Date: 2015-09-03T15:03:37+00:00

Actual source code: dsghiep.c
slepc-3.6.1 2015-09-03
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */
     21: #include <slepc/private/dsimpl.h>
     22: #include <slepcblaslapack.h>

     26: PetscErrorCode DSAllocate_GHIEP(DS ds,PetscInt ld)
     27: {

     31:   DSAllocateMat_Private(ds,DS_MAT_A);
     32:   DSAllocateMat_Private(ds,DS_MAT_B);
     33:   DSAllocateMat_Private(ds,DS_MAT_Q);
     34:   DSAllocateMatReal_Private(ds,DS_MAT_T);
     35:   DSAllocateMatReal_Private(ds,DS_MAT_D);
     36:   PetscFree(ds->perm);
     37:   PetscMalloc1(ld,&ds->perm);
     38:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     39:   return(0);
     40: }

     44: PetscErrorCode DSSwitchFormat_GHIEP(DS ds,PetscBool tocompact)
     45: {
     47:   PetscReal      *T,*S;
     48:   PetscScalar    *A,*B;
     49:   PetscInt       i,n,ld;

     52:   A = ds->mat[DS_MAT_A];
     53:   B = ds->mat[DS_MAT_B];
     54:   T = ds->rmat[DS_MAT_T];
     55:   S = ds->rmat[DS_MAT_D];
     56:   n = ds->n;
     57:   ld = ds->ld;
     58:   if (tocompact) { /* switch from dense (arrow) to compact storage */
     59:     PetscMemzero(T,3*ld*sizeof(PetscReal));
     60:     PetscMemzero(S,ld*sizeof(PetscReal));
     61:     for (i=0;i<n-1;i++) {
     62:       T[i] = PetscRealPart(A[i+i*ld]);
     63:       T[ld+i] = PetscRealPart(A[i+1+i*ld]);
     64:       S[i] = PetscRealPart(B[i+i*ld]);
     65:     }
     66:     T[n-1] = PetscRealPart(A[n-1+(n-1)*ld]);
     67:     S[n-1] = PetscRealPart(B[n-1+(n-1)*ld]);
     68:     for (i=ds->l;i< ds->k;i++) T[2*ld+i] = PetscRealPart(A[ds->k+i*ld]);
     69:   } else { /* switch from compact (arrow) to dense storage */
     70:     PetscMemzero(A,ld*ld*sizeof(PetscScalar));
     71:     PetscMemzero(B,ld*ld*sizeof(PetscScalar));
     72:     for (i=0;i<n-1;i++) {
     73:       A[i+i*ld] = T[i];
     74:       A[i+1+i*ld] = T[ld+i];
     75:       A[i+(i+1)*ld] = T[ld+i];
     76:       B[i+i*ld] = S[i];
     77:     }
     78:     A[n-1+(n-1)*ld] = T[n-1];
     79:     B[n-1+(n-1)*ld] = S[n-1];
     80:     for (i=ds->l;i<ds->k;i++) {
     81:       A[ds->k+i*ld] = T[2*ld+i];
     82:       A[i+ds->k*ld] = T[2*ld+i];
     83:     }
     84:   }
     85:   return(0);
     86: }

     90: PetscErrorCode DSView_GHIEP(DS ds,PetscViewer viewer)
     91: {
     92:   PetscErrorCode    ierr;
     93:   PetscViewerFormat format;
     94:   PetscInt          i,j;
     95:   PetscReal         value;
     96:   const char        *methodname[] = {
     97:                      "HR method",
     98:                      "QR + Inverse Iteration",
     99:                      "QR",
    100:                      "DQDS + Inverse Iteration "
    101:   };
    102:   const int         nmeth=sizeof(methodname)/sizeof(methodname[0]);

    105:   PetscViewerGetFormat(viewer,&format);
    106:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    107:     if (ds->method>=nmeth) {
    108:       PetscViewerASCIIPrintf(viewer,"solving the problem with: INVALID METHOD\n");
    109:     } else {
    110:       PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ds->method]);
    111:     }
    112:     return(0);
    113:   }
    114:   if (ds->compact) {
    115:     PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);
    116:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
    117:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
    118:       PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ds->n);
    119:       PetscViewerASCIIPrintf(viewer,"zzz = [\n");
    120:       for (i=0;i<ds->n;i++) {
    121:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_T]+i));
    122:       }
    123:       for (i=0;i<ds->n-1;i++) {
    124:         if (*(ds->rmat[DS_MAT_T]+ds->ld+i) !=0 && i!=ds->k-1) {
    125:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+2,i+1,*(ds->rmat[DS_MAT_T]+ds->ld+i));
    126:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+2,*(ds->rmat[DS_MAT_T]+ds->ld+i));
    127:         }
    128:       }
    129:       for (i = ds->l;i<ds->k;i++) {
    130:         if (*(ds->rmat[DS_MAT_T]+2*ds->ld+i)) {
    131:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",ds->k+1,i+1,*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
    132:           PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,ds->k+1,*(ds->rmat[DS_MAT_T]+2*ds->ld+i));
    133:         }
    134:       }
    135:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",DSMatName[DS_MAT_A]);

