clatms.f

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*> \brief \b CLATMS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
*                          KL, KU, PACK, A, LDA, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIST, PACK, SYM
*       INTEGER            INFO, KL, KU, LDA, M, MODE, N
*       REAL               COND, DMAX
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( 4 )
*       REAL               D( * )
*       COMPLEX            A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    CLATMS generates random matrices with specified singular values
*>    (or hermitian with specified eigenvalues)
*>    for testing LAPACK programs.
*>
*>    CLATMS operates by applying the following sequence of
*>    operations:
*>
*>      Set the diagonal to D, where D may be input or
*>         computed according to MODE, COND, DMAX, and SYM
*>         as described below.
*>
*>      Generate a matrix with the appropriate band structure, by one
*>         of two methods:
*>
*>      Method A:
*>          Generate a dense M x N matrix by multiplying D on the left
*>              and the right by random unitary matrices, then:
*>
*>          Reduce the bandwidth according to KL and KU, using
*>              Householder transformations.
*>
*>      Method B:
*>          Convert the bandwidth-0 (i.e., diagonal) matrix to a
*>              bandwidth-1 matrix using Givens rotations, "chasing"
*>              out-of-band elements back, much as in QR; then convert
*>              the bandwidth-1 to a bandwidth-2 matrix, etc.  Note
*>              that for reasonably small bandwidths (relative to M and
*>              N) this requires less storage, as a dense matrix is not
*>              generated.  Also, for hermitian or symmetric matrices,
*>              only one triangle is generated.
*>
*>      Method A is chosen if the bandwidth is a large fraction of the
*>          order of the matrix, and LDA is at least M (so a dense
*>          matrix can be stored.)  Method B is chosen if the bandwidth
*>          is small (< 1/2 N for hermitian or symmetric, < .3 N+M for
*>          non-symmetric), or LDA is less than M and not less than the
*>          bandwidth.
*>
*>      Pack the matrix if desired. Options specified by PACK are:
*>         no packing
*>         zero out upper half (if hermitian)
*>         zero out lower half (if hermitian)
*>         store the upper half columnwise (if hermitian or upper
*>               triangular)
*>         store the lower half columnwise (if hermitian or lower
*>               triangular)
*>         store the lower triangle in banded format (if hermitian or
*>               lower triangular)
*>         store the upper triangle in banded format (if hermitian or
*>               upper triangular)
*>         store the entire matrix in banded format
*>      If Method B is chosen, and band format is specified, then the
*>         matrix will be generated in the band format, so no repacking
*>         will be necessary.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>           The number of rows of A. Not modified.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           The number of columns of A. N must equal M if the matrix
*>           is symmetric or hermitian (i.e., if SYM is not 'N')
*>           Not modified.
*> \endverbatim
*>
*> \param[in] DIST
*> \verbatim
*>          DIST is CHARACTER*1
*>           On entry, DIST specifies the type of distribution to be used
*>           to generate the random eigen-/singular values.
*>           'U' => UNIFORM( 0, 1 )  ( 'U' for uniform )
*>           'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
*>           'N' => NORMAL( 0, 1 )   ( 'N' for normal )
*>           Not modified.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension ( 4 )
*>           On entry ISEED specifies the seed of the random number
*>           generator. They should lie between 0 and 4095 inclusive,
*>           and ISEED(4) should be odd. The random number generator
*>           uses a linear congruential sequence limited to small
*>           integers, and so should produce machine independent
*>           random numbers. The values of ISEED are changed on
*>           exit, and can be used in the next call to CLATMS
*>           to continue the same random number sequence.
*>           Changed on exit.
*> \endverbatim
*>
*> \param[in] SYM
*> \verbatim
*>          SYM is CHARACTER*1
*>           If SYM='H', the generated matrix is hermitian, with
*>             eigenvalues specified by D, COND, MODE, and DMAX; they
*>             may be positive, negative, or zero.
*>           If SYM='P', the generated matrix is hermitian, with
*>             eigenvalues (= singular values) specified by D, COND,
*>             MODE, and DMAX; they will not be negative.
*>           If SYM='N', the generated matrix is nonsymmetric, with
*>             singular values specified by D, COND, MODE, and DMAX;
*>             they will not be negative.
*>           If SYM='S', the generated matrix is (complex) symmetric,
*>             with singular values specified by D, COND, MODE, and
*>             DMAX; they will not be negative.
*>           Not modified.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is REAL array, dimension ( MIN( M, N ) )
*>           This array is used to specify the singular values or
*>           eigenvalues of A (see SYM, above.)  If MODE=0, then D is
*>           assumed to contain the singular/eigenvalues, otherwise
*>           they will be computed according to MODE, COND, and DMAX,
*>           and placed in D.
*>           Modified if MODE is nonzero.
*> \endverbatim
*>
*> \param[in] MODE
*> \verbatim
*>          MODE is INTEGER
*>           On entry this describes how the singular/eigenvalues are to
*>           be specified:
*>           MODE = 0 means use D as input
*>           MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
*>           MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
*>           MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
*>           MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
*>           MODE = 5 sets D to random numbers in the range
*>                    ( 1/COND , 1 ) such that their logarithms
*>                    are uniformly distributed.
*>           MODE = 6 set D to random numbers from same distribution
*>                    as the rest of the matrix.
*>           MODE < 0 has the same meaning as ABS(MODE), except that
*>              the order of the elements of D is reversed.
*>           Thus if MODE is positive, D has entries ranging from
*>              1 to 1/COND, if negative, from 1/COND to 1,
*>           If SYM='H', and MODE is neither 0, 6, nor -6, then
*>              the elements of D will also be multiplied by a random
*>              sign (i.e., +1 or -1.)
