Actual source code: aijperm.c

  1: /*
  2:   Defines basic operations for the MATSEQAIJPERM matrix class.
  3:   This class is derived from the MATSEQAIJ class and retains the
  4:   compressed row storage (aka Yale sparse matrix format) but augments
  5:   it with some permutation information that enables some operations
  6:   to be more vectorizable.  A physically rearranged copy of the matrix
  7:   may be stored if the user desires.

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

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

 14: #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)
 15:   #include <immintrin.h>

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

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

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

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

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

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

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

 66:   PetscFunctionBegin;
 67:   if (reuse == MAT_INITIAL_MATRIX) {
 68:     PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &B));
 69:     aijperm = (Mat_SeqAIJPERM *)B->spptr;
 70:   }

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

 79:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaijperm_seqaij_C", NULL));

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

 87:   /* Change the type of B to MATSEQAIJ. */
 88:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ));

 90:   *newmat = B;
 91:   PetscFunctionReturn(PETSC_SUCCESS);
 92: }

 94: static PetscErrorCode MatDestroy_SeqAIJPERM(Mat A)
 95: {
 96:   Mat_SeqAIJPERM *aijperm = (Mat_SeqAIJPERM *)A->spptr;

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

117: static PetscErrorCode MatDuplicate_SeqAIJPERM(Mat A, MatDuplicateOption op, Mat *M)
118: {
119:   Mat_SeqAIJPERM *aijperm = (Mat_SeqAIJPERM *)A->spptr;
120:   Mat_SeqAIJPERM *aijperm_dest;
121:   PetscBool       perm;

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

153: static PetscErrorCode MatSeqAIJPERM_create_perm(Mat A)
154: {
155:   Mat_SeqAIJ     *a       = (Mat_SeqAIJ *)(A)->data;
156:   Mat_SeqAIJPERM *aijperm = (Mat_SeqAIJPERM *)A->spptr;
157:   PetscInt        m;     /* Number of rows in the matrix. */
158:   PetscInt       *ia;    /* From the CSR representation; points to the beginning  of each row. */
159:   PetscInt        maxnz; /* Maximum number of nonzeros in any row. */
160:   PetscInt       *rows_in_bucket;
161:   /* To construct the permutation, we sort each row into one of maxnz
162:    * buckets based on how many nonzeros are in the row. */
163:   PetscInt  nz;
164:   PetscInt *nz_in_row; /* the number of nonzero elements in row k. */
165:   PetscInt *ipnz;
166:   /* When constructing the iperm permutation vector,
167:    * ipnz[nz] is used to point to the next place in the permutation vector
168:    * that a row with nz nonzero elements should be placed.*/
169:   PetscInt i, ngroup, istart, ipos;

171:   PetscFunctionBegin;
172:   if (aijperm->nonzerostate == A->nonzerostate) PetscFunctionReturn(PETSC_SUCCESS); /* permutation exists and matches current nonzero structure */
173:   aijperm->nonzerostate = A->nonzerostate;
174:   /* Free anything previously put in the Mat_SeqAIJPERM data structure. */
175:   PetscCall(PetscFree(aijperm->xgroup));
176:   PetscCall(PetscFree(aijperm->nzgroup));
177:   PetscCall(PetscFree(aijperm->iperm));

179:   m  = A->rmap->n;
180:   ia = a->i;

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

185:   /* Allocate some temporary work arrays that will be used in
186:    * calculating the permutation vector and groupings. */
187:   PetscCall(PetscMalloc1(m, &nz_in_row));

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

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

202:   for (i = 0; i <= maxnz; i++) rows_in_bucket[i] = 0;
203:   for (i = 0; i < m; i++) {
204:     nz = nz_in_row[i];
205:     rows_in_bucket[nz]++;
206:   }

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

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

232:   aijperm->xgroup[ngroup] = istart;
233:   aijperm->ngroup         = ngroup;

235:   /* Now fill in the permutation vector iperm. */
236:   ipnz[0] = 0;
237:   for (i = 0; i < maxnz; i++) ipnz[i + 1] = ipnz[i] + rows_in_bucket[i];

239:   for (i = 0; i < m; i++) {
240:     nz                   = nz_in_row[i];
241:     ipos                 = ipnz[nz];
242:     aijperm->iperm[ipos] = i;
243:     ipnz[nz]++;
244:   }

246:   /* Clean up temporary work arrays. */
247:   PetscCall(PetscFree(rows_in_bucket));
248:   PetscCall(PetscFree(ipnz));
249:   PetscCall(PetscFree(nz_in_row));
250:   PetscFunctionReturn(PETSC_SUCCESS);
251: }