    137:       PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ds->n,ds->n);
    138:       PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ds->n);
    139:       PetscViewerASCIIPrintf(viewer,"omega = [\n");
    140:       for (i=0;i<ds->n;i++) {
    141:         PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,i+1,*(ds->rmat[DS_MAT_D]+i));
    142:       }
    143:       PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",DSMatName[DS_MAT_B]);

    145:     } else {
    146:       PetscViewerASCIIPrintf(viewer,"T\n");
    147:       for (i=0;i<ds->n;i++) {
    148:         for (j=0;j<ds->n;j++) {
    149:           if (i==j) value = *(ds->rmat[DS_MAT_T]+i);
    150:           else if (i==j+1 || j==i+1) value = *(ds->rmat[DS_MAT_T]+ds->ld+PetscMin(i,j));
    151:           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));
    152:           else value = 0.0;
    153:           PetscViewerASCIIPrintf(viewer," %18.16e ",value);
    154:         }
    155:         PetscViewerASCIIPrintf(viewer,"\n");
    156:       }
    157:       PetscViewerASCIIPrintf(viewer,"omega\n");
    158:       for (i=0;i<ds->n;i++) {
    159:         for (j=0;j<ds->n;j++) {
    160:           if (i==j) value = *(ds->rmat[DS_MAT_D]+i);
    161:           else value = 0.0;
    162:           PetscViewerASCIIPrintf(viewer," %18.16e ",value);
    163:         }
    164:         PetscViewerASCIIPrintf(viewer,"\n");
    165:       }
    166:     }
    167:     PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);
    168:     PetscViewerFlush(viewer);
    169:   } else {
    170:     DSViewMat(ds,viewer,DS_MAT_A);
    171:     DSViewMat(ds,viewer,DS_MAT_B);
    172:   }
    173:   if (ds->state>DS_STATE_INTERMEDIATE) {
    174:     DSViewMat(ds,viewer,DS_MAT_Q);
    175:   }
    176:   return(0);
    177: }

    181: PetscErrorCode DSVectors_GHIEP_Eigen_Some(DS ds,PetscInt *idx,PetscReal *rnorm)
    182: {
    184:   PetscReal      b[4],M[4],d1,d2,s1,s2,e;
    185:   PetscReal      scal1,scal2,wr1,wr2,wi,ep,norm;
    186:   PetscScalar    *Q,*X,Y[4],alpha,zeroS = 0.0;
    187:   PetscInt       k;
    188:   PetscBLASInt   two = 2,n_,ld,one=1;
    189: #if !defined(PETSC_USE_COMPLEX)
    190:   PetscBLASInt   four=4;
    191: #endif

    194:   X = ds->mat[DS_MAT_X];
    195:   Q = ds->mat[DS_MAT_Q];
    196:   k = *idx;
    197:   PetscBLASIntCast(ds->n,&n_);
    198:   PetscBLASIntCast(ds->ld,&ld);
    199:   if (k < ds->n-1) {
    200:     e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ld+k):PetscRealPart(*(ds->mat[DS_MAT_A]+(k+1)+ld*k));
    201:   } else e = 0.0;
    202:   if (e == 0.0) {/* Real */
    203:     if (ds->state>=DS_STATE_CONDENSED) {
    204:       PetscMemcpy(X+k*ld,Q+k*ld,ld*sizeof(PetscScalar));
    205:     } else {
    206:       PetscMemzero(X+k*ds->ld,ds->ld*sizeof(PetscScalar));
    207:       X[k+k*ds->ld] = 1.0;
    208:     }
    209:     if (rnorm) {
    210:       *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
    211:     }
    212:   } else { /* 2x2 block */
    213:     if (ds->compact) {
    214:       s1 = *(ds->rmat[DS_MAT_D]+k);
    215:       d1 = *(ds->rmat[DS_MAT_T]+k);
    216:       s2 = *(ds->rmat[DS_MAT_D]+k+1);
    217:       d2 = *(ds->rmat[DS_MAT_T]+k+1);
    218:     } else {
    219:       s1 = PetscRealPart(*(ds->mat[DS_MAT_B]+k*ld+k));
    220:       d1 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+k*ld));
    221:       s2 = PetscRealPart(*(ds->mat[DS_MAT_B]+(k+1)*ld+k+1));
    222:       d2 = PetscRealPart(*(ds->mat[DS_MAT_A]+k+1+(k+1)*ld));
    223:     }
    224:     M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    225:     b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    226:     ep = LAPACKlamch_("S");
    227:     /* Compute eigenvalues of the block */
    228:     PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    229:     if (wi==0.0)  /* Real eigenvalues */
    230:       SETERRQ(PETSC_COMM_SELF,1,"Real block in DSVectors_GHIEP");
    231:     else { /* Complex eigenvalues */
    232:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    233:       wr1 /= scal1; wi /= scal1;
    234: #if !defined(PETSC_USE_COMPLEX)
    235:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
    236:         Y[0] = wr1-s2*d2; Y[1] = s2*e; Y[2] = wi; Y[3] = 0.0;
    237:       } else {
    238:         Y[0] = s1*e; Y[1] = wr1-s1*d1; Y[2] = 0.0; Y[3] = wi;
    239:       }
    240:       norm = BLASnrm2_(&four,Y,&one);
    241:       norm = 1/norm;
    242:       if (ds->state >= DS_STATE_CONDENSED) {
    243:         alpha = norm;
    244:         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&two,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&two,&zeroS,X+k*ld,&ld));
    245:         if (rnorm) *rnorm = SlepcAbsEigenvalue(X[ds->n-1+k*ld],X[ds->n-1+(k+1)*ld]);
    246:       } else {
    247:         PetscMemzero(X+k*ld,2*ld*sizeof(PetscScalar));
    248:         X[k*ld+k] = Y[0]*norm; X[k*ld+k+1] = Y[1]*norm;
    249:         X[(k+1)*ld+k] = Y[2]*norm; X[(k+1)*ld+k+1] = Y[3]*norm;
    250:       }
    251: #else
    252:       if (SlepcAbs(s1*d1-wr1,wi)<SlepcAbs(s2*d2-wr1,wi)) {
    253:         Y[0] = wr1-s2*d2+PETSC_i*wi; Y[1] = s2*e;
    254:       } else {
    255:         Y[0] = s1*e; Y[1] = wr1-s1*d1+PETSC_i*wi;
    256:       }
    257:       norm = BLASnrm2_(&two,Y,&one);
    258:       norm = 1/norm;
    259:       if (ds->state >= DS_STATE_CONDENSED) {
    260:         alpha = norm;
    261:         PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n_,&two,&alpha,ds->mat[DS_MAT_Q]+k*ld,&ld,Y,&one,&zeroS,X+k*ld,&one));
    262:         if (rnorm) *rnorm = PetscAbsScalar(X[ds->n-1+k*ld]);
    263:       } else {
    264:         PetscMemzero(X+k*ld,2*ld*sizeof(PetscScalar));
    265:         X[k*ld+k] = Y[0]*norm; X[k*ld+k+1] = Y[1]*norm;
    266:       }
    267:       X[(k+1)*ld+k] = PetscConj(X[k*ld+k]); X[(k+1)*ld+k+1] = PetscConj(X[k*ld+k+1]);
    268: #endif
    269:       (*idx)++;
    270:     }
    271:   }
    272:   return(0);
    273: }

