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

Actual source code: dsghiep.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_GHIEP(DS ds,PetscInt ld)
     15: {

     19:   DSAllocateMat_Private(ds,DS_MAT_A);
     20:   DSAllocateMat_Private(ds,DS_MAT_B);
     21:   DSAllocateMat_Private(ds,DS_MAT_Q);
     22:   DSAllocateMatReal_Private(ds,DS_MAT_T);
     23:   DSAllocateMatReal_Private(ds,DS_MAT_D);
     24:   PetscFree(ds->perm);
     25:   PetscMalloc1(ld,&ds->perm);
     26:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     27:   return(0);
     28: }

     30: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
     31: {
     33:   PetscReal      *T,*S;
     34:   PetscScalar    *A,*B;
     35:   PetscInt       i,n,ld;

     38:   A = ds->mat[DS_MAT_A];
     39:   B = ds->mat[DS_MAT_B];
     40:   T = ds->rmat[DS_MAT_T];
     41:   S = ds->rmat[DS_MAT_D];
     42:   n = ds->n;
     43:   ld = ds->ld;
     44:   if (tocompact) { /* switch from dense (arrow) to compact storage */
     45:     PetscArrayzero(T,3*ld);
     46:     PetscArrayzero(S,ld);
     47:     for (i=0;i<n-1;i++) {
     48:       T[i]    = PetscRealPart(A[i+i*ld]);
     49:       T[ld+i] = PetscRealPart(A[i+1+i*ld]);
     50:       S[i]    = PetscRealPart(B[i+i*ld]);
     51:     }
     52:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
     53:     S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
     54:     for (i=ds->l;i<ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
     55:   } else { /* switch from compact (arrow) to dense storage */
     56:     PetscArrayzero(A,ld*ld);
     57:     PetscArrayzero(B,ld*ld);
     58:     for (i=0;i<n-1;i++) {
     59:       A[i+i*ld]     = T[i];
     60:       A[i+1+i*ld]   = T[ld+i];
     61:       A[i+(i+1)*ld] = T[ld+i];
     62:       B[i+i*ld]     = S[i];
     63:     }
     64:     A[n-1+(n-1)*ld] = T[n-1];
     65:     B[n-1+(n-1)*ld] = S[n-1];
     66:     for (i=ds->l;i<ds->k;i++) {
     67:       A[ds->k+i*ld] = T[2*ld+i];
     68:       A[i+ds->k*ld] = T[2*ld+i];
     69:     }
     70:   }
     71:   return(0);
     72: }

     74: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
     75: {
     76:   PetscErrorCode    ierr;
     77:   PetscViewerFormat format;
     78:   PetscInt          i,j;
     79:   PetscReal         value;
     80:   const char        *methodname[] = {
     81:                      "QR + Inverse Iteration",
     82:                      "HZ method",
     83:                      "QR"
     84:   };
     85:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

     88:   PetscViewerGetFormat(viewer,&format);
     89:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
     90:     if (ds->method<nmeth) {
     91:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
     92:     }
     93:     return(0);
     94:   }
     95:   if (ds->compact) {
     96:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
     97:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
     98:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
     99:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
    100:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
    101:       for (i=0;i<ds->n;i++) {
    102:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
    103:       }
    104:       for (i=0;i<ds->n-1;i++) {
    105:         if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
    106:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+2,i+1,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    107:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+2,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    108:         }
    109:       }
    110:       for (i = ds->l;i<ds->k;i++) {
    111:         if (*(ds->rmat[DS_MAT_T]+2*ds->ld+i)) {
    112:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",ds->k+1,i+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
    113:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,ds->k+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
    114:         }
    115:       }
    116:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);

    118:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
    119:       PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ds->n);
    120:       PetscViewerASCIIPrintf(viewer,"omega = [\n");
    121:       for (i=0;i<ds->n;i++) {
    122:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_D]+i));
    123:       }
    124:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);

