1 files changed, 1047 insertions, 0 deletions

diff --git a/TESTING/MATGEN/slatmt.f b/TESTING/MATGEN/slatmt.f
new file mode 100644
index 00000000..c0119cc5
--- /dev/null
+++ b/TESTING/MATGEN/slatmt.f
@@ -0,0 +1,1047 @@
+      SUBROUTINE SLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
+     $                   RANK, KL, KU, PACK, A, LDA, WORK, INFO )
+*
+*  -- LAPACK test routine (version 3.1) --
+*     Craig Lucas, University of Manchester / NAG Ltd.
+*     October, 2008
+*
+*     .. Scalar Arguments ..
+      REAL               COND, DMAX
+      INTEGER            INFO, KL, KU, LDA, M, MODE, N, RANK
+      CHARACTER          DIST, PACK, SYM
+*     ..
+*     .. Array Arguments ..
+      REAL               A( LDA, * ), D( * ), WORK( * )
+      INTEGER            ISEED( 4 )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*     SLATMT generates random matrices with specified singular values
+*     (or symmetric/hermitian with specified eigenvalues)
+*     for testing LAPACK programs.
+*
+*     SLATMT 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 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 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 symmetric)
+*          zero out lower half (if symmetric)
+*          store the upper half columnwise (if symmetric or upper
+*                triangular)
+*          store the lower half columnwise (if symmetric or lower
+*                triangular)
+*          store the lower triangle in banded format (if symmetric
+*                or lower triangular)
+*          store the upper triangle in banded format (if symmetric
+*                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.
+*
+*  Arguments
+*  =========
+*
+*  M      - INTEGER
+*           The number of rows of A. Not modified.
+*
+*  N      - INTEGER
+*           The number of columns of A. Not modified.
+*
+*  DIST   - 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.
+*
+*  ISEED  - 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 SLATMT
+*           to continue the same random number sequence.
+*           Changed on exit.
+*
+*  SYM    - CHARACTER*1
+*           If SYM='S' or 'H', the generated matrix is symmetric, with
+*             eigenvalues specified by D, COND, MODE, and DMAX; they
+*             may be positive, negative, or zero.
+*           If SYM='P', the generated matrix is symmetric, 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.
+*           Not modified.
+*
+*  D      - 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.
+*
+*  MODE   - 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:RANK)=1.0/COND
+*           MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
+*           MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-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='S' or '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.
+*
+*  COND   - REAL
+*           On entry, this is used as described under MODE above.
+*           If used, it must be >= 1. Not modified.
+*
+*  DMAX   - 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.
+*
+*  RANK   - INTEGER
+*           The rank of matrix to be generated for modes 1,2,3 only.
+*           D( RANK+1:N ) = 0.
+*           Not modified.
+*
+*  KL     - 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.
+*           Not modified.
+*
+*  KU     - 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.
+*           Not modified.
+*
+*  PACK   - CHARACTER*1
+*           This 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 the matrix is symmetric or upper triangular)
+*           'R' => store the lower triangle columnwise
+*                  (only if the matrix is symmetric or lower triangular)
+*           'B' => store the lower triangle in band storage scheme
+*                  (only if matrix symmetric or lower triangular)
+*           'Q' => store the upper triangle in band storage scheme
+*                  (only if matrix symmetric 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 or TB     - use 'B' or 'Q'
+*           PP, SP or TP     - use 'C' or 'R'
+*
+*           If two calls to SLATMT differ only in the PACK parameter,
+*           they will generate mathematically equivalent matrices.
+*           Not modified.
+*
+*  A      - REAL 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.
+*
+*  LDA    - 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.
+*
+*  WORK   - REAL array, dimension ( 3*MAX( N , M ) )
+*           Workspace.
+*           Modified.
+*
+*  INFO   - 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='S' or 'H' and KU 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 SLATM7
+*            2  => Cannot scale to DMAX (max. sing. value is 0)
+*            3  => Error return from SLAGGE or SLAGSY
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      REAL               ZERO
+      PARAMETER          ( ZERO = 0.0E0 )
+      REAL               ONE
+      PARAMETER          ( ONE = 1.0E0 )
+      REAL               TWOPI
+      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+*     ..
