Date: 2021-02-01T14:41:44+00:00

Actual source code: dssvd.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: #include <slepc/private/dsimpl.h>
     12: #include <slepcblaslapack.h>

     14: PetscErrorCode DSAllocate_SVD(DS ds,PetscInt ld)
     15: {

     19:   DSAllocateMat_Private(ds,DS_MAT_A);
     20:   DSAllocateMat_Private(ds,DS_MAT_U);
     21:   DSAllocateMat_Private(ds,DS_MAT_VT);
     22:   DSAllocateMatReal_Private(ds,DS_MAT_T);
     23:   PetscFree(ds->perm);
     24:   PetscMalloc1(ld,&ds->perm);
     25:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     26:   return(0);
     27: }

     29: /*   0       l           k                 n-1
     30:     -----------------------------------------
     31:     |*       .           .                  |
     32:     |  *     .           .                  |
     33:     |    *   .           .                  |
     34:     |      * .           .                  |
     35:     |        o           o                  |
     36:     |          o         o                  |
     37:     |            o       o                  |
     38:     |              o     o                  |
     39:     |                o   o                  |
     40:     |                  o o                  |
     41:     |                    o x                |
     42:     |                      x x              |
     43:     |                        x x            |
     44:     |                          x x          |
     45:     |                            x x        |
     46:     |                              x x      |
     47:     |                                x x    |
     48:     |                                  x x  |
     49:     |                                    x x|
     50:     |                                      x|
     51:     -----------------------------------------
     52: */

     54: static PetscErrorCode DSSwitchFormat_SVD(DS ds)
     55: {
     57:   PetscReal      *T = ds->rmat[DS_MAT_T];
     58:   PetscScalar    *A = ds->mat[DS_MAT_A];
     59:   PetscInt       i,m=ds->m,k=ds->k,ld=ds->ld;

     62:   if (!m) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"m was not set");
     63:   /* switch from compact (arrow) to dense storage */
     64:   PetscArrayzero(A,ld*ld);
     65:   for (i=0;i<k;i++) {
     66:     A[i+i*ld] = T[i];
     67:     A[i+k*ld] = T[i+ld];
     68:   }
     69:   A[k+k*ld] = T[k];
     70:   for (i=k+1;i<m;i++) {
     71:     A[i+i*ld]   = T[i];
     72:     A[i-1+i*ld] = T[i-1+ld];
     73:   }
     74:   return(0);
     75: }

     77: PetscErrorCode DSView_SVD(DS ds,PetscViewer viewer)
     78: {
     79:   PetscErrorCode    ierr;
     80:   PetscViewerFormat format;
     81:   PetscInt          i,j,r,c;
     82:   PetscReal         value;

     85:   PetscViewerGetFormat(viewer,&format);
     86:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
     87:   if (ds->compact) {
     88:     if (!ds->m) SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_WRONG,"m was not set");
     89:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
     90:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
     91:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->m);
     92:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",2*ds->n);
     93:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
     94:       for (i=0;i<PetscMin(ds->n,ds->m);i++) {
     95:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
     96:       }
     97:       for (i=0;i<PetscMin(ds->n,ds->m)-1;i++) {
     98:         r = PetscMax(i+2,ds->k+1);
     99:         c = i+1;
    100:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",c,r,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    101:       }
    102:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_T]);
    103:     } else {
    104:       for (i=0;i<ds->n;i++) {
    105:         for (j=0;j<ds->m;j++) {
    106:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
    107:           else if (i<ds->k && j==ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
    108:           else if (i==j+1 && i>ds->k) value = *(ds->rmat[DS_MAT_T]+ds->ld+i-1);
    109:           else value = 0.0;
    110:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
    111:         }
    112:         PetscViewerASCIIPrintf(viewer,"\n");
    113:       }
    114:     }
    115:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    116:     PetscViewerFlush(viewer);
    117:   } else {
    118:     DSViewMat(ds,viewer,DS_MAT_A);
    119:   }
    120:   if (ds->state>DS_STATE_INTERMEDIATE) {
    121:     DSViewMat(ds,viewer,DS_MAT_U);
    122:     DSViewMat(ds,viewer,DS_MAT_VT);
    123:   }
    124:   return(0);
    125: }

    127: PetscErrorCode DSVectors_SVD(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
    128: {
    130:   switch (mat) {
    131:     case DS_MAT_U:
    132:     case DS_MAT_VT:
    133:       if (rnorm) *rnorm = 0.0;
    134:       break;
    135:     default:
    136:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    137:   }
    138:   return(0);
    139: }

