dlatmr.f

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*> \brief \b DLATMR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLATMR( 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
*       DOUBLE PRECISION   ANORM, COND, CONDL, CONDR, DMAX, SPARSE
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIVOT( * ), ISEED( 4 ), IWORK( * )
*       DOUBLE PRECISION   A( LDA, * ), D( * ), DL( * ), DR( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    DLATMR generates random matrices of various types for testing
*>    LAPACK programs.
*>
*>    DLATMR 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 DLATMR differ only in the PACK parameter,
*>          they will generate mathematically equivalent matrices.
*>
*>          If two calls to DLATMR 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 DLATMR
*>           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,out] D
*> \verbatim
*>          D is DOUBLE PRECISION 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 DOUBLE PRECISION
*>           On entry, used as described under MODE above.
*>           If used, it must be >= 1. Not modified.
*> \endverbatim
*>
*> \param[in] DMAX
*> \verbatim
*>          DMAX is DOUBLE PRECISION
*>           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 DOUBLE PRECISION 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 DOUBLE PRECISION
*>           When MODEL is not zero, this specifies the condition number
*>           of the computed DL.  Not modified.
*> \endverbatim
*>
*> \param[in,out] DR
*> \verbatim
*>          DR is DOUBLE PRECISION 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 DOUBLE PRECISION
*>           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 DLATMR 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, DLATMR
*>           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] SPARSE
*> \verbatim
*>          SPARSE is DOUBLE PRECISION
*>           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] 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] ANORM
*> \verbatim
*>          ANORM is DOUBLE PRECISION
*>           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 DLATMR differ only in the PACK parameter,
*>           they will generate mathematically equivalent matrices.
*>           Not modified.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*>          A is DOUBLE PRECISION 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, N-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 DLATM1 (computing D)
*>             2 => Cannot scale diagonal to DMAX (max. entry is 0)
*>             3 => Error return from DLATM1 (computing DL)
*>             4 => Error return from DLATM1 (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. 
*
*> \date November 2011
*
*> \ingroup double_matgen
*
*  =====================================================================
      SUBROUTINE dlatmr( 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 (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          DIST, GRADE, PACK, PIVTNG, RSIGN, SYM
      INTEGER            INFO, KL, KU, LDA, M, MODE, MODEL, MODER, N
      DOUBLE PRECISION   ANORM, COND, CONDL, CONDR, DMAX, SPARSE
*     ..
*     .. Array Arguments ..
      INTEGER            IPIVOT( * ), ISEED( 4 ), IWORK( * )
      DOUBLE PRECISION   A( lda, * ), D( * ), DL( * ), DR( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter                ( zero = 0.0d0 )
      DOUBLE PRECISION   ONE
      parameter                ( one = 1.0d0 )
*     ..
*     .. 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
      DOUBLE PRECISION   ALPHA, ONORM, TEMP
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   TEMPA( 1 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLANGB, DLANGE, DLANSB, DLANSP, DLANSY, DLATM2,
     $                   dlatm3
      EXTERNAL           lsame, dlangb, dlange, dlansb, dlansp, dlansy,
     $                   dlatm2, dlatm3
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlatm1, dscal, 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.
      IF( igrade.EQ.4 .AND. model.EQ.0 ) THEN
         DO 10 i = 1, m
            IF( dl( i ).EQ.zero )
     $         dzero = .true.
   10    CONTINUE
      END IF
*
*     Check values in IPIVOT
*
      badpvt = .false.
      IF( ipvtng.GT.0 ) THEN
         DO 20 j = 1, npvts
            IF( ipivot( j ).LE.0 .OR. ipivot( j ).GT.npvts )
     $         badpvt = .true.