*>           Not modified.
*> \endverbatim
*>
*> \param[in] COND
*> \verbatim
*>          COND is REAL
*>           On entry, this is used as described under MODE above.
*>           If used, it must be >= 1. Not modified.
*> \endverbatim
*>
*> \param[in] DMAX
*> \verbatim
*>          DMAX is REAL
*>           If MODE is neither -6, 0 nor 6, the contents of D, as
*>           computed according to MODE and COND, will be scaled by
*>           DMAX / max(abs(D(i))); thus, the maximum absolute eigen- or
*>           singular value (which is to say the norm) will be abs(DMAX).
*>           Note that DMAX need not be positive: if DMAX is negative
*>           (or zero), D will be scaled by a negative number (or zero).
*>           Not modified.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*>          KL is INTEGER
*>           This specifies the lower bandwidth of the  matrix. For
*>           example, KL=0 implies upper triangular, KL=1 implies upper
*>           Hessenberg, and KL being at least M-1 means that the matrix
*>           has full lower bandwidth.  KL must equal KU if the matrix
*>           is symmetric or hermitian.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*>          KU is INTEGER
*>           This specifies the upper bandwidth of the  matrix. For
*>           example, KU=0 implies lower triangular, KU=1 implies lower
*>           Hessenberg, and KU being at least N-1 means that the matrix
*>           has full upper bandwidth.  KL must equal KU if the matrix
*>           is symmetric or hermitian.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] PACK
*> \verbatim
*>          PACK is CHARACTER*1
*>           This specifies packing of matrix as follows:
*>           'N' => no packing
*>           'U' => zero out all subdiagonal entries (if symmetric
*>                  or hermitian)
*>           'L' => zero out all superdiagonal entries (if symmetric
*>                  or hermitian)
*>           'C' => store the upper triangle columnwise (only if the
*>                  matrix is symmetric, hermitian, or upper triangular)
*>           'R' => store the lower triangle columnwise (only if the
*>                  matrix is symmetric, hermitian, or lower triangular)
*>           'B' => store the lower triangle in band storage scheme
*>                  (only if the matrix is symmetric, hermitian, or
*>                  lower triangular)
*>           'Q' => store the upper triangle in band storage scheme
*>                  (only if the matrix is symmetric, hermitian, or
*>                  upper triangular)
*>           'Z' => store the entire matrix in band storage scheme
*>                      (pivoting can be provided for by using this
*>                      option to store A in the trailing rows of
*>                      the allocated storage)
*>
*>           Using these options, the various LAPACK packed and banded
*>           storage schemes can be obtained:
*>           GB                    - use 'Z'
*>           PB, SB, HB, or TB     - use 'B' or 'Q'
*>           PP, SP, HB, or TP     - use 'C' or 'R'
*>
*>           If two calls to CLATMS differ only in the PACK parameter,
*>           they will generate mathematically equivalent matrices.
*>           Not modified.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is COMPLEX array, dimension ( LDA, N )
*>           On exit A is the desired test matrix.  A is first generated
*>           in full (unpacked) form, and then packed, if so specified
*>           by PACK.  Thus, the first M elements of the first N
*>           columns will always be modified.  If PACK specifies a
*>           packed or banded storage scheme, all LDA elements of the
*>           first N columns will be modified; the elements of the
*>           array which do not correspond to elements of the generated
*>           matrix are set to zero.
*>           Modified.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           LDA specifies the first dimension of A as declared in the
*>           calling program.  If PACK='N', 'U', 'L', 'C', or 'R', then
*>           LDA must be at least M.  If PACK='B' or 'Q', then LDA must
*>           be at least MIN( KL, M-1) (which is equal to MIN(KU,N-1)).
*>           If PACK='Z', LDA must be large enough to hold the packed
*>           array: MIN( KU, N-1) + MIN( KL, M-1) + 1.
*>           Not modified.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension ( 3*MAX( N, M ) )
*>           Workspace.
*>           Modified.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>           Error code.  On exit, INFO will be set to one of the
*>           following values:
*>             0 => normal return
*>            -1 => M negative or unequal to N and SYM='S', 'H', or 'P'
*>            -2 => N negative
*>            -3 => DIST illegal string
*>            -5 => SYM illegal string
*>            -7 => MODE not in range -6 to 6
*>            -8 => COND less than 1.0, and MODE neither -6, 0 nor 6
*>           -10 => KL negative
*>           -11 => KU negative, or SYM is not 'N' and KU is not equal to
*>                  KL
*>           -12 => PACK illegal string, or PACK='U' or 'L', and SYM='N';
*>                  or PACK='C' or 'Q' and SYM='N' and KL is not zero;
*>                  or PACK='R' or 'B' and SYM='N' and KU is not zero;
*>                  or PACK='U', 'L', 'C', 'R', 'B', or 'Q', and M is not
*>                  N.
*>           -14 => LDA is less than M, or PACK='Z' and LDA is less than
*>                  MIN(KU,N-1) + MIN(KL,M-1) + 1.