    141: PetscErrorCode DSSort_SVD(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    142: {
    144:   PetscInt       n,l,i,*perm,ld=ds->ld;
    145:   PetscScalar    *A;
    146:   PetscReal      *d;

    149:   if (!ds->sc) return(0);
    150:   l = ds->l;
    151:   n = PetscMin(ds->n,ds->m);
    152:   A = ds->mat[DS_MAT_A];
    153:   d = ds->rmat[DS_MAT_T];
    154:   perm = ds->perm;
    155:   if (!rr) {
    156:     DSSortEigenvaluesReal_Private(ds,d,perm);
    157:   } else {
    158:     DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
    159:   }
    160:   for (i=l;i<n;i++) wr[i] = d[perm[i]];
    161:   DSPermuteBoth_Private(ds,l,n,DS_MAT_U,DS_MAT_VT,perm);
    162:   for (i=l;i<n;i++) d[i] = PetscRealPart(wr[i]);
    163:   if (!ds->compact) {
    164:     for (i=l;i<n;i++) A[i+i*ld] = wr[i];
    165:   }
    166:   return(0);
    167: }

    169: PetscErrorCode DSSolve_SVD_DC(DS ds,PetscScalar *wr,PetscScalar *wi)
    170: {
    172:   PetscInt       i;
    173:   PetscBLASInt   n1,m1,info,l = 0,n = 0,m = 0,nm,ld,off,lwork;
    174:   PetscScalar    *A,*U,*VT,qwork;
    175:   PetscReal      *d,*e,*Ur,*VTr;
    176: #if defined(PETSC_USE_COMPLEX)
    177:   PetscInt       j;
    178: #endif

    181:   PetscBLASIntCast(ds->n,&n);
    182:   PetscBLASIntCast(ds->m,&m);
    183:   PetscBLASIntCast(ds->l,&l);
    184:   PetscBLASIntCast(ds->ld,&ld);
    185:   n1 = n-l;     /* n1 = size of leading block, excl. locked + size of trailing block */
    186:   m1 = m-l;
    187:   off = l+l*ld;
    188:   A  = ds->mat[DS_MAT_A];
    189:   U  = ds->mat[DS_MAT_U];
    190:   VT = ds->mat[DS_MAT_VT];
    191:   d  = ds->rmat[DS_MAT_T];
    192:   e  = ds->rmat[DS_MAT_T]+ld;
    193:   PetscArrayzero(U,ld*ld);
    194:   for (i=0;i<l;i++) U[i+i*ld] = 1.0;
    195:   PetscArrayzero(VT,ld*ld);
    196:   for (i=0;i<l;i++) VT[i+i*ld] = 1.0;

    198:   if (ds->state>DS_STATE_RAW) {
    199:     /* solve bidiagonal SVD problem */
    200:     for (i=0;i<l;i++) wr[i] = d[i];
    201:     DSAllocateWork_Private(ds,0,3*ld*ld+4*ld,8*ld);
    202: #if defined(PETSC_USE_COMPLEX)
    203:     DSAllocateMatReal_Private(ds,DS_MAT_U);
    204:     DSAllocateMatReal_Private(ds,DS_MAT_VT);
    205:     Ur  = ds->rmat[DS_MAT_U];
    206:     VTr = ds->rmat[DS_MAT_VT];
    207: #else
    208:     Ur  = U;
    209:     VTr = VT;
    210: #endif
    211:     PetscStackCallBLAS("LAPACKbdsdc",LAPACKbdsdc_("U","I",&n1,d+l,e+l,Ur+off,&ld,VTr+off,&ld,NULL,NULL,ds->rwork,ds->iwork,&info));
    212:     SlepcCheckLapackInfo("bdsdc",info);
    213: #if defined(PETSC_USE_COMPLEX)
    214:     for (i=l;i<n;i++) {
    215:       for (j=0;j<n;j++) {
    216:         U[i+j*ld] = Ur[i+j*ld];
    217:         VT[i+j*ld] = VTr[i+j*ld];
    218:       }
    219:     }
    220: #endif
    221:   } else {
    222:     /* solve general rectangular SVD problem */
    223:     if (ds->compact) { DSSwitchFormat_SVD(ds); }
    224:     for (i=0;i<l;i++) wr[i] = d[i];
    225:     nm = PetscMin(n,m);
    226:     DSAllocateWork_Private(ds,0,0,8*nm);
    227:     lwork = -1;
    228: #if defined(PETSC_USE_COMPLEX)
    229:     DSAllocateWork_Private(ds,0,5*nm*nm+7*nm,0);
    230:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,&qwork,&lwork,ds->rwork,ds->iwork,&info));
    231: #else
    232:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,&qwork,&lwork,ds->iwork,&info));
    233: #endif
    234:     SlepcCheckLapackInfo("gesdd",info);
    235:     PetscBLASIntCast((PetscInt)PetscRealPart(qwork),&lwork);
    236:     DSAllocateWork_Private(ds,lwork,0,0);
    237: #if defined(PETSC_USE_COMPLEX)
    238:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,ds->work,&lwork,ds->rwork,ds->iwork,&info));
    239: #else
    240:     PetscStackCallBLAS("LAPACKgesdd",LAPACKgesdd_("A",&n1,&m1,A+off,&ld,d+l,U+off,&ld,VT+off,&ld,ds->work,&lwork,ds->iwork,&info));
    241: #endif
    242:     SlepcCheckLapackInfo("gesdd",info);
    243:   }
    244:   for (i=l;i<PetscMin(ds->n,ds->m);i++) wr[i] = d[i];

