Date: 2021-09-20T09:43:40+00:00

Actual source code: dsghiep.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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,n);
     46:     PetscArrayzero(T+ld,n);
     47:     PetscArrayzero(T+2*ld,n);
     48:     PetscArrayzero(S,n);
     49:     for (i=0;i<n-1;i++) {
     50:       T[i]    = PetscRealPart(A[i+i*ld]);
     51:       T[ld+i] = PetscRealPart(A[i+1+i*ld]);
     52:       S[i]    = PetscRealPart(B[i+i*ld]);
     53:     }
     54:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
     55:     S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
     56:     for (i=ds->l;i<ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
     57:   } else { /* switch from compact (arrow) to dense storage */
     58:     for (i=0;i<n;i++) {
     59:       PetscArrayzero(A+i*ld,n);
     60:       PetscArrayzero(B+i*ld,n);
     61:     }
     62:     for (i=0;i<n-1;i++) {
     63:       A[i+i*ld]     = T[i];
     64:       A[i+1+i*ld]   = T[ld+i];
     65:       A[i+(i+1)*ld] = T[ld+i];
     66:       B[i+i*ld]     = S[i];
     67:     }
     68:     A[n-1+(n-1)*ld] = T[n-1];
     69:     B[n-1+(n-1)*ld] = S[n-1];
     70:     for (i=ds->l;i<ds->k;i++) {
     71:       A[ds->k+i*ld] = T[2*ld+i];
     72:       A[i+ds->k*ld] = T[2*ld+i];
     73:     }
     74:   }
     75:   return(0);
     76: }

     78: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
     79: {
     80:   PetscErrorCode    ierr;
     81:   PetscViewerFormat format;
     82:   PetscInt          i,j;
     83:   PetscReal         value;
     84:   const char        *methodname[] = {
     85:                      "QR + Inverse Iteration",
     86:                      "HZ method",
     87:                      "QR"
     88:   };
     89:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

     92:   PetscViewerGetFormat(viewer,&format);
     93:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
     94:     if (ds->method<nmeth) {
     95:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
     96:     }
     97:     return(0);
     98:   }
     99:   if (ds->compact) {
    100:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    101:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
    102:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
    103:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
    104:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
    105:       for (i=0;i<ds->n;i++) {
    106:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_T]+i));
    107:       }
    108:       for (i=0;i<ds->n-1;i++) {
    109:         if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
    110:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+2,i+1,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    111:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+2,(double)*(ds->rmat[DS_MAT_T]+ds->ld+i));
    112:         }
    113:       }
    114:       for (i = ds->l;i<ds->k;i++) {
    115:         if (*(ds->rmat[DS_MAT_T]+2*ds->ld+i)) {
    116:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",ds->k+1,i+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
    117:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,ds->k+1,(double)*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
    118:         }
    119:       }
    120:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);

    122:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
    123:       PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ds->n);
    124:       PetscViewerASCIIPrintf(viewer,"omega = [\n");
    125:       for (i=0;i<ds->n;i++) {
    126:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,(double)*(ds->rmat[DS_MAT_D]+i));
    127:       }
    128:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);

    130:     } else {
    131:       PetscViewerASCIIPrintf(viewer,"T\n");
    132:       for (i=0;i<ds->n;i++) {
    133:         for (j=0;j<ds->n;j++) {
    134:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
    135:           else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
    136:           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));
    137:           else value = 0.0;
    138:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
    139:         }
    140:         PetscViewerASCIIPrintf(viewer,"\n");
    141:       }
    142:       PetscViewerASCIIPrintf(viewer,"omega\n");
    143:       for (i=0;i<ds->n;i++) {
    144:         for (j=0;j<ds->n;j++) {
    145:           if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
    146:           else value = 0.0;
    147:           PetscViewerASCIIPrintf(viewer," %18.16e ",(double)value);
    148:         }
    149:         PetscViewerASCIIPrintf(viewer,"\n");
    150:       }
    151:     }
    152:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    153:     PetscViewerFlush(viewer);
    154:   } else {
    155:     DSViewMat(ds,viewer,DS_MAT_A);
    156:     DSViewMat(ds,viewer,DS_MAT_B);
    157:   }
    158:   if (ds->state>DS_STATE_INTERMEDIATE) { DSViewMat(ds,viewer,DS_MAT_Q); }
    159:   return(0);
    160: }

