Actual source code: aijperm.c

petsc-master 2020-10-19
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  2: /*
  3:   Defines basic operations for the MATSEQAIJPERM matrix class.
  4:   This class is derived from the MATSEQAIJ class and retains the
  5:   compressed row storage (aka Yale sparse matrix format) but augments
  6:   it with some permutation information that enables some operations
  7:   to be more vectorizable.  A physically rearranged copy of the matrix
  8:   may be stored if the user desires.

 10:   Eventually a variety of permutations may be supported.
 11: */

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

 15: #if defined(PETSC_USE_AVX512_KERNELS) && defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
 16: #include <immintrin.h>

 18: #if !defined(_MM_SCALE_8)
 19: #define _MM_SCALE_8    8
 20: #endif
 21: #if !defined(_MM_SCALE_4)
 22: #define _MM_SCALE_4    4
 23: #endif
 24: #endif

 26: #define NDIM 512
 27: /* NDIM specifies how many rows at a time we should work with when
 28:  * performing the vectorized mat-vec.  This depends on various factors
 29:  * such as vector register length, etc., and I really need to add a
 30:  * way for the user (or the library) to tune this.  I'm setting it to
 31:  * 512 for now since that is what Ed D'Azevedo was using in his Fortran
 32:  * routines. */

 34: typedef struct {
 35:   PetscObjectState nonzerostate; /* used to determine if the nonzero structure has changed and hence the permutations need updating */

 37:   PetscInt         ngroup;
 38:   PetscInt         *xgroup;
 39:   /* Denotes where groups of rows with same number of nonzeros
 40:    * begin and end, i.e., xgroup[i] gives us the position in iperm[]
 41:    * where the ith group begins. */

 43:   PetscInt         *nzgroup; /*  how many nonzeros each row that is a member of group i has. */
 44:   PetscInt         *iperm;  /* The permutation vector. */

 46:   /* Some of this stuff is for Ed's recursive triangular solve.
 47:    * I'm not sure what I need yet. */
 48:   PetscInt         blocksize;
 49:   PetscInt         nstep;
 50:   PetscInt         *jstart_list;
 51:   PetscInt         *jend_list;
 52:   PetscInt         *action_list;
 53:   PetscInt         *ngroup_list;
 54:   PetscInt         **ipointer_list;
 55:   PetscInt         **xgroup_list;
 56:   PetscInt         **nzgroup_list;
 57:   PetscInt         **iperm_list;
 58: } Mat_SeqAIJPERM;

 60: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJPERM_SeqAIJ(Mat A,MatType type,MatReuse reuse,Mat *newmat)
 61: {
 62:   /* This routine is only called to convert a MATAIJPERM to its base PETSc type, */
 63:   /* so we will ignore 'MatType type'. */
 65:   Mat            B       = *newmat;
 66:   Mat_SeqAIJPERM *aijperm=(Mat_SeqAIJPERM*)A->spptr;

 69:   if (reuse == MAT_INITIAL_MATRIX) {
 70:     MatDuplicate(A,MAT_COPY_VALUES,&B);
 71:     aijperm=(Mat_SeqAIJPERM*)B->spptr;
 72:   }

 74:   /* Reset the original function pointers. */
 75:   B->ops->assemblyend = MatAssemblyEnd_SeqAIJ;
 76:   B->ops->destroy     = MatDestroy_SeqAIJ;
 77:   B->ops->duplicate   = MatDuplicate_SeqAIJ;
 78:   B->ops->mult        = MatMult_SeqAIJ;
 79:   B->ops->multadd     = MatMultAdd_SeqAIJ;

 81:   PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaijperm_seqaij_C",NULL);

 83:   /* Free everything in the Mat_SeqAIJPERM data structure.*/
 84:   PetscFree(aijperm->xgroup);
 85:   PetscFree(aijperm->nzgroup);
 86:   PetscFree(aijperm->iperm);
 87:   PetscFree(B->spptr);

 89:   /* Change the type of B to MATSEQAIJ. */
 90:   PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ);

