Actual source code: matptap.c
petsc-dev 2014-02-02
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> /*I "petscmat.h" I*/
8: #include <../src/mat/utils/freespace.h>
9: #include <petscbt.h>
10: #include <petsctime.h>
14: PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
15: {
17: const char *algTypes[2] = {"scalable","nonscalable"};
18: PetscInt alg=0; /* set default algorithm */
21: if (scall == MAT_INITIAL_MATRIX) {
22: /*
23: Alg 'scalable' determines which implementations to be used:
24: "nonscalable": do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P;
25: "scalable": do two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P.
26: */
27: PetscObjectOptionsBegin((PetscObject)A);
28: PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,2,algTypes[0],&alg,NULL);
29: PetscOptionsEnd();
30: PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);
31: switch (alg) {
32: case 1:
33: MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(A,P,fill,C);
34: break;
35: default:
36: MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
37: break;
38: }
39: PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);
40: }
41: PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);
42: (*(*C)->ops->ptapnumeric)(A,P,*C);
43: PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);
44: return(0);
45: }
49: PetscErrorCode MatDestroy_SeqAIJ_PtAP(Mat A)
50: {
52: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
53: Mat_PtAP *ptap = a->ptap;
56: PetscFree(ptap->apa);
57: PetscFree(ptap->api);
58: PetscFree(ptap->apj);
59: (ptap->destroy)(A);
60: PetscFree(ptap);
61: return(0);
62: }
66: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
67: {
68: PetscErrorCode ierr;
69: PetscFreeSpaceList free_space=NULL,current_space=NULL;
70: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
71: PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
72: PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
73: PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
74: PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
75: MatScalar *ca;
76: PetscBT lnkbt;
77: PetscReal afill;
80: /* Get ij structure of P^T */
81: MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
82: ptJ = ptj;
84: /* Allocate ci array, arrays for fill computation and */
85: /* free space for accumulating nonzero column info */
86: PetscMalloc1((pn+1),&ci);
87: ci[0] = 0;
89: PetscCalloc1(2*an+1,&ptadenserow);
90: ptasparserow = ptadenserow + an;
92: /* create and initialize a linked list */
93: nlnk = pn+1;
94: PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);
96: /* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
97: PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+pi[pm])),&free_space);
98: current_space = free_space;
100: /* Determine symbolic info for each row of C: */
101: for (i=0; i<pn; i++) {
102: ptnzi = pti[i+1] - pti[i];
103: ptanzi = 0;
104: /* Determine symbolic row of PtA: */
105: for (j=0; j<ptnzi; j++) {
106: arow = *ptJ++;
107: anzj = ai[arow+1] - ai[arow];
108: ajj = aj + ai[arow];
109: for (k=0; k<anzj; k++) {
110: if (!ptadenserow[ajj[k]]) {
111: ptadenserow[ajj[k]] = -1;
112: ptasparserow[ptanzi++] = ajj[k];
113: }
114: }
115: }
116: /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
117: ptaj = ptasparserow;
118: cnzi = 0;
119: for (j=0; j<ptanzi; j++) {
120: prow = *ptaj++;
121: pnzj = pi[prow+1] - pi[prow];
122: pjj = pj + pi[prow];
123: /* add non-zero cols of P into the sorted linked list lnk */
124: PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);
125: cnzi += nlnk;
126: }
128: /* If free space is not available, make more free space */
129: /* Double the amount of total space in the list */
130: if (current_space->local_remaining<cnzi) {
131: PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);
132: nspacedouble++;
133: }
135: /* Copy data into free space, and zero out denserows */
136: PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);
138: current_space->array += cnzi;
139: current_space->local_used += cnzi;
140: current_space->local_remaining -= cnzi;
142: for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