*>            1  => Error return from SLATM1
*>            2  => Cannot scale to DMAX (max. sing. value is 0)
*>            3  => Error return from CLAGGE, CLAGHE or CLAGSY
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_matgen
*
*  =====================================================================
      SUBROUTINE clatms( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
     $                   KL, KU, PACK, A, LDA, WORK, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          DIST, PACK, SYM
      INTEGER            INFO, KL, KU, LDA, M, MODE, N
      REAL               COND, DMAX
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      REAL               D( * )
      COMPLEX            A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
      parameter( zero = 0.0e+0 )
      REAL               ONE
      parameter( one = 1.0e+0 )
      COMPLEX            CZERO
      parameter( czero = ( 0.0e+0, 0.0e+0 ) )
      REAL               TWOPI
      parameter( twopi = 6.28318530717958647692528676655900576839e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            CSYM, GIVENS, ILEXTR, ILTEMP, TOPDWN
      INTEGER            I, IC, ICOL, IDIST, IENDCH, IINFO, IL, ILDA,
     $                   ioffg, ioffst, ipack, ipackg, ir, ir1, ir2,
     $                   irow, irsign, iskew, isym, isympk, j, jc, jch,
     $                   jkl, jku, jr, k, llb, minlda, mnmin, mr, nc,
     $                   uub
      REAL               ALPHA, ANGLE, REALC, TEMP
      COMPLEX            C, CT, CTEMP, DUMMY, EXTRA, S, ST
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLARND
      COMPLEX            CLARND
      EXTERNAL           lsame, slarnd, clarnd
*     ..
*     .. External Subroutines ..
      EXTERNAL           clagge, claghe, clagsy, clarot, clartg, claset,
     $                   slatm1, sscal, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, cmplx, conjg, cos, max, min, mod, real,
     $                   sin
*     ..
*     .. Executable Statements ..
*
*     1)      Decode and Test the input parameters.
*             Initialize flags & seed.
*
      info = 0
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 )
     $   RETURN
*
*     Decode DIST
*
      IF( lsame( dist, 'U' ) ) THEN
         idist = 1
      ELSE IF( lsame( dist, 'S' ) ) THEN
         idist = 2
      ELSE IF( lsame( dist, 'N' ) ) THEN
         idist = 3
      ELSE
         idist = -1
      END IF
*
*     Decode SYM
*
      IF( lsame( sym, 'N' ) ) THEN
         isym = 1
         irsign = 0
         csym = .false.
      ELSE IF( lsame( sym, 'P' ) ) THEN
         isym = 2
         irsign = 0
         csym = .false.
      ELSE IF( lsame( sym, 'S' ) ) THEN
         isym = 2
         irsign = 0
         csym = .true.
      ELSE IF( lsame( sym, 'H' ) ) THEN
         isym = 2
         irsign = 1
         csym = .false.
      ELSE
         isym = -1
      END IF
*
*     Decode PACK
*
      isympk = 0
      IF( lsame( pack, 'N' ) ) THEN
         ipack = 0
      ELSE IF( lsame( pack, 'U' ) ) THEN
         ipack = 1
         isympk = 1
      ELSE IF( lsame( pack, 'L' ) ) THEN
         ipack = 2
         isympk = 1
      ELSE IF( lsame( pack, 'C' ) ) THEN
         ipack = 3
         isympk = 2
      ELSE IF( lsame( pack, 'R' ) ) THEN
         ipack = 4
         isympk = 3
      ELSE IF( lsame( pack, 'B' ) ) THEN
         ipack = 5
         isympk = 3
      ELSE IF( lsame( pack, 'Q' ) ) THEN
         ipack = 6
         isympk = 2
      ELSE IF( lsame( pack, 'Z' ) ) THEN
         ipack = 7
      ELSE
         ipack = -1
      END IF
*
*     Set certain internal parameters
*
      mnmin = min( m, n )
      llb = min( kl, m-1 )
      uub = min( ku, n-1 )
      mr = min( m, n+llb )
      nc = min( n, m+uub )
*
      IF( ipack.EQ.5 .OR. ipack.EQ.6 ) THEN
         minlda = uub + 1
      ELSE IF( ipack.EQ.7 ) THEN
         minlda = llb + uub + 1
      ELSE
         minlda = m
      END IF
*
*     Use Givens rotation method if bandwidth small enough,
*     or if LDA is too small to store the matrix unpacked.
*
      givens = .false.
      IF( isym.EQ.1 ) THEN
         IF( real( llb+uub ).LT.0.3*real( max( 1, mr+nc ) ) )
     $      givens = .true.
      ELSE
         IF( 2*llb.LT.m )
     $      givens = .true.
      END IF
      IF( lda.LT.m .AND. lda.GE.minlda )
     $   givens = .true.
*
*     Set INFO if an error
*
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( m.NE.n .AND. isym.NE.1 ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( idist.EQ.-1 ) THEN
         info = -3
      ELSE IF( isym.EQ.-1 ) THEN
         info = -5
      ELSE IF( abs( mode ).GT.6 ) THEN
         info = -7
      ELSE IF( ( mode.NE.0 .AND. abs( mode ).NE.6 ) .AND. cond.LT.one )
     $          THEN
         info = -8
      ELSE IF( kl.LT.0 ) THEN
         info = -10
      ELSE IF( ku.LT.0 .OR. ( isym.NE.1 .AND. kl.NE.ku ) ) THEN
         info = -11
      ELSE IF( ipack.EQ.-1 .OR. ( isympk.EQ.1 .AND. isym.EQ.1 ) .OR.
     $         ( isympk.EQ.2 .AND. isym.EQ.1 .AND. kl.GT.0 ) .OR.
     $         ( isympk.EQ.3 .AND. isym.EQ.1 .AND. ku.GT.0 ) .OR.