253: static PetscErrorCode MatAssemblyEnd_SeqAIJPERM(Mat A, MatAssemblyType mode)
254: {
255:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

257:   PetscFunctionBegin;
258:   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(PETSC_SUCCESS);

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

271:   /* Now calculate the permutation and grouping information. */
272:   PetscCall(MatSeqAIJPERM_create_perm(A));
273:   PetscFunctionReturn(PETSC_SUCCESS);
274: }

276: static PetscErrorCode MatMult_SeqAIJPERM(Mat A, Vec xx, Vec yy)
277: {
278:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
279:   const PetscScalar *x;
280:   PetscScalar       *y;
281:   const MatScalar   *aa;
282:   const PetscInt    *aj, *ai;
283:   PetscInt           i, j;
284: #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)
285:   __m512d  vec_x, vec_y, vec_vals;
286:   __m256i  vec_idx, vec_ipos, vec_j;
287:   __mmask8 mask;
288: #endif

290:   /* Variables that don't appear in MatMult_SeqAIJ. */
291:   Mat_SeqAIJPERM *aijperm = (Mat_SeqAIJPERM *)A->spptr;
292:   PetscInt       *iperm; /* Points to the permutation vector. */
293:   PetscInt       *xgroup;
294:   /* Denotes where groups of rows with same number of nonzeros
295:    * begin and end in iperm. */
296:   PetscInt *nzgroup;
297:   PetscInt  ngroup;
298:   PetscInt  igroup;
299:   PetscInt  jstart, jend;
300:   /* jstart is used in loops to denote the position in iperm where a
301:    * group starts; jend denotes the position where it ends.
302:    * (jend + 1 is where the next group starts.) */
303:   PetscInt    iold, nz;
304:   PetscInt    istart, iend, isize;
305:   PetscInt    ipos;
306:   PetscScalar yp[NDIM];
307:   PetscInt    ip[NDIM]; /* yp[] and ip[] are treated as vector "registers" for performing the mat-vec. */

309: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
310:   #pragma disjoint(*x, *y, *aa)
311: #endif

313:   PetscFunctionBegin;
314:   PetscCall(VecGetArrayRead(xx, &x));
315:   PetscCall(VecGetArray(yy, &y));
316:   aj = a->j; /* aj[k] gives column index for element aa[k]. */
317:   aa = a->a; /* Nonzero elements stored row-by-row. */
318:   ai = a->i; /* ai[k] is the position in aa and aj where row k starts. */

320:   /* Get the info we need about the permutations and groupings. */
321:   iperm   = aijperm->iperm;
322:   ngroup  = aijperm->ngroup;
323:   xgroup  = aijperm->xgroup;
324:   nzgroup = aijperm->nzgroup;

326:   for (igroup = 0; igroup < ngroup; igroup++) {
327:     jstart = xgroup[igroup];
328:     jend   = xgroup[igroup + 1] - 1;
329:     nz     = nzgroup[igroup];

331:     /* Handle the special cases where the number of nonzeros per row
332:      * in the group is either 0 or 1. */
333:     if (nz == 0) {
334:       for (i = jstart; i <= jend; i++) y[iperm[i]] = 0.0;
335:     } else if (nz == 1) {
336:       for (i = jstart; i <= jend; i++) {
337:         iold    = iperm[i];
338:         ipos    = ai[iold];
339:         y[iold] = aa[ipos] * x[aj[ipos]];
340:       }
341:     } else {
342:       /* We work our way through the current group in chunks of NDIM rows
343:        * at a time. */

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

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

352:         isize = iend - istart + 1;

354:         /* Initialize the yp[] array that will be used to hold part of
355:          * the permuted results vector, and figure out where in aa each
356:          * row of the chunk will begin. */
357:         for (i = 0; i < isize; i++) {
358:           iold = iperm[istart + i];
359:           /* iold is a row number from the matrix A *before* reordering. */
360:           ip[i] = ai[iold];
361:           /* ip[i] tells us where the ith row of the chunk begins in aa. */
362:           yp[i] = (PetscScalar)0.0;
363:         }

365:         /* If the number of zeros per row exceeds the number of rows in
366:          * the chunk, we should vectorize along nz, that is, perform the
367:          * mat-vec one row at a time as in the usual CSR case. */
368:         if (nz > isize) {
369: #if defined(PETSC_HAVE_CRAY_VECTOR)
370:   #pragma _CRI preferstream
371: #endif
372:           for (i = 0; i < isize; i++) {
373: #if defined(PETSC_HAVE_CRAY_VECTOR)
374:   #pragma _CRI prefervector
375: #endif

