Date: 2020-01-13T11:59:13+00:00

Actual source code: dsghiep.c
slepc-3.12.2 2020-01-13
Report Typos and Errors

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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: {
    160: #if defined(SLEPC_MISSING_LAPACK_LAG2)
    162:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LAG2 - Lapack routine is unavailable");
    163: #else
    165:   PetscReal      b[4],M[4],d1,d2,s1,s2,e;
    166:   PetscReal      scal1,scal2,wr1,wr2,wi,ep,norm;
    167:   PetscScalar    *Q,*X,Y[4],alpha,zeroS = 0.0;
    168:   PetscInt       k;
    169:   PetscBLASInt   two = 2,n_,ld,one=1;
    170: #if !defined(PETSC_USE_COMPLEX)
    171:   PetscBLASInt   four=4;
    172: #endif

    175:   X = ds->mat[DS_MAT_X];
    176:   Q = ds->mat[DS_MAT_Q];
    177:   k = *idx;
    178:   PetscBLASIntCast(ds->n,&n_);
    179:   PetscBLASIntCast(ds->ld,&ld);
    180:   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));
    181:   else e = 0.0;
    182:   if (e == 0.0) { /* Real */
    183:     if (ds->state>=DS_STATE_CONDENSED) {
    184:       PetscArraycpy(X+k*ld,Q+k*ld,ld);
    185:     } else {
    186:       PetscArrayzero(X+k*ds->ld,ds->ld);
    187:       X[k+k*ds->ld] = 1.0;
    188:     }
    189:     if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
    190:   } else { /* 2x2 block */
    191:     if (ds->compact) {
    192:       s1 = *(ds->rmat[DS_MAT_D]+k);
    193:       d1 = *(ds->rmat[DS_MAT_T]+k);
    194:       s2 = *(ds->rmat[DS_MAT_D]+k+1);
    195:       d2 = *(ds->rmat[DS_MAT_T]+k+1);
    196:     } else {
    197:       s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
    198:       d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
    199:       s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
    200:       d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
    201:     }
    202:     M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    203:     b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    204:     ep = LAPACKlamch_("S");
    205:     /* Compute eigenvalues of the block */
    206:     PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    207:     if (wi==0.0) SETERRQ(PETSC_COMM_SELF,1,"Real block in DSVectors_GHIEP");
    208:     else { /* Complex eigenvalues */
    209:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    210:       wr1 /= scal1;
    211:       wi  /= scal1;
    212: #if !defined(PETSC_USE_COMPLEX)
    213:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
    214:         Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
    215:       } else {
    216:         Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
    217:       }
    218:       norm = BLASnrm2_(&four,Y,&one);
    219:       norm = 1.0/norm;
    220:       if (ds->state >= DS_STATE_CONDENSED) {
    221:         alpha = norm;
    222:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
    223:         if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
    224:       } else {
    225:         PetscArrayzero(X+k*ld,2*ld);
    226:         X[k*ld+k]       = Y[0]*norm;
    227:         X[k*ld+k+1]     = Y[1]*norm;
    228:         X[(k+1)*ld+k]   = Y[2]*norm;
    229:         X[(k+1)*ld+k+1] = Y[3]*norm;
    230:       }
    231: #else
    232:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
    233:         Y[0] = PetscCMPLX(wr1-s2*d2,wi);
    234:         Y[1] = s2*e;
    235:       } else {
    236:         Y[0] = s1*e;
    237:         Y[1] = PetscCMPLX(wr1-s1*d1,wi);
    238:       }
    239:       norm = BLASnrm2_(&two,Y,&one);
    240:       norm = 1.0/norm;
    241:       if (ds->state >= DS_STATE_CONDENSED) {
    242:         alpha = norm;
    243:         PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
    244:         if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
    245:       } else {
    246:         PetscArrayzero(X+k*ld,2*ld);
    247:         X[k*ld+k]   = Y[0]*norm;
    248:         X[k*ld+k+1] = Y[1]*norm;
    249:       }
    250:       X[(k+1)*ld+k]   = PetscConj(X[k*ld+k]);
    251:       X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
    252: #endif
    253:       (*idx)++;
    254:     }
    255:   }
    256:   return(0);
    257: #endif
    258: }