    277: PetscErrorCode DSVectors_GHIEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
    278: {
    279:   PetscInt       i;
    280:   PetscReal      e;

    284:   switch (mat) {
    285:     case DS_MAT_X:
    286:     case DS_MAT_Y:
    287:       if (k) {
    288:         DSVectors_GHIEP_Eigen_Some(ds,k,rnorm);
    289:       } else {
    290:         for (i=0; i<ds->n; i++) {
    291:           e = (ds->compact)?*(ds->rmat[DS_MAT_T]+ds->ld+i):PetscRealPart(*(ds->mat[DS_MAT_A]+(i+1)+ds->ld*i));
    292:           if (e == 0.0) {/* real */
    293:             if (ds->state >= DS_STATE_CONDENSED) {
    294:               PetscMemcpy(ds->mat[mat]+i*ds->ld,ds->mat[DS_MAT_Q]+i*ds->ld,ds->ld*sizeof(PetscScalar));
    295:             } else {
    296:               PetscMemzero(ds->mat[mat]+i*ds->ld,ds->ld*sizeof(PetscScalar));
    297:               *(ds->mat[mat]+i+i*ds->ld) = 1.0;
    298:             }
    299:           } else {
    300:             DSVectors_GHIEP_Eigen_Some(ds,&i,rnorm);
    301:           }
    302:         }
    303:       }
    304:       break;
    305:     case DS_MAT_U:
    306:     case DS_MAT_VT:
    307:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    308:       break;
    309:     default:
    310:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    311:   }
    312:   return(0);
    313: }

    317: /*
    318:   Extract the eigenvalues contained in the block-diagonal of the indefinite problem.
    319:   Only the index range n0..n1 is processed.
    320: */
    321: PetscErrorCode DSGHIEPComplexEigs(DS ds,PetscInt n0,PetscInt n1,PetscScalar *wr,PetscScalar *wi)
    322: {
    323:   PetscInt     k,ld;
    324:   PetscBLASInt two=2;
    325:   PetscScalar  *A,*B;
    326:   PetscReal    *D,*T;
    327:   PetscReal    b[4],M[4],d1,d2,s1,s2,e;
    328:   PetscReal    scal1,scal2,ep,wr1,wr2,wi1;