 92:   *newmat = B;
 93:   return(0);
 94: }

 96: PetscErrorCode MatDestroy_SeqAIJPERM(Mat A)
 97: {
 99:   Mat_SeqAIJPERM *aijperm = (Mat_SeqAIJPERM*) A->spptr;

102:   if (aijperm) {
103:     /* If MatHeaderMerge() was used then this SeqAIJPERM matrix will not have a spprt. */
104:     PetscFree(aijperm->xgroup);
105:     PetscFree(aijperm->nzgroup);
106:     PetscFree(aijperm->iperm);
107:     PetscFree(A->spptr);
108:   }
109:   /* Change the type of A back to SEQAIJ and use MatDestroy_SeqAIJ()
110:    * to destroy everything that remains. */
111:   PetscObjectChangeTypeName((PetscObject)A, MATSEQAIJ);
112:   /* Note that I don't call MatSetType().  I believe this is because that
113:    * is only to be called when *building* a matrix.  I could be wrong, but
114:    * that is how things work for the SuperLU matrix class. */
115:   MatDestroy_SeqAIJ(A);
116:   return(0);
117: }

119: PetscErrorCode MatDuplicate_SeqAIJPERM(Mat A, MatDuplicateOption op, Mat *M)
120: {
122:   Mat_SeqAIJPERM *aijperm      = (Mat_SeqAIJPERM*) A->spptr;
123:   Mat_SeqAIJPERM *aijperm_dest;
124:   PetscBool      perm;

127:   MatDuplicate_SeqAIJ(A,op,M);
128:   PetscObjectTypeCompare((PetscObject)*M,MATSEQAIJPERM,&perm);
129:   if (perm) {
130:     aijperm_dest = (Mat_SeqAIJPERM *) (*M)->spptr;
131:     PetscFree(aijperm_dest->xgroup);
132:     PetscFree(aijperm_dest->nzgroup);
133:     PetscFree(aijperm_dest->iperm);
134:   } else {
135:     PetscNewLog(*M,&aijperm_dest);
136:     (*M)->spptr = (void*) aijperm_dest;
137:     PetscObjectChangeTypeName((PetscObject)*M,MATSEQAIJPERM);
138:     PetscObjectComposeFunction((PetscObject)*M,"MatConvert_seqaijperm_seqaij_C",MatConvert_SeqAIJPERM_SeqAIJ);
139:   }
140:   PetscArraycpy(aijperm_dest,aijperm,1);
141:   /* Allocate space for, and copy the grouping and permutation info.
142:    * I note that when the groups are initially determined in
143:    * MatSeqAIJPERM_create_perm, xgroup and nzgroup may be sized larger than
144:    * necessary.  But at this point, we know how large they need to be, and
145:    * allocate only the necessary amount of memory.  So the duplicated matrix
146:    * may actually use slightly less storage than the original! */
147:   PetscMalloc1(A->rmap->n, &aijperm_dest->iperm);
148:   PetscMalloc1(aijperm->ngroup+1, &aijperm_dest->xgroup);
149:   PetscMalloc1(aijperm->ngroup, &aijperm_dest->nzgroup);
150:   PetscArraycpy(aijperm_dest->iperm,aijperm->iperm,A->rmap->n);
151:   PetscArraycpy(aijperm_dest->xgroup,aijperm->xgroup,aijperm->ngroup+1);
152:   PetscArraycpy(aijperm_dest->nzgroup,aijperm->nzgroup,aijperm->ngroup);
153:   return(0);
154: }

156: PetscErrorCode MatSeqAIJPERM_create_perm(Mat A)
157: {
159:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)(A)->data;
160:   Mat_SeqAIJPERM *aijperm = (Mat_SeqAIJPERM*) A->spptr;
161:   PetscInt       m;       /* Number of rows in the matrix. */
162:   PetscInt       *ia;       /* From the CSR representation; points to the beginning  of each row. */
163:   PetscInt       maxnz;      /* Maximum number of nonzeros in any row. */
164:   PetscInt       *rows_in_bucket;
165:   /* To construct the permutation, we sort each row into one of maxnz
166:    * buckets based on how many nonzeros are in the row. */
167:   PetscInt       nz;
168:   PetscInt       *nz_in_row;         /* the number of nonzero elements in row k. */
169:   PetscInt       *ipnz;
170:   /* When constructing the iperm permutation vector,
171:    * ipnz[nz] is used to point to the next place in the permutation vector
172:    * that a row with nz nonzero elements should be placed.*/
173:   PetscInt       i, ngroup, istart, ipos;

