Date: 2015-10-02T22:09:34+00:00

Actual source code: sbaij2.c
petsc-3.6.2 2015-10-02
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      2: #include <../src/mat/impls/baij/seq/baij.h>
      3: #include <petsc/private/kernels/blockinvert.h>
      4: #include <petscbt.h>
      5: #include <../src/mat/impls/sbaij/seq/sbaij.h>
      6: #include <petscblaslapack.h>

     10: PetscErrorCode MatIncreaseOverlap_SeqSBAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
     11: {
     12:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
     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_out,table_in;

     19:   if (ov < 0) SETERRQ(PETSC_COMM_SELF,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:   PetscBTCreate(mbs,&table_out);
     25:   PetscMalloc1(mbs+1,&nidx);
     26:   PetscMalloc1(A->rmap->N+1,&nidx2);
     27:   PetscBTCreate(mbs,&table_in);

     29:   for (i=0; i<is_max; i++) { /* for each is */
     30:     isz  = 0;
     31:     PetscBTMemzero(mbs,table_out);

     33:     /* Extract the indices, assume there can be duplicate entries */
     34:     ISGetIndices(is[i],&idx);
     35:     ISGetLocalSize(is[i],&n);

     37:     /* Enter these into the temp arrays i.e mark table_out[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_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"index greater than mat-dim");
     42:       if (!PetscBTLookupSet(table_out,brow)) {
     43:         nidx[isz++] = brow;
     44:         if (bcol_max < brow) bcol_max = brow;
     45:       }
     46:     }
     47:     ISRestoreIndices(is[i],&idx);
     48:     ISDestroy(&is[i]);

     50:     k = 0;
     51:     for (j=0; j<ov; j++) { /* for each overlap */
     52:       /* set table_in for lookup - only mark entries that are added onto nidx in (j-1)-th overlap */
     53:       PetscBTMemzero(mbs,table_in);
     54:       for (l=k; l<isz; l++) { PetscBTSet(table_in,nidx[l]); }

     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(table_in,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_out,bcol)) {
     63:               nidx[isz++] = bcol;
     64:               if (bcol_max < bcol) bcol_max = bcol;
     65:             }
     66:           }
     67:           k++;
     68:           if (k >= n) break; /* for (brow=0; brow<mbs; brow++) */
     69:         } else { /* brow is not on nidx - col serach: add brow onto nidx if there is a bcol in nidx */
     70:           for (l = start; l<end; l++) {
     71:             bcol = aj[l];
     72:             if (bcol > bcol_max) break;
     73:             if (PetscBTLookup(table_in,bcol)) {
     74:               if (!PetscBTLookupSet(table_out,brow)) nidx[isz++] = brow;
     75:               break; /* for l = start; l<end ; l++) */
     76:             }
     77:           }
     78:         }
     79:       }
     80:     } /* for each overlap */

     82:     /* expand the Index Set */
     83:     for (j=0; j<isz; j++) {
     84:       for (k=0; k<bs; k++) nidx2[j*bs+k] = nidx[j]*bs+k;
     85:     }
     86:     ISCreateGeneral(PETSC_COMM_SELF,isz*bs,nidx2,PETSC_COPY_VALUES,is+i);
     87:   }
     88:   PetscBTDestroy(&table_out);
     89:   PetscFree(nidx);
     90:   PetscFree(nidx2);
     91:   PetscBTDestroy(&table_in);
     92:   return(0);
     93: }

     97: PetscErrorCode MatGetSubMatrix_SeqSBAIJ_Private(Mat A,IS isrow,MatReuse scall,Mat *B)
     98: {
     99:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ*)A->data,*c;
    100:   PetscErrorCode  ierr;
    101:   PetscInt        *smap,i,k,kstart,kend,oldcols = a->mbs,*lens;
    102:   PetscInt        row,mat_i,*mat_j,tcol,*mat_ilen;
    103:   PetscInt        nrows,*ssmap,bs=A->rmap->bs,bs2=a->bs2;
    104:   const PetscInt  *irow,*aj = a->j,*ai = a->i;
    105:   MatScalar       *mat_a;
    106:   Mat             C;
    107:   PetscBool       flag,sorted;

    110:   ISSorted(isrow,&sorted);
    111:   if (!sorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"IS is not sorted");

    113:   ISGetIndices(isrow,&irow);
    114:   ISGetSize(isrow,&nrows);

    116:   PetscMalloc1(oldcols,&smap);
    117:   PetscMemzero(smap,oldcols*sizeof(PetscInt));
    118:   ssmap = smap;
    119:   PetscMalloc1(1+nrows,&lens);
    120:   for (i=0; i<nrows; i++) smap[irow[i]] = i+1; /* nrows = ncols */
    121:   /* determine lens of each row */
    122:   for (i=0; i<nrows; i++) {
    123:     kstart  = ai[irow[i]];
    124:     kend    = kstart + a->ilen[irow[i]];
    125:     lens[i] = 0;
    126:     for (k=kstart; k<kend; k++) {
    127:       if (ssmap[aj[k]]) lens[i]++;
    128:     }
    129:   }
    130:   /* Create and fill new matrix */
    131:   if (scall == MAT_REUSE_MATRIX) {
    132:     c = (Mat_SeqSBAIJ*)((*B)->data);

    134:     if (c->mbs!=nrows || (*B)->rmap->bs!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Submatrix wrong size");
    135:     PetscMemcmp(c->ilen,lens,c->mbs *sizeof(PetscInt),&flag);
    136:     if (!flag) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
    137:     PetscMemzero(c->ilen,c->mbs*sizeof(PetscInt));
    138:     C    = *B;
    139:   } else {
    140:     MatCreate(PetscObjectComm((PetscObject)A),&C);
    141:     MatSetSizes(C,nrows*bs,nrows*bs,PETSC_DETERMINE,PETSC_DETERMINE);
    142:     MatSetType(C,((PetscObject)A)->type_name);
    143:     MatSeqSBAIJSetPreallocation_SeqSBAIJ(C,bs,0,lens);
    144:   }
    145:   c = (Mat_SeqSBAIJ*)(C->data);
    146:   for (i=0; i<nrows; i++) {
    147:     row      = irow[i];
    148:     kstart   = ai[row];
    149:     kend     = kstart + a->ilen[row];
    150:     mat_i    = c->i[i];
    151:     mat_j    = c->j + mat_i;
    152:     mat_a    = c->a + mat_i*bs2;
    153:     mat_ilen = c->ilen + i;
    154:     for (k=kstart; k<kend; k++) {
    155:       if ((tcol=ssmap[a->j[k]])) {
    156:         *mat_j++ = tcol - 1;
    157:         PetscMemcpy(mat_a,a->a+k*bs2,bs2*sizeof(MatScalar));
    158:         mat_a   += bs2;
    159:         (*mat_ilen)++;
    160:       }
    161:     }
    162:   }

    164:   /* Free work space */
    165:   PetscFree(smap);
    166:   PetscFree(lens);
    167:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    168:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    170:   ISRestoreIndices(isrow,&irow);
    171:   *B   = C;
    172:   return(0);
    173: }

    177: PetscErrorCode MatGetSubMatrix_SeqSBAIJ(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
    178: {
    179:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
    180:   IS             is1;
    182:   PetscInt       *vary,*iary,nrows,i,bs=A->rmap->bs,count;
    183:   const PetscInt *irow;

    186:   if (isrow != iscol) {
    187:     PetscBool isequal;
    188:     ISEqual(isrow,iscol,&isequal);
    189:     if (!isequal)
    190:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"For symmetric format, iscol must equal isrow");
    191:   }

