Actual source code: matrart.c

petsc-3.11.3 2019-06-26
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  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(Mat A)
 12: {
 14:   Mat_SeqAIJ     *a    = (Mat_SeqAIJ*)A->data;
 15:   Mat_RARt       *rart = a->rart;

 18:   MatTransposeColoringDestroy(&rart->matcoloring);
 19:   MatDestroy(&rart->Rt);
 20:   MatDestroy(&rart->RARt);
 21:   MatDestroy(&rart->ARt);
 22:   PetscFree(rart->work);

 24:   A->ops->destroy = rart->destroy;
 25:   if (A->ops->destroy) {
 26:     (*A->ops->destroy)(A);
 27:   }
 28:   PetscFree(rart);
 29:   return(0);
 30: }

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

 45:   /* create symbolic P=Rt */
 46:   MatGetSymbolicTranspose_SeqAIJ(R,&rti,&rtj);
 47:   MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,R->cmap->n,R->rmap->n,rti,rtj,NULL,&P);

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

 54:   /* create a supporting struct */
 55:   PetscNew(&rart);
 56:   c       = (Mat_SeqAIJ*)(*C)->data;
 57:   c->rart = rart;

 59:   /* ------ Use coloring ---------- */
 60:   /* inode causes memory problem, don't know why */
 61:   if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");

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

 72:   rart->matcoloring = matcoloring;
 73:   ISColoringDestroy(&iscoloring);

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

 81:   Rt_dense->assembled = PETSC_TRUE;
 82:   rart->Rt            = Rt_dense;

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

 90:   rart->RARt = RARt_dense;

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

 95:   rart->destroy      = (*C)->ops->destroy;
 96:   (*C)->ops->destroy = MatDestroy_SeqAIJ_RARt;

 98:   /* clean up */
 99:   MatRestoreSymbolicTranspose_SeqAIJ(R,&rti,&rtj);
100:   MatDestroy(&P);

102: #if defined(PETSC_USE_INFO)
103:   {
104:     PetscReal density= (PetscReal)(c->nz)/(RARt_dense->rmap->n*RARt_dense->cmap->n);
105:     PetscInfo(*C,"C=R*(A*Rt) via coloring C - use sparse-dense inner products\n");
106:     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);
107:   }
108: #endif
109:   return(0);
110: }

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

128:   if (!dm || !dn) return(0);
129:   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);
130:   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);
131:   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);
132:   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);

134:   { /* 
135:      This approach is not as good as original ones (will be removed later), but it reveals that
136:      AB_den=A*B takes almost all execution time in R*A*B for src/ksp/ksp/examples/tutorials/ex56.c
137:      */
138:     PetscBool via_matmatmult=PETSC_FALSE;
139:     PetscOptionsGetBool(NULL,NULL,"-matrart_via_matmatmult",&via_matmatmult,NULL);
140:     if (via_matmatmult) {
141:       Mat AB_den;
142:       MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,0.0,&AB_den);
143:       MatMatMultNumeric_SeqAIJ_SeqDense(A,B,AB_den);
144:       MatMatMultNumeric_SeqAIJ_SeqDense(R,AB_den,RAB);
145:       MatDestroy(&AB_den);
146:       return(0);
147:     }
148:   }

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

176:     /* RAB[:,col] = R*C[:,col] */
177:     colrm = col*rm;
178:     for (i=0; i<rm; i++) {        /* over rows of R in those columns */
179:       r1 = r2 = r3 = r4 = 0.0;
180:       n  = r->i[i+1] - r->i[i];
181:       rj = r->j + r->i[i];
182:       ra = r->a + r->i[i];
183:       for (j=0; j<n; j++) {
184:         r1 += (*ra)*c[*rj];
185:         r2 += (*ra)*c2[*rj];
186:         r3 += (*ra)*c3[*rj];
187:         r4 += (*ra++)*c4[*rj++];
188:       }
189:       d[colrm + i]       = r1;
190:       d[colrm + rm + i]  = r2;
191:       d[colrm + rm2 + i] = r3;
192:       d[colrm + rm3 + i] = r4;
193:     }
194:   }
195:   for (; col<cn; col++) {     /* over extra columns of C */
196:     for (i=0; i<am; i++) {  /* over rows of A in those columns */
197:       r1 = 0.0;
198:       n  = a->i[i+1] - a->i[i];
199:       aj = a->j + a->i[i];
200:       aa = a->a + a->i[i];
201:       for (j=0; j<n; j++) {
202:         r1 += (*aa++)*b1[*aj++];
203:       }
204:       c[i] = r1;
205:     }
206:     b1 += bm;

208:     for (i=0; i<rm; i++) {  /* over rows of R in those columns */
209:       r1 = 0.0;
210:       n  = r->i[i+1] - r->i[i];
211:       rj = r->j + r->i[i];
212:       ra = r->a + r->i[i];
213:       for (j=0; j<n; j++) {
214:         r1 += (*ra++)*c[*rj++];
215:       }
216:       d[col*rm + i] = r1;
217:     }
218:   }
219:   PetscLogFlops(cn*2.0*(a->nz + r->nz));