    126:     } else {
    127:       PetscViewerASCIIPrintf(viewer,"T\n");
    128:       for (i=0;i<ds->n;i++) {
    129:         for (j=0;j<ds->n;j++) {
    130:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
    131:           else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
    132:           else if ((i<ds->k && j==ds->k) || (i==ds->k && j<ds->k)) value = *(ds->rmat[DS_MAT_T]+2*ds->ld+PetscMin(i,j));
    133:           else value = 0.0;
    134:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
    135:         }
    136:         PetscViewerASCIIPrintf(viewer,"\n");
    137:       }
    138:       PetscViewerASCIIPrintf(viewer,"omega\n");
    139:       for (i=0;i<ds->n;i++) {
    140:         for (j=0;j<ds->n;j++) {
    141:           if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
    142:           else value = 0.0;
    143:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
    144:         }
    145:         PetscViewerASCIIPrintf(viewer,"\n");
    146:       }
    147:     }
    148:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    149:     PetscViewerFlush(viewer);
    150:   } else {
    151:     DSViewMat(ds,viewer,DS_MAT_A);
    152:     DSViewMat(ds,viewer,DS_MAT_B);
    153:   }
    154:   if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_Q); }
    155:   return(0);
    156: }

    158: static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
    159: {
    161:   PetscReal      b[4],M[4],d1,d2,s1,s2,e;
    162:   PetscReal      scal1,scal2,wr1,wr2,wi,ep,norm;
    163:   PetscScalar    *Q,*X,Y[4],alpha,zeroS = 0.0;
    164:   PetscInt       k;
    165:   PetscBLASInt   two = 2,n_,ld,one=1;
    166: #if !defined(PETSC_USE_COMPLEX)
    167:   PetscBLASInt   four=4;
    168: #endif

    171:   X = ds->mat[DS_MAT_X];
    172:   Q = ds->mat[DS_MAT_Q];
    173:   k = *idx;
    174:   PetscBLASIntCast(ds->n,&n_);
    175:   PetscBLASIntCast(ds->ld,&ld);
    176:   if (k < ds->n-1) e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ld+k):PetscRealPart(*(ds->mat[DS_MAT_A]+(k+1)+ld*k));
    177:   else e = 0.0;
    178:   if (e == 0.0) { /* Real */
    179:     if (ds->state>=DS_STATE_CONDENSED) {
    180:       PetscArraycpy(X+k*ld,Q+k*ld,ld);
    181:     } else {
    182:       PetscArrayzero(X+k*ds->ld,ds->ld);
    183:       X[k+k*ds->ld] = 1.0;
    184:     }
    185:     if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
    186:   } else { /* 2x2 block */
    187:     if (ds->compact) {
    188:       s1 = *(ds->rmat[DS_MAT_D]+k);
    189:       d1 = *(ds->rmat[DS_MAT_T]+k);
    190:       s2 = *(ds->rmat[DS_MAT_D]+k+1);
    191:       d2 = *(ds->rmat[DS_MAT_T]+k+1);
    192:     } else {
    193:       s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
    194:       d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
    195:       s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
    196:       d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
    197:     }
    198:     M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    199:     b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    200:     ep = LAPACKlamch_("S");
    201:     /* Compute eigenvalues of the block */
    202:     PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    203:     if (wi==0.0) SETERRQ(PETSC_COMM_SELF,1,"Real block in DSVectors_GHIEP");
    204:     else { /* Complex eigenvalues */
    205:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    206:       wr1 /= scal1;
    207:       wi  /= scal1;
    208: #if !defined(PETSC_USE_COMPLEX)
    209:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
    210:         Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
    211:       } else {
    212:         Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
    213:       }
    214:       norm = BLASnrm2_(&four,Y,&one);
    215:       norm = 1.0/norm;
    216:       if (ds->state >= DS_STATE_CONDENSED) {
    217:         alpha = norm;
    218:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
    219:         if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
    220:       } else {
    221:         PetscArrayzero(X+k*ld,2*ld);
    222:         X[k*ld+k]       = Y[0]*norm;
    223:         X[k*ld+k+1]     = Y[1]*norm;
    224:         X[(k+1)*ld+k]   = Y[2]*norm;
    225:         X[(k+1)*ld+k+1] = Y[3]*norm;
    226:       }
    227: #else
    228:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
    229:         Y[0] = PetscCMPLX(wr1-s2*d2,wi);
    230:         Y[1] = s2*e;
    231:       } else {
    232:         Y[0] = s1*e;
    233:         Y[1] = PetscCMPLX(wr1-s1*d1,wi);
    234:       }
    235:       norm = BLASnrm2_(&two,Y,&one);
    236:       norm = 1.0/norm;
    237:       if (ds->state >= DS_STATE_CONDENSED) {
    238:         alpha = norm;
    239:         PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
    240:         if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
    241:       } else {
    242:         PetscArrayzero(X+k*ld,2*ld);
    243:         X[k*ld+k]   = Y[0]*norm;
    244:         X[k*ld+k+1] = Y[1]*norm;
    245:       }
    246:       X[(k+1)*ld+k]   = PetscConj(X[k*ld+k]);
    247:       X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
    248: #endif
    249:       (*idx)++;
    250:     }
    251:   }
    252:   return(0);
    253: }