    193:   ISGetIndices(isrow,&irow);
    194:   ISGetSize(isrow,&nrows);

    196:   /* Verify if the indices corespond to each element in a block
    197:    and form the IS with compressed IS */
    198:   PetscMalloc2(a->mbs,&vary,a->mbs,&iary);
    199:   PetscMemzero(vary,a->mbs*sizeof(PetscInt));
    200:   for (i=0; i<nrows; i++) vary[irow[i]/bs]++;

    202:   count = 0;
    203:   for (i=0; i<a->mbs; i++) {
    204:     if (vary[i]!=0 && vary[i]!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Index set does not match blocks");
    205:     if (vary[i]==bs) iary[count++] = i;
    206:   }
    207:   ISRestoreIndices(isrow,&irow);
    208:   ISCreateGeneral(PETSC_COMM_SELF,count,iary,PETSC_COPY_VALUES,&is1);
    209:   PetscFree2(vary,iary);

    211:   MatGetSubMatrix_SeqSBAIJ_Private(A,is1,scall,B);
    212:   ISDestroy(&is1);
    213:   return(0);
    214: }

    218: PetscErrorCode MatGetSubMatrices_SeqSBAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
    219: {
    221:   PetscInt       i;

    224:   if (scall == MAT_INITIAL_MATRIX) {
    225:     PetscMalloc1(n+1,B);
    226:   }

    228:   for (i=0; i<n; i++) {
    229:     MatGetSubMatrix_SeqSBAIJ(A,irow[i],icol[i],scall,&(*B)[i]);
    230:   }
    231:   return(0);
    232: }

    234: /* -------------------------------------------------------*/
    235: /* Should check that shapes of vectors and matrices match */
    236: /* -------------------------------------------------------*/

    240: PetscErrorCode MatMult_SeqSBAIJ_2(Mat A,Vec xx,Vec zz)
    241: {
    242:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    243:   PetscScalar       *z,x1,x2,zero=0.0;
    244:   const PetscScalar *x,*xb;
    245:   const MatScalar   *v;
    246:   PetscErrorCode    ierr;
    247:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    248:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    249:   PetscInt          nonzerorow=0;

    252:   VecSet(zz,zero);
    253:   VecGetArrayRead(xx,&x);
    254:   VecGetArray(zz,&z);

    256:   v  = a->a;
    257:   xb = x;

    259:   for (i=0; i<mbs; i++) {
    260:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    261:     x1          = xb[0]; x2 = xb[1];
    262:     ib          = aj + *ai;
    263:     jmin        = 0;
    264:     nonzerorow += (n>0);
    265:     if (*ib == i) {     /* (diag of A)*x */
    266:       z[2*i]   += v[0]*x1 + v[2]*x2;
    267:       z[2*i+1] += v[2]*x1 + v[3]*x2;
    268:       v        += 4; jmin++;
    269:     }
    270:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    271:     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
    272:     for (j=jmin; j<n; j++) {
    273:       /* (strict lower triangular part of A)*x  */
    274:       cval       = ib[j]*2;
    275:       z[cval]   += v[0]*x1 + v[1]*x2;
    276:       z[cval+1] += v[2]*x1 + v[3]*x2;
    277:       /* (strict upper triangular part of A)*x  */
    278:       z[2*i]   += v[0]*x[cval] + v[2]*x[cval+1];
    279:       z[2*i+1] += v[1]*x[cval] + v[3]*x[cval+1];
    280:       v        += 4;
    281:     }
    282:     xb +=2; ai++;
    283:   }

    285:   VecRestoreArrayRead(xx,&x);
    286:   VecRestoreArray(zz,&z);
    287:   PetscLogFlops(8.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
    288:   return(0);
    289: }

    293: PetscErrorCode MatMult_SeqSBAIJ_3(Mat A,Vec xx,Vec zz)
    294: {
    295:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    296:   PetscScalar       *z,x1,x2,x3,zero=0.0;
    297:   const PetscScalar *x,*xb;
    298:   const MatScalar   *v;
    299:   PetscErrorCode    ierr;
    300:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    301:   const PetscInt    *aj = a->j,*ai = a->i,*ib;
    302:   PetscInt          nonzerorow=0;

    305:   VecSet(zz,zero);
    306:   VecGetArrayRead(xx,&x);
    307:   VecGetArray(zz,&z);

    309:   v  = a->a;
    310:   xb = x;

    312:   for (i=0; i<mbs; i++) {
    313:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    314:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2];
    315:     ib          = aj + *ai;
    316:     jmin        = 0;
    317:     nonzerorow += (n>0);
    318:     if (*ib == i) {     /* (diag of A)*x */
    319:       z[3*i]   += v[0]*x1 + v[3]*x2 + v[6]*x3;
    320:       z[3*i+1] += v[3]*x1 + v[4]*x2 + v[7]*x3;
    321:       z[3*i+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
    322:       v        += 9; jmin++;
    323:     }
    324:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    325:     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
    326:     for (j=jmin; j<n; j++) {
    327:       /* (strict lower triangular part of A)*x  */
    328:       cval       = ib[j]*3;
    329:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3;
    330:       z[cval+1] += v[3]*x1 + v[4]*x2 + v[5]*x3;
    331:       z[cval+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
    332:       /* (strict upper triangular part of A)*x  */
    333:       z[3*i]   += v[0]*x[cval] + v[3]*x[cval+1]+ v[6]*x[cval+2];
    334:       z[3*i+1] += v[1]*x[cval] + v[4]*x[cval+1]+ v[7]*x[cval+2];
    335:       z[3*i+2] += v[2]*x[cval] + v[5]*x[cval+1]+ v[8]*x[cval+2];
    336:       v        += 9;
    337:     }
    338:     xb +=3; ai++;
    339:   }

    341:   VecRestoreArrayRead(xx,&x);
    342:   VecRestoreArray(zz,&z);
    343:   PetscLogFlops(18.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
    344:   return(0);
    345: }

    349: PetscErrorCode MatMult_SeqSBAIJ_4(Mat A,Vec xx,Vec zz)
    350: {
    351:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    352:   PetscScalar       *z,x1,x2,x3,x4,zero=0.0;
    353:   const PetscScalar *x,*xb;
    354:   const MatScalar   *v;
    355:   PetscErrorCode    ierr;
    356:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    357:   const PetscInt    *aj = a->j,*ai = a->i,*ib;
    358:   PetscInt          nonzerorow = 0;

    361:   VecSet(zz,zero);
    362:   VecGetArrayRead(xx,&x);
    363:   VecGetArray(zz,&z);

    365:   v  = a->a;
    366:   xb = x;

