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.

BLAS routine                                     16 October 1992                                        CGBMV(3)