    260: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
    261: {
    262:   PetscInt       i;
    263:   PetscReal      e;

    267:   switch (mat) {
    268:     case DS_MAT_X:
    269:     case DS_MAT_Y:
    270:       if (k) {
    271:         DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
    272:       } else {
    273:         for (i=0; i<ds->n; i++) {
    274:           e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
    275:           if (e == 0.0) { /* real */
    276:             if (ds->state >= DS_STATE_CONDENSED) {
    277:               PetscArraycpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld);
    278:             } else {
    279:               PetscArrayzero(ds->mat[mat]+i*ds->ld,ds->ld);
    280:               *(ds->mat[mat]+i+i*ds->ld) = 1.0;
    281:             }
    282:           } else {
    283:             DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
    284:           }
    285:         }
    286:       }
    287:       break;
    288:     case DS_MAT_U:
    289:     case DS_MAT_VT:
    290:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
    291:       break;
    292:     default:
    293:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    294:   }
    295:   return(0);
    296: }

    298: /*
    299:   Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
    300:   Only the index range n0..n1 is processed.
    301: */
    302: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
    303: {
    304: #if defined(SLEPC_MISSING_LAPACK_LAG2)
    306:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LAG2 - Lapack routine is unavailable");
    307: #else
    308:   PetscInt     k,ld;
    309:   PetscBLASInt two=2;
    310:   PetscScalar  *A,*B;
    311:   PetscReal    *D,*T;
    312:   PetscReal    b[4],M[4],d1,d2,s1,s2,e;
    313:   PetscReal    scal1,scal2,ep,wr1,wr2,wi1;

    316:   ld = ds->ld;
    317:   A = ds->mat[DS_MAT_A];
    318:   B = ds->mat[DS_MAT_B];
    319:   D = ds->rmat[DS_MAT_D];
    320:   T = ds->rmat[DS_MAT_T];
    321:   for (k=n0;k<n1;k++) {
    322:     if (k < n1-1) e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
    323:     else e = 0.0;
    324:     if (e==0.0) { /* real eigenvalue */
    325:       wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
    326: #if !defined(PETSC_USE_COMPLEX)
    327:       wi[k] = 0.0 ;
    328: #endif
    329:     } else { /* diagonal block */
    330:       if (ds->compact) {
    331:         s1 = D[k];
    332:         d1 = T[k];
    333:         s2 = D[k+1];
    334:         d2 = T[k+1];
    335:       } else {
    336:         s1 = PetscRealPart(B[k*ld+k]);
    337:         d1 = PetscRealPart(A[k+k*ld]);
    338:         s2 = PetscRealPart(B[(k+1)*ld+k+1]);
    339:         d2 = PetscRealPart(A[k+1+(k+1)*ld]);
    340:       }
    341:       M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    342:       b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    343:       ep = LAPACKlamch_("S");
    344:       /* Compute eigenvalues of the block */
    345:       PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
    346:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    347:       if (wi1==0.0) { /* Real eigenvalues */
    348:         if (scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    349:         wr[k] = wr1/scal1; wr[k+1] = wr2/scal2;
    350: #if !defined(PETSC_USE_COMPLEX)
    351:         wi[k] = wi[k+1] = 0.0;
    352: #endif
    353:       } else { /* Complex eigenvalues */
    354: #if !defined(PETSC_USE_COMPLEX)
    355:         wr[k]   = wr1/scal1;
    356:         wr[k+1] = wr[k];
    357:         wi[k]   = wi1/scal1;
    358:         wi[k+1] = -wi[k];
    359: #else
    360:         wr[k]   = PetscCMPLX(wr1,wi1)/scal1;
    361:         wr[k+1] = PetscConj(wr[k]);
    362: #endif
    363:       }
    364:       k++;
    365:     }
    366:   }
    367: #if defined(PETSC_USE_COMPLEX)
    368:   if (wi) {
    369:     for (k=n0;k<n1;k++) wi[k] = 0.0;
    370:   }
    371: #endif
    372:   return(0);
    373: #endif
    374: }