    255: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
    256: {
    257:   PetscInt       i;
    258:   PetscReal      e;

    262:   switch (mat) {
    263:     case DS_MAT_X:
    264:     case DS_MAT_Y:
    265:       if (k) {
    266:         DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
    267:       } else {
    268:         for (i=0; i<ds->n; i++) {
    269:           e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
    270:           if (e == 0.0) { /* real */
    271:             if (ds->state >= DS_STATE_CONDENSED) {
    272:               PetscArraycpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld);
    273:             } else {
    274:               PetscArrayzero(ds->mat[mat]+i*ds->ld,ds->ld);
    275:               *(ds->mat[mat]+i+i*ds->ld) = 1.0;
    276:             }
    277:           } else {
    278:             DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
    279:           }
    280:         }
    281:       }
    282:       break;
    283:     case DS_MAT_U:
    284:     case DS_MAT_VT:
    285:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    286:     default:
    287:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    288:   }
    289:   return(0);
    290: }

    292: /*
    293:   Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
    294:   Only the index range n0..n1 is processed.
    295: */
    296: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
    297: {
    298:   PetscInt     k,ld;
    299:   PetscBLASInt two=2;
    300:   PetscScalar  *A,*B;
    301:   PetscReal    *D,*T;
    302:   PetscReal    b[4],M[4],d1,d2,s1,s2,e;
    303:   PetscReal    scal1,scal2,ep,wr1,wr2,wi1;

    306:   ld = ds->ld;
    307:   A = ds->mat[DS_MAT_A];
    308:   B = ds->mat[DS_MAT_B];
    309:   D = ds->rmat[DS_MAT_D];
    310:   T = ds->rmat[DS_MAT_T];
    311:   for (k=n0;k<n1;k++) {
    312:     if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
    313:     else e = 0.0;
    314:     if (e==0.0) { /* real eigenvalue */
    315:       wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
    316: #if !defined(PETSC_USE_COMPLEX)
    317:       wi[k] = 0.0 ;
    318: #endif
    319:     } else { /* diagonal block */
    320:       if (ds->compact) {
    321:         s1 = D[k];
    322:         d1 = T[k];
    323:         s2 = D[k+1];
    324:         d2 = T[k+1];
    325:       } else {
    326:         s1 = PetscRealPart(B[k*ld+k]);
    327:         d1 = PetscRealPart(A[k+k*ld]);
    328:         s2 = PetscRealPart(B[(k+1)*ld+k+1]);
    329:         d2 = PetscRealPart(A[k+1+(k+1)*ld]);
    330:       }
    331:       M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    332:       b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    333:       ep = LAPACKlamch_("S");
    334:       /* Compute eigenvalues of the block */
    335:       PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
    336:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    337:       if (wi1==0.0) { /* Real eigenvalues */
    338:         if (scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    339:         wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
    340: #if !defined(PETSC_USE_COMPLEX)
    341:         wi[k] = wi[k+1] = 0.0;
    342: #endif
    343:       } else { /* Complex eigenvalues */
    344: #if !defined(PETSC_USE_COMPLEX)
    345:         wr[k]   = wr1/scal1;
    346:         wr[k+1] = wr[k];
    347:         wi[k]   = wi1/scal1;
    348:         wi[k+1] = -wi[k];
    349: #else
    350:         wr[k]   = PetscCMPLX(wr1,wi1)/scal1;
    351:         wr[k+1] = PetscConj(wr[k]);
    352: #endif
    353:       }
    354:       k++;
    355:     }
    356:   }
    357: #if defined(PETSC_USE_COMPLEX)
    358:   if (wi) {
    359:     for (k=n0;k<n1;k++) wi[k] = 0.0;
    360:   }
    361: #endif
    362:   return(0);
    363: }