     $         ( isympk.NE.0 .AND. m.NE.n ) ) THEN
         info = -12
      ELSE IF( lda.LT.max( 1, minlda ) ) THEN
         info = -14
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CLATMS', -info )
         RETURN
      END IF
*
*     Initialize random number generator
*
      DO 10 i = 1, 4
         iseed( i ) = mod( abs( iseed( i ) ), 4096 )
   10 CONTINUE
*
      IF( mod( iseed( 4 ), 2 ).NE.1 )
     $   iseed( 4 ) = iseed( 4 ) + 1
*
*     2)      Set up D  if indicated.
*
*             Compute D according to COND and MODE
*
      CALL slatm1( mode, cond, irsign, idist, iseed, d, mnmin, iinfo )
      IF( iinfo.NE.0 ) THEN
         info = 1
         RETURN
      END IF
*
*     Choose Top-Down if D is (apparently) increasing,
*     Bottom-Up if D is (apparently) decreasing.
*
      IF( abs( d( 1 ) ).LE.abs( d( mnmin ) ) ) THEN
         topdwn = .true.
      ELSE
         topdwn = .false.
      END IF
*
      IF( mode.NE.0 .AND. abs( mode ).NE.6 ) THEN
*
*        Scale by DMAX
*
         temp = abs( d( 1 ) )
         DO 20 i = 2, mnmin
            temp = max( temp, abs( d( i ) ) )
   20    CONTINUE
*
         IF( temp.GT.zero ) THEN
            alpha = dmax / temp
         ELSE
            info = 2
            RETURN
         END IF
*
         CALL sscal( mnmin, alpha, d, 1 )
*
      END IF
*
      CALL claset( 'full', LDA, N, CZERO, CZERO, A, LDA )
*
*     3)      Generate Banded Matrix using Givens rotations.
*             Also the special case of UUB=LLB=0
*
*               Compute Addressing constants to cover all
*               storage formats.  Whether GE, HE, SY, GB, HB, or SB,
*               upper or lower triangle or both,
*               the (i,j)-th element is in
*               A( i - ISKEW*j + IOFFST, j )
*
.GT.      IF( IPACK4 ) THEN
         ILDA = LDA - 1
         ISKEW = 1
.GT.         IF( IPACK5 ) THEN
            IOFFST = UUB + 1
         ELSE
            IOFFST = 1
         END IF
      ELSE
         ILDA = LDA
         ISKEW = 0
         IOFFST = 0
      END IF
*
*     IPACKG is the format that the matrix is generated in. If this is
*     different from IPACK, then the matrix must be repacked at the
*     end.  It also signals how to compute the norm, for scaling.
*
      IPACKG = 0
*
*     Diagonal Matrix -- We are done, unless it
*     is to be stored HP/SP/PP/TP (PACK='R' or 'C')
*
.EQ..AND..EQ.      IF( LLB0  UUB0 ) THEN
         DO 30 J = 1, MNMIN
            A( ( 1-ISKEW )*J+IOFFST, J ) = CMPLX( D( J ) )
   30    CONTINUE
*
.LE..OR..GE.         IF( IPACK2  IPACK5 )
     $      IPACKG = IPACK
*
      ELSE IF( GIVENS ) THEN
*
*        Check whether to use Givens rotations,
*        Householder transformations, or nothing.
*
.EQ.         IF( ISYM1 ) THEN
*
*           Non-symmetric -- A = U D V
*
.GT.            IF( IPACK4 ) THEN
               IPACKG = IPACK
            ELSE
               IPACKG = 0
            END IF
*
            DO 40 J = 1, MNMIN
               A( ( 1-ISKEW )*J+IOFFST, J ) = CMPLX( D( J ) )
   40       CONTINUE
*
            IF( TOPDWN ) THEN
               JKL = 0
               DO 70 JKU = 1, UUB
*
*                 Transform from bandwidth JKL, JKU-1 to JKL, JKU
*
*                 Last row actually rotated is M
*                 Last column actually rotated is MIN( M+JKU, N )
*
                  DO 60 JR = 1, MIN( M+JKU, N ) + JKL - 1
                     EXTRA = CZERO
                     ANGLE = TWOPI*SLARND( 1, ISEED )
                     C = COS( ANGLE )*CLARND( 5, ISEED )
                     S = SIN( ANGLE )*CLARND( 5, ISEED )
                     ICOL = MAX( 1, JR-JKL )
.LT.                     IF( JRM ) THEN
                        IL = MIN( N, JR+JKU ) + 1 - ICOL
.GT.                        CALL CLAROT( .TRUE., JRJKL, .FALSE., IL, C,
     $                               S, A( JR-ISKEW*ICOL+IOFFST, ICOL ),
     $                               ILDA, EXTRA, DUMMY )
                     END IF
*
*                    Chase "EXTRA" back up
*
                     IR = JR
                     IC = ICOL
                     DO 50 JCH = JR - JKL, 1, -JKL - JKU
.LT.                        IF( IRM ) THEN
                           CALL CLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST,
     $                                  IC+1 ), EXTRA, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = CONJG( REALC*DUMMY )
                           S = CONJG( -S*DUMMY )
                        END IF
                        IROW = MAX( 1, JCH-JKU )
                        IL = IR + 2 - IROW
                        CTEMP = CZERO
.GT.                        ILTEMP = JCHJKU
                        CALL CLAROT( .FALSE., ILTEMP, .TRUE., IL, C, S,
     $                               A( IROW-ISKEW*IC+IOFFST, IC ),
     $                               ILDA, CTEMP, EXTRA )
                        IF( ILTEMP ) THEN
                           CALL CLARTG( A( IROW+1-ISKEW*( IC+1 )+IOFFST,
     $                                  IC+1 ), CTEMP, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = CONJG( REALC*DUMMY )
                           S = CONJG( -S*DUMMY )
*
                           ICOL = MAX( 1, JCH-JKU-JKL )
                           IL = IC + 2 - ICOL
                           EXTRA = CZERO
.GT.                           CALL CLAROT( .TRUE., JCHJKU+JKL, .TRUE.,
     $                                  IL, C, S, A( IROW-ISKEW*ICOL+
     $                                  IOFFST, ICOL ), ILDA, EXTRA,
     $                                  CTEMP )
                           IC = ICOL
                           IR = IROW
                        END IF
   50                CONTINUE
   60             CONTINUE