    368:   for (i=0; i<mbs; i++) {
    369:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    370:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
    371:     ib          = aj + *ai;
    372:     jmin        = 0;
    373:     nonzerorow += (n>0);
    374:     if (*ib == i) {     /* (diag of A)*x */
    375:       z[4*i]   += v[0]*x1 + v[4]*x2 +  v[8]*x3 + v[12]*x4;
    376:       z[4*i+1] += v[4]*x1 + v[5]*x2 +  v[9]*x3 + v[13]*x4;
    377:       z[4*i+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[14]*x4;
    378:       z[4*i+3] += v[12]*x1+ v[13]*x2+ v[14]*x3 + v[15]*x4;
    379:       v        += 16; jmin++;
    380:     }
    381:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    382:     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    383:     for (j=jmin; j<n; j++) {
    384:       /* (strict lower triangular part of A)*x  */
    385:       cval       = ib[j]*4;
    386:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4;
    387:       z[cval+1] += v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4;
    388:       z[cval+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4;
    389:       z[cval+3] += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
    390:       /* (strict upper triangular part of A)*x  */
    391:       z[4*i]   += v[0]*x[cval] + v[4]*x[cval+1]+ v[8]*x[cval+2] + v[12]*x[cval+3];
    392:       z[4*i+1] += v[1]*x[cval] + v[5]*x[cval+1]+ v[9]*x[cval+2] + v[13]*x[cval+3];
    393:       z[4*i+2] += v[2]*x[cval] + v[6]*x[cval+1]+ v[10]*x[cval+2]+ v[14]*x[cval+3];
    394:       z[4*i+3] += v[3]*x[cval] + v[7]*x[cval+1]+ v[11]*x[cval+2]+ v[15]*x[cval+3];
    395:       v        += 16;
    396:     }
    397:     xb +=4; ai++;
    398:   }

    400:   VecRestoreArrayRead(xx,&x);
    401:   VecRestoreArray(zz,&z);
    402:   PetscLogFlops(32.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
    403:   return(0);
    404: }

    408: PetscErrorCode MatMult_SeqSBAIJ_5(Mat A,Vec xx,Vec zz)
    409: {
    410:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    411:   PetscScalar       *z,x1,x2,x3,x4,x5,zero=0.0;
    412:   const PetscScalar *x,*xb;
    413:   const MatScalar   *v;
    414:   PetscErrorCode    ierr;
    415:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    416:   const PetscInt    *aj = a->j,*ai = a->i,*ib;
    417:   PetscInt          nonzerorow=0;

    420:   VecSet(zz,zero);
    421:   VecGetArrayRead(xx,&x);
    422:   VecGetArray(zz,&z);

    424:   v  = a->a;
    425:   xb = x;

    427:   for (i=0; i<mbs; i++) {
    428:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    429:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4];
    430:     ib          = aj + *ai;
    431:     jmin        = 0;
    432:     nonzerorow += (n>0);
    433:     if (*ib == i) {      /* (diag of A)*x */
    434:       z[5*i]   += v[0]*x1  + v[5]*x2 + v[10]*x3 + v[15]*x4+ v[20]*x5;
    435:       z[5*i+1] += v[5]*x1  + v[6]*x2 + v[11]*x3 + v[16]*x4+ v[21]*x5;
    436:       z[5*i+2] += v[10]*x1 +v[11]*x2 + v[12]*x3 + v[17]*x4+ v[22]*x5;
    437:       z[5*i+3] += v[15]*x1 +v[16]*x2 + v[17]*x3 + v[18]*x4+ v[23]*x5;
    438:       z[5*i+4] += v[20]*x1 +v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
    439:       v        += 25; jmin++;
    440:     }
    441:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    442:     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    443:     for (j=jmin; j<n; j++) {
    444:       /* (strict lower triangular part of A)*x  */
    445:       cval       = ib[j]*5;
    446:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5;
    447:       z[cval+1] += v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5;
    448:       z[cval+2] += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4+ v[14]*x5;
    449:       z[cval+3] += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4+ v[19]*x5;
    450:       z[cval+4] += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
    451:       /* (strict upper triangular part of A)*x  */
    452:       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];
    453:       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];
    454:       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];
    455:       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];
    456:       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];
    457:       v        += 25;
    458:     }
    459:     xb +=5; ai++;
    460:   }

    462:   VecRestoreArrayRead(xx,&x);
    463:   VecRestoreArray(zz,&z);
    464:   PetscLogFlops(50.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
    465:   return(0);
    466: }

    471: PetscErrorCode MatMult_SeqSBAIJ_6(Mat A,Vec xx,Vec zz)
    472: {
    473:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    474:   PetscScalar       *z,x1,x2,x3,x4,x5,x6,zero=0.0;
    475:   const PetscScalar *x,*xb;
    476:   const MatScalar   *v;
    477:   PetscErrorCode    ierr;
    478:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    479:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    480:   PetscInt          nonzerorow=0;

    483:   VecSet(zz,zero);
    484:   VecGetArrayRead(xx,&x);
    485:   VecGetArray(zz,&z);

    487:   v  = a->a;
    488:   xb = x;

    490:   for (i=0; i<mbs; i++) {
    491:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    492:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5];
    493:     ib          = aj + *ai;
    494:     jmin        = 0;
    495:     nonzerorow += (n>0);
    496:     if (*ib == i) {      /* (diag of A)*x */
    497:       z[6*i]   += v[0]*x1  + v[6]*x2 + v[12]*x3 + v[18]*x4+ v[24]*x5 + v[30]*x6;
    498:       z[6*i+1] += v[6]*x1  + v[7]*x2 + v[13]*x3 + v[19]*x4+ v[25]*x5 + v[31]*x6;
    499:       z[6*i+2] += v[12]*x1 +v[13]*x2 + v[14]*x3 + v[20]*x4+ v[26]*x5 + v[32]*x6;
    500:       z[6*i+3] += v[18]*x1 +v[19]*x2 + v[20]*x3 + v[21]*x4+ v[27]*x5 + v[33]*x6;
    501:       z[6*i+4] += v[24]*x1 +v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[34]*x6;
    502:       z[6*i+5] += v[30]*x1 +v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
    503:       v        += 36; jmin++;
    504:     }
    505:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    506:     PetscPrefetchBlock(v+36*n,36*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    507:     for (j=jmin; j<n; j++) {
    508:       /* (strict lower triangular part of A)*x  */
    509:       cval       = ib[j]*6;
    510:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6;
    511:       z[cval+1] += v[6]*x1  + v[7]*x2 + v[8]*x3 + v[9]*x4+ v[10]*x5 + v[11]*x6;
    512:       z[cval+2] += v[12]*x1  + v[13]*x2 + v[14]*x3 + v[15]*x4+ v[16]*x5 + v[17]*x6;
    513:       z[cval+3] += v[18]*x1  + v[19]*x2 + v[20]*x3 + v[21]*x4+ v[22]*x5 + v[23]*x6;
    514:       z[cval+4] += v[24]*x1  + v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[29]*x6;
    515:       z[cval+5] += v[30]*x1  + v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
    516:       /* (strict upper triangular part of A)*x  */
    517:       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];
    518:       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];
    519:       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];
    520:       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];
    521:       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];
    522:       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];
    523:       v        += 36;
    524:     }
    525:     xb +=6; ai++;
    526:   }

    528:   VecRestoreArrayRead(xx,&x);
    529:   VecRestoreArray(zz,&z);
    530:   PetscLogFlops(72.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
    531:   return(0);
    532: }
    535: PetscErrorCode MatMult_SeqSBAIJ_7(Mat A,Vec xx,Vec zz)
    536: {
    537:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    538:   PetscScalar       *z,x1,x2,x3,x4,x5,x6,x7,zero=0.0;
    539:   const PetscScalar *x,*xb;
    540:   const MatScalar   *v;
    541:   PetscErrorCode    ierr;
    542:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    543:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    544:   PetscInt          nonzerorow=0;

    547:   VecSet(zz,zero);
    548:   VecGetArrayRead(xx,&x);
    549:   VecGetArray(zz,&z);

    551:   v  = a->a;
    552:   xb = x;

