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NAME
     dsbmv - perform the matrix-vector operation   y := alpha*A*x
     + beta*y

SYNOPSIS
     SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA,
               Y, INCY )

     DOUBLE PRECISION ALPHA, BETA

     INTEGER INCX, INCY, K, LDA, N

     CHARACTER*1 UPLO

     DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )



     #include <sunperf.h>

     void dsbmv(char uplo, int n, int  k,  double  alpha,  double
               *da,  int lda, double *dx, int incx, double dbeta,
               double *dy, int incy) ;

PURPOSE
     DSBMV  performs the matrix-vector  operation y :=  alpha*A*x
     +  beta*y  where  alpha  and beta are scalars, x and y are n
     element vectors and A is an n by n  symmetric  band  matrix,
     with k super-diagonals.


PARAMETERS
     UPLO      - CHARACTER*1.
               On entry, UPLO  specifies  whether  the  upper  or
               lower  triangular  part  of  the  band matrix A is
               being supplied as follows:

               UPLO = 'U' or 'u'   The upper triangular part of A
               is being supplied.

               UPLO = 'L' or 'l'   The lower triangular part of A
               is being supplied.

               Unchanged on exit.

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

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

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

     A         - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
               Before entry with UPLO = 'U' or 'u', the leading (
               k  + 1 ) by n part of the array A must contain the
               upper  triangular  band  part  of  the   symmetric
               matrix,  supplied column by column, with the lead-
               ing diagonal of the matrix in row ( k + 1 ) of the
               array,  the first super-diagonal starting at posi-
               tion 2 in row k, and so on. The top left  k  by  k
               triangle  of  the  array A is not referenced.  The
               following program segment will transfer the  upper
               triangular  part  of  a symmetric band matrix from
               conventional full matrix storage to band storage:

               DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J
               - K ), J A( M + I, J ) = matrix( I, J ) 10    CON-
               TINUE 20 CONTINUE

               Before entry with UPLO = 'L' or 'l', the leading (
               k  + 1 ) by n part of the array A must contain the
               lower  triangular  band  part  of  the   symmetric
               matrix,  supplied column by column, with the lead-
               ing diagonal of the matrix in row 1 of the  array,
               the  first  sub-diagonal starting at position 1 in
               row 2, and so on. The bottom right k by k triangle
               of  the  array A is not referenced.  The following
               program segment will transfer the lower triangular
               part  of a symmetric band matrix from conventional
               full matrix storage to band storage:

               DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N,  J
               +  K  )  A( M + I, J ) = matrix( I, J ) 10    CON-
               TINUE 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 ( k + 1 ).  Unchanged on exit.

     X         - DOUBLE PRECISION array of DIMENSION at least
               ( 1 + ( n - 1 )*abs( INCX ) ).  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      - DOUBLE PRECISION.
               On  entry,  BETA  specifies   the   scalar   beta.
               Unchanged on exit.

     Y         - DOUBLE PRECISION array of DIMENSION at least
               ( 1 + ( n - 1 )*abs( INCY ) ).  Before entry,  the
               incremented  array Y must contain the vector y. On
               exit, Y is overwritten 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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