   20    CONTINUE
      END IF
*
*     Set INFO if an error
*
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( m.NE.n .AND. isym.EQ.0 ) 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( mode.LT.-6 .OR. mode.GT.6 ) THEN
         info = -7
      ELSE IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
     $         cond.LT.one ) THEN
         info = -8
      ELSE IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
     $         irsign.EQ.-1 ) THEN
         info = -10
      ELSE IF( igrade.EQ.-1 .OR. ( igrade.EQ.4 .AND. m.NE.n ) .OR.
     $         ( ( igrade.GE.1 .AND. igrade.LE.4 ) .AND. isym.EQ.0 ) )
     $          THEN
         info = -11
      ELSE IF( igrade.EQ.4 .AND. dzero ) THEN
         info = -12
      ELSE IF( ( igrade.EQ.1 .OR. igrade.EQ.3 .OR. igrade.EQ.4 .OR.
     $         igrade.EQ.5 ) .AND. ( model.LT.-6 .OR. model.GT.6 ) )
     $          THEN
         info = -13
      ELSE IF( ( igrade.EQ.1 .OR. igrade.EQ.3 .OR. igrade.EQ.4 .OR.
     $         igrade.EQ.5 ) .AND. ( model.NE.-6 .AND. model.NE.0 .AND.
     $         model.NE.6 ) .AND. condl.LT.one ) THEN
         info = -14
      ELSE IF( ( igrade.EQ.2 .OR. igrade.EQ.3 ) .AND.
     $         ( moder.LT.-6 .OR. moder.GT.6 ) ) THEN
         info = -16
      ELSE IF( ( igrade.EQ.2 .OR. igrade.EQ.3 ) .AND.
     $         ( moder.NE.-6 .AND. moder.NE.0 .AND. moder.NE.6 ) .AND.
     $         condr.LT.one ) THEN
         info = -17
      ELSE IF( ipvtng.EQ.-1 .OR. ( ipvtng.EQ.3 .AND. m.NE.n ) .OR.
     $         ( ( ipvtng.EQ.1 .OR. ipvtng.EQ.2 ) .AND. isym.EQ.0 ) )
     $          THEN
         info = -18
      ELSE IF( ipvtng.NE.0 .AND. badpvt ) THEN
         info = -19
      ELSE IF( kl.LT.0 ) THEN
         info = -20
      ELSE IF( ku.LT.0 .OR. ( isym.EQ.0 .AND. kl.NE.ku ) ) THEN
         info = -21
      ELSE IF( sparse.LT.zero .OR. sparse.GT.one ) THEN
         info = -22
      ELSE IF( ipack.EQ.-1 .OR. ( ( ipack.EQ.1 .OR. ipack.EQ.2 .OR.
     $         ipack.EQ.5 .OR. ipack.EQ.6 ) .AND. isym.EQ.1 ) .OR.
     $         ( ipack.EQ.3 .AND. isym.EQ.1 .AND. ( kl.NE.0 .OR. m.NE.
     $         n ) ) .OR. ( ipack.EQ.4 .AND. isym.EQ.1 .AND. ( ku.NE.
     $         0 .OR. m.NE.n ) ) ) THEN
         info = -24
      ELSE IF( ( ( ipack.EQ.0 .OR. ipack.EQ.1 .OR. ipack.EQ.2 ) .AND.
     $         lda.LT.max( 1, m ) ) .OR. ( ( ipack.EQ.3 .OR. ipack.EQ.
     $         4 ) .AND. lda.LT.1 ) .OR. ( ( ipack.EQ.5 .OR. ipack.EQ.
     $         6 ) .AND. lda.LT.kuu+1 ) .OR.
     $         ( ipack.EQ.7 .AND. lda.LT.kll+kuu+1 ) ) THEN
         info = -26
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DLATMR', -info )
         RETURN
      END IF
*
*     Decide if we can pivot consistently
*
      fulbnd = .false.
