BLAS/SRC/zgbmv.f(3)

NAME
BLAS/SRC/zgbmv.f

SYNOPSIS

  Functions/Subroutines
subroutine zgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
ZGBMV

Function/Subroutine Documentation

  subroutine zgbmv (character trans, integer m, integer n, integer kl, integer ku, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZGBMV

Purpose:

    !>
    !> ZGBMV  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,
    !>
    !> 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

    !>          TRANS is 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.
    !>

    M

    !>          M is INTEGER
    !>           On entry, M specifies the number of rows of the matrix A.
    !>           M must be at least zero.
    !>

    N

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

    KL

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

    KU

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

    ALPHA

    !>          ALPHA is COMPLEX*16
    !>           On entry, ALPHA specifies the scalar alpha.
    !>

    A

    !>          A is COMPLEX*16 array, 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
    !>

    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
    !>           ( kl + ku + 1 ).
    !>

    X

    !>          X is COMPLEX*16 array, 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.
    !>

    INCX

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

    BETA

    !>          BETA is COMPLEX*16
    !>           On entry, BETA specifies the scalar beta. When BETA is
    !>           supplied as zero then Y need not be set on input.
    !>

    Y

    !>          Y is COMPLEX*16 array, 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.
    !>           If either m or n is zero, then Y not referenced and the function
    !>           performs a quick return.
    !>

    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 188 of file zgbmv.f.

Author

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