    331:   ld = ds->ld;
    332:   A = ds->mat[DS_MAT_A];
    333:   B = ds->mat[DS_MAT_B];
    334:   D = ds->rmat[DS_MAT_D];
    335:   T = ds->rmat[DS_MAT_T];
    336:   for (k=n0;k<n1;k++) {
    337:     if (k < n1-1) {
    338:       e = (ds->compact)?T[ld+k]:PetscRealPart(A[(k+1)+ld*k]);
    339:     } else {
    340:       e = 0.0;
    341:     }
    342:     if (e==0.0) {
    343:       /* real eigenvalue */
    344:       wr[k] = (ds->compact)?T[k]/D[k]:A[k+k*ld]/B[k+k*ld];
    345: #if !defined(PETSC_USE_COMPLEX)
    346:       wi[k] = 0.0 ;
    347: #endif
    348:     } else {
    349:       /* diagonal block */
    350:       if (ds->compact) {
    351:         s1 = D[k];
    352:         d1 = T[k];
    353:         s2 = D[k+1];
    354:         d2 = T[k+1];
    355:       } else {
    356:         s1 = PetscRealPart(B[k*ld+k]);
    357:         d1 = PetscRealPart(A[k+k*ld]);
    358:         s2 = PetscRealPart(B[(k+1)*ld+k+1]);
    359:         d2 = PetscRealPart(A[k+1+(k+1)*ld]);
    360:       }
    361:       M[0] = d1; M[1] = e; M[2] = e; M[3]= d2;
    362:       b[0] = s1; b[1] = 0.0; b[2] = 0.0; b[3] = s2;
    363:       ep = LAPACKlamch_("S");
    364:       /* Compute eigenvalues of the block */
    365:       PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi1));
    366:       if (scal1<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    367:       wr[k] = wr1/scal1;
    368:       if (wi1==0.0) { /* Real eigenvalues */
    369:         if (scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    370:         wr[k+1] = wr2/scal2;
    371: #if !defined(PETSC_USE_COMPLEX)
    372:         wi[k] = 0.0;
    373:         wi[k+1] = 0.0;
    374: #endif
    375:       } else { /* Complex eigenvalues */
    376: #if !defined(PETSC_USE_COMPLEX)
    377:         wr[k+1] = wr[k];
    378:         wi[k] = wi1/scal1;
    379:         wi[k+1] = -wi[k];
    380: #else
    381:         wr[k] += PETSC_i*wi1/scal1;
    382:         wr[k+1] = PetscConj(wr[k]);
    383: #endif
    384:       }
    385:       k++;
    386:     }
    387:   }
    388: #if defined(PETSC_USE_COMPLEX)
    389:   if (wi) {
    390:     for (k=n0;k<n1;k++) wi[k] = 0.0;
    391:   }
    392: #endif
    393:   return(0);
    394: }

    398: PetscErrorCode DSSort_GHIEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    399: {
    401:   PetscInt       n,i,*perm;
    402:   PetscReal      *d,*e,*s;

    405: #if !defined(PETSC_USE_COMPLEX)
    407: #endif
    408:   n = ds->n;
    409:   d = ds->rmat[DS_MAT_T];
    410:   e = d + ds->ld;
    411:   s = ds->rmat[DS_MAT_D];
    412:   DSAllocateWork_Private(ds,ds->ld,ds->ld,0);
    413:   perm = ds->perm;
    414:   if (!rr) {
    415:     rr = wr;
    416:     ri = wi;
    417:   }
    418:   DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_TRUE);
    419:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_TRUE); }
    420:   PetscMemcpy(ds->work,wr,n*sizeof(PetscScalar));
    421:   for (i=ds->l;i<n;i++) wr[i] = *(ds->work+perm[i]);
    422: #if !defined(PETSC_USE_COMPLEX)
    423:   PetscMemcpy(ds->work,wi,n*sizeof(PetscScalar));
    424:   for (i=ds->l;i<n;i++) wi[i] = *(ds->work+perm[i]);
    425: #endif
    426:   PetscMemcpy(ds->rwork,s,n*sizeof(PetscReal));
    427:   for (i=ds->l;i<n;i++) s[i] = *(ds->rwork+perm[i]);
    428:   PetscMemcpy(ds->rwork,d,n*sizeof(PetscReal));
    429:   for (i=ds->l;i<n;i++) d[i] = *(ds->rwork+perm[i]);
    430:   PetscMemcpy(ds->rwork,e,(n-1)*sizeof(PetscReal));
    431:   PetscMemzero(e+ds->l,(n-1-ds->l)*sizeof(PetscScalar));
    432:   for (i=ds->l;i<n-1;i++) {
    433:     if (perm[i]<n-1) e[i] = *(ds->rwork+perm[i]);
    434:   }
    435:   if (!ds->compact) { DSSwitchFormat_GHIEP(ds,PETSC_FALSE); }
    436:   DSPermuteColumns_Private(ds,ds->l,n,DS_MAT_Q,perm);
    437:   return(0);
    438: }

    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: {
    449: #if defined(PETSC_MISSING_LAPACK_HSEIN)
    451:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEIN - Lapack routine is unavailable");
    452: #else
    454:   PetscInt       i,off;
    455:   PetscBLASInt   *select,*infoC,ld,n1,mout,info;
    456:   PetscScalar    *A,*B,*H,*X;
    457:   PetscReal      *s,*d,*e;
    458: #if defined(PETSC_USE_COMPLEX)
    459:   PetscInt       j;
    460: #endif