    376: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    377: {
    379:   PetscInt       n,i,*perm;
    380:   PetscReal      *d,*e,*s;

    383: #if !defined(PETSC_USE_COMPLEX)
    385: #endif
    386:   n = ds->n;
    387:   d = ds->rmat[DS_MAT_T];
    388:   e = d + ds->ld;
    389:   s = ds->rmat[DS_MAT_D];
    390:   DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
    391:   perm = ds->perm;
    392:   if (!rr) {
    393:     rr = wr;
    394:     ri = wi;
    395:   }
    396:   DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
    397:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_TRUE); }
    398:   PetscArraycpy(ds->work,wr,n);
    399:   for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
    400: #if !defined(PETSC_USE_COMPLEX)
    401:   PetscArraycpy(ds->work,wi,n);
    402:   for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
    403: #endif
    404:   PetscArraycpy(ds->rwork,s,n);
    405:   for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
    406:   PetscArraycpy(ds->rwork,d,n);
    407:   for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
    408:   PetscArraycpy(ds->rwork,e,n-1);
    409:   PetscArrayzero(e+ds->l,n-1-ds->l);
    410:   for (i=ds->l;i<n-1;i++) {
    411:     if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
    412:   }
    413:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
    414:   DSPermuteColumns_Private(ds,ds->l,n,DS_MAT_Q,perm);
    415:   return(0);
    416: }

    418: /*
    419:   Get eigenvectors with inverse iteration.
    420:   The system matrix is in Hessenberg form.
    421: */
    422: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
    423: {
    424: #if defined(SLEPC_MISSING_LAPACK_HSEIN)
    426:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEIN - Lapack routine is unavailable");
    427: #else
    429:   PetscInt       i,off;
    430:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
    431:   PetscScalar    *A,*B,*H,*X;
    432:   PetscReal      *s,*d,*e;
    433: #if defined(PETSC_USE_COMPLEX)
    434:   PetscInt       j;
    435: #endif

    438:   PetscBLASIntCast(ds->ld,&ld);
    439:   PetscBLASIntCast(ds->n-ds->l,&n1);
    440:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
    441:   DSAllocateMat_Private(ds,DS_MAT_W);
    442:   A = ds->mat[DS_MAT_A];
    443:   B = ds->mat[DS_MAT_B];
    444:   H = ds->mat[DS_MAT_W];
    445:   s = ds->rmat[DS_MAT_D];
    446:   d = ds->rmat[DS_MAT_T];
    447:   e = d + ld;
    448:   select = ds->iwork;
    449:   infoC = ds->iwork + ld;
    450:   off = ds->l+ds->l*ld;
    451:   if (ds->compact) {
    452:     H[off] = d[ds->l]*s[ds->l];
    453:     H[off+ld] = e[ds->l]*s[ds->l];
    454:     for (i=ds->l+1;i<ds->n-1;i++) {
    455:       H[i+(i-1)*ld] = e[i-1]*s[i];
    456:       H[i+i*ld] = d[i]*s[i];
    457:       H[i+(i+1)*ld] = e[i]*s[i];
    458:     }
    459:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    460:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    461:   } else {
    462:     s[ds->l]  = PetscRealPart(B[off]);
    463:     H[off]    = A[off]*s[ds->l];
    464:     H[off+ld] = A[off+ld]*s[ds->l];
    465:     for (i=ds->l+1;i<ds->n-1;i++) {
    466:       s[i] = PetscRealPart(B[i+i*ld]);
    467:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    468:       H[i+i*ld]     = A[i+i*ld]*s[i];
    469:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    470:     }
    471:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    472:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    473:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    474:   }
    475:   DSAllocateMat_Private(ds,DS_MAT_X);
    476:   X = ds->mat[DS_MAT_X];
    477:   for (i=0;i<n1;i++) select[i] = 1;
    478: #if !defined(PETSC_USE_COMPLEX)
    479:   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));
    480: #else
    481:   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));

