Date: 2015-10-02T22:19:20+00:00

Actual source code: svd.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/pcimpl.h>   /*I "petscpc.h" I*/
      3: #include <petscblaslapack.h>

      5: /*
      6:    Private context (data structure) for the SVD preconditioner.
      7: */
      8: typedef struct {
      9:   Vec         diag,work;
     10:   Mat         A,U,Vt;
     11:   PetscInt    nzero;
     12:   PetscReal   zerosing;         /* measure of smallest singular value treated as nonzero */
     13:   PetscInt    essrank;          /* essential rank of operator */
     14:   VecScatter  left2red,right2red;
     15:   Vec         leftred,rightred;
     16:   PetscViewer monitor;
     17: } PC_SVD;

     19: typedef enum {READ=1, WRITE=2, READ_WRITE=3} AccessMode;

     21: /* -------------------------------------------------------------------------- */
     22: /*
     23:    PCSetUp_SVD - Prepares for the use of the SVD preconditioner
     24:                     by setting data structures and options.

     26:    Input Parameter:
     27: .  pc - the preconditioner context

     29:    Application Interface Routine: PCSetUp()

     31:    Notes:
     32:    The interface routine PCSetUp() is not usually called directly by
     33:    the user, but instead is called by PCApply() if necessary.
     34: */
     37: static PetscErrorCode PCSetUp_SVD(PC pc)
     38: {
     39: #if defined(PETSC_MISSING_LAPACK_GESVD)
     40:   SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable\nNot able to provide singular value estimates.");
     41: #else
     42:   PC_SVD         *jac = (PC_SVD*)pc->data;
     44:   PetscScalar    *a,*u,*v,*d,*work;
     45:   PetscBLASInt   nb,lwork;
     46:   PetscInt       i,n;
     47:   PetscMPIInt    size;