    463:   PetscBLASIntCast(ds->ld,&ld);
    464:   PetscBLASIntCast(ds->n-ds->l,&n1);
    465:   DSAllocateWork_Private(ds,ld*ld+2*ld,ld,2*ld);
    466:   DSAllocateMat_Private(ds,DS_MAT_W);
    467:   A = ds->mat[DS_MAT_A];
    468:   B = ds->mat[DS_MAT_B];
    469:   H = ds->mat[DS_MAT_W];
    470:   s = ds->rmat[DS_MAT_D];
    471:   d = ds->rmat[DS_MAT_T];
    472:   e = d + ld;
    473:   select = ds->iwork;
    474:   infoC = ds->iwork + ld;
    475:   off = ds->l+ds->l*ld;
    476:   if (ds->compact) {
    477:     H[off] = d[ds->l]*s[ds->l];
    478:     H[off+ld] = e[ds->l]*s[ds->l];
    479:     for (i=ds->l+1;i<ds->n-1;i++) {
    480:       H[i+(i-1)*ld] = e[i-1]*s[i];
    481:       H[i+i*ld] = d[i]*s[i];
    482:       H[i+(i+1)*ld] = e[i]*s[i];
    483:     }
    484:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    485:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    486:   } else {
    487:     s[ds->l] = PetscRealPart(B[off]);
    488:     H[off] = A[off]*s[ds->l];
    489:     H[off+ld] = A[off+ld]*s[ds->l];
    490:     for (i=ds->l+1;i<ds->n-1;i++) {
    491:       s[i] = PetscRealPart(B[i+i*ld]);
    492:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    493:       H[i+i*ld]     = A[i+i*ld]*s[i];
    494:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    495:     }
    496:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    497:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    498:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    499:   }
    500:   DSAllocateMat_Private(ds,DS_MAT_X);
    501:   X = ds->mat[DS_MAT_X];
    502:   for (i=0;i<n1;i++) select[i] = 1;
    503: #if !defined(PETSC_USE_COMPLEX)
    504:   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));
    505: #else
    506:   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));

    508:   /* Separate real and imaginary part of complex eigenvectors */
    509:   for (j=ds->l;j<ds->n;j++) {
    510:     if (PetscAbsReal(PetscImaginaryPart(wr[j])) > PetscAbsScalar(wr[j])*PETSC_SQRT_MACHINE_EPSILON) {
    511:       for (i=ds->l;i<ds->n;i++) {
    512:         X[i+(j+1)*ds->ld] = PetscImaginaryPart(X[i+j*ds->ld]);
    513:         X[i+j*ds->ld] = PetscRealPart(X[i+j*ds->ld]);
    514:       }
    515:       j++;
    516:     }
    517:   }
    518: #endif
    519:   if (info<0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in hsein routine %d",-i);
    520:   if (info>0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Convergence error in hsein routine %d",i);
    521:   DSGHIEPOrthogEigenv(ds,DS_MAT_X,wr,wi,PETSC_TRUE);
    522:   return(0);
    523: #endif
    524: }

    529: /*
    530:    Undo 2x2 blocks that have real eigenvalues.
    531: */
    532: PetscErrorCode DSGHIEPRealBlocks(DS ds)
    533: {
    535:   PetscInt       i;
    536:   PetscReal      e,d1,d2,s1,s2,ss1,ss2,t,dd,ss;
    537:   PetscReal      maxy,ep,scal1,scal2,snorm;
    538:   PetscReal      *T,*D,b[4],M[4],wr1,wr2,wi;
    539:   PetscScalar    *A,*B,Y[4],oneS = 1.0,zeroS = 0.0;
    540:   PetscBLASInt   m,two=2,ld;
    541:   PetscBool      isreal;

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

    588:         /* Compute eigenvalues of the block */
    589:         PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(M,&two,b,&two,&ep,&scal1,&scal2,&wr1,&wr2,&wi));
    590:         if (wi==0.0) { /* Real eigenvalues */
    591:           isreal = PETSC_TRUE;
    592:           if (scal1<ep||scal2<ep) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FP,"Nearly infinite eigenvalue");
    593:           wr1 /= scal1; wr2 /= scal2;
    594:           if (PetscAbsReal(s1*d1-wr1)<PetscAbsReal(s2*d2-wr1)) {
    595:             Y[0] = wr1-s2*d2;
    596:             Y[1] = s2*e;
    597:           } else {
    598:             Y[0] = s1*e;
    599:             Y[1] = wr1-s1*d1;
    600:           }
    601:           /* normalize with a signature*/
    602:           maxy = PetscMax(PetscAbsScalar(Y[0]),PetscAbsScalar(Y[1]));
    603:           scal1 = PetscRealPart(Y[0])/maxy; scal2 = PetscRealPart(Y[1])/maxy;
    604:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    605:           if (snorm<0) { ss1 = -1.0; snorm = -snorm; }
    606:           snorm = maxy*PetscSqrtReal(snorm); Y[0] = Y[0]/snorm; Y[1] = Y[1]/snorm;
    607:           if (PetscAbsReal(s1*d1-wr2)<PetscAbsReal(s2*d2-wr2)) {
    608:             Y[2] = wr2-s2*d2;
    609:             Y[3] = s2*e;
    610:           } else {
    611:             Y[2] = s1*e;
    612:             Y[3] = wr2-s1*d1;
    613:           }
    614:           maxy = PetscMax(PetscAbsScalar(Y[2]),PetscAbsScalar(Y[3]));
    615:           scal1 = PetscRealPart(Y[2])/maxy; scal2 = PetscRealPart(Y[3])/maxy;
    616:           snorm = scal1*scal1*s1 + scal2*scal2*s2;
    617:           if (snorm<0) { ss2 = -1.0; snorm = -snorm; }
    618:           snorm = maxy*PetscSqrtReal(snorm);Y[2] = Y[2]/snorm; Y[3] = Y[3]/snorm;
    619:         }
    620:         wr1 *= ss1; wr2 *= ss2;
    621:       }
    622:       if (isreal) {
    623:         if (ds->compact) {
    624:           D[i] = ss1;
    625:           T[i] = wr1;
    626:           D[i+1] = ss2;
    627:           T[i+1] = wr2;
    628:           T[ld+i] = 0.0;
    629:         } else {
    630:           B[i*ld+i] = ss1;
    631:           A[i*ld+i] = wr1;
    632:           B[(i+1)*ld+i+1] = ss2;
    633:           A[(i+1)*ld+i+1] = wr2;
    634:           A[(i+1)+ld*i] = 0.0;
    635:           A[i+ld*(i+1)] = 0.0;
    636:         }
    637:         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));
    638:         PetscMemcpy(ds->mat[DS_MAT_Q]+ds->l+i*ld,ds->work,m*sizeof(PetscScalar));
    639:         PetscMemcpy(ds->mat[DS_MAT_Q]+ds->l+(i+1)*ld,ds->work+m,m*sizeof(PetscScalar));
    640:       }
    641:       i++;
    642:     }
    643:   }
    644:   return(0);
    645: }