    365: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    366: {
    368:   PetscInt       n,i,*perm;
    369:   PetscReal      *d,*e,*s;

    372: #if !defined(PETSC_USE_COMPLEX)
    374: #endif
    375:   n = ds->n;
    376:   d = ds->rmat[DS_MAT_T];
    377:   e = d + ds->ld;
    378:   s = ds->rmat[DS_MAT_D];
    379:   DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
    380:   perm = ds->perm;
    381:   if (!rr) {
    382:     rr = wr;
    383:     ri = wi;
    384:   }
    385:   DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
    386:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_TRUE); }
    387:   PetscArraycpy(ds->work,wr,n);
    388:   for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
    389: #if !defined(PETSC_USE_COMPLEX)
    390:   PetscArraycpy(ds->work,wi,n);
    391:   for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
    392: #endif
    393:   PetscArraycpy(ds->rwork,s,n);
    394:   for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
    395:   PetscArraycpy(ds->rwork,d,n);
    396:   for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
    397:   PetscArraycpy(ds->rwork,e,n-1);
    398:   PetscArrayzero(e+ds->l,n-1-ds->l);
    399:   for (i=ds->l;i<n-1;i++) {
    400:     if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
    401:   }
    402:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
    403:   DSPermuteColumns_Private(ds,ds->l,n,DS_MAT_Q,perm);
    404:   return(0);
    405: }

    407: /*
    408:   Get eigenvectors with inverse iteration.
    409:   The system matrix is in Hessenberg form.
    410: */
    411: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
    412: {
    414:   PetscInt       i,off;
    415:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
    416:   PetscScalar    *A,*B,*H,*X;
    417:   PetscReal      *s,*d,*e;
    418: #if defined(PETSC_USE_COMPLEX)
    419:   PetscInt       j;
    420: #endif

    423:   PetscBLASIntCast(ds->ld,&ld);
    424:   PetscBLASIntCast(ds->n-ds->l,&n1);
    425:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
    426:   DSAllocateMat_Private(ds,DS_MAT_W);
    427:   A = ds->mat[DS_MAT_A];
    428:   B = ds->mat[DS_MAT_B];
    429:   H = ds->mat[DS_MAT_W];
    430:   s = ds->rmat[DS_MAT_D];
    431:   d = ds->rmat[DS_MAT_T];
    432:   e = d + ld;
    433:   select = ds->iwork;
    434:   infoC = ds->iwork + ld;
    435:   off = ds->l+ds->l*ld;
    436:   if (ds->compact) {
    437:     H[off] = d[ds->l]*s[ds->l];
    438:     H[off+ld] = e[ds->l]*s[ds->l];
    439:     for (i=ds->l+1;i<ds->n-1;i++) {
    440:       H[i+(i-1)*ld] = e[i-1]*s[i];
    441:       H[i+i*ld] = d[i]*s[i];
    442:       H[i+(i+1)*ld] = e[i]*s[i];
    443:     }
    444:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    445:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    446:   } else {
    447:     s[ds->l]  = PetscRealPart(B[off]);
    448:     H[off]    = A[off]*s[ds->l];
    449:     H[off+ld] = A[off+ld]*s[ds->l];
    450:     for (i=ds->l+1;i<ds->n-1;i++) {
    451:       s[i] = PetscRealPart(B[i+i*ld]);
    452:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    453:       H[i+i*ld]     = A[i+i*ld]*s[i];
    454:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    455:     }
    456:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    457:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    458:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    459:   }
    460:   DSAllocateMat_Private(ds,DS_MAT_X);
    461:   X = ds->mat[DS_MAT_X];
    462:   for (i=0;i<n1;i++) select[i] = 1;
    463: #if !defined(PETSC_USE_COMPLEX)
    464:   PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,NULL,infoC,&info));
    465: #else
    466:   PetscStackCallBLAS("LAPACKhsein",LAPACKhsein_("R","N","N",select,&n1,H+off,&ld,wr+ds->l,NULL,&ld,X+off,&ld,&n1,&mout,ds->work,ds->rwork,NULL,infoC,&info));

