Annotation of rpl/lapack/lapack/dgges.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
! 2: $ SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR,
! 3: $ LDVSR, WORK, LWORK, BWORK, 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, SORT
! 12: INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
! 13: * ..
! 14: * .. Array Arguments ..
! 15: LOGICAL BWORK( * )
! 16: DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
! 17: $ B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
! 18: $ VSR( LDVSR, * ), WORK( * )
! 19: * ..
! 20: * .. Function Arguments ..
! 21: LOGICAL SELCTG
! 22: EXTERNAL SELCTG
! 23: * ..
! 24: *
! 25: * Purpose
! 26: * =======
! 27: *
! 28: * DGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
! 29: * the generalized eigenvalues, the generalized real Schur form (S,T),
! 30: * optionally, the left and/or right matrices of Schur vectors (VSL and
! 31: * VSR). This gives the generalized Schur factorization
! 32: *
! 33: * (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
! 34: *
! 35: * Optionally, it also orders the eigenvalues so that a selected cluster
! 36: * of eigenvalues appears in the leading diagonal blocks of the upper
! 37: * quasi-triangular matrix S and the upper triangular matrix T.The
! 38: * leading columns of VSL and VSR then form an orthonormal basis for the
! 39: * corresponding left and right eigenspaces (deflating subspaces).
! 40: *
! 41: * (If only the generalized eigenvalues are needed, use the driver
! 42: * DGGEV instead, which is faster.)
! 43: *
! 44: * A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
! 45: * or a ratio alpha/beta = w, such that A - w*B is singular. It is
! 46: * usually represented as the pair (alpha,beta), as there is a
! 47: * reasonable interpretation for beta=0 or both being zero.
! 48: *
! 49: * A pair of matrices (S,T) is in generalized real Schur form if T is
! 50: * upper triangular with non-negative diagonal and S is block upper
! 51: * triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
! 52: * to real generalized eigenvalues, while 2-by-2 blocks of S will be
! 53: * "standardized" by making the corresponding elements of T have the
! 54: * form:
! 55: * [ a 0 ]
! 56: * [ 0 b ]
! 57: *
! 58: * and the pair of corresponding 2-by-2 blocks in S and T will have a
! 59: * complex conjugate pair of generalized eigenvalues.
! 60: *
! 61: *
! 62: * Arguments
! 63: * =========
! 64: *
! 65: * JOBVSL (input) CHARACTER*1
! 66: * = 'N': do not compute the left Schur vectors;
! 67: * = 'V': compute the left Schur vectors.
! 68: *
! 69: * JOBVSR (input) CHARACTER*1
! 70: * = 'N': do not compute the right Schur vectors;
! 71: * = 'V': compute the right Schur vectors.
! 72: *
! 73: * SORT (input) CHARACTER*1
! 74: * Specifies whether or not to order the eigenvalues on the
! 75: * diagonal of the generalized Schur form.
! 76: * = 'N': Eigenvalues are not ordered;
! 77: * = 'S': Eigenvalues are ordered (see SELCTG);
! 78: *
! 79: * SELCTG (external procedure) LOGICAL FUNCTION of three DOUBLE PRECISION arguments
! 80: * SELCTG must be declared EXTERNAL in the calling subroutine.
! 81: * If SORT = 'N', SELCTG is not referenced.
! 82: * If SORT = 'S', SELCTG is used to select eigenvalues to sort
! 83: * to the top left of the Schur form.
! 84: * An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if
! 85: * SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either
! 86: * one of a complex conjugate pair of eigenvalues is selected,
! 87: * then both complex eigenvalues are selected.
! 88: *
! 89: * Note that in the ill-conditioned case, a selected complex
! 90: * eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j),
! 91: * BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2
! 92: * in this case.
! 93: *
! 94: * N (input) INTEGER
! 95: * The order of the matrices A, B, VSL, and VSR. N >= 0.
! 96: *
! 97: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 98: * On entry, the first of the pair of matrices.
