Annotation of rpl/lapack/lapack/zggesx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA,
! 2: $ B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR,
! 3: $ LDVSR, RCONDE, RCONDV, WORK, LWORK, RWORK,
! 4: $ IWORK, LIWORK, BWORK, INFO )
! 5: *
! 6: * -- LAPACK driver routine (version 3.2) --
! 7: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 8: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 9: * November 2006
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER JOBVSL, JOBVSR, SENSE, SORT
! 13: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LIWORK, LWORK, N,
! 14: $ SDIM
! 15: * ..
! 16: * .. Array Arguments ..
! 17: LOGICAL BWORK( * )
! 18: INTEGER IWORK( * )
! 19: DOUBLE PRECISION RCONDE( 2 ), RCONDV( 2 ), RWORK( * )
! 20: COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
! 21: $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
! 22: $ WORK( * )
! 23: * ..
! 24: * .. Function Arguments ..
! 25: LOGICAL SELCTG
! 26: EXTERNAL SELCTG
! 27: * ..
! 28: *
! 29: * Purpose
! 30: * =======
! 31: *
! 32: * ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices
! 33: * (A,B), the generalized eigenvalues, the complex Schur form (S,T),
! 34: * and, optionally, the left and/or right matrices of Schur vectors (VSL
! 35: * and VSR). This gives the generalized Schur factorization
! 36: *
! 37: * (A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H )
! 38: *
! 39: * where (VSR)**H is the conjugate-transpose of VSR.
! 40: *
! 41: * Optionally, it also orders the eigenvalues so that a selected cluster
! 42: * of eigenvalues appears in the leading diagonal blocks of the upper
! 43: * triangular matrix S and the upper triangular matrix T; computes
! 44: * a reciprocal condition number for the average of the selected
! 45: * eigenvalues (RCONDE); and computes a reciprocal condition number for
! 46: * the right and left deflating subspaces corresponding to the selected
! 47: * eigenvalues (RCONDV). The leading columns of VSL and VSR then form
! 48: * an orthonormal basis for the corresponding left and right eigenspaces
! 49: * (deflating subspaces).
! 50: *
! 51: * A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
! 52: * or a ratio alpha/beta = w, such that A - w*B is singular. It is
! 53: * usually represented as the pair (alpha,beta), as there is a
! 54: * reasonable interpretation for beta=0 or for both being zero.
! 55: *
! 56: * A pair of matrices (S,T) is in generalized complex Schur form if T is
! 57: * upper triangular with non-negative diagonal and S is upper
! 58: * triangular.
! 59: *
! 60: * Arguments
! 61: * =========
! 62: *
! 63: * JOBVSL (input) CHARACTER*1
! 64: * = 'N': do not compute the left Schur vectors;
! 65: * = 'V': compute the left Schur vectors.
! 66: *
! 67: * JOBVSR (input) CHARACTER*1
! 68: * = 'N': do not compute the right Schur vectors;
! 69: * = 'V': compute the right Schur vectors.
! 70: *
! 71: * SORT (input) CHARACTER*1
! 72: * Specifies whether or not to order the eigenvalues on the
! 73: * diagonal of the generalized Schur form.
! 74: * = 'N': Eigenvalues are not ordered;
! 75: * = 'S': Eigenvalues are ordered (see SELCTG).
! 76: *
! 77: * SELCTG (external procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments
! 78: * SELCTG must be declared EXTERNAL in the calling subroutine.
! 79: * If SORT = 'N', SELCTG is not referenced.
! 80: * If SORT = 'S', SELCTG is used to select eigenvalues to sort
! 81: * to the top left of the Schur form.
! 82: * Note that a selected complex eigenvalue may no longer satisfy
! 83: * SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since
! 84: * ordering may change the value of complex eigenvalues
! 85: * (especially if the eigenvalue is ill-conditioned), in this
! 86: * case INFO is set to N+3 see INFO below).
! 87: *
! 88: * SENSE (input) CHARACTER*1
! 89: * Determines which reciprocal condition numbers are computed.
