CGBMV(1)

NAME
LAPACK-3 - performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*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
    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.

ARGUMENTS

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**T*x + beta*y.
     TRANS = 'C' or 'c' y := alpha*A**H*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.

FURTHER DETAILS
 Level 2 Blas routine.
 The vector and matrix arguments are not referenced when N = 0, or M = 0
 -- 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.