   70          CONTINUE
*
               JKU = UUB
               DO 100 JKL = 1, LLB
*
*                 Transform from bandwidth JKL-1, JKU to JKL, JKU
*
                  DO 90 JC = 1, MIN( N+JKL, M ) + JKU - 1
                     EXTRA = CZERO
                     ANGLE = TWOPI*SLARND( 1, ISEED )
                     C = COS( ANGLE )*CLARND( 5, ISEED )
                     S = SIN( ANGLE )*CLARND( 5, ISEED )
                     IROW = MAX( 1, JC-JKU )
.LT.                     IF( JCN ) THEN
                        IL = MIN( M, JC+JKL ) + 1 - IROW
.GT.                        CALL CLAROT( .FALSE., JCJKU, .FALSE., IL, C,
     $                               S, A( IROW-ISKEW*JC+IOFFST, JC ),
     $                               ILDA, EXTRA, DUMMY )
                     END IF
*
*                    Chase "EXTRA" back up
*
                     IC = JC
                     IR = IROW
                     DO 80 JCH = JC - JKU, 1, -JKL - JKU
.LT.                        IF( ICN ) THEN
                           CALL CLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST,
     $                                  IC+1 ), EXTRA, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = CONJG( REALC*DUMMY )
                           S = CONJG( -S*DUMMY )
                        END IF
                        ICOL = MAX( 1, JCH-JKL )
                        IL = IC + 2 - ICOL
                        CTEMP = CZERO
.GT.                        ILTEMP = JCHJKL
                        CALL CLAROT( .TRUE., ILTEMP, .TRUE., IL, C, S,
     $                               A( IR-ISKEW*ICOL+IOFFST, ICOL ),
     $                               ILDA, CTEMP, EXTRA )
                        IF( ILTEMP ) THEN
                           CALL CLARTG( A( IR+1-ISKEW*( ICOL+1 )+IOFFST,
     $                                  ICOL+1 ), CTEMP, REALC, S,
     $                                  DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = CONJG( REALC*DUMMY )
                           S = CONJG( -S*DUMMY )
                           IROW = MAX( 1, JCH-JKL-JKU )
                           IL = IR + 2 - IROW
                           EXTRA = CZERO
.GT.                           CALL CLAROT( .FALSE., JCHJKL+JKU, .TRUE.,
     $                                  IL, C, S, A( IROW-ISKEW*ICOL+
     $                                  IOFFST, ICOL ), ILDA, EXTRA,
     $                                  CTEMP )
                           IC = ICOL
                           IR = IROW
                        END IF
   80                CONTINUE
   90             CONTINUE
  100          CONTINUE
*
            ELSE
*
*              Bottom-Up -- Start at the bottom right.
*
               JKL = 0
               DO 130 JKU = 1, UUB
*
*                 Transform from bandwidth JKL, JKU-1 to JKL, JKU
*
*                 First row actually rotated is M
*                 First column actually rotated is MIN( M+JKU, N )
*
                  IENDCH = MIN( M, N+JKL ) - 1
                  DO 120 JC = MIN( M+JKU, N ) - 1, 1 - JKL, -1
                     EXTRA = CZERO
                     ANGLE = TWOPI*SLARND( 1, ISEED )
                     C = COS( ANGLE )*CLARND( 5, ISEED )
                     S = SIN( ANGLE )*CLARND( 5, ISEED )
                     IROW = MAX( 1, JC-JKU+1 )
.GT.                     IF( JC0 ) THEN
                        IL = MIN( M, JC+JKL+1 ) + 1 - IROW
.LT.                        CALL CLAROT( .FALSE., .FALSE., JC+JKLM, IL,
     $                               C, S, A( IROW-ISKEW*JC+IOFFST,
     $                               JC ), ILDA, DUMMY, EXTRA )
                     END IF
*
*                    Chase "EXTRA" back down
*
                     IC = JC
                     DO 110 JCH = JC + JKL, IENDCH, JKL + JKU
.GT.                        ILEXTR = IC0
                        IF( ILEXTR ) THEN
                           CALL CLARTG( A( JCH-ISKEW*IC+IOFFST, IC ),
     $                                  EXTRA, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = REALC*DUMMY
                           S = S*DUMMY
                        END IF
                        IC = MAX( 1, IC )
                        ICOL = MIN( N-1, JCH+JKU )
.LT.                        ILTEMP = JCH + JKUN
                        CTEMP = CZERO
                        CALL CLAROT( .TRUE., ILEXTR, ILTEMP, ICOL+2-IC,
     $                               C, S, A( JCH-ISKEW*IC+IOFFST, IC ),
     $                               ILDA, EXTRA, CTEMP )
                        IF( ILTEMP ) THEN
                           CALL CLARTG( A( JCH-ISKEW*ICOL+IOFFST,
     $                                  ICOL ), CTEMP, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = REALC*DUMMY
                           S = S*DUMMY
                           IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH
                           EXTRA = CZERO
                           CALL CLAROT( .FALSE., .TRUE.,
.LE.     $                                  JCH+JKL+JKUIENDCH, IL, C, S,
     $                                  A( JCH-ISKEW*ICOL+IOFFST,
     $                                  ICOL ), ILDA, CTEMP, EXTRA )
                           IC = ICOL
                        END IF
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
*
               JKU = UUB
               DO 160 JKL = 1, LLB
*
*                 Transform from bandwidth JKL-1, JKU to JKL, JKU
*
*                 First row actually rotated is MIN( N+JKL, M )
*                 First column actually rotated is N
*
                  IENDCH = MIN( N, M+JKU ) - 1
                  DO 150 JR = MIN( N+JKL, M ) - 1, 1 - JKU, -1
                     EXTRA = CZERO
                     ANGLE = TWOPI*SLARND( 1, ISEED )