    483:   /* Separate real and imaginary part of complex eigenvectors */
    484:   for (j=ds->l;j<ds->n;j++) {
    485:     if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
    486:       for (i=ds->l;i<ds->n;i++) {
    487:         X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
    488:         X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
    489:       }
    490:       j++;
    491:     }
    492:   }
    493: #endif
    494:   SlepcCheckLapackInfo("hsein",info);
    495:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
    496:   return(0);
    497: #endif
    498: }

    500: /*
    501:    Undo 2x2 blocks that have real eigenvalues.
    502: */
    503: PetscErrorCode DSGHIEPRealBlocks(DS ds)
    504: {
    505: #if defined(SLEPC_MISSING_LAPACK_LAG2)
    507:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LAG2 - Lapack routine is unavailable");
    508: #else
    510:   PetscInt       i;
    511:   PetscReal      e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
    512:   PetscReal      maxy,ep,scal1,scal2,snorm;
    513:   PetscReal      *T,*D,b[4],M[4],wr1,wr2,wi;
    514:   PetscScalar    *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
    515:   PetscBLASInt   m,two=2,ld;
    516:   PetscBool      isreal;

    519:   PetscBLASIntCast(ds->ld,&ld);
    520:   PetscBLASIntCast(ds->n-ds->l,&m);
    521:   A = ds->mat[DS_MAT_A];
    522:   B = ds->mat[DS_MAT_B];
    523:   T = ds->rmat[DS_MAT_T];
    524:   D = ds->rmat[DS_MAT_D];
    525:   DSAllocateWork_Private(ds,2*m,0,0);
    526:   for (i=ds->l;i<ds->n-1;i++) {
    527:     e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
    528:     if (e != 0.0) { /* 2x2 block */
    529:       if (ds->compact) {
    530:         s1 = D[i];
    531:         d1 = T[i];
    532:         s2 = D[i+1];
    533:         d2 = T[i+1];
    534:       } else {
    535:         s1 = PetscRealPart(B[i*ld+i]);
    536:         d1 = PetscRealPart(A[i*ld+i]);
    537:         s2 = PetscRealPart(B[(i+1)*ld+i+1]);
    538:         d2 = PetscRealPart(A[(i+1)*ld+i+1]);
    539:       }
    540:       isreal = PETSC_FALSE;
    541:       if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
    542:         dd = d1-d2;
    543:         if (2*PetscAbsReal(e) <= dd) {
    544:           t = 2*e/dd;
    545:           t = t/(1 + PetscSqrtReal(1+t*t));
    546:         } else {
    547:           t = dd/(2*e);
    548:           ss = (t>=0)?1.0:-1.0;
    549:           t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
    550:         }
    551:         Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
    552:         Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
    553:         wr1 = d1+t*e; wr2 = d2-t*e;
    554:         ss1 = s1; ss2 = s2;
    555:         isreal = PETSC_TRUE;
    556:       } else {
    557:         ss1 = 1.0; ss2 = 1.0,
    558:         M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    559:         b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    560:         ep = LAPACKlamch_("S");

