Actual source code: matptap.c
petsc-3.8.4 2018-03-24
2: /*
3: Defines projective product routines where A is a SeqAIJ matrix
4: C = P^T * A * P
5: */
7: #include <../src/mat/impls/aij/seq/aij.h>
8: #include <../src/mat/utils/freespace.h>
9: #include <petscbt.h>
10: #include <petsctime.h>
12: #if defined(PETSC_HAVE_HYPRE)
13: PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*);
14: #endif
16: PETSC_INTERN PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
17: {
19: #if !defined(PETSC_HAVE_HYPRE)
20: const char *algTypes[2] = {"scalable","nonscalable"};
21: PetscInt nalg = 2;
22: #else
23: const char *algTypes[3] = {"scalable","nonscalable","hypre"};
24: PetscInt nalg = 3;
25: #endif
26: PetscInt alg = 0; /* set default algorithm */
29: if (scall == MAT_INITIAL_MATRIX) {
30: /*
31: Alg 'scalable' determines which implementations to be used:
32: "nonscalable": do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P;
33: "scalable": do two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P.
34: "hypre": use boomerAMGBuildCoarseOperator.
35: */
36: PetscObjectOptionsBegin((PetscObject)A);
37: PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
38: PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,NULL);
39: PetscOptionsEnd();
40: PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);
41: switch (alg) {
42: case 1:
43: MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(A,P,fill,C);
44: break;
45: #if defined(PETSC_HAVE_HYPRE)
46: case 2:
47: MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);
48: break;
49: #endif
50: default:
51: MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
52: break;
53: }
54: PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);
55: }
56: PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);
57: (*(*C)->ops->ptapnumeric)(A,P,*C);
58: PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);
59: return(0);
60: }
62: PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A)
63: {
65: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
66: Mat_PtAP *ptap = a->ptap;
69: PetscFree(ptap->apa);
70: PetscFree(ptap->api);
71: PetscFree(ptap->apj);
72: (ptap->destroy)(A);
73: PetscFree(ptap);
74: return(0);
75: }
77: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
78: {
79: PetscErrorCode ierr;
80: PetscFreeSpaceList free_space=NULL,current_space=NULL;
81: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
82: PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
83: PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
84: PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
85: PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
86: MatScalar *ca;
87: PetscBT lnkbt;
88: PetscReal afill;
91: /* Get ij structure of P^T */
92: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
93: ptJ = ptj;
95: /* Allocate ci array, arrays for fill computation and */
96: /* free space for accumulating nonzero column info */
97: PetscMalloc1(pn+1,&ci);
98: ci[0] = 0;
100: PetscCalloc1(2*an+1,&ptadenserow);
101: ptasparserow = ptadenserow + an;
103: /* create and initialize a linked list */
104: nlnk = pn+1;
105: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
107: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
108: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);
109: current_space = free_space;
111: /* Determine symbolic info for each row of C: */
112: for (i=0; i<pn; i++) {
113: ptnzi = pti[i+1] - pti[i];
114: ptanzi = 0;
115: /* Determine symbolic row of PtA: */
116: for (j=0; j<ptnzi; j++) {
117: arow = *ptJ++;
118: anzj = ai[arow+1] - ai[arow];
119: ajj = aj + ai[arow];
120: for (k=0; k<anzj; k++) {
121: if (!ptadenserow[ajj[k]]) {
122: ptadenserow[ajj[k]] = -1;
123: ptasparserow[ptanzi++] = ajj[k];
124: }
125: }
126: }
127: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
128: ptaj = ptasparserow;
129: cnzi = 0;
130: for (j=0; j<ptanzi; j++) {
131: prow = *ptaj++;
132: pnzj = pi[prow+1] - pi[prow];
133: pjj = pj + pi[prow];
134: /* add non-zero cols of P into the sorted linked list lnk */
135: PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);
136: cnzi += nlnk;
137: }
139: /* If free space is not available, make more free space */
140: /* Double the amount of total space in the list */
