Annotation of rpl/lapack/lapack/zgegs.f, revision 1.1
1.1 ! bertrand 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! 24: * This routine is deprecated and has been replaced by routine ZGGES.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
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