Annotation of rpl/lapack/lapack/zgges3.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> ZGGES3 computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices (blocked algorithm)</b>
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGGES3 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgges3.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgges3.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgges3.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
! 22: * $ LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
! 23: * $ WORK, LWORK, RWORK, BWORK, INFO )
! 24: *
! 25: * .. Scalar Arguments ..
! 26: * CHARACTER JOBVSL, JOBVSR, SORT
! 27: * INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * LOGICAL BWORK( * )
! 31: * DOUBLE PRECISION RWORK( * )
! 32: * COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
! 33: * $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
! 34: * $ WORK( * )
! 35: * ..
! 36: * .. Function Arguments ..
! 37: * LOGICAL SELCTG
! 38: * EXTERNAL SELCTG
! 39: * ..
! 40: *
! 41: *
! 42: *> \par Purpose:
! 43: * =============
! 44: *>
! 45: *> \verbatim
! 46: *>
! 47: *> ZGGES3 computes for a pair of N-by-N complex nonsymmetric matrices
! 48: *> (A,B), the generalized eigenvalues, the generalized complex Schur
! 49: *> form (S, T), and optionally left and/or right Schur vectors (VSL
! 50: *> and VSR). This gives the generalized Schur factorization
! 51: *>
! 52: *> (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
! 53: *>
! 54: *> where (VSR)**H is the conjugate-transpose of VSR.
! 55: *>
! 56: *> Optionally, it also orders the eigenvalues so that a selected cluster
! 57: *> of eigenvalues appears in the leading diagonal blocks of the upper
! 58: *> triangular matrix S and the upper triangular matrix T. The leading
! 59: *> columns of VSL and VSR then form an unitary basis for the
! 60: *> corresponding left and right eigenspaces (deflating subspaces).
! 61: *>
! 62: *> (If only the generalized eigenvalues are needed, use the driver
! 63: *> ZGGEV instead, which is faster.)
! 64: *>
! 65: *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
! 66: *> or a ratio alpha/beta = w, such that A - w*B is singular. It is
! 67: *> usually represented as the pair (alpha,beta), as there is a
! 68: *> reasonable interpretation for beta=0, and even for both being zero.
! 69: *>
! 70: *> A pair of matrices (S,T) is in generalized complex Schur form if S
! 71: *> and T are upper triangular and, in addition, the diagonal elements
! 72: *> of T are non-negative real numbers.
! 73: *> \endverbatim
! 74: *
! 75: * Arguments:
! 76: * ==========
! 77: *
! 78: *> \param[in] JOBVSL
! 79: *> \verbatim
! 80: *> JOBVSL is CHARACTER*1
! 81: *> = 'N': do not compute the left Schur vectors;
! 82: *> = 'V': compute the left Schur vectors.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] JOBVSR
! 86: *> \verbatim
! 87: *> JOBVSR is CHARACTER*1
! 88: *> = 'N': do not compute the right Schur vectors;
! 89: *> = 'V': compute the right Schur vectors.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] SORT
! 93: *> \verbatim
! 94: *> SORT is CHARACTER*1
! 95: *> Specifies whether or not to order the eigenvalues on the
! 96: *> diagonal of the generalized Schur form.
! 97: *> = 'N': Eigenvalues are not ordered;
! 98: *> = 'S': Eigenvalues are ordered (see SELCTG).
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] SELCTG
! 102: *> \verbatim
! 103: *> SELCTG is a LOGICAL FUNCTION of two COMPLEX*16 arguments
! 104: *> SELCTG must be declared EXTERNAL in the calling subroutine.
! 105: *> If SORT = 'N', SELCTG is not referenced.
! 106: *> If SORT = 'S', SELCTG is used to select eigenvalues to sort
! 107: *> to the top left of the Schur form.
! 108: *> An eigenvalue ALPHA(j)/BETA(j) is selected if
! 109: *> SELCTG(ALPHA(j),BETA(j)) is true.
! 110: *>
! 111: *> Note that a selected complex eigenvalue may no longer satisfy
! 112: *> SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
! 113: *> ordering may change the value of complex eigenvalues
! 114: *> (especially if the eigenvalue is ill-conditioned), in this
! 115: *> case INFO is set to N+2 (See INFO below).
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[in] N
! 119: *> \verbatim
! 120: *> N is INTEGER
! 121: *> The order of the matrices A, B, VSL, and VSR. N >= 0.
