Date: 2022-08-09T09:05:21+00:00

Actual source code: dsgnhep.c
slepc-3.17.2 2022-08-09
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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: */

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

     32: PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
     33: {
     34:   DSAllocateMat_Private(ds,DS_MAT_A);
     35:   DSAllocateMat_Private(ds,DS_MAT_B);
     36:   DSAllocateMat_Private(ds,DS_MAT_Z);
     37:   DSAllocateMat_Private(ds,DS_MAT_Q);
     38:   PetscFree(ds->perm);
     39:   PetscMalloc1(ld,&ds->perm);
     40:   PetscLogObjectMemory((PetscObject)ds,ld*sizeof(PetscInt));
     41:   PetscFunctionReturn(0);
     42: }

     44: PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
     45: {
     46:   PetscViewerFormat format;

     48:   PetscViewerGetFormat(viewer,&format);
     49:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(0);
     50:   DSViewMat(ds,viewer,DS_MAT_A);
     51:   DSViewMat(ds,viewer,DS_MAT_B);
     52:   if (ds->state>DS_STATE_INTERMEDIATE) {
     53:     DSViewMat(ds,viewer,DS_MAT_Z);
     54:     DSViewMat(ds,viewer,DS_MAT_Q);
     55:   }
     56:   if (ds->mat[DS_MAT_X]) DSViewMat(ds,viewer,DS_MAT_X);
     57:   if (ds->mat[DS_MAT_Y]) DSViewMat(ds,viewer,DS_MAT_Y);
     58:   PetscFunctionReturn(0);
     59: }

     61: static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
     62: {
     63:   PetscInt       i;
     64:   PetscBLASInt   n,ld,mout,info,*select,mm,inc=1,cols=1,zero=0;
     65:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],fone=1.0,fzero=0.0;
     66:   PetscReal      norm,done=1.0;
     67:   PetscBool      iscomplex = PETSC_FALSE;
     68:   const char     *side;

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

     92:   /* compute k-th eigenvector */
     93:   select[*k] = (PetscBLASInt)PETSC_TRUE;
     94: #if defined(PETSC_USE_COMPLEX)
     95:   mm = 1;
     96:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
     97:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,ds->rwork,&info));
     98: #else
     99:   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
    100:   mm = iscomplex? 2: 1;
    101:   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
    102:   DSAllocateWork_Private(ds,6*ld,0,0);
    103:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&mm,&mout,ds->work,&info));
    104: #endif
    105:   SlepcCheckLapackInfo("tgevc",info);

    108:   /* accumulate and normalize eigenvectors */
    109:   PetscArraycpy(ds->work,Z,mm*ld);
    110:   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));
    111:   norm = BLASnrm2_(&n,Z,&inc);
    112: #if !defined(PETSC_USE_COMPLEX)
    113:   if (iscomplex) {
    114:     norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,Z+ld,&inc));
    115:     cols = 2;
    116:   }
    117: #endif
    118:   PetscStackCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,Z,&ld,&info));
    119:   SlepcCheckLapackInfo("lascl",info);

    121:   /* set output arguments */
    122:   if (iscomplex) (*k)++;
    123:   if (rnorm) {
    124:     if (iscomplex) *rnorm = SlepcAbsEigenvalue(Z[n-1],Z[n-1+ld]);
    125:     else *rnorm = PetscAbsScalar(Z[n-1]);
    126:   }
    127:   PetscFunctionReturn(0);
    128: }

    130: static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
    131: {
    132:   PetscInt       i;
    133:   PetscBLASInt   n,ld,mout,info,inc = 1;
    134:   PetscBool      iscomplex;
    135:   PetscScalar    *X,*Y,*Z,*A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B],tmp;
    136:   PetscReal      norm;
    137:   const char     *side,*back;

