xref: /petsc/src/mat/impls/sbaij/seq/sbaij2.c (revision 81f96dcc196638099f4f8062b7ddb72e8b817c95)
1 #define PETSCMAT_DLL
2 
3 #include "../src/mat/impls/baij/seq/baij.h"
4 #include "../src/mat/blockinvert.h"
5 #include "petscbt.h"
6 #include "../src/mat/impls/sbaij/seq/sbaij.h"
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "MatIncreaseOverlap_SeqSBAIJ"
10 PetscErrorCode MatIncreaseOverlap_SeqSBAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
11 {
12   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
13   PetscErrorCode ierr;
14   PetscInt       brow,i,j,k,l,mbs,n,*nidx,isz,bcol,bcol_max,start,end,*ai,*aj,bs,*nidx2;
15   const PetscInt *idx;
16   PetscBT        table,table0;
17 
18   PetscFunctionBegin;
19   if (ov < 0)  SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
20   mbs = a->mbs;
21   ai  = a->i;
22   aj  = a->j;
23   bs  = A->rmap->bs;
24   ierr = PetscBTCreate(mbs,table);CHKERRQ(ierr);
25   ierr = PetscMalloc((mbs+1)*sizeof(PetscInt),&nidx);CHKERRQ(ierr);
26   ierr = PetscMalloc((A->rmap->N+1)*sizeof(PetscInt),&nidx2);CHKERRQ(ierr);
27   ierr = PetscBTCreate(mbs,table0);CHKERRQ(ierr);
28 
29   for (i=0; i<is_max; i++) { /* for each is */
30     isz  = 0;
31     ierr = PetscBTMemzero(mbs,table);CHKERRQ(ierr);
32 
33     /* Extract the indices, assume there can be duplicate entries */
34     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
35     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
36 
37     /* Enter these into the temp arrays i.e mark table[brow], enter brow into new index */
38     bcol_max = 0;
39     for (j=0; j<n ; ++j){
40       brow = idx[j]/bs; /* convert the indices into block indices */
41       if (brow >= mbs) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"index greater than mat-dim");
42       if(!PetscBTLookupSet(table,brow)) {
43         nidx[isz++] = brow;
44         if (bcol_max < brow) bcol_max = brow;
45       }
46     }
47     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
48     ierr = ISDestroy(is[i]);CHKERRQ(ierr);
49 
50     k = 0;
51     for (j=0; j<ov; j++){ /* for each overlap */
52       /* set table0 for lookup - only mark entries that are added onto nidx in (j-1)-th overlap */
53       ierr = PetscBTMemzero(mbs,table0);CHKERRQ(ierr);
54       for (l=k; l<isz; l++) { ierr = PetscBTSet(table0,nidx[l]);CHKERRQ(ierr); }
55 
56       n = isz;  /* length of the updated is[i] */
57       for (brow=0; brow<mbs; brow++){
58         start = ai[brow]; end   = ai[brow+1];
59         if (PetscBTLookup(table0,brow)){ /* brow is on nidx - row search: collect all bcol in this brow */
60           for (l = start; l<end ; l++){
61             bcol = aj[l];
62             if (!PetscBTLookupSet(table,bcol)) {nidx[isz++] = bcol;}
63           }
64           k++;
65           if (k >= n) break; /* for (brow=0; brow<mbs; brow++) */
66         } else { /* brow is not on nidx - col serach: add brow onto nidx if there is a bcol in nidx */
67           for (l = start; l<end ; l++){
68             bcol = aj[l];
69             if (bcol > bcol_max) break;
70             if (PetscBTLookup(table0,bcol)){
71               if (!PetscBTLookupSet(table,brow)) {nidx[isz++] = brow;}
72               break; /* for l = start; l<end ; l++) */
73             }
74           }
75         }
76       }
77     } /* for each overlap */
78 
79     /* expand the Index Set */
80     for (j=0; j<isz; j++) {
81       for (k=0; k<bs; k++)
82         nidx2[j*bs+k] = nidx[j]*bs+k;
83     }
84     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz*bs,nidx2,is+i);CHKERRQ(ierr);
85   }
86   ierr = PetscBTDestroy(table);CHKERRQ(ierr);
87   ierr = PetscFree(nidx);CHKERRQ(ierr);
88   ierr = PetscFree(nidx2);CHKERRQ(ierr);
89   ierr = PetscBTDestroy(table0);CHKERRQ(ierr);
90   PetscFunctionReturn(0);
91 }
92 
93 #undef __FUNCT__
94 #define __FUNCT__ "MatGetSubMatrix_SeqSBAIJ_Private"
95 PetscErrorCode MatGetSubMatrix_SeqSBAIJ_Private(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
96 {
97   Mat_SeqSBAIJ  *a = (Mat_SeqSBAIJ*)A->data,*c;
98   PetscErrorCode ierr;
99   PetscInt       *smap,i,k,kstart,kend,oldcols = a->mbs,*lens;
100   PetscInt       row,mat_i,*mat_j,tcol,*mat_ilen;
101   PetscInt       nrows,*ssmap,bs=A->rmap->bs,bs2=a->bs2;
102   const PetscInt *irow,*aj = a->j,*ai = a->i;
103   MatScalar      *mat_a;
104   Mat            C;
105   PetscTruth     flag,sorted;
106 
107   PetscFunctionBegin;
108   if (isrow != iscol) SETERRQ(PETSC_ERR_ARG_INCOMP,"For symmetric format, iscol must equal isro");
109   ierr = ISSorted(iscol,&sorted);CHKERRQ(ierr);
110   if (!sorted) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"IS is not sorted");
111 
112   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
113   ierr = ISGetSize(isrow,&nrows);CHKERRQ(ierr);
114 
115   ierr  = PetscMalloc(oldcols*sizeof(PetscInt),&smap);CHKERRQ(ierr);
116   ierr  = PetscMemzero(smap,oldcols*sizeof(PetscInt));CHKERRQ(ierr);
117   ssmap = smap;
118   ierr  = PetscMalloc((1+nrows)*sizeof(PetscInt),&lens);CHKERRQ(ierr);
119   for (i=0; i<nrows; i++) smap[irow[i]] = i+1; /* nrows = ncols */
120   /* determine lens of each row */
121   for (i=0; i<nrows; i++) {
122     kstart  = ai[irow[i]];
123     kend    = kstart + a->ilen[irow[i]];
124     lens[i] = 0;
125       for (k=kstart; k<kend; k++) {
126         if (ssmap[aj[k]]) {
127           lens[i]++;
128         }
129       }
130     }
131   /* Create and fill new matrix */
132   if (scall == MAT_REUSE_MATRIX) {
133     c = (Mat_SeqSBAIJ *)((*B)->data);
134 
135     if (c->mbs!=nrows || (*B)->rmap->bs!=bs) SETERRQ(PETSC_ERR_ARG_SIZ,"Submatrix wrong size");
136     ierr = PetscMemcmp(c->ilen,lens,c->mbs *sizeof(PetscInt),&flag);CHKERRQ(ierr);
137     if (!flag) {
138       SETERRQ(PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
139     }
140     ierr = PetscMemzero(c->ilen,c->mbs*sizeof(PetscInt));CHKERRQ(ierr);
141     C = *B;
142   } else {
143     ierr = MatCreate(((PetscObject)A)->comm,&C);CHKERRQ(ierr);
144     ierr = MatSetSizes(C,nrows*bs,nrows*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
145     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
146     ierr = MatSeqSBAIJSetPreallocation_SeqSBAIJ(C,bs,0,lens);CHKERRQ(ierr);
147   }
148   c = (Mat_SeqSBAIJ *)(C->data);
149   for (i=0; i<nrows; i++) {
150     row    = irow[i];
151     kstart = ai[row];
152     kend   = kstart + a->ilen[row];
153     mat_i  = c->i[i];
154     mat_j  = c->j + mat_i;
155     mat_a  = c->a + mat_i*bs2;
156     mat_ilen = c->ilen + i;
157     for (k=kstart; k<kend; k++) {
158       if ((tcol=ssmap[a->j[k]])) {
159         *mat_j++ = tcol - 1;
160         ierr     = PetscMemcpy(mat_a,a->a+k*bs2,bs2*sizeof(MatScalar));CHKERRQ(ierr);
161         mat_a   += bs2;
162         (*mat_ilen)++;
163       }
164     }
165   }
166 
167   /* Free work space */
168   ierr = PetscFree(smap);CHKERRQ(ierr);
169   ierr = PetscFree(lens);CHKERRQ(ierr);
170   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
171   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
172 
173   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
174   *B = C;
175   PetscFunctionReturn(0);
176 }
177 
178 #undef __FUNCT__
179 #define __FUNCT__ "MatGetSubMatrix_SeqSBAIJ"
