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NAME
     sgbmv - perform one of the matrix-vector operations    y  :=
     alpha*A*x + beta*y or y := alpha*A'*x + beta*y

SYNOPSIS
     SUBROUTINE SGBMV ( TRANS, M, N, KL, KU, ALPHA,  A,  LDA,  X,
               INCX, BETA, Y, INCY )

     REAL ALPHA, BETA

     INTEGER INCX, INCY, KL, KU, LDA, M, N

     CHARACTER*1 TRANS

     REAL A( LDA, * ), X( * ), Y( * )



     #include <sunperf.h>

     void sgbmv(char trans, int m, int n, int kl, int  ku,  float
               alpha,  float  *sa,  int lda, float *sx, int incx,
               float sbeta, float *sy, int incy) ;

PURPOSE
     SGBMV  performs one of the  matrix-vector  operations  y  :=
     alpha*A*x  + beta*y or y := alpha*A'*x + beta*y, where alpha
     and beta are scalars, x and y are vectors and A is an m by n
     band matrix, with kl sub-diagonals and ku super-diagonals.


PARAMETERS
     TRANS     - CHARACTER*1.
               On entry, TRANS specifies the operation to be per-
               formed as follows:

               TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.

               TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.

               TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.

               Unchanged on exit.

     M         - INTEGER.
               On entry, M specifies the number of  rows  of  the
               matrix  A.  M must be at least zero.  Unchanged on
               exit.

     N         - INTEGER.
               On entry, N specifies the number of columns of the
               matrix  A.  N must be at least zero.  Unchanged on
               exit.

     KL        - INTEGER.
               On entry, KL specifies the number of sub-diagonals
               of  the  matrix  A.  KL  must  satisfy  0 .le. KL.
               Unchanged on exit.

     KU        - INTEGER.
               On  entry,  KU  specifies  the  number  of  super-
               diagonals of the matrix A. KU must satisfy  0 .le.
               KU.  Unchanged on exit.

     ALPHA     - REAL            .
               On  entry,  ALPHA  specifies  the  scalar   alpha.
               Unchanged on exit.

     A         - REAL             array of DIMENSION ( LDA, n ).
               Before entry, the leading ( kl + ku +  1  )  by  n
               part  of  the  array  A must contain the matrix of
               coefficients, supplied column by column, with  the
               leading  diagonal  of the matrix in row ( ku + 1 )
               of the array, the first super-diagonal starting at
               position  2  in  row  ku,  the  first sub-diagonal
               starting at position 1 in row ( ku + 2 ),  and  so
               on.    Elements   in  the  array  A  that  do  not
               correspond to elements in the band matrix (such as
               the  top  left  ku  by ku triangle) are not refer-
               enced.   The  following   program   segment   will
               transfer  a  band  matrix  from  conventional full
               matrix storage to band storage:

               DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX(  1,
               J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix(
               I, J ) 10    CONTINUE 20 CONTINUE

               Unchanged on exit.

     LDA       - INTEGER.
               On entry, LDA specifies the first dimension  of  A
               as declared in the calling (sub) program. LDA must
               be at least ( kl + ku + 1 ).  Unchanged on exit.

     X         - REAL             array of DIMENSION at least
               ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N'  or
               'n'  and  at  least  ( 1 + ( m - 1 )*abs( INCX ) )
               otherwise.  Before entry, the incremented array  X
               must contain the vector x.  Unchanged on exit.

     INCX      - INTEGER.
               On entry, INCX specifies  the  increment  for  the
               elements  of  X. INCX must not be zero.  Unchanged
               on exit.

     BETA      - REAL            .
               On entry, BETA specifies  the  scalar  beta.  When
               BETA is supplied as zero then Y need not be set on
               input.  Unchanged on exit.

     Y         - REAL             array of DIMENSION at least
               ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N'  or
               'n'  and  at  least  ( 1 + ( n - 1 )*abs( INCY ) )
               otherwise.  Before entry, the incremented array  Y
               must contain the vector y. On exit, Y is overwrit-
               ten by the updated vector y.

     INCY      - INTEGER.
               On entry, INCY specifies  the  increment  for  the
               elements  of  Y. INCY must not be zero.  Unchanged
               on exit.

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