                     C = COS( ANGLE )*CLARND( 5, ISEED )
                     S = SIN( ANGLE )*CLARND( 5, ISEED )
                     ICOL = MAX( 1, JR-JKL+1 )
.GT.                     IF( JR0 ) THEN
                        IL = MIN( N, JR+JKU+1 ) + 1 - ICOL
.LT.                        CALL CLAROT( .TRUE., .FALSE., JR+JKUN, IL,
     $                               C, S, A( JR-ISKEW*ICOL+IOFFST,
     $                               ICOL ), ILDA, DUMMY, EXTRA )
                     END IF
*
*                    Chase "EXTRA" back down
*
                     IR = JR
                     DO 140 JCH = JR + JKU, IENDCH, JKL + JKU
.GT.                        ILEXTR = IR0
                        IF( ILEXTR ) THEN
                           CALL CLARTG( A( IR-ISKEW*JCH+IOFFST, JCH ),
     $                                  EXTRA, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = REALC*DUMMY
                           S = S*DUMMY
                        END IF
                        IR = MAX( 1, IR )
                        IROW = MIN( M-1, JCH+JKL )
.LT.                        ILTEMP = JCH + JKLM
                        CTEMP = CZERO
                        CALL CLAROT( .FALSE., ILEXTR, ILTEMP, IROW+2-IR,
     $                               C, S, A( IR-ISKEW*JCH+IOFFST,
     $                               JCH ), ILDA, EXTRA, CTEMP )
                        IF( ILTEMP ) THEN
                           CALL CLARTG( A( IROW-ISKEW*JCH+IOFFST, JCH ),
     $                                  CTEMP, REALC, S, DUMMY )
                           DUMMY = CLARND( 5, ISEED )
                           C = REALC*DUMMY
                           S = S*DUMMY
                           IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH
                           EXTRA = CZERO
                           CALL CLAROT( .TRUE., .TRUE.,
.LE.     $                                  JCH+JKL+JKUIENDCH, IL, C, S,
     $                                  A( IROW-ISKEW*JCH+IOFFST, JCH ),
     $                                  ILDA, CTEMP, EXTRA )
                           IR = IROW
                        END IF
  140                CONTINUE
  150             CONTINUE
  160          CONTINUE
*
            END IF
*
         ELSE
*
*           Symmetric -- A = U D U'
*           Hermitian -- A = U D U*
*
            IPACKG = IPACK
            IOFFG = IOFFST
*
            IF( TOPDWN ) THEN
*
*              Top-Down -- Generate Upper triangle only
*
.GE.               IF( IPACK5 ) THEN
                  IPACKG = 6
                  IOFFG = UUB + 1
               ELSE
                  IPACKG = 1
               END IF
*
               DO 170 J = 1, MNMIN
                  A( ( 1-ISKEW )*J+IOFFG, J ) = CMPLX( D( J ) )
  170          CONTINUE
*
               DO 200 K = 1, UUB
                  DO 190 JC = 1, N - 1
                     IROW = MAX( 1, JC-K )
                     IL = MIN( JC+1, K+2 )
                     EXTRA = CZERO
                     CTEMP = A( JC-ISKEW*( JC+1 )+IOFFG, JC+1 )
                     ANGLE = TWOPI*SLARND( 1, ISEED )
                     C = COS( ANGLE )*CLARND( 5, ISEED )
                     S = SIN( ANGLE )*CLARND( 5, ISEED )
                     IF( CSYM ) THEN
                        CT = C
                        ST = S
                     ELSE
                        CTEMP = CONJG( CTEMP )
                        CT = CONJG( C )
                        ST = CONJG( S )
                     END IF
.GT.                     CALL CLAROT( .FALSE., JCK, .TRUE., IL, C, S,
     $                            A( IROW-ISKEW*JC+IOFFG, JC ), ILDA,
     $                            EXTRA, CTEMP )
                     CALL CLAROT( .TRUE., .TRUE., .FALSE.,
     $                            MIN( K, N-JC )+1, CT, ST,
     $                            A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA,
     $                            CTEMP, DUMMY )
*
*                    Chase EXTRA back up the matrix
*
                     ICOL = JC
                     DO 180 JCH = JC - K, 1, -K
                        CALL CLARTG( A( JCH+1-ISKEW*( ICOL+1 )+IOFFG,
     $                               ICOL+1 ), EXTRA, REALC, S, DUMMY )
                        DUMMY = CLARND( 5, ISEED )
                        C = CONJG( REALC*DUMMY )
                        S = CONJG( -S*DUMMY )
                        CTEMP = A( JCH-ISKEW*( JCH+1 )+IOFFG, JCH+1 )
                        IF( CSYM ) THEN
                           CT = C
                           ST = S
                        ELSE
                           CTEMP = CONJG( CTEMP )
                           CT = CONJG( C )
                           ST = CONJG( S )
                        END IF
                        CALL CLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S,
     $                               A( ( 1-ISKEW )*JCH+IOFFG, JCH ),
     $                               ILDA, CTEMP, EXTRA )
                        IROW = MAX( 1, JCH-K )
                        IL = MIN( JCH+1, K+2 )
                        EXTRA = CZERO
.GT.                        CALL CLAROT( .FALSE., JCHK, .TRUE., IL, CT,
     $                               ST, A( IROW-ISKEW*JCH+IOFFG, JCH ),
     $                               ILDA, EXTRA, CTEMP )
                        ICOL = JCH
  180                CONTINUE
  190             CONTINUE
  200          CONTINUE
*
*              If we need lower triangle, copy from upper. Note that
*              the order of copying is chosen to work for 'q' -> 'b'
*
.NE..AND..NE.               IF( IPACKIPACKG  IPACK3 ) THEN
                  DO 230 JC = 1, N
                     IROW = IOFFST - ISKEW*JC