180 PetscErrorCode MatGetSubMatrix_SeqSBAIJ(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
181 {
182   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
183   IS             is1;
184   PetscErrorCode ierr;
185   PetscInt       *vary,*iary,nrows,i,bs=A->rmap->bs,count;
186   const PetscInt *irow;
187 
188   PetscFunctionBegin;
189   if (isrow != iscol) SETERRQ(PETSC_ERR_ARG_INCOMP,"For symmetric format, iscol must equal isro");
190 
191   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
192   ierr = ISGetSize(isrow,&nrows);CHKERRQ(ierr);
193 
194   /* Verify if the indices corespond to each element in a block
195    and form the IS with compressed IS */
196   ierr = PetscMalloc2(a->mbs,PetscInt,&vary,a->mbs,PetscInt,&iary);CHKERRQ(ierr);
197   ierr = PetscMemzero(vary,a->mbs*sizeof(PetscInt));CHKERRQ(ierr);
198   for (i=0; i<nrows; i++) vary[irow[i]/bs]++;
199 
200   count = 0;
201   for (i=0; i<a->mbs; i++) {
202     if (vary[i]!=0 && vary[i]!=bs) SETERRQ(PETSC_ERR_ARG_INCOMP,"Index set does not match blocks");
203     if (vary[i]==bs) iary[count++] = i;
204   }
205   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
206   ierr = ISCreateGeneral(PETSC_COMM_SELF,count,iary,&is1);CHKERRQ(ierr);
207   ierr = PetscFree2(vary,iary);CHKERRQ(ierr);
208 
209   ierr = MatGetSubMatrix_SeqSBAIJ_Private(A,is1,is1,scall,B);CHKERRQ(ierr);
210   ierr = ISDestroy(is1);CHKERRQ(ierr);
211   PetscFunctionReturn(0);
212 }
213 
214 #undef __FUNCT__
215 #define __FUNCT__ "MatGetSubMatrices_SeqSBAIJ"
216 PetscErrorCode MatGetSubMatrices_SeqSBAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
217 {
218   PetscErrorCode ierr;
219   PetscInt       i;
220 
221   PetscFunctionBegin;
222   if (scall == MAT_INITIAL_MATRIX) {
223     ierr = PetscMalloc((n+1)*sizeof(Mat),B);CHKERRQ(ierr);
224   }
225 
226   for (i=0; i<n; i++) {
227     ierr = MatGetSubMatrix_SeqSBAIJ(A,irow[i],icol[i],scall,&(*B)[i]);CHKERRQ(ierr);
228   }
229   PetscFunctionReturn(0);
230 }
231 
232 /* -------------------------------------------------------*/
233 /* Should check that shapes of vectors and matrices match */
234 /* -------------------------------------------------------*/
235 
236 #undef __FUNCT__
237 #define __FUNCT__ "MatMult_SeqSBAIJ_2"
238 PetscErrorCode MatMult_SeqSBAIJ_2(Mat A,Vec xx,Vec zz)
239 {
240   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
241   PetscScalar    *x,*z,*xb,x1,x2,zero=0.0;
242   MatScalar      *v;
243   PetscErrorCode ierr;
244   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
245   PetscInt       nonzerorow=0;
246 
247   PetscFunctionBegin;
248   ierr = VecSet(zz,zero);CHKERRQ(ierr);
249   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
250   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
251 
252   v     = a->a;
253   xb = x;
254 
255   for (i=0; i<mbs; i++) {
256     n  = ai[1] - ai[0]; /* length of i_th block row of A */
257     x1 = xb[0]; x2 = xb[1];
258     ib = aj + *ai;
259     jmin = 0;
260     nonzerorow += (n>0);
261     if (*ib == i){     /* (diag of A)*x */
262       z[2*i]   += v[0]*x1 + v[2]*x2;
263       z[2*i+1] += v[2]*x1 + v[3]*x2;
264       v += 4; jmin++;
265     }
266     for (j=jmin; j<n; j++) {
267       /* (strict lower triangular part of A)*x  */
268       cval       = ib[j]*2;
269       z[cval]     += v[0]*x1 + v[1]*x2;
270       z[cval+1]   += v[2]*x1 + v[3]*x2;
271       /* (strict upper triangular part of A)*x  */
272       z[2*i]   += v[0]*x[cval] + v[2]*x[cval+1];
273       z[2*i+1] += v[1]*x[cval] + v[3]*x[cval+1];
274       v  += 4;
275     }
276     xb +=2; ai++;
277   }
278 
279   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
280   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
281   ierr = PetscLogFlops(8.0*(a->nz*2.0 - nonzerorow) - nonzerorow);CHKERRQ(ierr);
282   PetscFunctionReturn(0);
283 }
284 
285 #undef __FUNCT__
286 #define __FUNCT__ "MatMult_SeqSBAIJ_3"
287 PetscErrorCode MatMult_SeqSBAIJ_3(Mat A,Vec xx,Vec zz)
288 {
289   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
290   PetscScalar    *x,*z,*xb,x1,x2,x3,zero=0.0;
291   MatScalar      *v;
292   PetscErrorCode ierr;
293   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
294   PetscInt       nonzerorow=0;
295 
296   PetscFunctionBegin;
297   ierr = VecSet(zz,zero);CHKERRQ(ierr);
298   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
299   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
300 
301   v    = a->a;
302   xb   = x;
303 
304   for (i=0; i<mbs; i++) {
305     n  = ai[1] - ai[0]; /* length of i_th block row of A */
306     x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
307     ib = aj + *ai;
308     jmin = 0;
309     nonzerorow += (n>0);
310     if (*ib == i){     /* (diag of A)*x */
311       z[3*i]   += v[0]*x1 + v[3]*x2 + v[6]*x3;
312       z[3*i+1] += v[3]*x1 + v[4]*x2 + v[7]*x3;
313       z[3*i+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
314       v += 9; jmin++;
315     }
316     for (j=jmin; j<n; j++) {
317       /* (strict lower triangular part of A)*x  */
318       cval       = ib[j]*3;
319       z[cval]     += v[0]*x1 + v[1]*x2 + v[2]*x3;
320       z[cval+1]   += v[3]*x1 + v[4]*x2 + v[5]*x3;
321       z[cval+2]   += v[6]*x1 + v[7]*x2 + v[8]*x3;
322       /* (strict upper triangular part of A)*x  */
323       z[3*i]   += v[0]*x[cval] + v[3]*x[cval+1]+ v[6]*x[cval+2];
324       z[3*i+1] += v[1]*x[cval] + v[4]*x[cval+1]+ v[7]*x[cval+2];
325       z[3*i+2] += v[2]*x[cval] + v[5]*x[cval+1]+ v[8]*x[cval+2];
326       v  += 9;
327     }
328     xb +=3; ai++;
329   }
330 
331   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
332   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
333   ierr = PetscLogFlops(18.0*(a->nz*2.0 - nonzerorow) - nonzerorow);CHKERRQ(ierr);
334   PetscFunctionReturn(0);
335 }
336 
337 #undef __FUNCT__
338 #define __FUNCT__ "MatMult_SeqSBAIJ_4"
339 PetscErrorCode MatMult_SeqSBAIJ_4(Mat A,Vec xx,Vec zz)
340 {
341   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
342   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,zero=0.0;
343   MatScalar      *v;
344   PetscErrorCode ierr;
345   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
346   PetscInt       nonzerorow=0;
347 
348   PetscFunctionBegin;
349   ierr = VecSet(zz,zero);CHKERRQ(ierr);
350   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
351   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
352 
353   v     = a->a;
354   xb = x;
355 
356   for (i=0; i<mbs; i++) {
357     n  = ai[1] - ai[0]; /* length of i_th block row of A */
358     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
359     ib = aj + *ai;
360     jmin = 0;
361     nonzerorow += (n>0);
362     if (*ib == i){     /* (diag of A)*x */
363       z[4*i]   += v[0]*x1 + v[4]*x2 +  v[8]*x3 + v[12]*x4;
364       z[4*i+1] += v[4]*x1 + v[5]*x2 +  v[9]*x3 + v[13]*x4;
365       z[4*i+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[14]*x4;
366       z[4*i+3] += v[12]*x1+ v[13]*x2+ v[14]*x3 + v[15]*x4;
367       v += 16; jmin++;
368     }
369     for (j=jmin; j<n; j++) {
370       /* (strict lower triangular part of A)*x  */
371       cval       = ib[j]*4;
372       z[cval]     += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4;
373       z[cval+1]   += v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4;