221:   MatDenseRestoreArray(B,&b);
222:   MatDenseRestoreArray(RAB,&d);
223:   MatAssemblyBegin(RAB,MAT_FINAL_ASSEMBLY);
224:   MatAssemblyEnd(RAB,MAT_FINAL_ASSEMBLY);
225:   return(0);
226: }

228: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart(Mat A,Mat R,Mat C)
229: {
230:   PetscErrorCode       ierr;
231:   Mat_SeqAIJ           *c = (Mat_SeqAIJ*)C->data;
232:   Mat_RARt             *rart=c->rart;
233:   MatTransposeColoring matcoloring;
234:   Mat                  Rt,RARt;

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

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

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

251: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,PetscReal fill,Mat *C)
252: {
253:   PetscErrorCode  ierr;
254:   Mat             ARt,RARt;
255:   Mat_SeqAIJ     *c;
256:   Mat_RARt       *rart;

259:   /* must use '-mat_no_inode' with '-matmattransmult_color 1' - do not knwo why? */
260:   MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,R,fill,&ARt);
261:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(R,ARt,fill,&RARt);
262:   *C                     = RARt;
263:   RARt->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult;

265:   PetscNew(&rart);
266:   c         = (Mat_SeqAIJ*)(*C)->data;
267:   c->rart   = rart;
268:   rart->ARt = ARt;
269:   rart->destroy      = RARt->ops->destroy;
270:   RARt->ops->destroy = MatDestroy_SeqAIJ_RARt;
271: #if defined(PETSC_USE_INFO)
272:   PetscInfo(*C,"Use ARt=A*R^T, C=R*ARt via MatMatTransposeMult(). Coloring can be applied to A*R^T.\n");
273: #endif
274:   return(0);
275: }

277: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,Mat C)
278: {
279:   PetscErrorCode  ierr;
280:   Mat_SeqAIJ      *c=(Mat_SeqAIJ*)C->data;
281:   Mat_RARt        *rart=c->rart;
282:   Mat             ARt=rart->ARt;
283: 
285:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,R,ARt); /* dominate! */
286:   MatMatMultNumeric_SeqAIJ_SeqAIJ(R,ARt,C);
287:   return(0);
288: }

290: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat R,PetscReal fill,Mat *C)
291: {
292:   PetscErrorCode  ierr;
293:   Mat             Rt;
294:   Mat_SeqAIJ      *c;
295:   Mat_RARt        *rart;

298:   MatTranspose_SeqAIJ(R,MAT_INITIAL_MATRIX,&Rt);
299:   MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(R,A,Rt,fill,C);

301:   PetscNew(&rart);
302:   rart->Rt = Rt;
303:   c        = (Mat_SeqAIJ*)(*C)->data;
304:   c->rart  = rart;
305:   rart->destroy          = (*C)->ops->destroy;
306:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_RARt;
307:   (*C)->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ;
308: #if defined(PETSC_USE_INFO)
309:   PetscInfo(*C,"Use Rt=R^T and C=R*A*Rt via MatMatMatMult() to avoid sparse inner products\n");
310: #endif
311:   return(0);
312: }

314: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat A,Mat R,Mat C)
315: {
316:   PetscErrorCode  ierr;
317:   Mat_SeqAIJ      *c = (Mat_SeqAIJ*)C->data;
318:   Mat_RARt        *rart = c->rart;
319:   Mat             Rt = rart->Rt;

322:   MatTranspose_SeqAIJ(R,MAT_REUSE_MATRIX,&Rt);
323:   MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(R,A,Rt,C);
324:   return(0);
325: }

327: PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
328: {
330:   const char     *algTypes[3] = {"matmatmatmult","matmattransposemult","coloring_rart"};
331:   PetscInt       alg=0; /* set default algorithm */

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

339:     PetscLogEventBegin(MAT_RARtSymbolic,A,R,0,0);
340:     switch (alg) {
341:     case 1:
342:       /* via matmattransposemult: ARt=A*R^T, C=R*ARt - matrix coloring can be applied to A*R^T */
343:       MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(A,R,fill,C);
344:       break;
345:     case 2:
346:       /* via coloring_rart: apply coloring C = R*A*R^T                          */
347:       MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A,R,fill,C);
348:       break;
349:     default:
350:       /* via matmatmatmult: Rt=R^T, C=R*A*Rt - avoid inefficient sparse inner products */
351:       MatRARtSymbolic_SeqAIJ_SeqAIJ(A,R,fill,C);
352:       break;
353:     }
354:     PetscLogEventEnd(MAT_RARtSymbolic,A,R,0,0);
355:   }

357:   PetscLogEventBegin(MAT_RARtNumeric,A,R,0,0);
358:   (*(*C)->ops->rartnumeric)(A,R,*C);
359:   PetscLogEventEnd(MAT_RARtNumeric,A,R,0,0);
360:   return(0);
361: }