+*     .. Local Scalars ..
+      REAL               ALPHA, ANGLE, C, DUMMY, EXTRA, S, TEMP
+      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
+      LOGICAL            GIVENS, ILEXTR, ILTEMP, TOPDWN
+*     ..
+*     .. External Functions ..
+      REAL               SLARND
+      LOGICAL            LSAME
+      EXTERNAL           SLARND, LSAME
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           SLATM7, SCOPY, SLAGGE, SLAGSY, SLAROT,
+     $                   SLARTG, SLASET, SSCAL, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, 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
+      ELSE IF( LSAME( SYM, 'P' ) ) THEN
+         ISYM = 2
+         IRSIGN = 0
+      ELSE IF( LSAME( SYM, 'S' ) ) THEN
+         ISYM = 2
+         IRSIGN = 1
+      ELSE IF( LSAME( SYM, 'H' ) ) THEN
+         ISYM = 2
+         IRSIGN = 1
+      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( 'SLATMT', -INFO )
+         RETURN
+      END IF
+*
+*     Initialize random number generator
+*
+      DO 100 I = 1, 4
+         ISEED( I ) = MOD( ABS( ISEED( I ) ), 4096 )
+  100 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 SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, MNMIN, RANK,
+     $             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( RANK ) ) ) 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 110 I = 2, RANK
+            TEMP = MAX( TEMP, ABS( D( I ) ) )
+  110    CONTINUE
+*
+         IF( TEMP.GT.ZERO ) THEN
+            ALPHA = DMAX / TEMP
+         ELSE
+            INFO = 2
+            RETURN
+         END IF
+*
+         CALL SSCAL( RANK, ALPHA, D, 1 )
+*
+      END IF
+*
+*     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, SY, GB, or SB,
+*               upper or lower triangle or both,
+*               the (i,j)-th element is in
+*               A( i - ISKEW*j + IOFFST, j )
+*
+      IF( IPACK.GT.4 ) THEN
+         ILDA = LDA - 1
+         ISKEW = 1
+         IF( IPACK.GT.5 ) 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
+      CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
+*
+*     Diagonal Matrix -- We are done, unless it
+*     is to be stored SP/PP/TP (PACK='R' or 'C')
+*
+      IF( LLB.EQ.0 .AND. UUB.EQ.0 ) THEN
+         CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 )
+         IF( IPACK.LE.2 .OR. IPACK.GE.5 )
+     $      IPACKG = IPACK
+*
+      ELSE IF( GIVENS ) THEN
+*
+*        Check whether to use Givens rotations,
+*        Householder transformations, or nothing.
+*
+         IF( ISYM.EQ.1 ) THEN
+*
+*           Non-symmetric -- A = U D V
+*
+            IF( IPACK.GT.4 ) THEN
+               IPACKG = IPACK
+            ELSE
+               IPACKG = 0
+            END IF
+*
+            CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFST, 1 ), ILDA+1 )
+*
+            IF( TOPDWN ) THEN
+               JKL = 0
+               DO 140 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 130 JR = 1, MIN( M+JKU, N ) + JKL - 1
+                     EXTRA = ZERO
+                     ANGLE = TWOPI*SLARND( 1, ISEED )
+                     C = COS( ANGLE )
+                     S = SIN( ANGLE )
+                     ICOL = MAX( 1, JR-JKL )
+                     IF( JR.LT.M ) THEN
+                        IL = MIN( N, JR+JKU ) + 1 - ICOL
+                        CALL SLAROT( .TRUE., JR.GT.JKL, .FALSE., IL, C,
+     $                               S, A( JR-ISKEW*ICOL+IOFFST, ICOL ),
+     $                               ILDA, EXTRA, DUMMY )
+                     END IF
+*
+*                    Chase "EXTRA" back up
+*
+                     IR = JR
+                     IC = ICOL
+                     DO 120 JCH = JR - JKL, 1, -JKL - JKU
+                        IF( IR.LT.M ) THEN