374       z[cval+2]   += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4;
375       z[cval+3]   += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
376       /* (strict upper triangular part of A)*x  */
377       z[4*i]   += v[0]*x[cval] + v[4]*x[cval+1]+ v[8]*x[cval+2] + v[12]*x[cval+3];
378       z[4*i+1] += v[1]*x[cval] + v[5]*x[cval+1]+ v[9]*x[cval+2] + v[13]*x[cval+3];
379       z[4*i+2] += v[2]*x[cval] + v[6]*x[cval+1]+ v[10]*x[cval+2]+ v[14]*x[cval+3];
380       z[4*i+3] += v[3]*x[cval] + v[7]*x[cval+1]+ v[11]*x[cval+2]+ v[15]*x[cval+3];
381       v  += 16;
382     }
383     xb +=4; ai++;
384   }
385 
386   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
387   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
388   ierr = PetscLogFlops(32.0*(a->nz*2.0 - nonzerorow) - nonzerorow);CHKERRQ(ierr);
389   PetscFunctionReturn(0);
390 }
391 
392 #undef __FUNCT__
393 #define __FUNCT__ "MatMult_SeqSBAIJ_5"
394 PetscErrorCode MatMult_SeqSBAIJ_5(Mat A,Vec xx,Vec zz)
395 {
396   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
397   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,x5,zero=0.0;
398   MatScalar      *v;
399   PetscErrorCode ierr;
400   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
401   PetscInt       nonzerorow=0;
402 
403   PetscFunctionBegin;
404   ierr = VecSet(zz,zero);CHKERRQ(ierr);
405   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
406   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
407 
408   v     = a->a;
409   xb = x;
410 
411   for (i=0; i<mbs; i++) {
412     n  = ai[1] - ai[0]; /* length of i_th block row of A */
413     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4];
414     ib = aj + *ai;
415     jmin = 0;
416     nonzerorow += (n>0);
417     if (*ib == i){      /* (diag of A)*x */
418       z[5*i]   += v[0]*x1  + v[5]*x2 + v[10]*x3 + v[15]*x4+ v[20]*x5;
419       z[5*i+1] += v[5]*x1  + v[6]*x2 + v[11]*x3 + v[16]*x4+ v[21]*x5;
420       z[5*i+2] += v[10]*x1 +v[11]*x2 + v[12]*x3 + v[17]*x4+ v[22]*x5;
421       z[5*i+3] += v[15]*x1 +v[16]*x2 + v[17]*x3 + v[18]*x4+ v[23]*x5;
422       z[5*i+4] += v[20]*x1 +v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
423       v += 25; jmin++;
424     }
425     for (j=jmin; j<n; j++) {
426       /* (strict lower triangular part of A)*x  */
427       cval       = ib[j]*5;
428       z[cval]     += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5;
429       z[cval+1]   += v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5;
430       z[cval+2]   += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4+ v[14]*x5;
431       z[cval+3]   += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4+ v[19]*x5;
432       z[cval+4]   += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
433       /* (strict upper triangular part of A)*x  */
434       z[5*i]   +=v[0]*x[cval]+v[5]*x[cval+1]+v[10]*x[cval+2]+v[15]*x[cval+3]+v[20]*x[cval+4];
435       z[5*i+1] +=v[1]*x[cval]+v[6]*x[cval+1]+v[11]*x[cval+2]+v[16]*x[cval+3]+v[21]*x[cval+4];
436       z[5*i+2] +=v[2]*x[cval]+v[7]*x[cval+1]+v[12]*x[cval+2]+v[17]*x[cval+3]+v[22]*x[cval+4];
437       z[5*i+3] +=v[3]*x[cval]+v[8]*x[cval+1]+v[13]*x[cval+2]+v[18]*x[cval+3]+v[23]*x[cval+4];
438       z[5*i+4] +=v[4]*x[cval]+v[9]*x[cval+1]+v[14]*x[cval+2]+v[19]*x[cval+3]+v[24]*x[cval+4];
439       v  += 25;
440     }
441     xb +=5; ai++;
442   }
443 
444   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
445   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
446   ierr = PetscLogFlops(50.0*(a->nz*2.0 - nonzerorow) - nonzerorow);CHKERRQ(ierr);
447   PetscFunctionReturn(0);
448 }
449 
450 
451 #undef __FUNCT__
452 #define __FUNCT__ "MatMult_SeqSBAIJ_6"
453 PetscErrorCode MatMult_SeqSBAIJ_6(Mat A,Vec xx,Vec zz)
454 {
455   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
456   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,x5,x6,zero=0.0;
457   MatScalar      *v;
458   PetscErrorCode ierr;
459   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
460   PetscInt       nonzerorow=0;
461 
462   PetscFunctionBegin;
463   ierr = VecSet(zz,zero);CHKERRQ(ierr);
464   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
465   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
466 
467   v     = a->a;
468   xb = x;
469 
470   for (i=0; i<mbs; i++) {
471     n  = ai[1] - ai[0]; /* length of i_th block row of A */
472     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5];
473     ib = aj + *ai;
474     jmin = 0;
475     nonzerorow += (n>0);
476     if (*ib == i){      /* (diag of A)*x */
477       z[6*i]   += v[0]*x1  + v[6]*x2 + v[12]*x3 + v[18]*x4+ v[24]*x5 + v[30]*x6;
478       z[6*i+1] += v[6]*x1  + v[7]*x2 + v[13]*x3 + v[19]*x4+ v[25]*x5 + v[31]*x6;
479       z[6*i+2] += v[12]*x1 +v[13]*x2 + v[14]*x3 + v[20]*x4+ v[26]*x5 + v[32]*x6;
480       z[6*i+3] += v[18]*x1 +v[19]*x2 + v[20]*x3 + v[21]*x4+ v[27]*x5 + v[33]*x6;
481       z[6*i+4] += v[24]*x1 +v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[34]*x6;
482       z[6*i+5] += v[30]*x1 +v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
483       v += 36; jmin++;
484     }
485     for (j=jmin; j<n; j++) {
486       /* (strict lower triangular part of A)*x  */
487       cval       = ib[j]*6;
488       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6;
489       z[cval+1] += v[6]*x1  + v[7]*x2 + v[8]*x3 + v[9]*x4+ v[10]*x5 + v[11]*x6;
490       z[cval+2] += v[12]*x1  + v[13]*x2 + v[14]*x3 + v[15]*x4+ v[16]*x5 + v[17]*x6;
491       z[cval+3] += v[18]*x1  + v[19]*x2 + v[20]*x3 + v[21]*x4+ v[22]*x5 + v[23]*x6;
492       z[cval+4] += v[24]*x1  + v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[29]*x6;
493       z[cval+5] += v[30]*x1  + v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
494       /* (strict upper triangular part of A)*x  */
495       z[6*i]   +=v[0]*x[cval]+v[6]*x[cval+1]+v[12]*x[cval+2]+v[18]*x[cval+3]+v[24]*x[cval+4]+v[30]*x[cval+5];
496       z[6*i+1] +=v[1]*x[cval]+v[7]*x[cval+1]+v[13]*x[cval+2]+v[19]*x[cval+3]+v[25]*x[cval+4]+v[31]*x[cval+5];
497       z[6*i+2] +=v[2]*x[cval]+v[8]*x[cval+1]+v[14]*x[cval+2]+v[20]*x[cval+3]+v[26]*x[cval+4]+v[32]*x[cval+5];
498       z[6*i+3] +=v[3]*x[cval]+v[9]*x[cval+1]+v[15]*x[cval+2]+v[21]*x[cval+3]+v[27]*x[cval+4]+v[33]*x[cval+5];
499       z[6*i+4] +=v[4]*x[cval]+v[10]*x[cval+1]+v[16]*x[cval+2]+v[22]*x[cval+3]+v[28]*x[cval+4]+v[34]*x[cval+5];
500       z[6*i+5] +=v[5]*x[cval]+v[11]*x[cval+1]+v[17]*x[cval+2]+v[23]*x[cval+3]+v[29]*x[cval+4]+v[35]*x[cval+5];
501       v  += 36;
502     }
503     xb +=6; ai++;
504   }
505 
506   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
507   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
508   ierr = PetscLogFlops(72.0*(a->nz*2.0 - nonzerorow) - nonzerorow);CHKERRQ(ierr);
509   PetscFunctionReturn(0);
510 }
511 #undef __FUNCT__
512 #define __FUNCT__ "MatMult_SeqSBAIJ_7"
513 PetscErrorCode MatMult_SeqSBAIJ_7(Mat A,Vec xx,Vec zz)
514 {
515   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
516   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,x5,x6,x7,zero=0.0;
517   MatScalar      *v;
518   PetscErrorCode ierr;
519   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
520   PetscInt       nonzerorow=0;
521 
522   PetscFunctionBegin;
523   ierr = VecSet(zz,zero);CHKERRQ(ierr);