    554:   for (i=0; i<mbs; i++) {
    555:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    556:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5]; x7=xb[6];
    557:     ib          = aj + *ai;
    558:     jmin        = 0;
    559:     nonzerorow += (n>0);
    560:     if (*ib == i) {      /* (diag of A)*x */
    561:       z[7*i]   += v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4+ v[28]*x5 + v[35]*x6+ v[42]*x7;
    562:       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;
    563:       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;
    564:       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;
    565:       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;
    566:       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;
    567:       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;
    568:       v        += 49; jmin++;
    569:     }
    570:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    571:     PetscPrefetchBlock(v+49*n,49*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    572:     for (j=jmin; j<n; j++) {
    573:       /* (strict lower triangular part of A)*x  */
    574:       cval       = ib[j]*7;
    575:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6+ v[6]*x7;
    576:       z[cval+1] += v[7]*x1  + v[8]*x2 + v[9]*x3 + v[10]*x4+ v[11]*x5 + v[12]*x6+ v[13]*x7;
    577:       z[cval+2] += v[14]*x1  + v[15]*x2 + v[16]*x3 + v[17]*x4+ v[18]*x5 + v[19]*x6+ v[20]*x7;
    578:       z[cval+3] += v[21]*x1  + v[22]*x2 + v[23]*x3 + v[24]*x4+ v[25]*x5 + v[26]*x6+ v[27]*x7;
    579:       z[cval+4] += v[28]*x1  + v[29]*x2 + v[30]*x3 + v[31]*x4+ v[32]*x5 + v[33]*x6+ v[34]*x7;
    580:       z[cval+5] += v[35]*x1  + v[36]*x2 + v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[41]*x7;
    581:       z[cval+6] += v[42]*x1  + v[43]*x2 + v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
    582:       /* (strict upper triangular part of A)*x  */
    583:       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];
    584:       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];
    585:       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];
    586:       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];
    587:       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];
    588:       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];
    589:       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];
    590:       v       += 49;
    591:     }
    592:     xb +=7; ai++;
    593:   }
    594:   VecRestoreArrayRead(xx,&x);
    595:   VecRestoreArray(zz,&z);
    596:   PetscLogFlops(98.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
    597:   return(0);
    598: }

    600: /*
    601:     This will not work with MatScalar == float because it calls the BLAS
    602: */
    605: PetscErrorCode MatMult_SeqSBAIJ_N(Mat A,Vec xx,Vec zz)
    606: {
    607:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    608:   PetscScalar       *z,*z_ptr,*zb,*work,*workt,zero=0.0;
    609:   const PetscScalar *x,*x_ptr,*xb;
    610:   const MatScalar   *v;
    611:   PetscErrorCode    ierr;
    612:   PetscInt          mbs =a->mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2,ncols,k;
    613:   const PetscInt    *idx,*aj,*ii;
    614:   PetscInt          nonzerorow=0;

    617:   VecSet(zz,zero);
    618:   VecGetArrayRead(xx,&x);x_ptr = x;
    619:   VecGetArray(zz,&z); z_ptr=z;

    621:   aj = a->j;
    622:   v  = a->a;
    623:   ii = a->i;

    625:   if (!a->mult_work) {
    626:     PetscMalloc1(A->rmap->N+1,&a->mult_work);
    627:   }
    628:   work = a->mult_work;

    630:   for (i=0; i<mbs; i++) {
    631:     n           = ii[1] - ii[0]; ncols = n*bs;
    632:     workt       = work; idx=aj+ii[0];
    633:     nonzerorow += (n>0);

    635:     /* upper triangular part */
    636:     for (j=0; j<n; j++) {
    637:       xb = x_ptr + bs*(*idx++);
    638:       for (k=0; k<bs; k++) workt[k] = xb[k];
    639:       workt += bs;
    640:     }
    641:     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
    642:     PetscKernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);

    644:     /* strict lower triangular part */
    645:     idx = aj+ii[0];
    646:     if (*idx == i) {
    647:       ncols -= bs; v += bs2; idx++; n--;
    648:     }

    650:     if (ncols > 0) {
    651:       workt = work;
    652:       PetscMemzero(workt,ncols*sizeof(PetscScalar));
    653:       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,x,v,workt);
    654:       for (j=0; j<n; j++) {
    655:         zb = z_ptr + bs*(*idx++);
    656:         for (k=0; k<bs; k++) zb[k] += workt[k];
    657:         workt += bs;
    658:       }
    659:     }
    660:     x += bs; v += n*bs2; z += bs; ii++;
    661:   }

    663:   VecRestoreArrayRead(xx,&x);
    664:   VecRestoreArray(zz,&z);
    665:   PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow)*bs2 - nonzerorow);
    666:   return(0);
    667: }

    671: PetscErrorCode MatMultAdd_SeqSBAIJ_1(Mat A,Vec xx,Vec yy,Vec zz)
    672: {
    673:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    674:   PetscScalar       *z,x1;
    675:   const PetscScalar *x,*xb;
    676:   const MatScalar   *v;
    677:   PetscErrorCode    ierr;
    678:   PetscInt          mbs =a->mbs,i,n,cval,j,jmin;
    679:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    680:   PetscInt          nonzerorow=0;

    683:   VecCopy(yy,zz);
    684:   VecGetArrayRead(xx,&x);
    685:   VecGetArray(zz,&z);
    686:   v    = a->a;
    687:   xb   = x;

    689:   for (i=0; i<mbs; i++) {
    690:     n           = ai[1] - ai[0]; /* length of i_th row of A */
    691:     x1          = xb[0];
    692:     ib          = aj + *ai;
    693:     jmin        = 0;
    694:     nonzerorow += (n>0);
    695:     if (*ib == i) {            /* (diag of A)*x */
    696:       z[i] += *v++ * x[*ib++]; jmin++;
    697:     }
    698:     for (j=jmin; j<n; j++) {
    699:       cval    = *ib;
    700:       z[cval] += *v * x1;      /* (strict lower triangular part of A)*x  */
    701:       z[i] += *v++ * x[*ib++]; /* (strict upper triangular part of A)*x  */
    702:     }
    703:     xb++; ai++;
    704:   }

    706:   VecRestoreArrayRead(xx,&x);
    707:   VecRestoreArray(zz,&z);

    709:   PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow));
    710:   return(0);
    711: }

    715: PetscErrorCode MatMultAdd_SeqSBAIJ_2(Mat A,Vec xx,Vec yy,Vec zz)
    716: {
    717:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    718:   PetscScalar       *z,x1,x2;
    719:   const PetscScalar *x,*xb;
    720:   const MatScalar   *v;
    721:   PetscErrorCode    ierr;
    722:   PetscInt          mbs =a->mbs,i,n,cval,j,jmin;
    723:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    724:   PetscInt          nonzerorow=0;

    727:   VecCopy(yy,zz);
    728:   VecGetArrayRead(xx,&x);
    729:   VecGetArray(zz,&z);

    731:   v  = a->a;
    732:   xb = x;

    734:   for (i=0; i<mbs; i++) {
    735:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    736:     x1          = xb[0]; x2 = xb[1];
    737:     ib          = aj + *ai;
    738:     jmin        = 0;
    739:     nonzerorow += (n>0);
    740:     if (*ib == i) {      /* (diag of A)*x */
    741:       z[2*i]   += v[0]*x1 + v[2]*x2;
    742:       z[2*i+1] += v[2]*x1 + v[3]*x2;
    743:       v        += 4; jmin++;
    744:     }
    745:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    746:     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
    747:     for (j=jmin; j<n; j++) {
    748:       /* (strict lower triangular part of A)*x  */
    749:       cval       = ib[j]*2;
    750:       z[cval]   += v[0]*x1 + v[1]*x2;
    751:       z[cval+1] += v[2]*x1 + v[3]*x2;
    752:       /* (strict upper triangular part of A)*x  */
    753:       z[2*i]   += v[0]*x[cval] + v[2]*x[cval+1];
    754:       z[2*i+1] += v[1]*x[cval] + v[3]*x[cval+1];
    755:       v        += 4;
    756:     }
    757:     xb +=2; ai++;
    758:   }
    759:   VecRestoreArrayRead(xx,&x);
    760:   VecRestoreArray(zz,&z);