+                           CALL SLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST,
+     $                                  IC+1 ), EXTRA, C, S, DUMMY )
+                        END IF
+                        IROW = MAX( 1, JCH-JKU )
+                        IL = IR + 2 - IROW
+                        TEMP = ZERO
+                        ILTEMP = JCH.GT.JKU
+                        CALL SLAROT( .FALSE., ILTEMP, .TRUE., IL, C, -S,
+     $                               A( IROW-ISKEW*IC+IOFFST, IC ),
+     $                               ILDA, TEMP, EXTRA )
+                        IF( ILTEMP ) THEN
+                           CALL SLARTG( A( IROW+1-ISKEW*( IC+1 )+IOFFST,
+     $                                  IC+1 ), TEMP, C, S, DUMMY )
+                           ICOL = MAX( 1, JCH-JKU-JKL )
+                           IL = IC + 2 - ICOL
+                           EXTRA = ZERO
+                           CALL SLAROT( .TRUE., JCH.GT.JKU+JKL, .TRUE.,
+     $                                  IL, C, -S, A( IROW-ISKEW*ICOL+
+     $                                  IOFFST, ICOL ), ILDA, EXTRA,
+     $                                  TEMP )
+                           IC = ICOL
+                           IR = IROW
+                        END IF
+  120                CONTINUE
+  130             CONTINUE
+  140          CONTINUE
+*
+               JKU = UUB
+               DO 170 JKL = 1, LLB
+*
+*                 Transform from bandwidth JKL-1, JKU to JKL, JKU
+*
+                  DO 160 JC = 1, MIN( N+JKL, M ) + JKU - 1
+                     EXTRA = ZERO
+                     ANGLE = TWOPI*SLARND( 1, ISEED )
+                     C = COS( ANGLE )
+                     S = SIN( ANGLE )
+                     IROW = MAX( 1, JC-JKU )
+                     IF( JC.LT.N ) THEN
+                        IL = MIN( M, JC+JKL ) + 1 - IROW
+                        CALL SLAROT( .FALSE., JC.GT.JKU, .FALSE., IL, C,
+     $                               S, A( IROW-ISKEW*JC+IOFFST, JC ),
+     $                               ILDA, EXTRA, DUMMY )
+                     END IF
+*
+*                    Chase "EXTRA" back up
+*
+                     IC = JC
+                     IR = IROW
+                     DO 150 JCH = JC - JKU, 1, -JKL - JKU
+                        IF( IC.LT.N ) THEN
+                           CALL SLARTG( A( IR+1-ISKEW*( IC+1 )+IOFFST,
+     $                                  IC+1 ), EXTRA, C, S, DUMMY )
+                        END IF
+                        ICOL = MAX( 1, JCH-JKL )
+                        IL = IC + 2 - ICOL
+                        TEMP = ZERO
+                        ILTEMP = JCH.GT.JKL
+                        CALL SLAROT( .TRUE., ILTEMP, .TRUE., IL, C, -S,
+     $                               A( IR-ISKEW*ICOL+IOFFST, ICOL ),
+     $                               ILDA, TEMP, EXTRA )
+                        IF( ILTEMP ) THEN
+                           CALL SLARTG( A( IR+1-ISKEW*( ICOL+1 )+IOFFST,
+     $                                  ICOL+1 ), TEMP, C, S, DUMMY )
+                           IROW = MAX( 1, JCH-JKL-JKU )
+                           IL = IR + 2 - IROW
+                           EXTRA = ZERO
+                           CALL SLAROT( .FALSE., JCH.GT.JKL+JKU, .TRUE.,
+     $                                  IL, C, -S, A( IROW-ISKEW*ICOL+
+     $                                  IOFFST, ICOL ), ILDA, EXTRA,
+     $                                  TEMP )
+                           IC = ICOL
+                           IR = IROW
+                        END IF
+  150                CONTINUE
+  160             CONTINUE
+  170          CONTINUE
+*
+            ELSE
+*
+*              Bottom-Up -- Start at the bottom right.