524   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
525   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
526 
527   v     = a->a;
528   xb = x;
529 
530   for (i=0; i<mbs; i++) {
531     n  = ai[1] - ai[0]; /* length of i_th block row of A */
532     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5]; x7=xb[6];
533     ib = aj + *ai;
534     jmin = 0;
535     nonzerorow += (n>0);
536     if (*ib == i){      /* (diag of A)*x */
537       z[7*i]   += v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4+ v[28]*x5 + v[35]*x6+ v[42]*x7;
538       z[7*i+1] += v[7]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4+ v[29]*x5 + v[36]*x6+ v[43]*x7;
539       z[7*i+2] += v[14]*x1+ v[15]*x2 +v[16]*x3 + v[23]*x4+ v[30]*x5 + v[37]*x6+ v[44]*x7;
540       z[7*i+3] += v[21]*x1+ v[22]*x2 +v[23]*x3 + v[24]*x4+ v[31]*x5 + v[38]*x6+ v[45]*x7;
541       z[7*i+4] += v[28]*x1+ v[29]*x2 +v[30]*x3 + v[31]*x4+ v[32]*x5 + v[39]*x6+ v[46]*x7;
542       z[7*i+5] += v[35]*x1+ v[36]*x2 +v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[47]*x7;
543       z[7*i+6] += v[42]*x1+ v[43]*x2 +v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
544       v += 49; jmin++;
545     }
546     for (j=jmin; j<n; j++) {
547       /* (strict lower triangular part of A)*x  */
548       cval       = ib[j]*7;
549       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6+ v[6]*x7;
550       z[cval+1] += v[7]*x1  + v[8]*x2 + v[9]*x3 + v[10]*x4+ v[11]*x5 + v[12]*x6+ v[13]*x7;
551       z[cval+2] += v[14]*x1  + v[15]*x2 + v[16]*x3 + v[17]*x4+ v[18]*x5 + v[19]*x6+ v[20]*x7;
552       z[cval+3] += v[21]*x1  + v[22]*x2 + v[23]*x3 + v[24]*x4+ v[25]*x5 + v[26]*x6+ v[27]*x7;
553       z[cval+4] += v[28]*x1  + v[29]*x2 + v[30]*x3 + v[31]*x4+ v[32]*x5 + v[33]*x6+ v[34]*x7;
554       z[cval+5] += v[35]*x1  + v[36]*x2 + v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[41]*x7;
555       z[cval+6] += v[42]*x1  + v[43]*x2 + v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
556       /* (strict upper triangular part of A)*x  */
557       z[7*i]  +=v[0]*x[cval]+v[7]*x[cval+1]+v[14]*x[cval+2]+v[21]*x[cval+3]+v[28]*x[cval+4]+v[35]*x[cval+5]+v[42]*x[cval+6];
558       z[7*i+1]+=v[1]*x[cval]+v[8]*x[cval+1]+v[15]*x[cval+2]+v[22]*x[cval+3]+v[29]*x[cval+4]+v[36]*x[cval+5]+v[43]*x[cval+6];
559       z[7*i+2]+=v[2]*x[cval]+v[9]*x[cval+1]+v[16]*x[cval+2]+v[23]*x[cval+3]+v[30]*x[cval+4]+v[37]*x[cval+5]+v[44]*x[cval+6];
560       z[7*i+3]+=v[3]*x[cval]+v[10]*x[cval+1]+v[17]*x[cval+2]+v[24]*x[cval+3]+v[31]*x[cval+4]+v[38]*x[cval+5]+v[45]*x[cval+6];
561       z[7*i+4]+=v[4]*x[cval]+v[11]*x[cval+1]+v[18]*x[cval+2]+v[25]*x[cval+3]+v[32]*x[cval+4]+v[39]*x[cval+5]+v[46]*x[cval+6];
562       z[7*i+5]+=v[5]*x[cval]+v[12]*x[cval+1]+v[19]*x[cval+2]+v[26]*x[cval+3]+v[33]*x[cval+4]+v[40]*x[cval+5]+v[47]*x[cval+6];
563       z[7*i+6]+=v[6]*x[cval]+v[13]*x[cval+1]+v[20]*x[cval+2]+v[27]*x[cval+3]+v[34]*x[cval+4]+v[41]*x[cval+5]+v[48]*x[cval+6];
564       v  += 49;
565     }
566     xb +=7; ai++;
567   }
568   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
569   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
570   ierr = PetscLogFlops(98.0*(a->nz*2.0 - nonzerorow) - nonzerorow);CHKERRQ(ierr);
571   PetscFunctionReturn(0);
572 }
573 
574 /*
575     This will not work with MatScalar == float because it calls the BLAS
576 */
577 #undef __FUNCT__
578 #define __FUNCT__ "MatMult_SeqSBAIJ_N"
579 PetscErrorCode MatMult_SeqSBAIJ_N(Mat A,Vec xx,Vec zz)
580 {
581   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
582   PetscScalar    *x,*x_ptr,*z,*z_ptr,*xb,*zb,*work,*workt,zero=0.0;
583   MatScalar      *v;
584   PetscErrorCode ierr;
585   PetscInt       mbs=a->mbs,i,*idx,*aj,*ii,bs=A->rmap->bs,j,n,bs2=a->bs2,ncols,k;
586   PetscInt       nonzerorow=0;
587 
588   PetscFunctionBegin;
589   ierr = VecSet(zz,zero);CHKERRQ(ierr);
590   ierr = VecGetArray(xx,&x);CHKERRQ(ierr); x_ptr=x;
591   ierr = VecGetArray(zz,&z);CHKERRQ(ierr); z_ptr=z;
592 
593   aj   = a->j;
594   v    = a->a;
595   ii   = a->i;
596 
597   if (!a->mult_work) {
598     ierr = PetscMalloc((A->rmap->N+1)*sizeof(PetscScalar),&a->mult_work);CHKERRQ(ierr);
599   }
600   work = a->mult_work;
601 
602   for (i=0; i<mbs; i++) {
603     n     = ii[1] - ii[0]; ncols = n*bs;
604     workt = work; idx=aj+ii[0];
605     nonzerorow += (n>0);
606 
607     /* upper triangular part */
608     for (j=0; j<n; j++) {
609       xb = x_ptr + bs*(*idx++);
610       for (k=0; k<bs; k++) workt[k] = xb[k];
611       workt += bs;
612     }
613     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
614     Kernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);
615 
616     /* strict lower triangular part */
617     idx = aj+ii[0];
618     if (*idx == i){
619       ncols -= bs; v += bs2; idx++; n--;
620     }
621 
622     if (ncols > 0){
623       workt = work;
624       ierr  = PetscMemzero(workt,ncols*sizeof(PetscScalar));CHKERRQ(ierr);
625       Kernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,x,v,workt);
626       for (j=0; j<n; j++) {
627         zb = z_ptr + bs*(*idx++);
628         for (k=0; k<bs; k++) zb[k] += workt[k] ;
629         workt += bs;
630       }
631     }
632     x += bs; v += n*bs2; z += bs; ii++;
633   }
634 
635   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
636   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
637   ierr = PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow)*bs2 - nonzerorow);CHKERRQ(ierr);
638   PetscFunctionReturn(0);
639 }
640 
641 extern PetscErrorCode VecCopy_Seq(Vec,Vec);
642 #undef __FUNCT__
643 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_1"
644 PetscErrorCode MatMultAdd_SeqSBAIJ_1(Mat A,Vec xx,Vec yy,Vec zz)
645 {
646   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
647   PetscScalar    *x,*z,*xb,x1;
648   MatScalar      *v;
649   PetscErrorCode ierr;
650   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
651   PetscInt       nonzerorow=0;
652 
653   PetscFunctionBegin;
654   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
655   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
656   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
657   v  = a->a;
658   xb = x;
659 
660   for (i=0; i<mbs; i++) {
661     n  = ai[1] - ai[0];  /* length of i_th row of A */
662     x1 = xb[0];
663     ib = aj + *ai;
664     jmin = 0;
665     nonzerorow += (n>0);
666     if (*ib == i) {            /* (diag of A)*x */
667       z[i] += *v++ * x[*ib++]; jmin++;
668     }
669     for (j=jmin; j<n; j++) {
670       cval    = *ib;
671       z[cval] += *v * x1;      /* (strict lower triangular part of A)*x  */
672       z[i] += *v++ * x[*ib++]; /* (strict upper triangular part of A)*x  */
673     }
674     xb++; ai++;
675   }
676 
677   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
678   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
679 
680   ierr = PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
681   PetscFunctionReturn(0);
682 }
683 
684 #undef __FUNCT__
685 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_2"
686 PetscErrorCode MatMultAdd_SeqSBAIJ_2(Mat A,Vec xx,Vec yy,Vec zz)
687 {
688   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
689   PetscScalar    *x,*z,*xb,x1,x2;
690   MatScalar      *v;
691   PetscErrorCode ierr;
