BLAS/SRC/zgbmv.f(3)        Library Functions Manual        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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LAPACK                          Version 3.12.0             BLAS/SRC/zgbmv.f(3)