377: #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)
378:             vec_y = _mm512_setzero_pd();
379:             ipos  = ip[i];
380:             for (j = 0; j < (nz >> 3); j++) {
381:               vec_idx  = _mm256_loadu_si256((__m256i const *)&aj[ipos]);
382:               vec_vals = _mm512_loadu_pd(&aa[ipos]);
383:               vec_x    = _mm512_i32gather_pd(vec_idx, x, _MM_SCALE_8);
384:               vec_y    = _mm512_fmadd_pd(vec_x, vec_vals, vec_y);
385:               ipos += 8;
386:             }
387:             if ((nz & 0x07) > 2) {
388:               mask     = (__mmask8)(0xff >> (8 - (nz & 0x07)));
389:               vec_idx  = _mm256_loadu_si256((__m256i const *)&aj[ipos]);
390:               vec_vals = _mm512_loadu_pd(&aa[ipos]);
391:               vec_x    = _mm512_mask_i32gather_pd(vec_x, mask, vec_idx, x, _MM_SCALE_8);
392:               vec_y    = _mm512_mask3_fmadd_pd(vec_x, vec_vals, vec_y, mask);
393:             } else if ((nz & 0x07) == 2) {
394:               yp[i] += aa[ipos] * x[aj[ipos]];
395:               yp[i] += aa[ipos + 1] * x[aj[ipos + 1]];
396:             } else if ((nz & 0x07) == 1) {
397:               yp[i] += aa[ipos] * x[aj[ipos]];
398:             }
399:             yp[i] += _mm512_reduce_add_pd(vec_y);
400: #else
401:             for (j = 0; j < nz; j++) {
402:               ipos = ip[i] + j;
403:               yp[i] += aa[ipos] * x[aj[ipos]];
404:             }
405: #endif
406:           }
407:         } else {
408:           /* Otherwise, there are enough rows in the chunk to make it
409:            * worthwhile to vectorize across the rows, that is, to do the
410:            * matvec by operating with "columns" of the chunk. */
411:           for (j = 0; j < nz; j++) {
412: #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)
413:             vec_j = _mm256_set1_epi32(j);
414:             for (i = 0; i < ((isize >> 3) << 3); i += 8) {
415:               vec_y    = _mm512_loadu_pd(&yp[i]);
416:               vec_ipos = _mm256_loadu_si256((__m256i const *)&ip[i]);
417:               vec_ipos = _mm256_add_epi32(vec_ipos, vec_j);
418:               vec_idx  = _mm256_i32gather_epi32(aj, vec_ipos, _MM_SCALE_4);
419:               vec_vals = _mm512_i32gather_pd(vec_ipos, aa, _MM_SCALE_8);
420:               vec_x    = _mm512_i32gather_pd(vec_idx, x, _MM_SCALE_8);
421:               vec_y    = _mm512_fmadd_pd(vec_x, vec_vals, vec_y);
422:               _mm512_storeu_pd(&yp[i], vec_y);
423:             }
424:             for (i = isize - (isize & 0x07); i < isize; i++) {
425:               ipos = ip[i] + j;
426:               yp[i] += aa[ipos] * x[aj[ipos]];
427:             }
428: #else
429:             for (i = 0; i < isize; i++) {
430:               ipos = ip[i] + j;
431:               yp[i] += aa[ipos] * x[aj[ipos]];
432:             }
433: #endif
434:           }
435:         }

437: #if defined(PETSC_HAVE_CRAY_VECTOR)
438:   #pragma _CRI ivdep
439: #endif
440:         /* Put results from yp[] into non-permuted result vector y. */
441:         for (i = 0; i < isize; i++) y[iperm[istart + i]] = yp[i];
442:       } /* End processing chunk of isize rows of a group. */
443:     } /* End handling matvec for chunk with nz > 1. */
444:   } /* End loop over igroup. */
445:   PetscCall(PetscLogFlops(PetscMax(2.0 * a->nz - A->rmap->n, 0)));
446:   PetscCall(VecRestoreArrayRead(xx, &x));
447:   PetscCall(VecRestoreArray(yy, &y));
448:   PetscFunctionReturn(PETSC_SUCCESS);
449: }

451: /* MatMultAdd_SeqAIJPERM() calculates yy = ww + A * xx.
452:  * Note that the names I used to designate the vectors differs from that
453:  * used in MatMultAdd_SeqAIJ().  I did this to keep my notation consistent
454:  * with the MatMult_SeqAIJPERM() routine, which is very similar to this one. */
455: /*
456:     I hate having virtually identical code for the mult and the multadd!!!
457: */
458: static PetscErrorCode MatMultAdd_SeqAIJPERM(Mat A, Vec xx, Vec ww, Vec yy)
459: {
460:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
461:   const PetscScalar *x;
462:   PetscScalar       *y, *w;
463:   const MatScalar   *aa;
464:   const PetscInt    *aj, *ai;
465:   PetscInt           i, j;