692   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
693   PetscInt       nonzerorow=0;
694 
695   PetscFunctionBegin;
696   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
697   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
698   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
699 
700   v  = a->a;
701   xb = x;
702 
703   for (i=0; i<mbs; i++) {
704     n  = ai[1] - ai[0]; /* length of i_th block row of A */
705     x1 = xb[0]; x2 = xb[1];
706     ib = aj + *ai;
707     jmin = 0;
708     nonzerorow += (n>0);
709     if (*ib == i){      /* (diag of A)*x */
710       z[2*i]   += v[0]*x1 + v[2]*x2;
711       z[2*i+1] += v[2]*x1 + v[3]*x2;
712       v += 4; jmin++;
713     }
714     for (j=jmin; j<n; j++) {
715       /* (strict lower triangular part of A)*x  */
716       cval       = ib[j]*2;
717       z[cval]     += v[0]*x1 + v[1]*x2;
718       z[cval+1]   += v[2]*x1 + v[3]*x2;
719       /* (strict upper triangular part of A)*x  */
720       z[2*i]   += v[0]*x[cval] + v[2]*x[cval+1];
721       z[2*i+1] += v[1]*x[cval] + v[3]*x[cval+1];
722       v  += 4;
723     }
724     xb +=2; ai++;
725   }
726   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
727   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
728 
729   ierr = PetscLogFlops(4.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
730   PetscFunctionReturn(0);
731 }
732 
733 #undef __FUNCT__
734 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_3"
735 PetscErrorCode MatMultAdd_SeqSBAIJ_3(Mat A,Vec xx,Vec yy,Vec zz)
736 {
737   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
738   PetscScalar    *x,*z,*xb,x1,x2,x3;
739   MatScalar      *v;
740   PetscErrorCode ierr;
741   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
742   PetscInt       nonzerorow=0;
743 
744   PetscFunctionBegin;
745   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
746   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
747   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
748 
749   v     = a->a;
750   xb = x;
751 
752   for (i=0; i<mbs; i++) {
753     n  = ai[1] - ai[0]; /* length of i_th block row of A */
754     x1 = xb[0]; x2 = xb[1]; x3 = xb[2];
755     ib = aj + *ai;
756     jmin = 0;
757     nonzerorow += (n>0);
758     if (*ib == i){     /* (diag of A)*x */
759      z[3*i]   += v[0]*x1 + v[3]*x2 + v[6]*x3;
760      z[3*i+1] += v[3]*x1 + v[4]*x2 + v[7]*x3;
761      z[3*i+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
762      v += 9; jmin++;
763     }
764     for (j=jmin; j<n; j++) {
765       /* (strict lower triangular part of A)*x  */
766       cval       = ib[j]*3;
767       z[cval]     += v[0]*x1 + v[1]*x2 + v[2]*x3;
768       z[cval+1]   += v[3]*x1 + v[4]*x2 + v[5]*x3;
769       z[cval+2]   += v[6]*x1 + v[7]*x2 + v[8]*x3;
770       /* (strict upper triangular part of A)*x  */
771       z[3*i]   += v[0]*x[cval] + v[3]*x[cval+1]+ v[6]*x[cval+2];
772       z[3*i+1] += v[1]*x[cval] + v[4]*x[cval+1]+ v[7]*x[cval+2];
773       z[3*i+2] += v[2]*x[cval] + v[5]*x[cval+1]+ v[8]*x[cval+2];
774       v  += 9;
775     }
776     xb +=3; ai++;
777   }
778 
779   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
780   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
781 
782   ierr = PetscLogFlops(18.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
783   PetscFunctionReturn(0);
784 }
785 
786 #undef __FUNCT__
787 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_4"
788 PetscErrorCode MatMultAdd_SeqSBAIJ_4(Mat A,Vec xx,Vec yy,Vec zz)
789 {
790   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
791   PetscScalar    *x,*z,*xb,x1,x2,x3,x4;
792   MatScalar      *v;
793   PetscErrorCode ierr;
794   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
795   PetscInt       nonzerorow=0;
796 
797   PetscFunctionBegin;
798   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
799   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
800   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
801 
802   v     = a->a;
803   xb = x;
804 
805   for (i=0; i<mbs; i++) {
806     n  = ai[1] - ai[0]; /* length of i_th block row of A */
807     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
808     ib = aj + *ai;
809     jmin = 0;
810     nonzerorow += (n>0);
811     if (*ib == i){      /* (diag of A)*x */
812       z[4*i]   += v[0]*x1 + v[4]*x2 +  v[8]*x3 + v[12]*x4;
813       z[4*i+1] += v[4]*x1 + v[5]*x2 +  v[9]*x3 + v[13]*x4;
814       z[4*i+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[14]*x4;
815       z[4*i+3] += v[12]*x1+ v[13]*x2+ v[14]*x3 + v[15]*x4;
816       v += 16; jmin++;
817     }
818     for (j=jmin; j<n; j++) {
819       /* (strict lower triangular part of A)*x  */
820       cval       = ib[j]*4;
821       z[cval]     += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4;
822       z[cval+1]   += v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4;
823       z[cval+2]   += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4;
824       z[cval+3]   += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
825       /* (strict upper triangular part of A)*x  */
826       z[4*i]   += v[0]*x[cval] + v[4]*x[cval+1]+ v[8]*x[cval+2] + v[12]*x[cval+3];
827       z[4*i+1] += v[1]*x[cval] + v[5]*x[cval+1]+ v[9]*x[cval+2] + v[13]*x[cval+3];
828       z[4*i+2] += v[2]*x[cval] + v[6]*x[cval+1]+ v[10]*x[cval+2]+ v[14]*x[cval+3];
829       z[4*i+3] += v[3]*x[cval] + v[7]*x[cval+1]+ v[11]*x[cval+2]+ v[15]*x[cval+3];
830       v  += 16;
831     }
832     xb +=4; ai++;
833   }
834 
835   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
836   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
837 
838   ierr = PetscLogFlops(32.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
839   PetscFunctionReturn(0);
840 }
841 
842 #undef __FUNCT__
843 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_5"
844 PetscErrorCode MatMultAdd_SeqSBAIJ_5(Mat A,Vec xx,Vec yy,Vec zz)
845 {
846   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
847   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,x5;
848   MatScalar      *v;
849   PetscErrorCode ierr;
850   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
851   PetscInt       nonzerorow=0;
852 
853   PetscFunctionBegin;
854   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
855   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
856   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
857 
858   v     = a->a;
859   xb = x;
860 
861   for (i=0; i<mbs; i++) {
862     n  = ai[1] - ai[0]; /* length of i_th block row of A */
863     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4];
864     ib = aj + *ai;
865     jmin = 0;
866     nonzerorow += (n>0);
867     if (*ib == i){      /* (diag of A)*x */
868       z[5*i]   += v[0]*x1  + v[5]*x2 + v[10]*x3 + v[15]*x4+ v[20]*x5;
869       z[5*i+1] += v[5]*x1  + v[6]*x2 + v[11]*x3 + v[16]*x4+ v[21]*x5;
870       z[5*i+2] += v[10]*x1 +v[11]*x2 + v[12]*x3 + v[17]*x4+ v[22]*x5;
871       z[5*i+3] += v[15]*x1 +v[16]*x2 + v[17]*x3 + v[18]*x4+ v[23]*x5;
872       z[5*i+4] += v[20]*x1 +v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
873       v += 25; jmin++;
874     }
875     for (j=jmin; j<n; j++) {
876       /* (strict lower triangular part of A)*x  */
877       cval       = ib[j]*5;