176:   if (aijperm->nonzerostate == A->nonzerostate) return(0); /* permutation exists and matches current nonzero structure */
177:   aijperm->nonzerostate = A->nonzerostate;
178:  /* Free anything previously put in the Mat_SeqAIJPERM data structure. */
179:   PetscFree(aijperm->xgroup);
180:   PetscFree(aijperm->nzgroup);
181:   PetscFree(aijperm->iperm);

183:   m  = A->rmap->n;
184:   ia = a->i;

186:   /* Allocate the arrays that will hold the permutation vector. */
187:   PetscMalloc1(m, &aijperm->iperm);

189:   /* Allocate some temporary work arrays that will be used in
190:    * calculating the permuation vector and groupings. */
191:   PetscMalloc1(m, &nz_in_row);

193:   /* Now actually figure out the permutation and grouping. */

195:   /* First pass: Determine number of nonzeros in each row, maximum
196:    * number of nonzeros in any row, and how many rows fall into each
197:    * "bucket" of rows with same number of nonzeros. */
198:   maxnz = 0;
199:   for (i=0; i<m; i++) {
200:     nz_in_row[i] = ia[i+1]-ia[i];
201:     if (nz_in_row[i] > maxnz) maxnz = nz_in_row[i];
202:   }
203:   PetscMalloc1(PetscMax(maxnz,m)+1, &rows_in_bucket);
204:   PetscMalloc1(PetscMax(maxnz,m)+1, &ipnz);

206:   for (i=0; i<=maxnz; i++) {
207:     rows_in_bucket[i] = 0;
208:   }
209:   for (i=0; i<m; i++) {
210:     nz = nz_in_row[i];
211:     rows_in_bucket[nz]++;
212:   }

214:   /* Allocate space for the grouping info.  There will be at most (maxnz + 1)
215:    * groups.  (It is maxnz + 1 instead of simply maxnz because there may be
216:    * rows with no nonzero elements.)  If there are (maxnz + 1) groups,
217:    * then xgroup[] must consist of (maxnz + 2) elements, since the last
218:    * element of xgroup will tell us where the (maxnz + 1)th group ends.
219:    * We allocate space for the maximum number of groups;
220:    * that is potentially a little wasteful, but not too much so.
221:    * Perhaps I should fix it later. */
222:   PetscMalloc1(maxnz+2, &aijperm->xgroup);
223:   PetscMalloc1(maxnz+1, &aijperm->nzgroup);

225:   /* Second pass.  Look at what is in the buckets and create the groupings.
226:    * Note that it is OK to have a group of rows with no non-zero values. */
227:   ngroup = 0;
228:   istart = 0;
229:   for (i=0; i<=maxnz; i++) {
230:     if (rows_in_bucket[i] > 0) {
231:       aijperm->nzgroup[ngroup] = i;
232:       aijperm->xgroup[ngroup]  = istart;
233:       ngroup++;
234:       istart += rows_in_bucket[i];
235:     }
236:   }

238:   aijperm->xgroup[ngroup] = istart;
239:   aijperm->ngroup         = ngroup;

241:   /* Now fill in the permutation vector iperm. */
242:   ipnz[0] = 0;
243:   for (i=0; i<maxnz; i++) {
244:     ipnz[i+1] = ipnz[i] + rows_in_bucket[i];
245:   }

247:   for (i=0; i<m; i++) {
248:     nz                   = nz_in_row[i];
249:     ipos                 = ipnz[nz];
250:     aijperm->iperm[ipos] = i;
251:     ipnz[nz]++;
252:   }

