj = idx;
2555     vv = v;
2556     for (k=0; k<cn; k++) {
2557       idx = jj;
2558       v = vv;
2559       sum1    = 0.0; sum2 = 0.0;
2560       for (j=0; j<n; j++) {
2561         xb    = b + 2*(*idx++); x1 = xb[0+k*bm]; x2 = xb[1+k*bm];
2562         sum1 += v[0]*x1 + v[2]*x2;
2563         sum2 += v[1]*x1 + v[3]*x2;
2564         v    += 4;
2565       }
2566       z[0+k*cm] = sum1; z[1+k*cm] = sum2;
2567     }
2568     if (!usecprow) z += 2;
2569   }
2570   PetscFunctionReturn(0);
2571 }
2572 
2573 PetscErrorCode MatMatMult_SeqBAIJ_3_Private(Mat A,PetscScalar* b,PetscInt bm,PetscScalar* c,PetscInt cm,PetscInt cn)
2574 {
2575   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2576   PetscScalar       *z = NULL,sum1,sum2,sum3;
2577   const PetscScalar *xb;
2578   PetscScalar       x1,x2,x3;
2579   const MatScalar   *v,*vv;
2580   PetscInt          mbs,i,*idx,*ii,j,*jj,n,k,*ridx=NULL;
2581   PetscBool         usecprow=a->compressedrow.use;
2582 
2583   PetscFunctionBegin;
2584   idx = a->j;
2585   v   = a->a;
2586   if (usecprow) {
2587     mbs  = a->compressedrow.nrows;
2588     ii   = a->compressedrow.i;
2589     ridx = a->compressedrow.rindex;
2590   } else {
2591     mbs = a->mbs;
2592     ii  = a->i;
2593     z   = c;
2594   }
2595 
2596   for (i=0; i<mbs; i++) {
2597     n           = ii[1] - ii[0]; ii++;
2598     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
2599     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
2600     if (usecprow) z = c + 3*ridx[i];
2601     jj = idx;
2602     vv = v;
2603     for (k=0; k<cn; k++) {
2604       idx = jj;
2605       v = vv;
2606       sum1    = 0.0; sum2 = 0.0; sum3 = 0.0;
2607       for (j=0; j<n; j++) {
2608         xb    = b + 3*(*idx++); x1 = xb[0+k*bm]; x2 = xb[1+k*bm]; x3 = xb[2+k*bm];
2609         sum1 += v[0]*x1 + v[3]*x2 + v[6]*x3;
2610         sum2 += v[1]*x1 + v[4]*x2 + v[7]*x3;
2611         sum3 += v[2]*x1 + v[5]*x2 + v[8]*x3;
2612         v    += 9;
2613       }
2614       z[0+k*cm] = sum1; z[1+k*cm] = sum2; z[2+k*cm] = sum3;
2615     }
2616     if (!usecprow) z += 3;
2617   }
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 PetscErrorCode MatMatMult_SeqBAIJ_4_Private(Mat A,PetscScalar* b,PetscInt bm,PetscScalar* c,PetscInt cm,PetscInt cn)
2622 {
2623   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2624   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4;
2625   const PetscScalar *xb;
2626   PetscScalar       x1,x2,x3,x4;
2627   const MatScalar   *v,*vv;
2628   PetscInt          mbs,i,*idx,*ii,j,*jj,n,k,*ridx=NULL;
2629   PetscBool         usecprow=a->compressedrow.use;
2630 
2631   PetscFunctionBegin;
2632   idx = a->j;
2633   v   = a->a;
2634   if (usecprow) {
2635     mbs  = a->compressedrow.nrows;
2636     ii   = a->compressedrow.i;
2637     ridx = a->compressedrow.rindex;
2638   } else {
2639     mbs = a->mbs;
2640     ii  = a->i;
2641     z   = c;
2642   }
2643 
2644   for (i=0; i<mbs; i++) {
2645     n           = ii[1] - ii[0]; ii++;
2646     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
2647     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
2648     if (usecprow) z = c + 4*ridx[i];
2649     jj = idx;
2650     vv = v;
2651     for (k=0; k<cn; k++) {
2652       idx = jj;
2653       v = vv;
2654       sum1    = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0;
2655       for (j=0; j<n; j++) {
2656         xb    = b + 4*(*idx++); x1 = xb[0+k*bm]; x2 = xb[1+k*bm]; x3 = xb[2+k*bm]; x4 = xb[3+k*bm];
2657         sum1 += v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2658         sum2 += v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2659         sum3 += v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2660         sum4 += v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2661         v    += 16;
2662       }
2663       z[0+k*cm] = sum1; z[1+k*cm] = sum2; z[2+k*cm] = sum3; z[3+k*cm] = sum4;
2664     }
2665     if (!usecprow) z += 4;
2666   }
2667   PetscFunctionReturn(0);
2668 }
2669 
2670 PetscErrorCode MatMatMult_SeqBAIJ_5_Private(Mat A,PetscScalar* b,PetscInt bm,PetscScalar* c,PetscInt cm,PetscInt cn)
2671 {
2672   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2673   PetscScalar       *z = NULL,sum1,sum2,sum3,sum4,sum5;
2674   const PetscScalar *xb;
2675   PetscScalar       x1,x2,x3,x4,x5;
2676   const MatScalar   *v,*vv;
2677   PetscInt          mbs,i,*idx,*ii,j,*jj,n,k,*ridx=NULL;
2678   PetscBool         usecprow=a->compressedrow.use;
2679 
2680   PetscFunctionBegin;
2681   idx = a->j;
2682   v   = a->a;
2683   if (usecprow) {
