Date: 2015-10-02T22:05:52+00:00

Actual source code: matrart.c
petsc-3.6.2 2015-10-02
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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> /*I "petscmat.h" I*/

     13: PetscErrorCode MatDestroy_SeqAIJ_RARt(Mat A)
     14: {
     16:   Mat_SeqAIJ     *a    = (Mat_SeqAIJ*)A->data;
     17:   Mat_RARt       *rart = a->rart;

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

     26:   A->ops->destroy = rart->destroy;
     27:   if (A->ops->destroy) {
     28:     (*A->ops->destroy)(A);
     29:   }
     30:   PetscFree(rart);
     31:   return(0);
     32: }

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

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

     53:   /* get symbolic C=Pt*A*P */
     54:   MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);
     55:   MatSetBlockSizes(*C,PetscAbs(R->rmap->bs),PetscAbs(R->rmap->bs));
     56:   (*C)->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart;

     58:   /* create a supporting struct */
     59:   PetscNew(&rart);
     60:   c       = (Mat_SeqAIJ*)(*C)->data;
     61:   c->rart = rart;

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

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

     76:   rart->matcoloring = matcoloring;
     77:   ISColoringDestroy(&iscoloring);

     79:   /* Create Rt_dense */
     80:   MatCreate(PETSC_COMM_SELF,&Rt_dense);
     81:   MatSetSizes(Rt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);
     82:   MatSetType(Rt_dense,MATSEQDENSE);
     83:   MatSeqDenseSetPreallocation(Rt_dense,NULL);

     85:   Rt_dense->assembled = PETSC_TRUE;
     86:   rart->Rt            = Rt_dense;

     88:   /* Create RARt_dense = R*A*Rt_dense */
     89:   MatCreate(PETSC_COMM_SELF,&RARt_dense);
     90:   MatSetSizes(RARt_dense,(*C)->rmap->n,matcoloring->ncolors,(*C)->rmap->n,matcoloring->ncolors);
     91:   MatSetType(RARt_dense,MATSEQDENSE);
     92:   MatSeqDenseSetPreallocation(RARt_dense,NULL);

     94:   rart->RARt = RARt_dense;

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

     99:   rart->destroy      = (*C)->ops->destroy;
    100:   (*C)->ops->destroy = MatDestroy_SeqAIJ_RARt;

    102:   /* clean up */
    103:   MatRestoreSymbolicTranspose_SeqAIJ(R,&rti,&rtj);
    104:   MatDestroy(&P);

    106: #if defined(PETSC_USE_INFO)
    107:   {
    108:     PetscReal density= (PetscReal)(c->nz)/(RARt_dense->rmap->n*RARt_dense->cmap->n);
    109:     PetscInfo(*C,"C=R*(A*Rt) via coloring C - use sparse-dense inner products\n");
    110:     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);
    111:   }
    112: #endif
    113:   return(0);
    114: }

    116: /*
    117:  RAB = R * A * B, R and A in seqaij format, B in dense format;
    118: */
    121: PetscErrorCode MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(Mat R,Mat A,Mat B,Mat RAB,PetscScalar *work)
    122: {
    123:   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*r=(Mat_SeqAIJ*)R->data;
    125:   PetscScalar    *b,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
    126:   MatScalar      *aa,*ra;
    127:   PetscInt       cn =B->cmap->n,bm=B->rmap->n,col,i,j,n,*ai=a->i,*aj,am=A->rmap->n;
    128:   PetscInt       am2=2*am,am3=3*am,bm4=4*bm;
    129:   PetscScalar    *d,*c,*c2,*c3,*c4;
    130:   PetscInt       *rj,rm=R->rmap->n,dm=RAB->rmap->n,dn=RAB->cmap->n;
    131:   PetscInt       rm2=2*rm,rm3=3*rm,colrm;

    134:   if (!dm || !dn) return(0);
    135:   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);
    136:   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);
    137:   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);
    138:   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);

