Actual source code: matrart.c
petsc-3.13.6 2020-09-29
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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 */
     61:   MatSetOption(C,MAT_USE_INODES,PETSC_FALSE);

     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;
    118:   PetscErrorCode    ierr;
    119:   PetscScalar       r1,r2,r3,r4;
    120:   const PetscScalar *b,*b1,*b2,*b3,*b4;
    121:   MatScalar         *aa,*ra;
    122:   PetscInt          cn =B->cmap->n,bm=B->rmap->n,col,i,j,n,*ai=a->i,*aj,am=A->rmap->n;
    123:   PetscInt          am2=2*am,am3=3*am,bm4=4*bm;
    124:   PetscScalar       *d,*c,*c2,*c3,*c4;
    125:   PetscInt          *rj,rm=R->rmap->n,dm=RAB->rmap->n,dn=RAB->cmap->n;
    126:   PetscInt         rm2=2*rm,rm3=3*rm,colrm;

    129:   if (!dm || !dn) return(0);
    130:   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);
    131:   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);
    132:   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);
    133:   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);

    135:   { /*
    136:      This approach is not as good as original ones (will be removed later), but it reveals that
    137:      AB_den=A*B takes almost all execution time in R*A*B for src/ksp/ksp/tutorials/ex56.c
    138:      */
    139:     PetscBool via_matmatmult=PETSC_FALSE;
    140:     PetscOptionsGetBool(NULL,NULL,"-matrart_via_matmatmult",&via_matmatmult,NULL);
    141:     if (via_matmatmult) {
    142:       Mat AB_den = NULL;
    143:       MatCreate(PetscObjectComm((PetscObject)A),&AB_den);
    144:       MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,0.0,AB_den);
    145:       MatMatMultNumeric_SeqAIJ_SeqDense(A,B,AB_den);
    146:       MatMatMultNumeric_SeqAIJ_SeqDense(R,AB_den,RAB);
    147:       MatDestroy(&AB_den);
    148:       return(0);
    149:     }
    150:   }

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

    178:     /* RAB[:,col] = R*C[:,col] */
    179:     colrm = col*rm;
    180:     for (i=0; i<rm; i++) {        /* over rows of R in those columns */
    181:       r1 = r2 = r3 = r4 = 0.0;
    182:       n  = r->i[i+1] - r->i[i];
    183:       rj = r->j + r->i[i];
    184:       ra = r->a + r->i[i];
    185:       for (j=0; j<n; j++) {
    186:         r1 += (*ra)*c[*rj];
    187:         r2 += (*ra)*c2[*rj];
    188:         r3 += (*ra)*c3[*rj];
    189:         r4 += (*ra++)*c4[*rj++];
    190:       }
    191:       d[colrm + i]       = r1;
    192:       d[colrm + rm + i]  = r2;
    193:       d[colrm + rm2 + i] = r3;
    194:       d[colrm + rm3 + i] = r4;
    195:     }
    196:   }
    197:   for (; col<cn; col++) {     /* over extra columns of C */
    198:     for (i=0; i<am; i++) {  /* over rows of A in those columns */
    199:       r1 = 0.0;
    200:       n  = a->i[i+1] - a->i[i];
    201:       aj = a->j + a->i[i];
    202:       aa = a->a + a->i[i];
    203:       for (j=0; j<n; j++) {
    204:         r1 += (*aa++)*b1[*aj++];
    205:       }
    206:       c[i] = r1;
    207:     }
    208:     b1 += bm;

    210:     for (i=0; i<rm; i++) {  /* over rows of R in those columns */
    211:       r1 = 0.0;
    212:       n  = r->i[i+1] - r->i[i];
    213:       rj = r->j + r->i[i];
    214:       ra = r->a + r->i[i];
    215:       for (j=0; j<n; j++) {
    216:         r1 += (*ra++)*c[*rj++];
    217:       }
    218:       d[col*rm + i] = r1;
    219:     }
    220:   }
    221:   PetscLogFlops(cn*2.0*(a->nz + r->nz));

    223:   MatDenseRestoreArrayRead(B,&b);
    224:   MatDenseRestoreArray(RAB,&d);
    225:   MatAssemblyBegin(RAB,MAT_FINAL_ASSEMBLY);
    226:   MatAssemblyEnd(RAB,MAT_FINAL_ASSEMBLY);
    227:   return(0);
    228: }

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

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

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

    248:   /* Recover C from C_dense */
    249:   MatTransColoringApplyDenToSp(matcoloring,RARt,C);
    250:   return(0);
    251: }