878       z[cval]     += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5;
879       z[cval+1]   += v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5;
880       z[cval+2]   += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4+ v[14]*x5;
881       z[cval+3]   += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4+ v[19]*x5;
882       z[cval+4]   += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
883       /* (strict upper triangular part of A)*x  */
884       z[5*i]   +=v[0]*x[cval]+v[5]*x[cval+1]+v[10]*x[cval+2]+v[15]*x[cval+3]+v[20]*x[cval+4];
885       z[5*i+1] +=v[1]*x[cval]+v[6]*x[cval+1]+v[11]*x[cval+2]+v[16]*x[cval+3]+v[21]*x[cval+4];
886       z[5*i+2] +=v[2]*x[cval]+v[7]*x[cval+1]+v[12]*x[cval+2]+v[17]*x[cval+3]+v[22]*x[cval+4];
887       z[5*i+3] +=v[3]*x[cval]+v[8]*x[cval+1]+v[13]*x[cval+2]+v[18]*x[cval+3]+v[23]*x[cval+4];
888       z[5*i+4] +=v[4]*x[cval]+v[9]*x[cval+1]+v[14]*x[cval+2]+v[19]*x[cval+3]+v[24]*x[cval+4];
889       v  += 25;
890     }
891     xb +=5; ai++;
892   }
893 
894   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
895   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
896 
897   ierr = PetscLogFlops(50.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
898   PetscFunctionReturn(0);
899 }
900 #undef __FUNCT__
901 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_6"
902 PetscErrorCode MatMultAdd_SeqSBAIJ_6(Mat A,Vec xx,Vec yy,Vec zz)
903 {
904   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
905   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,x5,x6;
906   MatScalar      *v;
907   PetscErrorCode ierr;
908   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
909   PetscInt       nonzerorow=0;
910 
911   PetscFunctionBegin;
912   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
913   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
914   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
915 
916   v     = a->a;
917   xb = x;
918 
919   for (i=0; i<mbs; i++) {
920     n  = ai[1] - ai[0]; /* length of i_th block row of A */
921     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5];
922     ib = aj + *ai;
923     jmin = 0;
924     nonzerorow += (n>0);
925     if (*ib == i){     /* (diag of A)*x */
926       z[6*i]   += v[0]*x1  + v[6]*x2 + v[12]*x3 + v[18]*x4+ v[24]*x5 + v[30]*x6;
927       z[6*i+1] += v[6]*x1  + v[7]*x2 + v[13]*x3 + v[19]*x4+ v[25]*x5 + v[31]*x6;
928       z[6*i+2] += v[12]*x1 +v[13]*x2 + v[14]*x3 + v[20]*x4+ v[26]*x5 + v[32]*x6;
929       z[6*i+3] += v[18]*x1 +v[19]*x2 + v[20]*x3 + v[21]*x4+ v[27]*x5 + v[33]*x6;
930       z[6*i+4] += v[24]*x1 +v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[34]*x6;
931       z[6*i+5] += v[30]*x1 +v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
932       v += 36; jmin++;
933     }
934     for (j=jmin; j<n; j++) {
935       /* (strict lower triangular part of A)*x  */
936       cval       = ib[j]*6;
937       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6;
938       z[cval+1] += v[6]*x1  + v[7]*x2 + v[8]*x3 + v[9]*x4+ v[10]*x5 + v[11]*x6;
939       z[cval+2] += v[12]*x1  + v[13]*x2 + v[14]*x3 + v[15]*x4+ v[16]*x5 + v[17]*x6;
940       z[cval+3] += v[18]*x1  + v[19]*x2 + v[20]*x3 + v[21]*x4+ v[22]*x5 + v[23]*x6;
941       z[cval+4] += v[24]*x1  + v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[29]*x6;
942       z[cval+5] += v[30]*x1  + v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
943       /* (strict upper triangular part of A)*x  */
944       z[6*i]   +=v[0]*x[cval]+v[6]*x[cval+1]+v[12]*x[cval+2]+v[18]*x[cval+3]+v[24]*x[cval+4]+v[30]*x[cval+5];
945       z[6*i+1] +=v[1]*x[cval]+v[7]*x[cval+1]+v[13]*x[cval+2]+v[19]*x[cval+3]+v[25]*x[cval+4]+v[31]*x[cval+5];
946       z[6*i+2] +=v[2]*x[cval]+v[8]*x[cval+1]+v[14]*x[cval+2]+v[20]*x[cval+3]+v[26]*x[cval+4]+v[32]*x[cval+5];
947       z[6*i+3] +=v[3]*x[cval]+v[9]*x[cval+1]+v[15]*x[cval+2]+v[21]*x[cval+3]+v[27]*x[cval+4]+v[33]*x[cval+5];
948       z[6*i+4] +=v[4]*x[cval]+v[10]*x[cval+1]+v[16]*x[cval+2]+v[22]*x[cval+3]+v[28]*x[cval+4]+v[34]*x[cval+5];
949       z[6*i+5] +=v[5]*x[cval]+v[11]*x[cval+1]+v[17]*x[cval+2]+v[23]*x[cval+3]+v[29]*x[cval+4]+v[35]*x[cval+5];
950       v  += 36;
951     }
952     xb +=6; ai++;
953   }
954 
955   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
956   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
957 
958   ierr = PetscLogFlops(72.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
959   PetscFunctionReturn(0);
960 }
961 
962 #undef __FUNCT__
963 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_7"
964 PetscErrorCode MatMultAdd_SeqSBAIJ_7(Mat A,Vec xx,Vec yy,Vec zz)
965 {
966   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
967   PetscScalar    *x,*z,*xb,x1,x2,x3,x4,x5,x6,x7;
968   MatScalar      *v;
969   PetscErrorCode ierr;
970   PetscInt       mbs=a->mbs,i,*aj=a->j,*ai=a->i,n,*ib,cval,j,jmin;
971   PetscInt       nonzerorow=0;
972 
973   PetscFunctionBegin;
974   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
975   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
976   ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
977 
978   v     = a->a;
979   xb = x;
980 
981   for (i=0; i<mbs; i++) {
982     n  = ai[1] - ai[0]; /* length of i_th block row of A */
983     x1 = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5]; x7=xb[6];
984     ib = aj + *ai;
985     jmin = 0;
986     nonzerorow += (n>0);
987     if (*ib == i){     /* (diag of A)*x */
988       z[7*i]   += v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4+ v[28]*x5 + v[35]*x6+ v[42]*x7;
989       z[7*i+1] += v[7]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4+ v[29]*x5 + v[36]*x6+ v[43]*x7;
990       z[7*i+2] += v[14]*x1+ v[15]*x2 +v[16]*x3 + v[23]*x4+ v[30]*x5 + v[37]*x6+ v[44]*x7;
991       z[7*i+3] += v[21]*x1+ v[22]*x2 +v[23]*x3 + v[24]*x4+ v[31]*x5 + v[38]*x6+ v[45]*x7;
992       z[7*i+4] += v[28]*x1+ v[29]*x2 +v[30]*x3 + v[31]*x4+ v[32]*x5 + v[39]*x6+ v[46]*x7;
993       z[7*i+5] += v[35]*x1+ v[36]*x2 +v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[47]*x7;
994       z[7*i+6] += v[42]*x1+ v[43]*x2 +v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
995       v += 49; jmin++;
996     }
997     for (j=jmin; j<n; j++) {
998       /* (strict lower triangular part of A)*x  */
999       cval       = ib[j]*7;
1000       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6+ v[6]*x7;
1001       z[cval+1] += v[7]*x1  + v[8]*x2 + v[9]*x3 + v[10]*x4+ v[11]*x5 + v[12]*x6+ v[13]*x7;
1002       z[cval+2] += v[14]*x1  + v[15]*x2 + v[16]*x3 + v[17]*x4+ v[18]*x5 + v[19]*x6+ v[20]*x7;
1003       z[cval+3] += v[21]*x1  + v[22]*x2 + v[23]*x3 + v[24]*x4+ v[25]*x5 + v[26]*x6+ v[27]*x7;
1004       z[cval+4] += v[28]*x1  + v[29]*x2 + v[30]*x3 + v[31]*x4+ v[32]*x5 + v[33]*x6+ v[34]*x7;
1005       z[cval+5] += v[35]*x1  + v[36]*x2 + v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[41]*x7;
1006       z[cval+6] += v[42]*x1  + v[43]*x2 + v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
1007       /* (strict upper triangular part of A)*x  */
1008       z[7*i]  +=v[0]*x[cval]+v[7]*x[cval+1]+v[14]*x[cval+2]+v[21]*x[cval+3]+v[28]*x[cval+4]+v[35]*x[cval+5]+v[42]*x[cval+6];
1009       z[7*i+1]+=v[1]*x[cval]+v[8]*x[cval+1]+v[15]*x[cval+2]+v[22]*x[cval+3]+v[29]*x[cval+4]+v[36]*x[cval+5]+v[43]*x[cval+6];
