slatmr.f

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*> \brief \b SLATMR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE SLATMR( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
*                          RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
*                          CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM,
*                          PACK, A, LDA, IWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIST, GRADE, PACK, PIVTNG, RSIGN, SYM
*       INTEGER            INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N
*       REAL               ANORM, COND, CONDL, CONDR, DMAX, SPARSE
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIVOT( * ), ISEED( 4 ), IWORK( * )
*       REAL               A( LDA, * ), D( * ), DL( * ), DR( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    SLATMR generates random matrices of various types for testing
*>    LAPACK programs.
*>
*>    SLATMR operates by applying the following sequence of
*>    operations:
*>
*>      Generate a matrix A with random entries of distribution DIST
*>         which is symmetric if SYM='S', and nonsymmetric
*>         if SYM='N'.
*>
*>      Set the diagonal to D, where D may be input or
*>         computed according to MODE, COND, DMAX and RSIGN
*>         as described below.
*>
*>      Grade the matrix, if desired, from the left and/or right
*>         as specified by GRADE. The inputs DL, MODEL, CONDL, DR,
*>         MODER and CONDR also determine the grading as described
*>         below.
*>
*>      Permute, if desired, the rows and/or columns as specified by
*>         PIVTNG and IPIVOT.
*>
*>      Set random entries to zero, if desired, to get a random sparse
*>         matrix as specified by SPARSE.
*>
*>      Make A a band matrix, if desired, by zeroing out the matrix
*>         outside a band of lower bandwidth KL and upper bandwidth KU.
*>
*>      Scale A, if desired, to have maximum entry ANORM.
*>
*>      Pack the matrix if desired. Options specified by PACK are:
*>         no packing
*>         zero out upper half (if symmetric)
*>         zero out lower half (if symmetric)
*>         store the upper half columnwise (if symmetric or
*>             square upper triangular)
*>         store the lower half columnwise (if symmetric or
*>             square lower triangular)
*>             same as upper half rowwise if symmetric
*>         store the lower triangle in banded format (if symmetric)
*>         store the upper triangle in banded format (if symmetric)
*>         store the entire matrix in banded format
*>
*>    Note: If two calls to SLATMR differ only in the PACK parameter,
*>          they will generate mathematically equivalent matrices.
*>
*>          If two calls to SLATMR both have full bandwidth (KL = M-1
*>          and KU = N-1), and differ only in the PIVTNG and PACK
*>          parameters, then the matrices generated will differ only
*>          in the order of the rows and/or columns, and otherwise
*>          contain the same data. This consistency cannot be and
*>          is not maintained with less than full bandwidth.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>           Number of rows of A. Not modified.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           Number of columns of A. Not modified.
*> \endverbatim
*>
*> \param[in] DIST
*> \verbatim
*>          DIST is CHARACTER*1
*>           On entry, DIST specifies the type of distribution to be used
*>           to generate a random matrix .
*>           '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 SLATMR
*>           to continue the same random number sequence.
*>           Changed on exit.
*> \endverbatim
*>
*> \param[in] SYM
*> \verbatim
*>          SYM is CHARACTER*1
*>           If SYM='S' or 'H', generated matrix is symmetric.
*>           If SYM='N', generated matrix is nonsymmetric.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is REAL array, dimension (min(M,N))
*>           On entry this array specifies the diagonal entries
*>           of the diagonal of A.  D may either be specified
*>           on entry, or set according to MODE and COND as described
*>           below. May be changed on exit if MODE is nonzero.
*> \endverbatim
*>
*> \param[in] MODE
*> \verbatim
*>          MODE is INTEGER
*>           On entry describes how D is to be used:
*>           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,
*>           Not modified.
*> \endverbatim
*>
*> \param[in] COND
*> \verbatim
*>          COND is REAL
*>           On entry, used as described under MODE above.
*>           If used, it must be >= 1. Not modified.
*> \endverbatim
*>
*> \param[in] DMAX
*> \verbatim
*>          DMAX is REAL
*>           If MODE neither -6, 0 nor 6, the diagonal is scaled by
*>           DMAX / max(abs(D(i))), so that maximum absolute entry
*>           of diagonal is abs(DMAX). If DMAX is negative (or zero),
*>           diagonal will be scaled by a negative number (or zero).
*> \endverbatim
*>
*> \param[in] RSIGN
*> \verbatim
*>          RSIGN is CHARACTER*1
*>           If MODE neither -6, 0 nor 6, specifies sign of diagonal
*>           as follows:
*>           'T' => diagonal entries are multiplied by 1 or -1
*>                  with probability .5
*>           'F' => diagonal unchanged
*>           Not modified.
*> \endverbatim
*>
*> \param[in] GRADE
*> \verbatim
*>          GRADE is CHARACTER*1
*>           Specifies grading of matrix as follows:
*>           'N'  => no grading
*>           'L'  => matrix premultiplied by diag( DL )
*>                   (only if matrix nonsymmetric)
*>           'R'  => matrix postmultiplied by diag( DR )
*>                   (only if matrix nonsymmetric)
*>           'B'  => matrix premultiplied by diag( DL ) and
*>                         postmultiplied by diag( DR )
*>                   (only if matrix nonsymmetric)
*>           'S' or 'H'  => matrix premultiplied by diag( DL ) and
*>                          postmultiplied by diag( DL )
*>                          ('S' for symmetric, or 'H' for Hermitian)
*>           'E'  => matrix premultiplied by diag( DL ) and
*>                         postmultiplied by inv( diag( DL ) )
*>                         ( 'E' for eigenvalue invariance)
*>                   (only if matrix nonsymmetric)
*>                   Note: if GRADE='E', then M must equal N.