    562:         /* Compute eigenvalues of the block */
    563:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    564:         if (wi==0.0) { /* Real eigenvalues */
    565:           isreal = PETSC_TRUE;
    566:           if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    567:           wr1 /= scal1;
    568:           wr2 /= scal2;
    569:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
    570:             Y[0] = wr1-s2*d2;
    571:             Y[1] = s2*e;
    572:           } else {
    573:             Y[0] = s1*e;
    574:             Y[1] = wr1-s1*d1;
    575:           }
    576:           /* normalize with a signature*/
    577:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
    578:           scal1 = PetscRealPart(Y[0])/maxy;
    579:           scal2 = PetscRealPart(Y[1])/maxy;
    580:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    581:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
    582:           snorm = maxy*PetscSqrtReal(snorm);
    583:           Y[0] = Y[0]/snorm;
    584:           Y[1] = Y[1]/snorm;
    585:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
    586:             Y[2] = wr2-s2*d2;
    587:             Y[3] = s2*e;
    588:           } else {
    589:             Y[2] = s1*e;
    590:             Y[3] = wr2-s1*d1;
    591:           }
    592:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
    593:           scal1 = PetscRealPart(Y[2])/maxy;
    594:           scal2 = PetscRealPart(Y[3])/maxy;
    595:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    596:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
    597:           snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
    598:         }
    599:         wr1 *= ss1; wr2 *= ss2;
    600:       }
    601:       if (isreal) {
    602:         if (ds->compact) {
    603:           D[i]    = ss1;
    604:           T[i]    = wr1;
    605:           D[i+1]  = ss2;
    606:           T[i+1]  = wr2;
    607:           T[ld+i] = 0.0;
    608:         } else {
    609:           B[i*ld+i]       = ss1;
    610:           A[i*ld+i]       = wr1;
    611:           B[(i+1)*ld+i+1] = ss2;
    612:           A[(i+1)*ld+i+1] = wr2;
    613:           A[(i+1)+ld*i]   = 0.0;
    614:           A[i+ld*(i+1)]   = 0.0;
    615:         }
    616:         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));
    617:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m);
    618:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m);
    619:       }
    620:       i++;
    621:     }
    622:   }
    623:   return(0);
    624: #endif
    625: }

    627: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
    628: {
    629: #if defined(PETSC_MISSING_LAPACK_HSEQR)
    631:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable");
    632: #else
    634:   PetscInt       i,off;
    635:   PetscBLASInt   n1,ld,one,info,lwork;
    636:   PetscScalar    *H,*A,*B,*Q;
    637:   PetscReal      *d,*e,*s;
    638: #if defined(PETSC_USE_COMPLEX)
    639:   PetscInt       j;
    640: #endif

    643: #if !defined(PETSC_USE_COMPLEX)
    645: #endif
    646:   one = 1;
    647:   PetscBLASIntCast(ds->n-ds->l,&n1);
    648:   PetscBLASIntCast(ds->ld,&ld);
    649:   off = ds->l + ds->l*ld;
    650:   A = ds->mat[DS_MAT_A];
    651:   B = ds->mat[DS_MAT_B];
    652:   Q = ds->mat[DS_MAT_Q];
    653:   d = ds->rmat[DS_MAT_T];
    654:   e = ds->rmat[DS_MAT_T] + ld;
    655:   s = ds->rmat[DS_MAT_D];
    656:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
    657:   lwork = ld*ld;

    659:   /* Quick return if possible */
    660:   if (n1 == 1) {
    661:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
    662:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    663:     if (!ds->compact) {
    664:       d[ds->l] = PetscRealPart(A[off]);
    665:       s[ds->l] = PetscRealPart(B[off]);
    666:     }
    667:     wr[ds->l] = d[ds->l]/s[ds->l];
    668:     if (wi) wi[ds->l] = 0.0;
    669:     return(0);
    670:   }
    671:   /* Reduce to pseudotriadiagonal form */
    672:   DSIntermediate_GHIEP(ds);

    674:   /* Compute Eigenvalues (QR)*/
    675:   DSAllocateMat_Private(ds,DS_MAT_W);
    676:   H = ds->mat[DS_MAT_W];
    677:   if (ds->compact) {
    678:     H[off]    = d[ds->l]*s[ds->l];
    679:     H[off+ld] = e[ds->l]*s[ds->l];
    680:     for (i=ds->l+1;i<ds->n-1;i++) {
    681:       H[i+(i-1)*ld] = e[i-1]*s[i];
    682:       H[i+i*ld]     = d[i]*s[i];
    683:       H[i+(i+1)*ld] = e[i]*s[i];
    684:     }
    685:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    686:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    687:   } else {
    688:     s[ds->l]  = PetscRealPart(B[off]);
    689:     H[off]    = A[off]*s[ds->l];
    690:     H[off+ld] = A[off+ld]*s[ds->l];
    691:     for (i=ds->l+1;i<ds->n-1;i++) {
    692:       s[i] = PetscRealPart(B[i+i*ld]);
    693:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    694:       H[i+i*ld]     = A[i+i*ld]*s[i];
    695:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    696:     }
    697:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    698:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    699:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    700:   }