254:   /* Clean up temporary work arrays. */
255:   PetscFree(rows_in_bucket);
256:   PetscFree(ipnz);
257:   PetscFree(nz_in_row);
258:   return(0);
259: }


262: PetscErrorCode MatAssemblyEnd_SeqAIJPERM(Mat A, MatAssemblyType mode)
263: {
265:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

268:   if (mode == MAT_FLUSH_ASSEMBLY) return(0);

270:   /* Since a MATSEQAIJPERM matrix is really just a MATSEQAIJ with some
271:    * extra information, call the AssemblyEnd routine for a MATSEQAIJ.
272:    * I'm not sure if this is the best way to do this, but it avoids
273:    * a lot of code duplication.
274:    * I also note that currently MATSEQAIJPERM doesn't know anything about
275:    * the Mat_CompressedRow data structure that SeqAIJ now uses when there
276:    * are many zero rows.  If the SeqAIJ assembly end routine decides to use
277:    * this, this may break things.  (Don't know... haven't looked at it.) */
278:   a->inode.use = PETSC_FALSE;
279:   MatAssemblyEnd_SeqAIJ(A, mode);

281:   /* Now calculate the permutation and grouping information. */
282:   MatSeqAIJPERM_create_perm(A);
283:   return(0);
284: }

286: PetscErrorCode MatMult_SeqAIJPERM(Mat A,Vec xx,Vec yy)
287: {
288:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
289:   const PetscScalar *x;
290:   PetscScalar       *y;
291:   const MatScalar   *aa;
292:   PetscErrorCode    ierr;
293:   const PetscInt    *aj,*ai;
294: #if !(defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJPERM) && defined(notworking))
295:   PetscInt          i,j;
296: #endif
297: #if defined(PETSC_USE_AVX512_KERNELS) && defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
298:   __m512d           vec_x,vec_y,vec_vals;
299:   __m256i           vec_idx,vec_ipos,vec_j;
300:   __mmask8           mask;
301: #endif

303:   /* Variables that don't appear in MatMult_SeqAIJ. */
304:   Mat_SeqAIJPERM    *aijperm = (Mat_SeqAIJPERM*) A->spptr;
305:   PetscInt          *iperm;  /* Points to the permutation vector. */
306:   PetscInt          *xgroup;
307:   /* Denotes where groups of rows with same number of nonzeros
308:    * begin and end in iperm. */
309:   PetscInt          *nzgroup;
310:   PetscInt          ngroup;
311:   PetscInt          igroup;
312:   PetscInt          jstart,jend;
313:   /* jstart is used in loops to denote the position in iperm where a
314:    * group starts; jend denotes the position where it ends.
315:    * (jend + 1 is where the next group starts.) */
316:   PetscInt          iold,nz;
317:   PetscInt          istart,iend,isize;
318:   PetscInt          ipos;
319:   PetscScalar       yp[NDIM];
320:   PetscInt          ip[NDIM];    /* yp[] and ip[] are treated as vector "registers" for performing the mat-vec. */

322: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
323: #pragma disjoint(*x,*y,*aa)
324: #endif

327:   VecGetArrayRead(xx,&x);
328:   VecGetArray(yy,&y);
329:   aj   = a->j;   /* aj[k] gives column index for element aa[k]. */
330:   aa   = a->a; /* Nonzero elements stored row-by-row. */
331:   ai   = a->i;  /* ai[k] is the position in aa and aj where row k starts. */

333:   /* Get the info we need about the permutations and groupings. */
334:   iperm   = aijperm->iperm;
335:   ngroup  = aijperm->ngroup;
336:   xgroup  = aijperm->xgroup;
337:   nzgroup = aijperm->nzgroup;

339: #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJPERM) && defined(notworking)
340:   fortranmultaijperm_(&m,x,ii,aj,aa,y);
341: #else

343:   for (igroup=0; igroup<ngroup; igroup++) {
344:     jstart = xgroup[igroup];
345:     jend   = xgroup[igroup+1] - 1;
346:     nz     = nzgroup[igroup];