    253: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,PetscReal fill,Mat C)
    254: {
    256:   Mat            ARt;
    257:   Mat_SeqAIJ     *c;
    258:   Mat_RARt       *rart;
    259:   Mat_Product    *product = C->product;
    260:   MatProductAlgorithm alg=product->alg;

    263:   /* create symbolic ARt = A*R^T  */
    264:   MatProductCreate(A,R,NULL,&ARt);
    265:   MatProductSetType(ARt,MATPRODUCT_ABt);
    266:   MatProductSetAlgorithm(ARt,"sorted");
    267:   MatProductSetFill(ARt,fill);
    268:   MatProductSetFromOptions(ARt);
    269:   MatProductSymbolic(ARt);

    271:   /* compute symbolic C = R*ARt */
    272:   C->product->alg = "sorted"; /* set algorithm for C = R*ARt */
    273:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(R,ARt,fill,C);
    274:   C->product->alg = alg; /* resume original algorithm for C */

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

    278:   PetscNew(&rart);
    279:   c         = (Mat_SeqAIJ*)C->data;
    280:   c->rart   = rart;
    281:   rart->ARt = ARt;
    282:   rart->destroy   = C->ops->destroy;
    283:   C->ops->destroy = MatDestroy_SeqAIJ_RARt;
    284: #if defined(PETSC_USE_INFO)
    285:   PetscInfo(C,"Use ARt=A*R^T, C=R*ARt via MatMatTransposeMult(). Coloring can be applied to A*R^T.\n");
    286: #endif
    287:   return(0);
    288: }

    290: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,Mat C)
    291: {
    292:   PetscErrorCode  ierr;
    293:   Mat_SeqAIJ      *c=(Mat_SeqAIJ*)C->data;
    294:   Mat_RARt        *rart=c->rart;
    295:   Mat             ARt=rart->ARt;

    298:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,R,ARt); /* dominate! */
    299:   MatMatMultNumeric_SeqAIJ_SeqAIJ(R,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_SeqAIJ     *c;
    308:   Mat_RARt       *rart;

    311:   MatTranspose_SeqAIJ(R,MAT_INITIAL_MATRIX,&Rt);
    312:   MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(R,A,Rt,fill,C);

    314:   PetscNew(&rart);
    315:   rart->Rt = Rt;
    316:   c        = (Mat_SeqAIJ*)C->data;
    317:   c->rart  = rart;
    318:   rart->destroy       = C->ops->destroy;
    319:   C->ops->destroy     = MatDestroy_SeqAIJ_RARt;
    320:   C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ;
    321: #if defined(PETSC_USE_INFO)
    322:   PetscInfo(C,"Use Rt=R^T and C=R*A*Rt via MatMatMatMult() to avoid sparse inner products\n");
    323: #endif
    324:   return(0);
    325: }

    327: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat A,Mat R,Mat C)
    328: {
    329:   PetscErrorCode  ierr;
    330:   Mat_SeqAIJ      *c = (Mat_SeqAIJ*)C->data;
    331:   Mat_RARt        *rart = c->rart;
    332:   Mat             Rt = rart->Rt;

    335:   MatTranspose_SeqAIJ(R,MAT_REUSE_MATRIX,&Rt);
    336:   MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(R,A,Rt,C);
    337:   return(0);
    338: }

    340: PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
    341: {
    343:   const char     *algTypes[3] = {"matmatmatmult","matmattransposemult","coloring_rart"};
    344:   PetscInt       alg=0; /* set default algorithm */

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

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

    371:   PetscLogEventBegin(MAT_RARtNumeric,A,R,0,0);
    372:   ((*C)->ops->rartnumeric)(A,R,*C);
    373:   PetscLogEventEnd(MAT_RARtNumeric,A,R,0,0);
    374:   return(0);
    375: }

    377: /* ------------------------------------------------------------- */
    378: PetscErrorCode MatProductSymbolic_RARt_SeqAIJ_SeqAIJ(Mat C)
    379: {
    380:   PetscErrorCode      ierr;
    381:   Mat_Product         *product = C->product;
    382:   Mat                 A=product->A,R=product->B;
    383:   MatProductAlgorithm alg=product->alg;
    384:   PetscReal           fill=product->fill;
    385:   PetscBool           flg;

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

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

    400:   PetscStrcmp(alg,"coloring_rart",&flg);
    401:   if (flg) {
    402:     MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A,R,fill,C);
    403:     goto next;
    404:   }

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

    408: next:
    409:   C->ops->productnumeric = MatProductNumeric_RARt;
    410:   return(0);
    411: }