*>           Not modified.
*> \endverbatim
*>
*> \param[in,out] DL
*> \verbatim
*>          DL is REAL array, dimension (M)
*>           If MODEL=0, then on entry this array specifies the diagonal
*>           entries of a diagonal matrix used as described under GRADE
*>           above. If MODEL is not zero, then DL will be set according
*>           to MODEL and CONDL, analogous to the way D is set according
*>           to MODE and COND (except there is no DMAX parameter for DL).
*>           If GRADE='E', then DL cannot have zero entries.
*>           Not referenced if GRADE = 'N' or 'R'. Changed on exit.
*> \endverbatim
*>
*> \param[in] MODEL
*> \verbatim
*>          MODEL is INTEGER
*>           This specifies how the diagonal array DL is to be computed,
*>           just as MODE specifies how D is to be computed.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] CONDL
*> \verbatim
*>          CONDL is REAL
*>           When MODEL is not zero, this specifies the condition number
*>           of the computed DL.  Not modified.
*> \endverbatim
*>
*> \param[in,out] DR
*> \verbatim
*>          DR is REAL array, dimension (N)
*>           If MODER=0, then on entry this array specifies the diagonal
*>           entries of a diagonal matrix used as described under GRADE
*>           above. If MODER is not zero, then DR will be set according
*>           to MODER and CONDR, analogous to the way D is set according
*>           to MODE and COND (except there is no DMAX parameter for DR).
*>           Not referenced if GRADE = 'N', 'L', 'H', 'S' or 'E'.
*>           Changed on exit.
*> \endverbatim
*>
*> \param[in] MODER
*> \verbatim
*>          MODER is INTEGER
*>           This specifies how the diagonal array DR is to be computed,
*>           just as MODE specifies how D is to be computed.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] CONDR
*> \verbatim
*>          CONDR is REAL
*>           When MODER is not zero, this specifies the condition number
*>           of the computed DR.  Not modified.
*> \endverbatim
*>
*> \param[in] PIVTNG
*> \verbatim
*>          PIVTNG is CHARACTER*1
*>           On entry specifies pivoting permutations as follows:
*>           'N' or ' ' => none.
*>           'L' => left or row pivoting (matrix must be nonsymmetric).
*>           'R' => right or column pivoting (matrix must be
*>                  nonsymmetric).
*>           'B' or 'F' => both or full pivoting, i.e., on both sides.
*>                         In this case, M must equal N
*>
*>           If two calls to SLATMR both have full bandwidth (KL = M-1
*>           and KU = N-1), and differ only in the PIVTNG and PACK
*>           parameters, then the matrices generated will differ only
*>           in the order of the rows and/or columns, and otherwise
*>           contain the same data. This consistency cannot be
*>           maintained with less than full bandwidth.
*> \endverbatim
*>
*> \param[in] IPIVOT
*> \verbatim
*>          IPIVOT is INTEGER array, dimension (N or M)
*>           This array specifies the permutation used.  After the
*>           basic matrix is generated, the rows, columns, or both
*>           are permuted.   If, say, row pivoting is selected, SLATMR
*>           starts with the *last* row and interchanges the M-th and
*>           IPIVOT(M)-th rows, then moves to the next-to-last row,
*>           interchanging the (M-1)-th and the IPIVOT(M-1)-th rows,
*>           and so on.  In terms of "2-cycles", the permutation is
*>           (1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M))
*>           where the rightmost cycle is applied first.  This is the
*>           *inverse* of the effect of pivoting in LINPACK.  The idea
*>           is that factoring (with pivoting) an identity matrix
*>           which has been inverse-pivoted in this way should
*>           result in a pivot vector identical to IPIVOT.
*>           Not referenced if PIVTNG = 'N'. Not modified.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*>          KL is INTEGER
*>           On entry specifies the lower bandwidth of the  matrix. For
*>           example, KL=0 implies upper triangular, KL=1 implies upper
*>           Hessenberg, and KL at least M-1 implies the matrix is not
*>           banded. Must equal KU if matrix is symmetric.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*>          KU is INTEGER
*>           On entry specifies the upper bandwidth of the  matrix. For
*>           example, KU=0 implies lower triangular, KU=1 implies lower
*>           Hessenberg, and KU at least N-1 implies the matrix is not
*>           banded. Must equal KL if matrix is symmetric.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] SPARSE
*> \verbatim
*>          SPARSE is REAL
*>           On entry specifies the sparsity of the matrix if a sparse
*>           matrix is to be generated. SPARSE should lie between
*>           0 and 1. To generate a sparse matrix, for each matrix entry
*>           a uniform ( 0, 1 ) random number x is generated and
*>           compared to SPARSE; if x is larger the matrix entry
*>           is unchanged and if x is smaller the entry is set
*>           to zero. Thus on the average a fraction SPARSE of the
*>           entries will be set to zero.
*>           Not modified.