    649: PetscErrorCode DSSolve_GHIEP_QR_II(DS ds,PetscScalar *wr,PetscScalar *wi)
    650: {
    651: #if defined(PETSC_MISSING_LAPACK_HSEQR)
    653:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HSEQR - Lapack routine is unavailable");
    654: #else
    656:   PetscInt       i,off;
    657:   PetscBLASInt   n1,ld,one,info,lwork;
    658:   PetscScalar    *H,*A,*B,*Q;
    659:   PetscReal      *d,*e,*s;
    660: #if defined(PETSC_USE_COMPLEX)
    661:   PetscInt       j;
    662: #endif

    665: #if !defined(PETSC_USE_COMPLEX)
    667: #endif
    668:   one = 1;
    669:   PetscBLASIntCast(ds->n-ds->l,&n1);
    670:   PetscBLASIntCast(ds->ld,&ld);
    671:   off = ds->l + ds->l*ld;
    672:   A = ds->mat[DS_MAT_A];
    673:   B = ds->mat[DS_MAT_B];
    674:   Q = ds->mat[DS_MAT_Q];
    675:   d = ds->rmat[DS_MAT_T];
    676:   e = ds->rmat[DS_MAT_T] + ld;
    677:   s = ds->rmat[DS_MAT_D];
    678:   DSAllocateWork_Private(ds,ld*ld,2*ld,ld*2);
    679:   lwork = ld*ld;

    681:   /* Quick return if possible */
    682:   if (n1 == 1) {
    683:     *(Q+off) = 1;
    684:     if (!ds->compact) {
    685:       d[ds->l] = PetscRealPart(A[off]);
    686:       s[ds->l] = PetscRealPart(B[off]);
    687:     }
    688:     wr[ds->l] = d[ds->l]/s[ds->l];
    689:     if (wi) wi[ds->l] = 0.0;
    690:     return(0);
    691:   }
    692:   /* Reduce to pseudotriadiagonal form */
    693:   DSIntermediate_GHIEP(ds);

    695:   /* Compute Eigenvalues (QR)*/
    696:   DSAllocateMat_Private(ds,DS_MAT_W);
    697:   H = ds->mat[DS_MAT_W];
    698:   if (ds->compact) {
    699:     H[off] = d[ds->l]*s[ds->l];
    700:     H[off+ld] = e[ds->l]*s[ds->l];
    701:     for (i=ds->l+1;i<ds->n-1;i++) {
    702:       H[i+(i-1)*ld] = e[i-1]*s[i];
    703:       H[i+i*ld]     = d[i]*s[i];
    704:       H[i+(i+1)*ld] = e[i]*s[i];
    705:     }
    706:     H[ds->n-1+(ds->n-2)*ld] = e[ds->n-2]*s[ds->n-1];
    707:     H[ds->n-1+(ds->n-1)*ld] = d[ds->n-1]*s[ds->n-1];
    708:   } else {
    709:     s[ds->l] = PetscRealPart(B[off]);
    710:     H[off] = A[off]*s[ds->l];
    711:     H[off+ld] = A[off+ld]*s[ds->l];
    712:     for (i=ds->l+1;i<ds->n-1;i++) {
    713:       s[i] = PetscRealPart(B[i+i*ld]);
    714:       H[i+(i-1)*ld] = A[i+(i-1)*ld]*s[i];
    715:       H[i+i*ld]     = A[i+i*ld]*s[i];
    716:       H[i+(i+1)*ld] = A[i+(i+1)*ld]*s[i];
    717:     }
    718:     s[ds->n-1] = PetscRealPart(B[ds->n-1+(ds->n-1)*ld]);
    719:     H[ds->n-1+(ds->n-2)*ld] = A[ds->n-1+(ds->n-2)*ld]*s[ds->n-1];
    720:     H[ds->n-1+(ds->n-1)*ld] = A[ds->n-1+(ds->n-1)*ld]*s[ds->n-1];
    721:   }

    723: #if !defined(PETSC_USE_COMPLEX)
    724:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,wi+ds->l,NULL,&ld,ds->work,&lwork,&info));
    725: #else
    726:   PetscStackCallBLAS("LAPACKhseqr",LAPACKhseqr_("E","N",&n1,&one,&n1,H+off,&ld,wr+ds->l,NULL,&ld,ds->work,&lwork,&info));