! 122: *> \endverbatim
! 123: *>
! 124: *> \param[in,out] A
! 125: *> \verbatim
! 126: *> A is COMPLEX*16 array, dimension (LDA, N)
! 127: *> On entry, the first of the pair of matrices.
! 128: *> On exit, A has been overwritten by its generalized Schur
! 129: *> form S.
! 130: *> \endverbatim
! 131: *>
! 132: *> \param[in] LDA
! 133: *> \verbatim
! 134: *> LDA is INTEGER
! 135: *> The leading dimension of A. LDA >= max(1,N).
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[in,out] B
! 139: *> \verbatim
! 140: *> B is COMPLEX*16 array, dimension (LDB, N)
! 141: *> On entry, the second of the pair of matrices.
! 142: *> On exit, B has been overwritten by its generalized Schur
! 143: *> form T.
! 144: *> \endverbatim
! 145: *>
! 146: *> \param[in] LDB
! 147: *> \verbatim
! 148: *> LDB is INTEGER
! 149: *> The leading dimension of B. LDB >= max(1,N).
! 150: *> \endverbatim
! 151: *>
! 152: *> \param[out] SDIM
! 153: *> \verbatim
! 154: *> SDIM is INTEGER
! 155: *> If SORT = 'N', SDIM = 0.
! 156: *> If SORT = 'S', SDIM = number of eigenvalues (after sorting)
! 157: *> for which SELCTG is true.
! 158: *> \endverbatim
! 159: *>
! 160: *> \param[out] ALPHA
! 161: *> \verbatim
! 162: *> ALPHA is COMPLEX*16 array, dimension (N)
! 163: *> \endverbatim
! 164: *>
! 165: *> \param[out] BETA
! 166: *> \verbatim
! 167: *> BETA is COMPLEX*16 array, dimension (N)
! 168: *> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
! 169: *> generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j),
! 170: *> j=1,...,N are the diagonals of the complex Schur form (A,B)
! 171: *> output by ZGGES3. The BETA(j) will be non-negative real.
! 172: *>
! 173: *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or
! 174: *> underflow, and BETA(j) may even be zero. Thus, the user
! 175: *> should avoid naively computing the ratio alpha/beta.
! 176: *> However, ALPHA will be always less than and usually
! 177: *> comparable with norm(A) in magnitude, and BETA always less
! 178: *> than and usually comparable with norm(B).
! 179: *> \endverbatim
! 180: *>
! 181: *> \param[out] VSL
! 182: *> \verbatim
! 183: *> VSL is COMPLEX*16 array, dimension (LDVSL,N)
! 184: *> If JOBVSL = 'V', VSL will contain the left Schur vectors.
! 185: *> Not referenced if JOBVSL = 'N'.
! 186: *> \endverbatim
! 187: *>
! 188: *> \param[in] LDVSL
! 189: *> \verbatim
! 190: *> LDVSL is INTEGER
! 191: *> The leading dimension of the matrix VSL. LDVSL >= 1, and
! 192: *> if JOBVSL = 'V', LDVSL >= N.
! 193: *> \endverbatim
! 194: *>
! 195: *> \param[out] VSR
! 196: *> \verbatim
! 197: *> VSR is COMPLEX*16 array, dimension (LDVSR,N)
! 198: *> If JOBVSR = 'V', VSR will contain the right Schur vectors.
! 199: *> Not referenced if JOBVSR = 'N'.
! 200: *> \endverbatim
! 201: *>
! 202: *> \param[in] LDVSR
! 203: *> \verbatim
! 204: *> LDVSR is INTEGER
! 205: *> The leading dimension of the matrix VSR. LDVSR >= 1, and
! 206: *> if JOBVSR = 'V', LDVSR >= N.
! 207: *> \endverbatim
! 208: *>
! 209: *> \param[out] WORK
! 210: *> \verbatim
! 211: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 212: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 213: *> \endverbatim
! 214: *>
! 215: *> \param[in] LWORK
! 216: *> \verbatim
! 217: *> LWORK is INTEGER
! 218: *> The dimension of the array WORK.
! 219: *>
! 220: *> If LWORK = -1, then a workspace query is assumed; the routine
! 221: *> only calculates the optimal size of the WORK array, returns
! 222: *> this value as the first entry of the WORK array, and no error
! 223: *> message related to LWORK is issued by XERBLA.