+*
+               JKL = 0
+               DO 200 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 190 JC = MIN( M+JKU, N ) - 1, 1 - JKL, -1
+                     EXTRA = ZERO
+                     ANGLE = TWOPI*SLARND( 1, ISEED )
+                     C = COS( ANGLE )
+                     S = SIN( ANGLE )
+                     IROW = MAX( 1, JC-JKU+1 )
+                     IF( JC.GT.0 ) THEN
+                        IL = MIN( M, JC+JKL+1 ) + 1 - IROW
+                        CALL SLAROT( .FALSE., .FALSE., JC+JKL.LT.M, IL,
+     $                               C, S, A( IROW-ISKEW*JC+IOFFST,
+     $                               JC ), ILDA, DUMMY, EXTRA )
+                     END IF
+*
+*                    Chase "EXTRA" back down
+*
+                     IC = JC
+                     DO 180 JCH = JC + JKL, IENDCH, JKL + JKU
+                        ILEXTR = IC.GT.0
+                        IF( ILEXTR ) THEN
+                           CALL SLARTG( A( JCH-ISKEW*IC+IOFFST, IC ),
+     $                                  EXTRA, C, S, DUMMY )
+                        END IF
+                        IC = MAX( 1, IC )
+                        ICOL = MIN( N-1, JCH+JKU )
+                        ILTEMP = JCH + JKU.LT.N
+                        TEMP = ZERO
+                        CALL SLAROT( .TRUE., ILEXTR, ILTEMP, ICOL+2-IC,
+     $                               C, S, A( JCH-ISKEW*IC+IOFFST, IC ),
+     $                               ILDA, EXTRA, TEMP )
+                        IF( ILTEMP ) THEN
+                           CALL SLARTG( A( JCH-ISKEW*ICOL+IOFFST,
+     $                                  ICOL ), TEMP, C, S, DUMMY )
+                           IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH
+                           EXTRA = ZERO
+                           CALL SLAROT( .FALSE., .TRUE.,
+     $                                  JCH+JKL+JKU.LE.IENDCH, IL, C, S,
+     $                                  A( JCH-ISKEW*ICOL+IOFFST,
+     $                                  ICOL ), ILDA, TEMP, EXTRA )
+                           IC = ICOL
+                        END IF
+  180                CONTINUE
+  190             CONTINUE
+  200          CONTINUE
+*
+               JKU = UUB
+               DO 230 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 220 JR = MIN( N+JKL, M ) - 1, 1 - JKU, -1
+                     EXTRA = ZERO
+                     ANGLE = TWOPI*SLARND( 1, ISEED )
+                     C = COS( ANGLE )
+                     S = SIN( ANGLE )
+                     ICOL = MAX( 1, JR-JKL+1 )
+                     IF( JR.GT.0 ) THEN
+                        IL = MIN( N, JR+JKU+1 ) + 1 - ICOL
+                        CALL SLAROT( .TRUE., .FALSE., JR+JKU.LT.N, IL,
+     $                               C, S, A( JR-ISKEW*ICOL+IOFFST,
+     $                               ICOL ), ILDA, DUMMY, EXTRA )
+                     END IF
+*
+*                    Chase "EXTRA" back down
+*
+                     IR = JR
+                     DO 210 JCH = JR + JKU, IENDCH, JKL + JKU
+                        ILEXTR = IR.GT.0
+                        IF( ILEXTR ) THEN
+                           CALL SLARTG( A( IR-ISKEW*JCH+IOFFST, JCH ),
+     $                                  EXTRA, C, S, DUMMY )
+                        END IF
+                        IR = MAX( 1, IR )
+                        IROW = MIN( M-1, JCH+JKL )
+                        ILTEMP = JCH + JKL.LT.M
+                        TEMP = ZERO
+                        CALL SLAROT( .FALSE., ILEXTR, ILTEMP, IROW+2-IR,