! 90: * = 'N' : None are computed;
! 91: * = 'E' : Computed for average of selected eigenvalues only;
! 92: * = 'V' : Computed for selected deflating subspaces only;
! 93: * = 'B' : Computed for both.
! 94: * If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
! 95: *
! 96: * N (input) INTEGER
! 97: * The order of the matrices A, B, VSL, and VSR. N >= 0.
! 98: *
! 99: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
! 100: * On entry, the first of the pair of matrices.
! 101: * On exit, A has been overwritten by its generalized Schur
! 102: * form S.
! 103: *
! 104: * LDA (input) INTEGER
! 105: * The leading dimension of A. LDA >= max(1,N).
! 106: *
! 107: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
! 108: * On entry, the second of the pair of matrices.
! 109: * On exit, B has been overwritten by its generalized Schur
! 110: * form T.
! 111: *
! 112: * LDB (input) INTEGER
! 113: * The leading dimension of B. LDB >= max(1,N).
! 114: *
! 115: * SDIM (output) INTEGER
! 116: * If SORT = 'N', SDIM = 0.
! 117: * If SORT = 'S', SDIM = number of eigenvalues (after sorting)
! 118: * for which SELCTG is true.
! 119: *
! 120: * ALPHA (output) COMPLEX*16 array, dimension (N)
! 121: * BETA (output) COMPLEX*16 array, dimension (N)
! 122: * On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
! 123: * generalized eigenvalues. ALPHA(j) and BETA(j),j=1,...,N are
! 124: * the diagonals of the complex Schur form (S,T). BETA(j) will
! 125: * be non-negative real.
! 126: *
! 127: * Note: the quotients ALPHA(j)/BETA(j) may easily over- or
! 128: * underflow, and BETA(j) may even be zero. Thus, the user
! 129: * should avoid naively computing the ratio alpha/beta.
! 130: * However, ALPHA will be always less than and usually
! 131: * comparable with norm(A) in magnitude, and BETA always less
! 132: * than and usually comparable with norm(B).
! 133: *
! 134: * VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
! 135: * If JOBVSL = 'V', VSL will contain the left Schur vectors.
! 136: * Not referenced if JOBVSL = 'N'.
! 137: *
! 138: * LDVSL (input) INTEGER
! 139: * The leading dimension of the matrix VSL. LDVSL >=1, and
! 140: * if JOBVSL = 'V', LDVSL >= N.
! 141: *
! 142: * VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
! 143: * If JOBVSR = 'V', VSR will contain the right Schur vectors.
! 144: * Not referenced if JOBVSR = 'N'.
! 145: *
! 146: * LDVSR (input) INTEGER
! 147: * The leading dimension of the matrix VSR. LDVSR >= 1, and
! 148: * if JOBVSR = 'V', LDVSR >= N.
! 149: *
! 150: * RCONDE (output) DOUBLE PRECISION array, dimension ( 2 )
! 151: * If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the
! 152: * reciprocal condition numbers for the average of the selected
! 153: * eigenvalues.
! 154: * Not referenced if SENSE = 'N' or 'V'.
! 155: *
! 156: * RCONDV (output) DOUBLE PRECISION array, dimension ( 2 )
! 157: * If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
! 158: * reciprocal condition number for the selected deflating
! 159: * subspaces.
! 160: * Not referenced if SENSE = 'N' or 'E'.
! 161: *
! 162: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 163: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 164: *
! 165: * LWORK (input) INTEGER
! 166: * The dimension of the array WORK.
! 167: * If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B',
! 168: * LWORK >= MAX(1,2*N,2*SDIM*(N-SDIM)), else
! 169: * LWORK >= MAX(1,2*N). Note that 2*SDIM*(N-SDIM) <= N*N/2.
! 170: * Note also that an error is only returned if
! 171: * LWORK < MAX(1,2*N), but if SENSE = 'E' or 'V' or 'B' this may
! 172: * not be large enough.
