Actual source code: matrart.c

petsc-master 2020-09-24
Report Typos and Errors

  2: /*
  3:   Defines projective product routines where A is a SeqAIJ matrix
  4:           C = R * A * R^T
  5: */

  7: #include <../src/mat/impls/aij/seq/aij.h>
  8: #include <../src/mat/utils/freespace.h>
  9: #include <../src/mat/impls/dense/seq/dense.h>

 11: PetscErrorCode MatDestroy_SeqAIJ_RARt(void *data)
 12: {
 14:   Mat_RARt       *rart = (Mat_RARt*)data;

 17:   MatTransposeColoringDestroy(&rart->matcoloring);
 18:   MatDestroy(&rart->Rt);
 19:   MatDestroy(&rart->RARt);
 20:   MatDestroy(&rart->ARt);
 21:   PetscFree(rart->work);
 22:   if (rart->destroy) {
 23:     (*rart->destroy)(rart->data);
 24:   }
 25:   PetscFree(rart);
 26:   return(0);
 27: }

 29: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(Mat A,Mat R,PetscReal fill,Mat C)
 30: {
 31:   PetscErrorCode       ierr;
 32:   Mat                  P;
 33:   PetscInt             *rti,*rtj;
 34:   Mat_RARt             *rart;
 35:   MatColoring          coloring;
 36:   MatTransposeColoring matcoloring;
 37:   ISColoring           iscoloring;
 38:   Mat                  Rt_dense,RARt_dense;

 41:   MatCheckProduct(C,4);
 42:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
 43:   /* create symbolic P=Rt */
 44:   MatGetSymbolicTranspose_SeqAIJ(R,&rti,&rtj);
 45:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,R->cmap->n,R->rmap->n,rti,rtj,NULL,&P);

 47:   /* get symbolic C=Pt*A*P */
 48:   MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
 49:   MatSetBlockSizes(C,PetscAbs(R->rmap->bs),PetscAbs(R->rmap->bs));
 50:   C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart;

 52:   /* create a supporting struct */
 53:   PetscNew(&rart);
 54:   C->product->data    = rart;
 55:   C->product->destroy = MatDestroy_SeqAIJ_RARt;

 57:   /* ------ Use coloring ---------- */
 58:   /* inode causes memory problem */
 59:   MatSetOption(C,MAT_USE_INODES,PETSC_FALSE);

 61:   /* Create MatTransposeColoring from symbolic C=R*A*R^T */
 62:   MatColoringCreate(C,&coloring);
 63:   MatColoringSetDistance(coloring,2);
 64:   MatColoringSetType(coloring,MATCOLORINGSL);
 65:   MatColoringSetFromOptions(coloring);
 66:   MatColoringApply(coloring,&iscoloring);
 67:   MatColoringDestroy(&coloring);
 68:   MatTransposeColoringCreate(C,iscoloring,&matcoloring);

 70:   rart->matcoloring = matcoloring;
 71:   ISColoringDestroy(&iscoloring);

 73:   /* Create Rt_dense */
 74:   MatCreate(PETSC_COMM_SELF,&Rt_dense);
 75:   MatSetSizes(Rt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
 76:   MatSetType(Rt_dense,MATSEQDENSE);
 77:   MatSeqDenseSetPreallocation(Rt_dense,NULL);

 79:   Rt_dense->assembled = PETSC_TRUE;
 80:   rart->Rt            = Rt_dense;

 82:   /* Create RARt_dense = R*A*Rt_dense */
 83:   MatCreate(PETSC_COMM_SELF,&RARt_dense);
 84:   MatSetSizes(RARt_dense,C->rmap->n,matcoloring->ncolors,C->rmap->n,matcoloring->ncolors);
 85:   MatSetType(RARt_dense,MATSEQDENSE);
 86:   MatSeqDenseSetPreallocation(RARt_dense,NULL);

 88:   rart->RARt = RARt_dense;

 90:   /* Allocate work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
 91:   PetscMalloc1(A->rmap->n*4,&rart->work);

 93:   /* clean up */
 94:   MatRestoreSymbolicTranspose_SeqAIJ(R,&rti,&rtj);
 95:   MatDestroy(&P);

