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Mise à jour de lapack vers la version 3.3.0.

    1:       SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
    2:      $                  VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
    3:      $                  INFO )
    4: *
    5: *  -- LAPACK driver routine (version 3.2) --
    6: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    7: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    8: *     November 2006
    9: *
   10: *     .. Scalar Arguments ..
   11:       CHARACTER          JOBVSL, JOBVSR
   12:       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
   13: *     ..
   14: *     .. Array Arguments ..
   15:       DOUBLE PRECISION   RWORK( * )
   16:       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
   17:      $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
   18:      $                   WORK( * )
   19: *     ..
   20: *
   21: *  Purpose
   22: *  =======
   23: *
   24: *  This routine is deprecated and has been replaced by routine ZGGES.
   25: *
   26: *  ZGEGS computes the eigenvalues, Schur form, and, optionally, the
   27: *  left and or/right Schur vectors of a complex matrix pair (A,B).
   28: *  Given two square matrices A and B, the generalized Schur
   29: *  factorization has the form
   30: *  
   31: *     A = Q*S*Z**H,  B = Q*T*Z**H
   32: *  
   33: *  where Q and Z are unitary matrices and S and T are upper triangular.
   34: *  The columns of Q are the left Schur vectors
   35: *  and the columns of Z are the right Schur vectors.
   36: *  
   37: *  If only the eigenvalues of (A,B) are needed, the driver routine
   38: *  ZGEGV should be used instead.  See ZGEGV for a description of the
   39: *  eigenvalues of the generalized nonsymmetric eigenvalue problem
   40: *  (GNEP).
   41: *
   42: *  Arguments
   43: *  =========
   44: *
   45: *  JOBVSL   (input) CHARACTER*1
   46: *          = 'N':  do not compute the left Schur vectors;
   47: *          = 'V':  compute the left Schur vectors (returned in VSL).
   48: *
   49: *  JOBVSR   (input) CHARACTER*1
   50: *          = 'N':  do not compute the right Schur vectors;
   51: *          = 'V':  compute the right Schur vectors (returned in VSR).
   52: *
   53: *  N       (input) INTEGER
   54: *          The order of the matrices A, B, VSL, and VSR.  N >= 0.
   55: *
   56: *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)
   57: *          On entry, the matrix A.
   58: *          On exit, the upper triangular matrix S from the generalized
   59: *          Schur factorization.
   60: *
   61: *  LDA     (input) INTEGER
   62: *          The leading dimension of A.  LDA >= max(1,N).
   63: *
   64: *  B       (input/output) COMPLEX*16 array, dimension (LDB, N)
   65: *          On entry, the matrix B.
   66: *          On exit, the upper triangular matrix T from the generalized
   67: *          Schur factorization.
   68: *
   69: *  LDB     (input) INTEGER
   70: *          The leading dimension of B.  LDB >= max(1,N).
   71: *
   72: *  ALPHA   (output) COMPLEX*16 array, dimension (N)
   73: *          The complex scalars alpha that define the eigenvalues of
   74: *          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
   75: *          form of A.
   76: *
   77: *  BETA    (output) COMPLEX*16 array, dimension (N)
   78: *          The non-negative real scalars beta that define the
   79: *          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
   80: *          of the triangular factor T.
   81: *
   82: *          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
   83: *          represent the j-th eigenvalue of the matrix pair (A,B), in
   84: *          one of the forms lambda = alpha/beta or mu = beta/alpha.
   85: *          Since either lambda or mu may overflow, they should not,
   86: *          in general, be computed.
   87: *
   88: *
   89: *  VSL     (output) COMPLEX*16 array, dimension (LDVSL,N)
   90: *          If JOBVSL = 'V', the matrix of left Schur vectors Q.
   91: *          Not referenced if JOBVSL = 'N'.
   92: *
   93: *  LDVSL   (input) INTEGER
   94: *          The leading dimension of the matrix VSL. LDVSL >= 1, and
   95: *          if JOBVSL = 'V', LDVSL >= N.
   96: *
   97: *  VSR     (output) COMPLEX*16 array, dimension (LDVSR,N)
   98: *          If JOBVSR = 'V', the matrix of right Schur vectors Z.
   99: *          Not referenced if JOBVSR = 'N'.
