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

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

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

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

     14: /*
     15:   1) Patterns of A and B
     16:       DS_STATE_RAW:       DS_STATE_INTERM/CONDENSED
     17:        0       n-1              0       n-1
     18:       -------------            -------------
     19:     0 |* * * * * *|          0 |* * * * * *|
     20:       |* * * * * *|            |  * * * * *|
     21:       |* * * * * *|            |    * * * *|
     22:       |* * * * * *|            |    * * * *|
     23:       |* * * * * *|            |        * *|
     24:   n-1 |* * * * * *|        n-1 |          *|
     25:       -------------            -------------

     27:   2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
     28: */

     31: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY);

     33: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
     34: {

     38:   DSAllocateMat_Private(ds,DS_MAT_A);
     39:   DSAllocateMat_Private(ds,DS_MAT_B);
     40:   DSAllocateMat_Private(ds,DS_MAT_Z);
     41:   DSAllocateMat_Private(ds,DS_MAT_Q);
     42:   PetscFree(ds->perm);
     43:   PetscMalloc1(ld,&ds->perm);
     44:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     45:   return(0);
     46: }

     48: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
     49: {
     50:   PetscErrorCode    ierr;
     51:   PetscViewerFormat format;

     54:   PetscViewerGetFormat(viewer,&format);
     55:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return(0);
     56:   DSViewMat(ds,viewer,DS_MAT_A);
     57:   DSViewMat(ds,viewer,DS_MAT_B);
     58:   if (ds->state>DS_STATE_INTERMEDIATE) {
     59:     DSViewMat(ds,viewer,DS_MAT_Z);
     60:     DSViewMat(ds,viewer,DS_MAT_Q);
     61:   }
     62:   if (ds->mat[DS_MAT_X]) { DSViewMat(ds,viewer,DS_MAT_X); }
     63:   if (ds->mat[DS_MAT_Y]) { DSViewMat(ds,viewer,DS_MAT_Y); }
     64:   return(0);
     65: }

     67: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
     68: {
     70:   PetscInt       i;
     71:   PetscBLASInt   n,ld,mout,info,*select,mm,inc = 1;
     72:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp,fone=1.0,fzero=0.0;
     73:   PetscReal      norm;
     74:   PetscBool      iscomplex = PETSC_FALSE;
     75:   const char     *side;

     78:   PetscBLASIntCast(ds->n,&n);
     79:   PetscBLASIntCast(ds->ld,&ld);
     80:   if (left) {
     81:     X = NULL;
     82:     Y = &ds->mat[DS_MAT_Y][ld*(*k)];
     83:     side = "L";
     84:   } else {
     85:     X = &ds->mat[DS_MAT_X][ld*(*k)];
     86:     Y = NULL;
     87:     side = "R";
     88:   }
     89:   Z = left? Y: X;
     90:   DSAllocateWork_Private(ds,0,0,ld);
     91:   select = ds->iwork;
     92:   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
     93:   if (ds->state <= DS_STATE_INTERMEDIATE) {
     94:     DSSetIdentity(ds,DS_MAT_Q);
     95:     DSSetIdentity(ds,DS_MAT_Z);
     96:   }
     97:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
     98:   if (ds->state < DS_STATE_CONDENSED) { DSSetState(ds,DS_STATE_CONDENSED); }

    100:   /* compute k-th eigenvector */
    101:   select[*k] = (PetscBLASInt)PETSC_TRUE;
    102: #if defined(PETSC_USE_COMPLEX)
    103:   mm = 1;
    104:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
    105:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
    106: #else
    107:   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
    108:   mm = iscomplex? 2: 1;
    109:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
    110:   DSAllocateWork_Private(ds,6*ld,0,0);
    111:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
    112: #endif
    113:   SlepcCheckLapackInfo("tgevc",info);
    114:   if (!select[*k] || mout != mm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");

    116:   /* accumulate and normalize eigenvectors */
    117:   PetscArraycpy(ds->work,Z,mm*ld);
    118:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,ds->mat[left?DS_MAT_Z:DS_MAT_Q],&ld,ds->work,&ld,&fzero,Z,&ld));
    119:   norm = BLASnrm2_(&n,Z,&inc);
    120: #if !defined(PETSC_USE_COMPLEX)
    121:   if (iscomplex) {
    122:     tmp = BLASnrm2_(&n,Z+ld,&inc);
    123:     norm = SlepcAbsEigenvalue(norm,tmp);
    124:   }
    125: #endif
    126:   tmp = 1.0 / norm;
    127:   PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z,&inc));
    128: #if !defined(PETSC_USE_COMPLEX)
    129:   if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+ld,&inc));
    130: #endif

    132:   /* set output arguments */
    133:   if (iscomplex) (*k)++;
    134:   if (rnorm) {
    135:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
    136:     else *rnorm = PetscAbsScalar(Z[n-1]);
    137:   }
    138:   return(0);
    139: }