348:     /* Handle the special cases where the number of nonzeros per row
349:      * in the group is either 0 or 1. */
350:     if (nz == 0) {
351:       for (i=jstart; i<=jend; i++) {
352:         y[iperm[i]] = 0.0;
353:       }
354:     } else if (nz == 1) {
355:       for (i=jstart; i<=jend; i++) {
356:         iold    = iperm[i];
357:         ipos    = ai[iold];
358:         y[iold] = aa[ipos] * x[aj[ipos]];
359:       }
360:     } else {

362:       /* We work our way through the current group in chunks of NDIM rows
363:        * at a time. */

365:       for (istart=jstart; istart<=jend; istart+=NDIM) {
366:         /* Figure out where the chunk of 'isize' rows ends in iperm.
367:          * 'isize may of course be less than NDIM for the last chunk. */
368:         iend = istart + (NDIM - 1);

370:         if (iend > jend) iend = jend;

372:         isize = iend - istart + 1;

374:         /* Initialize the yp[] array that will be used to hold part of
375:          * the permuted results vector, and figure out where in aa each
376:          * row of the chunk will begin. */
377:         for (i=0; i<isize; i++) {
378:           iold = iperm[istart + i];
379:           /* iold is a row number from the matrix A *before* reordering. */
380:           ip[i] = ai[iold];
381:           /* ip[i] tells us where the ith row of the chunk begins in aa. */
382:           yp[i] = (PetscScalar) 0.0;
383:         }

385:         /* If the number of zeros per row exceeds the number of rows in
386:          * the chunk, we should vectorize along nz, that is, perform the
387:          * mat-vec one row at a time as in the usual CSR case. */
388:         if (nz > isize) {
389: #if defined(PETSC_HAVE_CRAY_VECTOR)
390: #pragma _CRI preferstream
391: #endif
392:           for (i=0; i<isize; i++) {
393: #if defined(PETSC_HAVE_CRAY_VECTOR)
394: #pragma _CRI prefervector
395: #endif

397: #if defined(PETSC_USE_AVX512_KERNELS) && defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
398:             vec_y = _mm512_setzero_pd();
399:             ipos = ip[i];
400:             for (j=0; j<(nz>>3); j++) {
401:               vec_idx  = _mm256_loadu_si256((__m256i const*)&aj[ipos]);
402:               vec_vals = _mm512_loadu_pd(&aa[ipos]);
403:               vec_x    = _mm512_i32gather_pd(vec_idx,x,_MM_SCALE_8);
404:               vec_y    = _mm512_fmadd_pd(vec_x,vec_vals,vec_y);
405:               ipos += 8;
406:             }
407:             if ((nz&0x07)>2) {
408:               mask     = (__mmask8)(0xff >> (8-(nz&0x07)));
409:               vec_idx  = _mm256_loadu_si256((__m256i const*)&aj[ipos]);
410:               vec_vals = _mm512_loadu_pd(&aa[ipos]);
411:               vec_x    = _mm512_mask_i32gather_pd(vec_x,mask,vec_idx,x,_MM_SCALE_8);
412:               vec_y    = _mm512_mask3_fmadd_pd(vec_x,vec_vals,vec_y,mask);
413:             } else if ((nz&0x07)==2) {
414:               yp[i] += aa[ipos]*x[aj[ipos]];
415:               yp[i] += aa[ipos+1]*x[aj[ipos+1]];
416:             } else if ((nz&0x07)==1) {
417:               yp[i] += aa[ipos]*x[aj[ipos]];
418:             }
419:             yp[i] += _mm512_reduce_add_pd(vec_y);
420: #else
421:             for (j=0; j<nz; j++) {
422:               ipos   = ip[i] + j;
423:               yp[i] += aa[ipos] * x[aj[ipos]];
424:             }
425: #endif
426:           }
427:         } else {
428:           /* Otherwise, there are enough rows in the chunk to make it
429:            * worthwhile to vectorize across the rows, that is, to do the
430:            * matvec by operating with "columns" of the chunk. */
431:           for (j=0; j<nz; j++) {
432: #if defined(PETSC_USE_AVX512_KERNELS) && defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
433:             vec_j = _mm256_set1_epi32(j);
434:             for (i=0; i<((isize>>3)<<3); i+=8) {
435:               vec_y    = _mm512_loadu_pd(&yp[i]);
436:               vec_ipos = _mm256_loadu_si256((__m256i const*)&ip[i]);
437:               vec_ipos = _mm256_add_epi32(vec_ipos,vec_j);
438:               vec_idx  = _mm256_i32gather_epi32(aj,vec_ipos,_MM_SCALE_4);
439:               vec_vals = _mm512_i32gather_pd(vec_ipos,aa,_MM_SCALE_8);
440:               vec_x    = _mm512_i32gather_pd(vec_idx,x,_MM_SCALE_8);
441:               vec_y    = _mm512_fmadd_pd(vec_x,vec_vals,vec_y);
442:               _mm512_storeu_pd(&yp[i],vec_y);
443:             }
444:             for (i=isize-(isize&0x07); i<isize; i++) {
445:               ipos = ip[i]+j;
446:               yp[i] += aa[ipos]*x[aj[ipos]];
447:             }
448: #else
449:             for (i=0; i<isize; i++) {
450:               ipos   = ip[i] + j;
451:               yp[i] += aa[ipos] * x[aj[ipos]];
452:             }
453: #endif
454:           }
455:         }

