BLAS/SRC/dsbmv.f(3)

NAME
BLAS/SRC/dsbmv.f

SYNOPSIS

  Functions/Subroutines
subroutine dsbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
DSBMV

Function/Subroutine Documentation

  subroutine dsbmv (character uplo, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(*) x, integer incx, double precision beta, double precision, dimension(*) y, integer incy)

DSBMV

Purpose:

    !>
    !> DSBMV  performs the matrix-vector  operation
    !>
    !>    y := alpha*A*x + beta*y,
    !>
    !> 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.
    !>

Parameters
    UPLO

    !>          UPLO is 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.
    !>

    N

    !>          N is INTEGER
    !>           On entry, N specifies the order of the matrix A.
    !>           N must be at least zero.
    !>

    K

    !>          K is INTEGER
    !>           On entry, K specifies the number of super-diagonals of the
    !>           matrix A. K must satisfy  0 .le. K.
    !>

    ALPHA

    !>          ALPHA is DOUBLE PRECISION.
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    A

    !>          A is DOUBLE PRECISION array, 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
    !>

    LDA

    !>          LDA is INTEGER
    !>           On entry, LDA specifies the first dimension of A as declared
    !>           in the calling (sub) program. LDA must be at least
    !>           ( k + 1 ).
    !>

    X

    !>          X is DOUBLE PRECISION array, dimension at least
    !>           ( 1 + ( n - 1 )*abs( INCX ) ).
    !>           Before entry, the incremented array X must contain the
    !>           vector x.
    !>

    INCX

    !>          INCX is INTEGER
    !>           On entry, INCX specifies the increment for the elements of
    !>           X. INCX must not be zero.
    !>

    BETA

    !>          BETA is DOUBLE PRECISION.
    !>           On entry, BETA specifies the scalar beta.
    !>

    Y

    !>          Y is DOUBLE PRECISION array, 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

    !>          INCY is INTEGER
    !>           On entry, INCY specifies the increment for the elements of
    !>           Y. INCY must not be zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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.
    !>

Definition at line 183 of file dsbmv.f.

Author

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