      IF( kuu.EQ.n-1 .AND. kll.EQ.m-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 dlatm1( mode, cond, irsign, idist, iseed, d, mnmin, info )
      IF( info.NE.0 ) THEN
         info = 1
         RETURN
      END IF
      IF( mode.NE.0 .AND. mode.NE.-6 .AND. mode.NE.6 ) THEN
*
*        Scale by DMAX
*
         temp = abs( d( 1 ) )
         DO 40 i = 2, mnmin
            temp = max( temp, abs( d( i ) ) )
   40    CONTINUE
         IF( temp.EQ.zero .AND. dmax.NE.zero ) THEN
            info = 2
            RETURN
         END IF
         IF( temp.NE.zero ) 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
*
      IF( igrade.EQ.1 .OR. igrade.EQ.3 .OR. igrade.EQ.4 .OR. igrade.EQ.
     $    5 ) THEN
         CALL dlatm1( model, condl, 0, idist, iseed, dl, m, info )
         IF( info.NE.0 ) THEN
            info = 3
            RETURN
         END IF
      END IF
*
*     Compute DR if grading set
*
      IF( igrade.EQ.2 .OR. igrade.EQ.3 ) THEN
         CALL dlatm1( moder, condr, 0, idist, iseed, dr, n, info )
         IF( info.NE.0 ) THEN
            info = 4
            RETURN
         END IF
      END IF
*
*     3)     Generate IWORK if pivoting
*
      IF( ipvtng.GT.0 ) 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 DLATM3 so matrices generated with differing PIVOTing only
*        differ only in the order of their rows and/or columns.
*
         IF( ipack.EQ.0 ) THEN
            IF( isym.EQ.0 ) THEN
               DO 100 j = 1, n
                  DO 90 i = 1, j
                     temp = dlatm3( 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
            ELSE IF( isym.EQ.1 ) THEN
               DO 120 j = 1, n
                  DO 110 i = 1, m
                     temp = dlatm3( 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
*
         ELSE IF( ipack.EQ.1 ) THEN
*
            DO 140 j = 1, n
               DO 130 i = 1, j
                  temp = dlatm3( 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
                  IF( mnsub.NE.mxsub )
     $               a( mxsub, mnsub ) = zero
  130          CONTINUE
  140       CONTINUE
*
         ELSE IF( ipack.EQ.2 ) THEN
*
            DO 160 j = 1, n
               DO 150 i = 1, j
                  temp = dlatm3( 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
                  IF( mnsub.NE.mxsub )
     $               a( mnsub, mxsub ) = zero
  150          CONTINUE
  160       CONTINUE
*
         ELSE IF( ipack.EQ.3 ) THEN
*
            DO 180 j = 1, n
               DO 170 i = 1, j
                  temp = dlatm3( 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
*
         ELSE IF( ipack.EQ.4 ) THEN
*
            DO 200 j = 1, n
               DO 190 i = 1, j
                  temp = dlatm3( 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 )
                  IF( mnsub.EQ.1 ) 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
*
         ELSE IF( ipack.EQ.5 ) THEN
*
            DO 220 j = 1, n
               DO 210 i = j - kuu, j
                  IF( i.LT.1 ) THEN
                     a( j-i+1, i+n ) = zero
                  ELSE
                     temp = dlatm3( 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
*
         ELSE IF( ipack.EQ.6 ) THEN
*
            DO 240 j = 1, n
               DO 230 i = j - kuu, j
                  temp = dlatm3( 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
*
         ELSE IF( ipack.EQ.7 ) THEN
*
            IF( isym.EQ.0 ) THEN
               DO 260 j = 1, n
                  DO 250 i = j - kuu, j
