DSBMV(1)

NAME
LAPACK-3 - performs the matrix-vector operation y := alpha*A*x + beta*y,

SYNOPSIS

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

DOUBLE
    PRECISION ALPHA,BETA

INTEGER
    INCX,INCY,K,LDA,N

CHARACTER
    UPLO

DOUBLE
    PRECISION A(LDA,*),X(*),Y(*)

PURPOSE
DSBMV 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 symmetric band matrix, with k super-diagonals.

ARGUMENTS

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  - DOUBLE PRECISION.
     On entry, ALPHA specifies the scalar alpha.
     Unchanged on exit.

A      - DOUBLE PRECISION 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 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      - DOUBLE PRECISION 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   - DOUBLE PRECISION.
     On entry, BETA specifies the scalar beta.
     Unchanged on exit.

Y      - DOUBLE PRECISION 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.

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.