    162: static PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
    163: {
    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: }

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

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

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

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

    369: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    370: {
    372:   PetscInt       n,i,*perm;
    373:   PetscReal      *d,*e,*s;

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

    411: PetscErrorCode DSUpdateExtraRow_GHIEP(DS ds)
    412: {
    414:   PetscInt       i;
    415:   PetscBLASInt   n,ld,incx=1;
    416:   PetscScalar    *A,*Q,*x,*y,one=1.0,zero=0.0;
    417:   PetscReal      *b,*r,beta;

    420:   PetscBLASIntCast(ds->n,&n);
    421:   PetscBLASIntCast(ds->ld,&ld);
    422:   A  = ds->mat[DS_MAT_A];
    423:   Q  = ds->mat[DS_MAT_Q];
    424:   b  = ds->rmat[DS_MAT_T]+ld;
    425:   r  = ds->rmat[DS_MAT_T]+2*ld;

    427:   if (ds->compact) {
    428:     beta = b[n-1];   /* in compact, we assume all entries are zero except the last one */
    429:     for (i=0;i<n;i++) r[i] = PetscRealPart(beta*Q[n-1+i*ld]);
    430:     ds->k = n;
    431:   } else {
    432:     DSAllocateWork_Private(ds,2*ld,0,0);
    433:     x = ds->work;
    434:     y = ds->work+ld;
    435:     for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    436:     PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    437:     for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    438:     ds->k = n;
    439:   }
    440:   return(0);
    441: }

    443: /*
    444:   Get eigenvectors with inverse iteration.
    445:   The system matrix is in Hessenberg form.
    446: */
    447: PetscErrorCode DSGHIEPInverseIteration(DS ds,PetscScalar *wr,PetscScalar *wi)
    448: {
    450:   PetscInt       i,off;
    451:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
    452:   PetscScalar    *A,*B,*H,*X;
    453:   PetscReal      *s,*d,*e;
    454: #if defined(PETSC_USE_COMPLEX)
    455:   PetscInt       j;
    456: #endif

    459:   PetscBLASIntCast(ds->ld,&ld);
    460:   PetscBLASIntCast(ds->n-ds->l,&n1);
    461:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
    462:   DSAllocateMat_Private(ds,DS_MAT_W);
    463:   A = ds->mat[DS_MAT_A];
    464:   B = ds->mat[DS_MAT_B];
    465:   H = ds->mat[DS_MAT_W];
    466:   s = ds->rmat[DS_MAT_D];
    467:   d = ds->rmat[DS_MAT_T];
    468:   e = d + ld;
    469:   select = ds->iwork;
    470:   infoC = ds->iwork + ld;
    471:   off = ds->l+ds->l*ld;
    472:   if (ds->compact) {
    473:     H[off] = d[ds->l]*s[ds->l];
    474:     H[off+ld] = e[ds->l]*s[ds->l];
    475:     for (i=ds->l+1;i<ds->n-1;i++) {
    476:       H[i+(i-1)*ld] = e[i-1]*s[i];
    477:       H[i+i*ld] = d[i]*s[i];
    478:       H[i+(i+1)*ld] = e[i]*s[i];
    479:     }
    480:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    481:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    482:   } else {
    483:     s[ds->l]  = PetscRealPart(B[off]);
    484:     H[off]    = A[off]*s[ds->l];
    485:     H[off+ld] = A[off+ld]*s[ds->l];
    486:     for (i=ds->l+1;i<ds->n-1;i++) {
    487:       s[i] = PetscRealPart(B[i+i*ld]);
    488:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    489:       H[i+i*ld]     = A[i+i*ld]*s[i];
    490:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    491:     }
    492:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    493:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    494:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    495:   }
    496:   DSAllocateMat_Private(ds,DS_MAT_X);
    497:   X = ds->mat[DS_MAT_X];
    498:   for (i=0;i<n1;i++) select[i] = 1;
    499: #if !defined(PETSC_USE_COMPLEX)
    500:   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));
    501: #else
    502:   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));