    468:   /* Separate real and imaginary part of complex eigenvectors */
    469:   for (j=ds->l;j<ds->n;j++) {
    470:     if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
    471:       for (i=ds->l;i<ds->n;i++) {
    472:         X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
    473:         X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
    474:       }
    475:       j++;
    476:     }
    477:   }
    478: #endif
    479:   SlepcCheckLapackInfo("hsein",info);
    480:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
    481:   return(0);
    482: }

    484: /*
    485:    Undo 2x2 blocks that have real eigenvalues.
    486: */
    487: PetscErrorCode DSGHIEPRealBlocks(DS ds)
    488: {
    490:   PetscInt       i;
    491:   PetscReal      e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
    492:   PetscReal      maxy,ep,scal1,scal2,snorm;
    493:   PetscReal      *T,*D,b[4],M[4],wr1,wr2,wi;
    494:   PetscScalar    *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
    495:   PetscBLASInt   m,two=2,ld;
    496:   PetscBool      isreal;

    499:   PetscBLASIntCast(ds->ld,&ld);
    500:   PetscBLASIntCast(ds->n-ds->l,&m);
    501:   A = ds->mat[DS_MAT_A];
    502:   B = ds->mat[DS_MAT_B];
    503:   T = ds->rmat[DS_MAT_T];
    504:   D = ds->rmat[DS_MAT_D];
    505:   DSAllocateWork_Private(ds,2*m,0,0);
    506:   for (i=ds->l;i<ds->n-1;i++) {
    507:     e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
    508:     if (e != 0.0) { /* 2x2 block */
    509:       if (ds->compact) {
    510:         s1 = D[i];
    511:         d1 = T[i];
    512:         s2 = D[i+1];
    513:         d2 = T[i+1];
    514:       } else {
    515:         s1 = PetscRealPart(B[i*ld+i]);
    516:         d1 = PetscRealPart(A[i*ld+i]);
    517:         s2 = PetscRealPart(B[(i+1)*ld+i+1]);
    518:         d2 = PetscRealPart(A[(i+1)*ld+i+1]);
    519:       }
    520:       isreal = PETSC_FALSE;
    521:       if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
    522:         dd = d1-d2;
    523:         if (2*PetscAbsReal(e) <= dd) {
    524:           t = 2*e/dd;
    525:           t = t/(1 + PetscSqrtReal(1+t*t));
    526:         } else {
    527:           t = dd/(2*e);
    528:           ss = (t>=0)?1.0:-1.0;
    529:           t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
    530:         }
    531:         Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
    532:         Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
    533:         wr1 = d1+t*e; wr2 = d2-t*e;
    534:         ss1 = s1; ss2 = s2;
    535:         isreal = PETSC_TRUE;
    536:       } else {
    537:         ss1 = 1.0; ss2 = 1.0,
    538:         M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    539:         b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    540:         ep = LAPACKlamch_("S");

