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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