    504:   /* Separate real and imaginary part of complex eigenvectors */
    505:   for (j=ds->l;j<ds->n;j++) {
    506:     if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
    507:       for (i=ds->l;i<ds->n;i++) {
    508:         X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
    509:         X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
    510:       }
    511:       j++;
    512:     }
    513:   }
    514: #endif
    515:   SlepcCheckLapackInfo("hsein",info);
    516:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
    517:   return(0);
    518: }

    520: /*
    521:    Undo 2x2 blocks that have real eigenvalues.
    522: */
    523: PetscErrorCode DSGHIEPRealBlocks(DS ds)
    524: {
    526:   PetscInt       i;
    527:   PetscReal      e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
    528:   PetscReal      maxy,ep,scal1,scal2,snorm;
    529:   PetscReal      *T,*D,b[4],M[4],wr1,wr2,wi;
    530:   PetscScalar    *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
    531:   PetscBLASInt   m,two=2,ld;
    532:   PetscBool      isreal;

    535:   PetscBLASIntCast(ds->ld,&ld);
    536:   PetscBLASIntCast(ds->n-ds->l,&m);
    537:   A = ds->mat[DS_MAT_A];
    538:   B = ds->mat[DS_MAT_B];
    539:   T = ds->rmat[DS_MAT_T];
    540:   D = ds->rmat[DS_MAT_D];
    541:   DSAllocateWork_Private(ds,2*m,0,0);
    542:   for (i=ds->l;i<ds->n-1;i++) {
    543:     e = (ds->compact)?T[ld+i]:PetscRealPart(A[(i+1)+ld*i]);
    544:     if (e != 0.0) { /* 2x2 block */
    545:       if (ds->compact) {
    546:         s1 = D[i];
    547:         d1 = T[i];
    548:         s2 = D[i+1];
    549:         d2 = T[i+1];
    550:       } else {
    551:         s1 = PetscRealPart(B[i*ld+i]);
    552:         d1 = PetscRealPart(A[i*ld+i]);
    553:         s2 = PetscRealPart(B[(i+1)*ld+i+1]);
    554:         d2 = PetscRealPart(A[(i+1)*ld+i+1]);
    555:       }
    556:       isreal = PETSC_FALSE;
    557:       if (s1==s2) { /* apply a Jacobi rotation to compute the eigendecomposition */
    558:         dd = d1-d2;
    559:         if (2*PetscAbsReal(e) <= dd) {
    560:           t = 2*e/dd;
    561:           t = t/(1 + PetscSqrtReal(1+t*t));
    562:         } else {
    563:           t = dd/(2*e);
    564:           ss = (t>=0)?1.0:-1.0;
    565:           t = ss/(PetscAbsReal(t)+PetscSqrtReal(1+t*t));
    566:         }
    567:         Y[0] = 1/PetscSqrtReal(1 + t*t); Y[3] = Y[0]; /* c */
    568:         Y[1] = Y[0]*t; Y[2] = -Y[1]; /* s */
    569:         wr1 = d1+t*e; wr2 = d2-t*e;
    570:         ss1 = s1; ss2 = s2;
    571:         isreal = PETSC_TRUE;
    572:       } else {
    573:         ss1 = 1.0; ss2 = 1.0,
    574:         M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    575:         b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    576:         ep = LAPACKlamch_("S");

