LCOV - code coverage report
Current view: top level - sys/classes/ds/impls/gnhep - dsgnhep.c (source / functions) Hit Total Coverage
Test: SLEPc Lines: 392 411 95.4 %
Date: 2024-03-29 00:55:19 Functions: 14 14 100.0 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /*
       2             :    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
       3             :    SLEPc - Scalable Library for Eigenvalue Problem Computations
       4             :    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
       5             : 
       6             :    This file is part of SLEPc.
       7             :    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
       8             :    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
       9             : */
      10             : 
      11             : #include <slepc/private/dsimpl.h>
      12             : #include <slepcblaslapack.h>
      13             : 
      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             :       -------------            -------------
      26             : 
      27             :   2) Moreover, P and Q are assumed to be the identity in DS_STATE_INTERMEDIATE.
      28             : */
      29             : 
      30             : static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY);
      31             : 
      32          29 : static PetscErrorCode DSAllocate_GNHEP(DS ds,PetscInt ld)
      33             : {
      34          29 :   PetscFunctionBegin;
      35          29 :   PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
      36          29 :   PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
      37          29 :   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Z));
      38          29 :   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
      39          29 :   PetscCall(PetscFree(ds->perm));
      40          29 :   PetscCall(PetscMalloc1(ld,&ds->perm));
      41          29 :   PetscFunctionReturn(PETSC_SUCCESS);
      42             : }
      43             : 
      44           4 : static PetscErrorCode DSView_GNHEP(DS ds,PetscViewer viewer)
      45             : {
      46           4 :   PetscViewerFormat format;
      47             : 
      48           4 :   PetscFunctionBegin;
      49           4 :   PetscCall(PetscViewerGetFormat(viewer,&format));
      50           4 :   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(PETSC_SUCCESS);
      51           0 :   PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
      52           0 :   PetscCall(DSViewMat(ds,viewer,DS_MAT_B));
      53           0 :   if (ds->state>DS_STATE_INTERMEDIATE) {
      54           0 :     PetscCall(DSViewMat(ds,viewer,DS_MAT_Z));
      55           0 :     PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
      56             :   }
      57           0 :   if (ds->omat[DS_MAT_X]) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
      58           0 :   if (ds->omat[DS_MAT_Y]) PetscCall(DSViewMat(ds,viewer,DS_MAT_Y));
      59           0 :   PetscFunctionReturn(PETSC_SUCCESS);
      60             : }
      61             : 
      62       11732 : static PetscErrorCode DSVectors_GNHEP_Eigen_Some(DS ds,PetscInt *k,PetscReal *rnorm,PetscBool left)
      63             : {
      64       11732 :   PetscInt       i;
      65       11732 :   PetscBLASInt   n,ld,mout,info,*select,mm,inc=1,cols=1,zero=0;
      66       11732 :   PetscScalar    *X,*Y,*XY,*Z,*Q,*A,*B,fone=1.0,fzero=0.0;
      67       11732 :   PetscReal      norm,done=1.0;
      68       11732 :   PetscBool      iscomplex = PETSC_FALSE;
      69       11732 :   const char     *side;
      70             : 
      71       11732 :   PetscFunctionBegin;
      72       11732 :   PetscCall(PetscBLASIntCast(ds->n,&n));
      73       11732 :   PetscCall(PetscBLASIntCast(ds->ld,&ld));
      74       11732 :   if (left) {
      75         613 :     X = NULL;
      76         613 :     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Y],&Y));
      77             :     side = "L";
      78             :   } else {
      79       11119 :     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
      80       11119 :     Y = NULL;
      81       11119 :     side = "R";
      82             :   }
      83       11732 :   XY = left? Y: X;
      84       11732 :   PetscCall(DSAllocateWork_Private(ds,0,0,ld));
      85       11732 :   select = ds->iwork;
      86      157042 :   for (i=0;i<n;i++) select[i] = (PetscBLASInt)PETSC_FALSE;
      87       11732 :   if (ds->state <= DS_STATE_INTERMEDIATE) {
      88           1 :     PetscCall(DSSetIdentity(ds,DS_MAT_Q));
      89           1 :     PetscCall(DSSetIdentity(ds,DS_MAT_Z));
      90             :   }
      91       11732 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
      92       11732 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
      93       11732 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
      94       11732 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
      95       11732 :   PetscCall(CleanDenseSchur(n,0,A,ld,B,ld,Q,ld,Z,ld));
      96       11732 :   if (ds->state < DS_STATE_CONDENSED) PetscCall(DSSetState(ds,DS_STATE_CONDENSED));