    702: #if !defined(PETSC_USE_COMPLEX)
    703:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
    704: #else
    705:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
    706:   for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
    707:   /* Sort to have consecutive conjugate pairs */
    708:   for (i=ds->l;i<ds->n;i++) {
    709:       j=i+1;
    710:       while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    711:       if (j==ds->n) {
    712:         if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) wr[i]=PetscRealPart(wr[i]);
    713:         else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
    714:       } else { /* complex eigenvalue */
    715:         wr[j] = wr[i+1];
    716:         if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
    717:         wr[i+1] = PetscConj(wr[i]);
    718:         i++;
    719:       }
    720:   }
    721: #endif
    722:   SlepcCheckLapackInfo("hseqr",info);
    723:   /* Compute Eigenvectors with Inverse Iteration */
    724:   DSGHIEPInverseIteration(ds,wr,wi);

    726:   /* Recover eigenvalues from diagonal */
    727:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    728: #if defined(PETSC_USE_COMPLEX)
    729:   if (wi) {
    730:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    731:   }
    732: #endif
    733:   return(0);
    734: #endif
    735: }

    737: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
    738: {
    739: #if defined(SLEPC_MISSING_LAPACK_GEEVX)
    741:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEEVX - Lapack routine is unavailable");
    742: #else
    744:   PetscInt       i,j,off,nwu=0,n,lw,lwr,nwru=0;
    745:   PetscBLASInt   n_,ld,info,lwork,ilo,ihi;
    746:   PetscScalar    *H,*A,*B,*Q,*X;
    747:   PetscReal      *d,*s,*scale,nrm,*rcde,*rcdv;
    748: #if defined(PETSC_USE_COMPLEX)
    749:   PetscInt       k;
    750: #endif

    753: #if !defined(PETSC_USE_COMPLEX)
    755: #endif
    756:   n = ds->n-ds->l;
    757:   PetscBLASIntCast(n,&n_);
    758:   PetscBLASIntCast(ds->ld,&ld);
    759:   off = ds->l + ds->l*ld;
    760:   A = ds->mat[DS_MAT_A];
    761:   B = ds->mat[DS_MAT_B];
    762:   Q = ds->mat[DS_MAT_Q];
    763:   d = ds->rmat[DS_MAT_T];
    764:   s = ds->rmat[DS_MAT_D];
    765:   lw = 14*ld+ld*ld;
    766:   lwr = 7*ld;
    767:   DSAllocateWork_Private(ds,lw,lwr,0);
    768:   scale = ds->rwork+nwru;
    769:   nwru += ld;
    770:   rcde = ds->rwork+nwru;
    771:   nwru += ld;
    772:   rcdv = ds->rwork+nwru;
    773:   nwru += ld;
    774:   /* Quick return if possible */
    775:   if (n_ == 1) {
    776:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
    777:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    778:     if (!ds->compact) {
    779:       d[ds->l] = PetscRealPart(A[off]);
    780:       s[ds->l] = PetscRealPart(B[off]);
    781:     }
    782:     wr[ds->l] = d[ds->l]/s[ds->l];
    783:     if (wi) wi[ds->l] = 0.0;
    784:     return(0);
    785:   }

    787:   /* Form pseudo-symmetric matrix */
    788:   H =  ds->work+nwu;
    789:   nwu += n*n;
    790:   PetscArrayzero(H,n*n);
    791:   if (ds->compact) {
    792:     for (i=0;i<n-1;i++) {
    793:       H[i+i*n]     = s[ds->l+i]*d[ds->l+i];
    794:       H[i+1+i*n]   = s[ds->l+i+1]*d[ld+ds->l+i];
    795:       H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
    796:     }
    797:     H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
    798:     for (i=0;i<ds->k-ds->l;i++) {
    799:       H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
    800:       H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
    801:     }
    802:   } else {
    803:     for (j=0;j<n;j++) {
    804:       for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
    805:     }
    806:   }