    139:   PetscBLASIntCast(ds->n,&n);
    140:   PetscBLASIntCast(ds->ld,&ld);
    141:   if (left) {
    142:     X = NULL;
    143:     Y = ds->mat[DS_MAT_Y];
    144:     side = "L";
    145:   } else {
    146:     X = ds->mat[DS_MAT_X];
    147:     Y = NULL;
    148:     side = "R";
    149:   }
    150:   Z = left? Y: X;
    151:   if (ds->state <= DS_STATE_INTERMEDIATE) {
    152:     DSSetIdentity(ds,DS_MAT_Q);
    153:     DSSetIdentity(ds,DS_MAT_Z);
    154:   }
    155:   CleanDenseSchur(n,0,A,ld,B,ld,ds->mat[DS_MAT_Q],ld,ds->mat[DS_MAT_Z],ld);
    156:   if (ds->state>=DS_STATE_CONDENSED) {
    157:     /* DSSolve() has been called, backtransform with matrix Q */
    158:     back = "B";
    159:     PetscArraycpy(left?Y:X,ds->mat[left?DS_MAT_Z:DS_MAT_Q],ld*ld);
    160:   } else {
    161:     back = "A";
    162:     DSSetState(ds,DS_STATE_CONDENSED);
    163:   }
    164: #if defined(PETSC_USE_COMPLEX)
    165:   DSAllocateWork_Private(ds,2*ld,2*ld,0);
    166:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
    167: #else
    168:   DSAllocateWork_Private(ds,6*ld,0,0);
    169:   PetscStackCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
    170: #endif
    171:   SlepcCheckLapackInfo("tgevc",info);

    173:   /* normalize eigenvectors */
    174:   for (i=0;i<n;i++) {
    175:     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
    176:     norm = BLASnrm2_(&n,Z+i*ld,&inc);
    177: #if !defined(PETSC_USE_COMPLEX)
    178:     if (iscomplex) {
    179:       tmp = BLASnrm2_(&n,Z+(i+1)*ld,&inc);
    180:       norm = SlepcAbsEigenvalue(norm,tmp);
    181:     }
    182: #endif
    183:     tmp = 1.0 / norm;
    184:     PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+i*ld,&inc));
    185: #if !defined(PETSC_USE_COMPLEX)
    186:     if (iscomplex) PetscStackCallBLAS("BLASscal",BLASscal_(&n,&tmp,Z+(i+1)*ld,&inc));
    187: #endif
    188:     if (iscomplex) i++;
    189:   }
    190:   PetscFunctionReturn(0);
    191: }

    193: PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
    194: {
    195:   switch (mat) {
    196:     case DS_MAT_X:
    197:     case DS_MAT_Y:
    198:       if (k) DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
    199:       else DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE);
    200:       break;
    201:     default:
    202:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
    203:   }
    204:   PetscFunctionReturn(0);
    205: }

    207: static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    208: {
    209:   PetscInt       i;
    210:   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
    211:   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;

    213:   if (!ds->sc) PetscFunctionReturn(0);
    214:   PetscBLASIntCast(ds->n,&n);
    215:   PetscBLASIntCast(ds->ld,&ld);
    216: #if !defined(PETSC_USE_COMPLEX)
    217:   lwork = 4*n+16;
    218: #else
    219:   lwork = 1;
    220: #endif
    221:   liwork = 1;
    222:   DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n);
    223:   beta      = ds->work;
    224:   work      = ds->work + n;
    225:   lwork     = ds->lwork - n;
    226:   selection = ds->iwork;
    227:   iwork     = ds->iwork + n;
    228:   liwork    = ds->liwork - n;
    229:   /* Compute the selected eigenvalue to be in the leading position */
    230:   DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE);
    231:   PetscArrayzero(selection,n);
    232:   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
    233: #if !defined(PETSC_USE_COMPLEX)
    234:   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));
    235: #else
    236:   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));
    237: #endif
    238:   SlepcCheckLapackInfo("tgsen",info);
    239:   *k = mout;
    240:   for (i=0;i<n;i++) {
    241:     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    242:     else wr[i] /= beta[i];
    243: #if !defined(PETSC_USE_COMPLEX)
    244:     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    245:     else wi[i] /= beta[i];
    246: #endif
    247:   }
    248:   PetscFunctionReturn(0);
    249: }

    251: static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
    252: {
    253:   PetscScalar    re;
    254:   PetscInt       i,j,pos,result;
    255:   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
    256:   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];
    257: #if !defined(PETSC_USE_COMPLEX)
    258:   PetscBLASInt   lwork;
    259:   PetscScalar    *work,a,safmin,scale1,scale2,im;
    260: #endif

