BLAS/SRC/zhbmv.f(3)        Library Functions Manual        BLAS/SRC/zhbmv.f(3)

NAME
       BLAS/SRC/zhbmv.f

SYNOPSIS
   Functions/Subroutines
       subroutine zhbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
           ZHBMV

Function/Subroutine Documentation
   subroutine zhbmv (character uplo, integer n, integer k, 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)
       ZHBMV

       Purpose:


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

           A

           !>          A is COMPLEX*16 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 hermitian 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 hermitian 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 hermitian 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 hermitian 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
           !>
           !>           Note that the imaginary parts of the diagonal elements need
           !>           not be set and are assumed to be zero.
           !>

           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 COMPLEX*16 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 COMPLEX*16
           !>           On entry, BETA specifies the scalar beta.
           !>

           Y

           !>          Y is COMPLEX*16 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 186 of file zhbmv.f.

Author
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LAPACK                          Version 3.12.0             BLAS/SRC/zhbmv.f(3)