    808:   /* Compute eigenpairs */
    809:   PetscBLASIntCast(lw-nwu,&lwork);
    810:   DSAllocateMat_Private(ds,DS_MAT_X);
    811:   X = ds->mat[DS_MAT_X];
    812: #if !defined(PETSC_USE_COMPLEX)
    813:   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));
    814: #else
    815:   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));

    817:   /* Sort to have consecutive conjugate pairs
    818:      Separate real and imaginary part of complex eigenvectors*/
    819:   for (i=ds->l;i<ds->n;i++) {
    820:     j=i+1;
    821:     while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    822:     if (j==ds->n) {
    823:       if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) {
    824:         wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
    825:         for (k=ds->l;k<ds->n;k++) {
    826:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    827:         }
    828:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
    829:     } else { /* complex eigenvalue */
    830:       if (j!=i+1) {
    831:         wr[j] = wr[i+1];
    832:         PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld);
    833:       }
    834:       if (PetscImaginaryPart(wr[i])<0) {
    835:         wr[i] = PetscConj(wr[i]);
    836:         for (k=ds->l;k<ds->n;k++) {
    837:           X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
    838:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    839:         }
    840:       } else {
    841:         for (k=ds->l;k<ds->n;k++) {
    842:           X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
    843:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    844:         }
    845:       }
    846:       wr[i+1] = PetscConj(wr[i]);
    847:       i++;
    848:     }
    849:   }
    850: #endif
    851:   SlepcCheckLapackInfo("geevx",info);

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

    856:   /* Recover eigenvalues from diagonal */
    857:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    858: #if defined(PETSC_USE_COMPLEX)
    859:   if (wi) {
    860:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    861:   }
    862: #endif
    863:   return(0);
    864: #endif
    865: }

    867: PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    868: {
    870:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
    871:   PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;

    874:   if (ds->compact) kr = 4*ld;
    875:   else k = 2*(ds->n-l)*ld;
    876:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    877:   if (eigr) k += (ds->n-l);
    878:   if (eigi) k += (ds->n-l);
    879:   DSAllocateWork_Private(ds,k+kr,0,0);
    880:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
    881:   PetscMPIIntCast(ds->n-l,&n);
    882:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    883:   PetscMPIIntCast(ld*3,&ld3);
    884:   PetscMPIIntCast(ld,&ld_);
    885:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    886:   if (!rank) {
    887:     if (ds->compact) {
    888:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    889:       MPI_Pack(ds->rmat[DS_MAT_D],ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    890:     } else {
    891:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    892:       MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    893:     }
    894:     if (ds->state>DS_STATE_RAW) {
    895:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    896:     }
    897:     if (eigr) {
    898:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    899:     }
    900:     if (eigi) {
    901:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    902:     }
    903:   }
    904:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    905:   if (rank) {
    906:     if (ds->compact) {
    907:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));
    908:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_D],ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds));
    909:     } else {
    910:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    911:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    912:     }
    913:     if (ds->state>DS_STATE_RAW) {
    914:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    915:     }
    916:     if (eigr) {
    917:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    918:     }
    919:     if (eigi) {
    920:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    921:     }
    922:   }
    923:   return(0);
    924: }

    926: PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
    927: {
    929:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
    930:   else *flg = PETSC_FALSE;
    931:   return(0);
    932: }

    934: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
    935: {
    937:   ds->ops->allocate      = DSAllocate_GHIEP;
    938:   ds->ops->view          = DSView_GHIEP;
    939:   ds->ops->vectors       = DSVectors_GHIEP;
    940:   ds->ops->solve[0]      = DSSolve_GHIEP_QR_II;
    941:   ds->ops->solve[1]      = DSSolve_GHIEP_HZ;
    942:   ds->ops->solve[2]      = DSSolve_GHIEP_QR;
    943:   ds->ops->sort          = DSSort_GHIEP;
    944:   ds->ops->synchronize   = DSSynchronize_GHIEP;
    945:   ds->ops->hermitian     = DSHermitian_GHIEP;
    946:   return(0);
    947: }