    728:   /* Sort to have consecutive conjugate pairs */
    729:   for (i=ds->l;i<ds->n;i++) {
    730:       j=i+1;
    731:       while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    732:       if (j==ds->n) {
    733:         if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) wr[i]=PetscRealPart(wr[i]);
    734:         else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"In QR_II complex without conjugate pair");
    735:       } else { /* complex eigenvalue */
    736:         wr[j] = wr[i+1];
    737:         if (PetscImaginaryPart(wr[i])<0) wr[i] = PetscConj(wr[i]);
    738:         wr[i+1] = PetscConj(wr[i]);
    739:         i++;
    740:       }
    741:   }
    742: #endif
    743:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);
    744:   /* Compute Eigenvectors with Inverse Iteration */
    745:   DSGHIEPInverseIteration(ds,wr,wi);

    747:   /* Recover eigenvalues from diagonal */
    748:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    749: #if defined(PETSC_USE_COMPLEX)
    750:   if (wi) {
    751:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    752:   }
    753: #endif
    754:   return(0);
    755: #endif
    756: }

    760: PetscErrorCode DSSolve_GHIEP_QR(DS ds,PetscScalar *wr,PetscScalar *wi)
    761: {
    762: #if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
    764:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable");
    765: #else
    767:   PetscInt       i,off,nwu=0,n,lw;
    768:   PetscBLASInt   n_,ld,info,lwork;
    769:   PetscScalar    *H,*A,*B,*Q,*X;
    770:   PetscReal      *d,*s;
    771: #if defined(PETSC_USE_COMPLEX)
    772:   PetscInt       j,k;
    773: #endif

    776: #if !defined(PETSC_USE_COMPLEX)
    778: #endif
    779:   n = ds->n-ds->l;
    780:   PetscBLASIntCast(n,&n_);
    781:   PetscBLASIntCast(ds->ld,&ld);
    782:   off = ds->l + ds->l*ld;
    783:   A = ds->mat[DS_MAT_A];
    784:   B = ds->mat[DS_MAT_B];
    785:   Q = ds->mat[DS_MAT_Q];
    786:   d = ds->rmat[DS_MAT_T];
    787:   s = ds->rmat[DS_MAT_D];
    788:   lw = 14*ld+ld*ld;
    789:   DSAllocateWork_Private(ds,lw,2*ld,0);

    791:   /* Quick return if possible */
    792:   if (n_ == 1) {
    793:     *(Q+off) = 1;
    794:     if (!ds->compact) {
    795:       d[ds->l] = PetscRealPart(A[off]);
    796:       s[ds->l] = PetscRealPart(B[off]);
    797:     }
    798:     wr[ds->l] = d[ds->l]/s[ds->l];
    799:     if (wi) wi[ds->l] = 0.0;
    800:     return(0);
    801:   }

    803:   /* Form pseudo-symmetric matrix */
    804:   H =  ds->work+nwu;
    805:   nwu += n*n;
    806:   PetscMemzero(H,n*n*sizeof(PetscScalar));
    807:   if (ds->compact) {
    808:     for (i=0;i<n-1;i++) {
    809:       H[i+i*n]     = s[ds->l+i]*d[ds->l+i];
    810:       H[i+1+i*n]   = s[ds->l+i+1]*d[ld+ds->l+i];
    811:       H[i+(i+1)*n] = s[ds->l+i]*d[ld+ds->l+i];
    812:     }
    813:     H[n-1+(n-1)*n] = s[ds->l+n-1]*d[ds->l+n-1];
    814:     for (i=0;i<ds->k-ds->l;i++) {
    815:       H[ds->k-ds->l+i*n] = s[ds->k]*d[2*ld+ds->l+i];
    816:       H[i+(ds->k-ds->l)*n] = s[i+ds->l]*d[2*ld+ds->l+i];
    817:     }
    818:   } else {
    819:     for (i=0;i<n-1;i++) {
    820:       H[i+i*n]     = B[off+i+i*ld]*A[off+i+i*ld];
    821:       H[i+1+i*n]   = B[off+i+1+(i+1)*ld]*A[off+i+1+i*ld];
    822:       H[i+(i+1)*n] = B[off+i+i*ld]*A[off+i+(i+1)*ld];
    823:     }
    824:     H[n-1+(n-1)*n] = B[off+n-1+(n-1)*ld]*A[off+n-1+(n-1)*n];
    825:     for (i=0;i<ds->k-ds->l;i++) {
    826:       H[ds->k-ds->l+i*n] = B[ds->k*(1+ld)]*A[off+ds->k-ds->l+i*ld];
    827:       H[i+(ds->k-ds->l)*n] = B[(i+ds->l)*(1+ld)]*A[off+i+(ds->k-ds->l)*ld];
    828:     }
    829:   }
    830:
    831:   /* Compute eigenpairs */
    832:   PetscBLASIntCast(lw-nwu,&lwork);
    833:   DSAllocateMat_Private(ds,DS_MAT_X);
    834:   X = ds->mat[DS_MAT_X];
    835: #if !defined(PETSC_USE_COMPLEX)
    836:   PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&n_,H,&n_,wr+ds->l,wi+ds->l,NULL,&ld,X+off,&ld,ds->work+nwu,&lwork,&info));
    837: #else
    838:   PetscStackCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&n_,H,&n_,wr+ds->l,NULL,&ld,X+off,&ld,ds->work+nwu,&lwork,ds->rwork,&info));