    542:         /* Compute eigenvalues of the block */
    543:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    544:         if (wi==0.0) { /* Real eigenvalues */
    545:           isreal = PETSC_TRUE;
    546:           if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    547:           wr1 /= scal1;
    548:           wr2 /= scal2;
    549:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
    550:             Y[0] = wr1-s2*d2;
    551:             Y[1] = s2*e;
    552:           } else {
    553:             Y[0] = s1*e;
    554:             Y[1] = wr1-s1*d1;
    555:           }
    556:           /* normalize with a signature*/
    557:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
    558:           scal1 = PetscRealPart(Y[0])/maxy;
    559:           scal2 = PetscRealPart(Y[1])/maxy;
    560:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    561:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
    562:           snorm = maxy*PetscSqrtReal(snorm);
    563:           Y[0] = Y[0]/snorm;
    564:           Y[1] = Y[1]/snorm;
    565:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
    566:             Y[2] = wr2-s2*d2;
    567:             Y[3] = s2*e;
    568:           } else {
    569:             Y[2] = s1*e;
    570:             Y[3] = wr2-s1*d1;
    571:           }
    572:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
    573:           scal1 = PetscRealPart(Y[2])/maxy;
    574:           scal2 = PetscRealPart(Y[3])/maxy;
    575:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    576:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
    577:           snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
    578:         }
    579:         wr1 *= ss1; wr2 *= ss2;
    580:       }
    581:       if (isreal) {
    582:         if (ds->compact) {
    583:           D[i]    = ss1;
    584:           T[i]    = wr1;
    585:           D[i+1]  = ss2;
    586:           T[i+1]  = wr2;
    587:           T[ld+i] = 0.0;
    588:         } else {
    589:           B[i*ld+i]       = ss1;
    590:           A[i*ld+i]       = wr1;
    591:           B[(i+1)*ld+i+1] = ss2;
    592:           A[(i+1)*ld+i+1] = wr2;
    593:           A[(i+1)+ld*i]   = 0.0;
    594:           A[i+ld*(i+1)]   = 0.0;
    595:         }
    596:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&two,&two,&oneS,ds->mat[DS_MAT_Q]+ds->l+i*ld,&ld,Y,&two,&zeroS,ds->work,&m));
    597:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m);
    598:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m);
    599:       }
    600:       i++;
    601:     }
    602:   }
    603:   return(0);
    604: }

    606: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
    607: {
    609:   PetscInt       i,off;
    610:   PetscBLASInt   n1,ld,one,info,lwork;
    611:   PetscScalar    *H,*A,*B,*Q;
    612:   PetscReal      *d,*e,*s;
    613: #if defined(PETSC_USE_COMPLEX)
    614:   PetscInt       j;
    615: #endif

    618: #if !defined(PETSC_USE_COMPLEX)
    620: #endif
    621:   one = 1;
    622:   PetscBLASIntCast(ds->n-ds->l,&n1);
    623:   PetscBLASIntCast(ds->ld,&ld);
    624:   off = ds->l + ds->l*ld;
    625:   A = ds->mat[DS_MAT_A];
    626:   B = ds->mat[DS_MAT_B];
    627:   Q = ds->mat[DS_MAT_Q];
    628:   d = ds->rmat[DS_MAT_T];
    629:   e = ds->rmat[DS_MAT_T] + ld;
    630:   s = ds->rmat[DS_MAT_D];
    631:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
    632:   lwork = ld*ld;

    634:   /* Quick return if possible */
    635:   if (n1 == 1) {
    636:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
    637:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    638:     if (!ds->compact) {
    639:       d[ds->l] = PetscRealPart(A[off]);
    640:       s[ds->l] = PetscRealPart(B[off]);
    641:     }
    642:     wr[ds->l] = d[ds->l]/s[ds->l];
    643:     if (wi) wi[ds->l] = 0.0;
    644:     return(0);
    645:   }
    646:   /* Reduce to pseudotriadiagonal form */
    647:   DSIntermediate_GHIEP(ds);

    649:   /* Compute Eigenvalues (QR)*/
    650:   DSAllocateMat_Private(ds,DS_MAT_W);
    651:   H = ds->mat[DS_MAT_W];
    652:   if (ds->compact) {
    653:     H[off]    = d[ds->l]*s[ds->l];
    654:     H[off+ld] = e[ds->l]*s[ds->l];
    655:     for (i=ds->l+1;i<ds->n-1;i++) {
    656:       H[i+(i-1)*ld] = e[i-1]*s[i];
    657:       H[i+i*ld]     = d[i]*s[i];
    658:       H[i+(i+1)*ld] = e[i]*s[i];
    659:     }
    660:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    661:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    662:   } else {
    663:     s[ds->l]  = PetscRealPart(B[off]);
    664:     H[off]    = A[off]*s[ds->l];
    665:     H[off+ld] = A[off+ld]*s[ds->l];
    666:     for (i=ds->l+1;i<ds->n-1;i++) {
    667:       s[i] = PetscRealPart(B[i+i*ld]);
    668:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    669:       H[i+i*ld]     = A[i+i*ld]*s[i];
    670:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    671:     }
    672:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    673:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    674:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    675:   }