! 224: *> \endverbatim
! 225: *>
! 226: *> \param[out] RWORK
! 227: *> \verbatim
! 228: *> RWORK is DOUBLE PRECISION array, dimension (8*N)
! 229: *> \endverbatim
! 230: *>
! 231: *> \param[out] BWORK
! 232: *> \verbatim
! 233: *> BWORK is LOGICAL array, dimension (N)
! 234: *> Not referenced if SORT = 'N'.
! 235: *> \endverbatim
! 236: *>
! 237: *> \param[out] INFO
! 238: *> \verbatim
! 239: *> INFO is INTEGER
! 240: *> = 0: successful exit
! 241: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 242: *> =1,...,N:
! 243: *> The QZ iteration failed. (A,B) are not in Schur
! 244: *> form, but ALPHA(j) and BETA(j) should be correct for
! 245: *> j=INFO+1,...,N.
! 246: *> > N: =N+1: other than QZ iteration failed in ZHGEQZ
! 247: *> =N+2: after reordering, roundoff changed values of
! 248: *> some complex eigenvalues so that leading
! 249: *> eigenvalues in the Generalized Schur form no
! 250: *> longer satisfy SELCTG=.TRUE. This could also
! 251: *> be caused due to scaling.
! 252: *> =N+3: reordering failed in ZTGSEN.
! 253: *> \endverbatim
! 254: *
! 255: * Authors:
! 256: * ========
! 257: *
! 258: *> \author Univ. of Tennessee
! 259: *> \author Univ. of California Berkeley
! 260: *> \author Univ. of Colorado Denver
! 261: *> \author NAG Ltd.
! 262: *
! 263: *> \date January 2015
! 264: *
! 265: *> \ingroup complex16GEeigen
! 266: *
! 267: * =====================================================================
! 268: SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
! 269: $ LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR,
! 270: $ WORK, LWORK, RWORK, BWORK, INFO )
! 271: *
! 272: * -- LAPACK driver routine (version 3.6.0) --
! 273: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 274: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 275: * January 2015
! 276: *
! 277: * .. Scalar Arguments ..
! 278: CHARACTER JOBVSL, JOBVSR, SORT
! 279: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
! 280: * ..
! 281: * .. Array Arguments ..
! 282: LOGICAL BWORK( * )
! 283: DOUBLE PRECISION RWORK( * )
! 284: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
! 285: $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
! 286: $ WORK( * )
! 287: * ..
! 288: * .. Function Arguments ..
! 289: LOGICAL SELCTG
! 290: EXTERNAL SELCTG
! 291: * ..
! 292: *
! 293: * =====================================================================
! 294: *
! 295: * .. Parameters ..
! 296: DOUBLE PRECISION ZERO, ONE
! 297: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 298: COMPLEX*16 CZERO, CONE
! 299: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
! 300: $ CONE = ( 1.0D0, 0.0D0 ) )
! 301: * ..
! 302: * .. Local Scalars ..
! 303: LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
! 304: $ LQUERY, WANTST
! 305: INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
! 306: $ ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKOPT
! 307: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
! 308: $ PVSR, SMLNUM
! 309: * ..
! 310: * .. Local Arrays ..
! 311: INTEGER IDUM( 1 )
! 312: DOUBLE PRECISION DIF( 2 )
! 313: * ..
! 314: * .. External Subroutines ..
! 315: EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHD3,
! 316: $ ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR,
! 317: $ ZUNMQR
! 318: * ..
! 319: * .. External Functions ..
! 320: LOGICAL LSAME
! 321: DOUBLE PRECISION DLAMCH, ZLANGE
! 322: EXTERNAL LSAME, DLAMCH, ZLANGE
! 323: * ..
! 324: * .. Intrinsic Functions ..
! 325: INTRINSIC MAX, SQRT
! 326: * ..
! 327: * .. Executable Statements ..
! 328: *
! 329: * Decode the input arguments
! 330: *
! 331: IF( LSAME( JOBVSL, 'N' ) ) THEN
! 332: IJOBVL = 1
! 333: ILVSL = .FALSE.
! 334: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
! 335: IJOBVL = 2
! 336: ILVSL = .TRUE.
! 337: ELSE
! 338: IJOBVL = -1
! 339: ILVSL = .FALSE.