+     $                               C, S, A( IR-ISKEW*JCH+IOFFST,
+     $                               JCH ), ILDA, EXTRA, TEMP )
+                        IF( ILTEMP ) THEN
+                           CALL SLARTG( A( IROW-ISKEW*JCH+IOFFST, JCH ),
+     $                                  TEMP, C, S, DUMMY )
+                           IL = MIN( IENDCH, JCH+JKL+JKU ) + 2 - JCH
+                           EXTRA = ZERO
+                           CALL SLAROT( .TRUE., .TRUE.,
+     $                                  JCH+JKL+JKU.LE.IENDCH, IL, C, S,
+     $                                  A( IROW-ISKEW*JCH+IOFFST, JCH ),
+     $                                  ILDA, TEMP, EXTRA )
+                           IR = IROW
+                        END IF
+  210                CONTINUE
+  220             CONTINUE
+  230          CONTINUE
+            END IF
+*
+         ELSE
+*
+*           Symmetric -- A = U D U'
+*
+            IPACKG = IPACK
+            IOFFG = IOFFST
+*
+            IF( TOPDWN ) THEN
+*
+*              Top-Down -- Generate Upper triangle only
+*
+               IF( IPACK.GE.5 ) THEN
+                  IPACKG = 6
+                  IOFFG = UUB + 1
+               ELSE
+                  IPACKG = 1
+               END IF
+               CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 )
+*
+               DO 260 K = 1, UUB
+                  DO 250 JC = 1, N - 1
+                     IROW = MAX( 1, JC-K )
+                     IL = MIN( JC+1, K+2 )
+                     EXTRA = ZERO
+                     TEMP = A( JC-ISKEW*( JC+1 )+IOFFG, JC+1 )
+                     ANGLE = TWOPI*SLARND( 1, ISEED )
+                     C = COS( ANGLE )
+                     S = SIN( ANGLE )
+                     CALL SLAROT( .FALSE., JC.GT.K, .TRUE., IL, C, S,
+     $                            A( IROW-ISKEW*JC+IOFFG, JC ), ILDA,
+     $                            EXTRA, TEMP )
+                     CALL SLAROT( .TRUE., .TRUE., .FALSE.,
+     $                            MIN( K, N-JC )+1, C, S,
+     $                            A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA,
+     $                            TEMP, DUMMY )
+*
+*                    Chase EXTRA back up the matrix
+*
+                     ICOL = JC
+                     DO 240 JCH = JC - K, 1, -K
+                        CALL SLARTG( A( JCH+1-ISKEW*( ICOL+1 )+IOFFG,
+     $                               ICOL+1 ), EXTRA, C, S, DUMMY )
+                        TEMP = A( JCH-ISKEW*( JCH+1 )+IOFFG, JCH+1 )
+                        CALL SLAROT( .TRUE., .TRUE., .TRUE., K+2, C, -S,
+     $                               A( ( 1-ISKEW )*JCH+IOFFG, JCH ),
+     $                               ILDA, TEMP, EXTRA )
+                        IROW = MAX( 1, JCH-K )
+                        IL = MIN( JCH+1, K+2 )
+                        EXTRA = ZERO
+                        CALL SLAROT( .FALSE., JCH.GT.K, .TRUE., IL, C,
+     $                               -S, A( IROW-ISKEW*JCH+IOFFG, JCH ),
+     $                               ILDA, EXTRA, TEMP )
+                        ICOL = JCH
+  240                CONTINUE
+  250             CONTINUE
+  260          CONTINUE
+*
+*              If we need lower triangle, copy from upper. Note that
+*              the order of copying is chosen to work for 'q' -> 'b'
+*
+               IF( IPACK.NE.IPACKG .AND. IPACK.NE.3 ) THEN
+                  DO 280 JC = 1, N
+                     IROW = IOFFST - ISKEW*JC
+                     DO 270 JR = JC, MIN( N, JC+UUB )