  100: *
  101: *  LDVSR   (input) INTEGER
  102: *          The leading dimension of the matrix VSR. LDVSR >= 1, and
  103: *          if JOBVSR = 'V', LDVSR >= N.
  104: *
  105: *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
  106: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  107: *
  108: *  LWORK   (input) INTEGER
  109: *          The dimension of the array WORK.  LWORK >= max(1,2*N).
  110: *          For good performance, LWORK must generally be larger.
  111: *          To compute the optimal value of LWORK, call ILAENV to get
  112: *          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:
  113: *          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
  114: *          the optimal LWORK is N*(NB+1).
  115: *
  116: *          If LWORK = -1, then a workspace query is assumed; the routine
  117: *          only calculates the optimal size of the WORK array, returns
  118: *          this value as the first entry of the WORK array, and no error
  119: *          message related to LWORK is issued by XERBLA.
  120: *
  121: *  RWORK   (workspace) DOUBLE PRECISION array, dimension (3*N)
  122: *
  123: *  INFO    (output) INTEGER
  124: *          = 0:  successful exit
  125: *          < 0:  if INFO = -i, the i-th argument had an illegal value.
  126: *          =1,...,N:
  127: *                The QZ iteration failed.  (A,B) are not in Schur
  128: *                form, but ALPHA(j) and BETA(j) should be correct for
  129: *                j=INFO+1,...,N.
  130: *          > N:  errors that usually indicate LAPACK problems:
  131: *                =N+1: error return from ZGGBAL
  132: *                =N+2: error return from ZGEQRF
  133: *                =N+3: error return from ZUNMQR
  134: *                =N+4: error return from ZUNGQR
  135: *                =N+5: error return from ZGGHRD
  136: *                =N+6: error return from ZHGEQZ (other than failed
  137: *                                               iteration)
  138: *                =N+7: error return from ZGGBAK (computing VSL)
  139: *                =N+8: error return from ZGGBAK (computing VSR)
  140: *                =N+9: error return from ZLASCL (various places)
  141: *
  142: *  =====================================================================
  143: *
  144: *     .. Parameters ..
  145:       DOUBLE PRECISION   ZERO, ONE
  146:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
  147:       COMPLEX*16         CZERO, CONE
  148:       PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
  149:      $                   CONE = ( 1.0D0, 0.0D0 ) )
  150: *     ..
  151: *     .. Local Scalars ..
  152:       LOGICAL            ILASCL, ILBSCL, ILVSL, ILVSR, LQUERY
  153:       INTEGER            ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
  154:      $                   IRIGHT, IROWS, IRWORK, ITAU, IWORK, LOPT,
  155:      $                   LWKMIN, LWKOPT, NB, NB1, NB2, NB3
  156:       DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
  157:      $                   SAFMIN, SMLNUM
  158: *     ..
  159: *     .. External Subroutines ..
  160:       EXTERNAL           XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD, ZHGEQZ,
  161:      $                   ZLACPY, ZLASCL, ZLASET, ZUNGQR, ZUNMQR
  162: *     ..
  163: *     .. External Functions ..
  164:       LOGICAL            LSAME
  165:       INTEGER            ILAENV
  166:       DOUBLE PRECISION   DLAMCH, ZLANGE
  167:       EXTERNAL           LSAME, ILAENV, DLAMCH, ZLANGE
  168: *     ..
  169: *     .. Intrinsic Functions ..
  170:       INTRINSIC          INT, MAX
  171: *     ..
  172: *     .. Executable Statements ..
  173: *
  174: *     Decode the input arguments
  175: *
  176:       IF( LSAME( JOBVSL, 'N' ) ) THEN
  177:          IJOBVL = 1
  178:          ILVSL = .FALSE.
  179:       ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
  180:          IJOBVL = 2
  181:          ILVSL = .TRUE.
  182:       ELSE
  183:          IJOBVL = -1
  184:          ILVSL = .FALSE.
  185:       END IF
  186: *
  187:       IF( LSAME( JOBVSR, 'N' ) ) THEN
  188:          IJOBVR = 1
  189:          ILVSR = .FALSE.
  190:       ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
  191:          IJOBVR = 2
  192:          ILVSR = .TRUE.
  193:       ELSE
  194:          IJOBVR = -1
  195:          ILVSR = .FALSE.
