NAME

       CHBMV - perform the matrix-vector operation   y := alpha*A*x + beta*y,

SYNOPSIS

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

           COMPLEX      ALPHA, BETA

           INTEGER      INCX, INCY, K, LDA, N

           CHARACTER*1  UPLO

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

PURPOSE

       CHBMV  performs the matrix-vector  operation

       where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian 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  - COMPLEX         .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - COMPLEX          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 hermitian  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 hermitian  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  hermitian 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 hermitian 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

              Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
              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          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   - COMPLEX         .
              On entry, BETA specifies the scalar beta.  Unchanged on exit.

       Y      - COMPLEX          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.

              Level 2 Blas routine.

              --  Written on 22-October-1986.  Jack Dongarra, Argonne National Lab.  Jeremy Du Croz, Nag Central
              Office.  Sven Hammarling, Nag Central Office.  Richard Hanson, Sandia National Labs.

BLAS routine                                     16 October 1992                                        CHBMV(3)