457: #if defined(PETSC_HAVE_CRAY_VECTOR)
458: #pragma _CRI ivdep
459: #endif
460:         /* Put results from yp[] into non-permuted result vector y. */
461:         for (i=0; i<isize; i++) {
462:           y[iperm[istart+i]] = yp[i];
463:         }
464:       } /* End processing chunk of isize rows of a group. */
465:     } /* End handling matvec for chunk with nz > 1. */
466:   } /* End loop over igroup. */
467: #endif
468:   PetscLogFlops(PetscMax(2.0*a->nz - A->rmap->n,0));
469:   VecRestoreArrayRead(xx,&x);
470:   VecRestoreArray(yy,&y);
471:   return(0);
472: }


475: /* MatMultAdd_SeqAIJPERM() calculates yy = ww + A * xx.
476:  * Note that the names I used to designate the vectors differs from that
477:  * used in MatMultAdd_SeqAIJ().  I did this to keep my notation consistent
478:  * with the MatMult_SeqAIJPERM() routine, which is very similar to this one. */
479: /*
480:     I hate having virtually identical code for the mult and the multadd!!!
481: */
482: PetscErrorCode MatMultAdd_SeqAIJPERM(Mat A,Vec xx,Vec ww,Vec yy)
483: {
484:   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
485:   const PetscScalar *x;
486:   PetscScalar       *y,*w;
487:   const MatScalar   *aa;
488:   PetscErrorCode    ierr;
489:   const PetscInt    *aj,*ai;
490: #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJPERM)
491:   PetscInt i,j;
492: #endif

494:   /* Variables that don't appear in MatMultAdd_SeqAIJ. */
495:   Mat_SeqAIJPERM * aijperm;
496:   PetscInt       *iperm;    /* Points to the permutation vector. */
497:   PetscInt       *xgroup;
498:   /* Denotes where groups of rows with same number of nonzeros
499:    * begin and end in iperm. */
500:   PetscInt *nzgroup;
501:   PetscInt ngroup;
502:   PetscInt igroup;
503:   PetscInt jstart,jend;
504:   /* jstart is used in loops to denote the position in iperm where a
505:    * group starts; jend denotes the position where it ends.
506:    * (jend + 1 is where the next group starts.) */
507:   PetscInt    iold,nz;
508:   PetscInt    istart,iend,isize;
509:   PetscInt    ipos;
510:   PetscScalar yp[NDIM];
511:   PetscInt    ip[NDIM];
512:   /* yp[] and ip[] are treated as vector "registers" for performing
513:    * the mat-vec. */

515: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
516: #pragma disjoint(*x,*y,*aa)
517: #endif