     50:   MatDestroy(&jac->A);
     51:   MPI_Comm_size(((PetscObject)pc->pmat)->comm,&size);
     52:   if (size > 1) {
     53:     Mat          redmat;
     54:     MatCreateRedundantMatrix(pc->pmat,size,PETSC_COMM_SELF,MAT_INITIAL_MATRIX,&redmat);
     55:     MatConvert(redmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);
     56:     MatDestroy(&redmat);
     57:   } else {
     58:     MatConvert(pc->pmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);
     59:   }
     60:   if (!jac->diag) {    /* assume square matrices */
     61:     MatCreateVecs(jac->A,&jac->diag,&jac->work);
     62:   }
     63:   if (!jac->U) {
     64:     MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->U);
     65:     MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->Vt);
     66:   }
     67:   MatGetSize(pc->pmat,&n,NULL);
     68:   PetscBLASIntCast(n,&nb);
     69:   lwork = 5*nb;
     70:   PetscMalloc1(lwork,&work);
     71:   MatDenseGetArray(jac->A,&a);
     72:   MatDenseGetArray(jac->U,&u);
     73:   MatDenseGetArray(jac->Vt,&v);
     74:   VecGetArray(jac->diag,&d);
     75: #if !defined(PETSC_USE_COMPLEX)
     76:   {
     77:     PetscBLASInt lierr;
     78:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     79:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,d,u,&nb,v,&nb,work,&lwork,&lierr));
     80:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
     81:     PetscFPTrapPop();
     82:   }
     83: #else
     84:   {
     85:     PetscBLASInt lierr;
     86:     PetscReal    *rwork,*dd;
     87:     PetscMalloc1(5*nb,&rwork);
     88:     PetscMalloc1(nb,&dd);
     89:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     90:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,dd,u,&nb,v,&nb,work,&lwork,rwork,&lierr));
     91:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
     92:     PetscFree(rwork);
     93:     for (i=0; i<nb; i++) d[i] = dd[i];
     94:     PetscFree(dd);
     95:     PetscFPTrapPop();
     96:   }
     97: #endif
     98:   MatDenseRestoreArray(jac->A,&a);
     99:   MatDenseRestoreArray(jac->U,&u);
    100:   MatDenseRestoreArray(jac->Vt,&v);
    101:   for (i=n-1; i>=0; i--) if (PetscRealPart(d[i]) > jac->zerosing) break;
    102:   jac->nzero = n-1-i;
    103:   if (jac->monitor) {
    104:     PetscViewerASCIIAddTab(jac->monitor,((PetscObject)pc)->tablevel);
    105:     PetscViewerASCIIPrintf(jac->monitor,"    SVD: condition number %14.12e, %D of %D singular values are (nearly) zero\n",(double)PetscRealPart(d[0]/d[n-1]),jac->nzero,n);
    106:     if (n >= 10) {              /* print 5 smallest and 5 largest */
    107:       PetscViewerASCIIPrintf(jac->monitor,"    SVD: smallest singular values: %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[n-1]),(double)PetscRealPart(d[n-2]),(double)PetscRealPart(d[n-3]),(double)PetscRealPart(d[n-4]),(double)PetscRealPart(d[n-5]));
    108:       PetscViewerASCIIPrintf(jac->monitor,"    SVD: largest singular values : %14.12e %14.12e %14.12e %14.12e %14.12e\n",(double)PetscRealPart(d[4]),(double)PetscRealPart(d[3]),(double)PetscRealPart(d[2]),(double)PetscRealPart(d[1]),(double)PetscRealPart(d[0]));
    109:     } else {                    /* print all singular values */
    110:       char     buf[256],*p;
    111:       size_t   left = sizeof(buf),used;
    112:       PetscInt thisline;
    113:       for (p=buf,i=n-1,thisline=1; i>=0; i--,thisline++) {
    114:         PetscSNPrintfCount(p,left," %14.12e",&used,(double)PetscRealPart(d[i]));
    115:         left -= used;
    116:         p    += used;
    117:         if (thisline > 4 || i==0) {
    118:           PetscViewerASCIIPrintf(jac->monitor,"    SVD: singular values:%s\n",buf);
    119:           p        = buf;
    120:           thisline = 0;
    121:         }
    122:       }
    123:     }
    124:     PetscViewerASCIISubtractTab(jac->monitor,((PetscObject)pc)->tablevel);
    125:   }
    126:   PetscInfo2(pc,"Largest and smallest singular values %14.12e %14.12e\n",(double)PetscRealPart(d[0]),(double)PetscRealPart(d[n-1]));
    127:   for (i=0; i<n-jac->nzero; i++) d[i] = 1.0/d[i];
    128:   for (; i<n; i++) d[i] = 0.0;
    129:   if (jac->essrank > 0) for (i=0; i<n-jac->nzero-jac->essrank; i++) d[i] = 0.0; /* Skip all but essrank eigenvalues */
    130:   PetscInfo1(pc,"Number of zero or nearly singular values %D\n",jac->nzero);
    131:   VecRestoreArray(jac->diag,&d);
    132: #if defined(foo)
    133:   {
    134:     PetscViewer viewer;
    135:     PetscViewerBinaryOpen(PETSC_COMM_SELF,"joe",FILE_MODE_WRITE,&viewer);
    136:     MatView(jac->A,viewer);
    137:     MatView(jac->U,viewer);
    138:     MatView(jac->Vt,viewer);
    139:     VecView(jac->diag,viewer);
    140:     PetscViewerDestroy(viewer);
    141:   }
    142: #endif
    143:   PetscFree(work);
    144:   return(0);
    145: #endif
    146: }

    150: static PetscErrorCode PCSVDGetVec(PC pc,PCSide side,AccessMode amode,Vec x,Vec *xred)
    151: {
    152:   PC_SVD         *jac = (PC_SVD*)pc->data;
    154:   PetscMPIInt    size;

    157:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    158:   *xred = NULL;
    159:   switch (side) {
    160:   case PC_LEFT:
    161:     if (size == 1) *xred = x;
    162:     else {
    163:       if (!jac->left2red) {VecScatterCreateToAll(x,&jac->left2red,&jac->leftred);}
    164:       if (amode & READ) {
    165:         VecScatterBegin(jac->left2red,x,jac->leftred,INSERT_VALUES,SCATTER_FORWARD);
    166:         VecScatterEnd(jac->left2red,x,jac->leftred,INSERT_VALUES,SCATTER_FORWARD);
    167:       }
    168:       *xred = jac->leftred;
    169:     }
    170:     break;
    171:   case PC_RIGHT:
    172:     if (size == 1) *xred = x;
    173:     else {
    174:       if (!jac->right2red) {VecScatterCreateToAll(x,&jac->right2red,&jac->rightred);}
    175:       if (amode & READ) {
    176:         VecScatterBegin(jac->right2red,x,jac->rightred,INSERT_VALUES,SCATTER_FORWARD);
    177:         VecScatterEnd(jac->right2red,x,jac->rightred,INSERT_VALUES,SCATTER_FORWARD);
    178:       }
    179:       *xred = jac->rightred;
    180:     }
    181:     break;
    182:   default: SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Side must be LEFT or RIGHT");
    183:   }
    184:   return(0);
    185: }

