Actual source code: svd.c
petsc-3.10.5 2019-03-28
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      2:  #include <petsc/private/pcimpl.h>
      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: */
     35: static PetscErrorCode PCSetUp_SVD(PC pc)
     36: {
     37: #if defined(PETSC_MISSING_LAPACK_GESVD)
     38:   SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable\nNot able to provide singular value estimates.");
     39: #else
     40:   PC_SVD         *jac = (PC_SVD*)pc->data;
     42:   PetscScalar    *a,*u,*v,*d,*work;
     43:   PetscBLASInt   nb,lwork;
     44:   PetscInt       i,n;
     45:   PetscMPIInt    size;

     48:   MatDestroy(&jac->A);
     49:   MPI_Comm_size(((PetscObject)pc->pmat)->comm,&size);
     50:   if (size > 1) {
     51:     Mat          redmat;
     52:     MatCreateRedundantMatrix(pc->pmat,size,PETSC_COMM_SELF,MAT_INITIAL_MATRIX,&redmat);
     53:     MatConvert(redmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);
     54:     MatDestroy(&redmat);
     55:   } else {
     56:     MatConvert(pc->pmat,MATSEQDENSE,MAT_INITIAL_MATRIX,&jac->A);
     57:   }
     58:   if (!jac->diag) {    /* assume square matrices */
     59:     MatCreateVecs(jac->A,&jac->diag,&jac->work);
     60:   }
     61:   if (!jac->U) {
     62:     MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->U);
     63:     MatDuplicate(jac->A,MAT_DO_NOT_COPY_VALUES,&jac->Vt);
     64:   }
     65:   MatGetSize(jac->A,&n,NULL);
     66:   if (!n) {
     67:     PetscInfo(pc,"Matrix has zero rows, skipping svd\n");
     68:     return(0);
     69:   }
     70:   PetscBLASIntCast(n,&nb);
     71:   lwork = 5*nb;
     72:   PetscMalloc1(lwork,&work);
     73:   MatDenseGetArray(jac->A,&a);
     74:   MatDenseGetArray(jac->U,&u);
     75:   MatDenseGetArray(jac->Vt,&v);
     76:   VecGetArray(jac->diag,&d);
     77: #if !defined(PETSC_USE_COMPLEX)
     78:   {
     79:     PetscBLASInt lierr;
     80:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     81:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,d,u,&nb,v,&nb,work,&lwork,&lierr));
     82:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
     83:     PetscFPTrapPop();
     84:   }
     85: #else
     86:   {
     87:     PetscBLASInt lierr;
     88:     PetscReal    *rwork,*dd;
     89:     PetscMalloc1(5*nb,&rwork);
     90:     PetscMalloc1(nb,&dd);
     91:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     92:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nb,&nb,a,&nb,dd,u,&nb,v,&nb,work,&lwork,rwork,&lierr));
     93:     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"gesv() error %d",lierr);
     94:     PetscFree(rwork);
     95:     for (i=0; i<n; i++) d[i] = dd[i];
     96:     PetscFree(dd);
     97:     PetscFPTrapPop();
     98:   }
     99: #endif
    100:   MatDenseRestoreArray(jac->A,&a);
    101:   MatDenseRestoreArray(jac->U,&u);
    102:   MatDenseRestoreArray(jac->Vt,&v);
    103:   for (i=n-1; i>=0; i--) if (PetscRealPart(d[i]) > jac->zerosing) break;
    104:   jac->nzero = n-1-i;
    105:   if (jac->monitor) {
    106:     PetscViewerASCIIAddTab(jac->monitor,((PetscObject)pc)->tablevel);
    107:     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);
    108:     if (n >= 10) {              /* print 5 smallest and 5 largest */
    109:       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]));
    110:       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]));
    111:     } else {                    /* print all singular values */
    112:       char     buf[256],*p;
    113:       size_t   left = sizeof(buf),used;
    114:       PetscInt thisline;
    115:       for (p=buf,i=n-1,thisline=1; i>=0; i--,thisline++) {
    116:         PetscSNPrintfCount(p,left," %14.12e",&used,(double)PetscRealPart(d[i]));
    117:         left -= used;
    118:         p    += used;
    119:         if (thisline > 4 || i==0) {
    120:           PetscViewerASCIIPrintf(jac->monitor,"    SVD: singular values:%s\n",buf);
    121:           p        = buf;
    122:           thisline = 0;
    123:         }
    124:       }
    125:     }
    126:     PetscViewerASCIISubtractTab(jac->monitor,((PetscObject)pc)->tablevel);
    127:   }
    128:   PetscInfo2(pc,"Largest and smallest singular values %14.12e %14.12e\n",(double)PetscRealPart(d[0]),(double)PetscRealPart(d[n-1]));
    129:   for (i=0; i<n-jac->nzero; i++) d[i] = 1.0/d[i];
    130:   for (; i<n; i++) d[i] = 0.0;
    131:   if (jac->essrank > 0) for (i=0; i<n-jac->nzero-jac->essrank; i++) d[i] = 0.0; /* Skip all but essrank eigenvalues */
    132:   PetscInfo1(pc,"Number of zero or nearly singular values %D\n",jac->nzero);
    133:   VecRestoreArray(jac->diag,&d);
    134: #if defined(foo)
    135:   {
    136:     PetscViewer viewer;
    137:     PetscViewerBinaryOpen(PETSC_COMM_SELF,"joe",FILE_MODE_WRITE,&viewer);
    138:     MatView(jac->A,viewer);
    139:     MatView(jac->U,viewer);
    140:     MatView(jac->Vt,viewer);
    141:     VecView(jac->diag,viewer);
    142:     PetscViewerDestroy(viewer);
    143:   }
    144: #endif
    145:   PetscFree(work);
    146:   return(0);
    147: #endif
    148: }