2684     mbs  = a->compressedrow.nrows;
2685     ii   = a->compressedrow.i;
2686     ridx = a->compressedrow.rindex;
2687   } else {
2688     mbs = a->mbs;
2689     ii  = a->i;
2690     z   = c;
2691   }
2692 
2693   for (i=0; i<mbs; i++) {
2694     n           = ii[1] - ii[0]; ii++;
2695     PetscPrefetchBlock(idx+n,n,0,PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
2696     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
2697     if (usecprow) z = c + 5*ridx[i];
2698     jj = idx;
2699     vv = v;
2700     for (k=0; k<cn; k++) {
2701       idx = jj;
2702       v = vv;
2703       sum1    = 0.0; sum2 = 0.0; sum3 = 0.0; sum4 = 0.0; sum5 = 0.0;
2704       for (j=0; j<n; j++) {
2705         xb    = b + 5*(*idx++); x1 = xb[0+k*bm]; x2 = xb[1+k*bm]; x3 = xb[2+k*bm]; x4 = xb[3+k*bm]; x5 = xb[4+k*bm];
2706         sum1 += v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2707         sum2 += v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2708         sum3 += v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2709         sum4 += v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2710         sum5 += v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2711         v    += 25;
2712       }
2713       z[0+k*cm] = sum1; z[1+k*cm] = sum2; z[2+k*cm] = sum3; z[3+k*cm] = sum4; z[4+k*cm] = sum5;
2714     }
2715     if (!usecprow) z += 5;
2716   }
2717   PetscFunctionReturn(0);
2718 }
2719 
2720 PetscErrorCode MatMatMultNumeric_SeqBAIJ_SeqDense(Mat A,Mat B,Mat C)
2721 {
2722   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ*)A->data;
2723   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
2724   Mat_SeqDense      *cd = (Mat_SeqDense*)C->data;
2725   PetscInt          cm=cd->lda,cn=B->cmap->n,bm=bd->lda;
2726   PetscInt          mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2;
2727   PetscBLASInt      bbs,bcn,bbm,bcm;
2728   PetscScalar       *z = NULL;
2729   PetscScalar       *c,*b;
2730   const MatScalar   *v;
2731   const PetscInt    *idx,*ii,*ridx=NULL;
2732   PetscScalar       _DZero=0.0,_DOne=1.0;
2733   PetscBool         usecprow=a->compressedrow.use;
2734   PetscErrorCode    ierr;
2735 
2736   PetscFunctionBegin;
2737   if (!cm || !cn) PetscFunctionReturn(0);
2738   if (B->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,B->rmap->n);
2739   if (A->rmap->n != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap->n,A->rmap->n);
2740   if (B->cmap->n != C->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap->n,C->cmap->n);
2741   b = bd->v;
2742   if (a->nonzerorowcnt != A->rmap->n) {
2743     ierr = MatZeroEntries(C);CHKERRQ(ierr);
2744   }
2745   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
2746   switch (bs) {
2747   case 1:
2748     ierr = MatMatMult_SeqBAIJ_1_Private(A, b, bm, c, cm, cn);
2749     break;
2750   case 2:
2751     ierr = MatMatMult_SeqBAIJ_2_Private(A, b, bm, c, cm, cn);
2752     break;
2753   case 3:
2754     ierr = MatMatMult_SeqBAIJ_3_Private(A, b, bm, c, cm, cn);
2755     break;
2756   case 4:
2757     ierr = MatMatMult_SeqBAIJ_4_Private(A, b, bm, c, cm, cn);
2758     break;
2759   case 5:
2760     ierr = MatMatMult_SeqBAIJ_5_Private(A, b, bm, c, cm, cn);
2761     break;
2762   default: /* block sizes larger than 5 by 5 are handled by BLAS */
2763     ierr = PetscBLASIntCast(bs,&bbs);CHKERRQ(ierr);
2764     ierr = PetscBLASIntCast(cn,&bcn);CHKERRQ(ierr);
2765     ierr = PetscBLASIntCast(bm,&bbm);CHKERRQ(ierr);
2766     ierr = PetscBLASIntCast(cm,&bcm);CHKERRQ(ierr);
2767     idx = a->j;
2768     v   = a->a;
2769     if (usecprow) {
2770       mbs  = a->compressedrow.nrows;
2771       ii   = a->compressedrow.i;
2772       ridx = a->compressedrow.rindex;
2773     } else {
2774       mbs = a->mbs;
2775       ii  = a->i;
2776       z   = c;
2777     }
2778     for (i=0; i<mbs; i++) {
2779       n = ii[1] - ii[0]; ii++;
2780       if (usecprow) z = c + bs*ridx[i];
2781       if (n) {
2782         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&bbs,&bcn,&bbs,&_DOne,v,&bbs,b+bs*(*idx++),&bbm,&_DZero,z,&bcm));
2783         v += bs2;
2784       }
2785       for (j=1; j<n; j++) {
2786         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&bbs,&bcn,&bbs,&_DOne,v,&bbs,b+bs*(*idx++),&bbm,&_DOne,z,&bcm));
2787         v += bs2;
2788       }
2789       if (!usecprow) z += bs;
2790     }
2791   }
2792   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
2793   ierr = PetscLogFlops((2.0*a->nz*bs2 - bs*a->nonzerorowcnt)*cn);CHKERRQ(ierr);
2794   PetscFunctionReturn(0);
2795 }
2796