! 99: * On exit, A has been overwritten by its generalized Schur
! 100: * form S.
! 101: *
! 102: * LDA (input) INTEGER
! 103: * The leading dimension of A. LDA >= max(1,N).
! 104: *
! 105: * B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
! 106: * On entry, the second of the pair of matrices.
! 107: * On exit, B has been overwritten by its generalized Schur
! 108: * form T.
! 109: *
! 110: * LDB (input) INTEGER
! 111: * The leading dimension of B. LDB >= max(1,N).
! 112: *
! 113: * SDIM (output) INTEGER
! 114: * If SORT = 'N', SDIM = 0.
! 115: * If SORT = 'S', SDIM = number of eigenvalues (after sorting)
! 116: * for which SELCTG is true. (Complex conjugate pairs for which
! 117: * SELCTG is true for either eigenvalue count as 2.)
! 118: *
! 119: * ALPHAR (output) DOUBLE PRECISION array, dimension (N)
! 120: * ALPHAI (output) DOUBLE PRECISION array, dimension (N)
! 121: * BETA (output) DOUBLE PRECISION array, dimension (N)
! 122: * On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
! 123: * be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i,
! 124: * and BETA(j),j=1,...,N are the diagonals of the complex Schur
! 125: * form (S,T) that would result if the 2-by-2 diagonal blocks of
! 126: * the real Schur form of (A,B) were further reduced to
! 127: * triangular form using 2-by-2 complex unitary transformations.
! 128: * If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
! 129: * positive, then the j-th and (j+1)-st eigenvalues are a
! 130: * complex conjugate pair, with ALPHAI(j+1) negative.
! 131: *
! 132: * Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
! 133: * may easily over- or underflow, and BETA(j) may even be zero.
! 134: * Thus, the user should avoid naively computing the ratio.
! 135: * However, ALPHAR and ALPHAI will be always less than and
! 136: * usually comparable with norm(A) in magnitude, and BETA always
! 137: * less than and usually comparable with norm(B).
! 138: *
! 139: * VSL (output) DOUBLE PRECISION array, dimension (LDVSL,N)
! 140: * If JOBVSL = 'V', VSL will contain the left Schur vectors.
! 141: * Not referenced if JOBVSL = 'N'.
! 142: *
! 143: * LDVSL (input) INTEGER
! 144: * The leading dimension of the matrix VSL. LDVSL >=1, and
! 145: * if JOBVSL = 'V', LDVSL >= N.
! 146: *
! 147: * VSR (output) DOUBLE PRECISION array, dimension (LDVSR,N)
! 148: * If JOBVSR = 'V', VSR will contain the right Schur vectors.
! 149: * Not referenced if JOBVSR = 'N'.
! 150: *
! 151: * LDVSR (input) INTEGER
! 152: * The leading dimension of the matrix VSR. LDVSR >= 1, and
! 153: * if JOBVSR = 'V', LDVSR >= N.
! 154: *
! 155: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 156: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 157: *
! 158: * LWORK (input) INTEGER
! 159: * The dimension of the array WORK.
! 160: * If N = 0, LWORK >= 1, else LWORK >= 8*N+16.
! 161: * For good performance , LWORK must generally be larger.
! 162: *
! 163: * If LWORK = -1, then a workspace query is assumed; the routine
! 164: * only calculates the optimal size of the WORK array, returns
! 165: * this value as the first entry of the WORK array, and no error
! 166: * message related to LWORK is issued by XERBLA.
! 167: *
! 168: * BWORK (workspace) LOGICAL array, dimension (N)
! 169: * Not referenced if SORT = 'N'.
! 170: *
! 171: * INFO (output) INTEGER
! 172: * = 0: successful exit
! 173: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 174: * = 1,...,N:
! 175: * The QZ iteration failed. (A,B) are not in Schur
! 176: * form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
! 177: * be correct for j=INFO+1,...,N.
! 178: * > N: =N+1: other than QZ iteration failed in DHGEQZ.