+                        A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR )
+  270                CONTINUE
+  280             CONTINUE
+                  IF( IPACK.EQ.5 ) THEN
+                     DO 300 JC = N - UUB + 1, N
+                        DO 290 JR = N + 2 - JC, UUB + 1
+                           A( JR, JC ) = ZERO
+  290                   CONTINUE
+  300                CONTINUE
+                  END IF
+                  IF( IPACKG.EQ.6 ) THEN
+                     IPACKG = IPACK
+                  ELSE
+                     IPACKG = 0
+                  END IF
+               END IF
+            ELSE
+*
+*              Bottom-Up -- Generate Lower triangle only
+*
+               IF( IPACK.GE.5 ) THEN
+                  IPACKG = 5
+                  IF( IPACK.EQ.6 )
+     $               IOFFG = 1
+               ELSE
+                  IPACKG = 2
+               END IF
+               CALL SCOPY( MNMIN, D, 1, A( 1-ISKEW+IOFFG, 1 ), ILDA+1 )
+*
+               DO 330 K = 1, UUB
+                  DO 320 JC = N - 1, 1, -1
+                     IL = MIN( N+1-JC, K+2 )
+                     EXTRA = ZERO
+                     TEMP = A( 1+( 1-ISKEW )*JC+IOFFG, JC )
+                     ANGLE = TWOPI*SLARND( 1, ISEED )
+                     C = COS( ANGLE )
+                     S = -SIN( ANGLE )
+                     CALL SLAROT( .FALSE., .TRUE., N-JC.GT.K, IL, C, S,
+     $                            A( ( 1-ISKEW )*JC+IOFFG, JC ), ILDA,
+     $                            TEMP, EXTRA )
+                     ICOL = MAX( 1, JC-K+1 )
+                     CALL SLAROT( .TRUE., .FALSE., .TRUE., JC+2-ICOL, C,
+     $                            S, A( JC-ISKEW*ICOL+IOFFG, ICOL ),
+     $                            ILDA, DUMMY, TEMP )
+*
+*                    Chase EXTRA back down the matrix
+*
+                     ICOL = JC
+                     DO 310 JCH = JC + K, N - 1, K
+                        CALL SLARTG( A( JCH-ISKEW*ICOL+IOFFG, ICOL ),
+     $                               EXTRA, C, S, DUMMY )
+                        TEMP = A( 1+( 1-ISKEW )*JCH+IOFFG, JCH )
+                        CALL SLAROT( .TRUE., .TRUE., .TRUE., K+2, C, S,
+     $                               A( JCH-ISKEW*ICOL+IOFFG, ICOL ),
+     $                               ILDA, EXTRA, TEMP )
+                        IL = MIN( N+1-JCH, K+2 )
+                        EXTRA = ZERO
+                        CALL SLAROT( .FALSE., .TRUE., N-JCH.GT.K, IL, C,
+     $                               S, A( ( 1-ISKEW )*JCH+IOFFG, JCH ),
+     $                               ILDA, TEMP, EXTRA )
+                        ICOL = JCH
+  310                CONTINUE
+  320             CONTINUE
+  330          CONTINUE
+*
+*              If we need upper triangle, copy from lower. Note that
+*              the order of copying is chosen to work for 'b' -> 'q'
+*
+               IF( IPACK.NE.IPACKG .AND. IPACK.NE.4 ) THEN
+                  DO 350 JC = N, 1, -1
+                     IROW = IOFFST - ISKEW*JC
+                     DO 340 JR = JC, MAX( 1, JC-UUB ), -1
+                        A( JR+IROW, JC ) = A( JC-ISKEW*JR+IOFFG, JR )
+  340                CONTINUE
+  350             CONTINUE
+                  IF( IPACK.EQ.6 ) THEN
+                     DO 370 JC = 1, UUB
+                        DO 360 JR = 1, UUB + 1 - JC
+                           A( JR, JC ) = ZERO
+  360                   CONTINUE
+  370                CONTINUE
+                  END IF
+                  IF( IPACKG.EQ.5 ) THEN
