Date: 2022-08-02T03:13:53+00:00

Actual source code: lrc.c

      2: #include <petsc/private/matimpl.h>

      4: PETSC_EXTERN PetscErrorCode VecGetRootType_Private(Vec,VecType*);

      6: typedef struct {
      7:   Mat A;           /* sparse matrix */
      8:   Mat U,V;         /* dense tall-skinny matrices */
      9:   Vec c;           /* sequential vector containing the diagonal of C */
     10:   Vec work1,work2; /* sequential vectors that hold partial products */
     11:   Vec xl,yl;       /* auxiliary sequential vectors for matmult operation */
     12: } Mat_LRC;

     14: static PetscErrorCode MatMult_LRC_kernel(Mat N,Vec x,Vec y,PetscBool transpose)
     15: {
     16:   Mat_LRC        *Na = (Mat_LRC*)N->data;
     17:   PetscMPIInt    size;
     18:   Mat            U,V;

     20:   U = transpose ? Na->V : Na->U;
     21:   V = transpose ? Na->U : Na->V;
     22:   MPI_Comm_size(PetscObjectComm((PetscObject)N),&size);
     23:   if (size == 1) {
     24:     MatMultHermitianTranspose(V,x,Na->work1);
     25:     if (Na->c) {
     26:       VecPointwiseMult(Na->work1,Na->c,Na->work1);
     27:     }
     28:     if (Na->A) {
     29:       if (transpose) {
     30:         MatMultTranspose(Na->A,x,y);
     31:       } else {
     32:         MatMult(Na->A,x,y);
     33:       }
     34:       MatMultAdd(U,Na->work1,y,y);
     35:     } else {
     36:       MatMult(U,Na->work1,y);
     37:     }
     38:   } else {
     39:     Mat               Uloc,Vloc;
     40:     Vec               yl,xl;
     41:     const PetscScalar *w1;
     42:     PetscScalar       *w2;
     43:     PetscInt          nwork;
     44:     PetscMPIInt       mpinwork;

     46:     xl = transpose ? Na->yl : Na->xl;
     47:     yl = transpose ? Na->xl : Na->yl;
     48:     VecGetLocalVector(y,yl);
     49:     MatDenseGetLocalMatrix(U,&Uloc);
     50:     MatDenseGetLocalMatrix(V,&Vloc);

     52:     /* multiply the local part of V with the local part of x */
     53:     VecGetLocalVectorRead(x,xl);
     54:     MatMultHermitianTranspose(Vloc,xl,Na->work1);
     55:     VecRestoreLocalVectorRead(x,xl);

     57:     /* form the sum of all the local multiplies: this is work2 = V'*x =
     58:        sum_{all processors} work1 */
     59:     VecGetArrayRead(Na->work1,&w1);
     60:     VecGetArrayWrite(Na->work2,&w2);
     61:     VecGetLocalSize(Na->work1,&nwork);
     62:     PetscMPIIntCast(nwork,&mpinwork);
     63:     MPIU_Allreduce(w1,w2,mpinwork,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)N));
     64:     VecRestoreArrayRead(Na->work1,&w1);
     65:     VecRestoreArrayWrite(Na->work2,&w2);

     67:     if (Na->c) {  /* work2 = C*work2 */
     68:       VecPointwiseMult(Na->work2,Na->c,Na->work2);
     69:     }

     71:     if (Na->A) {
     72:       /* form y = A*x or A^t*x */
     73:       if (transpose) {
     74:         MatMultTranspose(Na->A,x,y);
     75:       } else {
     76:         MatMult(Na->A,x,y);
     77:       }
     78:       /* multiply-add y = y + U*work2 */
     79:       MatMultAdd(Uloc,Na->work2,yl,yl);
     80:     } else {
     81:       /* multiply y = U*work2 */
     82:       MatMult(Uloc,Na->work2,yl);
     83:     }

     85:     VecRestoreLocalVector(y,yl);
     86:   }
     87:   return 0;
     88: }

     90: static PetscErrorCode MatMult_LRC(Mat N,Vec x,Vec y)
     91: {
     92:   MatMult_LRC_kernel(N,x,y,PETSC_FALSE);
     93:   return 0;
     94: }

     96: static PetscErrorCode MatMultTranspose_LRC(Mat N,Vec x,Vec y)
     97: {
     98:   MatMult_LRC_kernel(N,x,y,PETSC_TRUE);
     99:   return 0;
    100: }