1010       z[7*i+2]+=v[2]*x[cval]+v[9]*x[cval+1]+v[16]*x[cval+2]+v[23]*x[cval+3]+v[30]*x[cval+4]+v[37]*x[cval+5]+v[44]*x[cval+6];
1011       z[7*i+3]+=v[3]*x[cval]+v[10]*x[cval+1]+v[17]*x[cval+2]+v[24]*x[cval+3]+v[31]*x[cval+4]+v[38]*x[cval+5]+v[45]*x[cval+6];
1012       z[7*i+4]+=v[4]*x[cval]+v[11]*x[cval+1]+v[18]*x[cval+2]+v[25]*x[cval+3]+v[32]*x[cval+4]+v[39]*x[cval+5]+v[46]*x[cval+6];
1013       z[7*i+5]+=v[5]*x[cval]+v[12]*x[cval+1]+v[19]*x[cval+2]+v[26]*x[cval+3]+v[33]*x[cval+4]+v[40]*x[cval+5]+v[47]*x[cval+6];
1014       z[7*i+6]+=v[6]*x[cval]+v[13]*x[cval+1]+v[20]*x[cval+2]+v[27]*x[cval+3]+v[34]*x[cval+4]+v[41]*x[cval+5]+v[48]*x[cval+6];
1015       v  += 49;
1016     }
1017     xb +=7; ai++;
1018   }
1019 
1020   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1021   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
1022 
1023   ierr = PetscLogFlops(98.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 #undef __FUNCT__
1028 #define __FUNCT__ "MatMultAdd_SeqSBAIJ_N"
1029 PetscErrorCode MatMultAdd_SeqSBAIJ_N(Mat A,Vec xx,Vec yy,Vec zz)
1030 {
1031   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
1032   PetscScalar    *x,*x_ptr,*z,*z_ptr=0,*xb,*zb,*work,*workt;
1033   MatScalar      *v;
1034   PetscErrorCode ierr;
1035   PetscInt       mbs=a->mbs,i,*idx,*aj,*ii,bs=A->rmap->bs,j,n,bs2=a->bs2,ncols,k;
1036   PetscInt       nonzerorow=0;
1037 
1038   PetscFunctionBegin;
1039   ierr = VecCopy_Seq(yy,zz);CHKERRQ(ierr);
1040   ierr = VecGetArray(xx,&x);CHKERRQ(ierr); x_ptr=x;
1041   ierr = VecGetArray(zz,&z);CHKERRQ(ierr); z_ptr=z;
1042 
1043   aj   = a->j;
1044   v    = a->a;
1045   ii   = a->i;
1046 
1047   if (!a->mult_work) {
1048     ierr = PetscMalloc((A->rmap->n+1)*sizeof(PetscScalar),&a->mult_work);CHKERRQ(ierr);
1049   }
1050   work = a->mult_work;
1051 
1052 
1053   for (i=0; i<mbs; i++) {
1054     n     = ii[1] - ii[0]; ncols = n*bs;
1055     workt = work; idx=aj+ii[0];
1056     nonzerorow += (n>0);
1057 
1058     /* upper triangular part */
1059     for (j=0; j<n; j++) {
1060       xb = x_ptr + bs*(*idx++);
1061       for (k=0; k<bs; k++) workt[k] = xb[k];
1062       workt += bs;
1063     }
1064     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
1065     Kernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);
1066 
1067     /* strict lower triangular part */
1068     idx = aj+ii[0];
1069     if (*idx == i){
1070       ncols -= bs; v += bs2; idx++; n--;
1071     }
1072     if (ncols > 0){
1073       workt = work;
1074       ierr  = PetscMemzero(workt,ncols*sizeof(PetscScalar));CHKERRQ(ierr);
1075       Kernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,x,v,workt);
1076       for (j=0; j<n; j++) {
1077         zb = z_ptr + bs*(*idx++);
1078         for (k=0; k<bs; k++) zb[k] += workt[k] ;
1079         workt += bs;
1080       }
1081     }
1082 
1083     x += bs; v += n*bs2; z += bs; ii++;
1084   }
1085 
1086   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1087   ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
1088 
1089   ierr = PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow));CHKERRQ(ierr);
1090   PetscFunctionReturn(0);
1091 }
1092 
1093 #undef __FUNCT__
1094 #define __FUNCT__ "MatScale_SeqSBAIJ"
1095 PetscErrorCode MatScale_SeqSBAIJ(Mat inA,PetscScalar alpha)
1096 {
1097   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)inA->data;
1098   PetscScalar    oalpha = alpha;
1099   PetscErrorCode ierr;
1100   PetscBLASInt   one = 1,totalnz = PetscBLASIntCast(a->bs2*a->nz);
1101 
1102   PetscFunctionBegin;
1103   BLASscal_(&totalnz,&oalpha,a->a,&one);
1104   ierr = PetscLogFlops(totalnz);CHKERRQ(ierr);
1105   PetscFunctionReturn(0);
1106 }
1107 
1108 #undef __FUNCT__
1109 #define __FUNCT__ "MatNorm_SeqSBAIJ"
1110 PetscErrorCode MatNorm_SeqSBAIJ(Mat A,NormType type,PetscReal *norm)
1111 {
1112   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
1113   MatScalar      *v = a->a;
1114   PetscReal      sum_diag = 0.0, sum_off = 0.0, *sum;
1115   PetscInt       i,j,k,bs = A->rmap->bs,bs2=a->bs2,k1,mbs=a->mbs,*aj=a->j;
1116   PetscErrorCode ierr;
1117   PetscInt       *jl,*il,jmin,jmax,nexti,ik,*col;
1118 
1119   PetscFunctionBegin;
1120   if (type == NORM_FROBENIUS) {
1121     for (k=0; k<mbs; k++){
1122       jmin = a->i[k]; jmax = a->i[k+1];
1123       col  = aj + jmin;
1124       if (*col == k){         /* diagonal block */
1125         for (i=0; i<bs2; i++){
1126 #if defined(PETSC_USE_COMPLEX)
1127           sum_diag += PetscRealPart(PetscConj(*v)*(*v)); v++;
1128 #else
1129           sum_diag += (*v)*(*v); v++;
1130 #endif
1131         }
1132         jmin++;
1133       }
1134       for (j=jmin; j<jmax; j++){  /* off-diagonal blocks */
1135         for (i=0; i<bs2; i++){
1136 #if defined(PETSC_USE_COMPLEX)
1137           sum_off += PetscRealPart(PetscConj(*v)*(*v)); v++;
1138 #else
1139           sum_off += (*v)*(*v); v++;
1140 #endif
1141         }
1142       }
1143     }
1144     *norm = sqrt(sum_diag + 2*sum_off);
1145   }  else if (type == NORM_INFINITY || type == NORM_1) { /* maximum row/column sum */
1146     ierr = PetscMalloc3(bs,PetscReal,&sum,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
1147     for (i=0; i<mbs; i++) jl[i] = mbs;
1148     il[0] = 0;
1149 
1150     *norm = 0.0;
1151     for (k=0; k<mbs; k++) { /* k_th block row */
1152       for (j=0; j<bs; j++) sum[j]=0.0;
1153       /*-- col sum --*/
1154       i = jl[k]; /* first |A(i,k)| to be added */
1155       /* jl[k]=i: first nozero element in row i for submatrix A(1:k,k:n) (active window)
1156                   at step k */
1157       while (i<mbs){
1158         nexti = jl[i];  /* next block row to be added */
1159         ik    = il[i];  /* block index of A(i,k) in the array a */
1160         for (j=0; j<bs; j++){
1161           v = a->a + ik*bs2 + j*bs;
1162           for (k1=0; k1<bs; k1++) {
1163             sum[j] += PetscAbsScalar(*v); v++;
1164           }
1165         }
1166         /* update il, jl */
1167         jmin = ik + 1; /* block index of array a: points to the next nonzero of A in row i */
1168         jmax = a->i[i+1];
1169         if (jmin < jmax){
1170           il[i] = jmin;
1171           j   = a->j[jmin];
1172           jl[i] = jl[j]; jl[j]=i;
1173         }
1174         i = nexti;
1175       }
1176       /*-- row sum --*/
1177       jmin = a->i[k]; jmax = a->i[k+1];
1178       for (i=jmin; i<jmax; i++) {
1179         for (j=0; j<bs; j++){
1180           v = a->a + i*bs2 + j;
1181           for (k1=0; k1<bs; k1++){
1182             sum[j] += PetscAbsScalar(*v); v += bs;
1183           }
1184         }
1185       }
1186       /* add k_th block row to il, jl */
1187       col = aj+jmin;
1188       if (*col == k) jmin++;
1189       if (jmin < jmax){
1190         il[k] = jmin;
1191         j = a->j[jmin]; jl[k] = jl[j]; jl[j] = k;
1192       }
1193       for (j=0; j<bs; j++){
1194         if (sum[j] > *norm) *norm = sum[j];
1195       }
1196     }
1197     ierr = PetscFree3(sum,il,jl);CHKERRQ(ierr);
1198   } else {
1199     SETERRQ(PETSC_ERR_SUP,"No support for this norm yet");
1200   }
1201   PetscFunctionReturn(0);
1202 }
1203 
1204 #undef __FUNCT__
1205 #define __FUNCT__ "MatEqual_SeqSBAIJ"
1206 PetscErrorCode MatEqual_SeqSBAIJ(Mat A,Mat B,PetscTruth* flg)
1207 {