    578:         /* Compute eigenvalues of the block */
    579:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    580:         if (wi==0.0) { /* Real eigenvalues */
    581:           isreal = PETSC_TRUE;
    582:           if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    583:           wr1 /= scal1;
    584:           wr2 /= scal2;
    585:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
    586:             Y[0] = wr1-s2*d2;
    587:             Y[1] = s2*e;
    588:           } else {
    589:             Y[0] = s1*e;
    590:             Y[1] = wr1-s1*d1;
    591:           }
    592:           /* normalize with a signature*/
    593:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
    594:           scal1 = PetscRealPart(Y[0])/maxy;
    595:           scal2 = PetscRealPart(Y[1])/maxy;
    596:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    597:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
    598:           snorm = maxy*PetscSqrtReal(snorm);
    599:           Y[0] = Y[0]/snorm;
    600:           Y[1] = Y[1]/snorm;
    601:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
    602:             Y[2] = wr2-s2*d2;
    603:             Y[3] = s2*e;
    604:           } else {
    605:             Y[2] = s1*e;
    606:             Y[3] = wr2-s1*d1;
    607:           }
    608:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
    609:           scal1 = PetscRealPart(Y[2])/maxy;
    610:           scal2 = PetscRealPart(Y[3])/maxy;
    611:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    612:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
    613:           snorm = maxy*PetscSqrtReal(snorm); Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
    614:         }
    615:         wr1 *= ss1; wr2 *= ss2;
    616:       }
    617:       if (isreal) {
    618:         if (ds->compact) {
    619:           D[i]    = ss1;
    620:           T[i]    = wr1;
    621:           D[i+1]  = ss2;
    622:           T[i+1]  = wr2;
    623:           T[ld+i] = 0.0;
    624:         } else {
    625:           B[i*ld+i]       = ss1;
    626:           A[i*ld+i]       = wr1;
    627:           B[(i+1)*ld+i+1] = ss2;
    628:           A[(i+1)*ld+i+1] = wr2;
    629:           A[(i+1)+ld*i]   = 0.0;
    630:           A[i+ld*(i+1)]   = 0.0;
    631:         }
    632:         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));
    633:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m);
    634:         PetscArraycpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m);
    635:       }
    636:       i++;
    637:     }
    638:   }
    639:   return(0);
    640: }

    642: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
    643: {
    645:   PetscInt       i,off;
    646:   PetscBLASInt   n1,ld,one,info,lwork;
    647:   PetscScalar    *H,*A,*B,*Q;
    648:   PetscReal      *d,*e,*s;
    649: #if defined(PETSC_USE_COMPLEX)
    650:   PetscInt       j;
    651: #endif

    654: #if !defined(PETSC_USE_COMPLEX)
    656: #endif
    657:   one = 1;
    658:   PetscBLASIntCast(ds->n-ds->l,&n1);
    659:   PetscBLASIntCast(ds->ld,&ld);
    660:   off = ds->l + ds->l*ld;
    661:   A = ds->mat[DS_MAT_A];
    662:   B = ds->mat[DS_MAT_B];
    663:   Q = ds->mat[DS_MAT_Q];
    664:   d = ds->rmat[DS_MAT_T];
    665:   e = ds->rmat[DS_MAT_T] + ld;
    666:   s = ds->rmat[DS_MAT_D];
    667: #if defined(PETSC_USE_DEBUG)
    668:   /* Check signature */
    669:   for (i=0;i<ds->n;i++) {
    670:     PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
    671:     if (de != 1.0 && de != -1.0) SETERRQ(PETSC_COMM_SELF,1,"Diagonal elements of the signature matrix must be 1 or -1");
    672:   }
    673: #endif
    674:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
    675:   lwork = ld*ld;

    677:   /* Quick return if possible */
    678:   if (n1 == 1) {
    679:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
    680:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    681:     if (!ds->compact) {
    682:       d[ds->l] = PetscRealPart(A[off]);
    683:       s[ds->l] = PetscRealPart(B[off]);
    684:     }
    685:     wr[ds->l] = d[ds->l]/s[ds->l];
    686:     if (wi) wi[ds->l] = 0.0;
    687:     return(0);
    688:   }
    689:   /* Reduce to pseudotriadiagonal form */
    690:   DSIntermediate_GHIEP(ds);

    692:   /* Compute Eigenvalues (QR)*/
    693:   DSAllocateMat_Private(ds,DS_MAT_W);
    694:   H = ds->mat[DS_MAT_W];
    695:   if (ds->compact) {
    696:     H[off]    = d[ds->l]*s[ds->l];
    697:     H[off+ld] = e[ds->l]*s[ds->l];
    698:     for (i=ds->l+1;i<ds->n-1;i++) {
    699:       H[i+(i-1)*ld] = e[i-1]*s[i];
    700:       H[i+i*ld]     = d[i]*s[i];
    701:       H[i+(i+1)*ld] = e[i]*s[i];
    702:     }
    703:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    704:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    705:   } else {
    706:     s[ds->l]  = PetscRealPart(B[off]);
    707:     H[off]    = A[off]*s[ds->l];
    708:     H[off+ld] = A[off+ld]*s[ds->l];
    709:     for (i=ds->l+1;i<ds->n-1;i++) {
    710:       s[i] = PetscRealPart(B[i+i*ld]);
    711:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    712:       H[i+i*ld]     = A[i+i*ld]*s[i];
    713:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    714:     }
    715:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    716:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    717:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    718:   }