    141: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
    142: {
    144:   PetscInt       i;
    145:   PetscBLASInt   n,ld,mout,info,inc = 1;
    146:   PetscBool      iscomplex;
    147:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp;
    148:   PetscReal      norm;
    149:   const char     *side,*back;

    152:   PetscBLASIntCast(ds->n,&n);
    153:   PetscBLASIntCast(ds->ld,&ld);
    154:   if (left) {
    155:     X = NULL;
    156:     Y = ds->mat[DS_MAT_Y];
    157:     side = "L";
    158:   } else {
    159:     X = ds->mat[DS_MAT_X];
    160:     Y = NULL;
    161:     side = "R";
    162:   }
    163:   Z = left? Y: X;
    164:   if (ds->state <= DS_STATE_INTERMEDIATE) {
    165:     DSSetIdentity(ds,DS_MAT_Q);
    166:     DSSetIdentity(ds,DS_MAT_Z);
    167:   }
    168:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
    169:   if (ds->state>=DS_STATE_CONDENSED) {
    170:     /* DSSolve() has been called, backtransform with matrix Q */
    171:     back = "B";
    172:     PetscArraycpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld);
    173:   } else {
    174:     back = "A";
    175:     DSSetState(ds,DS_STATE_CONDENSED);
    176:   }
    177: #if defined(PETSC_USE_COMPLEX)
    178:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
    179:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
    180: #else
    181:   DSAllocateWork_Private(ds,6*ld,0,0);
    182:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
    183: #endif
    184:   SlepcCheckLapackInfo("tgevc",info);

    186:   /* normalize eigenvectors */
    187:   for (i=0;i<n;i++) {
    188:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
    189:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
    190: #if !defined(PETSC_USE_COMPLEX)
    191:     if (iscomplex) {
    192:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
    193:       norm = SlepcAbsEigenvalue(norm,tmp);
    194:     }
    195: #endif
    196:     tmp = 1.0 / norm;
    197:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
    198: #if !defined(PETSC_USE_COMPLEX)
    199:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
    200: #endif
    201:     if (iscomplex) i++;
    202:   }
    203:   return(0);
    204: }

    206: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
    207: {

    211:   switch (mat) {
    212:     case DS_MAT_X:
    213:     case DS_MAT_Y:
    214:       if (k) {
    215:         DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
    216:       } else {
    217:         DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
    218:       }
    219:       break;
    220:     default:
    221:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    222:   }
    223:   return(0);
    224: }

    226: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    227: {
    229:   PetscInt       i;
    230:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
    231:   PetscScalar    *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Q = ds->mat[DS_MAT_Q],*Z = ds->mat[DS_MAT_Z],*work,*beta;

    234:   if (!ds->sc) return(0);
    235:   PetscBLASIntCast(ds->n,&n);
    236:   PetscBLASIntCast(ds->ld,&ld);
    237: #if !defined(PETSC_USE_COMPLEX)
    238:   lwork = 4*n+16;
    239: #else
    240:   lwork = 1;
    241: #endif
    242:   liwork = 1;
    243:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
    244:   beta      = ds->work;
    245:   work      = ds->work + n;
    246:   lwork     = ds->lwork - n;
    247:   selection = ds->iwork;
    248:   iwork     = ds->iwork + n;
    249:   liwork    = ds->liwork - n;
    250:   /* Compute the selected eigenvalue to be in the leading position */
    251:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
    252:   PetscArrayzero(selection,n);
    253:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
    254: #if !defined(PETSC_USE_COMPLEX)
    255:   PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,wi,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
    256: #else
    257:   PetscStackCallBLAS("LAPACKtgsen",LAPACKtgsen_(&zero_,&true_,&true_,selection,&n,S,&ld,T,&ld,wr,beta,Z,&ld,Q,&ld,&mout,NULL,NULL,NULL,work,&lwork,iwork,&liwork,&info));
    258: #endif
    259:   SlepcCheckLapackInfo("tgsen",info);
    260:   *k = mout;
    261:   for (i=0;i<n;i++) {
    262:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    263:     else wr[i] /= beta[i];
    264: #if !defined(PETSC_USE_COMPLEX)
    265:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    266:     else wi[i] /= beta[i];
    267: #endif
    268:   }
    269:   return(0);
    270: }

    272: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
    273: {
    275:   PetscScalar    re;
    276:   PetscInt       i,j,pos,result;
    277:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
    278:   PetscScalar    *S = ds->mat[DS_MAT_A],*T = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];
    279: #if !defined(PETSC_USE_COMPLEX)
    280:   PetscBLASInt   lwork;
    281:   PetscScalar    *work,a,safmin,scale1,scale2,im;
    282: #endif