! 173: *
! 174: * If LWORK = -1, then a workspace query is assumed; the routine
! 175: * only calculates the bound on the optimal size of the WORK
! 176: * array and the minimum size of the IWORK array, returns these
! 177: * values as the first entries of the WORK and IWORK arrays, and
! 178: * no error message related to LWORK or LIWORK is issued by
! 179: * XERBLA.
! 180: *
! 181: * RWORK (workspace) DOUBLE PRECISION array, dimension ( 8*N )
! 182: * Real workspace.
! 183: *
! 184: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 185: * On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
! 186: *
! 187: * LIWORK (input) INTEGER
! 188: * The dimension of the array IWORK.
! 189: * If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise
! 190: * LIWORK >= N+2.
! 191: *
! 192: * If LIWORK = -1, then a workspace query is assumed; the
! 193: * routine only calculates the bound on the optimal size of the
! 194: * WORK array and the minimum size of the IWORK array, returns
! 195: * these values as the first entries of the WORK and IWORK
! 196: * arrays, and no error message related to LWORK or LIWORK is
! 197: * issued by XERBLA.
! 198: *
! 199: * BWORK (workspace) LOGICAL array, dimension (N)
! 200: * Not referenced if SORT = 'N'.
! 201: *
! 202: * INFO (output) INTEGER
! 203: * = 0: successful exit
! 204: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 205: * = 1,...,N:
! 206: * The QZ iteration failed. (A,B) are not in Schur
! 207: * form, but ALPHA(j) and BETA(j) should be correct for
! 208: * j=INFO+1,...,N.
! 209: * > N: =N+1: other than QZ iteration failed in ZHGEQZ
! 210: * =N+2: after reordering, roundoff changed values of
! 211: * some complex eigenvalues so that leading
! 212: * eigenvalues in the Generalized Schur form no
! 213: * longer satisfy SELCTG=.TRUE. This could also
! 214: * be caused due to scaling.
! 215: * =N+3: reordering failed in ZTGSEN.
! 216: *
! 217: * =====================================================================
! 218: *
! 219: * .. Parameters ..
! 220: DOUBLE PRECISION ZERO, ONE
! 221: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 222: COMPLEX*16 CZERO, CONE
! 223: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
! 224: $ CONE = ( 1.0D+0, 0.0D+0 ) )
! 225: * ..
! 226: * .. Local Scalars ..
! 227: LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
! 228: $ LQUERY, WANTSB, WANTSE, WANTSN, WANTST, WANTSV
! 229: INTEGER I, ICOLS, IERR, IHI, IJOB, IJOBVL, IJOBVR,
! 230: $ ILEFT, ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK,
! 231: $ LIWMIN, LWRK, MAXWRK, MINWRK
! 232: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PL,
! 233: $ PR, SMLNUM
! 234: * ..
! 235: * .. Local Arrays ..
! 236: DOUBLE PRECISION DIF( 2 )
! 237: * ..
! 238: * .. External Subroutines ..
! 239: EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHRD,
! 240: $ ZHGEQZ, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR,
! 241: $ ZUNMQR
! 242: * ..
! 243: * .. External Functions ..
! 244: LOGICAL LSAME
! 245: INTEGER ILAENV
! 246: DOUBLE PRECISION DLAMCH, ZLANGE
! 247: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE
! 248: * ..
! 249: * .. Intrinsic Functions ..
! 250: INTRINSIC MAX, SQRT
! 251: * ..
! 252: * .. Executable Statements ..
! 253: *
! 254: * Decode the input arguments
! 255: *
! 256: IF( LSAME( JOBVSL, 'N' ) ) THEN
! 257: IJOBVL = 1
! 258: ILVSL = .FALSE.
! 259: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
! 260: IJOBVL = 2
! 261: ILVSL = .TRUE.
! 262: ELSE
! 263: IJOBVL = -1
! 264: ILVSL = .FALSE.
! 265: END IF
! 266: *
! 267: IF( LSAME( JOBVSR, 'N' ) ) THEN
! 268: IJOBVR = 1
! 269: ILVSR = .FALSE.
! 270: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
! 271: IJOBVR = 2
! 272: ILVSR = .TRUE.