                     IF( CSYM ) THEN
                        DO 210 JR = JC, MIN( N, JC+UUB )
                           A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR )
  210                   CONTINUE
                     ELSE
                        DO 220 JR = JC, MIN( N, JC+UUB )
                           A( JR+IROW, JC ) = CONJG( A( JC-ISKEW*JR+
     $                                        IOFFG, JR ) )
  220                   CONTINUE
                     END IF
  230             CONTINUE
.EQ.                  IF( IPACK5 ) THEN
                     DO 250 JC = N - UUB + 1, N
                        DO 240 JR = N + 2 - JC, UUB + 1
                           A( JR, JC ) = CZERO
  240                   CONTINUE
  250                CONTINUE
                  END IF
.EQ.                  IF( IPACKG6 ) THEN
                     IPACKG = IPACK
                  ELSE
                     IPACKG = 0
                  END IF
               END IF
            ELSE
*
*              Bottom-Up -- Generate Lower triangle only
*
.GE.               IF( IPACK5 ) THEN
                  IPACKG = 5
.EQ.                  IF( IPACK6 )
     $               IOFFG = 1
               ELSE
                  IPACKG = 2
               END IF
*
               DO 260 J = 1, MNMIN
                  A( ( 1-ISKEW )*J+IOFFG, J ) = CMPLX( D( J ) )
  260          CONTINUE
*
               DO 290 K = 1, UUB
                  DO 280 JC = N - 1, 1, -1
                     IL = MIN( N+1-JC, K+2 )
                     EXTRA = CZERO
                     CTEMP = A( 1+( 1-ISKEW )*JC+IOFFG, JC )
                     ANGLE = TWOPI*SLARND( 1, ISEED )
                     C = COS( ANGLE )*CLARND( 5, ISEED )
                     S = SIN( ANGLE )*CLARND( 5, ISEED )
                     IF( CSYM ) THEN
                        CT = C
                        ST = S
                     ELSE
                        CTEMP = CONJG( CTEMP )
                        CT = CONJG( C )
                        ST = CONJG( S )
                     END IF
.GT.                     CALL CLAROT( .FALSE., .TRUE., N-JCK, IL, C, S,
     $                            A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA,
     $                            CTEMP, EXTRA )
                     ICOL = MAX( 1, JC-K+1 )
                     CALL CLAROT( .TRUE., .FALSE., .TRUE., JC+2-ICOL,
     $                            CT, ST, A( JC-ISKEW*ICOL+IOFFG,
     $                            ICOL ), ILDA, DUMMY, CTEMP )
*
*                    Chase EXTRA back down the matrix
*
                     ICOL = JC
                     DO 270 JCH = JC + K, N - 1, K
                        CALL CLARTG( A( JCH-ISKEW*ICOL+IOFFG, ICOL ),
     $                               EXTRA, REALC, S, DUMMY )
                        DUMMY = CLARND( 5, ISEED )
                        C = REALC*DUMMY
                        S = S*DUMMY
                        CTEMP = A( 1+( 1-ISKEW )*JCH+IOFFG, JCH )
                        IF( CSYM ) THEN
                           CT = C
                           ST = S
                        ELSE
                           CTEMP = CONJG( CTEMP )
                           CT = CONJG( C )
                           ST = CONJG( S )
                        END IF
                        CALL CLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S,
     $                               A( JCH-ISKEW*ICOL+IOFFG, ICOL ),
     $                               ILDA, EXTRA, CTEMP )
                        IL = MIN( N+1-JCH, K+2 )
                        EXTRA = CZERO
.GT.                        CALL CLAROT( .FALSE., .TRUE., N-JCHK, IL,
     $                               CT, ST, A( ( 1-ISKEW )*JCH+IOFFG,
     $                               JCH ), ILDA, CTEMP, EXTRA )
                        ICOL = JCH
  270                CONTINUE
  280             CONTINUE
  290          CONTINUE
*
*              If we need upper triangle, copy from lower. Note that
*              the order of copying is chosen to work for 'b' -> 'q'
*
.NE..AND..NE.               IF( IPACKIPACKG  IPACK4 ) THEN
                  DO 320 JC = N, 1, -1
                     IROW = IOFFST - ISKEW*JC
                     IF( CSYM ) THEN
                        DO 300 JR = JC, MAX( 1, JC-UUB ), -1
                           A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR )
  300                   CONTINUE
                     ELSE
                        DO 310 JR = JC, MAX( 1, JC-UUB ), -1
                           A( JR+IROW, JC ) = CONJG( A( JC-ISKEW*JR+
     $                                        IOFFG, JR ) )
  310                   CONTINUE
                     END IF
  320             CONTINUE
.EQ.                  IF( IPACK6 ) THEN
                     DO 340 JC = 1, UUB
                        DO 330 JR = 1, UUB + 1 - JC
                           A( JR, JC ) = CZERO
  330                   CONTINUE
  340                CONTINUE
                  END IF
.EQ.                  IF( IPACKG5 ) THEN
                     IPACKG = IPACK
                  ELSE
                     IPACKG = 0
                  END IF
               END IF
            END IF
*
*           Ensure that the diagonal is real if Hermitian
*
.NOT.            IF( CSYM ) THEN
               DO 350 JC = 1, N
                  IROW = IOFFST + ( 1-ISKEW )*JC
                  A( IROW, JC ) = CMPLX( REAL( A( IROW, JC ) ) )
  350          CONTINUE
            END IF
*
         END IF
*
      ELSE
*
*        4)      Generate Banded Matrix by first
*                Rotating by random Unitary matrices,
*                then reducing the bandwidth using Householder
*                transformations.