    762:   PetscLogFlops(4.0*(a->nz*2.0 - nonzerorow));
    763:   return(0);
    764: }

    768: PetscErrorCode MatMultAdd_SeqSBAIJ_3(Mat A,Vec xx,Vec yy,Vec zz)
    769: {
    770:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    771:   PetscScalar       *z,x1,x2,x3;
    772:   const PetscScalar *x,*xb;
    773:   const MatScalar   *v;
    774:   PetscErrorCode    ierr;
    775:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    776:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    777:   PetscInt          nonzerorow=0;

    780:   VecCopy(yy,zz);
    781:   VecGetArrayRead(xx,&x);
    782:   VecGetArray(zz,&z);

    784:   v  = a->a;
    785:   xb = x;

    787:   for (i=0; i<mbs; i++) {
    788:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    789:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2];
    790:     ib          = aj + *ai;
    791:     jmin        = 0;
    792:     nonzerorow += (n>0);
    793:     if (*ib == i) {     /* (diag of A)*x */
    794:       z[3*i]   += v[0]*x1 + v[3]*x2 + v[6]*x3;
    795:       z[3*i+1] += v[3]*x1 + v[4]*x2 + v[7]*x3;
    796:       z[3*i+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
    797:       v        += 9; jmin++;
    798:     }
    799:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    800:     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
    801:     for (j=jmin; j<n; j++) {
    802:       /* (strict lower triangular part of A)*x  */
    803:       cval       = ib[j]*3;
    804:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3;
    805:       z[cval+1] += v[3]*x1 + v[4]*x2 + v[5]*x3;
    806:       z[cval+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
    807:       /* (strict upper triangular part of A)*x  */
    808:       z[3*i]   += v[0]*x[cval] + v[3]*x[cval+1]+ v[6]*x[cval+2];
    809:       z[3*i+1] += v[1]*x[cval] + v[4]*x[cval+1]+ v[7]*x[cval+2];
    810:       z[3*i+2] += v[2]*x[cval] + v[5]*x[cval+1]+ v[8]*x[cval+2];
    811:       v        += 9;
    812:     }
    813:     xb +=3; ai++;
    814:   }

    816:   VecRestoreArrayRead(xx,&x);
    817:   VecRestoreArray(zz,&z);

    819:   PetscLogFlops(18.0*(a->nz*2.0 - nonzerorow));
    820:   return(0);
    821: }

    825: PetscErrorCode MatMultAdd_SeqSBAIJ_4(Mat A,Vec xx,Vec yy,Vec zz)
    826: {
    827:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    828:   PetscScalar       *z,x1,x2,x3,x4;
    829:   const PetscScalar *x,*xb;
    830:   const MatScalar   *v;
    831:   PetscErrorCode    ierr;
    832:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    833:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    834:   PetscInt          nonzerorow=0;

    837:   VecCopy(yy,zz);
    838:   VecGetArrayRead(xx,&x);
    839:   VecGetArray(zz,&z);

    841:   v  = a->a;
    842:   xb = x;

    844:   for (i=0; i<mbs; i++) {
    845:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    846:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
    847:     ib          = aj + *ai;
    848:     jmin        = 0;
    849:     nonzerorow += (n>0);
    850:     if (*ib == i) {      /* (diag of A)*x */
    851:       z[4*i]   += v[0]*x1 + v[4]*x2 +  v[8]*x3 + v[12]*x4;
    852:       z[4*i+1] += v[4]*x1 + v[5]*x2 +  v[9]*x3 + v[13]*x4;
    853:       z[4*i+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[14]*x4;
    854:       z[4*i+3] += v[12]*x1+ v[13]*x2+ v[14]*x3 + v[15]*x4;
    855:       v        += 16; jmin++;
    856:     }
    857:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    858:     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    859:     for (j=jmin; j<n; j++) {
    860:       /* (strict lower triangular part of A)*x  */
    861:       cval       = ib[j]*4;
    862:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4;
    863:       z[cval+1] += v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4;
    864:       z[cval+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4;
    865:       z[cval+3] += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
    866:       /* (strict upper triangular part of A)*x  */
    867:       z[4*i]   += v[0]*x[cval] + v[4]*x[cval+1]+ v[8]*x[cval+2] + v[12]*x[cval+3];
    868:       z[4*i+1] += v[1]*x[cval] + v[5]*x[cval+1]+ v[9]*x[cval+2] + v[13]*x[cval+3];
    869:       z[4*i+2] += v[2]*x[cval] + v[6]*x[cval+1]+ v[10]*x[cval+2]+ v[14]*x[cval+3];
    870:       z[4*i+3] += v[3]*x[cval] + v[7]*x[cval+1]+ v[11]*x[cval+2]+ v[15]*x[cval+3];
    871:       v        += 16;
    872:     }
    873:     xb +=4; ai++;
    874:   }

    876:   VecRestoreArrayRead(xx,&x);
    877:   VecRestoreArray(zz,&z);

    879:   PetscLogFlops(32.0*(a->nz*2.0 - nonzerorow));
    880:   return(0);
    881: }

    885: PetscErrorCode MatMultAdd_SeqSBAIJ_5(Mat A,Vec xx,Vec yy,Vec zz)
    886: {
    887:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    888:   PetscScalar       *z,x1,x2,x3,x4,x5;
    889:   const PetscScalar *x,*xb;
    890:   const MatScalar   *v;
    891:   PetscErrorCode    ierr;
    892:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    893:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    894:   PetscInt          nonzerorow=0;

    897:   VecCopy(yy,zz);
    898:   VecGetArrayRead(xx,&x);
    899:   VecGetArray(zz,&z);

    901:   v  = a->a;
    902:   xb = x;

    904:   for (i=0; i<mbs; i++) {
    905:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    906:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4];
    907:     ib          = aj + *ai;
    908:     jmin        = 0;
    909:     nonzerorow += (n>0);
    910:     if (*ib == i) {      /* (diag of A)*x */
    911:       z[5*i]   += v[0]*x1  + v[5]*x2 + v[10]*x3 + v[15]*x4+ v[20]*x5;
    912:       z[5*i+1] += v[5]*x1  + v[6]*x2 + v[11]*x3 + v[16]*x4+ v[21]*x5;
    913:       z[5*i+2] += v[10]*x1 +v[11]*x2 + v[12]*x3 + v[17]*x4+ v[22]*x5;
    914:       z[5*i+3] += v[15]*x1 +v[16]*x2 + v[17]*x3 + v[18]*x4+ v[23]*x5;
    915:       z[5*i+4] += v[20]*x1 +v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
    916:       v        += 25; jmin++;
    917:     }
    918:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    919:     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    920:     for (j=jmin; j<n; j++) {
    921:       /* (strict lower triangular part of A)*x  */
    922:       cval       = ib[j]*5;
    923:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5;
    924:       z[cval+1] += v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5;
    925:       z[cval+2] += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4+ v[14]*x5;
    926:       z[cval+3] += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4+ v[19]*x5;
    927:       z[cval+4] += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
    928:       /* (strict upper triangular part of A)*x  */
    929:       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];
    930:       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];
    931:       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];
    932:       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];
    933:       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];
    934:       v        += 25;
    935:     }
    936:     xb +=5; ai++;
    937:   }