      97             : 
      98             :   /* compute k-th eigenvector */
      99       11732 :   select[*k] = (PetscBLASInt)PETSC_TRUE;
     100             : #if defined(PETSC_USE_COMPLEX)
     101             :   mm = 1;
     102             :   PetscCall(DSAllocateWork_Private(ds,2*ld,2*ld,0));
     103             :   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y+(*k)*ld,&ld,X+(*k)*ld,&ld,&mm,&mout,ds->work,ds->rwork,&info));
     104             : #else
     105       11732 :   if ((*k)<n-1 && (A[ld*(*k)+(*k)+1] != 0.0 || B[ld*(*k)+(*k)+1] != 0.0)) iscomplex = PETSC_TRUE;
     106       11732 :   mm = iscomplex? 2: 1;
     107       11732 :   if (iscomplex) select[(*k)+1] = (PetscBLASInt)PETSC_TRUE;
     108       11732 :   PetscCall(DSAllocateWork_Private(ds,6*ld,0,0));
     109       11732 :   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,"S",select,&n,A,&ld,B,&ld,Y+(*k)*ld,&ld,X+(*k)*ld,&ld,&mm,&mout,ds->work,&info));
     110             : #endif
     111       11732 :   SlepcCheckLapackInfo("tgevc",info);
     112       11732 :   PetscCheck(select[*k] && mout==mm,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Wrong arguments in call to Lapack xTGEVC");
     113       11732 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     114       11732 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
     115             : 
     116             :   /* accumulate and normalize eigenvectors */
     117       11732 :   PetscCall(PetscArraycpy(ds->work,XY+(*k)*ld,mm*ld));
     118       11732 :   PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n,&mm,&n,&fone,left?Z:Q,&ld,ds->work,&ld,&fzero,XY+(*k)*ld,&ld));
     119       11732 :   norm = BLASnrm2_(&n,XY+(*k)*ld,&inc);
     120             : #if !defined(PETSC_USE_COMPLEX)
     121       11732 :   if (iscomplex) {
     122         100 :     norm = SlepcAbsEigenvalue(norm,BLASnrm2_(&n,XY+(*k+1)*ld,&inc));
     123         100 :     cols = 2;
     124             :   }
     125             : #endif
     126       11732 :   PetscCallBLAS("LAPACKlascl",LAPACKlascl_("G",&zero,&zero,&norm,&done,&n,&cols,XY+(*k)*ld,&ld,&info));
     127       11732 :   SlepcCheckLapackInfo("lascl",info);
     128       11732 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
     129       11732 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
     130             : 
     131             :   /* set output arguments */
     132       11732 :   if (rnorm) {
     133          18 :     if (iscomplex) *rnorm = SlepcAbsEigenvalue(XY[n-1+(*k)*ld],XY[n-1+(*k+1)*ld]);
     134          16 :     else *rnorm = PetscAbsScalar(XY[n-1+(*k)*ld]);
     135             :   }
     136       11732 :   if (iscomplex) (*k)++;
     137       22851 :   PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&XY));
     138       11732 :   PetscFunctionReturn(PETSC_SUCCESS);
     139             : }
     140             : 
     141          44 : static PetscErrorCode DSVectors_GNHEP_Eigen_All(DS ds,PetscBool left)
     142             : {
     143          44 :   PetscInt       i;
     144          44 :   PetscBLASInt   n,ld,mout,info,inc = 1;
     145          44 :   PetscBool      iscomplex;
     146          44 :   PetscScalar    *X,*Y,*XY,*Q,*Z,*A,*B,tmp;
     147          44 :   PetscReal      norm;
     148          44 :   const char     *side,*back;
     149             : 
     150          44 :   PetscFunctionBegin;
     151          44 :   PetscCall(PetscBLASIntCast(ds->n,&n));
     152          44 :   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     153          44 :   if (left) {
     154           0 :     X = NULL;
     155           0 :     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Y],&Y));
     156             :     side = "L";
     157             :   } else {
     158          44 :     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_X],&X));
     159          44 :     Y = NULL;
     160          44 :     side = "R";
     161             :   }
     162          44 :   XY = left? Y: X;
     163          44 :   if (ds->state <= DS_STATE_INTERMEDIATE) {
     164           3 :     PetscCall(DSSetIdentity(ds,DS_MAT_Q));
     165           3 :     PetscCall(DSSetIdentity(ds,DS_MAT_Z));
     166             :   }
     167          44 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
     168          44 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
     169          44 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
     170          44 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
     171          44 :   PetscCall(CleanDenseSchur(n,0,A,ld,B,ld,Q,ld,Z,ld));
     172          44 :   if (ds->state>=DS_STATE_CONDENSED) {
     173             :     /* DSSolve() has been called, backtransform with matrix Q */
     174          41 :     back = "B";
     175          41 :     PetscCall(PetscArraycpy(left?Y:X,left?Z:Q,ld*ld));
     176             :   } else {
     177           3 :     back = "A";
     178           3 :     PetscCall(DSSetState(ds,DS_STATE_CONDENSED));
     179             :   }
     180             : #if defined(PETSC_USE_COMPLEX)
     181             :   PetscCall(DSAllocateWork_Private(ds,2*ld,2*ld,0));