    140:   { /*
    141:      This approach is not as good as original ones (will be removed later), but it reveals that
    142:      AB_den=A*B takes almost all execution time in R*A*B for src/ksp/ksp/examples/tutorials/ex56.c
    143:      */
    144:     PetscBool via_matmatmult=PETSC_FALSE;
    145:     PetscOptionsGetBool(NULL,"-matrart_via_matmatmult",&via_matmatmult,NULL);
    146:     if (via_matmatmult) {
    147:       Mat AB_den;
    148:       MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,0.0,&AB_den);
    149:       MatMatMultNumeric_SeqAIJ_SeqDense(A,B,AB_den);
    150:       MatMatMultNumeric_SeqAIJ_SeqDense(R,AB_den,RAB);
    151:       MatDestroy(&AB_den);
    152:       return(0);
    153:     }
    154:   }

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

    182:     /* RAB[:,col] = R*C[:,col] */
    183:     colrm = col*rm;
    184:     for (i=0; i<rm; i++) {        /* over rows of R in those columns */
    185:       r1 = r2 = r3 = r4 = 0.0;
    186:       n  = r->i[i+1] - r->i[i];
    187:       rj = r->j + r->i[i];
    188:       ra = r->a + r->i[i];
    189:       for (j=0; j<n; j++) {
    190:         r1 += (*ra)*c[*rj];
    191:         r2 += (*ra)*c2[*rj];
    192:         r3 += (*ra)*c3[*rj];
    193:         r4 += (*ra++)*c4[*rj++];
    194:       }
    195:       d[colrm + i]       = r1;
    196:       d[colrm + rm + i]  = r2;
    197:       d[colrm + rm2 + i] = r3;
    198:       d[colrm + rm3 + i] = r4;
    199:     }
    200:   }
    201:   for (; col<cn; col++) {     /* over extra columns of C */
    202:     for (i=0; i<am; i++) {  /* over rows of A in those columns */
    203:       r1 = 0.0;
    204:       n  = a->i[i+1] - a->i[i];
    205:       aj = a->j + a->i[i];
    206:       aa = a->a + a->i[i];
    207:       for (j=0; j<n; j++) {
    208:         r1 += (*aa++)*b1[*aj++];
    209:       }
    210:       c[i] = r1;
    211:     }
    212:     b1 += bm;

    214:     for (i=0; i<rm; i++) {  /* over rows of R in those columns */
    215:       r1 = 0.0;
    216:       n  = r->i[i+1] - r->i[i];
    217:       rj = r->j + r->i[i];
    218:       ra = r->a + r->i[i];
    219:       for (j=0; j<n; j++) {
    220:         r1 += (*ra++)*c[*rj++];
    221:       }
    222:       d[col*rm + i] = r1;
    223:     }
    224:   }
    225:   PetscLogFlops(cn*2.0*(a->nz + r->nz));

    227:   MatDenseRestoreArray(B,&b);
    228:   MatDenseRestoreArray(RAB,&d);
    229:   MatAssemblyBegin(RAB,MAT_FINAL_ASSEMBLY);
    230:   MatAssemblyEnd(RAB,MAT_FINAL_ASSEMBLY);
    231:   return(0);
    232: }

    236: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart(Mat A,Mat R,Mat C)
    237: {
    238:   PetscErrorCode       ierr;
    239:   Mat_SeqAIJ           *c = (Mat_SeqAIJ*)C->data;
    240:   Mat_RARt             *rart=c->rart;
    241:   MatTransposeColoring matcoloring;
    242:   Mat                  Rt,RARt;

    245:   /* Get dense Rt by Apply MatTransposeColoring to R */
    246:   matcoloring = rart->matcoloring;
    247:   Rt          = rart->Rt;
    248:   MatTransColoringApplySpToDen(matcoloring,R,Rt);

    250:   /* Get dense RARt = R*A*Rt -- dominates! */
    251:   RARt = rart->RARt;
    252:   MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(R,A,Rt,RARt,rart->work);

