Actual source code: aijperm.c

petsc-3.13.6 2020-09-29
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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);
 82:   PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaijperm_C",NULL);
 83:   PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaijperm_C",NULL);

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

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

 94:   *newmat = B;
 95:   return(0);
 96: }

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

104:   if (aijperm) {
105:     /* If MatHeaderMerge() was used then this SeqAIJPERM matrix will not have a spprt. */
106:     PetscFree(aijperm->xgroup);
107:     PetscFree(aijperm->nzgroup);
108:     PetscFree(aijperm->iperm);
109:     PetscFree(A->spptr);
110:   }
111:   /* Change the type of A back to SEQAIJ and use MatDestroy_SeqAIJ()
112:    * to destroy everything that remains. */
113:   PetscObjectChangeTypeName((PetscObject)A, MATSEQAIJ);
114:   /* Note that I don't call MatSetType().  I believe this is because that
115:    * is only to be called when *building* a matrix.  I could be wrong, but
116:    * that is how things work for the SuperLU matrix class. */
117:   MatDestroy_SeqAIJ(A);
118:   return(0);
119: }

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

129:   MatDuplicate_SeqAIJ(A,op,M);
130:   PetscObjectTypeCompare((PetscObject)*M,MATSEQAIJPERM,&perm);
131:   if (perm) {
132:     aijperm_dest = (Mat_SeqAIJPERM *) (*M)->spptr;
133:     PetscFree(aijperm_dest->xgroup);
134:     PetscFree(aijperm_dest->nzgroup);
135:     PetscFree(aijperm_dest->iperm);
136:   } else {
137:     PetscNewLog(*M,&aijperm_dest);
138:     (*M)->spptr = (void*) aijperm_dest;
139:     PetscObjectChangeTypeName((PetscObject)*M,MATSEQAIJPERM);
140:     PetscObjectComposeFunction((PetscObject)*M,"MatConvert_seqaijperm_seqaij_C",MatConvert_SeqAIJPERM_SeqAIJ);
141:     PetscObjectComposeFunction((PetscObject)*M,"MatMatMultSymbolic_seqdense_seqaijperm_C",MatMatMultSymbolic_SeqDense_SeqAIJ);
142:     PetscObjectComposeFunction((PetscObject)*M,"MatMatMultNumeric_seqdense_seqaijperm_C",MatMatMultNumeric_SeqDense_SeqAIJ);
143:   }
144:   PetscArraycpy(aijperm_dest,aijperm,1);
145:   /* Allocate space for, and copy the grouping and permutation info.
146:    * I note that when the groups are initially determined in
147:    * MatSeqAIJPERM_create_perm, xgroup and nzgroup may be sized larger than
148:    * necessary.  But at this point, we know how large they need to be, and
149:    * allocate only the necessary amount of memory.  So the duplicated matrix
150:    * may actually use slightly less storage than the original! */
151:   PetscMalloc1(A->rmap->n, &aijperm_dest->iperm);
152:   PetscMalloc1(aijperm->ngroup+1, &aijperm_dest->xgroup);
153:   PetscMalloc1(aijperm->ngroup, &aijperm_dest->nzgroup);
154:   PetscArraycpy(aijperm_dest->iperm,aijperm->iperm,A->rmap->n);
155:   PetscArraycpy(aijperm_dest->xgroup,aijperm->xgroup,aijperm->ngroup+1);
156:   PetscArraycpy(aijperm_dest->nzgroup,aijperm->nzgroup,aijperm->ngroup);
157:   return(0);
158: }

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

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

187:   m  = A->rmap->n;
188:   ia = a->i;

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

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

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

199:   /* First pass: Determine number of nonzeros in each row, maximum
200:    * number of nonzeros in any row, and how many rows fall into each
201:    * "bucket" of rows with same number of nonzeros. */
202:   maxnz = 0;
203:   for (i=0; i<m; i++) {
204:     nz_in_row[i] = ia[i+1]-ia[i];
205:     if (nz_in_row[i] > maxnz) maxnz = nz_in_row[i];
206:   }
207:   PetscMalloc1(PetscMax(maxnz,m)+1, &rows_in_bucket);
208:   PetscMalloc1(PetscMax(maxnz,m)+1, &ipnz);

210:   for (i=0; i<=maxnz; i++) {
211:     rows_in_bucket[i] = 0;
212:   }
213:   for (i=0; i<m; i++) {
214:     nz = nz_in_row[i];
215:     rows_in_bucket[nz]++;
216:   }