    262:   if (!ds->sc) PetscFunctionReturn(0);
    263:   PetscBLASIntCast(ds->n,&n);
    264:   PetscBLASIntCast(ds->ld,&ld);
    265: #if !defined(PETSC_USE_COMPLEX)
    266:   lwork = -1;
    267:   PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
    268:   SlepcCheckLapackInfo("tgexc",info);
    269:   safmin = LAPACKlamch_("S");
    270:   PetscBLASIntCast((PetscInt)a,&lwork);
    271:   DSAllocateWork_Private(ds,lwork,0,0);
    272:   work = ds->work;
    273: #endif
    274:   /* selection sort */
    275:   for (i=ds->l;i<n-1;i++) {
    276:     re = wr[i];
    277: #if !defined(PETSC_USE_COMPLEX)
    278:     im = wi[i];
    279: #endif
    280:     pos = 0;
    281:     j = i+1; /* j points to the next eigenvalue */
    282: #if !defined(PETSC_USE_COMPLEX)
    283:     if (im != 0) j=i+2;
    284: #endif
    285:     /* find minimum eigenvalue */
    286:     for (;j<n;j++) {
    287: #if !defined(PETSC_USE_COMPLEX)
    288:       SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result);
    289: #else
    290:       SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result);
    291: #endif
    292:       if (result > 0) {
    293:         re = wr[j];
    294: #if !defined(PETSC_USE_COMPLEX)
    295:         im = wi[j];
    296: #endif
    297:         pos = j;
    298:       }
    299: #if !defined(PETSC_USE_COMPLEX)
    300:       if (wi[j] != 0) j++;
    301: #endif
    302:     }
    303:     if (pos) {
    304:       /* interchange blocks */
    305:       PetscBLASIntCast(pos+1,&ifst);
    306:       PetscBLASIntCast(i+1,&ilst);
    307: #if !defined(PETSC_USE_COMPLEX)
    308:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
    309: #else
    310:       PetscStackCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
    311: #endif
    312:       SlepcCheckLapackInfo("tgexc",info);
    313:       /* recover original eigenvalues from T and S matrices */
    314:       for (j=i;j<n;j++) {
    315: #if !defined(PETSC_USE_COMPLEX)
    316:         if (j<n-1 && S[j*ld+j+1] != 0.0) {
    317:           /* complex conjugate eigenvalue */
    318:           PetscStackCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
    319:           wr[j] = re / scale1;
    320:           wi[j] = im / scale1;
    321:           wr[j+1] = a / scale2;
    322:           wi[j+1] = -wi[j];
    323:           j++;
    324:         } else
    325: #endif
    326:         {
    327:           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
    328:           else wr[j] = S[j*ld+j] / T[j*ld+j];
    329: #if !defined(PETSC_USE_COMPLEX)
    330:           wi[j] = 0.0;
    331: #endif
    332:         }
    333:       }
    334:     }
    335: #if !defined(PETSC_USE_COMPLEX)
    336:     if (wi[i] != 0.0) i++;
    337: #endif
    338:   }
    339:   PetscFunctionReturn(0);
    340: }

    342: PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
    343: {
    344:   if (!rr || wr == rr) DSSort_GNHEP_Total(ds,wr,wi);
    345:   else DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k);
    346:   PetscFunctionReturn(0);
    347: }

    349: PetscErrorCode DSUpdateExtraRow_GNHEP(DS ds)
    350: {
    351:   PetscInt       i;
    352:   PetscBLASInt   n,ld,incx=1;
    353:   PetscScalar    *A,*B,*Q,*x,*y,one=1.0,zero=0.0;

    355:   PetscBLASIntCast(ds->n,&n);
    356:   PetscBLASIntCast(ds->ld,&ld);
    357:   A  = ds->mat[DS_MAT_A];
    358:   B  = ds->mat[DS_MAT_B];
    359:   Q  = ds->mat[DS_MAT_Q];
    360:   DSAllocateWork_Private(ds,2*ld,0,0);
    361:   x = ds->work;
    362:   y = ds->work+ld;
    363:   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
    364:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    365:   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
    366:   for (i=0;i<n;i++) x[i] = PetscConj(B[n+i*ld]);
    367:   PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
    368:   for (i=0;i<n;i++) B[n+i*ld] = PetscConj(y[i]);
    369:   ds->k = n;
    370:   PetscFunctionReturn(0);
    371: }

    373: /*
    374:    Write zeros from the column k to n in the lower triangular part of the
    375:    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
    376:    make (S,T) a valid Schur decompositon.
    377: */
    378: static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
    379: {
    380:   PetscInt       i;
    381: #if defined(PETSC_USE_COMPLEX)
    382:   PetscInt       j;
    383:   PetscScalar    s;
    384: #else
    385:   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
    386:   PetscScalar    b11,b22,sr,cr,sl,cl;
    387: #endif

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

    451: PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
    452: {
    453:   PetscScalar    *work,*beta,a;
    454:   PetscInt       i;
    455:   PetscBLASInt   lwork,info,n,ld,iaux;
    456:   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];

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

    495: PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    496: {
    497:   PetscInt       ld=ds->ld,l=ds->l,k;
    498:   PetscMPIInt    n,rank,off=0,size,ldn;