144: /* Aside: Perhaps we should save the pta info for the numerical factorization. */
145: /* For now, we will recompute what is needed. */
146: ci[i+1] = ci[i] + cnzi;
147: }
148: /* nnz is now stored in ci[ptm], column indices are in the list of free space */
149: /* Allocate space for cj, initialize cj, and */
150: /* destroy list of free space and other temporary array(s) */
151: PetscMalloc1((ci[pn]+1),&cj);
152: PetscFreeSpaceContiguous(&free_space,cj);
153: PetscFree(ptadenserow);
154: PetscLLDestroy(lnk,lnkbt);
156: PetscCalloc1((ci[pn]+1),&ca);
158: /* put together the new matrix */
159: MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);
161: (*C)->rmap->bs = P->cmap->bs;
162: (*C)->cmap->bs = P->cmap->bs;
164: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
165: /* Since these are PETSc arrays, change flags to free them as necessary. */
166: c = (Mat_SeqAIJ*)((*C)->data);
167: c->free_a = PETSC_TRUE;
168: c->free_ij = PETSC_TRUE;
169: c->nonew = 0;
170: (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
172: /* set MatInfo */
173: afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
174: if (afill < 1.0) afill = 1.0;
175: c->maxnz = ci[pn];
176: c->nz = ci[pn];
177: (*C)->info.mallocs = nspacedouble;
178: (*C)->info.fill_ratio_given = fill;
179: (*C)->info.fill_ratio_needed = afill;
181: /* Clean up. */
182: MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);
183: #if defined(PETSC_USE_INFO)
184: if (ci[pn] != 0) {
185: PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
186: PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);
187: } else {
188: PetscInfo((*C),"Empty matrix product\n");
189: }
190: #endif
191: return(0);
192: }
196: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,Mat C)
197: {
199: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
200: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
201: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
202: PetscInt *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
203: PetscInt *ci=c->i,*cj=c->j,*cjj;
204: PetscInt am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
205: PetscInt i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
206: MatScalar *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
209: /* Allocate temporary array for storage of one row of A*P (cn: non-scalable) */
210: PetscMalloc3(cn,&apa,cn,&apjdense,c->rmax,&apj);
211: PetscMemzero(apa,cn*sizeof(MatScalar));
212: PetscMemzero(apjdense,cn*sizeof(PetscInt));
214: /* Clear old values in C */
215: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
217: for (i=0; i<am; i++) {
218: /* Form sparse row of A*P */
219: anzi = ai[i+1] - ai[i];
220: apnzj = 0;
221: for (j=0; j<anzi; j++) {
222: prow = *aj++;
223: pnzj = pi[prow+1] - pi[prow];
224: pjj = pj + pi[prow];
225: paj = pa + pi[prow];
226: for (k=0; k<pnzj; k++) {
227: if (!apjdense[pjj[k]]) {
228: apjdense[pjj[k]] = -1;
229: apj[apnzj++] = pjj[k];
230: }
231: apa[pjj[k]] += (*aa)*paj[k];
232: }
233: PetscLogFlops(2.0*pnzj);
234: aa++;
235: }
237: /* Sort the j index array for quick sparse axpy. */
238: /* Note: a array does not need sorting as it is in dense storage locations. */
239: PetscSortInt(apnzj,apj);
241: /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
242: pnzi = pi[i+1] - pi[i];
243: for (j=0; j<pnzi; j++) {
244: nextap = 0;
245: crow = *pJ++;
246: cjj = cj + ci[crow];
247: caj = ca + ci[crow];
248: /* Perform sparse axpy operation. Note cjj includes apj. */
249: for (k=0; nextap<apnzj; k++) {
250: #if defined(PETSC_USE_DEBUG)
251: if (k >= ci[crow+1] - ci[crow]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
252: #endif
253: if (cjj[k]==apj[nextap]) {
254: caj[k] += (*pA)*apa[apj[nextap++]];
255: }
256: }
257: PetscLogFlops(2.0*apnzj);
258: pA++;
259: }
261: /* Zero the current row info for A*P */
262: for (j=0; j<apnzj; j++) {
263: apa[apj[j]] = 0.;
264: apjdense[apj[j]] = 0;
265: }
266: }
268: /* Assemble the final matrix and clean up */
269: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
270: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
272: PetscFree3(apa,apjdense,apj);