467:   /* Variables that don't appear in MatMultAdd_SeqAIJ. */
468:   Mat_SeqAIJPERM *aijperm;
469:   PetscInt       *iperm; /* Points to the permutation vector. */
470:   PetscInt       *xgroup;
471:   /* Denotes where groups of rows with same number of nonzeros
472:    * begin and end in iperm. */
473:   PetscInt *nzgroup;
474:   PetscInt  ngroup;
475:   PetscInt  igroup;
476:   PetscInt  jstart, jend;
477:   /* jstart is used in loops to denote the position in iperm where a
478:    * group starts; jend denotes the position where it ends.
479:    * (jend + 1 is where the next group starts.) */
480:   PetscInt    iold, nz;
481:   PetscInt    istart, iend, isize;
482:   PetscInt    ipos;
483:   PetscScalar yp[NDIM];
484:   PetscInt    ip[NDIM];
485:   /* yp[] and ip[] are treated as vector "registers" for performing
486:    * the mat-vec. */

488: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
489:   #pragma disjoint(*x, *y, *aa)
490: #endif

492:   PetscFunctionBegin;
493:   PetscCall(VecGetArrayRead(xx, &x));
494:   PetscCall(VecGetArrayPair(yy, ww, &y, &w));

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

500:   /* Get the info we need about the permutations and groupings. */
501:   aijperm = (Mat_SeqAIJPERM *)A->spptr;
502:   iperm   = aijperm->iperm;
503:   ngroup  = aijperm->ngroup;
504:   xgroup  = aijperm->xgroup;
505:   nzgroup = aijperm->nzgroup;

507:   for (igroup = 0; igroup < ngroup; igroup++) {
508:     jstart = xgroup[igroup];
509:     jend   = xgroup[igroup + 1] - 1;

511:     nz = nzgroup[igroup];

513:     /* Handle the special cases where the number of nonzeros per row
514:      * in the group is either 0 or 1. */
515:     if (nz == 0) {
516:       for (i = jstart; i <= jend; i++) {
517:         iold    = iperm[i];
518:         y[iold] = w[iold];
519:       }
520:     } else if (nz == 1) {
521:       for (i = jstart; i <= jend; i++) {
522:         iold    = iperm[i];
523:         ipos    = ai[iold];
524:         y[iold] = w[iold] + aa[ipos] * x[aj[ipos]];
525:       }
526:     }
527:     /* For the general case: */
528:     else {
529:       /* We work our way through the current group in chunks of NDIM rows
530:        * at a time. */

532:       for (istart = jstart; istart <= jend; istart += NDIM) {
533:         /* Figure out where the chunk of 'isize' rows ends in iperm.
534:          * 'isize may of course be less than NDIM for the last chunk. */
535:         iend = istart + (NDIM - 1);
536:         if (iend > jend) iend = jend;
537:         isize = iend - istart + 1;

539:         /* Initialize the yp[] array that will be used to hold part of
540:          * the permuted results vector, and figure out where in aa each
541:          * row of the chunk will begin. */
542:         for (i = 0; i < isize; i++) {
543:           iold = iperm[istart + i];
544:           /* iold is a row number from the matrix A *before* reordering. */
545:           ip[i] = ai[iold];
546:           /* ip[i] tells us where the ith row of the chunk begins in aa. */
547:           yp[i] = w[iold];
548:         }

550:         /* If the number of zeros per row exceeds the number of rows in
551:          * the chunk, we should vectorize along nz, that is, perform the
552:          * mat-vec one row at a time as in the usual CSR case. */
553:         if (nz > isize) {
554: #if defined(PETSC_HAVE_CRAY_VECTOR)
555:   #pragma _CRI preferstream
556: #endif
557:           for (i = 0; i < isize; i++) {
558: #if defined(PETSC_HAVE_CRAY_VECTOR)
559:   #pragma _CRI prefervector
560: #endif
561:             for (j = 0; j < nz; j++) {
562:               ipos = ip[i] + j;
563:               yp[i] += aa[ipos] * x[aj[ipos]];
564:             }
565:           }
566:         }
567:         /* Otherwise, there are enough rows in the chunk to make it
568:          * worthwhile to vectorize across the rows, that is, to do the
569:          * matvec by operating with "columns" of the chunk. */
570:         else {
571:           for (j = 0; j < nz; j++) {
572:             for (i = 0; i < isize; i++) {
573:               ipos = ip[i] + j;
574:               yp[i] += aa[ipos] * x[aj[ipos]];
575:             }
576:           }
577:         }

