ZSBMV  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.

  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  - COMPLEX*16


           On entry, ALPHA specifies the scalar alpha.


           Unchanged on exit.


  A      - COMPLEX*16 array, 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 leading diagonal of the matrix in row


           ( k + 1 ) of the array, the first super-diagonal starting at


           position 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    CONTINUE


              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 leading 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    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


           ( k + 1 ).


           Unchanged on exit.


  X      - COMPLEX*16 array, 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   - COMPLEX*16


           On entry, BETA specifies the scalar beta.


           Unchanged on exit.


  Y      - COMPLEX*16 array, 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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