                     temp = dlatm3( 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
                     IF( i.LT.1 )
     $                  a( j-i+1+kuu, i+n ) = zero
                     IF( i.GE.1 .AND. mnsub.NE.mxsub )
     $                  a( mxsub-mnsub+1+kuu, mnsub ) = temp
  250             CONTINUE
  260          CONTINUE
            ELSE IF( isym.EQ.1 ) THEN
               DO 280 j = 1, n
                  DO 270 i = j - kuu, j + kll
                     temp = dlatm3( 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 DLATM2
*
         IF( ipack.EQ.0 ) THEN
            IF( isym.EQ.0 ) THEN
               DO 300 j = 1, n
                  DO 290 i = 1, j
                     a( i, j ) = dlatm2( 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
            ELSE IF( isym.EQ.1 ) THEN
               DO 320 j = 1, n
                  DO 310 i = 1, m
                     a( i, j ) = dlatm2( m, n, i, j, kl, ku, idist,
     $                           iseed, d, igrade, dl, dr, ipvtng,
     $                           iwork, sparse )
  310             CONTINUE
  320          CONTINUE
            END IF
*
         ELSE IF( ipack.EQ.1 ) THEN
*
            DO 340 j = 1, n
               DO 330 i = 1, j
                  a( i, j ) = dlatm2( m, n, i, j, kl, ku, idist, iseed,
     $                        d, igrade, dl, dr, ipvtng, iwork, sparse )
                  IF( i.NE.j )
     $               a( j, i ) = zero
  330          CONTINUE
  340       CONTINUE
*
         ELSE IF( ipack.EQ.2 ) THEN
*
            DO 360 j = 1, n
               DO 350 i = 1, j
                  a( j, i ) = dlatm2( m, n, i, j, kl, ku, idist, iseed,
     $                        d, igrade, dl, dr, ipvtng, iwork, sparse )
                  IF( i.NE.j )
     $               a( i, j ) = zero
  350          CONTINUE
  360       CONTINUE
*
         ELSE IF( ipack.EQ.3 ) THEN
*
            isub = 0
            jsub = 1
            DO 380 j = 1, n
               DO 370 i = 1, j
                  isub = isub + 1
                  IF( isub.GT.lda ) THEN
                     isub = 1
                     jsub = jsub + 1
                  END IF
                  a( isub, jsub ) = dlatm2( m, n, i, j, kl, ku, idist,
     $                              iseed, d, igrade, dl, dr, ipvtng,
     $                              iwork, sparse )
  370          CONTINUE
  380       CONTINUE
*
         ELSE IF( ipack.EQ.4 ) THEN
*
            IF( isym.EQ.0 ) THEN
               DO 400 j = 1, n
                  DO 390 i = 1, j
*
*                    Compute K = location of (I,J) entry in packed array
*
                     IF( i.EQ.1 ) 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 ) = dlatm2( 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
                     IF( isub.GT.lda ) THEN
                        isub = 1
                        jsub = jsub + 1
                     END IF
                     a( isub, jsub ) = dlatm2( m, n, i, j, kl, ku,
     $                                 idist, iseed, d, igrade, dl, dr,
     $                                 ipvtng, iwork, sparse )
  410             CONTINUE
  420          CONTINUE
            END IF
*
         ELSE IF( ipack.EQ.5 ) THEN
*
            DO 440 j = 1, n
               DO 430 i = j - kuu, j
                  IF( i.LT.1 ) THEN
                     a( j-i+1, i+n ) = zero
                  ELSE
                     a( j-i+1, i ) = dlatm2( m, n, i, j, kl, ku, idist,
     $                               iseed, d, igrade, dl, dr, ipvtng,
     $                               iwork, sparse )