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

229:   /* Second pass.  Look at what is in the buckets and create the groupings.
230:    * Note that it is OK to have a group of rows with no non-zero values. */
231:   ngroup = 0;
232:   istart = 0;
233:   for (i=0; i<=maxnz; i++) {
234:     if (rows_in_bucket[i] > 0) {
235:       aijperm->nzgroup[ngroup] = i;
236:       aijperm->xgroup[ngroup]  = istart;
237:       ngroup++;
238:       istart += rows_in_bucket[i];
239:     }
240:   }

242:   aijperm->xgroup[ngroup] = istart;
243:   aijperm->ngroup         = ngroup;

245:   /* Now fill in the permutation vector iperm. */
246:   ipnz[0] = 0;
247:   for (i=0; i<maxnz; i++) {
248:     ipnz[i+1] = ipnz[i] + rows_in_bucket[i];
249:   }

251:   for (i=0; i<m; i++) {
252:     nz                   = nz_in_row[i];
253:     ipos                 = ipnz[nz];
254:     aijperm->iperm[ipos] = i;
255:     ipnz[nz]++;
256:   }

258:   /* Clean up temporary work arrays. */
259:   PetscFree(rows_in_bucket);
260:   PetscFree(ipnz);
261:   PetscFree(nz_in_row);
262:   return(0);
263: }


266: PetscErrorCode MatAssemblyEnd_SeqAIJPERM(Mat A, MatAssemblyType mode)
267: {
269:   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;

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

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

285:   /* Now calculate the permutation and grouping information. */
286:   MatSeqAIJPERM_create_perm(A);
287:   return(0);
288: }

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

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

326: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
327: #pragma disjoint(*x,*y,*aa)
328: #endif

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

337:   /* Get the info we need about the permutations and groupings. */
338:   iperm   = aijperm->iperm;
339:   ngroup  = aijperm->ngroup;
340:   xgroup  = aijperm->xgroup;
341:   nzgroup = aijperm->nzgroup;

343: #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJPERM) && defined(notworking)
344:   fortranmultaijperm_(&m,x,ii,aj,aa,y);
345: #else

347:   for (igroup=0; igroup<ngroup; igroup++) {
348:     jstart = xgroup[igroup];
349:     jend   = xgroup[igroup+1] - 1;
350:     nz     = nzgroup[igroup];

352:     /* Handle the special cases where the number of nonzeros per row
353:      * in the group is either 0 or 1. */
354:     if (nz == 0) {
355:       for (i=jstart; i<=jend; i++) {
356:         y[iperm[i]] = 0.0;
357:       }
358:     } else if (nz == 1) {
359:       for (i=jstart; i<=jend; i++) {
360:         iold    = iperm[i];
361:         ipos    = ai[iold];
362:         y[iold] = aa[ipos] * x[aj[ipos]];
363:       }
364:     } else {

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

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

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

376:         isize = iend - istart + 1;

378:         /* Initialize the yp[] array that will be used to hold part of
379:          * the permuted results vector, and figure out where in aa each
380:          * row of the chunk will begin. */
381:         for (i=0; i<isize; i++) {
382:           iold = iperm[istart + i];
383:           /* iold is a row number from the matrix A *before* reordering. */
384:           ip[i] = ai[iold];
385:           /* ip[i] tells us where the ith row of the chunk begins in aa. */
386:           yp[i] = (PetscScalar) 0.0;
387:         }