    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: }

    187: static PetscErrorCode PCSVDRestoreVec(PC pc,PCSide side,AccessMode amode,Vec x,Vec *xred)
    188: {
    189:   PC_SVD         *jac = (PC_SVD*)pc->data;
    191:   PetscMPIInt    size;

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

    214: /* -------------------------------------------------------------------------- */
    215: /*
    216:    PCApply_SVD - Applies the SVD preconditioner to a vector.

    218:    Input Parameters:
    219: .  pc - the preconditioner context
    220: .  x - input vector

    222:    Output Parameter:
    223: .  y - output vector

    225:    Application Interface Routine: PCApply()
    226:  */
    227: static PetscErrorCode PCApply_SVD(PC pc,Vec x,Vec y)
    228: {
    229:   PC_SVD         *jac = (PC_SVD*)pc->data;
    230:   Vec            work = jac->work,xred,yred;

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

    252: static PetscErrorCode PCApplyTranspose_SVD(PC pc,Vec x,Vec y)
    253: {
    254:   PC_SVD         *jac = (PC_SVD*)pc->data;
    255:   Vec            work = jac->work,xred,yred;

    259:   PCSVDGetVec(pc,PC_LEFT,READ,x,&xred);
    260:   PCSVDGetVec(pc,PC_RIGHT,WRITE,y,&yred);
    261:   MatMult(jac->Vt,xred,work);
    262:   VecPointwiseMult(work,work,jac->diag);
    263:   MatMult(jac->U,work,yred);
    264:   PCSVDRestoreVec(pc,PC_LEFT,READ,x,&xred);
    265:   PCSVDRestoreVec(pc,PC_RIGHT,WRITE,y,&yred);
    266:   return(0);
    267: }

    269: static PetscErrorCode PCReset_SVD(PC pc)
    270: {
    271:   PC_SVD         *jac = (PC_SVD*)pc->data;

    275:   MatDestroy(&jac->A);
    276:   MatDestroy(&jac->U);
    277:   MatDestroy(&jac->Vt);
    278:   VecDestroy(&jac->diag);
    279:   VecDestroy(&jac->work);
    280:   VecScatterDestroy(&jac->right2red);
    281:   VecScatterDestroy(&jac->left2red);
    282:   VecDestroy(&jac->rightred);
    283:   VecDestroy(&jac->leftred);
    284:   return(0);
    285: }

    287: /* -------------------------------------------------------------------------- */
    288: /*
    289:    PCDestroy_SVD - Destroys the private context for the SVD preconditioner
    290:    that was created with PCCreate_SVD().