! 340: END IF
! 341: *
! 342: IF( LSAME( JOBVSR, 'N' ) ) THEN
! 343: IJOBVR = 1
! 344: ILVSR = .FALSE.
! 345: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
! 346: IJOBVR = 2
! 347: ILVSR = .TRUE.
! 348: ELSE
! 349: IJOBVR = -1
! 350: ILVSR = .FALSE.
! 351: END IF
! 352: *
! 353: WANTST = LSAME( SORT, 'S' )
! 354: *
! 355: * Test the input arguments
! 356: *
! 357: INFO = 0
! 358: LQUERY = ( LWORK.EQ.-1 )
! 359: IF( IJOBVL.LE.0 ) THEN
! 360: INFO = -1
! 361: ELSE IF( IJOBVR.LE.0 ) THEN
! 362: INFO = -2
! 363: ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
! 364: INFO = -3
! 365: ELSE IF( N.LT.0 ) THEN
! 366: INFO = -5
! 367: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 368: INFO = -7
! 369: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 370: INFO = -9
! 371: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
! 372: INFO = -14
! 373: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
! 374: INFO = -16
! 375: ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
! 376: INFO = -18
! 377: END IF
! 378: *
! 379: * Compute workspace
! 380: *
! 381: IF( INFO.EQ.0 ) THEN
! 382: CALL ZGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR )
! 383: LWKOPT = MAX( 1, N + INT ( WORK( 1 ) ) )
! 384: CALL ZUNMQR( 'L', 'C', N, N, N, B, LDB, WORK, A, LDA, WORK,
! 385: $ -1, IERR )
! 386: LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
! 387: IF( ILVSL ) THEN
! 388: CALL ZUNGQR( N, N, N, VSL, LDVSL, WORK, WORK, -1, IERR )
! 389: LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
! 390: END IF
! 391: CALL ZGGHD3( JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB, VSL,
! 392: $ LDVSL, VSR, LDVSR, WORK, -1, IERR )
! 393: LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
! 394: CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB,
! 395: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
! 396: $ -1, RWORK, IERR )
! 397: LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) )
! 398: IF( WANTST ) THEN
! 399: CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
! 400: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, SDIM,
! 401: $ PVSL, PVSR, DIF, WORK, -1, IDUM, 1, IERR )
! 402: LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) )
! 403: END IF
! 404: WORK( 1 ) = DCMPLX( LWKOPT )
! 405: END IF
! 406: *
! 407: IF( INFO.NE.0 ) THEN
! 408: CALL XERBLA( 'ZGGES3 ', -INFO )
! 409: RETURN
! 410: ELSE IF( LQUERY ) THEN
! 411: RETURN
! 412: END IF
! 413: *
! 414: * Quick return if possible
! 415: *
! 416: IF( N.EQ.0 ) THEN
! 417: SDIM = 0
! 418: RETURN
! 419: END IF
! 420: *
! 421: * Get machine constants
! 422: *
! 423: EPS = DLAMCH( 'P' )
! 424: SMLNUM = DLAMCH( 'S' )
! 425: BIGNUM = ONE / SMLNUM
! 426: CALL DLABAD( SMLNUM, BIGNUM )
! 427: SMLNUM = SQRT( SMLNUM ) / EPS
! 428: BIGNUM = ONE / SMLNUM
! 429: *
! 430: * Scale A if max element outside range [SMLNUM,BIGNUM]
! 431: *
! 432: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
! 433: ILASCL = .FALSE.
! 434: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
! 435: ANRMTO = SMLNUM
! 436: ILASCL = .TRUE.
! 437: ELSE IF( ANRM.GT.BIGNUM ) THEN
! 438: ANRMTO = BIGNUM
! 439: ILASCL = .TRUE.
! 440: END IF
! 441: *
! 442: IF( ILASCL )
! 443: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
! 444: *
! 445: * Scale B if max element outside range [SMLNUM,BIGNUM]
! 446: *
! 447: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
! 448: ILBSCL = .FALSE.
! 449: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
! 450: BNRMTO = SMLNUM
! 451: ILBSCL = .TRUE.
! 452: ELSE IF( BNRM.GT.BIGNUM ) THEN
! 453: BNRMTO = BIGNUM
! 454: ILBSCL = .TRUE.