! 273: ELSE
! 274: IJOBVR = -1
! 275: ILVSR = .FALSE.
! 276: END IF
! 277: *
! 278: WANTST = LSAME( SORT, 'S' )
! 279: WANTSN = LSAME( SENSE, 'N' )
! 280: WANTSE = LSAME( SENSE, 'E' )
! 281: WANTSV = LSAME( SENSE, 'V' )
! 282: WANTSB = LSAME( SENSE, 'B' )
! 283: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 284: IF( WANTSN ) THEN
! 285: IJOB = 0
! 286: ELSE IF( WANTSE ) THEN
! 287: IJOB = 1
! 288: ELSE IF( WANTSV ) THEN
! 289: IJOB = 2
! 290: ELSE IF( WANTSB ) THEN
! 291: IJOB = 4
! 292: END IF
! 293: *
! 294: * Test the input arguments
! 295: *
! 296: INFO = 0
! 297: IF( IJOBVL.LE.0 ) THEN
! 298: INFO = -1
! 299: ELSE IF( IJOBVR.LE.0 ) THEN
! 300: INFO = -2
! 301: ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
! 302: INFO = -3
! 303: ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSV .OR. WANTSB ) .OR.
! 304: $ ( .NOT.WANTST .AND. .NOT.WANTSN ) ) THEN
! 305: INFO = -5
! 306: ELSE IF( N.LT.0 ) THEN
! 307: INFO = -6
! 308: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 309: INFO = -8
! 310: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 311: INFO = -10
! 312: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
! 313: INFO = -15
! 314: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
! 315: INFO = -17
! 316: END IF
! 317: *
! 318: * Compute workspace
! 319: * (Note: Comments in the code beginning "Workspace:" describe the
! 320: * minimal amount of workspace needed at that point in the code,
! 321: * as well as the preferred amount for good performance.
! 322: * NB refers to the optimal block size for the immediately
! 323: * following subroutine, as returned by ILAENV.)
! 324: *
! 325: IF( INFO.EQ.0 ) THEN
! 326: IF( N.GT.0) THEN
! 327: MINWRK = 2*N
! 328: MAXWRK = N*(1 + ILAENV( 1, 'ZGEQRF', ' ', N, 1, N, 0 ) )
! 329: MAXWRK = MAX( MAXWRK, N*( 1 +
! 330: $ ILAENV( 1, 'ZUNMQR', ' ', N, 1, N, -1 ) ) )
! 331: IF( ILVSL ) THEN
! 332: MAXWRK = MAX( MAXWRK, N*( 1 +
! 333: $ ILAENV( 1, 'ZUNGQR', ' ', N, 1, N, -1 ) ) )
! 334: END IF
! 335: LWRK = MAXWRK
! 336: IF( IJOB.GE.1 )
! 337: $ LWRK = MAX( LWRK, N*N/2 )
! 338: ELSE
! 339: MINWRK = 1
! 340: MAXWRK = 1
! 341: LWRK = 1
! 342: END IF
! 343: WORK( 1 ) = LWRK
! 344: IF( WANTSN .OR. N.EQ.0 ) THEN
! 345: LIWMIN = 1
! 346: ELSE
! 347: LIWMIN = N + 2
! 348: END IF
! 349: IWORK( 1 ) = LIWMIN
! 350: *
! 351: IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
! 352: INFO = -21
! 353: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY) THEN
! 354: INFO = -24
! 355: END IF
! 356: END IF
! 357: *
! 358: IF( INFO.NE.0 ) THEN
! 359: CALL XERBLA( 'ZGGESX', -INFO )
! 360: RETURN
! 361: ELSE IF (LQUERY) THEN
! 362: RETURN
! 363: END IF
! 364: *
! 365: * Quick return if possible
! 366: *
! 367: IF( N.EQ.0 ) THEN
! 368: SDIM = 0
! 369: RETURN
! 370: END IF
! 371: *
! 372: * Get machine constants
! 373: *
! 374: EPS = DLAMCH( 'P' )
! 375: SMLNUM = DLAMCH( 'S' )
! 376: BIGNUM = ONE / SMLNUM
! 377: CALL DLABAD( SMLNUM, BIGNUM )
! 378: SMLNUM = SQRT( SMLNUM ) / EPS
! 379: BIGNUM = ONE / SMLNUM
! 380: *
! 381: * Scale A if max element outside range [SMLNUM,BIGNUM]
! 382: *
! 383: ANRM = ZLANGE( 'M', N, N, A, LDA, RWORK )
! 384: ILASCL = .FALSE.