    840:   /* Sort to have consecutive conjugate pairs
    841:      Separate real and imaginary part of complex eigenvectors*/
    842:   for (i=ds->l;i<ds->n;i++) {
    843:     j=i+1;
    844:     while (j<ds->n && (PetscAbsScalar(wr[i]-PetscConj(wr[j]))>PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON)) j++;
    845:     if (j==ds->n) {
    846:       if (PetscAbsReal(PetscImaginaryPart(wr[i]))<PetscAbsScalar(wr[i])*PETSC_SQRT_MACHINE_EPSILON) {
    847:         wr[i]=PetscRealPart(wr[i]); /* real eigenvalue */
    848:         for (k=ds->l;k<ds->n;k++) {
    849:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    850:         }
    851:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"In QR_II complex without conjugate pair");
    852:     } else { /* complex eigenvalue */
    853:       if (j!=i+1) {
    854:         wr[j] = wr[i+1];
    855:         PetscMemcpy(X+j*ds->ld,X+(i+1)*ds->ld,ds->ld*sizeof(PetscScalar));
    856:       }
    857:       if (PetscImaginaryPart(wr[i])<0) {
    858:         wr[i] = PetscConj(wr[i]);
    859:         for (k=ds->l;k<ds->n;k++) {
    860:           X[k+(i+1)*ds->ld] = -PetscImaginaryPart(X[k+i*ds->ld]);
    861:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    862:         }
    863:       } else {
    864:         for (k=ds->l;k<ds->n;k++) {
    865:           X[k+(i+1)*ds->ld] = PetscImaginaryPart(X[k+i*ds->ld]);
    866:           X[k+i*ds->ld] = PetscRealPart(X[k+i*ds->ld]);
    867:         }
    868:       }
    869:       wr[i+1] = PetscConj(wr[i]);
    870:       i++;
    871:     }
    872:   }
    873: #endif
    874:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);

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

    879:   /* Recover eigenvalues from diagonal */
    880:   DSGHIEPComplexEigs(ds,0,ds->l,wr,wi);
    881: #if defined(PETSC_USE_COMPLEX)
    882:   if (wi) {
    883:     for (i=ds->l;i<ds->n;i++) wi[i] = 0.0;
    884:   }
    885: #endif
    886:   return(0);
    887: #endif
    888: }

    892: PetscErrorCode DSNormalize_GHIEP(DS ds,DSMatType mat,PetscInt col)
    893: {
    895:   PetscInt       i,i0,i1;
    896:   PetscBLASInt   ld,n,one = 1;
    897:   PetscScalar    *A = ds->mat[DS_MAT_A],norm,*x;
    898: #if !defined(PETSC_USE_COMPLEX)
    899:   PetscScalar    norm0;
    900: #endif

    903:   switch (mat) {
    904:     case DS_MAT_X:
    905:     case DS_MAT_Y:
    906:     case DS_MAT_Q:
    907:       /* Supported matrices */
    908:       break;
    909:     case DS_MAT_U:
    910:     case DS_MAT_VT:
    911:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
    912:       break;
    913:     default:
    914:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    915:   }

    917:   PetscBLASIntCast(ds->n,&n);
    918:   PetscBLASIntCast(ds->ld,&ld);
    919:   DSGetArray(ds,mat,&x);
    920:   if (col < 0) {
    921:     i0 = 0; i1 = ds->n;
    922:   } else if (col>0 && A[ds->ld*(col-1)+col] != 0.0) {
    923:     i0 = col-1; i1 = col+1;
    924:   } else {
    925:     i0 = col; i1 = col+1;
    926:   }
    927:   for (i=i0; i<i1; i++) {
    928: #if !defined(PETSC_USE_COMPLEX)
    929:     if (i<n-1 && A[ds->ld*i+i+1] != 0.0) {
    930:       norm = BLASnrm2_(&n,&x[ld*i],&one);
    931:       norm0 = BLASnrm2_(&n,&x[ld*(i+1)],&one);
    932:       norm = 1.0/SlepcAbsEigenvalue(norm,norm0);
    933:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
    934:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*(i+1)],&one));
    935:       i++;
    936:     } else
    937: #endif
    938:     {
    939:       norm = BLASnrm2_(&n,&x[ld*i],&one);
    940:       norm = 1.0/norm;
    941:       PetscStackCallBLAS("BLASscal",BLASscal_(&n,&norm,&x[ld*i],&one));
    942:     }
    943:   }
    944:   return(0);
    945: }

    949: PETSC_EXTERN PetscErrorCode DSCreate_GHIEP(DS ds)
    950: {
    952:   ds->ops->allocate      = DSAllocate_GHIEP;
    953:   ds->ops->view          = DSView_GHIEP;
    954:   ds->ops->vectors       = DSVectors_GHIEP;
    955:   ds->ops->solve[0]      = DSSolve_GHIEP_HZ;
    956:   ds->ops->solve[1]      = DSSolve_GHIEP_QR_II;
    957:   ds->ops->solve[2]      = DSSolve_GHIEP_QR;
    958:   ds->ops->solve[3]      = DSSolve_GHIEP_DQDS_II;
    959:   ds->ops->sort          = DSSort_GHIEP;
    960:   ds->ops->normalize     = DSNormalize_GHIEP;
    961:   return(0);
    962: }