    102: static PetscErrorCode MatDestroy_LRC(Mat N)
    103: {
    104:   Mat_LRC        *Na = (Mat_LRC*)N->data;

    106:   MatDestroy(&Na->A);
    107:   MatDestroy(&Na->U);
    108:   MatDestroy(&Na->V);
    109:   VecDestroy(&Na->c);
    110:   VecDestroy(&Na->work1);
    111:   VecDestroy(&Na->work2);
    112:   VecDestroy(&Na->xl);
    113:   VecDestroy(&Na->yl);
    114:   PetscFree(N->data);
    115:   PetscObjectComposeFunction((PetscObject)N,"MatLRCGetMats_C",NULL);
    116:   return 0;
    117: }

    119: static PetscErrorCode MatLRCGetMats_LRC(Mat N,Mat *A,Mat *U,Vec *c,Mat *V)
    120: {
    121:   Mat_LRC *Na = (Mat_LRC*)N->data;

    123:   if (A) *A = Na->A;
    124:   if (U) *U = Na->U;
    125:   if (c) *c = Na->c;
    126:   if (V) *V = Na->V;
    127:   return 0;
    128: }

    130: /*@
    131:    MatLRCGetMats - Returns the constituents of an LRC matrix

    133:    Collective on Mat

    135:    Input Parameter:
    136: .  N - matrix of type LRC

    138:    Output Parameters:
    139: +  A - the (sparse) matrix
    140: .  U - first dense rectangular (tall and skinny) matrix
    141: .  c - a sequential vector containing the diagonal of C
    142: -  V - second dense rectangular (tall and skinny) matrix

    144:    Note:
    145:    The returned matrices need not be destroyed by the caller.

    147:    Level: intermediate

    149: .seealso: MatCreateLRC()
    150: @*/
    151: PetscErrorCode MatLRCGetMats(Mat N,Mat *A,Mat *U,Vec *c,Mat *V)
    152: {
    153:   PetscUseMethod(N,"MatLRCGetMats_C",(Mat,Mat*,Mat*,Vec*,Mat*),(N,A,U,c,V));
    154:   return 0;
    155: }

    157: /*@
    158:    MatCreateLRC - Creates a new matrix object that behaves like A + U*C*V'

    160:    Collective on Mat

    162:    Input Parameters:
    163: +  A    - the (sparse) matrix (can be NULL)
    164: .  U, V - two dense rectangular (tall and skinny) matrices
    165: -  c    - a vector containing the diagonal of C (can be NULL)

    167:    Output Parameter:
    168: .  N    - the matrix that represents A + U*C*V'

    170:    Notes:
    171:    The matrix A + U*C*V' is not formed! Rather the new matrix
    172:    object performs the matrix-vector product by first multiplying by
    173:    A and then adding the other term.

    175:    C is a diagonal matrix (represented as a vector) of order k,
    176:    where k is the number of columns of both U and V.

    178:    If A is NULL then the new object behaves like a low-rank matrix U*C*V'.

    180:    Use V=U (or V=NULL) for a symmetric low-rank correction, A + U*C*U'.

    182:    If c is NULL then the low-rank correction is just U*V'.
    183:    If a sequential c vector is used for a parallel matrix,
    184:    PETSc assumes that the values of the vector are consistently set across processors.

    186:    Level: intermediate

    188: .seealso: MatLRCGetMats()
    189: @*/
    190: PetscErrorCode MatCreateLRC(Mat A,Mat U,Vec c,Mat V,Mat *N)
    191: {
    192:   PetscBool      match;
    193:   PetscInt       m,n,k,m1,n1,k1;
    194:   Mat_LRC        *Na;
    195:   Mat            Uloc;
    196:   PetscMPIInt    size, csize = 0;

    201:   if (V) {
    204:   }

    207:   if (!V) V = U;
    208:   PetscObjectBaseTypeCompareAny((PetscObject)U,&match,MATSEQDENSE,MATMPIDENSE,"");
    210:   PetscObjectBaseTypeCompareAny((PetscObject)V,&match,MATSEQDENSE,MATMPIDENSE,"");
    212:   PetscStrcmp(U->defaultvectype,V->defaultvectype,&match);
    214:   if (A) {
    215:     PetscStrcmp(A->defaultvectype,U->defaultvectype,&match);
    217:   }