*
*                Note: we should get here only if LDA .ge. N
*
.EQ.         IF( ISYM1 ) THEN
*
*           Non-symmetric -- A = U D V
*
            CALL CLAGGE( MR, NC, LLB, UUB, D, A, LDA, ISEED, WORK,
     $                   IINFO )
         ELSE
*
*           Symmetric -- A = U D U' or
*           Hermitian -- A = U D U*
*
            IF( CSYM ) THEN
               CALL CLAGSY( M, LLB, D, A, LDA, ISEED, WORK, IINFO )
            ELSE
               CALL CLAGHE( M, LLB, D, A, LDA, ISEED, WORK, IINFO )
            END IF
         END IF
*
.NE.         IF( IINFO0 ) THEN
            INFO = 3
            RETURN
         END IF
      END IF
*
*     5)      Pack the matrix
*
.NE.      IF( IPACKIPACKG ) THEN
.EQ.         IF( IPACK1 ) THEN
*
*           'U' -- Upper triangular, not packed
*
            DO 370 J = 1, M
               DO 360 I = J + 1, M
                  A( I, J ) = CZERO
  360          CONTINUE
  370       CONTINUE
*
.EQ.         ELSE IF( IPACK2 ) THEN
*
*           'L' -- Lower triangular, not packed
*
            DO 390 J = 2, M
               DO 380 I = 1, J - 1
                  A( I, J ) = CZERO
  380          CONTINUE
  390       CONTINUE
*
.EQ.         ELSE IF( IPACK3 ) THEN
*
*           'C' -- Upper triangle packed Columnwise.
*
            ICOL = 1
            IROW = 0
            DO 410 J = 1, M
               DO 400 I = 1, J
                  IROW = IROW + 1
.GT.                  IF( IROWLDA ) THEN
                     IROW = 1
                     ICOL = ICOL + 1
                  END IF
                  A( IROW, ICOL ) = A( I, J )
  400          CONTINUE
  410       CONTINUE
*
.EQ.         ELSE IF( IPACK4 ) THEN
*
*           'R' -- Lower triangle packed Columnwise.
*
            ICOL = 1
            IROW = 0
            DO 430 J = 1, M
               DO 420 I = J, M
                  IROW = IROW + 1
.GT.                  IF( IROWLDA ) THEN
                     IROW = 1
                     ICOL = ICOL + 1
                  END IF
                  A( IROW, ICOL ) = A( I, J )
  420          CONTINUE
  430       CONTINUE
*
.GE.         ELSE IF( IPACK5 ) THEN
*
*           'B' -- The lower triangle is packed as a band matrix.
*           'Q' -- The upper triangle is packed as a band matrix.
*           'Z' -- The whole matrix is packed as a band matrix.
*
.EQ.            IF( IPACK5 )
     $         UUB = 0
.EQ.            IF( IPACK6 )
     $         LLB = 0
*
            DO 450 J = 1, UUB
               DO 440 I = MIN( J+LLB, M ), 1, -1
                  A( I-J+UUB+1, J ) = A( I, J )
  440          CONTINUE
  450       CONTINUE
*
            DO 470 J = UUB + 2, N
               DO 460 I = J - UUB, MIN( J+LLB, M )
                  A( I-J+UUB+1, J ) = A( I, J )
  460          CONTINUE
  470       CONTINUE
         END IF
*
*        If packed, zero out extraneous elements.
*
*        Symmetric/Triangular Packed --
*        zero out everything after A(IROW,ICOL)
*
.EQ..OR..EQ.         IF( IPACK3  IPACK4 ) THEN
            DO 490 JC = ICOL, M
               DO 480 JR = IROW + 1, LDA
                  A( JR, JC ) = CZERO
  480          CONTINUE
               IROW = 0
  490       CONTINUE
*
.GE.         ELSE IF( IPACK5 ) THEN
*
*           Packed Band --
*              1st row is now in A( UUB+2-j, j), zero above it
*              m-th row is now in A( M+UUB-j,j), zero below it
*              last non-zero diagonal is now in A( UUB+LLB+1,j ),
*                 zero below it, too.
*
            IR1 = UUB + LLB + 2
            IR2 = UUB + M + 2
            DO 520 JC = 1, N
               DO 500 JR = 1, UUB + 1 - JC
                  A( JR, JC ) = CZERO
  500          CONTINUE
               DO 510 JR = MAX( 1, MIN( IR1, IR2-JC ) ), LDA
                  A( JR, JC ) = CZERO
  510          CONTINUE
  520       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of CLATMS
*
      END