520:   VecGetArrayRead(xx,&x);
521:   VecGetArrayPair(yy,ww,&y,&w);

523:   aj = a->j;   /* aj[k] gives column index for element aa[k]. */
524:   aa = a->a;   /* Nonzero elements stored row-by-row. */
525:   ai = a->i;   /* ai[k] is the position in aa and aj where row k starts. */

527:   /* Get the info we need about the permutations and groupings. */
528:   aijperm = (Mat_SeqAIJPERM*) A->spptr;
529:   iperm   = aijperm->iperm;
530:   ngroup  = aijperm->ngroup;
531:   xgroup  = aijperm->xgroup;
532:   nzgroup = aijperm->nzgroup;

534: #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJPERM)
535:   fortranmultaddaijperm_(&m,x,ii,aj,aa,y,w);
536: #else

538:   for (igroup=0; igroup<ngroup; igroup++) {
539:     jstart = xgroup[igroup];
540:     jend   = xgroup[igroup+1] - 1;

542:     nz = nzgroup[igroup];

544:     /* Handle the special cases where the number of nonzeros per row
545:      * in the group is either 0 or 1. */
546:     if (nz == 0) {
547:       for (i=jstart; i<=jend; i++) {
548:         iold    = iperm[i];
549:         y[iold] = w[iold];
550:       }
551:     }
552:     else if (nz == 1) {
553:       for (i=jstart; i<=jend; i++) {
554:         iold    = iperm[i];
555:         ipos    = ai[iold];
556:         y[iold] = w[iold] + aa[ipos] * x[aj[ipos]];
557:       }
558:     }
559:     /* For the general case: */
560:     else {

562:       /* We work our way through the current group in chunks of NDIM rows
563:        * at a time. */

565:       for (istart=jstart; istart<=jend; istart+=NDIM) {
566:         /* Figure out where the chunk of 'isize' rows ends in iperm.
567:          * 'isize may of course be less than NDIM for the last chunk. */
568:         iend = istart + (NDIM - 1);
569:         if (iend > jend) iend = jend;
570:         isize = iend - istart + 1;

572:         /* Initialize the yp[] array that will be used to hold part of
573:          * the permuted results vector, and figure out where in aa each
574:          * row of the chunk will begin. */
575:         for (i=0; i<isize; i++) {
576:           iold = iperm[istart + i];
577:           /* iold is a row number from the matrix A *before* reordering. */
578:           ip[i] = ai[iold];
579:           /* ip[i] tells us where the ith row of the chunk begins in aa. */
580:           yp[i] = w[iold];
581:         }

583:         /* If the number of zeros per row exceeds the number of rows in
584:          * the chunk, we should vectorize along nz, that is, perform the
585:          * mat-vec one row at a time as in the usual CSR case. */
586:         if (nz > isize) {
587: #if defined(PETSC_HAVE_CRAY_VECTOR)
588: #pragma _CRI preferstream
589: #endif
590:           for (i=0; i<isize; i++) {
591: #if defined(PETSC_HAVE_CRAY_VECTOR)
592: #pragma _CRI prefervector
593: #endif
594:             for (j=0; j<nz; j++) {
595:               ipos   = ip[i] + j;
596:               yp[i] += aa[ipos] * x[aj[ipos]];
597:             }
598:           }
599:         }
600:         /* Otherwise, there are enough rows in the chunk to make it
601:          * worthwhile to vectorize across the rows, that is, to do the
602:          * matvec by operating with "columns" of the chunk. */
603:         else {
604:           for (j=0; j<nz; j++) {
605:             for (i=0; i<isize; i++) {
606:               ipos   = ip[i] + j;
607:               yp[i] += aa[ipos] * x[aj[ipos]];
608:             }
609:           }
610:         }

612: #if defined(PETSC_HAVE_CRAY_VECTOR)
613: #pragma _CRI ivdep
614: #endif
615:         /* Put results from yp[] into non-permuted result vector y. */
616:         for (i=0; i<isize; i++) {
617:           y[iperm[istart+i]] = yp[i];
618:         }
619:       } /* End processing chunk of isize rows of a group. */