    939:   VecRestoreArrayRead(xx,&x);
    940:   VecRestoreArray(zz,&z);

    942:   PetscLogFlops(50.0*(a->nz*2.0 - nonzerorow));
    943:   return(0);
    944: }
    947: PetscErrorCode MatMultAdd_SeqSBAIJ_6(Mat A,Vec xx,Vec yy,Vec zz)
    948: {
    949:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    950:   PetscScalar       *z,x1,x2,x3,x4,x5,x6;
    951:   const PetscScalar *x,*xb;
    952:   const MatScalar   *v;
    953:   PetscErrorCode    ierr;
    954:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    955:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    956:   PetscInt          nonzerorow=0;

    959:   VecCopy(yy,zz);
    960:   VecGetArrayRead(xx,&x);
    961:   VecGetArray(zz,&z);

    963:   v  = a->a;
    964:   xb = x;

    966:   for (i=0; i<mbs; i++) {
    967:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    968:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5];
    969:     ib          = aj + *ai;
    970:     jmin        = 0;
    971:     nonzerorow += (n>0);
    972:     if (*ib == i) {     /* (diag of A)*x */
    973:       z[6*i]   += v[0]*x1  + v[6]*x2 + v[12]*x3 + v[18]*x4+ v[24]*x5 + v[30]*x6;
    974:       z[6*i+1] += v[6]*x1  + v[7]*x2 + v[13]*x3 + v[19]*x4+ v[25]*x5 + v[31]*x6;
    975:       z[6*i+2] += v[12]*x1 +v[13]*x2 + v[14]*x3 + v[20]*x4+ v[26]*x5 + v[32]*x6;
    976:       z[6*i+3] += v[18]*x1 +v[19]*x2 + v[20]*x3 + v[21]*x4+ v[27]*x5 + v[33]*x6;
    977:       z[6*i+4] += v[24]*x1 +v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[34]*x6;
    978:       z[6*i+5] += v[30]*x1 +v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
    979:       v        += 36; jmin++;
    980:     }
    981:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    982:     PetscPrefetchBlock(v+36*n,36*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    983:     for (j=jmin; j<n; j++) {
    984:       /* (strict lower triangular part of A)*x  */
    985:       cval       = ib[j]*6;
    986:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6;
    987:       z[cval+1] += v[6]*x1  + v[7]*x2 + v[8]*x3 + v[9]*x4+ v[10]*x5 + v[11]*x6;
    988:       z[cval+2] += v[12]*x1  + v[13]*x2 + v[14]*x3 + v[15]*x4+ v[16]*x5 + v[17]*x6;
    989:       z[cval+3] += v[18]*x1  + v[19]*x2 + v[20]*x3 + v[21]*x4+ v[22]*x5 + v[23]*x6;
    990:       z[cval+4] += v[24]*x1  + v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[29]*x6;
    991:       z[cval+5] += v[30]*x1  + v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
    992:       /* (strict upper triangular part of A)*x  */
    993:       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];
    994:       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];
    995:       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];
    996:       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];
    997:       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];
    998:       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];
    999:       v        += 36;
    1000:     }
    1001:     xb +=6; ai++;
    1002:   }

    1004:   VecRestoreArrayRead(xx,&x);
    1005:   VecRestoreArray(zz,&z);

    1007:   PetscLogFlops(72.0*(a->nz*2.0 - nonzerorow));
    1008:   return(0);
    1009: }

    1013: PetscErrorCode MatMultAdd_SeqSBAIJ_7(Mat A,Vec xx,Vec yy,Vec zz)
    1014: {
    1015:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    1016:   PetscScalar       *z,x1,x2,x3,x4,x5,x6,x7;
    1017:   const PetscScalar *x,*xb;
    1018:   const MatScalar   *v;
    1019:   PetscErrorCode    ierr;
    1020:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
    1021:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
    1022:   PetscInt          nonzerorow=0;

    1025:   VecCopy(yy,zz);
    1026:   VecGetArrayRead(xx,&x);
    1027:   VecGetArray(zz,&z);

    1029:   v  = a->a;
    1030:   xb = x;

    1032:   for (i=0; i<mbs; i++) {
    1033:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
    1034:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5]; x7=xb[6];
    1035:     ib          = aj + *ai;
    1036:     jmin        = 0;
    1037:     nonzerorow += (n>0);
    1038:     if (*ib == i) {     /* (diag of A)*x */
    1039:       z[7*i]   += v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4+ v[28]*x5 + v[35]*x6+ v[42]*x7;
    1040:       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;
    1041:       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;
    1042:       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;
    1043:       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;
    1044:       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;
    1045:       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;
    1046:       v        += 49; jmin++;
    1047:     }
    1048:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    1049:     PetscPrefetchBlock(v+49*n,49*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1050:     for (j=jmin; j<n; j++) {
    1051:       /* (strict lower triangular part of A)*x  */
    1052:       cval       = ib[j]*7;
    1053:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6+ v[6]*x7;
    1054:       z[cval+1] += v[7]*x1  + v[8]*x2 + v[9]*x3 + v[10]*x4+ v[11]*x5 + v[12]*x6+ v[13]*x7;
    1055:       z[cval+2] += v[14]*x1  + v[15]*x2 + v[16]*x3 + v[17]*x4+ v[18]*x5 + v[19]*x6+ v[20]*x7;
    1056:       z[cval+3] += v[21]*x1  + v[22]*x2 + v[23]*x3 + v[24]*x4+ v[25]*x5 + v[26]*x6+ v[27]*x7;
    1057:       z[cval+4] += v[28]*x1  + v[29]*x2 + v[30]*x3 + v[31]*x4+ v[32]*x5 + v[33]*x6+ v[34]*x7;
    1058:       z[cval+5] += v[35]*x1  + v[36]*x2 + v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[41]*x7;
    1059:       z[cval+6] += v[42]*x1  + v[43]*x2 + v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
    1060:       /* (strict upper triangular part of A)*x  */
    1061:       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];
    1062:       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];
    1063:       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];
    1064:       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];
    1065:       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];
    1066:       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];
    1067:       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];
    1068:       v       += 49;
    1069:     }
    1070:     xb +=7; ai++;
    1071:   }

    1073:   VecRestoreArrayRead(xx,&x);
    1074:   VecRestoreArray(zz,&z);

    1076:   PetscLogFlops(98.0*(a->nz*2.0 - nonzerorow));
    1077:   return(0);
    1078: }

    1082: PetscErrorCode MatMultAdd_SeqSBAIJ_N(Mat A,Vec xx,Vec yy,Vec zz)
    1083: {
    1084:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    1085:   PetscScalar       *z,*z_ptr=0,*zb,*work,*workt;
    1086:   const PetscScalar *x,*x_ptr,*xb;
    1087:   const MatScalar   *v;
    1088:   PetscErrorCode    ierr;
    1089:   PetscInt          mbs = a->mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2,ncols,k;
    1090:   const PetscInt    *idx,*aj,*ii;
    1091:   PetscInt          nonzerorow=0;

    1094:   VecCopy(yy,zz);
    1095:   VecGetArrayRead(xx,&x); x_ptr=x;
    1096:   VecGetArray(zz,&z); z_ptr=z;