    500:   k = 2*(ds->n-l)*ld;
    501:   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
    502:   if (eigr) k += (ds->n-l);
    503:   if (eigi) k += (ds->n-l);
    504:   DSAllocateWork_Private(ds,k,0,0);
    505:   PetscMPIIntCast(k*sizeof(PetscScalar),&size);
    506:   PetscMPIIntCast(ds->n-l,&n);
    507:   PetscMPIIntCast(ld*(ds->n-l),&ldn);
    508:   MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank);
    509:   if (!rank) {
    510:     MPI_Pack(ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    511:     MPI_Pack(ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    512:     if (ds->state>DS_STATE_RAW) {
    513:       MPI_Pack(ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    514:       MPI_Pack(ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    515:     }
    516:     if (eigr) MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    517: #if !defined(PETSC_USE_COMPLEX)
    518:     if (eigi) MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds));
    519: #endif
    520:   }
    521:   MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds));
    522:   if (rank) {
    523:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_A]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    524:     MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_B]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    525:     if (ds->state>DS_STATE_RAW) {
    526:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Q]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    527:       MPI_Unpack(ds->work,size,&off,ds->mat[DS_MAT_Z]+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    528:     }
    529:     if (eigr) MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    530: #if !defined(PETSC_USE_COMPLEX)
    531:     if (eigi) MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds));
    532: #endif
    533:   }
    534:   PetscFunctionReturn(0);
    535: }

    537: PetscErrorCode DSTruncate_GNHEP(DS ds,PetscInt n,PetscBool trim)
    538: {
    539:   PetscInt    i,ld=ds->ld,l=ds->l;
    540:   PetscScalar *A = ds->mat[DS_MAT_A],*B = ds->mat[DS_MAT_B];

    542: #if defined(PETSC_USE_DEBUG)
    543:   /* make sure diagonal 2x2 block is not broken */
    545: #endif
    546:   if (trim) {
    547:     if (ds->extrarow) {   /* clean extra row */
    548:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    549:       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
    550:     }
    551:     ds->l = 0;
    552:     ds->k = 0;
    553:     ds->n = n;
    554:     ds->t = ds->n;   /* truncated length equal to the new dimension */
    555:   } else {
    556:     if (ds->extrarow && ds->k==ds->n) {
    557:       /* copy entries of extra row to the new position, then clean last row */
    558:       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
    559:       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
    560:       for (i=l;i<n;i++) B[n+i*ld] = B[ds->n+i*ld];
    561:       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
    562:     }
    563:     ds->k = (ds->extrarow)? n: 0;
    564:     ds->t = ds->n;   /* truncated length equal to previous dimension */
    565:     ds->n = n;
    566:   }
    567:   PetscFunctionReturn(0);
    568: }

    570: /*MC
    571:    DSGNHEP - Dense Generalized Non-Hermitian Eigenvalue Problem.

    573:    Level: beginner

    575:    Notes:
    576:    The problem is expressed as A*X = B*X*Lambda, where (A,B) is the input
    577:    matrix pencil. Lambda is a diagonal matrix whose diagonal elements are the
    578:    arguments of DSSolve(). After solve, (A,B) is overwritten with the
    579:    generalized (real) Schur form (S,T) = (Z'*A*Q,Z'*B*Q), with the first
    580:    matrix being upper quasi-triangular and the second one triangular.

    582:    Used DS matrices:
    583: +  DS_MAT_A - first problem matrix
    584: .  DS_MAT_B - second problem matrix
    585: .  DS_MAT_Q - first orthogonal/unitary transformation that reduces to
    586:    generalized (real) Schur form
    587: -  DS_MAT_Z - second orthogonal/unitary transformation that reduces to
    588:    generalized (real) Schur form

    590:    Implemented methods:
    591: .  0 - QZ iteration (_gges)

    593: .seealso: DSCreate(), DSSetType(), DSType
    594: M*/
    595: SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
    596: {
    597:   ds->ops->allocate        = DSAllocate_GNHEP;
    598:   ds->ops->view            = DSView_GNHEP;
    599:   ds->ops->vectors         = DSVectors_GNHEP;
    600:   ds->ops->solve[0]        = DSSolve_GNHEP;
    601:   ds->ops->sort            = DSSort_GNHEP;
    602:   ds->ops->synchronize     = DSSynchronize_GNHEP;
    603:   ds->ops->gettruncatesize = DSGetTruncateSize_Default;
    604:   ds->ops->truncate        = DSTruncate_GNHEP;
    605:   ds->ops->update          = DSUpdateExtraRow_GNHEP;
    606:   PetscFunctionReturn(0);
    607: }