! 455: END IF
! 456: *
! 457: IF( ILBSCL )
! 458: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
! 459: *
! 460: * Permute the matrix to make it more nearly triangular
! 461: *
! 462: ILEFT = 1
! 463: IRIGHT = N + 1
! 464: IRWRK = IRIGHT + N
! 465: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
! 466: $ RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
! 467: *
! 468: * Reduce B to triangular form (QR decomposition of B)
! 469: *
! 470: IROWS = IHI + 1 - ILO
! 471: ICOLS = N + 1 - ILO
! 472: ITAU = 1
! 473: IWRK = ITAU + IROWS
! 474: CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
! 475: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
! 476: *
! 477: * Apply the orthogonal transformation to matrix A
! 478: *
! 479: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
! 480: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
! 481: $ LWORK+1-IWRK, IERR )
! 482: *
! 483: * Initialize VSL
! 484: *
! 485: IF( ILVSL ) THEN
! 486: CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
! 487: IF( IROWS.GT.1 ) THEN
! 488: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
! 489: $ VSL( ILO+1, ILO ), LDVSL )
! 490: END IF
! 491: CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
! 492: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
! 493: END IF
! 494: *
! 495: * Initialize VSR
! 496: *
! 497: IF( ILVSR )
! 498: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
! 499: *
! 500: * Reduce to generalized Hessenberg form
! 501: *
! 502: CALL ZGGHD3( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
! 503: $ LDVSL, VSR, LDVSR, WORK( IWRK ), LWORK+1-IWRK, IERR )
! 504: *
! 505: SDIM = 0
! 506: *
! 507: * Perform QZ algorithm, computing Schur vectors if desired
! 508: *
! 509: IWRK = ITAU
! 510: CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
! 511: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
! 512: $ LWORK+1-IWRK, RWORK( IRWRK ), IERR )
! 513: IF( IERR.NE.0 ) THEN
! 514: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
! 515: INFO = IERR
! 516: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
! 517: INFO = IERR - N
! 518: ELSE
! 519: INFO = N + 1
! 520: END IF
! 521: GO TO 30
! 522: END IF
! 523: *
! 524: * Sort eigenvalues ALPHA/BETA if desired
! 525: *
! 526: IF( WANTST ) THEN
! 527: *
! 528: * Undo scaling on eigenvalues before selecting
! 529: *
! 530: IF( ILASCL )
! 531: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, 1, ALPHA, N, IERR )
! 532: IF( ILBSCL )
! 533: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, 1, BETA, N, IERR )
! 534: *
! 535: * Select eigenvalues
! 536: *
! 537: DO 10 I = 1, N
! 538: BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
! 539: 10 CONTINUE
! 540: *
! 541: CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHA,
! 542: $ BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL, PVSR,
! 543: $ DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1, IERR )
! 544: IF( IERR.EQ.1 )
! 545: $ INFO = N + 3
! 546: *
! 547: END IF
! 548: *
! 549: * Apply back-permutation to VSL and VSR
! 550: *
! 551: IF( ILVSL )
! 552: $ CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
! 553: $ RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
! 554: IF( ILVSR )
! 555: $ CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
! 556: $ RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
! 557: *
! 558: * Undo scaling
! 559: *
! 560: IF( ILASCL ) THEN
! 561: CALL ZLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
! 562: CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
! 563: END IF
! 564: *
! 565: IF( ILBSCL ) THEN
! 566: CALL ZLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
! 567: CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
! 568: END IF
! 569: *
! 570: IF( WANTST ) THEN
! 571: *
! 572: * Check if reordering is correct
! 573: *
! 574: LASTSL = .TRUE.
! 575: SDIM = 0
! 576: DO 20 I = 1, N
! 577: CURSL = SELCTG( ALPHA( I ), BETA( I ) )
! 578: IF( CURSL )
! 579: $ SDIM = SDIM + 1
! 580: IF( CURSL .AND. .NOT.LASTSL )
! 581: $ INFO = N + 2
! 582: LASTSL = CURSL
! 583: 20 CONTINUE
! 584: *
! 585: END IF
! 586: *
! 587: 30 CONTINUE
! 588: *
! 589: WORK( 1 ) = DCMPLX( LWKOPT )
! 590: *
! 591: RETURN
! 592: *
! 593: * End of ZGGES3
! 594: *
! 595: END
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