+                     IPACKG = IPACK
+                  ELSE
+                     IPACKG = 0
+                  END IF
+               END IF
+            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
+*
+         IF( ISYM.EQ.1 ) THEN
+*
+*           Non-symmetric -- A = U D V
+*
+            CALL SLAGGE( MR, NC, LLB, UUB, D, A, LDA, ISEED, WORK,
+     $                   IINFO )
+         ELSE
+*
+*           Symmetric -- A = U D U'
+*
+            CALL SLAGSY( M, LLB, D, A, LDA, ISEED, WORK, IINFO )
+*
+         END IF
+         IF( IINFO.NE.0 ) THEN
+            INFO = 3
+            RETURN
+         END IF
+      END IF
+*
+*     5)      Pack the matrix
+*
+      IF( IPACK.NE.IPACKG ) THEN
+         IF( IPACK.EQ.1 ) THEN
+*
+*           'U' -- Upper triangular, not packed
+*
+            DO 390 J = 1, M
+               DO 380 I = J + 1, M
+                  A( I, J ) = ZERO
+  380          CONTINUE
+  390       CONTINUE
+*
+         ELSE IF( IPACK.EQ.2 ) THEN
+*
+*           'L' -- Lower triangular, not packed
+*
+            DO 410 J = 2, M
+               DO 400 I = 1, J - 1
+                  A( I, J ) = ZERO
+  400          CONTINUE
+  410       CONTINUE
+*
+         ELSE IF( IPACK.EQ.3 ) THEN
+*
+*           'C' -- Upper triangle packed Columnwise.
+*
+            ICOL = 1
+            IROW = 0
+            DO 430 J = 1, M
+               DO 420 I = 1, J
+                  IROW = IROW + 1
+                  IF( IROW.GT.LDA ) THEN
+                     IROW = 1
+                     ICOL = ICOL + 1
+                  END IF
+                  A( IROW, ICOL ) = A( I, J )
+  420          CONTINUE
+  430       CONTINUE
+*
+         ELSE IF( IPACK.EQ.4 ) THEN
+*
+*           'R' -- Lower triangle packed Columnwise.
+*
+            ICOL = 1
+            IROW = 0
+            DO 450 J = 1, M
+               DO 440 I = J, M
+                  IROW = IROW + 1
+                  IF( IROW.GT.LDA ) THEN
+                     IROW = 1
+                     ICOL = ICOL + 1
+                  END IF
+                  A( IROW, ICOL ) = A( I, J )
+  440          CONTINUE
+  450       CONTINUE
+*
+         ELSE IF( IPACK.GE.5 ) 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.
+*
+            IF( IPACK.EQ.5 )
+     $         UUB = 0
+            IF( IPACK.EQ.6 )
+     $         LLB = 0
+*
+            DO 470 J = 1, UUB
+               DO 460 I = MIN( J+LLB, M ), 1, -1
+                  A( I-J+UUB+1, J ) = A( I, J )
+  460          CONTINUE
+  470       CONTINUE
+*
+            DO 490 J = UUB + 2, N
+               DO 480 I = J - UUB, MIN( J+LLB, M )
+                  A( I-J+UUB+1, J ) = A( I, J )
+  480          CONTINUE
+  490       CONTINUE
+         END IF
+*
+*        If packed, zero out extraneous elements.
+*
+*        Symmetric/Triangular Packed --
+*        zero out everything after A(IROW,ICOL)
+*
+         IF( IPACK.EQ.3 .OR. IPACK.EQ.4 ) THEN
+            DO 510 JC = ICOL, M
+               DO 500 JR = IROW + 1, LDA
+                  A( JR, JC ) = ZERO
+  500          CONTINUE
+               IROW = 0
+  510       CONTINUE
+*
+         ELSE IF( IPACK.GE.5 ) 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 540 JC = 1, N
+               DO 520 JR = 1, UUB + 1 - JC
+                  A( JR, JC ) = ZERO
+  520          CONTINUE
+               DO 530 JR = MAX( 1, MIN( IR1, IR2-JC ) ), LDA
+                  A( JR, JC ) = ZERO
+  530          CONTINUE
+  540       CONTINUE
+         END IF
+      END IF
+*
+      RETURN
+*
+*     End of SLATMT
+*
+      END