                  END IF
  430          CONTINUE
  440       CONTINUE
*
         ELSE IF( ipack.EQ.6 ) THEN
*
            DO 460 j = 1, n
               DO 450 i = j - kuu, j
                  a( i-j+kuu+1, j ) = dlatm2( m, n, i, j, kl, ku, idist,
     $                                iseed, d, igrade, dl, dr, ipvtng,
     $                                iwork, sparse )
  450          CONTINUE
  460       CONTINUE
*
         ELSE IF( ipack.EQ.7 ) THEN
*
            IF( isym.EQ.0 ) THEN
               DO 480 j = 1, n
                  DO 470 i = j - kuu, j
                     a( i-j+kuu+1, j ) = dlatm2( m, n, i, j, kl, ku,
     $                                   idist, iseed, d, igrade, dl,
     $                                   dr, ipvtng, iwork, sparse )
                     IF( i.LT.1 )
     $                  a( j-i+1+kuu, i+n ) = zero
                     IF( i.GE.1 .AND. i.NE.j )
     $                  a( j-i+1+kuu, i ) = a( i-j+kuu+1, j )
  470             CONTINUE
  480          CONTINUE
            ELSE IF( isym.EQ.1 ) THEN
               DO 500 j = 1, n
                  DO 490 i = j - kuu, j + kll
                     a( i-j+kuu+1, j ) = dlatm2( 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
*
      IF( ipack.EQ.0 ) THEN
         onorm = dlange( 'M', m, n, a, lda, tempa )
      ELSE IF( ipack.EQ.1 ) THEN
         onorm = dlansy( 'M', 'U', n, a, lda, tempa )
      ELSE IF( ipack.EQ.2 ) THEN
         onorm = dlansy( 'M', 'L', n, a, lda, tempa )
      ELSE IF( ipack.EQ.3 ) THEN
         onorm = dlansp( 'M', 'U', n, a, tempa )
      ELSE IF( ipack.EQ.4 ) THEN
         onorm = dlansp( 'M', 'L', n, a, tempa )
      ELSE IF( ipack.EQ.5 ) THEN
         onorm = dlansb( 'M', 'L', n, kll, a, lda, tempa )
      ELSE IF( ipack.EQ.6 ) THEN
         onorm = dlansb( 'M', 'U', n, kuu, a, lda, tempa )
      ELSE IF( ipack.EQ.7 ) THEN
         onorm = dlangb( 'M', n, kll, kuu, a, lda, tempa )
      END IF
*
      IF( anorm.GE.zero ) THEN
*
         IF( anorm.GT.zero .AND. onorm.EQ.zero ) THEN
*
*           Desired scaling impossible
*
            info = 5
            RETURN
*
         ELSE IF( ( anorm.GT.one .AND. onorm.LT.one ) .OR.
     $            ( anorm.LT.one .AND. onorm.GT.one ) ) THEN
*
*           Scale carefully to avoid over / underflow
*
            IF( ipack.LE.2 ) THEN
               DO 510 j = 1, n
                  CALL dscal( m, one / onorm, a( 1, j ), 1 )
                  CALL dscal( m, anorm, a( 1, j ), 1 )
  510          CONTINUE
*
            ELSE IF( ipack.EQ.3 .OR. ipack.EQ.4 ) THEN
*
               CALL dscal( n*( n+1 ) / 2, one / onorm, a, 1 )
               CALL dscal( n*( n+1 ) / 2, anorm, a, 1 )
*
            ELSE IF( ipack.GE.5 ) THEN
*
               DO 520 j = 1, n
                  CALL dscal( kll+kuu+1, one / onorm, a( 1, j ), 1 )
                  CALL dscal( kll+kuu+1, anorm, a( 1, j ), 1 )
  520          CONTINUE
*
            END IF
*
         ELSE
*
*           Scale straightforwardly
*
            IF( ipack.LE.2 ) THEN
               DO 530 j = 1, n
                  CALL dscal( m, anorm / onorm, a( 1, j ), 1 )
  530          CONTINUE
*
            ELSE IF( ipack.EQ.3 .OR. ipack.EQ.4 ) THEN
*
               CALL dscal( n*( n+1 ) / 2, anorm / onorm, a, 1 )
*
            ELSE IF( ipack.GE.5 ) THEN
*
               DO 540 j = 1, n
                  CALL dscal( kll+kuu+1, anorm / onorm, a( 1, j ), 1 )
  540          CONTINUE
            END IF
*
         END IF
*
      END IF
*
*     End of DLATMR
*
      END