  196:       END IF
  197: *
  198: *     Test the input arguments
  199: *
  200:       LWKMIN = MAX( 2*N, 1 )
  201:       LWKOPT = LWKMIN
  202:       WORK( 1 ) = LWKOPT
  203:       LQUERY = ( LWORK.EQ.-1 )
  204:       INFO = 0
  205:       IF( IJOBVL.LE.0 ) THEN
  206:          INFO = -1
  207:       ELSE IF( IJOBVR.LE.0 ) THEN
  208:          INFO = -2
  209:       ELSE IF( N.LT.0 ) THEN
  210:          INFO = -3
  211:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  212:          INFO = -5
  213:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  214:          INFO = -7
  215:       ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
  216:          INFO = -11
  217:       ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
  218:          INFO = -13
  219:       ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
  220:          INFO = -15
  221:       END IF
  222: *
  223:       IF( INFO.EQ.0 ) THEN
  224:          NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, N, -1, -1 )
  225:          NB2 = ILAENV( 1, 'ZUNMQR', ' ', N, N, N, -1 )
  226:          NB3 = ILAENV( 1, 'ZUNGQR', ' ', N, N, N, -1 )
  227:          NB = MAX( NB1, NB2, NB3 )
  228:          LOPT = N*( NB+1 )
  229:          WORK( 1 ) = LOPT
  230:       END IF
  231: *
  232:       IF( INFO.NE.0 ) THEN
  233:          CALL XERBLA( 'ZGEGS ', -INFO )
  234:          RETURN
  235:       ELSE IF( LQUERY ) THEN
  236:          RETURN
  237:       END IF
  238: *
  239: *     Quick return if possible
  240: *
  241:       IF( N.EQ.0 )
  242:      $   RETURN
  243: *
  244: *     Get machine constants
  245: *
  246:       EPS = DLAMCH( 'E' )*DLAMCH( 'B' )
  247:       SAFMIN = DLAMCH( 'S' )
  248:       SMLNUM = N*SAFMIN / EPS
  249:       BIGNUM = ONE / SMLNUM
  250: *
  251: *     Scale A if max element outside range [SMLNUM,BIGNUM]
  252: *
  253:       ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
  254:       ILASCL = .FALSE.
  255:       IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
  256:          ANRMTO = SMLNUM
  257:          ILASCL = .TRUE.
  258:       ELSE IF( ANRM.GT.BIGNUM ) THEN
  259:          ANRMTO = BIGNUM
  260:          ILASCL = .TRUE.
  261:       END IF
  262: *
  263:       IF( ILASCL ) THEN
  264:          CALL ZLASCL( 'G', -1, -1, ANRM, ANRMTO, N, N, A, LDA, IINFO )
  265:          IF( IINFO.NE.0 ) THEN
  266:             INFO = N + 9
  267:             RETURN
  268:          END IF
  269:       END IF
  270: *
  271: *     Scale B if max element outside range [SMLNUM,BIGNUM]
  272: *
  273:       BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
  274:       ILBSCL = .FALSE.
  275:       IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
  276:          BNRMTO = SMLNUM
  277:          ILBSCL = .TRUE.
  278:       ELSE IF( BNRM.GT.BIGNUM ) THEN
  279:          BNRMTO = BIGNUM
  280:          ILBSCL = .TRUE.