*> \endverbatim
*>
*> \param[in] ANORM
*> \verbatim
*>          ANORM is REAL
*>           On entry specifies maximum entry of output matrix
*>           (output matrix will by multiplied by a constant so that
*>           its largest absolute entry equal ANORM)
*>           if ANORM is nonnegative. If ANORM is negative no scaling
*>           is done. Not modified.
*> \endverbatim
*>
*> \param[in] PACK
*> \verbatim
*>          PACK is CHARACTER*1
*>           On entry specifies packing of matrix as follows:
*>           'N' => no packing
*>           'U' => zero out all subdiagonal entries (if symmetric)
*>           'L' => zero out all superdiagonal entries (if symmetric)
*>           'C' => store the upper triangle columnwise
*>                  (only if matrix symmetric or square upper triangular)
*>           'R' => store the lower triangle columnwise
*>                  (only if matrix symmetric or square lower triangular)
*>                  (same as upper half rowwise if symmetric)
*>           'B' => store the lower triangle in band storage scheme
*>                  (only if matrix symmetric)
*>           'Q' => store the upper triangle in band storage scheme
*>                  (only if matrix symmetric)
*>           '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 or TB     - use 'B' or 'Q'
*>           PP, SP or TP     - use 'C' or 'R'
*>
*>           If two calls to SLATMR differ only in the PACK parameter,
*>           they will generate mathematically equivalent matrices.
*>           Not modified.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>           On exit A is the desired test matrix. Only those
*>           entries of A which are significant on output
*>           will be referenced (even if A is in packed or band
*>           storage format). The 'unoccupied corners' of A in
*>           band format will be zeroed out.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           on entry LDA specifies the first dimension of A as
*>           declared in the calling program.
*>           If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ).
*>           If PACK='C' or 'R', LDA must be at least 1.
*>           If PACK='B', or 'Q', LDA must be MIN ( KU+1, N )
*>           If PACK='Z', LDA must be at least KUU+KLL+1, where
*>           KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, M-1 )
*>           Not modified.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension ( N or M)
*>           Workspace. Not referenced if PIVTNG = 'N'. Changed on exit.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>           Error parameter on exit:
*>             0 => normal return
*>            -1 => M negative or unequal to N and SYM='S' or 'H'
*>            -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 => MODE neither -6, 0 nor 6 and RSIGN illegal string
*>           -11 => GRADE illegal string, or GRADE='E' and
*>                  M not equal to N, or GRADE='L', 'R', 'B' or 'E' and
*>                  SYM = 'S' or 'H'
*>           -12 => GRADE = 'E' and DL contains zero
*>           -13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H',
*>                  'S' or 'E'
*>           -14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E',
*>                  and MODEL neither -6, 0 nor 6
*>           -16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B'
*>           -17 => CONDR less than 1.0, GRADE='R' or 'B', and
*>                  MODER neither -6, 0 nor 6
*>           -18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and
*>                  M not equal to N, or PIVTNG='L' or 'R' and SYM='S'
*>                  or 'H'
*>           -19 => IPIVOT contains out of range number and
*>                  PIVTNG not equal to 'N'
*>           -20 => KL negative
*>           -21 => KU negative, or SYM='S' or 'H' and KU not equal to KL
*>           -22 => SPARSE not in range 0. to 1.
*>           -24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q'
*>                  and SYM='N', or PACK='C' and SYM='N' and either KL
*>                  not equal to 0 or N not equal to M, or PACK='R' and
*>                  SYM='N', and either KU not equal to 0 or N not equal
*>                  to M
*>           -26 => LDA too small
*>             1 => Error return from SLATM1 (computing D)
*>             2 => Cannot scale diagonal to DMAX (max. entry is 0)
*>             3 => Error return from SLATM1 (computing DL)
*>             4 => Error return from SLATM1 (computing DR)
*>             5 => ANORM is positive, but matrix constructed prior to
*>                  attempting to scale it to have norm ANORM, is zero
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup real_matgen
*
*  =====================================================================
      SUBROUTINE slatmr( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
     $                   RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER,
     $                   CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM,
     $                   PACK, A, LDA, IWORK, 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, GRADE, PACK, PIVTNG, RSIGN, SYM
      INTEGER            INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N
      REAL               ANORM, COND, CONDL, CONDR, DMAX, SPARSE
*     ..
*     .. Array Arguments ..
      INTEGER            IPIVOT( * ), ISEED( 4 ), IWORK( * )
      REAL               A( LDA, * ), D( * ), DL( * ), DR( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
      PARAMETER          ( ZERO = 0.0e0 )
      REAL               ONE
      parameter( one = 1.0e0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADPVT, DZERO, FULBND
      INTEGER            I, IDIST, IGRADE, IISUB, IPACK, IPVTNG, IRSIGN,
     $                   ISUB, ISYM, J, JJSUB, JSUB, K, KLL, KUU, MNMIN,
     $                   mnsub, mxsub, npvts
      REAL               ALPHA, ONORM, TEMP
*     ..
*     .. Local Arrays ..
      REAL               TEMPA( 1 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLANGB, SLANGE, SLANSB, SLANSP, SLANSY, SLATM2,
     $                   SLATM3
      EXTERNAL           lsame, slangb, slange, slansb, slansp, slansy,
     $                   slatm2, slatm3
*     ..
*     .. External Subroutines ..