     182             :   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,ds->rwork,&info));
     183             : #else
     184          44 :   PetscCall(DSAllocateWork_Private(ds,6*ld,0,0));
     185          44 :   PetscCallBLAS("LAPACKtgevc",LAPACKtgevc_(side,back,NULL,&n,A,&ld,B,&ld,Y,&ld,X,&ld,&n,&mout,ds->work,&info));
     186             : #endif
     187          44 :   SlepcCheckLapackInfo("tgevc",info);
     188          44 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
     189          44 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
     190             : 
     191             :   /* normalize eigenvectors */
     192         213 :   for (i=0;i<n;i++) {
     193         169 :     iscomplex = (i<n-1 && (A[i+1+i*ld]!=0.0 || B[i+1+i*ld]!=0.0))? PETSC_TRUE: PETSC_FALSE;
     194         169 :     norm = BLASnrm2_(&n,XY+i*ld,&inc);
     195             : #if !defined(PETSC_USE_COMPLEX)
     196         169 :     if (iscomplex) {
     197           9 :       tmp = BLASnrm2_(&n,XY+(i+1)*ld,&inc);
     198           9 :       norm = SlepcAbsEigenvalue(norm,tmp);
     199             :     }
     200             : #endif
     201         169 :     tmp = 1.0 / norm;
     202         169 :     PetscCallBLAS("BLASscal",BLASscal_(&n,&tmp,XY+i*ld,&inc));
     203             : #if !defined(PETSC_USE_COMPLEX)
     204         169 :     if (iscomplex) PetscCallBLAS("BLASscal",BLASscal_(&n,&tmp,XY+(i+1)*ld,&inc));
     205             : #endif
     206         169 :     if (iscomplex) i++;
     207             :   }
     208          44 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     209          44 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
     210          88 :   PetscCall(MatDenseRestoreArray(ds->omat[left?DS_MAT_Y:DS_MAT_X],&XY));
     211          44 :   PetscFunctionReturn(PETSC_SUCCESS);
     212             : }
     213             : 
     214       11776 : static PetscErrorCode DSVectors_GNHEP(DS ds,DSMatType mat,PetscInt *k,PetscReal *rnorm)
     215             : {
     216       11776 :   PetscFunctionBegin;
     217       11776 :   switch (mat) {
     218       11776 :     case DS_MAT_X:
     219             :     case DS_MAT_Y:
     220       11776 :       if (k) PetscCall(DSVectors_GNHEP_Eigen_Some(ds,k,rnorm,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE));
     221          44 :       else PetscCall(DSVectors_GNHEP_Eigen_All(ds,mat == DS_MAT_Y?PETSC_TRUE:PETSC_FALSE));
     222       11776 :       break;
     223           0 :     default:
     224           0 :       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
     225             :   }
     226       11776 :   PetscFunctionReturn(PETSC_SUCCESS);
     227             : }
     228             : 
     229        2210 : static PetscErrorCode DSSort_GNHEP_Arbitrary(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
     230             : {
     231        2210 :   PetscInt       i;
     232        2210 :   PetscBLASInt   info,n,ld,mout,lwork,liwork,*iwork,*selection,zero_=0,true_=1;
     233        2210 :   PetscScalar    *S,*T,*Q,*Z,*work,*beta;
     234             : 
     235        2210 :   PetscFunctionBegin;
     236        2210 :   if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
     237        2210 :   PetscCall(PetscBLASIntCast(ds->n,&n));
     238        2210 :   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     239             : #if !defined(PETSC_USE_COMPLEX)
     240        2210 :   lwork = 4*n+16;
     241             : #else
     242             :   lwork = 1;
     243             : #endif
     244        2210 :   liwork = 1;
     245        2210 :   PetscCall(DSAllocateWork_Private(ds,lwork+2*n,0,liwork+n));
     246        2210 :   beta      = ds->work;
     247        2210 :   work      = ds->work + n;
     248        2210 :   lwork     = ds->lwork - n;
     249        2210 :   selection = ds->iwork;
     250        2210 :   iwork     = ds->iwork + n;
     251        2210 :   liwork    = ds->liwork - n;
     252             :   /* Compute the selected eigenvalue to be in the leading position */
     253        2210 :   PetscCall(DSSortEigenvalues_Private(ds,rr,ri,ds->perm,PETSC_FALSE));
     254        2210 :   PetscCall(PetscArrayzero(selection,n));
     255        9638 :   for (i=0; i<*k; i++) selection[ds->perm[i]] = 1;
     256        2210 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&S));
     257        2210 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&T));
     258        2210 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
     259        2210 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
     260             : #if !defined(PETSC_USE_COMPLEX)
     261        2210 :   PetscCallBLAS("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));
     262             : #else
     263             :   PetscCallBLAS("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));
     264             : #endif
     265        2210 :   SlepcCheckLapackInfo("tgsen",info);
     266        2210 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&S));
     267        2210 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&T));