1208   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ *)A->data,*b = (Mat_SeqSBAIJ *)B->data;
1209   PetscErrorCode ierr;
1210 
1211   PetscFunctionBegin;
1212 
1213   /* If the  matrix/block dimensions are not equal, or no of nonzeros or shift */
1214   if ((A->rmap->N != B->rmap->N) || (A->cmap->n != B->cmap->n) || (A->rmap->bs != B->rmap->bs)|| (a->nz != b->nz)) {
1215     *flg = PETSC_FALSE;
1216     PetscFunctionReturn(0);
1217   }
1218 
1219   /* if the a->i are the same */
1220   ierr = PetscMemcmp(a->i,b->i,(a->mbs+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
1221   if (!*flg) {
1222     PetscFunctionReturn(0);
1223   }
1224 
1225   /* if a->j are the same */
1226   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
1227   if (!*flg) {
1228     PetscFunctionReturn(0);
1229   }
1230   /* if a->a are the same */
1231   ierr = PetscMemcmp(a->a,b->a,(a->nz)*(A->rmap->bs)*(A->rmap->bs)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
1232   PetscFunctionReturn(0);
1233 }
1234 
1235 #undef __FUNCT__
1236 #define __FUNCT__ "MatGetDiagonal_SeqSBAIJ"
1237 PetscErrorCode MatGetDiagonal_SeqSBAIJ(Mat A,Vec v)
1238 {
1239   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
1240   PetscErrorCode ierr;
1241   PetscInt       i,j,k,n,row,bs,*ai,*aj,ambs,bs2;
1242   PetscScalar    *x,zero = 0.0;
1243   MatScalar      *aa,*aa_j;
1244 
1245   PetscFunctionBegin;
1246   bs   = A->rmap->bs;
1247   if (A->factor && bs>1) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix with bs>1");
1248 
1249   aa   = a->a;
1250   ai   = a->i;
1251   aj   = a->j;
1252   ambs = a->mbs;
1253   bs2  = a->bs2;
1254 
1255   ierr = VecSet(v,zero);CHKERRQ(ierr);
1256   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1257   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1258   if (n != A->rmap->N) SETERRQ(PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1259   for (i=0; i<ambs; i++) {
1260     j=ai[i];
1261     if (aj[j] == i) {             /* if this is a diagonal element */
1262       row  = i*bs;
1263       aa_j = aa + j*bs2;
1264       if (A->factor && bs==1){
1265         for (k=0; k<bs2; k+=(bs+1),row++) x[row] = 1.0/aa_j[k];
1266       } else {
1267         for (k=0; k<bs2; k+=(bs+1),row++) x[row] = aa_j[k];
1268       }
1269     }
1270   }
1271 
1272   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1273   PetscFunctionReturn(0);
1274 }
1275 
1276 #undef __FUNCT__
1277 #define __FUNCT__ "MatDiagonalScale_SeqSBAIJ"
1278 PetscErrorCode MatDiagonalScale_SeqSBAIJ(Mat A,Vec ll,Vec rr)
1279 {
1280   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
1281   PetscScalar    *l,x,*li,*ri;
1282   MatScalar      *aa,*v;
1283   PetscErrorCode ierr;
1284   PetscInt       i,j,k,lm,M,m,*ai,*aj,mbs,tmp,bs,bs2;
1285   PetscTruth     flg;
1286 
1287   PetscFunctionBegin;
1288   if (ll != rr){
1289     ierr = VecEqual(ll,rr,&flg);CHKERRQ(ierr);
1290     if (!flg)
1291       SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"For symmetric format, left and right scaling vectors must be same\n");
1292   }
1293   if (!ll) PetscFunctionReturn(0);
1294   ai  = a->i;
1295   aj  = a->j;
1296   aa  = a->a;
1297   m   = A->rmap->N;
1298   bs  = A->rmap->bs;
1299   mbs = a->mbs;
1300   bs2 = a->bs2;
1301 
1302   ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
1303   ierr = VecGetLocalSize(ll,&lm);CHKERRQ(ierr);
1304   if (lm != m) SETERRQ(PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
1305   for (i=0; i<mbs; i++) { /* for each block row */
1306     M  = ai[i+1] - ai[i];
1307     li = l + i*bs;
1308     v  = aa + bs2*ai[i];
1309     for (j=0; j<M; j++) { /* for each block */
1310       ri = l + bs*aj[ai[i]+j];
1311       for (k=0; k<bs; k++) {
1312         x = ri[k];
1313         for (tmp=0; tmp<bs; tmp++) (*v++) *= li[tmp]*x;
1314       }
1315     }
1316   }
1317   ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
1318   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1319   PetscFunctionReturn(0);
1320 }
1321 
1322 #undef __FUNCT__
1323 #define __FUNCT__ "MatGetInfo_SeqSBAIJ"
1324 PetscErrorCode MatGetInfo_SeqSBAIJ(Mat A,MatInfoType flag,MatInfo *info)
1325 {
1326   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data;
1327 
1328   PetscFunctionBegin;
1329   info->block_size     = a->bs2;
1330   info->nz_allocated   = a->maxnz; /*num. of nonzeros in upper triangular part */
1331   info->nz_used        = a->bs2*a->nz; /*num. of nonzeros in upper triangular part */
1332   info->nz_unneeded    = (double)(info->nz_allocated - info->nz_used);
1333   info->assemblies   = A->num_ass;
1334   info->mallocs      = a->reallocs;
1335   info->memory       = ((PetscObject)A)->mem;
1336   if (A->factor) {
1337     info->fill_ratio_given  = A->info.fill_ratio_given;
1338     info->fill_ratio_needed = A->info.fill_ratio_needed;
1339     info->factor_mallocs    = A->info.factor_mallocs;
1340   } else {
1341     info->fill_ratio_given  = 0;
1342     info->fill_ratio_needed = 0;
1343     info->factor_mallocs    = 0;
1344   }
1345   PetscFunctionReturn(0);
1346 }
1347 
1348 
1349 #undef __FUNCT__
1350 #define __FUNCT__ "MatZeroEntries_SeqSBAIJ"
1351 PetscErrorCode MatZeroEntries_SeqSBAIJ(Mat A)
1352 {
1353   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data;
1354   PetscErrorCode ierr;
1355 
1356   PetscFunctionBegin;
1357   ierr = PetscMemzero(a->a,a->bs2*a->i[a->mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1358   PetscFunctionReturn(0);
1359 }
1360 
1361 #undef __FUNCT__
1362 #define __FUNCT__ "MatGetRowMaxAbs_SeqSBAIJ"
1363 /*
1364    This code does not work since it only checks the upper triangular part of
1365   the matrix. Hence it is not listed in the function table.
1366 */
1367 PetscErrorCode MatGetRowMaxAbs_SeqSBAIJ(Mat A,Vec v,PetscInt idx[])
1368 {
1369   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
1370   PetscErrorCode ierr;
1371   PetscInt       i,j,n,row,col,bs,*ai,*aj,mbs;
1372   PetscReal      atmp;
1373   MatScalar      *aa;
1374   PetscScalar    *x;
1375   PetscInt       ncols,brow,bcol,krow,kcol;
1376 
1377   PetscFunctionBegin;
1378   if (idx) SETERRQ(PETSC_ERR_SUP,"Send email to petsc-maint@mcs.anl.gov");
1379   if (A->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
1380   bs   = A->rmap->bs;
1381   aa   = a->a;
1382   ai   = a->i;
1383   aj   = a->j;
1384   mbs = a->mbs;
1385 
1386   ierr = VecSet(v,0.0);CHKERRQ(ierr);
1387   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1388   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1389   if (n != A->rmap->N) SETERRQ(PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1390   for (i=0; i<mbs; i++) {
1391     ncols = ai[1] - ai[0]; ai++;
1392     brow  = bs*i;
1393     for (j=0; j<ncols; j++){
1394       bcol = bs*(*aj);
1395       for (kcol=0; kcol<bs; kcol++){
1396         col = bcol + kcol;      /* col index */
1397         for (krow=0; krow<bs; krow++){
1398           atmp = PetscAbsScalar(*aa); aa++;
1399           row = brow + krow;    /* row index */
1400           if (PetscRealPart(x[row]) < atmp) x[row] = atmp;
1401           if (*aj > i && PetscRealPart(x[col]) < atmp) x[col] = atmp;
1402         }
1403       }
1404       aj++;
1405     }
1406   }
1407   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1408   PetscFunctionReturn(0);
1409 }
1410