      EXTERNAL           slatm1, sscal, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, min, mod
*     ..
*     .. 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, 'S' ) ) THEN
         isym = 0
      ELSE IF( lsame( sym, 'N' ) ) THEN
         isym = 1
      ELSE IF( lsame( sym, 'H' ) ) THEN
         isym = 0
      ELSE
         isym = -1
      END IF
*
*     Decode RSIGN
*
      IF( lsame( rsign, 'F' ) ) THEN
         irsign = 0
      ELSE IF( lsame( rsign, 'T' ) ) THEN
         irsign = 1
      ELSE
         irsign = -1
      END IF
*
*     Decode PIVTNG
*
      IF( lsame( pivtng, 'N' ) ) THEN
         ipvtng = 0
      ELSE IF( lsame( pivtng, ' ' ) ) THEN
         ipvtng = 0
      ELSE IF( lsame( pivtng, 'L' ) ) THEN
         ipvtng = 1
         npvts = m
      ELSE IF( lsame( pivtng, 'R' ) ) THEN
         ipvtng = 2
         npvts = n
      ELSE IF( lsame( pivtng, 'B' ) ) THEN
         ipvtng = 3
         npvts = min( n, m )
      ELSE IF( lsame( pivtng, 'F' ) ) THEN
         ipvtng = 3
         npvts = min( n, m )
      ELSE
         ipvtng = -1
      END IF
*
*     Decode GRADE
*
      IF( lsame( grade, 'N' ) ) THEN
         igrade = 0
      ELSE IF( lsame( grade, 'L' ) ) THEN
         igrade = 1
      ELSE IF( lsame( grade, 'R' ) ) THEN
         igrade = 2
      ELSE IF( lsame( grade, 'b' ) ) THEN
         IGRADE = 3
      ELSE IF( LSAME( GRADE, 'e' ) ) THEN
         IGRADE = 4
      ELSE IF( LSAME( GRADE, 'h.OR.' )  LSAME( GRADE, 's' ) ) THEN
         IGRADE = 5
      ELSE
         IGRADE = -1
      END IF
*
*     Decode PACK
*
      IF( LSAME( PACK, 'n' ) ) THEN
         IPACK = 0
      ELSE IF( LSAME( PACK, 'u' ) ) THEN
         IPACK = 1
      ELSE IF( LSAME( PACK, 'l' ) ) THEN
         IPACK = 2
      ELSE IF( LSAME( PACK, 'c' ) ) THEN
         IPACK = 3
      ELSE IF( LSAME( PACK, 'r' ) ) THEN
         IPACK = 4
      ELSE IF( LSAME( PACK, 'b' ) ) THEN
         IPACK = 5
      ELSE IF( LSAME( PACK, 'q' ) ) THEN
         IPACK = 6
      ELSE IF( LSAME( PACK, 'z' ) ) THEN
         IPACK = 7
      ELSE
         IPACK = -1
      END IF
*
*     Set certain internal parameters
*
      MNMIN = MIN( M, N )
      KLL = MIN( KL, M-1 )
      KUU = MIN( KU, N-1 )
*
*     If inv(DL) is used, check to see if DL has a zero entry.
*
      DZERO = .FALSE.
.EQ..AND..EQ.      IF( IGRADE4  MODEL0 ) THEN
         DO 10 I = 1, M
.EQ.            IF( DL( I )ZERO )
     $         DZERO = .TRUE.
   10    CONTINUE
      END IF
*
*     Check values in IPIVOT
*
      BADPVT = .FALSE.
.GT.      IF( IPVTNG0 ) THEN
         DO 20 J = 1, NPVTS
.LE..OR..GT.            IF( IPIVOT( J )0  IPIVOT( J )NPVTS )
     $         BADPVT = .TRUE.