  281:       END IF
  282: *
  283:       IF( ILBSCL ) THEN
  284:          CALL ZLASCL( 'G', -1, -1, BNRM, BNRMTO, N, N, B, LDB, IINFO )
  285:          IF( IINFO.NE.0 ) THEN
  286:             INFO = N + 9
  287:             RETURN
  288:          END IF
  289:       END IF
  290: *
  291: *     Permute the matrix to make it more nearly triangular
  292: *
  293:       ILEFT = 1
  294:       IRIGHT = N + 1
  295:       IRWORK = IRIGHT + N
  296:       IWORK = 1
  297:       CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
  298:      $             RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
  299:       IF( IINFO.NE.0 ) THEN
  300:          INFO = N + 1
  301:          GO TO 10
  302:       END IF
  303: *
  304: *     Reduce B to triangular form, and initialize VSL and/or VSR
  305: *
  306:       IROWS = IHI + 1 - ILO
  307:       ICOLS = N + 1 - ILO
  308:       ITAU = IWORK
  309:       IWORK = ITAU + IROWS
  310:       CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
  311:      $             WORK( IWORK ), LWORK+1-IWORK, IINFO )
  312:       IF( IINFO.GE.0 )
  313:      $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
  314:       IF( IINFO.NE.0 ) THEN
  315:          INFO = N + 2
  316:          GO TO 10
  317:       END IF
  318: *
  319:       CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
  320:      $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
  321:      $             LWORK+1-IWORK, IINFO )
  322:       IF( IINFO.GE.0 )
  323:      $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
  324:       IF( IINFO.NE.0 ) THEN
  325:          INFO = N + 3
  326:          GO TO 10
  327:       END IF
  328: *
  329:       IF( ILVSL ) THEN
  330:          CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
  331:          CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
  332:      $                VSL( ILO+1, ILO ), LDVSL )
  333:          CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
  334:      $                WORK( ITAU ), WORK( IWORK ), LWORK+1-IWORK,
  335:      $                IINFO )
  336:          IF( IINFO.GE.0 )
  337:      $      LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
  338:          IF( IINFO.NE.0 ) THEN
  339:             INFO = N + 4
  340:             GO TO 10
  341:          END IF
  342:       END IF
  343: *
  344:       IF( ILVSR )
  345:      $   CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
  346: *
  347: *     Reduce to generalized Hessenberg form
  348: *
  349:       CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
  350:      $             LDVSL, VSR, LDVSR, IINFO )
  351:       IF( IINFO.NE.0 ) THEN
  352:          INFO = N + 5
  353:          GO TO 10
  354:       END IF
  355: *
  356: *     Perform QZ algorithm, computing Schur vectors if desired
  357: *
  358:       IWORK = ITAU
  359:       CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
  360:      $             ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWORK ),
  361:      $             LWORK+1-IWORK, RWORK( IRWORK ), IINFO )
  362:       IF( IINFO.GE.0 )
  363:      $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
  364:       IF( IINFO.NE.0 ) THEN
  365:          IF( IINFO.GT.0 .AND. IINFO.LE.N ) THEN
  366:             INFO = IINFO
  367:          ELSE IF( IINFO.GT.N .AND. IINFO.LE.2*N ) THEN
  368:             INFO = IINFO - N
  369:          ELSE
  370:             INFO = N + 6
  371:          END IF
  372:          GO TO 10
  373:       END IF
  374: *
  375: *     Apply permutation to VSL and VSR
  376: *
  377:       IF( ILVSL ) THEN
  378:          CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
  379:      $                RWORK( IRIGHT ), N, VSL, LDVSL, IINFO )
  380:          IF( IINFO.NE.0 ) THEN
  381:             INFO = N + 7
  382:             GO TO 10
  383:          END IF
  384:       END IF
  385:       IF( ILVSR ) THEN
  386:          CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
  387:      $                RWORK( IRIGHT ), N, VSR, LDVSR, IINFO )
  388:          IF( IINFO.NE.0 ) THEN
  389:             INFO = N + 8
  390:             GO TO 10
  391:          END IF
  392:       END IF
  393: *
  394: *     Undo scaling
  395: *
  396:       IF( ILASCL ) THEN
  397:          CALL ZLASCL( 'U', -1, -1, ANRMTO, ANRM, N, N, A, LDA, IINFO )
  398:          IF( IINFO.NE.0 ) THEN
  399:             INFO = N + 9
  400:             RETURN
  401:          END IF
  402:          CALL ZLASCL( 'G', -1, -1, ANRMTO, ANRM, N, 1, ALPHA, N, IINFO )
  403:          IF( IINFO.NE.0 ) THEN
  404:             INFO = N + 9
  405:             RETURN
  406:          END IF
  407:       END IF
  408: *
  409:       IF( ILBSCL ) THEN
  410:          CALL ZLASCL( 'U', -1, -1, BNRMTO, BNRM, N, N, B, LDB, IINFO )
  411:          IF( IINFO.NE.0 ) THEN
  412:             INFO = N + 9
  413:             RETURN
  414:          END IF
  415:          CALL ZLASCL( 'G', -1, -1, BNRMTO, BNRM, N, 1, BETA, N, IINFO )
  416:          IF( IINFO.NE.0 ) THEN
  417:             INFO = N + 9
  418:             RETURN
  419:          END IF
  420:       END IF
  421: *
  422:    10 CONTINUE
  423:       WORK( 1 ) = LWKOPT
  424: *
  425:       RETURN
  426: *
  427: *     End of ZGEGS
  428: *
  429:       END