    1098:   aj = a->j;
    1099:   v  = a->a;
    1100:   ii = a->i;

    1102:   if (!a->mult_work) {
    1103:     PetscMalloc1(A->rmap->n+1,&a->mult_work);
    1104:   }
    1105:   work = a->mult_work;

    1108:   for (i=0; i<mbs; i++) {
    1109:     n           = ii[1] - ii[0]; ncols = n*bs;
    1110:     workt       = work; idx=aj+ii[0];
    1111:     nonzerorow += (n>0);

    1113:     /* upper triangular part */
    1114:     for (j=0; j<n; j++) {
    1115:       xb = x_ptr + bs*(*idx++);
    1116:       for (k=0; k<bs; k++) workt[k] = xb[k];
    1117:       workt += bs;
    1118:     }
    1119:     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
    1120:     PetscKernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);

    1122:     /* strict lower triangular part */
    1123:     idx = aj+ii[0];
    1124:     if (*idx == i) {
    1125:       ncols -= bs; v += bs2; idx++; n--;
    1126:     }
    1127:     if (ncols > 0) {
    1128:       workt = work;
    1129:       PetscMemzero(workt,ncols*sizeof(PetscScalar));
    1130:       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,x,v,workt);
    1131:       for (j=0; j<n; j++) {
    1132:         zb = z_ptr + bs*(*idx++);
    1133:         for (k=0; k<bs; k++) zb[k] += workt[k];
    1134:         workt += bs;
    1135:       }
    1136:     }

    1138:     x += bs; v += n*bs2; z += bs; ii++;
    1139:   }

    1141:   VecRestoreArrayRead(xx,&x);
    1142:   VecRestoreArray(zz,&z);

    1144:   PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow));
    1145:   return(0);
    1146: }

    1150: PetscErrorCode MatScale_SeqSBAIJ(Mat inA,PetscScalar alpha)
    1151: {
    1152:   Mat_SeqSBAIJ   *a     = (Mat_SeqSBAIJ*)inA->data;
    1153:   PetscScalar    oalpha = alpha;
    1155:   PetscBLASInt   one = 1,totalnz;

    1158:   PetscBLASIntCast(a->bs2*a->nz,&totalnz);
    1159:   PetscStackCallBLAS("BLASscal",BLASscal_(&totalnz,&oalpha,a->a,&one));
    1160:   PetscLogFlops(totalnz);
    1161:   return(0);
    1162: }

    1166: PetscErrorCode MatNorm_SeqSBAIJ(Mat A,NormType type,PetscReal *norm)
    1167: {
    1168:   Mat_SeqSBAIJ    *a       = (Mat_SeqSBAIJ*)A->data;
    1169:   const MatScalar *v       = a->a;
    1170:   PetscReal       sum_diag = 0.0, sum_off = 0.0, *sum;
    1171:   PetscInt        i,j,k,bs = A->rmap->bs,bs2=a->bs2,k1,mbs=a->mbs,jmin,jmax,nexti,ik,*jl,*il;
    1172:   PetscErrorCode  ierr;
    1173:   const PetscInt  *aj=a->j,*col;

    1176:   if (type == NORM_FROBENIUS) {
    1177:     for (k=0; k<mbs; k++) {
    1178:       jmin = a->i[k]; jmax = a->i[k+1];
    1179:       col  = aj + jmin;
    1180:       if (*col == k) {         /* diagonal block */
    1181:         for (i=0; i<bs2; i++) {
    1182:           sum_diag += PetscRealPart(PetscConj(*v)*(*v)); v++;
    1183:         }
    1184:         jmin++;
    1185:       }
    1186:       for (j=jmin; j<jmax; j++) {  /* off-diagonal blocks */
    1187:         for (i=0; i<bs2; i++) {
    1188:           sum_off += PetscRealPart(PetscConj(*v)*(*v)); v++;
    1189:         }
    1190:       }
    1191:     }
    1192:     *norm = PetscSqrtReal(sum_diag + 2*sum_off);
    1193:   } else if (type == NORM_INFINITY || type == NORM_1) {  /* maximum row/column sum */
    1194:     PetscMalloc3(bs,&sum,mbs,&il,mbs,&jl);
    1195:     for (i=0; i<mbs; i++) jl[i] = mbs;
    1196:     il[0] = 0;

    1198:     *norm = 0.0;
    1199:     for (k=0; k<mbs; k++) { /* k_th block row */
    1200:       for (j=0; j<bs; j++) sum[j]=0.0;
    1201:       /*-- col sum --*/
    1202:       i = jl[k]; /* first |A(i,k)| to be added */
    1203:       /* jl[k]=i: first nozero element in row i for submatrix A(1:k,k:n) (active window)
    1204:                   at step k */
    1205:       while (i<mbs) {
    1206:         nexti = jl[i];  /* next block row to be added */
    1207:         ik    = il[i];  /* block index of A(i,k) in the array a */
    1208:         for (j=0; j<bs; j++) {
    1209:           v = a->a + ik*bs2 + j*bs;
    1210:           for (k1=0; k1<bs; k1++) {
    1211:             sum[j] += PetscAbsScalar(*v); v++;
    1212:           }
    1213:         }
    1214:         /* update il, jl */
    1215:         jmin = ik + 1; /* block index of array a: points to the next nonzero of A in row i */
    1216:         jmax = a->i[i+1];
    1217:         if (jmin < jmax) {
    1218:           il[i] = jmin;
    1219:           j     = a->j[jmin];
    1220:           jl[i] = jl[j]; jl[j]=i;
    1221:         }
    1222:         i = nexti;
    1223:       }
    1224:       /*-- row sum --*/
    1225:       jmin = a->i[k]; jmax = a->i[k+1];
    1226:       for (i=jmin; i<jmax; i++) {
    1227:         for (j=0; j<bs; j++) {
    1228:           v = a->a + i*bs2 + j;
    1229:           for (k1=0; k1<bs; k1++) {
    1230:             sum[j] += PetscAbsScalar(*v); v += bs;
    1231:           }
    1232:         }
    1233:       }
    1234:       /* add k_th block row to il, jl */
    1235:       col = aj+jmin;
    1236:       if (*col == k) jmin++;
    1237:       if (jmin < jmax) {
    1238:         il[k] = jmin;
    1239:         j = a->j[jmin]; jl[k] = jl[j]; jl[j] = k;
    1240:       }
    1241:       for (j=0; j<bs; j++) {
    1242:         if (sum[j] > *norm) *norm = sum[j];
    1243:       }
    1244:     }
    1245:     PetscFree3(sum,il,jl);
    1246:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for this norm yet");
    1247:   return(0);
    1248: }

    1252: PetscErrorCode MatEqual_SeqSBAIJ(Mat A,Mat B,PetscBool * flg)
    1253: {
    1254:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)B->data;

    1258:   /* If the  matrix/block dimensions are not equal, or no of nonzeros or shift */
    1259:   if ((A->rmap->N != B->rmap->N) || (A->cmap->n != B->cmap->n) || (A->rmap->bs != B->rmap->bs)|| (a->nz != b->nz)) {
    1260:     *flg = PETSC_FALSE;
    1261:     return(0);
    1262:   }

    1264:   /* if the a->i are the same */
    1265:   PetscMemcmp(a->i,b->i,(a->mbs+1)*sizeof(PetscInt),flg);
    1266:   if (!*flg) return(0);

    1268:   /* if a->j are the same */
    1269:   PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);
    1270:   if (!*flg) return(0);