    720: #if !defined(PETSC_USE_COMPLEX)
    721:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
    722: #else
    723:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));
    724:   for (i=ds->l;i<ds->n;i++) if (PetscAbsReal(PetscImaginaryPart(wr[i]))<10*PETSC_MACHINE_EPSILON) wr[i] = PetscRealPart(wr[i]);
    725:   /* Sort to have consecutive conjugate pairs */
    726:   for (i=ds->l;i<ds->n;i++) {
    727:       j=i+1;
    728:       while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    729:       if (j==ds->n) {
    730:         if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) wr[i]=PetscRealPart(wr[i]);
    731:         else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
    732:       } else { /* complex eigenvalue */
    733:         wr[j] = wr[i+1];
    734:         if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
    735:         wr[i+1] = PetscConj(wr[i]);
    736:         i++;
    737:       }
    738:   }
    739: #endif
    740:   SlepcCheckLapackInfo("hseqr",info);
    741:   /* Compute Eigenvectors with Inverse Iteration */
    742:   DSGHIEPInverseIteration(ds,wr,wi);

    744:   /* Recover eigenvalues from diagonal */
    745:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    746: #if defined(PETSC_USE_COMPLEX)
    747:   if (wi) {
    748:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    749:   }
    750: #endif
    751:   return(0);
    752: }

    754: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
    755: {
    757:   PetscInt       i,j,off,nwu=0,n,lw,lwr,nwru=0;
    758:   PetscBLASInt   n_,ld,info,lwork,ilo,ihi;
    759:   PetscScalar    *H,*A,*B,*Q,*X;
    760:   PetscReal      *d,*s,*scale,nrm,*rcde,*rcdv;
    761: #if defined(PETSC_USE_COMPLEX)
    762:   PetscInt       k;
    763: #endif

    766: #if !defined(PETSC_USE_COMPLEX)
    768: #endif
    769:   n = ds->n-ds->l;
    770:   PetscBLASIntCast(n,&n_);
    771:   PetscBLASIntCast(ds->ld,&ld);
    772:   off = ds->l + ds->l*ld;
    773:   A = ds->mat[DS_MAT_A];
    774:   B = ds->mat[DS_MAT_B];
    775:   Q = ds->mat[DS_MAT_Q];
    776:   d = ds->rmat[DS_MAT_T];
    777:   s = ds->rmat[DS_MAT_D];
    778: #if defined(PETSC_USE_DEBUG)
    779:   /* Check signature */
    780:   for (i=0;i<ds->n;i++) {
    781:     PetscReal de = (ds->compact)?s[i]:PetscRealPart(B[i*ld+i]);
    782:     if (de != 1.0 && de != -1.0) SETERRQ(PETSC_COMM_SELF,1,"Diagonal elements of the signature matrix must be 1 or -1");
    783:   }
    784: #endif
    785:   lw = 14*ld+ld*ld;
    786:   lwr = 7*ld;
    787:   DSAllocateWork_Private(ds,lw,lwr,0);
    788:   scale = ds->rwork+nwru;
    789:   nwru += ld;
    790:   rcde = ds->rwork+nwru;
    791:   nwru += ld;
    792:   rcdv = ds->rwork+nwru;
    793:   nwru += ld;
    794:   /* Quick return if possible */
    795:   if (n_ == 1) {
    796:     for (i=0;i<=ds->l;i++) Q[i+i*ld] = 1.0;
    797:     DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    798:     if (!ds->compact) {
    799:       d[ds->l] = PetscRealPart(A[off]);
    800:       s[ds->l] = PetscRealPart(B[off]);
    801:     }
    802:     wr[ds->l] = d[ds->l]/s[ds->l];
    803:     if (wi) wi[ds->l] = 0.0;
    804:     return(0);
    805:   }