141: if (current_space->local_remaining<cnzi) {
142: PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);
143: nspacedouble++;
144: }
146: /* Copy data into free space, and zero out denserows */
147: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
149: current_space->array += cnzi;
150: current_space->local_used += cnzi;
151: current_space->local_remaining -= cnzi;
153: for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
155: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
156: /* For now, we will recompute what is needed. */
157: ci[i+1] = ci[i] + cnzi;
158: }
159: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
160: /* Allocate space for cj, initialize cj, and */
161: /* destroy list of free space and other temporary array(s) */
162: PetscMalloc1(ci[pn]+1,&cj);
163: PetscFreeSpaceContiguous(&free_space,cj);
164: PetscFree(ptadenserow);
165: PetscLLDestroy(lnk,lnkbt);
167: PetscCalloc1(ci[pn]+1,&ca);
169: /* put together the new matrix */
170: MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);
171: MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));
173: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
174: /* Since these are PETSc arrays, change flags to free them as necessary. */
175: c = (Mat_SeqAIJ*)((*C)->data);
176: c->free_a = PETSC_TRUE;
177: c->free_ij = PETSC_TRUE;
178: c->nonew = 0;
179: (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
181: /* set MatInfo */
182: afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
183: if (afill < 1.0) afill = 1.0;
184: c->maxnz = ci[pn];
185: c->nz = ci[pn];
186: (*C)->info.mallocs = nspacedouble;
187: (*C)->info.fill_ratio_given = fill;
188: (*C)->info.fill_ratio_needed = afill;
190: /* Clean up. */
191: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
192: #if defined(PETSC_USE_INFO)
193: if (ci[pn] != 0) {
194: PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
195: PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
196: } else {
197: PetscInfo((*C),"Empty matrix product\n");
198: }
199: #endif
200: return(0);
201: }
203: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
204: {
206: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
207: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
208: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
209: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
210: PetscInt *ci=c->i,*cj=c->j,*cjj;
211: PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
212: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
213: MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
216: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
217: PetscMalloc3(cn,&apa,cn,&apjdense,cn,&apj);
218: PetscMemzero(apa,cn*sizeof(MatScalar));
219: PetscMemzero(apjdense,cn*sizeof(PetscInt));
221: /* Clear old values in C */
222: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
224: for (i=0; i<am; i++) {
225: /* Form sparse row of A*P */
226: anzi = ai[i+1] - ai[i];
227: apnzj = 0;
228: for (j=0; j<anzi; j++) {
229: prow = *aj++;
230: pnzj = pi[prow+1] - pi[prow];
231: pjj = pj + pi[prow];
232: paj = pa + pi[prow];
233: for (k=0; k<pnzj; k++) {
234: if (!apjdense[pjj[k]]) {
235: apjdense[pjj[k]] = -1;
236: apj[apnzj++] = pjj[k];
237: }
238: apa[pjj[k]] += (*aa)*paj[k];
239: }
240: PetscLogFlops(2.0*pnzj);
241: aa++;
242: }
244: /* Sort the j index array for quick sparse axpy. */
245: /* Note: a array does not need sorting as it is in dense storage locations. */
246: PetscSortInt(apnzj,apj);
248: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
249: pnzi = pi[i+1] - pi[i];
250: for (j=0; j<pnzi; j++) {
251: nextap = 0;
252: crow = *pJ++;
253: cjj = cj + ci[crow];
254: caj = ca + ci[crow];
255: /* Perform sparse axpy operation. Note cjj includes apj. */
256: for (k=0; nextap<apnzj; k++) {
257: #if defined(PETSC_USE_DEBUG)
258: if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
259: #endif
260: if (cjj[k]==apj[nextap]) {
261: caj[k] += (*pA)*apa[apj[nextap++]];
262: }
263: }
264: PetscLogFlops(2.0*apnzj);
265: pA++;
266: }
268: /* Zero the current row info for A*P */
269: for (j=0; j<apnzj; j++) {
270: apa[apj[j]] = 0.;
271: apjdense[apj[j]] = 0;
272: }
273: }
275: /* Assemble the final matrix and clean up */