   20    CONTINUE
      END IF
*
*     Set INFO if an error
*
.LT.      IF( M0 ) THEN
         INFO = -1
.NE..AND..EQ.      ELSE IF( MN  ISYM0 ) THEN
         INFO = -1
.LT.      ELSE IF( N0 ) THEN
         INFO = -2
.EQ.      ELSE IF( IDIST-1 ) THEN
         INFO = -3
.EQ.      ELSE IF( ISYM-1 ) THEN
         INFO = -5
.LT..OR..GT.      ELSE IF( MODE-6  MODE6 ) THEN
         INFO = -7
.NE..AND..NE..AND..NE..AND.      ELSE IF( ( MODE-6  MODE0  MODE6 ) 
.LT.     $         CONDONE ) THEN
         INFO = -8
.NE..AND..NE..AND..NE..AND.      ELSE IF( ( MODE-6  MODE0  MODE6 ) 
.EQ.     $         IRSIGN-1 ) THEN
         INFO = -10
.EQ..OR..EQ..AND..NE..OR.      ELSE IF( IGRADE-1  ( IGRADE4  MN ) 
.GE..AND..LE..AND..EQ.     $         ( ( IGRADE1  IGRADE4 )  ISYM0 ) )
     $          THEN
         INFO = -11
.EQ..AND.      ELSE IF( IGRADE4  DZERO ) THEN
         INFO = -12
.EQ..OR..EQ..OR..EQ..OR.      ELSE IF( ( IGRADE1  IGRADE3  IGRADE4 
.EQ..AND..LT..OR..GT.     $         IGRADE5 )  ( MODEL-6  MODEL6 ) )
     $          THEN
         INFO = -13
.EQ..OR..EQ..OR..EQ..OR.      ELSE IF( ( IGRADE1  IGRADE3  IGRADE4 
.EQ..AND..NE..AND..NE..AND.     $         IGRADE5 )  ( MODEL-6  MODEL0 
.NE..AND..LT.     $         MODEL6 )  CONDLONE ) THEN
         INFO = -14
.EQ..OR..EQ..AND.      ELSE IF( ( IGRADE2  IGRADE3 ) 
.LT..OR..GT.     $         ( MODER-6  MODER6 ) ) THEN
         INFO = -16
.EQ..OR..EQ..AND.      ELSE IF( ( IGRADE2  IGRADE3 ) 
.NE..AND..NE..AND..NE..AND.     $         ( MODER-6  MODER0  MODER6 ) 
.LT.     $         CONDRONE ) THEN
         INFO = -17
.EQ..OR..EQ..AND..NE..OR.      ELSE IF( IPVTNG-1  ( IPVTNG3  MN ) 
.EQ..OR..EQ..AND..EQ.     $         ( ( IPVTNG1  IPVTNG2 )  ISYM0 ) )
     $          THEN
         INFO = -18
.NE..AND.      ELSE IF( IPVTNG0  BADPVT ) THEN
         INFO = -19
.LT.      ELSE IF( KL0 ) THEN
         INFO = -20
.LT..OR..EQ..AND..NE.      ELSE IF( KU0  ( ISYM0  KLKU ) ) THEN
         INFO = -21
.LT..OR..GT.      ELSE IF( SPARSEZERO  SPARSEONE ) THEN
         INFO = -22
.EQ..OR..EQ..OR..EQ..OR.      ELSE IF( IPACK-1  ( ( IPACK1  IPACK2 
.EQ..OR..EQ..AND..EQ..OR.     $         IPACK5  IPACK6 )  ISYM1 ) 
.EQ..AND..EQ..AND..NE..OR..NE.     $         ( IPACK3  ISYM1  ( KL0  M
.OR..EQ..AND..EQ..AND..NE.     $         N ) )  ( IPACK4  ISYM1  ( KU
.OR..NE.     $         0  MN ) ) ) THEN
         INFO = -24
.EQ..OR..EQ..OR..EQ..AND.      ELSE IF( ( ( IPACK0  IPACK1  IPACK2 ) 
.LT..OR..EQ..OR..EQ.     $         LDAMAX( 1, M ) )  ( ( IPACK3  IPACK
.AND..LT..OR..EQ..OR..EQ.     $         4 )  LDA1 )  ( ( IPACK5  IPACK
.AND..LT..OR.     $         6 )  LDAKUU+1 ) 
.EQ..AND..LT.     $         ( IPACK7  LDAKLL+KUU+1 ) ) THEN
         INFO = -26
      END IF
*
.NE.      IF( INFO0 ) THEN
         CALL XERBLA( 'slatmr', -INFO )
         RETURN
      END IF
*
*     Decide if we can pivot consistently
*
      FULBND = .FALSE.
.EQ..AND..EQ.      IF( KUUN-1  KLLM-1 )
     $   FULBND = .TRUE.
*
*     Initialize random number generator
*
      DO 30 I = 1, 4
         ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 )
   30 CONTINUE
*
      ISEED( 4 ) = 2*( ISEED( 4 ) / 2 ) + 1
*
*     2)      Set up D, DL, and DR, if indicated.
*
*             Compute D according to COND and MODE
*
      CALL SLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, INFO )
.NE.      IF( INFO0 ) THEN
         INFO = 1
         RETURN
      END IF
.NE..AND..NE..AND..NE.      IF( MODE0  MODE-6  MODE6 ) THEN
*
*        Scale by DMAX
*
         TEMP = ABS( D( 1 ) )
         DO 40 I = 2, MNMIN
            TEMP = MAX( TEMP, ABS( D( I ) ) )
   40    CONTINUE
.EQ..AND..NE.         IF( TEMPZERO  DMAXZERO ) THEN
            INFO = 2
            RETURN
         END IF
.NE.         IF( TEMPZERO ) THEN
            ALPHA = DMAX / TEMP
         ELSE
            ALPHA = ONE
         END IF
         DO 50 I = 1, MNMIN
            D( I ) = ALPHA*D( I )
   50    CONTINUE
*
      END IF
*
*     Compute DL if grading set
*
.EQ..OR..EQ..OR..EQ..OR..EQ.      IF( IGRADE1  IGRADE3  IGRADE4  IGRADE
     $    5 ) THEN
         CALL SLATM1( MODEL, CONDL, 0, IDIST, ISEED, DL, M, INFO )
.NE.         IF( INFO0 ) THEN
            INFO = 3
            RETURN
         END IF
      END IF
*
*     Compute DR if grading set
*
.EQ..OR..EQ.      IF( IGRADE2  IGRADE3 ) THEN
         CALL SLATM1( MODER, CONDR, 0, IDIST, ISEED, DR, N, INFO )
.NE.         IF( INFO0 ) THEN
            INFO = 4
            RETURN
         END IF
      END IF
*
*     3)     Generate IWORK if pivoting
*
.GT.      IF( IPVTNG0 ) THEN
         DO 60 I = 1, NPVTS
            IWORK( I ) = I
   60    CONTINUE
         IF( FULBND ) THEN
            DO 70 I = 1, NPVTS
               K = IPIVOT( I )
               J = IWORK( I )
               IWORK( I ) = IWORK( K )
               IWORK( K ) = J
   70       CONTINUE
         ELSE
            DO 80 I = NPVTS, 1, -1
               K = IPIVOT( I )
               J = IWORK( I )
               IWORK( I ) = IWORK( K )
               IWORK( K ) = J
   80       CONTINUE
         END IF
      END IF
*
*     4)      Generate matrices for each kind of PACKing
*             Always sweep matrix columnwise (if symmetric, upper
*             half only) so that matrix generated does not depend
*             on PACK
*
      IF( FULBND ) THEN
*
*        Use SLATM3 so matrices generated with differing PIVOTing only
*        differ only in the order of their rows and/or columns.
