zdrvgg.f

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*          the matrices in A and B.
*
*  VL      (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
*          The (lower triangular) left eigenvector matrix for the
*          matrices in A and B.
*
*  VR      (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
*          The (upper triangular) right eigenvector matrix for the
*          matrices in A and B.
*
*  WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
*
*  LWORK   (input) INTEGER
*          The number of entries in WORK.  This must be at least
*          MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the
*          sum of the blocksize and number-of-shifts for ZHGEQZ, and
*          NB is the greatest of the blocksizes for ZGEQRF, ZUNMQR,
*          and ZUNGQR.  (The blocksizes and the number-of-shifts are
*          retrieved through calls to ILAENV.)
*
*  RWORK   (workspace) DOUBLE PRECISION array, dimension (8*N)
*
*  RESULT  (output) DOUBLE PRECISION array, dimension (7)
*          The values computed by the tests described above.
*          The values are currently limited to 1/ulp, to avoid
*          overflow.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value.
*          > 0:  A routine returned an error code.  INFO is the
*                absolute value of the INFO value returned.
*
*  =====================================================================
*
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), NN( * )
      DOUBLE PRECISION   RESULT( * ), RWORK( * )
      COMPLEX*16         A( LDA, * ), ALPHA1( * ), ALPHA2( * ),
     $                   B( LDA, * ), BETA1( * ), BETA2( * ),
     $                   Q( LDQ, * ), S( LDA, * ), S2( LDA, * ),
     $                   T( LDA, * ), T2( LDA, * ), VL( LDQ, * ),
     $                   VR( LDQ, * ), WORK( * ), Z( LDQ, * )
*     ..
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
      INTEGER            MAXTYP
      PARAMETER          ( MAXTYP = 26 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADNN
      INTEGER            I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
     $                   LWKOPT, MTYPES, N, N1, NB, NBZ, NERRS, NMATS,
     $                   NMAX, NS, NTEST, NTESTT
      DOUBLE PRECISION   SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
      COMPLEX*16         CTEMP, X
*     ..
*     .. Local Arrays ..
      LOGICAL            LASIGN( MAXTYP ), LBSIGN( MAXTYP )
      INTEGER            IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
     $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
     $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
     $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
     $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
      DOUBLE PRECISION   DUMMA( 4 ), RMAGN( 0: 3 )
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      DOUBLE PRECISION   DLAMCH
      COMPLEX*16         ZLARND
      EXTERNAL           ILAENV, DLAMCH, ZLARND
*     ..
*     .. External Subroutines ..
      EXTERNAL           ALASVM, DLABAD, XERBLA, ZGEGS, ZGEGV, ZGET51,
     $                   ZGET52, ZLACPY, ZLARFG, ZLASET, ZLATM4, ZUNM2R
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, DCONJG, DIMAG, MAX, MIN, SIGN
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   ABS1
*     ..
*     .. Statement Function definitions ..
      ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
*     ..
*     .. Data statements ..
      DATA               KCLASS / 15*1, 10*2, 1*3 /
      DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
      DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
      DATA               KADD / 0, 0, 0, 0, 3, 2 /
      DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
     $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
      DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
     $                   1, 1, -4, 2, -4, 8*8, 0 /
      DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
     $                   4*5, 4*3, 1 /
      DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
     $                   4*6, 4*4, 1 /
      DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
     $                   2, 1 /
      DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
     $                   2, 1 /
      DATA               KTRIAN / 16*0, 10*1 /
      DATA               LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
     $                   2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
     $                   3*.FALSE., 5*.TRUE., .FALSE. /
      DATA               LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
     $                   2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
     $                   9*.FALSE. /
*     ..
*     .. Executable Statements ..
*
*     Check for errors
*
      INFO = 0
*
      BADNN = .FALSE.
      NMAX = 1
      DO 10 J = 1, NSIZES
         NMAX = MAX( NMAX, NN( J ) )
         IF( NN( J ).LT.0 )
     $      BADNN = .TRUE.
   10 CONTINUE
*
*     Maximum blocksize and shift -- we assume that blocksize and number
*     of shifts are monotone increasing functions of N.