    292:    Input Parameter:
    293: .  pc - the preconditioner context

    295:    Application Interface Routine: PCDestroy()
    296: */
    297: static PetscErrorCode PCDestroy_SVD(PC pc)
    298: {
    299:   PC_SVD         *jac = (PC_SVD*)pc->data;

    303:   PCReset_SVD(pc);
    304:   PetscViewerDestroy(&jac->monitor);
    305:   PetscFree(pc->data);
    306:   return(0);
    307: }

    309: static PetscErrorCode PCSetFromOptions_SVD(PetscOptionItems *PetscOptionsObject,PC pc)
    310: {
    312:   PC_SVD         *jac = (PC_SVD*)pc->data;
    313:   PetscBool      flg,set;

    316:   PetscOptionsHead(PetscOptionsObject,"SVD options");
    317:   PetscOptionsReal("-pc_svd_zero_sing","Singular values smaller than this treated as zero","None",jac->zerosing,&jac->zerosing,NULL);
    318:   PetscOptionsInt("-pc_svd_ess_rank","Essential rank of operator (0 to use entire operator)","None",jac->essrank,&jac->essrank,NULL);
    319:   PetscOptionsBool("-pc_svd_monitor","Monitor the conditioning, and extremal singular values","None",jac->monitor ? PETSC_TRUE : PETSC_FALSE,&flg,&set);
    320:   if (set) {                    /* Should make PCSVDSetMonitor() */
    321:     if (flg && !jac->monitor) {
    322:       PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),"stdout",&jac->monitor);
    323:     } else if (!flg) {
    324:       PetscViewerDestroy(&jac->monitor);
    325:     }
    326:   }
    327:   PetscOptionsTail();
    328:   return(0);
    329: }

    331: static PetscErrorCode PCView_SVD(PC pc,PetscViewer viewer)
    332: {
    333:   PC_SVD         *svd = (PC_SVD*)pc->data;
    335:   PetscBool      iascii;

    338:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    339:   if (iascii) {
    340:     PetscViewerASCIIPrintf(viewer,"  All singular values smaller than %g treated as zero\n",(double)svd->zerosing);
    341:     PetscViewerASCIIPrintf(viewer,"  Provided essential rank of the matrix %D (all other eigenvalues are zeroed)\n",svd->essrank);
    342:   }
    343:   return(0);
    344: }
    345: /* -------------------------------------------------------------------------- */
    346: /*
    347:    PCCreate_SVD - Creates a SVD preconditioner context, PC_SVD,
    348:    and sets this as the private data within the generic preconditioning
    349:    context, PC, that was created within PCCreate().

    351:    Input Parameter:
    352: .  pc - the preconditioner context

    354:    Application Interface Routine: PCCreate()
    355: */

    357: /*MC
    358:      PCSVD - Use pseudo inverse defined by SVD of operator

    360:    Level: advanced

    362:   Concepts: SVD

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

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

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

    375: PETSC_EXTERN PetscErrorCode PCCreate_SVD(PC pc)
    376: {
    377:   PC_SVD         *jac;

    381:   /*
    382:      Creates the private data structure for this preconditioner and
    383:      attach it to the PC object.
    384:   */
    385:   PetscNewLog(pc,&jac);
    386:   jac->zerosing = 1.e-12;
    387:   pc->data      = (void*)jac;

    389:   /*
    390:       Set the pointers for the functions that are provided above.
    391:       Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
    392:       are called, they will automatically call these functions.  Note we
    393:       choose not to provide a couple of these functions since they are
    394:       not needed.
    395:   */
    396:   pc->ops->apply           = PCApply_SVD;
    397:   pc->ops->applytranspose  = PCApplyTranspose_SVD;
    398:   pc->ops->setup           = PCSetUp_SVD;
    399:   pc->ops->reset           = PCReset_SVD;
    400:   pc->ops->destroy         = PCDestroy_SVD;
    401:   pc->ops->setfromoptions  = PCSetFromOptions_SVD;
    402:   pc->ops->view            = PCView_SVD;
    403:   pc->ops->applyrichardson = 0;
    404:   return(0);
    405: }