    189: static PetscErrorCode PCSVDRestoreVec(PC pc,PCSide side,AccessMode amode,Vec x,Vec *xred)
    190: {
    191:   PC_SVD         *jac = (PC_SVD*)pc->data;
    193:   PetscMPIInt    size;

    196:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    197:   switch (side) {
    198:   case PC_LEFT:
    199:     if (size != 1 && amode & WRITE) {
    200:       VecScatterBegin(jac->left2red,jac->leftred,x,INSERT_VALUES,SCATTER_REVERSE);
    201:       VecScatterEnd(jac->left2red,jac->leftred,x,INSERT_VALUES,SCATTER_REVERSE);
    202:     }
    203:     break;
    204:   case PC_RIGHT:
    205:     if (size != 1 && amode & WRITE) {
    206:       VecScatterBegin(jac->right2red,jac->rightred,x,INSERT_VALUES,SCATTER_REVERSE);
    207:       VecScatterEnd(jac->right2red,jac->rightred,x,INSERT_VALUES,SCATTER_REVERSE);
    208:     }
    209:     break;
    210:   default: SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Side must be LEFT or RIGHT");
    211:   }
    212:   *xred = NULL;
    213:   return(0);
    214: }

    216: /* -------------------------------------------------------------------------- */
    217: /*
    218:    PCApply_SVD - Applies the SVD preconditioner to a vector.

    220:    Input Parameters:
    221: .  pc - the preconditioner context
    222: .  x - input vector

    224:    Output Parameter:
    225: .  y - output vector

    227:    Application Interface Routine: PCApply()
    228:  */
    231: static PetscErrorCode PCApply_SVD(PC pc,Vec x,Vec y)
    232: {
    233:   PC_SVD         *jac = (PC_SVD*)pc->data;
    234:   Vec            work = jac->work,xred,yred;

    238:   PCSVDGetVec(pc,PC_RIGHT,READ,x,&xred);
    239:   PCSVDGetVec(pc,PC_LEFT,WRITE,y,&yred);
    240: #if !defined(PETSC_USE_COMPLEX)
    241:   MatMultTranspose(jac->U,xred,work);
    242: #else
    243:   MatMultHermitianTranspose(jac->U,xred,work);
    244: #endif
    245:   VecPointwiseMult(work,work,jac->diag);
    246: #if !defined(PETSC_USE_COMPLEX)
    247:   MatMultTranspose(jac->Vt,work,yred);
    248: #else
    249:   MatMultHermitianTranspose(jac->Vt,work,yred);
    250: #endif
    251:   PCSVDRestoreVec(pc,PC_RIGHT,READ,x,&xred);
    252:   PCSVDRestoreVec(pc,PC_LEFT,WRITE,y,&yred);
    253:   return(0);
    254: }

    258: static PetscErrorCode PCApplyTranspose_SVD(PC pc,Vec x,Vec y)
    259: {
    260:   PC_SVD         *jac = (PC_SVD*)pc->data;
    261:   Vec            work = jac->work,xred,yred;

    265:   PCSVDGetVec(pc,PC_LEFT,READ,x,&xred);
    266:   PCSVDGetVec(pc,PC_RIGHT,WRITE,y,&yred);
    267: #if !defined(PETSC_USE_COMPLEX)
    268:   MatMultTranspose(jac->Vt,work,yred);
    269: #else
    270:   MatMultHermitianTranspose(jac->Vt,work,yred);
    271: #endif
    272:   VecPointwiseMult(work,work,jac->diag);
    273: #if !defined(PETSC_USE_COMPLEX)
    274:   MatMultTranspose(jac->U,xred,work);
    275: #else
    276:   MatMultHermitianTranspose(jac->U,xred,work);
    277: #endif
    278:   PCSVDRestoreVec(pc,PC_LEFT,READ,x,&xred);
    279:   PCSVDRestoreVec(pc,PC_RIGHT,WRITE,y,&yred);
    280:   return(0);
    281: }

    285: static PetscErrorCode PCReset_SVD(PC pc)
    286: {
    287:   PC_SVD         *jac = (PC_SVD*)pc->data;

    291:   MatDestroy(&jac->A);
    292:   MatDestroy(&jac->U);
    293:   MatDestroy(&jac->Vt);
    294:   VecDestroy(&jac->diag);
    295:   VecDestroy(&jac->work);
    296:   VecScatterDestroy(&jac->right2red);
    297:   VecScatterDestroy(&jac->left2red);
    298:   VecDestroy(&jac->rightred);
    299:   VecDestroy(&jac->leftred);
    300:   return(0);
    301: }

    303: /* -------------------------------------------------------------------------- */
    304: /*
    305:    PCDestroy_SVD - Destroys the private context for the SVD preconditioner
    306:    that was created with PCCreate_SVD().