*
.EQ.         IF( IPACK0 ) THEN
.EQ.            IF( ISYM0 ) THEN
               DO 100 J = 1, N
                  DO 90 I = 1, J
                     TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
     $                      IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                      IWORK, SPARSE )
                     A( ISUB, JSUB ) = TEMP
                     A( JSUB, ISUB ) = TEMP
   90             CONTINUE
  100          CONTINUE
.EQ.            ELSE IF( ISYM1 ) THEN
               DO 120 J = 1, N
                  DO 110 I = 1, M
                     TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
     $                      IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                      IWORK, SPARSE )
                     A( ISUB, JSUB ) = TEMP
  110             CONTINUE
  120          CONTINUE
            END IF
*
.EQ.         ELSE IF( IPACK1 ) THEN
*
            DO 140 J = 1, N
               DO 130 I = 1, J
                  TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
     $                   ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
     $                   SPARSE )
                  MNSUB = MIN( ISUB, JSUB )
                  MXSUB = MAX( ISUB, JSUB )
                  A( MNSUB, MXSUB ) = TEMP
.NE.                  IF( MNSUBMXSUB )
     $               A( MXSUB, MNSUB ) = ZERO
  130          CONTINUE
  140       CONTINUE
*
.EQ.         ELSE IF( IPACK2 ) THEN
*
            DO 160 J = 1, N
               DO 150 I = 1, J
                  TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
     $                   ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
     $                   SPARSE )
                  MNSUB = MIN( ISUB, JSUB )
                  MXSUB = MAX( ISUB, JSUB )
                  A( MXSUB, MNSUB ) = TEMP
.NE.                  IF( MNSUBMXSUB )
     $               A( MNSUB, MXSUB ) = ZERO
  150          CONTINUE
  160       CONTINUE
*
.EQ.         ELSE IF( IPACK3 ) THEN
*
            DO 180 J = 1, N
               DO 170 I = 1, J
                  TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
     $                   ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
     $                   SPARSE )
*
*                 Compute K = location of (ISUB,JSUB) entry in packed
*                 array
*
                  MNSUB = MIN( ISUB, JSUB )
                  MXSUB = MAX( ISUB, JSUB )
                  K = MXSUB*( MXSUB-1 ) / 2 + MNSUB
*
*                 Convert K to (IISUB,JJSUB) location
*
                  JJSUB = ( K-1 ) / LDA + 1
                  IISUB = K - LDA*( JJSUB-1 )
*
                  A( IISUB, JJSUB ) = TEMP
  170          CONTINUE
  180       CONTINUE
*
.EQ.         ELSE IF( IPACK4 ) THEN
*
            DO 200 J = 1, N
               DO 190 I = 1, J
                  TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
     $                   ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
     $                   SPARSE )
*
*                 Compute K = location of (I,J) entry in packed array
*
                  MNSUB = MIN( ISUB, JSUB )
                  MXSUB = MAX( ISUB, JSUB )
.EQ.                  IF( MNSUB1 ) THEN
                     K = MXSUB
                  ELSE
                     K = N*( N+1 ) / 2 - ( N-MNSUB+1 )*( N-MNSUB+2 ) /
     $                   2 + MXSUB - MNSUB + 1
                  END IF
*
*                 Convert K to (IISUB,JJSUB) location
*
                  JJSUB = ( K-1 ) / LDA + 1
                  IISUB = K - LDA*( JJSUB-1 )
*
                  A( IISUB, JJSUB ) = TEMP
  190          CONTINUE
  200       CONTINUE
*
.EQ.         ELSE IF( IPACK5 ) THEN
*
            DO 220 J = 1, N
               DO 210 I = J - KUU, J
.LT.                  IF( I1 ) THEN
                     A( J-I+1, I+N ) = ZERO
                  ELSE
                     TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
     $                      IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                      IWORK, SPARSE )
                     MNSUB = MIN( ISUB, JSUB )
                     MXSUB = MAX( ISUB, JSUB )
                     A( MXSUB-MNSUB+1, MNSUB ) = TEMP
                  END IF
  210          CONTINUE
  220       CONTINUE
*
.EQ.         ELSE IF( IPACK6 ) THEN
*
            DO 240 J = 1, N
               DO 230 I = J - KUU, J
                  TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
     $                   ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
     $                   SPARSE )