     268        2210 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
     269        2210 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
     270        2210 :   *k = mout;
     271       26858 :   for (i=0;i<n;i++) {
     272       24648 :     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
     273       24648 :     else wr[i] /= beta[i];
     274             : #if !defined(PETSC_USE_COMPLEX)
     275       24648 :     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
     276       24648 :     else wi[i] /= beta[i];
     277             : #endif
     278             :   }
     279        2210 :   PetscFunctionReturn(PETSC_SUCCESS);
     280             : }
     281             : 
     282           6 : static PetscErrorCode DSSort_GNHEP_Total(DS ds,PetscScalar *wr,PetscScalar *wi)
     283             : {
     284           6 :   PetscScalar    re;
     285           6 :   PetscInt       i,j,pos,result;
     286           6 :   PetscBLASInt   ifst,ilst,info,n,ld,one=1;
     287           6 :   PetscScalar    *S,*T,*Z,*Q;
     288             : #if !defined(PETSC_USE_COMPLEX)
     289           6 :   PetscBLASInt   lwork;
     290           6 :   PetscScalar    *work,a,safmin,scale1,scale2,im;
     291             : #endif
     292             : 
     293           6 :   PetscFunctionBegin;
     294           6 :   if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
     295           6 :   PetscCall(PetscBLASIntCast(ds->n,&n));
     296           6 :   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     297           6 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&S));
     298           6 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&T));
     299           6 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
     300           6 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
     301             : #if !defined(PETSC_USE_COMPLEX)
     302           6 :   lwork = -1;
     303           6 :   PetscCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&ld,NULL,&ld,NULL,&ld,NULL,&ld,NULL,&ld,&one,&one,&a,&lwork,&info));
     304           6 :   SlepcCheckLapackInfo("tgexc",info);
     305           6 :   safmin = LAPACKlamch_("S");
     306           6 :   PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
     307           6 :   PetscCall(DSAllocateWork_Private(ds,lwork,0,0));
     308           6 :   work = ds->work;
     309             : #endif
     310             :   /* selection sort */
     311          84 :   for (i=ds->l;i<n-1;i++) {
     312          78 :     re = wr[i];
     313             : #if !defined(PETSC_USE_COMPLEX)
     314          78 :     im = wi[i];
     315             : #endif
     316          78 :     pos = 0;
     317          78 :     j = i+1; /* j points to the next eigenvalue */
     318             : #if !defined(PETSC_USE_COMPLEX)
     319          78 :     if (im != 0) j=i+2;
     320             : #endif
     321             :     /* find minimum eigenvalue */
     322         618 :     for (;j<n;j++) {
     323             : #if !defined(PETSC_USE_COMPLEX)
     324         540 :       PetscCall(SlepcSCCompare(ds->sc,re,im,wr[j],wi[j],&result));
     325             : #else
     326             :       PetscCall(SlepcSCCompare(ds->sc,re,0.0,wr[j],0.0,&result));
     327             : #endif
     328         540 :       if (result > 0) {
     329         443 :         re = wr[j];
     330             : #if !defined(PETSC_USE_COMPLEX)
     331         443 :         im = wi[j];
     332             : #endif
     333         443 :         pos = j;
     334             :       }
     335             : #if !defined(PETSC_USE_COMPLEX)
     336         540 :       if (wi[j] != 0) j++;
     337             : #endif
     338             :     }
     339          78 :     if (pos) {
     340             :       /* interchange blocks */
     341          72 :       PetscCall(PetscBLASIntCast(pos+1,&ifst));
     342          72 :       PetscCall(PetscBLASIntCast(i+1,&ilst));
     343             : #if !defined(PETSC_USE_COMPLEX)
     344          72 :       PetscCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,work,&lwork,&info));
     345             : #else
     346             :       PetscCallBLAS("LAPACKtgexc",LAPACKtgexc_(&one,&one,&n,S,&ld,T,&ld,Z,&ld,Q,&ld,&ifst,&ilst,&info));
     347             : #endif
     348          72 :       SlepcCheckLapackInfo("tgexc",info);
     349             :       /* recover original eigenvalues from T and S matrices */
     350         672 :       for (j=i;j<n;j++) {
     351             : #if !defined(PETSC_USE_COMPLEX)
     352         600 :         if (j<n-1 && S[j*ld+j+1] != 0.0) {
     353             :           /* complex conjugate eigenvalue */
     354         151 :           PetscCallBLAS("LAPACKlag2",LAPACKlag2_(S+j*ld+j,&ld,T+j*ld+j,&ld,&safmin,&scale1,&scale2,&re,&a,&im));
     355         151 :           wr[j] = re / scale1;
     356         151 :           wi[j] = im / scale1;
     357         151 :           wr[j+1] = a / scale2;
     358         151 :           wi[j+1] = -wi[j];
     359         151 :           j++;
     360             :         } else
     361             : #endif
     362             :         {