! 179: * =N+2: after reordering, roundoff changed values of
! 180: * some complex eigenvalues so that leading
! 181: * eigenvalues in the Generalized Schur form no
! 182: * longer satisfy SELCTG=.TRUE. This could also
! 183: * be caused due to scaling.
! 184: * =N+3: reordering failed in DTGSEN.
! 185: *
! 186: * =====================================================================
! 187: *
! 188: * .. Parameters ..
! 189: DOUBLE PRECISION ZERO, ONE
! 190: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 191: * ..
! 192: * .. Local Scalars ..
! 193: LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
! 194: $ LQUERY, LST2SL, WANTST
! 195: INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
! 196: $ ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK,
! 197: $ MINWRK
! 198: DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
! 199: $ PVSR, SAFMAX, SAFMIN, SMLNUM
! 200: * ..
! 201: * .. Local Arrays ..
! 202: INTEGER IDUM( 1 )
! 203: DOUBLE PRECISION DIF( 2 )
! 204: * ..
! 205: * .. External Subroutines ..
! 206: EXTERNAL DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
! 207: $ DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGSEN,
! 208: $ XERBLA
! 209: * ..
! 210: * .. External Functions ..
! 211: LOGICAL LSAME
! 212: INTEGER ILAENV
! 213: DOUBLE PRECISION DLAMCH, DLANGE
! 214: EXTERNAL LSAME, ILAENV, DLAMCH, DLANGE
! 215: * ..
! 216: * .. Intrinsic Functions ..
! 217: INTRINSIC ABS, MAX, SQRT
! 218: * ..
! 219: * .. Executable Statements ..
! 220: *
! 221: * Decode the input arguments
! 222: *
! 223: IF( LSAME( JOBVSL, 'N' ) ) THEN
! 224: IJOBVL = 1
! 225: ILVSL = .FALSE.
! 226: ELSE IF( LSAME( JOBVSL, 'V' ) ) THEN
! 227: IJOBVL = 2
! 228: ILVSL = .TRUE.
! 229: ELSE
! 230: IJOBVL = -1
! 231: ILVSL = .FALSE.
! 232: END IF
! 233: *
! 234: IF( LSAME( JOBVSR, 'N' ) ) THEN
! 235: IJOBVR = 1
! 236: ILVSR = .FALSE.
! 237: ELSE IF( LSAME( JOBVSR, 'V' ) ) THEN
! 238: IJOBVR = 2
! 239: ILVSR = .TRUE.
! 240: ELSE
! 241: IJOBVR = -1
! 242: ILVSR = .FALSE.
! 243: END IF
! 244: *
! 245: WANTST = LSAME( SORT, 'S' )
! 246: *
! 247: * Test the input arguments
! 248: *
! 249: INFO = 0
! 250: LQUERY = ( LWORK.EQ.-1 )
! 251: IF( IJOBVL.LE.0 ) THEN
! 252: INFO = -1
! 253: ELSE IF( IJOBVR.LE.0 ) THEN
! 254: INFO = -2
! 255: ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.LSAME( SORT, 'N' ) ) ) THEN
! 256: INFO = -3
! 257: ELSE IF( N.LT.0 ) THEN
! 258: INFO = -5
! 259: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 260: INFO = -7
! 261: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 262: INFO = -9
! 263: ELSE IF( LDVSL.LT.1 .OR. ( ILVSL .AND. LDVSL.LT.N ) ) THEN
! 264: INFO = -15
! 265: ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
! 266: INFO = -17
! 267: END IF
! 268: *
! 269: * Compute workspace
! 270: * (Note: Comments in the code beginning "Workspace:" describe the
! 271: * minimal amount of workspace needed at that point in the code,
! 272: * as well as the preferred amount for good performance.
! 273: * NB refers to the optimal block size for the immediately
! 274: * following subroutine, as returned by ILAENV.)
