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NAME

       CGBMV  - perform one of the matrix-vector operations   y := alpha*A*x +
       beta*y, or y := alpha*A’*x + beta*y, or   y := alpha*conjg(  A’  )*x  +
       beta*y,

SYNOPSIS

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

           COMPLEX      ALPHA, BETA

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

           CHARACTER*1  TRANS

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

PURPOSE

       CGBMV  performs one of the matrix-vector operations

       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 performed 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*conjg( 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  - COMPLEX         .
              On entry, ALPHA specifies the scalar alpha.  Unchanged on  exit.

       A      - COMPLEX          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 referenced.   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      - COMPLEX          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   - COMPLEX         .
              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      - COMPLEX          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
              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.