     363         449 :           if (T[j*ld+j] == 0.0) wr[j] = (PetscRealPart(S[j*ld+j])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
     364         449 :           else wr[j] = S[j*ld+j] / T[j*ld+j];
     365             : #if !defined(PETSC_USE_COMPLEX)
     366         449 :           wi[j] = 0.0;
     367             : #endif
     368             :         }
     369             :       }
     370             :     }
     371             : #if !defined(PETSC_USE_COMPLEX)
     372          78 :     if (wi[i] != 0.0) i++;
     373             : #endif
     374             :   }
     375           6 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&S));
     376           6 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&T));
     377           6 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
     378           6 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
     379           6 :   PetscFunctionReturn(PETSC_SUCCESS);
     380             : }
     381             : 
     382        2216 : static PetscErrorCode DSSort_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
     383             : {
     384        2216 :   PetscFunctionBegin;
     385        2216 :   if (!rr || wr == rr) PetscCall(DSSort_GNHEP_Total(ds,wr,wi));
     386        2210 :   else PetscCall(DSSort_GNHEP_Arbitrary(ds,wr,wi,rr,ri,k));
     387        2216 :   PetscFunctionReturn(PETSC_SUCCESS);
     388             : }
     389             : 
     390           5 : static PetscErrorCode DSUpdateExtraRow_GNHEP(DS ds)
     391             : {
     392           5 :   PetscInt          i;
     393           5 :   PetscBLASInt      n,ld,incx=1;
     394           5 :   PetscScalar       *A,*B,*x,*y,one=1.0,zero=0.0;
     395           5 :   const PetscScalar *Q;
     396             : 
     397           5 :   PetscFunctionBegin;
     398           5 :   PetscCall(PetscBLASIntCast(ds->n,&n));
     399           5 :   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     400           5 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
     401           5 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
     402           5 :   PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
     403           5 :   PetscCall(DSAllocateWork_Private(ds,2*ld,0,0));
     404           5 :   x = ds->work;
     405           5 :   y = ds->work+ld;
     406          95 :   for (i=0;i<n;i++) x[i] = PetscConj(A[n+i*ld]);
     407           5 :   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
     408          95 :   for (i=0;i<n;i++) A[n+i*ld] = PetscConj(y[i]);
     409          95 :   for (i=0;i<n;i++) x[i] = PetscConj(B[n+i*ld]);
     410           5 :   PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&one,Q,&ld,x,&incx,&zero,y,&incx));
     411          95 :   for (i=0;i<n;i++) B[n+i*ld] = PetscConj(y[i]);
     412           5 :   ds->k = n;
     413           5 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     414           5 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
     415           5 :   PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
     416           5 :   PetscFunctionReturn(PETSC_SUCCESS);
     417             : }
     418             : 
     419             : /*
     420             :    Write zeros from the column k to n in the lower triangular part of the
     421             :    matrices S and T, and inside 2-by-2 diagonal blocks of T in order to
     422             :    make (S,T) a valid Schur decompositon.
     423             : */
     424       11776 : static PetscErrorCode CleanDenseSchur(PetscInt n,PetscInt k,PetscScalar *S,PetscInt ldS,PetscScalar *T,PetscInt ldT,PetscScalar *X,PetscInt ldX,PetscScalar *Y,PetscInt ldY)
     425             : {
     426       11776 :   PetscInt       i;
     427             : #if defined(PETSC_USE_COMPLEX)
     428             :   PetscInt       j;
     429             :   PetscScalar    s;
     430             : #else
     431       11776 :   PetscBLASInt   ldS_,ldT_,n_i,n_i_2,one=1,n_,i_2,i_;
     432       11776 :   PetscScalar    b11,b22,sr,cr,sl,cl;
     433             : #endif
     434             : 
     435       11776 :   PetscFunctionBegin;
     436             : #if defined(PETSC_USE_COMPLEX)
     437             :   for (i=k; i<n; i++) {
     438             :     /* Some functions need the diagonal elements in T be real */
     439             :     if (T && PetscImaginaryPart(T[ldT*i+i]) != 0.0) {
     440             :       s = PetscConj(T[ldT*i+i])/PetscAbsScalar(T[ldT*i+i]);
     441             :       for (j=0;j<=i;j++) {
     442             :         T[ldT*i+j] *= s;
     443             :         S[ldS*i+j] *= s;
     444             :       }
     445             :       T[ldT*i+i] = PetscRealPart(T[ldT*i+i]);
     446             :       if (X) for (j=0;j<n;j++) X[ldX*i+j] *= s;
     447             :     }
     448             :     j = i+1;
     449             :     if (j<n) {
     450             :       S[ldS*i+j] = 0.0;
     451             :       if (T) T[ldT*i+j] = 0.0;
     452             :     }
     453             :   }
     454             : #else
     455       11776 :   PetscCall(PetscBLASIntCast(ldS,&ldS_));