! 275: *
! 276: IF( INFO.EQ.0 ) THEN
! 277: IF( N.GT.0 )THEN
! 278: MINWRK = MAX( 8*N, 6*N + 16 )
! 279: MAXWRK = MINWRK - N +
! 280: $ N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 )
! 281: MAXWRK = MAX( MAXWRK, MINWRK - N +
! 282: $ N*ILAENV( 1, 'DORMQR', ' ', N, 1, N, -1 ) )
! 283: IF( ILVSL ) THEN
! 284: MAXWRK = MAX( MAXWRK, MINWRK - N +
! 285: $ N*ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) )
! 286: END IF
! 287: ELSE
! 288: MINWRK = 1
! 289: MAXWRK = 1
! 290: END IF
! 291: WORK( 1 ) = MAXWRK
! 292: *
! 293: IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
! 294: $ INFO = -19
! 295: END IF
! 296: *
! 297: IF( INFO.NE.0 ) THEN
! 298: CALL XERBLA( 'DGGES ', -INFO )
! 299: RETURN
! 300: ELSE IF( LQUERY ) THEN
! 301: RETURN
! 302: END IF
! 303: *
! 304: * Quick return if possible
! 305: *
! 306: IF( N.EQ.0 ) THEN
! 307: SDIM = 0
! 308: RETURN
! 309: END IF
! 310: *
! 311: * Get machine constants
! 312: *
! 313: EPS = DLAMCH( 'P' )
! 314: SAFMIN = DLAMCH( 'S' )
! 315: SAFMAX = ONE / SAFMIN
! 316: CALL DLABAD( SAFMIN, SAFMAX )
! 317: SMLNUM = SQRT( SAFMIN ) / EPS
! 318: BIGNUM = ONE / SMLNUM
! 319: *
! 320: * Scale A if max element outside range [SMLNUM,BIGNUM]
! 321: *
! 322: ANRM = DLANGE( 'M', N, N, A, LDA, WORK )
! 323: ILASCL = .FALSE.
! 324: IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
! 325: ANRMTO = SMLNUM
! 326: ILASCL = .TRUE.
! 327: ELSE IF( ANRM.GT.BIGNUM ) THEN
! 328: ANRMTO = BIGNUM
! 329: ILASCL = .TRUE.
! 330: END IF
! 331: IF( ILASCL )
! 332: $ CALL DLASCL( 'G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
! 333: *
! 334: * Scale B if max element outside range [SMLNUM,BIGNUM]
! 335: *
! 336: BNRM = DLANGE( 'M', N, N, B, LDB, WORK )
! 337: ILBSCL = .FALSE.
! 338: IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
! 339: BNRMTO = SMLNUM
! 340: ILBSCL = .TRUE.
! 341: ELSE IF( BNRM.GT.BIGNUM ) THEN
! 342: BNRMTO = BIGNUM
! 343: ILBSCL = .TRUE.
! 344: END IF
! 345: IF( ILBSCL )
! 346: $ CALL DLASCL( 'G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
! 347: *
! 348: * Permute the matrix to make it more nearly triangular
! 349: * (Workspace: need 6*N + 2*N space for storing balancing factors)
! 350: *
! 351: ILEFT = 1
! 352: IRIGHT = N + 1
! 353: IWRK = IRIGHT + N
! 354: CALL DGGBAL( 'P', N, A, LDA, B, LDB, ILO, IHI, WORK( ILEFT ),
! 355: $ WORK( IRIGHT ), WORK( IWRK ), IERR )
! 356: *
! 357: * Reduce B to triangular form (QR decomposition of B)
! 358: * (Workspace: need N, prefer N*NB)
! 359: *
! 360: IROWS = IHI + 1 - ILO
! 361: ICOLS = N + 1 - ILO
! 362: ITAU = IWRK
! 363: IWRK = ITAU + IROWS
! 364: CALL DGEQRF( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
! 365: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
! 366: *
! 367: * Apply the orthogonal transformation to matrix A
! 368: * (Workspace: need N, prefer N*NB)
! 369: *
! 370: CALL DORMQR( 'L', 'T', IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
! 371: $ WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
! 372: $ LWORK+1-IWRK, IERR )
! 373: *