    285:   if (!ds->sc) return(0);
    286:   PetscBLASIntCast(ds->n,&n);
    287:   PetscBLASIntCast(ds->ld,&ld);
    288: #if !defined(PETSC_USE_COMPLEX)
    289:   lwork = -1;
    290:   PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
    291:   SlepcCheckLapackInfo("tgexc",info);
    292:   safmin = LAPACKlamch_("S");
    293:   PetscBLASIntCast((PetscInt)a,&lwork);
    294:   DSAllocateWork_Private(ds,lwork,0,0);
    295:   work = ds->work;
    296: #endif
    297:   /* selection sort */
    298:   for (i=ds->l;i<n-1;i++) {
    299:     re = wr[i];
    300: #if !defined(PETSC_USE_COMPLEX)
    301:     im = wi[i];
    302: #endif
    303:     pos = 0;
    304:     j = i+1; /* j points to the next eigenvalue */
    305: #if !defined(PETSC_USE_COMPLEX)
    306:     if (im != 0) j=i+2;
    307: #endif
    308:     /* find minimum eigenvalue */
    309:     for (;j<n;j++) {
    310: #if !defined(PETSC_USE_COMPLEX)
    311:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
    312: #else
    313:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
    314: #endif
    315:       if (result > 0) {
    316:         re = wr[j];
    317: #if !defined(PETSC_USE_COMPLEX)
    318:         im = wi[j];
    319: #endif
    320:         pos = j;
    321:       }
    322: #if !defined(PETSC_USE_COMPLEX)
    323:       if (wi[j] != 0) j++;
    324: #endif
    325:     }
    326:     if (pos) {
    327:       /* interchange blocks */
    328:       PetscBLASIntCast(pos+1,&ifst);
    329:       PetscBLASIntCast(i+1,&ilst);
    330: #if !defined(PETSC_USE_COMPLEX)
    331:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
    332: #else
    333:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
    334: #endif
    335:       SlepcCheckLapackInfo("tgexc",info);
    336:       /* recover original eigenvalues from T and S matrices */
    337:       for (j=i;j<n;j++) {
    338: #if !defined(PETSC_USE_COMPLEX)
    339:         if (j<n-1 && S[j*ld+j+1] != 0.0) {
    340:           /* complex conjugate eigenvalue */
    341:           PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
    342:           wr[j] = re / scale1;
    343:           wi[j] = im / scale1;
    344:           wr[j+1] = a / scale2;
    345:           wi[j+1] = -wi[j];
    346:           j++;
    347:         } else
    348: #endif
    349:         {
    350:           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    351:           else wr[j] = S[j*ld+j] / T[j*ld+j];
    352: #if !defined(PETSC_USE_COMPLEX)
    353:           wi[j] = 0.0;
    354: #endif
    355:         }
    356:       }
    357:     }
    358: #if !defined(PETSC_USE_COMPLEX)
    359:     if (wi[i] != 0.0) i++;
    360: #endif
    361:   }
    362:   return(0);
    363: }

    365: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    366: {

    370:   if (!rr || wr == rr) {
    371:     DSSort_GNHEP_Total(ds,wr,wi);
    372:   } else {
    373:     DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
    374:   }
    375:   return(0);
    376: }

    378: /*
    379:    Write zeros from the column k to n in the lower triangular part of the
    380:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
    381:    make (S,T) a valid Schur decompositon.
    382: */
    383: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
    384: {
    385:   PetscInt       i;
    386: #if defined(PETSC_USE_COMPLEX)
    387:   PetscInt       j;
    388:   PetscScalar    s;
    389: #else
    391:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
    392:   PetscScalar    b11,b22,sr,cr,sl,cl;
    393: #endif