                  MNSUB = MIN( ISUB, JSUB )
                  MXSUB = MAX( ISUB, JSUB )
                  A( MNSUB-MXSUB+KUU+1, MXSUB ) = TEMP
  230          CONTINUE
  240       CONTINUE
*
.EQ.         ELSE IF( IPACK7 ) THEN
*
.EQ.            IF( ISYM0 ) THEN
               DO 260 J = 1, N
                  DO 250 I = J - KUU, J
                     TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
     $                      IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                      IWORK, SPARSE )
                     MNSUB = MIN( ISUB, JSUB )
                     MXSUB = MAX( ISUB, JSUB )
                     A( MNSUB-MXSUB+KUU+1, MXSUB ) = TEMP
.LT.                     IF( I1 )
     $                  A( J-I+1+KUU, I+N ) = ZERO
.GE..AND..NE.                     IF( I1  MNSUBMXSUB )
     $                  A( MXSUB-MNSUB+1+KUU, MNSUB ) = TEMP
  250             CONTINUE
  260          CONTINUE
.EQ.            ELSE IF( ISYM1 ) THEN
               DO 280 J = 1, N
                  DO 270 I = J - KUU, J + KLL
                     TEMP = SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
     $                      IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                      IWORK, SPARSE )
                     A( ISUB-JSUB+KUU+1, JSUB ) = TEMP
  270             CONTINUE
  280          CONTINUE
            END IF
*
         END IF
*
      ELSE
*
*        Use SLATM2
*
.EQ.         IF( IPACK0 ) THEN
.EQ.            IF( ISYM0 ) THEN
               DO 300 J = 1, N
                  DO 290 I = 1, J
                     A( I, J ) = SLATM2( M, N, I, J, KL, KU, IDIST,
     $                           ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                           IWORK, SPARSE )
                     A( J, I ) = A( I, J )
  290             CONTINUE
  300          CONTINUE
.EQ.            ELSE IF( ISYM1 ) THEN
               DO 320 J = 1, N
                  DO 310 I = 1, M
                     A( I, J ) = SLATM2( M, N, I, J, KL, KU, IDIST,
     $                           ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                           IWORK, SPARSE )
  310             CONTINUE
  320          CONTINUE
            END IF
*
.EQ.         ELSE IF( IPACK1 ) THEN
*
            DO 340 J = 1, N
               DO 330 I = 1, J
                  A( I, J ) = SLATM2( M, N, I, J, KL, KU, IDIST, ISEED,
     $                        D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
.NE.                  IF( IJ )
     $               A( J, I ) = ZERO
  330          CONTINUE
  340       CONTINUE
*
.EQ.         ELSE IF( IPACK2 ) THEN
*
            DO 360 J = 1, N
               DO 350 I = 1, J
                  A( J, I ) = SLATM2( M, N, I, J, KL, KU, IDIST, ISEED,
     $                        D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
.NE.                  IF( IJ )
     $               A( I, J ) = ZERO
  350          CONTINUE
  360       CONTINUE
*
.EQ.         ELSE IF( IPACK3 ) THEN
*
            ISUB = 0
            JSUB = 1
            DO 380 J = 1, N
               DO 370 I = 1, J
                  ISUB = ISUB + 1
.GT.                  IF( ISUBLDA ) THEN
                     ISUB = 1
                     JSUB = JSUB + 1
                  END IF
                  A( ISUB, JSUB ) = SLATM2( M, N, I, J, KL, KU, IDIST,
     $                              ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                              IWORK, SPARSE )
  370          CONTINUE
  380       CONTINUE
*
.EQ.         ELSE IF( IPACK4 ) THEN
*
.EQ.            IF( ISYM0 ) THEN
               DO 400 J = 1, N
                  DO 390 I = 1, J
*
*                    Compute K = location of (I,J) entry in packed array
*
.EQ.                     IF( I1 ) THEN
                        K = J
                     ELSE
                        K = N*( N+1 ) / 2 - ( N-I+1 )*( N-I+2 ) / 2 +
     $                      J - I + 1
                     END IF
*
*                    Convert K to (ISUB,JSUB) location
*
                     JSUB = ( K-1 ) / LDA + 1
                     ISUB = K - LDA*( JSUB-1 )
*
                     A( ISUB, JSUB ) = SLATM2( M, N, I, J, KL, KU,
     $                                 IDIST, ISEED, D, IGRADE, DL, DR,
     $                                 IPVTNG, IWORK, SPARSE )
  390             CONTINUE
  400          CONTINUE
            ELSE
               ISUB = 0
               JSUB = 1
               DO 420 J = 1, N
                  DO 410 I = J, M
                     ISUB = ISUB + 1
.GT.                     IF( ISUBLDA ) THEN