    308:    Input Parameter:
    309: .  pc - the preconditioner context

    311:    Application Interface Routine: PCDestroy()
    312: */
    315: static PetscErrorCode PCDestroy_SVD(PC pc)
    316: {
    317:   PC_SVD         *jac = (PC_SVD*)pc->data;

    321:   PCReset_SVD(pc);
    322:   PetscViewerDestroy(&jac->monitor);
    323:   PetscFree(pc->data);
    324:   return(0);
    325: }

    329: static PetscErrorCode PCSetFromOptions_SVD(PetscOptions *PetscOptionsObject,PC pc)
    330: {
    332:   PC_SVD         *jac = (PC_SVD*)pc->data;
    333:   PetscBool      flg,set;

    336:   PetscOptionsHead(PetscOptionsObject,"SVD options");
    337:   PetscOptionsReal("-pc_svd_zero_sing","Singular values smaller than this treated as zero","None",jac->zerosing,&jac->zerosing,NULL);
    338:   PetscOptionsInt("-pc_svd_ess_rank","Essential rank of operator (0 to use entire operator)","None",jac->essrank,&jac->essrank,NULL);
    339:   PetscOptionsBool("-pc_svd_monitor","Monitor the conditioning, and extremal singular values","None",jac->monitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);
    340:   if (set) {                    /* Should make PCSVDSetMonitor() */
    341:     if (flg && !jac->monitor) {
    342:       PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),"stdout",&jac->monitor);
    343:     } else if (!flg) {
    344:       PetscViewerDestroy(&jac->monitor);
    345:     }
    346:   }
    347:   PetscOptionsTail();
    348:   return(0);
    349: }

    351: /* -------------------------------------------------------------------------- */
    352: /*
    353:    PCCreate_SVD - Creates a SVD preconditioner context, PC_SVD,
    354:    and sets this as the private data within the generic preconditioning
    355:    context, PC, that was created within PCCreate().

    357:    Input Parameter:
    358: .  pc - the preconditioner context

    360:    Application Interface Routine: PCCreate()
    361: */

    363: /*MC
    364:      PCSVD - Use pseudo inverse defined by SVD of operator

    366:    Level: advanced

    368:   Concepts: SVD

    370:   Options Database:
    371: -  -pc_svd_zero_sing <rtol> Singular values smaller than this are treated as zero
    372: +  -pc_svd_monitor  Print information on the extreme singular values of the operator

    374:   Developer Note: This implementation automatically creates a redundant copy of the
    375:    matrix on each process and uses a sequential SVD solve. Why does it do this instead
    376:    of using the composable PCREDUNDANT object?

    378: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC
    379: M*/

    383: PETSC_EXTERN PetscErrorCode PCCreate_SVD(PC pc)
    384: {
    385:   PC_SVD         *jac;

    389:   /*
    390:      Creates the private data structure for this preconditioner and
    391:      attach it to the PC object.
    392:   */
    393:   PetscNewLog(pc,&jac);
    394:   jac->zerosing = 1.e-12;
    395:   pc->data      = (void*)jac;

    397:   /*
    398:       Set the pointers for the functions that are provided above.
    399:       Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
    400:       are called, they will automatically call these functions.  Note we
    401:       choose not to provide a couple of these functions since they are
    402:       not needed.
    403:   */
    404:   pc->ops->apply           = PCApply_SVD;
    405:   pc->ops->applytranspose  = PCApplyTranspose_SVD;
    406:   pc->ops->setup           = PCSetUp_SVD;
    407:   pc->ops->reset           = PCReset_SVD;
    408:   pc->ops->destroy         = PCDestroy_SVD;
    409:   pc->ops->setfromoptions  = PCSetFromOptions_SVD;
    410:   pc->ops->view            = 0;
    411:   pc->ops->applyrichardson = 0;
    412:   return(0);
    413: }