     456       11776 :   PetscCall(PetscBLASIntCast(ldT,&ldT_));
     457       11776 :   PetscCall(PetscBLASIntCast(n,&n_));
     458      144882 :   for (i=k;i<n-1;i++) {
     459      133106 :     if (S[ldS*i+i+1] != 0.0) {
     460             :       /* Check if T(i+1,i) and T(i,i+1) are zero */
     461         700 :       if (T[ldT*(i+1)+i] != 0.0 || T[ldT*i+i+1] != 0.0) {
     462             :         /* Check if T(i+1,i) and T(i,i+1) are negligible */
     463           1 :         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) {
     464           0 :           T[ldT*i+i+1] = 0.0;
     465           0 :           T[ldT*(i+1)+i] = 0.0;
     466             :         } else {
     467             :           /* If one of T(i+1,i) or T(i,i+1) is negligible, we make zero the other element */
     468           1 :           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) {
     469           1 :             PetscCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*(i+1)+i],&T[ldT*(i+1)+i+1],&b22,&b11,&sl,&cl,&sr,&cr));
     470           0 :           } 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) {
     471           0 :             PetscCallBLAS("LAPACKlasv2",LAPACKlasv2_(&T[ldT*i+i],&T[ldT*i+i+1],&T[ldT*(i+1)+i+1],&b22,&b11,&sr,&cr,&sl,&cl));
     472           0 :           } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported format. Call DSSolve before this function");
     473           1 :           PetscCall(PetscBLASIntCast(n-i,&n_i));
     474           1 :           n_i_2 = n_i - 2;
     475           1 :           PetscCall(PetscBLASIntCast(i+2,&i_2));
     476           1 :           PetscCall(PetscBLASIntCast(i,&i_));
     477           1 :           if (b11 < 0.0) {
     478           0 :             cr = -cr; sr = -sr;
     479           0 :             b11 = -b11; b22 = -b22;
     480             :           }
     481           1 :           PetscCallBLAS("BLASrot",BLASrot_(&n_i,&S[ldS*i+i],&ldS_,&S[ldS*i+i+1],&ldS_,&cl,&sl));
     482           1 :           PetscCallBLAS("BLASrot",BLASrot_(&i_2,&S[ldS*i],&one,&S[ldS*(i+1)],&one,&cr,&sr));
     483           1 :           PetscCallBLAS("BLASrot",BLASrot_(&n_i_2,&T[ldT*(i+2)+i],&ldT_,&T[ldT*(i+2)+i+1],&ldT_,&cl,&sl));
     484           1 :           PetscCallBLAS("BLASrot",BLASrot_(&i_,&T[ldT*i],&one,&T[ldT*(i+1)],&one,&cr,&sr));
     485           1 :           if (X) PetscCallBLAS("BLASrot",BLASrot_(&n_,&X[ldX*i],&one,&X[ldX*(i+1)],&one,&cr,&sr));
     486           1 :           if (Y) PetscCallBLAS("BLASrot",BLASrot_(&n_,&Y[ldY*i],&one,&Y[ldY*(i+1)],&one,&cl,&sl));
     487           1 :           T[ldT*i+i] = b11; T[ldT*i+i+1] = 0.0;
     488           1 :           T[ldT*(i+1)+i] = 0.0; T[ldT*(i+1)+i+1] = b22;
     489             :         }
     490             :       }
     491             :       i++;
     492             :     }
     493             :   }
     494             : #endif
     495       11776 :   PetscFunctionReturn(PETSC_SUCCESS);
     496             : }
     497             : 
     498        1160 : static PetscErrorCode DSSolve_GNHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
     499             : {
     500        1160 :   PetscScalar    *work,*beta,a;
     501        1160 :   PetscInt       i;
     502        1160 :   PetscBLASInt   lwork,info,n,ld,iaux;
     503        1160 :   PetscScalar    *A,*B,*Z,*Q;
     504        1160 :   PetscBool      usegges3=(ds->method==1)?PETSC_TRUE:PETSC_FALSE;
     505             : 
     506        1160 :   PetscFunctionBegin;
     507             : #if !defined(PETSC_USE_COMPLEX)
     508        1160 :   PetscAssertPointer(wi,3);
     509             : #endif
     510        1160 :   PetscCall(PetscBLASIntCast(ds->n,&n));
     511        1160 :   PetscCall(PetscBLASIntCast(ds->ld,&ld));
     512        1160 :   lwork = -1;
     513        1160 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
     514        1160 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
     515        1160 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
     516        1160 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
     517             : #if !defined(PETSC_USE_COMPLEX)
     518        1160 :   if (usegges3) PetscCallBLAS("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
     519        1160 :   else PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,&info));
     520        1160 :   PetscCall(PetscBLASIntCast((PetscInt)a,&lwork));
     521        1160 :   PetscCall(DSAllocateWork_Private(ds,lwork+ld,0,0));
     522        1160 :   beta = ds->work;
     523        1160 :   work = beta+ds->n;
     524        1160 :   PetscCall(PetscBLASIntCast(ds->lwork-ds->n,&lwork));
     525        1160 :   if (usegges3) PetscCallBLAS("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
     526        1160 :   else PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,wi,beta,Z,&ld,Q,&ld,work,&lwork,NULL,&info));
     527             : #else
     528             :   if (usegges3) PetscCallBLAS("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
     529             :   else PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,NULL,Z,&ld,Q,&ld,&a,&lwork,NULL,NULL,&info));