    677: #if !defined(PETSC_USE_COMPLEX)
    678:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
    679: #else
    680:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
    681:   for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
    682:   /* Sort to have consecutive conjugate pairs */
    683:   for (i=ds->l;i<ds->n;i++) {
    684:       j=i+1;
    685:       while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    686:       if (j==ds->n) {
    687:         if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) wr[i]=PetscRealPart(wr[i]);
    688:         else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
    689:       } else { /* complex eigenvalue */
    690:         wr[j] = wr[i+1];
    691:         if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
    692:         wr[i+1] = PetscConj(wr[i]);
    693:         i++;
    694:       }
    695:   }
    696: #endif
    697:   SlepcCheckLapackInfo("hseqr",info);
    698:   /* Compute Eigenvectors with Inverse Iteration */
    699:   DSGHIEPInverseIteration(ds,wr,wi);

    701:   /* Recover eigenvalues from diagonal */
    702:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    703: #if defined(PETSC_USE_COMPLEX)
    704:   if (wi) {
    705:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    706:   }
    707: #endif
    708:   return(0);
    709: }

    711: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
    712: {
    714:   PetscInt       i,j,off,nwu=0,n,lw,lwr,nwru=0;
    715:   PetscBLASInt   n_,ld,info,lwork,ilo,ihi;
    716:   PetscScalar    *H,*A,*B,*Q,*X;
    717:   PetscReal      *d,*s,*scale,nrm,*rcde,*rcdv;
    718: #if defined(PETSC_USE_COMPLEX)
    719:   PetscInt       k;
    720: #endif

    723: #if !defined(PETSC_USE_COMPLEX)
    725: #endif
    726:   n = ds->n-ds->l;
    727:   PetscBLASIntCast(n,&n_);
    728:   PetscBLASIntCast(ds->ld,&ld);
    729:   off = ds->l + ds->l*ld;
    730:   A = ds->mat[DS_MAT_A];
    731:   B = ds->mat[DS_MAT_B];
    732:   Q = ds->mat[DS_MAT_Q];
    733:   d = ds->rmat[DS_MAT_T];
    734:   s = ds->rmat[DS_MAT_D];
    735:   lw = 14*ld+ld*ld;
    736:   lwr = 7*ld;
    737:   DSAllocateWork_Private(ds,lw,lwr,0);
    738:   scale = ds->rwork+nwru;
    739:   nwru += ld;
    740:   rcde = ds->rwork+nwru;
    741:   nwru += ld;
    742:   rcdv = ds->rwork+nwru;
    743:   nwru += ld;
    744:   /* Quick return if possible */
    745:   if (n_ == 1) {
    746:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
    747:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    748:     if (!ds->compact) {
    749:       d[ds->l] = PetscRealPart(A[off]);
    750:       s[ds->l] = PetscRealPart(B[off]);
    751:     }
    752:     wr[ds->l] = d[ds->l]/s[ds->l];
    753:     if (wi) wi[ds->l] = 0.0;
    754:     return(0);
    755:   }

    757:   /* Form pseudo-symmetric matrix */
    758:   H =  ds->work+nwu;
    759:   nwu += n*n;
    760:   PetscArrayzero(H,n*n);
    761:   if (ds->compact) {
    762:     for (i=0;i<n-1;i++) {
    763:       H[i+i*n]     = s[ds->l+i]*d[ds->l+i];
    764:       H[i+1+i*n]   = s[ds->l+i+1]*d[ld+ds->l+i];
    765:       H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
    766:     }
    767:     H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
    768:     for (i=0;i<ds->k-ds->l;i++) {
    769:       H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
    770:       H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
    771:     }
    772:   } else {
    773:     for (j=0;j<n;j++) {
    774:       for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
    775:     }
    776:   }

    778:   /* Compute eigenpairs */
    779:   PetscBLASIntCast(lw-nwu,&lwork);
    780:   DSAllocateMat_Private(ds,DS_MAT_X);
    781:   X = ds->mat[DS_MAT_X];
    782: #if !defined(PETSC_USE_COMPLEX)
    783:   PetscStackCallBLAS("LAPACKgeevx",LAPACKgeevx_("B","N","V","N",&n_,H,&n_,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,&ilo,&ihi,scale,&nrm,rcde,rcdv,ds->work+nwu,&lwork,NULL,&info));
    784: #else
    785:   PetscStackCallBLAS("LAPACKgeevx",LAPACKgeevx_("B","N","V","N",&n_,H,&n_,wr+ds->l,NULL,&ld,X+off,&ld,&ilo,&ihi,scale,&nrm,rcde,rcdv,ds->work+nwu,&lwork,ds->rwork+nwru,&info));