*
      NB = MAX( 1, ILAENV( 1, 'ZGEQRF', ' ', NMAX, NMAX, -1, -1 ),
     $     ILAENV( 1, 'ZUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
     $     ILAENV( 1, 'ZUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
      NBZ = ILAENV( 1, 'ZHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
      NS = ILAENV( 4, 'ZHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
      I1 = NBZ + NS
      LWKOPT = MAX( 2*NMAX, NMAX*( NB+1 ), ( 2*I1+NMAX+1 )*( I1+1 ) )
*
*     Check for errors
*
      IF( NSIZES.LT.0 ) THEN
         INFO = -1
      ELSE IF( BADNN ) THEN
         INFO = -2
      ELSE IF( NTYPES.LT.0 ) THEN
         INFO = -3
      ELSE IF( THRESH.LT.ZERO ) THEN
         INFO = -6
      ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
         INFO = -10
      ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
         INFO = -19
      ELSE IF( LWKOPT.GT.LWORK ) THEN
         INFO = -30
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZDRVGG', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
     $   RETURN
*
      ULP = DLAMCH( 'Precision' )
      SAFMIN = DLAMCH( 'Safe minimum' )
      SAFMIN = SAFMIN / ULP
      SAFMAX = ONE / SAFMIN
      CALL DLABAD( SAFMIN, SAFMAX )
      ULPINV = ONE / ULP
*
*     The values RMAGN(2:3) depend on N, see below.
*
      RMAGN( 0 ) = ZERO
      RMAGN( 1 ) = ONE
*
*     Loop over sizes, types
*
      NTESTT = 0
      NERRS = 0
      NMATS = 0
*
      DO 160 JSIZE = 1, NSIZES
         N = NN( JSIZE )
         N1 = MAX( 1, N )
         RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 )
         RMAGN( 3 ) = SAFMIN*ULPINV*N1
*
         IF( NSIZES.NE.1 ) THEN
            MTYPES = MIN( MAXTYP, NTYPES )
         ELSE
            MTYPES = MIN( MAXTYP+1, NTYPES )
         END IF
*
         DO 150 JTYPE = 1, MTYPES
            IF( .NOT.DOTYPE( JTYPE ) )
     $         GO TO 150
            NMATS = NMATS + 1
            NTEST = 0
*
*           Save ISEED in case of an error.
*
            DO 20 J = 1, 4
               IOLDSD( J ) = ISEED( J )
   20       CONTINUE
*
*           Initialize RESULT
*
            DO 30 J = 1, 7
               RESULT( J ) = ZERO
   30       CONTINUE
*
*           Compute A and B
*
*           Description of control parameters:
*
*           KZLASS: =1 means w/o rotation, =2 means w/ rotation,
*                   =3 means random.
*           KATYPE: the "type" to be passed to ZLATM4 for computing A.
*           KAZERO: the pattern of zeros on the diagonal for A:
*                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
*                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
*                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
*                   non-zero entries.)
*           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
*                   =2: large, =3: small.
*           LASIGN: .TRUE. if the diagonal elements of A are to be
*                   multiplied by a random magnitude 1 number.
*           KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
*           KTRIAN: =0: don't fill in the upper triangle, =1: do.
*           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
*           RMAGN:  used to implement KAMAGN and KBMAGN.
*
            IF( MTYPES.GT.MAXTYP )
     $         GO TO 110
            IINFO = 0
            IF( KCLASS( JTYPE ).LT.3 ) THEN
*
*              Generate A (w/o rotation)
*
               IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
                  IN = 2*( ( N-1 ) / 2 ) + 1
                  IF( IN.NE.N )
     $               CALL ZLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
               ELSE
                  IN = N
               END IF
               CALL ZLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
     $                      KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
     $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
     $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
     $                      ISEED, A, LDA )
               IADD = KADD( KAZERO( JTYPE ) )
               IF( IADD.GT.0 .AND. IADD.LE.N )
     $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
*
*              Generate B (w/o rotation)
*
               IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
                  IN = 2*( ( N-1 ) / 2 ) + 1
                  IF( IN.NE.N )
     $               CALL ZLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
               ELSE
                  IN = N
               END IF
               CALL ZLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
     $                      KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
     $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
     $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,