    254:   /* Recover C from C_dense */
    255:   MatTransColoringApplyDenToSp(matcoloring,RARt,C);
    256:   return(0);
    257: }

    261: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,PetscReal fill,Mat *C)
    262: {
    263:   PetscErrorCode  ierr;
    264:   Mat             ARt,RARt;
    265:   Mat_SeqAIJ     *c;
    266:   Mat_RARt       *rart;

    269:   /* must use '-mat_no_inode' with '-matmattransmult_color 1' - do not knwo why? */
    270:   MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,R,fill,&ARt);
    271:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(R,ARt,fill,&RARt);
    272:   *C                     = RARt;
    273:   RARt->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult;

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

    289: PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat A,Mat R,Mat C)
    290: {
    291:   PetscErrorCode  ierr;
    292:   Mat_SeqAIJ      *c=(Mat_SeqAIJ*)C->data;
    293:   Mat_RARt        *rart=c->rart;
    294:   Mat             ARt=rart->ARt;
    295:
    297:   MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,R,ARt); /* dominate! */
    298:   MatMatMultNumeric_SeqAIJ_SeqAIJ(R,ARt,C);
    299:   return(0);
    300: }

    304: PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat R,PetscReal fill,Mat *C)
    305: {
    306:   PetscErrorCode  ierr;
    307:   Mat             Rt;
    308:   Mat_SeqAIJ      *c;
    309:   Mat_RARt        *rart;

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

    315:   PetscNew(&rart);
    316:   rart->Rt = Rt;
    317:   c        = (Mat_SeqAIJ*)(*C)->data;
    318:   c->rart  = rart;
    319:   rart->destroy          = (*C)->ops->destroy;
    320:   (*C)->ops->destroy     = MatDestroy_SeqAIJ_RARt;
    321:   (*C)->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ;
    322: #if defined(PETSC_USE_INFO)
    323:   PetscInfo(*C,"Use Rt=R^T and C=R*A*Rt via MatMatMatMult() to avoid sparse inner products\n");
    324: #endif
    325:   return(0);
    326: }

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

    338:   MatTranspose_SeqAIJ(R,MAT_REUSE_MATRIX,&Rt);
    339:   MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(R,A,Rt,C);
    340:   return(0);
    341: }

    345: PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
    346: {
    348:   const char     *algTypes[3] = {"matmatmatmult","matmattransposemult","coloring_rart"};
    349:   PetscInt       alg=0; /* set default algorithm */
    350:
    352:   if (scall == MAT_INITIAL_MATRIX) {
    353:     PetscObjectOptionsBegin((PetscObject)A);
    354:     PetscOptionsEList("-matrart_via","Algorithmic approach","MatRARt",algTypes,3,algTypes[0],&alg,NULL);
    355:     PetscOptionsEnd();

    357:     PetscLogEventBegin(MAT_RARtSymbolic,A,R,0,0);
    358:     switch (alg) {
    359:     case 1:
    360:       /* via matmattransposemult: ARt=A*R^T, C=R*ARt - matrix coloring can be applied to A*R^T */
    361:       MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(A,R,fill,C);
    362:       break;
    363:     case 2:
    364:       /* via coloring_rart: apply coloring C = R*A*R^T                          */
    365:       MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A,R,fill,C);
    366:       break;
    367:     default:
    368:       /* via matmatmatmult: Rt=R^T, C=R*A*Rt - avoid inefficient sparse inner products */
    369:       MatRARtSymbolic_SeqAIJ_SeqAIJ(A,R,fill,C);
    370:       break;
    371:     }
    372:     PetscLogEventEnd(MAT_RARtSymbolic,A,R,0,0);
    373:   }

    375:   PetscLogEventBegin(MAT_RARtNumeric,A,R,0,0);
    376:   (*(*C)->ops->rartnumeric)(A,R,*C);
    377:   PetscLogEventEnd(MAT_RARtNumeric,A,R,0,0);
    378:   return(0);
    379: }