 97: #if defined(PETSC_USE_INFO)
 98:   {
 99:     Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
100:     PetscReal density = (PetscReal)(c->nz)/(RARt_dense->rmap->n*RARt_dense->cmap->n);
101:     PetscInfo(C,"C=R*(A*Rt) via coloring C - use sparse-dense inner products\n");
102:     PetscInfo6(C,"RARt_den %D %D; Rt %D %D (RARt->nz %D)/(m*ncolors)=%g\n",RARt_dense->rmap->n,RARt_dense->cmap->n,R->cmap->n,R->rmap->n,c->nz,density);
103:   }
104: #endif
105:   return(0);
106: }

108: /*
109:  RAB = R * A * B, R and A in seqaij format, B in dense format;
110: */
111: PetscErrorCode MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(Mat R,Mat A,Mat B,Mat RAB,PetscScalar *work)
112: {
113:   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data,*r=(Mat_SeqAIJ*)R->data;
114:   PetscErrorCode    ierr;
115:   PetscScalar       r1,r2,r3,r4;
116:   const PetscScalar *b,*b1,*b2,*b3,*b4;
117:   MatScalar         *aa,*ra;
118:   PetscInt          cn =B->cmap->n,bm=B->rmap->n,col,i,j,n,*ai=a->i,*aj,am=A->rmap->n;
119:   PetscInt          am2=2*am,am3=3*am,bm4=4*bm;
120:   PetscScalar       *d,*c,*c2,*c3,*c4;
121:   PetscInt          *rj,rm=R->rmap->n,dm=RAB->rmap->n,dn=RAB->cmap->n;
122:   PetscInt         rm2=2*rm,rm3=3*rm,colrm;

125:   if (!dm || !dn) return(0);
126:   if (bm != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,bm);
127:   if (am != R->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in R %D not equal rows in A %D\n",R->cmap->n,am);
128:   if (R->rmap->n != RAB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in RAB %D not equal rows in R %D\n",RAB->rmap->n,R->rmap->n);
129:   if (B->cmap->n != RAB->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in RAB %D not equal columns in B %D\n",RAB->cmap->n,B->cmap->n);

131:   { /*
132:      This approach is not as good as original ones (will be removed later), but it reveals that
133:      AB_den=A*B takes almost all execution time in R*A*B for src/ksp/ksp/tutorials/ex56.c
134:      */
135:     PetscBool via_matmatmult=PETSC_FALSE;
136:     PetscOptionsGetBool(NULL,NULL,"-matrart_via_matmatmult",&via_matmatmult,NULL);
137:     if (via_matmatmult) {
138:       Mat AB_den = NULL;
139:       MatCreate(PetscObjectComm((PetscObject)A),&AB_den);
140:       MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,0.0,AB_den);
141:       MatMatMultNumeric_SeqAIJ_SeqDense(A,B,AB_den);
142:       MatMatMultNumeric_SeqAIJ_SeqDense(R,AB_den,RAB);
143:       MatDestroy(&AB_den);
144:       return(0);
145:     }
146:   }

148:   MatDenseGetArrayRead(B,&b);
149:   MatDenseGetArray(RAB,&d);
150:   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
151:   c    = work; c2 = c + am; c3 = c2 + am; c4 = c3 + am;
152:   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
153:     for (i=0; i<am; i++) {        /* over rows of A in those columns */
154:       r1 = r2 = r3 = r4 = 0.0;
155:       n  = ai[i+1] - ai[i];
156:       aj = a->j + ai[i];
157:       aa = a->a + ai[i];
158:       for (j=0; j<n; j++) {
159:         r1 += (*aa)*b1[*aj];
160:         r2 += (*aa)*b2[*aj];
161:         r3 += (*aa)*b3[*aj];
162:         r4 += (*aa++)*b4[*aj++];
163:       }
164:       c[i]       = r1;
165:       c[am  + i] = r2;
166:       c[am2 + i] = r3;
167:       c[am3 + i] = r4;
168:     }
169:     b1 += bm4;
170:     b2 += bm4;
171:     b3 += bm4;
172:     b4 += bm4;