    807:   /* Form pseudo-symmetric matrix */
    808:   H =  ds->work+nwu;
    809:   nwu += n*n;
    810:   PetscArrayzero(H,n*n);
    811:   if (ds->compact) {
    812:     for (i=0;i<n-1;i++) {
    813:       H[i+i*n]     = s[ds->l+i]*d[ds->l+i];
    814:       H[i+1+i*n]   = s[ds->l+i+1]*d[ld+ds->l+i];
    815:       H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
    816:     }
    817:     H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
    818:     for (i=0;i<ds->k-ds->l;i++) {
    819:       H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
    820:       H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
    821:     }
    822:   } else {
    823:     for (j=0;j<n;j++) {
    824:       for (i=0;i<n;i++) H[i+j*n] = B[off+i+i*ld]*A[off+i+j*ld];
    825:     }
    826:   }

    828:   /* Compute eigenpairs */
    829:   PetscBLASIntCast(lw-nwu,&lwork);
    830:   DSAllocateMat_Private(ds,DS_MAT_X);
    831:   X = ds->mat[DS_MAT_X];
    832: #if !defined(PETSC_USE_COMPLEX)
    833:   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));
    834: #else
    835:   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));

    837:   /* Sort to have consecutive conjugate pairs
    838:      Separate real and imaginary part of complex eigenvectors*/
    839:   for (i=ds->l;i<ds->n;i++) {
    840:     j=i+1;
    841:     while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    842:     if (j==ds->n) {
    843:       if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) {
    844:         wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
    845:         for (k=ds->l;k<ds->n;k++) {
    846:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    847:         }
    848:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Found complex without conjugate pair");
    849:     } else { /* complex eigenvalue */
    850:       if (j!=i+1) {
    851:         wr[j] = wr[i+1];
    852:         PetscArraycpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld);
    853:       }
    854:       if (PetscImaginaryPart(wr[i])<0) {
    855:         wr[i] = PetscConj(wr[i]);
    856:         for (k=ds->l;k<ds->n;k++) {
    857:           X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
    858:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    859:         }
    860:       } else {
    861:         for (k=ds->l;k<ds->n;k++) {
    862:           X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
    863:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    864:         }
    865:       }
    866:       wr[i+1] = PetscConj(wr[i]);
    867:       i++;
    868:     }
    869:   }
    870: #endif
    871:   SlepcCheckLapackInfo("geevx",info);

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

    876:   /* Recover eigenvalues from diagonal */
    877:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    878: #if defined(PETSC_USE_COMPLEX)
    879:   if (wi) {
    880:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    881:   }
    882: #endif
    883:   return(0);
    884: }

    886: PetscErrorCode DSGetTruncateSize_GHIEP(DS ds,PetscInt l,PetscInt n,PetscInt *k)
    887: {
    888:   PetscReal *T = ds->rmat[DS_MAT_T];

    891:   if (T[l+(*k)-1+ds->ld] !=0.0) {
    892:     if (l+(*k)<n-1) (*k)++;
    893:     else (*k)--;
    894:   }
    895:   return(0);
    896: }

    898: PetscErrorCode DSTruncate_GHIEP(DS ds,PetscInt n,PetscBool trim)
    899: {
    900:   PetscInt    i,ld=ds->ld,l=ds->l;
    901:   PetscScalar *A = ds->mat[DS_MAT_A];
    902:   PetscReal   *T = ds->rmat[DS_MAT_T],*b,*r,*omega;