579: #if defined(PETSC_HAVE_CRAY_VECTOR)
580:   #pragma _CRI ivdep
581: #endif
582:         /* Put results from yp[] into non-permuted result vector y. */
583:         for (i = 0; i < isize; i++) y[iperm[istart + i]] = yp[i];
584:       } /* End processing chunk of isize rows of a group. */

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

589:   PetscCall(PetscLogFlops(2.0 * a->nz));
590:   PetscCall(VecRestoreArrayRead(xx, &x));
591:   PetscCall(VecRestoreArrayPair(yy, ww, &y, &w));
592:   PetscFunctionReturn(PETSC_SUCCESS);
593: }

595: /* MatConvert_SeqAIJ_SeqAIJPERM converts a SeqAIJ matrix into a
596:  * SeqAIJPERM matrix.  This routine is called by the MatCreate_SeqAIJPERM()
597:  * routine, but can also be used to convert an assembled SeqAIJ matrix
598:  * into a SeqAIJPERM one. */
599: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJPERM(Mat A, MatType type, MatReuse reuse, Mat *newmat)
600: {
601:   Mat             B = *newmat;
602:   Mat_SeqAIJPERM *aijperm;
603:   PetscBool       sametype;

605:   PetscFunctionBegin;
606:   if (reuse == MAT_INITIAL_MATRIX) PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &B));
607:   PetscCall(PetscObjectTypeCompare((PetscObject)A, type, &sametype));
608:   if (sametype) PetscFunctionReturn(PETSC_SUCCESS);

610:   PetscCall(PetscNew(&aijperm));
611:   B->spptr = (void *)aijperm;

613:   /* Set function pointers for methods that we inherit from AIJ but override. */
614:   B->ops->duplicate   = MatDuplicate_SeqAIJPERM;
615:   B->ops->assemblyend = MatAssemblyEnd_SeqAIJPERM;
616:   B->ops->destroy     = MatDestroy_SeqAIJPERM;
617:   B->ops->mult        = MatMult_SeqAIJPERM;
618:   B->ops->multadd     = MatMultAdd_SeqAIJPERM;

620:   aijperm->nonzerostate = -1; /* this will trigger the generation of the permutation information the first time through MatAssembly()*/
621:   /* If A has already been assembled, compute the permutation. */
622:   if (A->assembled) PetscCall(MatSeqAIJPERM_create_perm(B));

624:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaijperm_seqaij_C", MatConvert_SeqAIJPERM_SeqAIJ));

626:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJPERM));
627:   *newmat = B;
628:   PetscFunctionReturn(PETSC_SUCCESS);
629: }

631: /*@C
632:   MatCreateSeqAIJPERM - Creates a sparse matrix of type `MATSEQAIJPERM`.

634:   Collective

636:   Input Parameters:
637: + comm - MPI communicator, set to `PETSC_COMM_SELF`
638: . m    - number of rows
639: . n    - number of columns
640: . nz   - number of nonzeros per row (same for all rows), ignored if `nnz` is given
641: - nnz  - array containing the number of nonzeros in the various rows (possibly different for each row) or `NULL`

643:   Output Parameter:
644: . A - the matrix

646:   Level: intermediate

648:   Notes:
649:   This type inherits from `MATSEQAIJ`, but calculates some additional permutation information
650:   that is used to allow better vectorization of some operations.  At the cost of increased
651:   storage, the `MATSEQAIJ` formatted matrix can be copied to a format in which pieces of the
652:   matrix are stored in ELLPACK format, allowing the vectorized matrix multiply routine to use
653:   stride-1 memory accesses.

655: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateMPIAIJPERM()`, `MatSetValues()`
656: @*/
657: PetscErrorCode MatCreateSeqAIJPERM(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
658: {
659:   PetscFunctionBegin;
660:   PetscCall(MatCreate(comm, A));
661:   PetscCall(MatSetSizes(*A, m, n, m, n));
662:   PetscCall(MatSetType(*A, MATSEQAIJPERM));
663:   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, nnz));
664:   PetscFunctionReturn(PETSC_SUCCESS);
665: }

667: PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJPERM(Mat A)
668: {
669:   PetscFunctionBegin;
670:   PetscCall(MatSetType(A, MATSEQAIJ));
671:   PetscCall(MatConvert_SeqAIJ_SeqAIJPERM(A, MATSEQAIJPERM, MAT_INPLACE_MATRIX, &A));
672:   PetscFunctionReturn(PETSC_SUCCESS);
673: }