174:     /* RAB[:,col] = R*C[:,col] */
175:     colrm = col*rm;
176:     for (i=0; i<rm; i++) {        /* over rows of R in those columns */
177:       r1 = r2 = r3 = r4 = 0.0;
178:       n  = r->i[i+1] - r->i[i];
179:       rj = r->j + r->i[i];
180:       ra = r->a + r->i[i];
181:       for (j=0; j<n; j++) {
182:         r1 += (*ra)*c[*rj];
183:         r2 += (*ra)*c2[*rj];
184:         r3 += (*ra)*c3[*rj];
185:         r4 += (*ra++)*c4[*rj++];
186:       }
187:       d[colrm + i]       = r1;
188:       d[colrm + rm + i]  = r2;
189:       d[colrm + rm2 + i] = r3;
190:       d[colrm + rm3 + i] = r4;
191:     }
192:   }
193:   for (; col<cn; col++) {     /* over extra columns of C */
194:     for (i=0; i<am; i++) {  /* over rows of A in those columns */
195:       r1 = 0.0;
196:       n  = a->i[i+1] - a->i[i];
197:       aj = a->j + a->i[i];
198:       aa = a->a + a->i[i];
199:       for (j=0; j<n; j++) {
200:         r1 += (*aa++)*b1[*aj++];
201:       }
202:       c[i] = r1;
203:     }
204:     b1 += bm;

206:     for (i=0; i<rm; i++) {  /* over rows of R in those columns */
207:       r1 = 0.0;
208:       n  = r->i[i+1] - r->i[i];
209:       rj = r->j + r->i[i];
210:       ra = r->a + r->i[i];
211:       for (j=0; j<n; j++) {
212:         r1 += (*ra++)*c[*rj++];
213:       }
214:       d[col*rm + i] = r1;
215:     }
216:   }
217:   PetscLogFlops(cn*2.0*(a->nz + r->nz));

219:   MatDenseRestoreArrayRead(B,&b);
220:   MatDenseRestoreArray(RAB,&d);
221:   MatAssemblyBegin(RAB,MAT_FINAL_ASSEMBLY);
222:   MatAssemblyEnd(RAB,MAT_FINAL_ASSEMBLY);
223:   return(0);
224: }

226: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart(Mat A,Mat R,Mat C)
227: {
228:   PetscErrorCode       ierr;
229:   Mat_RARt             *rart;
230:   MatTransposeColoring matcoloring;
231:   Mat                  Rt,RARt;

234:   MatCheckProduct(C,3);
235:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
236:   rart = (Mat_RARt*)C->product->data;

238:   /* Get dense Rt by Apply MatTransposeColoring to R */
239:   matcoloring = rart->matcoloring;
240:   Rt          = rart->Rt;
241:   MatTransColoringApplySpToDen(matcoloring,R,Rt);

243:   /* Get dense RARt = R*A*Rt -- dominates! */
244:   RARt = rart->RARt;
245:   MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(R,A,Rt,RARt,rart->work);

247:   /* Recover C from C_dense */
248:   MatTransColoringApplyDenToSp(matcoloring,RARt,C);
249:   return(0);
250: }

252: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,PetscReal fill,Mat C)
253: {
255:   Mat            ARt;
256:   Mat_RARt       *rart;
257:   char           *alg;

260:   MatCheckProduct(C,4);
261:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
262:   /* create symbolic ARt = A*R^T  */
263:   MatProductCreate(A,R,NULL,&ARt);
264:   MatProductSetType(ARt,MATPRODUCT_ABt);
265:   MatProductSetAlgorithm(ARt,"sorted");
266:   MatProductSetFill(ARt,fill);
267:   MatProductSetFromOptions(ARt);
268:   MatProductSymbolic(ARt);

270:   /* compute symbolic C = R*ARt */
271:   /* set algorithm for C = R*ARt */
272:   PetscStrallocpy(C->product->alg,&alg);
273:   MatProductSetAlgorithm(C,"sorted");
274:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(R,ARt,fill,C);
275:   /* resume original algorithm for C */
276:   MatProductSetAlgorithm(C,alg);
277:   PetscFree(alg);

279:   C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult;

281:   PetscNew(&rart);
282:   rart->ARt = ARt;
283:   C->product->data    = rart;
284:   C->product->destroy = MatDestroy_SeqAIJ_RARt;
285:   PetscInfo(C,"Use ARt=A*R^T, C=R*ARt via MatMatTransposeMult(). Coloring can be applied to A*R^T.\n");
286:   return(0);
287: }

289: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,Mat C)
290: {
292:   Mat_RARt       *rart;