    787:   /* Sort to have consecutive conjugate pairs
    788:      Separate real and imaginary part of complex eigenvectors*/
    789:   for (i=ds->l;i<ds->n;i++) {
    790:     j=i+1;
    791:     while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    792:     if (j==ds->n) {
    793:       if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) {
    794:         wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
    795:         for (k=ds->l;k<ds->n;k++) {
    796:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    797:         }
    798:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
    799:     } else { /* complex eigenvalue */
    800:       if (j!=i+1) {
    801:         wr[j] = wr[i+1];
    802:         PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld);
    803:       }
    804:       if (PetscImaginaryPart(wr[i])<0) {
    805:         wr[i] = PetscConj(wr[i]);
    806:         for (k=ds->l;k<ds->n;k++) {
    807:           X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
    808:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    809:         }
    810:       } else {
    811:         for (k=ds->l;k<ds->n;k++) {
    812:           X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
    813:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    814:         }
    815:       }
    816:       wr[i+1] = PetscConj(wr[i]);
    817:       i++;
    818:     }
    819:   }
    820: #endif
    821:   SlepcCheckLapackInfo("geevx",info);

    823:   /* Compute real s-orthonormal basis */
    824:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_FALSE);

    826:   /* Recover eigenvalues from diagonal */
    827:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    828: #if defined(PETSC_USE_COMPLEX)
    829:   if (wi) {
    830:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    831:   }
    832: #endif
    833:   return(0);
    834: }

    836: PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    837: {
    839:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
    840:   PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;

    843:   if (ds->compact) kr = 4*ld;
    844:   else k = 2*(ds->n-l)*ld;
    845:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    846:   if (eigr) k += (ds->n-l);
    847:   if (eigi) k += (ds->n-l);
    848:   DSAllocateWork_Private(ds,k+kr,0,0);
    849:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
    850:   PetscMPIIntCast(ds->n-l,&n);
    851:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    852:   PetscMPIIntCast(ld*3,&ld3);
    853:   PetscMPIIntCast(ld,&ld_);
    854:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    855:   if (!rank) {
    856:     if (ds->compact) {
    857:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    858:       MPI_Pack(ds->rmat[DS_MAT_D],ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    859:     } else {
    860:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    861:       MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    862:     }
    863:     if (ds->state>DS_STATE_RAW) {
    864:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    865:     }
    866:     if (eigr) {
    867:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    868:     }
    869:     if (eigi) {
    870:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    871:     }
    872:   }
    873:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    874:   if (rank) {
    875:     if (ds->compact) {
    876:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
    877:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_D],ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds));
    878:     } else {
    879:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    880:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    881:     }
    882:     if (ds->state>DS_STATE_RAW) {
    883:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    884:     }
    885:     if (eigr) {
    886:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    887:     }
    888:     if (eigi) {
    889:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    890:     }
    891:   }
    892:   return(0);
    893: }

    895: PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
    896: {
    898:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
    899:   else *flg = PETSC_FALSE;
    900:   return(0);
    901: }

    903: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
    904: {
    906:   ds->ops->allocate      = DSAllocate_GHIEP;
    907:   ds->ops->view          = DSView_GHIEP;
    908:   ds->ops->vectors       = DSVectors_GHIEP;
    909:   ds->ops->solve[0]      = DSSolve_GHIEP_QR_II;
    910:   ds->ops->solve[1]      = DSSolve_GHIEP_HZ;
    911:   ds->ops->solve[2]      = DSSolve_GHIEP_QR;
    912:   ds->ops->sort          = DSSort_GHIEP;
    913:   ds->ops->synchronize   = DSSynchronize_GHIEP;
    914:   ds->ops->hermitian     = DSHermitian_GHIEP;
    915:   return(0);
    916: }