Actual source code: aijperm.c
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: }