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

401: #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)
402:             vec_y = _mm512_setzero_pd();
403:             ipos = ip[i];
404:             for (j=0; j<(nz>>3); j++) {
405:               vec_idx  = _mm256_loadu_si256((__m256i const*)&aj[ipos]);
406:               vec_vals = _mm512_loadu_pd(&aa[ipos]);
407:               vec_x    = _mm512_i32gather_pd(vec_idx,x,_MM_SCALE_8);
408:               vec_y    = _mm512_fmadd_pd(vec_x,vec_vals,vec_y);
409:               ipos += 8;
410:             }
411:             if ((nz&0x07)>2) {
412:               mask     = (__mmask8)(0xff >> (8-(nz&0x07)));
413:               vec_idx  = _mm256_loadu_si256((__m256i const*)&aj[ipos]);
414:               vec_vals = _mm512_loadu_pd(&aa[ipos]);
415:               vec_x    = _mm512_mask_i32gather_pd(vec_x,mask,vec_idx,x,_MM_SCALE_8);
416:               vec_y    = _mm512_mask3_fmadd_pd(vec_x,vec_vals,vec_y,mask);
417:             } else if ((nz&0x07)==2) {
418:               yp[i] += aa[ipos]*x[aj[ipos]];
419:               yp[i] += aa[ipos+1]*x[aj[ipos+1]];
420:             } else if ((nz&0x07)==1) {
421:               yp[i] += aa[ipos]*x[aj[ipos]];
422:             }
423:             yp[i] += _mm512_reduce_add_pd(vec_y);
424: #else
425:             for (j=0; j<nz; j++) {
426:               ipos   = ip[i] + j;
427:               yp[i] += aa[ipos] * x[aj[ipos]];
428:             }
429: #endif
430:           }
431:         } else {
432:           /* Otherwise, there are enough rows in the chunk to make it
433:            * worthwhile to vectorize across the rows, that is, to do the
434:            * matvec by operating with "columns" of the chunk. */
435:           for (j=0; j<nz; j++) {
436: #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)
437:             vec_j = _mm256_set1_epi32(j);
438:             for (i=0; i<((isize>>3)<<3); i+=8) {
439:               vec_y    = _mm512_loadu_pd(&yp[i]);
440:               vec_ipos = _mm256_loadu_si256((__m256i const*)&ip[i]);
441:               vec_ipos = _mm256_add_epi32(vec_ipos,vec_j);
442:               vec_idx  = _mm256_i32gather_epi32(aj,vec_ipos,_MM_SCALE_4);
443:               vec_vals = _mm512_i32gather_pd(vec_ipos,aa,_MM_SCALE_8);
444:               vec_x    = _mm512_i32gather_pd(vec_idx,x,_MM_SCALE_8);
445:               vec_y    = _mm512_fmadd_pd(vec_x,vec_vals,vec_y);
446:               _mm512_storeu_pd(&yp[i],vec_y);
447:             }
448:             for (i=isize-(isize&0x07); i<isize; i++) {
449:               ipos = ip[i]+j;
450:               yp[i] += aa[ipos]*x[aj[ipos]];
451:             }
452: #else
453:             for (i=0; i<isize; i++) {
454:               ipos   = ip[i] + j;
455:               yp[i] += aa[ipos] * x[aj[ipos]];
456:             }
457: #endif
458:           }
459:         }

461: #if defined(PETSC_HAVE_CRAY_VECTOR)
462: #pragma _CRI ivdep
463: #endif
464:         /* Put results from yp[] into non-permuted result vector y. */
465:         for (i=0; i<isize; i++) {
466:           y[iperm[istart+i]] = yp[i];
467:         }
468:       } /* End processing chunk of isize rows of a group. */
469:     } /* End handling matvec for chunk with nz > 1. */
470:   } /* End loop over igroup. */
471: #endif
472:   PetscLogFlops(PetscMax(2.0*a->nz - A->rmap->n,0));
473:   VecRestoreArrayRead(xx,&x);
474:   VecRestoreArray(yy,&y);
475:   return(0);
476: }


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

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

519: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
520: #pragma disjoint(*x,*y,*aa)
521: #endif

524:   VecGetArrayRead(xx,&x);
525:   VecGetArrayPair(yy,ww,&y,&w);

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

531:   /* Get the info we need about the permutations and groupings. */
532:   aijperm = (Mat_SeqAIJPERM*) A->spptr;
533:   iperm   = aijperm->iperm;
534:   ngroup  = aijperm->ngroup;
535:   xgroup  = aijperm->xgroup;
536:   nzgroup = aijperm->nzgroup;

538: #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJPERM)
539:   fortranmultaddaijperm_(&m,x,ii,aj,aa,y,w);
540: #else

542:   for (igroup=0; igroup<ngroup; igroup++) {
543:     jstart = xgroup[igroup];
544:     jend   = xgroup[igroup+1] - 1;

546:     nz = nzgroup[igroup];

548:     /* Handle the special cases where the number of nonzeros per row
549:      * in the group is either 0 or 1. */
550:     if (nz == 0) {
551:       for (i=jstart; i<=jend; i++) {
552:         iold    = iperm[i];
553:         y[iold] = w[iold];
554:       }
555:     }
556:     else if (nz == 1) {
557:       for (i=jstart; i<=jend; i++) {
558:         iold    = iperm[i];
559:         ipos    = ai[iold];
560:         y[iold] = w[iold] + aa[ipos] * x[aj[ipos]];
561:       }
562:     }
563:     /* For the general case: */
564:     else {