295:   MatCheckProduct(C,3);
296:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
297:   rart = (Mat_RARt*)C->product->data;
298:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,R,rart->ARt); /* dominate! */
299:   MatMatMultNumeric_SeqAIJ_SeqAIJ(R,rart->ARt,C);
300:   return(0);
301: }

303: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat R,PetscReal fill,Mat C)
304: {
306:   Mat            Rt;
307:   Mat_RARt       *rart;

310:   MatCheckProduct(C,4);
311:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
312:   MatTranspose_SeqAIJ(R,MAT_INITIAL_MATRIX,&Rt);
313:   MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(R,A,Rt,fill,C);

315:   PetscNew(&rart);
316:   rart->data = C->product->data;
317:   rart->destroy = C->product->destroy;
318:   rart->Rt = Rt;
319:   C->product->data    = rart;
320:   C->product->destroy = MatDestroy_SeqAIJ_RARt;
321:   C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ;
322:   PetscInfo(C,"Use Rt=R^T and C=R*A*Rt via MatMatMatMult() to avoid sparse inner products\n");
323:   return(0);
324: }

326: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat A,Mat R,Mat C)
327: {
329:   Mat_RARt       *rart;

332:   MatCheckProduct(C,3);
333:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
334:   rart = (Mat_RARt*)C->product->data;
335:   MatTranspose_SeqAIJ(R,MAT_REUSE_MATRIX,&rart->Rt);
336:   /* MatMatMatMultSymbolic used a different data */
337:   C->product->data = rart->data;
338:   MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(R,A,rart->Rt,C);
339:   C->product->data = rart;
340:   return(0);
341: }

343: PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
344: {
346:   const char     *algTypes[3] = {"matmatmatmult","matmattransposemult","coloring_rart"};
347:   PetscInt       alg=0; /* set default algorithm */

350:   if (scall == MAT_INITIAL_MATRIX) {
351:     PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"MatRARt","Mat");
352:     PetscOptionsEList("-matrart_via","Algorithmic approach","MatRARt",algTypes,3,algTypes[0],&alg,NULL);
353:     PetscOptionsEnd();

355:     PetscLogEventBegin(MAT_RARtSymbolic,A,R,0,0);
356:     MatCreate(PETSC_COMM_SELF,C);
357:     switch (alg) {
358:     case 1:
359:       /* via matmattransposemult: ARt=A*R^T, C=R*ARt - matrix coloring can be applied to A*R^T */
360:       MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(A,R,fill,*C);
361:       break;
362:     case 2:
363:       /* via coloring_rart: apply coloring C = R*A*R^T                          */
364:       MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A,R,fill,*C);
365:       break;
366:     default:
367:       /* via matmatmatmult: Rt=R^T, C=R*A*Rt - avoid inefficient sparse inner products */
368:       MatRARtSymbolic_SeqAIJ_SeqAIJ(A,R,fill,*C);
369:       break;
370:     }
371:     PetscLogEventEnd(MAT_RARtSymbolic,A,R,0,0);
372:   }

374:   PetscLogEventBegin(MAT_RARtNumeric,A,R,0,0);
375:   ((*C)->ops->rartnumeric)(A,R,*C);
376:   PetscLogEventEnd(MAT_RARtNumeric,A,R,0,0);
377:   return(0);
378: }

380: /* ------------------------------------------------------------- */
381: PetscErrorCode MatProductSymbolic_RARt_SeqAIJ_SeqAIJ(Mat C)
382: {
383:   PetscErrorCode      ierr;
384:   Mat_Product         *product = C->product;
385:   Mat                 A=product->A,R=product->B;
386:   MatProductAlgorithm alg=product->alg;
387:   PetscReal           fill=product->fill;
388:   PetscBool           flg;

391:   PetscStrcmp(alg,"r*a*rt",&flg);
392:   if (flg) {
393:     MatRARtSymbolic_SeqAIJ_SeqAIJ(A,R,fill,C);
394:     goto next;
395:   }

397:   PetscStrcmp(alg,"r*art",&flg);
398:   if (flg) {
399:     MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(A,R,fill,C);
400:     goto next;
401:   }

403:   PetscStrcmp(alg,"coloring_rart",&flg);
404:   if (flg) {
405:     MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A,R,fill,C);
406:     goto next;
407:   }

409:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductAlgorithm is not supported");

411: next:
412:   C->ops->productnumeric = MatProductNumeric_RARt;
413:   return(0);
414: }