    905: #if defined(PETSC_USE_DEBUG)
    906:   /* make sure diagonal 2x2 block is not broken */
    907:   if (ds->state>=DS_STATE_CONDENSED && n>0 && n<ds->n && T[n-1+ld]!=0.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
    908: #endif
    909:   if (trim) {
    910:     if (!ds->compact && ds->extrarow) {   /* clean extra row */
    911:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    912:     }
    913:     ds->l = 0;
    914:     ds->k = 0;
    915:     ds->n = n;
    916:     ds->t = ds->n;   /* truncated length equal to the new dimension */
    917:   } else {
    918:     if (!ds->compact && ds->extrarow && ds->k==ds->n) {
    919:       /* copy entries of extra row to the new position, then clean last row */
    920:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
    921:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    922:     }
    923:     if (ds->compact) {
    924:       b = T+ld;
    925:       r = T+2*ld;
    926:       omega = ds->rmat[DS_MAT_D];
    927:       b[n-1] = r[n-1];
    928:       b[n] = b[ds->n];
    929:       omega[n] = omega[ds->n];
    930:     }
    931:     ds->k = (ds->extrarow)? n: 0;
    932:     ds->t = ds->n;   /* truncated length equal to previous dimension */
    933:     ds->n = n;
    934:   }
    935:   return(0);
    936: }

    938: PetscErrorCode DSSynchronize_GHIEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    939: {
    941:   PetscInt       ld=ds->ld,l=ds->l,k=0,kr=0;
    942:   PetscMPIInt    n,rank,off=0,size,ldn,ld3,ld_;

    945:   if (ds->compact) kr = 4*ld;
    946:   else k = 2*(ds->n-l)*ld;
    947:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    948:   if (eigr) k += (ds->n-l);
    949:   if (eigi) k += (ds->n-l);
    950:   DSAllocateWork_Private(ds,k+kr,0,0);
    951:   PetscMPIIntCast(k*sizeof(PetscScalar)+kr*sizeof(PetscReal),&size);
    952:   PetscMPIIntCast(ds->n-l,&n);
    953:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    954:   PetscMPIIntCast(ld*3,&ld3);
    955:   PetscMPIIntCast(ld,&ld_);
    956:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);CHKERRMPI(ierr);
    957:   if (!rank) {
    958:     if (ds->compact) {
    959:       MPI_Pack(ds->rmat[DS_MAT_T],ld3,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    960:       MPI_Pack(ds->rmat[DS_MAT_D],ld_,MPIU_REAL,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    961:     } else {
    962:       MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    963:       MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    964:     }
    965:     if (ds->state>DS_STATE_RAW) {
    966:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    967:     }
    968:     if (eigr) {
    969:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    970:     }
    971:     if (eigi) {
    972:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    973:     }
    974:   }
    975:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    976:   if (rank) {
    977:     if (ds->compact) {
    978:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_T],ld3,MPIU_REAL,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    979:       MPI_Unpack(ds->work,size,&off,ds->rmat[DS_MAT_D],ld_,MPIU_REAL,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    980:     } else {
    981:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    982:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    983:     }
    984:     if (ds->state>DS_STATE_RAW) {
    985:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    986:     }
    987:     if (eigr) {
    988:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    989:     }
    990:     if (eigi) {
    991:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));CHKERRMPI(ierr);
    992:     }
    993:   }
    994:   return(0);
    995: }

    997: PetscErrorCode DSHermitian_GHIEP(DS ds,DSMatType m,PetscBool *flg)
    998: {
    1000:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
    1001:   else *flg = PETSC_FALSE;
    1002:   return(0);
    1003: }

    1005: SLEPC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
    1006: {
    1008:   ds->ops->allocate        = DSAllocate_GHIEP;
    1009:   ds->ops->view            = DSView_GHIEP;
    1010:   ds->ops->vectors         = DSVectors_GHIEP;
    1011:   ds->ops->solve[0]        = DSSolve_GHIEP_QR_II;
    1012:   ds->ops->solve[1]        = DSSolve_GHIEP_HZ;
    1013:   ds->ops->solve[2]        = DSSolve_GHIEP_QR;
    1014:   ds->ops->sort            = DSSort_GHIEP;
    1015:   ds->ops->synchronize     = DSSynchronize_GHIEP;
    1016:   ds->ops->gettruncatesize = DSGetTruncateSize_GHIEP;
    1017:   ds->ops->truncate        = DSTruncate_GHIEP;
    1018:   ds->ops->update          = DSUpdateExtraRow_GHIEP;
    1019:   ds->ops->hermitian       = DSHermitian_GHIEP;
    1020:   return(0);
    1021: }