! 385: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
! 386: ANRMTO = SMLNUM
! 387: ILASCL = .TRUE.
! 388: ELSE IF( ANRM.GT.BIGNUM ) THEN
! 389: ANRMTO = BIGNUM
! 390: ILASCL = .TRUE.
! 391: END IF
! 392: IF( ILASCL )
! 393: $ CALL ZLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
! 394: *
! 395: * Scale B if max element outside range [SMLNUM,BIGNUM]
! 396: *
! 397: BNRM = ZLANGE( 'M', N, N, B, LDB, RWORK )
! 398: ILBSCL = .FALSE.
! 399: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
! 400: BNRMTO = SMLNUM
! 401: ILBSCL = .TRUE.
! 402: ELSE IF( BNRM.GT.BIGNUM ) THEN
! 403: BNRMTO = BIGNUM
! 404: ILBSCL = .TRUE.
! 405: END IF
! 406: IF( ILBSCL )
! 407: $ CALL ZLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
! 408: *
! 409: * Permute the matrix to make it more nearly triangular
! 410: * (Real Workspace: need 6*N)
! 411: *
! 412: ILEFT = 1
! 413: IRIGHT = N + 1
! 414: IRWRK = IRIGHT + N
! 415: CALL ZGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
! 416: $ RWORK( IRIGHT ), RWORK( IRWRK ), IERR )
! 417: *
! 418: * Reduce B to triangular form (QR decomposition of B)
! 419: * (Complex Workspace: need N, prefer N*NB)
! 420: *
! 421: IROWS = IHI + 1 - ILO
! 422: ICOLS = N + 1 - ILO
! 423: ITAU = 1
! 424: IWRK = ITAU + IROWS
! 425: CALL ZGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
! 426: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
! 427: *
! 428: * Apply the unitary transformation to matrix A
! 429: * (Complex Workspace: need N, prefer N*NB)
! 430: *
! 431: CALL ZUNMQR( 'L', 'C', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
! 432: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
! 433: $ LWORK+1-IWRK, IERR )
! 434: *
! 435: * Initialize VSL
! 436: * (Complex Workspace: need N, prefer N*NB)
! 437: *
! 438: IF( ILVSL ) THEN
! 439: CALL ZLASET( 'Full', N, N, CZERO, CONE, VSL, LDVSL )
! 440: IF( IROWS.GT.1 ) THEN
! 441: CALL ZLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
! 442: $ VSL( ILO+1, ILO ), LDVSL )
! 443: END IF
! 444: CALL ZUNGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
! 445: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
! 446: END IF
! 447: *
! 448: * Initialize VSR
! 449: *
! 450: IF( ILVSR )
! 451: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, VSR, LDVSR )
! 452: *
! 453: * Reduce to generalized Hessenberg form
! 454: * (Workspace: none needed)
! 455: *
! 456: CALL ZGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
! 457: $ LDVSL, VSR, LDVSR, IERR )
! 458: *
! 459: SDIM = 0
! 460: *
! 461: * Perform QZ algorithm, computing Schur vectors if desired
! 462: * (Complex Workspace: need N)
! 463: * (Real Workspace: need N)
! 464: *
! 465: IWRK = ITAU
! 466: CALL ZHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
! 467: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK( IWRK ),
! 468: $ LWORK+1-IWRK, RWORK( IRWRK ), IERR )
! 469: IF( IERR.NE.0 ) THEN
! 470: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
! 471: INFO = IERR