276: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
277: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
279: PetscFree3(apa,apjdense,apj);
280: return(0);
281: }
283: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
284: {
286: Mat_SeqAIJ *ap,*c;
287: PetscInt *api,*apj,*ci,pn=P->cmap->N;
288: MatScalar *ca;
289: Mat_PtAP *ptap;
290: Mat Pt,AP;
293: /* Get symbolic Pt = P^T */
294: MatTransposeSymbolic_SeqAIJ(P,&Pt);
296: /* Get symbolic AP = A*P */
297: MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);
299: ap = (Mat_SeqAIJ*)AP->data;
300: api = ap->i;
301: apj = ap->j;
302: ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */
304: /* Get C = Pt*AP */
305: MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);
307: c = (Mat_SeqAIJ*)(*C)->data;
308: ci = c->i;
309: PetscCalloc1(ci[pn]+1,&ca);
310: c->a = ca;
311: c->free_a = PETSC_TRUE;
313: /* Create a supporting struct for reuse by MatPtAPNumeric() */
314: PetscNew(&ptap);
316: c->ptap = ptap;
317: ptap->destroy = (*C)->ops->destroy;
318: (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP;
320: /* Allocate temporary array for storage of one row of A*P */
321: PetscCalloc1(pn+1,&ptap->apa);
323: (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
325: ptap->api = api;
326: ptap->apj = apj;
328: /* Clean up. */
329: MatDestroy(&Pt);
330: MatDestroy(&AP);
331: #if defined(PETSC_USE_INFO)
332: PetscInfo1((*C),"given fill %g\n",(double)fill);
333: #endif
334: return(0);
335: }
337: /* #define PROFILE_MatPtAPNumeric */
338: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
339: {
340: PetscErrorCode ierr;
341: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
342: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
343: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
344: const PetscInt *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j;
345: const PetscScalar *aa=a->a,*pa=p->a,*pval;
346: const PetscInt *apj,*pcol,*cjj;
347: const PetscInt am=A->rmap->N,cm=C->rmap->N;
348: PetscInt i,j,k,anz,apnz,pnz,prow,crow,cnz;
349: PetscScalar *apa,*ca=c->a,*caj,pvalj;
350: Mat_PtAP *ptap = c->ptap;
351: #if defined(PROFILE_MatPtAPNumeric)
352: PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0;
353: PetscInt flops0=0,flops1=0;
354: #endif
357: /* Get temporary array for storage of one row of A*P */
358: apa = ptap->apa;
360: /* Clear old values in C */
361: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
363: for (i=0; i<am; i++) {
364: /* Form sparse row of AP[i,:] = A[i,:]*P */
365: #if defined(PROFILE_MatPtAPNumeric)
366: PetscTime(&t0);
367: #endif
368: anz = ai[i+1] - ai[i];
369: for (j=0; j<anz; j++) {
370: prow = aj[j];
371: pnz = pi[prow+1] - pi[prow];
372: pcol = pj + pi[prow];
373: pval = pa + pi[prow];
374: for (k=0; k<pnz; k++) {
375: apa[pcol[k]] += aa[j]*pval[k];
376: }
377: PetscLogFlops(2.0*pnz);
378: #if defined(PROFILE_MatPtAPNumeric)
379: flops0 += 2.0*pnz;
380: #endif
381: }
382: aj += anz; aa += anz;
383: #if defined(PROFILE_MatPtAPNumeric)
384: PetscTime(&tf);
386: time_Cseq0 += tf - t0;
387: #endif
389: /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */
390: #if defined(PROFILE_MatPtAPNumeric)
391: PetscTime(&t0);
392: #endif
393: apj = ptap->apj + ptap->api[i];
394: apnz = ptap->api[i+1] - ptap->api[i];
395: pnz = pi[i+1] - pi[i];
396: pcol = pj + pi[i];
397: pval = pa + pi[i];
399: /* Perform dense axpy */
400: for (j=0; j<pnz; j++) {
401: crow = pcol[j];
402: cjj = cj + ci[crow];
403: caj = ca + ci[crow];
404: pvalj = pval[j];
405: cnz = ci[crow+1] - ci[crow];
406: for (k=0; k<cnz; k++) caj[k] += pvalj*apa[cjj[k]];
407: PetscLogFlops(2.0*cnz);
408: #if defined(PROFILE_MatPtAPNumeric)
409: flops1 += 2.0*cnz;
410: #endif
411: }
412: #if defined(PROFILE_MatPtAPNumeric)
413: PetscTime(&tf);
414: time_Cseq1 += tf - t0;
415: #endif
417: /* Zero the current row info for A*P */
418: for (j=0; j<apnz; j++) apa[apj[j]] = 0.0;
419: }
421: /* Assemble the final matrix and clean up */
422: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
423: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
424: #if defined(PROFILE_MatPtAPNumeric)
425: printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1);
426: #endif
427: return(0);
428: }