    219:   MPI_Comm_size(PetscObjectComm((PetscObject)U),&size);
    220:   MatGetSize(U,NULL,&k);
    221:   MatGetSize(V,NULL,&k1);
    223:   MatGetLocalSize(U,&m,NULL);
    224:   MatGetLocalSize(V,&n,NULL);
    225:   if (A) {
    226:     MatGetLocalSize(A,&m1,&n1);
    229:   }
    230:   if (c) {
    231:     MPI_Comm_size(PetscObjectComm((PetscObject)c),&csize);
    232:     VecGetSize(c,&k1);
    235:   }

    237:   MatCreate(PetscObjectComm((PetscObject)U),N);
    238:   MatSetSizes(*N,m,n,PETSC_DECIDE,PETSC_DECIDE);
    239:   MatSetVecType(*N,U->defaultvectype);
    240:   PetscObjectChangeTypeName((PetscObject)*N,MATLRC);
    241:   /* Flag matrix as symmetric if A is symmetric and U == V */
    242:   MatSetOption(*N,MAT_SYMMETRIC,(PetscBool)((A ? A->symmetric : PETSC_TRUE) && U == V));

    244:   PetscNewLog(*N,&Na);
    245:   (*N)->data = (void*)Na;
    246:   Na->A      = A;
    247:   Na->U      = U;
    248:   Na->c      = c;
    249:   Na->V      = V;

    251:   PetscObjectReference((PetscObject)A);
    252:   PetscObjectReference((PetscObject)Na->U);
    253:   PetscObjectReference((PetscObject)Na->V);
    254:   PetscObjectReference((PetscObject)c);

    256:   MatDenseGetLocalMatrix(Na->U,&Uloc);
    257:   MatCreateVecs(Uloc,&Na->work1,NULL);
    258:   if (size != 1) {
    259:     Mat Vloc;

    261:     if (Na->c && csize != 1) { /* scatter parallel vector to sequential */
    262:       VecScatter sct;

    264:       VecScatterCreateToAll(Na->c,&sct,&c);
    265:       VecScatterBegin(sct,Na->c,c,INSERT_VALUES,SCATTER_FORWARD);
    266:       VecScatterEnd(sct,Na->c,c,INSERT_VALUES,SCATTER_FORWARD);
    267:       VecScatterDestroy(&sct);
    268:       VecDestroy(&Na->c);
    269:       PetscLogObjectParent((PetscObject)*N,(PetscObject)c);
    270:       Na->c = c;
    271:     }
    272:     MatDenseGetLocalMatrix(Na->V,&Vloc);
    273:     VecDuplicate(Na->work1,&Na->work2);
    274:     MatCreateVecs(Vloc,NULL,&Na->xl);
    275:     MatCreateVecs(Uloc,NULL,&Na->yl);
    276:   }
    277:   PetscLogObjectParent((PetscObject)*N,(PetscObject)Na->work1);
    278:   PetscLogObjectParent((PetscObject)*N,(PetscObject)Na->work1);
    279:   PetscLogObjectParent((PetscObject)*N,(PetscObject)Na->xl);
    280:   PetscLogObjectParent((PetscObject)*N,(PetscObject)Na->yl);

    282:   /* Internally create a scaling vector if roottypes do not match */
    283:   if (Na->c) {
    284:     VecType rt1,rt2;

    286:     VecGetRootType_Private(Na->work1,&rt1);
    287:     VecGetRootType_Private(Na->c,&rt2);
    288:     PetscStrcmp(rt1,rt2,&match);
    289:     if (!match) {
    290:       VecDuplicate(Na->c,&c);
    291:       VecCopy(Na->c,c);
    292:       VecDestroy(&Na->c);
    293:       PetscLogObjectParent((PetscObject)*N,(PetscObject)c);
    294:       Na->c = c;
    295:     }
    296:   }

    298:   (*N)->ops->destroy       = MatDestroy_LRC;
    299:   (*N)->ops->mult          = MatMult_LRC;
    300:   (*N)->ops->multtranspose = MatMultTranspose_LRC;

    302:   (*N)->assembled    = PETSC_TRUE;
    303:   (*N)->preallocated = PETSC_TRUE;

    305:   PetscObjectComposeFunction((PetscObject)(*N),"MatLRCGetMats_C",MatLRCGetMats_LRC);
    306:   MatSetUp(*N);
    307:   return 0;
    308: }