    1272:   /* if a->a are the same */
    1273:   PetscMemcmp(a->a,b->a,(a->nz)*(A->rmap->bs)*(A->rmap->bs)*sizeof(PetscScalar),flg);
    1274:   return(0);
    1275: }

    1279: PetscErrorCode MatGetDiagonal_SeqSBAIJ(Mat A,Vec v)
    1280: {
    1281:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ*)A->data;
    1282:   PetscErrorCode  ierr;
    1283:   PetscInt        i,j,k,row,bs,ambs,bs2;
    1284:   const PetscInt  *ai,*aj;
    1285:   PetscScalar     *x,zero = 0.0;
    1286:   const MatScalar *aa,*aa_j;

    1289:   bs = A->rmap->bs;
    1290:   if (A->factortype && bs>1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix with bs>1");

    1292:   aa   = a->a;
    1293:   ambs = a->mbs;

    1295:   if (A->factortype == MAT_FACTOR_CHOLESKY || A->factortype == MAT_FACTOR_ICC) {
    1296:     PetscInt *diag=a->diag;
    1297:     aa   = a->a;
    1298:     ambs = a->mbs;
    1299:     VecGetArray(v,&x);
    1300:     for (i=0; i<ambs; i++) x[i] = 1.0/aa[diag[i]];
    1301:     VecRestoreArray(v,&x);
    1302:     return(0);
    1303:   }

    1305:   ai   = a->i;
    1306:   aj   = a->j;
    1307:   bs2  = a->bs2;
    1308:   VecSet(v,zero);
    1309:   VecGetArray(v,&x);
    1310:   for (i=0; i<ambs; i++) {
    1311:     j=ai[i];
    1312:     if (aj[j] == i) {    /* if this is a diagonal element */
    1313:       row  = i*bs;
    1314:       aa_j = aa + j*bs2;
    1315:       for (k=0; k<bs2; k+=(bs+1),row++) x[row] = aa_j[k];
    1316:     }
    1317:   }
    1318:   VecRestoreArray(v,&x);
    1319:   return(0);
    1320: }

    1324: PetscErrorCode MatDiagonalScale_SeqSBAIJ(Mat A,Vec ll,Vec rr)
    1325: {
    1326:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    1327:   PetscScalar       x;
    1328:   const PetscScalar *l,*li,*ri;
    1329:   MatScalar         *aa,*v;
    1330:   PetscErrorCode    ierr;
    1331:   PetscInt          i,j,k,lm,M,m,*ai,*aj,mbs,tmp,bs,bs2;
    1332:   PetscBool         flg;

    1335:   if (ll != rr) {
    1336:     VecEqual(ll,rr,&flg);
    1337:     if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"For symmetric format, left and right scaling vectors must be same\n");
    1338:   }
    1339:   if (!ll) return(0);
    1340:   ai  = a->i;
    1341:   aj  = a->j;
    1342:   aa  = a->a;
    1343:   m   = A->rmap->N;
    1344:   bs  = A->rmap->bs;
    1345:   mbs = a->mbs;
    1346:   bs2 = a->bs2;

    1348:   VecGetArrayRead(ll,&l);
    1349:   VecGetLocalSize(ll,&lm);
    1350:   if (lm != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
    1351:   for (i=0; i<mbs; i++) { /* for each block row */
    1352:     M  = ai[i+1] - ai[i];
    1353:     li = l + i*bs;
    1354:     v  = aa + bs2*ai[i];
    1355:     for (j=0; j<M; j++) { /* for each block */
    1356:       ri = l + bs*aj[ai[i]+j];
    1357:       for (k=0; k<bs; k++) {
    1358:         x = ri[k];
    1359:         for (tmp=0; tmp<bs; tmp++) (*v++) *= li[tmp]*x;
    1360:       }
    1361:     }
    1362:   }
    1363:   VecRestoreArrayRead(ll,&l);
    1364:   PetscLogFlops(2.0*a->nz);
    1365:   return(0);
    1366: }

    1370: PetscErrorCode MatGetInfo_SeqSBAIJ(Mat A,MatInfoType flag,MatInfo *info)
    1371: {
    1372:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data;

    1375:   info->block_size   = a->bs2;
    1376:   info->nz_allocated = a->bs2*a->maxnz;   /*num. of nonzeros in upper triangular part */
    1377:   info->nz_used      = a->bs2*a->nz;   /*num. of nonzeros in upper triangular part */
    1378:   info->nz_unneeded  = (double)(info->nz_allocated - info->nz_used);
    1379:   info->assemblies   = A->num_ass;
    1380:   info->mallocs      = A->info.mallocs;
    1381:   info->memory       = ((PetscObject)A)->mem;
    1382:   if (A->factortype) {
    1383:     info->fill_ratio_given  = A->info.fill_ratio_given;
    1384:     info->fill_ratio_needed = A->info.fill_ratio_needed;
    1385:     info->factor_mallocs    = A->info.factor_mallocs;
    1386:   } else {
    1387:     info->fill_ratio_given  = 0;
    1388:     info->fill_ratio_needed = 0;
    1389:     info->factor_mallocs    = 0;
    1390:   }
    1391:   return(0);
    1392: }

    1397: PetscErrorCode MatZeroEntries_SeqSBAIJ(Mat A)
    1398: {
    1399:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;

    1403:   PetscMemzero(a->a,a->bs2*a->i[a->mbs]*sizeof(MatScalar));
    1404:   return(0);
    1405: }

    1409: /*
    1410:    This code does not work since it only checks the upper triangular part of
    1411:   the matrix. Hence it is not listed in the function table.
    1412: */
    1413: PetscErrorCode MatGetRowMaxAbs_SeqSBAIJ(Mat A,Vec v,PetscInt idx[])
    1414: {
    1415:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ*)A->data;
    1416:   PetscErrorCode  ierr;
    1417:   PetscInt        i,j,n,row,col,bs,mbs;
    1418:   const PetscInt  *ai,*aj;
    1419:   PetscReal       atmp;
    1420:   const MatScalar *aa;
    1421:   PetscScalar     *x;
    1422:   PetscInt        ncols,brow,bcol,krow,kcol;

    1425:   if (idx) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Send email to petsc-maint@mcs.anl.gov");
    1426:   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1427:   bs  = A->rmap->bs;
    1428:   aa  = a->a;
    1429:   ai  = a->i;
    1430:   aj  = a->j;
    1431:   mbs = a->mbs;

    1433:   VecSet(v,0.0);
    1434:   VecGetArray(v,&x);
    1435:   VecGetLocalSize(v,&n);
    1436:   if (n != A->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
    1437:   for (i=0; i<mbs; i++) {
    1438:     ncols = ai[1] - ai[0]; ai++;
    1439:     brow  = bs*i;
    1440:     for (j=0; j<ncols; j++) {
    1441:       bcol = bs*(*aj);
    1442:       for (kcol=0; kcol<bs; kcol++) {
    1443:         col = bcol + kcol;      /* col index */
    1444:         for (krow=0; krow<bs; krow++) {
    1445:           atmp = PetscAbsScalar(*aa); aa++;
    1446:           row  = brow + krow;   /* row index */
    1447:           if (PetscRealPart(x[row]) < atmp) x[row] = atmp;
    1448:           if (*aj > i && PetscRealPart(x[col]) < atmp) x[col] = atmp;
    1449:         }
    1450:       }
    1451:       aj++;
    1452:     }
    1453:   }
    1454:   VecRestoreArray(v,&x);
    1455:   return(0);
    1456: }