! 472: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
! 473: INFO = IERR - N
! 474: ELSE
! 475: INFO = N + 1
! 476: END IF
! 477: GO TO 40
! 478: END IF
! 479: *
! 480: * Sort eigenvalues ALPHA/BETA and compute the reciprocal of
! 481: * condition number(s)
! 482: *
! 483: IF( WANTST ) THEN
! 484: *
! 485: * Undo scaling on eigenvalues before SELCTGing
! 486: *
! 487: IF( ILASCL )
! 488: $ CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
! 489: IF( ILBSCL )
! 490: $ CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
! 491: *
! 492: * Select eigenvalues
! 493: *
! 494: DO 10 I = 1, N
! 495: BWORK( I ) = SELCTG( ALPHA( I ), BETA( I ) )
! 496: 10 CONTINUE
! 497: *
! 498: * Reorder eigenvalues, transform Generalized Schur vectors, and
! 499: * compute reciprocal condition numbers
! 500: * (Complex Workspace: If IJOB >= 1, need MAX(1, 2*SDIM*(N-SDIM))
! 501: * otherwise, need 1 )
! 502: *
! 503: CALL ZTGSEN( IJOB, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
! 504: $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PL, PR,
! 505: $ DIF, WORK( IWRK ), LWORK-IWRK+1, IWORK, LIWORK,
! 506: $ IERR )
! 507: *
! 508: IF( IJOB.GE.1 )
! 509: $ MAXWRK = MAX( MAXWRK, 2*SDIM*( N-SDIM ) )
! 510: IF( IERR.EQ.-21 ) THEN
! 511: *
! 512: * not enough complex workspace
! 513: *
! 514: INFO = -21
! 515: ELSE
! 516: IF( IJOB.EQ.1 .OR. IJOB.EQ.4 ) THEN
! 517: RCONDE( 1 ) = PL
! 518: RCONDE( 2 ) = PR
! 519: END IF
! 520: IF( IJOB.EQ.2 .OR. IJOB.EQ.4 ) THEN
! 521: RCONDV( 1 ) = DIF( 1 )
! 522: RCONDV( 2 ) = DIF( 2 )
! 523: END IF
! 524: IF( IERR.EQ.1 )
! 525: $ INFO = N + 3
! 526: END IF
! 527: *
! 528: END IF
! 529: *
! 530: * Apply permutation to VSL and VSR
! 531: * (Workspace: none needed)
! 532: *
! 533: IF( ILVSL )
! 534: $ CALL ZGGBAK( 'P', 'L', N, ILO, IHI, RWORK( ILEFT ),
! 535: $ RWORK( IRIGHT ), N, VSL, LDVSL, IERR )
! 536: *
! 537: IF( ILVSR )
! 538: $ CALL ZGGBAK( 'P', 'R', N, ILO, IHI, RWORK( ILEFT ),
! 539: $ RWORK( IRIGHT ), N, VSR, LDVSR, IERR )
! 540: *
! 541: * Undo scaling
! 542: *
! 543: IF( ILASCL ) THEN
! 544: CALL ZLASCL( 'U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
! 545: CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
! 546: END IF
! 547: *
! 548: IF( ILBSCL ) THEN
! 549: CALL ZLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
! 550: CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
! 551: END IF
! 552: *
! 553: IF( WANTST ) THEN
! 554: *
! 555: * Check if reordering is correct
! 556: *
! 557: LASTSL = .TRUE.
! 558: SDIM = 0
! 559: DO 30 I = 1, N
! 560: CURSL = SELCTG( ALPHA( I ), BETA( I ) )
! 561: IF( CURSL )
! 562: $ SDIM = SDIM + 1
! 563: IF( CURSL .AND. .NOT.LASTSL )
! 564: $ INFO = N + 2
! 565: LASTSL = CURSL
! 566: 30 CONTINUE
! 567: *
! 568: END IF
! 569: *
! 570: 40 CONTINUE
! 571: *
! 572: WORK( 1 ) = MAXWRK
! 573: IWORK( 1 ) = LIWMIN
! 574: *
! 575: RETURN
! 576: *
! 577: * End of ZGGESX
! 578: *
! 579: END
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