                        ISUB = 1
                        JSUB = JSUB + 1
                     END IF
                     A( ISUB, JSUB ) = SLATM2( M, N, I, J, KL, KU,
     $                                 IDIST, ISEED, D, IGRADE, DL, DR,
     $                                 IPVTNG, IWORK, SPARSE )
  410             CONTINUE
  420          CONTINUE
            END IF
*
.EQ.         ELSE IF( IPACK5 ) THEN
*
            DO 440 J = 1, N
               DO 430 I = J - KUU, J
.LT.                  IF( I1 ) THEN
                     A( J-I+1, I+N ) = ZERO
                  ELSE
                     A( J-I+1, I ) = SLATM2( M, N, I, J, KL, KU, IDIST,
     $                               ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                               IWORK, SPARSE )
                  END IF
  430          CONTINUE
  440       CONTINUE
*
.EQ.         ELSE IF( IPACK6 ) THEN
*
            DO 460 J = 1, N
               DO 450 I = J - KUU, J
                  A( I-J+KUU+1, J ) = SLATM2( M, N, I, J, KL, KU, IDIST,
     $                                ISEED, D, IGRADE, DL, DR, IPVTNG,
     $                                IWORK, SPARSE )
  450          CONTINUE
  460       CONTINUE
*
.EQ.         ELSE IF( IPACK7 ) THEN
*
.EQ.            IF( ISYM0 ) THEN
               DO 480 J = 1, N
                  DO 470 I = J - KUU, J
                     A( I-J+KUU+1, J ) = SLATM2( M, N, I, J, KL, KU,
     $                                   IDIST, ISEED, D, IGRADE, DL,
     $                                   DR, IPVTNG, IWORK, SPARSE )
.LT.                     IF( I1 )
     $                  A( J-I+1+KUU, I+N ) = ZERO
.GE..AND..NE.                     IF( I1  IJ )
     $                  A( J-I+1+KUU, I ) = A( I-J+KUU+1, J )
  470             CONTINUE
  480          CONTINUE
.EQ.            ELSE IF( ISYM1 ) THEN
               DO 500 J = 1, N
                  DO 490 I = J - KUU, J + KLL
                     A( I-J+KUU+1, J ) = SLATM2( M, N, I, J, KL, KU,
     $                                   IDIST, ISEED, D, IGRADE, DL,
     $                                   DR, IPVTNG, IWORK, SPARSE )
  490             CONTINUE
  500          CONTINUE
            END IF
*
         END IF
*
      END IF
*
*     5)      Scaling the norm
*
.EQ.      IF( IPACK0 ) THEN
         ONORM = SLANGE( 'm', M, N, A, LDA, TEMPA )
.EQ.      ELSE IF( IPACK1 ) THEN
         ONORM = SLANSY( 'm', 'u', N, A, LDA, TEMPA )
.EQ.      ELSE IF( IPACK2 ) THEN
         ONORM = SLANSY( 'm', 'l', N, A, LDA, TEMPA )
.EQ.      ELSE IF( IPACK3 ) THEN
         ONORM = SLANSP( 'm', 'u', N, A, TEMPA )
.EQ.      ELSE IF( IPACK4 ) THEN
         ONORM = SLANSP( 'm', 'l', N, A, TEMPA )
.EQ.      ELSE IF( IPACK5 ) THEN
         ONORM = SLANSB( 'm', 'l', N, KLL, A, LDA, TEMPA )
.EQ.      ELSE IF( IPACK6 ) THEN
         ONORM = SLANSB( 'm', 'u', N, KUU, A, LDA, TEMPA )
.EQ.      ELSE IF( IPACK7 ) THEN
         ONORM = SLANGB( 'm', N, KLL, KUU, A, LDA, TEMPA )
      END IF
*
.GE.      IF( ANORMZERO ) THEN
*
.GT..AND..EQ.         IF( ANORMZERO  ONORMZERO ) THEN
*
*           Desired scaling impossible
*
            INFO = 5
            RETURN
*
.GT..AND..LT..OR.         ELSE IF( ( ANORMONE  ONORMONE ) 
.LT..AND..GT.     $            ( ANORMONE  ONORMONE ) ) THEN
*
*           Scale carefully to avoid over / underflow
*
.LE.            IF( IPACK2 ) THEN
               DO 510 J = 1, N
                  CALL SSCAL( M, ONE / ONORM, A( 1, J ), 1 )
                  CALL SSCAL( M, ANORM, A( 1, J ), 1 )
  510          CONTINUE
*
.EQ..OR..EQ.            ELSE IF( IPACK3  IPACK4 ) THEN
*
               CALL SSCAL( N*( N+1 ) / 2, ONE / ONORM, A, 1 )
               CALL SSCAL( N*( N+1 ) / 2, ANORM, A, 1 )
*
.GE.            ELSE IF( IPACK5 ) THEN
*
               DO 520 J = 1, N
                  CALL SSCAL( KLL+KUU+1, ONE / ONORM, A( 1, J ), 1 )
                  CALL SSCAL( KLL+KUU+1, ANORM, A( 1, J ), 1 )
  520          CONTINUE
*
            END IF
*
         ELSE
*
*           Scale straightforwardly
*
.LE.            IF( IPACK2 ) THEN
               DO 530 J = 1, N
                  CALL SSCAL( M, ANORM / ONORM, A( 1, J ), 1 )
  530          CONTINUE
*
.EQ..OR..EQ.            ELSE IF( IPACK3  IPACK4 ) THEN
*
               CALL SSCAL( N*( N+1 ) / 2, ANORM / ONORM, A, 1 )
*
.GE.            ELSE IF( IPACK5 ) THEN
*
               DO 540 J = 1, N
                  CALL SSCAL( KLL+KUU+1, ANORM / ONORM, A( 1, J ), 1 )
  540          CONTINUE
            END IF
*
         END IF
*
      END IF
*
*     End of SLATMR
*
      END