273: return(0);
274: }
278: PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
279: {
281: Mat_SeqAIJ *ap,*c;
282: PetscInt *api,*apj,*ci,pn=P->cmap->N;
283: MatScalar *ca;
284: Mat_PtAP *ptap;
285: Mat Pt,AP;
288: /* Get symbolic Pt = P^T */
289: MatTransposeSymbolic_SeqAIJ(P,&Pt);
291: /* Get symbolic AP = A*P */
292: MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);
294: ap = (Mat_SeqAIJ*)AP->data;
295: api = ap->i;
296: apj = ap->j;
297: ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */
299: /* Get C = Pt*AP */
300: MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);
302: c = (Mat_SeqAIJ*)(*C)->data;
303: ci = c->i;
304: PetscCalloc1(ci[pn]+1,&ca);
305: c->a = ca;
306: c->free_a = PETSC_TRUE;
308: /* Create a supporting struct for reuse by MatPtAPNumeric() */
309: PetscNew(&ptap);
311: c->ptap = ptap;
312: ptap->destroy = (*C)->ops->destroy;
313: (*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP;
315: /* Allocate temporary array for storage of one row of A*P */
316: PetscCalloc1(pn+1,&ptap->apa);
318: (*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
320: ptap->api = api;
321: ptap->apj = apj;
323: /* Clean up. */
324: MatDestroy(&Pt);
325: MatDestroy(&AP);
326: #if defined(PETSC_USE_INFO)
327: PetscInfo1((*C),"given fill %g\n",(double)fill);
328: #endif
329: return(0);
330: }
332: /* #define PROFILE_MatPtAPNumeric */
335: PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
336: {
337: PetscErrorCode ierr;
338: Mat_SeqAIJ *a = (Mat_SeqAIJ*) A->data;
339: Mat_SeqAIJ *p = (Mat_SeqAIJ*) P->data;
340: Mat_SeqAIJ *c = (Mat_SeqAIJ*) C->data;
341: const PetscInt *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*ci=c->i,*cj=c->j;
342: const PetscScalar *aa=a->a,*pa=p->a,*pval;
343: const PetscInt *apj,*pcol,*cjj;
344: const PetscInt am=A->rmap->N,cm=C->rmap->N;
345: PetscInt i,j,k,anz,apnz,pnz,prow,crow,cnz;
346: PetscScalar *apa,*ca=c->a,*caj,pvalj;
347: Mat_PtAP *ptap = c->ptap;
348: #if defined(PROFILE_MatPtAPNumeric)
349: PetscLogDouble t0,tf,time_Cseq0=0.0,time_Cseq1=0.0;
350: PetscInt flops0=0,flops1=0;
351: #endif
354: /* Get temporary array for storage of one row of A*P */
355: apa = ptap->apa;
357: /* Clear old values in C */
358: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
360: for (i=0; i<am; i++) {
361: /* Form sparse row of AP[i,:] = A[i,:]*P */
362: #if defined(PROFILE_MatPtAPNumeric)
363: PetscTime(&t0);
364: #endif
365: anz = ai[i+1] - ai[i];
366: apnz = 0;
367: for (j=0; j<anz; j++) {
368: prow = aj[j];
369: pnz = pi[prow+1] - pi[prow];
370: pcol = pj + pi[prow];
371: pval = pa + pi[prow];
372: for (k=0; k<pnz; k++) {
373: apa[pcol[k]] += aa[j]*pval[k];
374: }
375: PetscLogFlops(2.0*pnz);
376: #if defined(PROFILE_MatPtAPNumeric)
377: flops0 += 2.0*pnz;
378: #endif
379: }
380: aj += anz; aa += anz;
381: #if defined(PROFILE_MatPtAPNumeric)
382: PetscTime(&tf);
384: time_Cseq0 += tf - t0;
385: #endif
387: /* Compute P^T*A*P using outer product P[i,:]^T*AP[i,:]. */
388: #if defined(PROFILE_MatPtAPNumeric)
389: PetscTime(&t0);
390: #endif
391: apj = ptap->apj + ptap->api[i];
392: apnz = ptap->api[i+1] - ptap->api[i];
393: pnz = pi[i+1] - pi[i];
394: pcol = pj + pi[i];
395: pval = pa + pi[i];
397: /* Perform dense axpy */
398: for (j=0; j<pnz; j++) {
399: crow = pcol[j];
400: cjj = cj + ci[crow];
401: caj = ca + ci[crow];
402: pvalj = pval[j];
403: cnz = ci[crow+1] - ci[crow];
404: for (k=0; k<cnz; k++) caj[k] += pvalj*apa[cjj[k]];
405: PetscLogFlops(2.0*cnz);
406: #if defined(PROFILE_MatPtAPNumeric)
407: flops1 += 2.0*cnz;
408: #endif
409: }
410: #if defined(PROFILE_MatPtAPNumeric)
411: PetscTime(&tf);
412: time_Cseq1 += tf - t0;
413: #endif
415: /* Zero the current row info for A*P */
416: for (j=0; j<apnz; j++) apa[apj[j]] = 0.0;
417: }
419: /* Assemble the final matrix and clean up */
420: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
421: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
422: #if defined(PROFILE_MatPtAPNumeric)
423: printf("PtAPNumeric_SeqAIJ time %g + %g, flops %d %d\n",time_Cseq0,time_Cseq1,flops0,flops1);
424: #endif
425: return(0);
426: }