! 374: * Initialize VSL
! 375: * (Workspace: need N, prefer N*NB)
! 376: *
! 377: IF( ILVSL ) THEN
! 378: CALL DLASET( 'Full', N, N, ZERO, ONE, VSL, LDVSL )
! 379: IF( IROWS.GT.1 ) THEN
! 380: CALL DLACPY( 'L', IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
! 381: $ VSL( ILO+1, ILO ), LDVSL )
! 382: END IF
! 383: CALL DORGQR( IROWS, IROWS, IROWS, VSL( ILO, ILO ), LDVSL,
! 384: $ WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
! 385: END IF
! 386: *
! 387: * Initialize VSR
! 388: *
! 389: IF( ILVSR )
! 390: $ CALL DLASET( 'Full', N, N, ZERO, ONE, VSR, LDVSR )
! 391: *
! 392: * Reduce to generalized Hessenberg form
! 393: * (Workspace: none needed)
! 394: *
! 395: CALL DGGHRD( JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB, VSL,
! 396: $ LDVSL, VSR, LDVSR, IERR )
! 397: *
! 398: * Perform QZ algorithm, computing Schur vectors if desired
! 399: * (Workspace: need N)
! 400: *
! 401: IWRK = ITAU
! 402: CALL DHGEQZ( 'S', JOBVSL, JOBVSR, N, ILO, IHI, A, LDA, B, LDB,
! 403: $ ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
! 404: $ WORK( IWRK ), LWORK+1-IWRK, IERR )
! 405: IF( IERR.NE.0 ) THEN
! 406: IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
! 407: INFO = IERR
! 408: ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
! 409: INFO = IERR - N
! 410: ELSE
! 411: INFO = N + 1
! 412: END IF
! 413: GO TO 50
! 414: END IF
! 415: *
! 416: * Sort eigenvalues ALPHA/BETA if desired
! 417: * (Workspace: need 4*N+16 )
! 418: *
! 419: SDIM = 0
! 420: IF( WANTST ) THEN
! 421: *
! 422: * Undo scaling on eigenvalues before SELCTGing
! 423: *
! 424: IF( ILASCL ) THEN
! 425: CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N,
! 426: $ IERR )
! 427: CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N,
! 428: $ IERR )
! 429: END IF
! 430: IF( ILBSCL )
! 431: $ CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
! 432: *
! 433: * Select eigenvalues
! 434: *
! 435: DO 10 I = 1, N
! 436: BWORK( I ) = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
! 437: 10 CONTINUE
! 438: *
! 439: CALL DTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, ALPHAR,
! 440: $ ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, PVSL,
! 441: $ PVSR, DIF, WORK( IWRK ), LWORK-IWRK+1, IDUM, 1,
! 442: $ IERR )
! 443: IF( IERR.EQ.1 )
! 444: $ INFO = N + 3
! 445: *
! 446: END IF
! 447: *
! 448: * Apply back-permutation to VSL and VSR
! 449: * (Workspace: none needed)
! 450: *
! 451: IF( ILVSL )
! 452: $ CALL DGGBAK( 'P', 'L', N, ILO, IHI, WORK( ILEFT ),
! 453: $ WORK( IRIGHT ), N, VSL, LDVSL, IERR )
! 454: *
! 455: IF( ILVSR )
! 456: $ CALL DGGBAK( 'P', 'R', N, ILO, IHI, WORK( ILEFT ),
! 457: $ WORK( IRIGHT ), N, VSR, LDVSR, IERR )
! 458: *
! 459: * Check if unscaling would cause over/underflow, if so, rescale
! 460: * (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of
! 461: * B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I)
! 462: *
! 463: IF( ILASCL ) THEN
! 464: DO 20 I = 1, N
! 465: IF( ALPHAI( I ).NE.ZERO ) THEN
! 466: IF( ( ALPHAR( I ) / SAFMAX ).GT.( ANRMTO / ANRM ) .OR.