621:     } /* End handling matvec for chunk with nz > 1. */
622:   } /* End loop over igroup. */

624: #endif
625:   PetscLogFlops(2.0*a->nz);
626:   VecRestoreArrayRead(xx,&x);
627:   VecRestoreArrayPair(yy,ww,&y,&w);
628:   return(0);
629: }

631: /* MatConvert_SeqAIJ_SeqAIJPERM converts a SeqAIJ matrix into a
632:  * SeqAIJPERM matrix.  This routine is called by the MatCreate_SeqAIJPERM()
633:  * routine, but can also be used to convert an assembled SeqAIJ matrix
634:  * into a SeqAIJPERM one. */
635: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJPERM(Mat A,MatType type,MatReuse reuse,Mat *newmat)
636: {
638:   Mat            B = *newmat;
639:   Mat_SeqAIJPERM *aijperm;
640:   PetscBool      sametype;

643:   if (reuse == MAT_INITIAL_MATRIX) {
644:     MatDuplicate(A,MAT_COPY_VALUES,&B);
645:   }
646:   PetscObjectTypeCompare((PetscObject)A,type,&sametype);
647:   if (sametype) return(0);

649:   PetscNewLog(B,&aijperm);
650:   B->spptr = (void*) aijperm;

652:   /* Set function pointers for methods that we inherit from AIJ but override. */
653:   B->ops->duplicate   = MatDuplicate_SeqAIJPERM;
654:   B->ops->assemblyend = MatAssemblyEnd_SeqAIJPERM;
655:   B->ops->destroy     = MatDestroy_SeqAIJPERM;
656:   B->ops->mult        = MatMult_SeqAIJPERM;
657:   B->ops->multadd     = MatMultAdd_SeqAIJPERM;

659:   aijperm->nonzerostate = -1;  /* this will trigger the generation of the permutation information the first time through MatAssembly()*/
660:   /* If A has already been assembled, compute the permutation. */
661:   if (A->assembled) {
662:     MatSeqAIJPERM_create_perm(B);
663:   }

665:   PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaijperm_seqaij_C",MatConvert_SeqAIJPERM_SeqAIJ);

667:   PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJPERM);
668:   *newmat = B;
669:   return(0);
670: }

672: /*@C
673:    MatCreateSeqAIJPERM - Creates a sparse matrix of type SEQAIJPERM.
674:    This type inherits from AIJ, but calculates some additional permutation
675:    information that is used to allow better vectorization of some
676:    operations.  At the cost of increased storage, the AIJ formatted
677:    matrix can be copied to a format in which pieces of the matrix are
678:    stored in ELLPACK format, allowing the vectorized matrix multiply
679:    routine to use stride-1 memory accesses.  As with the AIJ type, it is
680:    important to preallocate matrix storage in order to get good assembly
681:    performance.

683:    Collective

685:    Input Parameters:
686: +  comm - MPI communicator, set to PETSC_COMM_SELF
687: .  m - number of rows
688: .  n - number of columns
689: .  nz - number of nonzeros per row (same for all rows)
690: -  nnz - array containing the number of nonzeros in the various rows
691:          (possibly different for each row) or NULL

693:    Output Parameter:
694: .  A - the matrix

696:    Notes:
697:    If nnz is given then nz is ignored

699:    Level: intermediate

701: .seealso: MatCreate(), MatCreateMPIAIJPERM(), MatSetValues()
702: @*/
703: PetscErrorCode  MatCreateSeqAIJPERM(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
704: {

708:   MatCreate(comm,A);
709:   MatSetSizes(*A,m,n,m,n);
710:   MatSetType(*A,MATSEQAIJPERM);
711:   MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);
712:   return(0);
713: }

715: PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJPERM(Mat A)
716: {

720:   MatSetType(A,MATSEQAIJ);
721:   MatConvert_SeqAIJ_SeqAIJPERM(A,MATSEQAIJPERM,MAT_INPLACE_MATRIX,&A);
722:   return(0);
723: }