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

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

576:         /* Initialize the yp[] array that will be used to hold part of
577:          * the permuted results vector, and figure out where in aa each
578:          * row of the chunk will begin. */
579:         for (i=0; i<isize; i++) {
580:           iold = iperm[istart + i];
581:           /* iold is a row number from the matrix A *before* reordering. */
582:           ip[i] = ai[iold];
583:           /* ip[i] tells us where the ith row of the chunk begins in aa. */
584:           yp[i] = w[iold];
585:         }

587:         /* If the number of zeros per row exceeds the number of rows in
588:          * the chunk, we should vectorize along nz, that is, perform the
589:          * mat-vec one row at a time as in the usual CSR case. */
590:         if (nz > isize) {
591: #if defined(PETSC_HAVE_CRAY_VECTOR)
592: #pragma _CRI preferstream
593: #endif
594:           for (i=0; i<isize; i++) {
595: #if defined(PETSC_HAVE_CRAY_VECTOR)
596: #pragma _CRI prefervector
597: #endif
598:             for (j=0; j<nz; j++) {
599:               ipos   = ip[i] + j;
600:               yp[i] += aa[ipos] * x[aj[ipos]];
601:             }
602:           }
603:         }
604:         /* Otherwise, there are enough rows in the chunk to make it
605:          * worthwhile to vectorize across the rows, that is, to do the
606:          * matvec by operating with "columns" of the chunk. */
607:         else {
608:           for (j=0; j<nz; j++) {
609:             for (i=0; i<isize; i++) {
610:               ipos   = ip[i] + j;
611:               yp[i] += aa[ipos] * x[aj[ipos]];
612:             }
613:           }
614:         }

616: #if defined(PETSC_HAVE_CRAY_VECTOR)
617: #pragma _CRI ivdep
618: #endif
619:         /* Put results from yp[] into non-permuted result vector y. */
620:         for (i=0; i<isize; i++) {
621:           y[iperm[istart+i]] = yp[i];
622:         }
623:       } /* End processing chunk of isize rows of a group. */

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

628: #endif
629:   PetscLogFlops(2.0*a->nz);
630:   VecRestoreArrayRead(xx,&x);
631:   VecRestoreArrayPair(yy,ww,&y,&w);
632:   return(0);
633: }

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

647:   if (reuse == MAT_INITIAL_MATRIX) {
648:     MatDuplicate(A,MAT_COPY_VALUES,&B);
649:   }
650:   PetscObjectTypeCompare((PetscObject)A,type,&sametype);
651:   if (sametype) return(0);

653:   PetscNewLog(B,&aijperm);
654:   B->spptr = (void*) aijperm;

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

663:   aijperm->nonzerostate = -1;  /* this will trigger the generation of the permutation information the first time through MatAssembly()*/
664:   /* If A has already been assembled, compute the permutation. */
665:   if (A->assembled) {
666:     MatSeqAIJPERM_create_perm(B);
667:   }

669:   PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaijperm_seqaij_C",MatConvert_SeqAIJPERM_SeqAIJ);
670:   PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaijperm_C",MatMatMultSymbolic_SeqDense_SeqAIJ);
671:   PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaijperm_C",MatMatMultNumeric_SeqDense_SeqAIJ);

673:   PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJPERM);
674:   *newmat = B;
675:   return(0);
676: }

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

689:    Collective

691:    Input Parameters:
692: +  comm - MPI communicator, set to PETSC_COMM_SELF
693: .  m - number of rows
694: .  n - number of columns
695: .  nz - number of nonzeros per row (same for all rows)
696: -  nnz - array containing the number of nonzeros in the various rows
697:          (possibly different for each row) or NULL

699:    Output Parameter:
700: .  A - the matrix

702:    Notes:
703:    If nnz is given then nz is ignored

705:    Level: intermediate

707: .seealso: MatCreate(), MatCreateMPIAIJPERM(), MatSetValues()
708: @*/
709: PetscErrorCode  MatCreateSeqAIJPERM(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
710: {

714:   MatCreate(comm,A);
715:   MatSetSizes(*A,m,n,m,n);
716:   MatSetType(*A,MATSEQAIJPERM);
717:   MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);
718:   return(0);
719: }

721: PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJPERM(Mat A)
722: {

726:   MatSetType(A,MATSEQAIJ);
727:   MatConvert_SeqAIJ_SeqAIJPERM(A,MATSEQAIJPERM,MAT_INPLACE_MATRIX,&A);
728:   return(0);
729: }