    396: #if defined(PETSC_USE_COMPLEX)
    397:   for (i=k; i<n; i++) {
    398:     /* Some functions need the diagonal elements in T be real */
    399:     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
    400:       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
    401:       for (j=0;j<=i;j++) {
    402:         T[ldT*i+j] *= s;
    403:         S[ldS*i+j] *= s;
    404:       }
    405:       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
    406:       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
    407:     }
    408:     j = i+1;
    409:     if (j<n) {
    410:       S[ldS*i+j] = 0.0;
    411:       if (T) T[ldT*i+j] = 0.0;
    412:     }
    413:   }
    414: #else
    415:   PetscBLASIntCast(ldS,&ldS_);
    416:   PetscBLASIntCast(ldT,&ldT_);
    417:   PetscBLASIntCast(n,&n_);
    418:   for (i=k;i<n-1;i++) {
    419:     if (S[ldS*i+i+1] != 0.0) {
    420:       /* Check if T(i+1,i) and T(i,i+1) are zero */
    421:       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
    422:         /* Check if T(i+1,i) and T(i,i+1) are negligible */
    423:         if (PetscAbs(T[ldT*(i+1)+i])+PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1]))*PETSC_MACHINE_EPSILON) {
    424:           T[ldT*i+i+1] = 0.0;
    425:           T[ldT*(i+1)+i] = 0.0;
    426:         } else {
    427:           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
    428:           if (PetscAbs(T[ldT*i+i+1]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*(i+1)+i]))*PETSC_MACHINE_EPSILON) {
    429:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
    430:           } else if (PetscAbs(T[ldT*(i+1)+i]) < (PetscAbs(T[ldT*i+i])+PetscAbs(T[ldT*(i+1)+i+1])+PetscAbs(T[ldT*i+i+1]))*PETSC_MACHINE_EPSILON) {
    431:             PetscStackCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
    432:           } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
    433:           PetscBLASIntCast(n-i,&n_i);
    434:           n_i_2 = n_i - 2;
    435:           PetscBLASIntCast(i+2,&i_2);
    436:           PetscBLASIntCast(i,&i_);
    437:           if (b11 < 0.0) {
    438:             cr = -cr; sr = -sr;
    439:             b11 = -b11; b22 = -b22;
    440:           }
    441:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
    442:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
    443:           PetscStackCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
    444:           PetscStackCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
    445:           if (X) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
    446:           if (Y) PetscStackCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
    447:           T[ldT*i+i] = b11; T[ldT*i+i+1] = 0.0;
    448:           T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
    449:         }
    450:       }
    451:       i++;
    452:     }
    453:   }
    454: #endif
    455:   return(0);
    456: }

    458: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
    459: {
    461:   PetscScalar    *work,*beta,a;
    462:   PetscInt       i;
    463:   PetscBLASInt   lwork,info,n,ld,iaux;
    464:   PetscScalar    *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],*Z = ds->mat[DS_MAT_Z],*Q = ds->mat[DS_MAT_Q];

    467: #if !defined(PETSC_USE_COMPLEX)
    469: #endif
    470:   PetscBLASIntCast(ds->n,&n);
    471:   PetscBLASIntCast(ds->ld,&ld);
    472:   lwork = -1;
    473: #if !defined(PETSC_USE_COMPLEX)
    474:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
    475:   PetscBLASIntCast((PetscInt)a,&lwork);
    476:   DSAllocateWork_Private(ds,lwork+ld,0,0);
    477:   beta = ds->work;
    478:   work = beta+ds->n;
    479:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
    480:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
    481: #else
    482:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
    483:   PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork);
    484:   DSAllocateWork_Private(ds,lwork+ld,8*ld,0);
    485:   beta = ds->work;
    486:   work = beta+ds->n;
    487:   PetscBLASIntCast(ds->lwork-ds->n,&lwork);
    488:   PetscStackCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
    489: #endif
    490:   SlepcCheckLapackInfo("gges",info);
    491:   for (i=0;i<n;i++) {
    492:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    493:     else wr[i] /= beta[i];
    494: #if !defined(PETSC_USE_COMPLEX)
    495:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    496:     else wi[i] /= beta[i];
    497: #else
    498:     if (wi) wi[i] = 0.0;
    499: #endif
    500:   }
    501:   return(0);
    502: }

    504: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    505: {
    507:   PetscInt       ld=ds->ld,l=ds->l,k;
    508:   PetscMPIInt    n,rank,off=0,size,ldn;

    511:   k = 2*(ds->n-l)*ld;
    512:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
    513:   if (eigr) k += (ds->n-l);
    514:   if (eigi) k += (ds->n-l);
    515:   DSAllocateWork_Private(ds,k,0,0);
    516:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
    517:   PetscMPIIntCast(ds->n-l,&n);
    518:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    519:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    520:   if (!rank) {
    521:     MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    522:     MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    523:     if (ds->state>DS_STATE_RAW) {
    524:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    525:       MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    526:     }
    527:     if (eigr) {
    528:       MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    529:     }
    530:     if (eigi) {
    531:       MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    532:     }
    533:   }
    534:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    535:   if (rank) {
    536:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    537:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    538:     if (ds->state>DS_STATE_RAW) {
    539:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    540:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    541:     }
    542:     if (eigr) {
    543:       MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    544:     }
    545:     if (eigi) {
    546:       MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    547:     }
    548:   }
    549:   return(0);
    550: }

    552: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
    553: {
    555:   ds->ops->allocate      = DSAllocate_GNHEP;
    556:   ds->ops->view          = DSView_GNHEP;
    557:   ds->ops->vectors       = DSVectors_GNHEP;
    558:   ds->ops->solve[0]      = DSSolve_GNHEP;
    559:   ds->ops->sort          = DSSort_GNHEP;
    560:   ds->ops->synchronize   = DSSynchronize_GNHEP;
    561:   return(0);
    562: }