    246:   /* create diagonal matrix as a result */
    247:   if (ds->compact) {
    248:     PetscArrayzero(e,n-1);
    249:   } else {
    250:     for (i=l;i<n;i++) {
    251:       PetscArrayzero(A+l+i*ld,n-l);
    252:     }
    253:     for (i=l;i<n;i++) A[i+i*ld] = d[i];
    254:   }
    255:   return(0);
    256: }

    258: PetscErrorCode DSSynchronize_SVD(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    259: {
    261:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
    262:   PetscMPIInt    n,rank,off=0,size,ldn,ld3;

    265:   if (ds->compact) kr = 3*ld;
    266:   else k = (ds->n-l)*ld;
    267:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
    268:   if (eigr) k += ds->n-l;
    269:   DSAllocateWork_Private(ds,k+kr,0,0);
    270:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
    271:   PetscMPIIntCast(ds->n-l,&n);
    272:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    273:   PetscMPIIntCast(3*ld,&ld3);
    274:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    275:   if (!rank) {
    276:     if (ds->compact) {
    277:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    278:     } else {
    279:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    280:     }
    281:     if (ds->state>DS_STATE_RAW) {
    282:       MPI_Pack(ds->mat[DS_MAT_U]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    283:       MPI_Pack(ds->mat[DS_MAT_VT]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    284:     }
    285:     if (eigr) {
    286:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    287:     }
    288:   }
    289:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    290:   if (rank) {
    291:     if (ds->compact) {
    292:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
    293:     } else {
    294:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    295:     }
    296:     if (ds->state>DS_STATE_RAW) {
    297:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_U]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    298:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_VT]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    299:     }
    300:     if (eigr) {
    301:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    302:     }
    303:   }
    304:   return(0);
    305: }

    307: PetscErrorCode DSMatGetSize_SVD(DS ds,DSMatType t,PetscInt *rows,PetscInt *cols)
    308: {
    310:   switch (t) {
    311:     case DS_MAT_A:
    312:     case DS_MAT_T:
    313:       *rows = ds->n;
    314:       *cols = ds->m;
    315:       break;
    316:     case DS_MAT_U:
    317:       *rows = ds->n;
    318:       *cols = ds->n;
    319:       break;
    320:     case DS_MAT_VT:
    321:       *rows = ds->m;
    322:       *cols = ds->m;
    323:       break;
    324:     default:
    325:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid t parameter");
    326:   }
    327:   return(0);
    328: }

    330: SLEPC_EXTERN PetscErrorCode DSCreate_SVD(DS ds)
    331: {
    333:   ds->ops->allocate      = DSAllocate_SVD;
    334:   ds->ops->view          = DSView_SVD;
    335:   ds->ops->vectors       = DSVectors_SVD;
    336:   ds->ops->solve[0]      = DSSolve_SVD_DC;
    337:   ds->ops->sort          = DSSort_SVD;
    338:   ds->ops->synchronize   = DSSynchronize_SVD;
    339:   ds->ops->matgetsize    = DSMatGetSize_SVD;
    340:   return(0);
    341: }