hpmv(3F)

NAME
     CHPMV, ZHPMV - Multiplies a complex vector by a packed complex
     Hermitian matrix

SYNOPSIS
     Complex

        CALL CHPMV (uplo, n, alpha, ap, x, incx, beta, y, incy)

     Double complex

        CALL ZHPMV (uplo, n, alpha, ap, x, incx, beta, y, incy)

DESCRIPTION
     These routines perform the following matrix-vector operation:

          y <- alpha Ax + beta y

     where alpha and beta are complex scalars, x and y are n-element
     vectors, and A is an n-by-n packed complex Hermitian matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               matrix A is packed into the array argument ap, as follows:

               uplo= 'U' or 'u': the upper triangular part of A is being
               supplied in the argument ap.
               uplo= 'L' or 'l': the lower triangular part of A is being
               supplied in the argument ap.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     alpha     Scalar alpha.
               CHPMV: Complex.
               ZHPMV: Double complex.

     ap        Array of dimension (n(n+1))/2 .  (input)
               CHPMV: Complex array.
               ZHPMV: Double complex array.

               Before entry with uplo = 'U' or 'u', array ap must contain
               the upper triangular part of the Hermitian matrix packed
               sequentially, column-by-column, so that ap(1) contains
               A(1,1), ap(2) contains A(1,2), ap(3) contains A(2,2), and so
               on.

               Before entry with uplo = 'L' or 'l', array ap must contain
               the lower triangular part of the Hermitian matrix packed
               sequentially, column-by-column, so that ap(1) contains
               A(1,1), ap(2) contains A(2,1), ap(3) contains A(3,1), and so
               on.

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               CHPMV: Complex array.
               ZHPMV: Double complex array.
               Contains vector x.

     incx      Integer.  (input)
               Specifies the increment for the elements of x.  incx must
               not be 0.

     beta      Scalar beta.  (input)
               CHPMV: Complex.
               ZHPMV: Double complex.
               If beta is supplied as 0, y need not be set on input.

     y         Array of dimension 1+(n-1) * |incy|.  (input and output)
               CHPMV: Complex array.
               ZHPMV: Double complex array.
               Contains vector y.  On exit, y is overwritten by updated
               vector y.

     incy      Integer.  (input)
               Specifies the increment for the elements of y.  incy must
               not be 0.

NOTES
     CHPMV/ZHPMV is a Level 2 Basic Linear Algebra Subprogram (Level 2
     BLAS).

     When working backward (incx < 0 or incy < 0), this routine starts at
     the end of the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)) , ..., x(1)

          y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(1)

SEE ALSO
     SPMV(3F)