! 467: $ ( SAFMIN / ALPHAR( I ) ).GT.( ANRM / ANRMTO ) ) THEN
! 468: WORK( 1 ) = ABS( A( I, I ) / ALPHAR( I ) )
! 469: BETA( I ) = BETA( I )*WORK( 1 )
! 470: ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
! 471: ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
! 472: ELSE IF( ( ALPHAI( I ) / SAFMAX ).GT.
! 473: $ ( ANRMTO / ANRM ) .OR.
! 474: $ ( SAFMIN / ALPHAI( I ) ).GT.( ANRM / ANRMTO ) )
! 475: $ THEN
! 476: WORK( 1 ) = ABS( A( I, I+1 ) / ALPHAI( I ) )
! 477: BETA( I ) = BETA( I )*WORK( 1 )
! 478: ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
! 479: ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
! 480: END IF
! 481: END IF
! 482: 20 CONTINUE
! 483: END IF
! 484: *
! 485: IF( ILBSCL ) THEN
! 486: DO 30 I = 1, N
! 487: IF( ALPHAI( I ).NE.ZERO ) THEN
! 488: IF( ( BETA( I ) / SAFMAX ).GT.( BNRMTO / BNRM ) .OR.
! 489: $ ( SAFMIN / BETA( I ) ).GT.( BNRM / BNRMTO ) ) THEN
! 490: WORK( 1 ) = ABS( B( I, I ) / BETA( I ) )
! 491: BETA( I ) = BETA( I )*WORK( 1 )
! 492: ALPHAR( I ) = ALPHAR( I )*WORK( 1 )
! 493: ALPHAI( I ) = ALPHAI( I )*WORK( 1 )
! 494: END IF
! 495: END IF
! 496: 30 CONTINUE
! 497: END IF
! 498: *
! 499: * Undo scaling
! 500: *
! 501: IF( ILASCL ) THEN
! 502: CALL DLASCL( 'H', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR )
! 503: CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAR, N, IERR )
! 504: CALL DLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHAI, N, IERR )
! 505: END IF
! 506: *
! 507: IF( ILBSCL ) THEN
! 508: CALL DLASCL( 'U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR )
! 509: CALL DLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
! 510: END IF
! 511: *
! 512: IF( WANTST ) THEN
! 513: *
! 514: * Check if reordering is correct
! 515: *
! 516: LASTSL = .TRUE.
! 517: LST2SL = .TRUE.
! 518: SDIM = 0
! 519: IP = 0
! 520: DO 40 I = 1, N
! 521: CURSL = SELCTG( ALPHAR( I ), ALPHAI( I ), BETA( I ) )
! 522: IF( ALPHAI( I ).EQ.ZERO ) THEN
! 523: IF( CURSL )
! 524: $ SDIM = SDIM + 1
! 525: IP = 0
! 526: IF( CURSL .AND. .NOT.LASTSL )
! 527: $ INFO = N + 2
! 528: ELSE
! 529: IF( IP.EQ.1 ) THEN
! 530: *
! 531: * Last eigenvalue of conjugate pair
! 532: *
! 533: CURSL = CURSL .OR. LASTSL
! 534: LASTSL = CURSL
! 535: IF( CURSL )
! 536: $ SDIM = SDIM + 2
! 537: IP = -1
! 538: IF( CURSL .AND. .NOT.LST2SL )
! 539: $ INFO = N + 2
! 540: ELSE
! 541: *
! 542: * First eigenvalue of conjugate pair
! 543: *
! 544: IP = 1
! 545: END IF
! 546: END IF
! 547: LST2SL = LASTSL
! 548: LASTSL = CURSL
! 549: 40 CONTINUE
! 550: *
! 551: END IF
! 552: *
! 553: 50 CONTINUE
! 554: *
! 555: WORK( 1 ) = MAXWRK
! 556: *
! 557: RETURN
! 558: *
! 559: * End of DGGES
! 560: *
! 561: END
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