     530             :   PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(a),&lwork));
     531             :   PetscCall(DSAllocateWork_Private(ds,lwork+ld,8*ld,0));
     532             :   beta = ds->work;
     533             :   work = beta+ds->n;
     534             :   PetscCall(PetscBLASIntCast(ds->lwork-ds->n,&lwork));
     535             :   if (usegges3) PetscCallBLAS("LAPACKgges3",LAPACKgges3_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
     536             :   else PetscCallBLAS("LAPACKgges",LAPACKgges_("V","V","N",NULL,&n,A,&ld,B,&ld,&iaux,wr,beta,Z,&ld,Q,&ld,work,&lwork,ds->rwork,NULL,&info));
     537             : #endif
     538        1160 :   SlepcCheckLapackInfo(usegges3?"gges3":"gges",info);
     539       13859 :   for (i=0;i<n;i++) {
     540       12699 :     if (beta[i]==0.0) wr[i] = (PetscRealPart(wr[i])>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
     541       12699 :     else wr[i] /= beta[i];
     542             : #if !defined(PETSC_USE_COMPLEX)
     543       12699 :     if (beta[i]==0.0) wi[i] = (wi[i]>0.0)? PETSC_MAX_REAL: PETSC_MIN_REAL;
     544       12699 :     else wi[i] /= beta[i];
     545             : #else
     546             :     if (wi) wi[i] = 0.0;
     547             : #endif
     548             :   }
     549        1160 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     550        1160 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
     551        1160 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
     552        1160 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
     553        1160 :   PetscFunctionReturn(PETSC_SUCCESS);
     554             : }
     555             : 
     556             : #if !defined(PETSC_HAVE_MPIUNI)
     557          56 : static PetscErrorCode DSSynchronize_GNHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
     558             : {
     559          56 :   PetscInt       ld=ds->ld,l=ds->l,k;
     560          56 :   PetscMPIInt    n,rank,off=0,size,ldn;
     561          56 :   PetscScalar    *A,*B,*Q,*Z;
     562             : 
     563          56 :   PetscFunctionBegin;
     564          56 :   k = 2*(ds->n-l)*ld;
     565          56 :   if (ds->state>DS_STATE_RAW) k += 2*(ds->n-l)*ld;
     566          56 :   if (eigr) k += (ds->n-l);
     567          56 :   if (eigi) k += (ds->n-l);
     568          56 :   PetscCall(DSAllocateWork_Private(ds,k,0,0));
     569          56 :   PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
     570          56 :   PetscCall(PetscMPIIntCast(ds->n-l,&n));
     571          56 :   PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
     572          56 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
     573          56 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
     574          56 :   if (ds->state>DS_STATE_RAW) {
     575          56 :     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
     576          56 :     PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Z],&Z));
     577             :   }
     578          56 :   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
     579          56 :   if (!rank) {
     580          28 :     PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
     581          28 :     PetscCallMPI(MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
     582          28 :     if (ds->state>DS_STATE_RAW) {
     583          28 :       PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
     584          28 :       PetscCallMPI(MPI_Pack(Z+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
     585             :     }
     586          28 :     if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
     587             : #if !defined(PETSC_USE_COMPLEX)
     588          28 :     if (eigi) PetscCallMPI(MPI_Pack(eigi+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
     589             : #endif
     590             :   }
     591         112 :   PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
     592          56 :   if (rank) {
     593          28 :     PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
     594          28 :     PetscCallMPI(MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
     595          28 :     if (ds->state>DS_STATE_RAW) {
     596          28 :       PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
     597          28 :       PetscCallMPI(MPI_Unpack(ds->work,size,&off,Z+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
     598             :     }
     599          28 :     if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
     600             : #if !defined(PETSC_USE_COMPLEX)
     601          28 :     if (eigi) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigi+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
     602             : #endif
     603             :   }
     604          56 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     605          56 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
     606          56 :   if (ds->state>DS_STATE_RAW) {
     607          56 :     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
     608          56 :     PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Z],&Z));
     609             :   }
     610          56 :   PetscFunctionReturn(PETSC_SUCCESS);
     611             : }
     612             : #endif
     613             : 
     614           5 : static PetscErrorCode DSTruncate_GNHEP(DS ds,PetscInt n,PetscBool trim)
     615             : {
     616           5 :   PetscInt    i,ld=ds->ld,l=ds->l;
     617           5 :   PetscScalar *A,*B;
     618             : 
     619           5 :   PetscFunctionBegin;
     620           5 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
     621           5 :   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
     622             : #if defined(PETSC_USE_DEBUG)
     623             :   /* make sure diagonal 2x2 block is not broken */
     624           5 :   PetscCheck(ds->state<DS_STATE_CONDENSED || n==0 || n==ds->n || (A[n+(n-1)*ld]==0.0 && B[n+(n-1)*ld]==0.0),PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"The given size would break a 2x2 block, call DSGetTruncateSize() first");
     625             : #endif
     626           5 :   if (trim) {
     627           3 :     if (ds->extrarow) {   /* clean extra row */
     628          53 :       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
     629          53 :       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
     630             :     }
     631           3 :     ds->l = 0;
     632           3 :     ds->k = 0;
     633           3 :     ds->n = n;
     634           3 :     ds->t = ds->n;   /* truncated length equal to the new dimension */
     635             :   } else {
     636           2 :     if (ds->extrarow && ds->k==ds->n) {
     637             :       /* copy entries of extra row to the new position, then clean last row */
     638          18 :       for (i=l;i<n;i++) A[n+i*ld] = A[ds->n+i*ld];
     639          34 :       for (i=l;i<ds->n;i++) A[ds->n+i*ld] = 0.0;
     640          18 :       for (i=l;i<n;i++) B[n+i*ld] = B[ds->n+i*ld];
     641          34 :       for (i=l;i<ds->n;i++) B[ds->n+i*ld] = 0.0;
     642             :     }
     643           2 :     ds->k = (ds->extrarow)? n: 0;
     644           2 :     ds->t = ds->n;   /* truncated length equal to previous dimension */
     645           2 :     ds->n = n;
     646             :   }
     647           5 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     648           5 :   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
     649           5 :   PetscFunctionReturn(PETSC_SUCCESS);
     650             : }
     651             : 
     652             : /*MC
     653             :    DSGNHEP - Dense Generalized Non-Hermitian Eigenvalue Problem.
     654             : 
     655             :    Level: beginner
     656             : 
     657             :    Notes:
     658             :    The problem is expressed as A*X = B*X*Lambda, where (A,B) is the input
     659             :    matrix pencil. Lambda is a diagonal matrix whose diagonal elements are the
     660             :    arguments of DSSolve(). After solve, (A,B) is overwritten with the
     661             :    generalized (real) Schur form (S,T) = (Z'*A*Q,Z'*B*Q), with the first
     662             :    matrix being upper quasi-triangular and the second one triangular.
     663             : 
     664             :    Used DS matrices:
     665             : +  DS_MAT_A - first problem matrix
     666             : .  DS_MAT_B - second problem matrix
     667             : .  DS_MAT_Q - first orthogonal/unitary transformation that reduces to
     668             :    generalized (real) Schur form
     669             : -  DS_MAT_Z - second orthogonal/unitary transformation that reduces to
     670             :    generalized (real) Schur form
     671             : 
     672             :    Implemented methods:
     673             : .  0 - QZ iteration (_gges)
     674             : 
     675             : .seealso: DSCreate(), DSSetType(), DSType
     676             : M*/
     677          29 : SLEPC_EXTERN PetscErrorCode DSCreate_GNHEP(DS ds)
     678             : {
     679          29 :   PetscFunctionBegin;
     680          29 :   ds->ops->allocate        = DSAllocate_GNHEP;
     681          29 :   ds->ops->view            = DSView_GNHEP;
     682          29 :   ds->ops->vectors         = DSVectors_GNHEP;
     683          29 :   ds->ops->solve[0]        = DSSolve_GNHEP;
     684             : #if !defined(SLEPC_MISSING_LAPACK_GGES3)
     685          29 :   ds->ops->solve[1]        = DSSolve_GNHEP;
     686             : #endif
     687          29 :   ds->ops->sort            = DSSort_GNHEP;
     688             : #if !defined(PETSC_HAVE_MPIUNI)
     689          29 :   ds->ops->synchronize     = DSSynchronize_GNHEP;
     690             : #endif
     691          29 :   ds->ops->gettruncatesize = DSGetTruncateSize_Default;
     692          29 :   ds->ops->truncate        = DSTruncate_GNHEP;
     693          29 :   ds->ops->update          = DSUpdateExtraRow_GNHEP;
     694          29 :   PetscFunctionReturn(PETSC_SUCCESS);
     695             : }

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