her2(3F)

NAME
     CHER2, ZHER2 - Performs Hermitian rank 2 update of a complex Hermitian
     matrix

SYNOPSIS
     Complex

        CALL CHER2 (uplo, n, alpha, x, incx, y, incy, a, lda)

     Double complex

        CALL ZHER2 (uplo, n, alpha, x, incx, y, incy, a, lda)

DESCRIPTION
     These routines perform the following Hermitian rank 2 operation:

          A  <- alpha xyH + (complex conjugate of alpha)* yxH + A

     where alpha is a scalar, x and y are n-element vectors, xH and yH

     conjugate transposes of x and y, respectively, and A is an n-by-n
     Hermitian matrix.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               array a is referenced, as follows:

               uplo= 'U' or 'u': only the upper triangular part of a is
               referenced.
               uplo= 'L' or 'l': only the lower triangular part of a is
               referenced.

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

     alpha     Scalar alpha.
               CHER2: Complex.
               ZHER2: Double complex.

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               CHER2: Complex array.
               ZHER2: Double complex array.
               Contains vector x.

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

     y         Array of dimension 1+(n-1) * |incy|.  (input)
               CHER2: Complex array.
               ZHER2: Double complex array.
               Contains vector y.

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

     a         Array of dimension (lda,n).  (input and output)
               CHER2: Complex array.
               ZHER2: Double complex array.

               Before entry with uplo = 'U' or 'u', the leading n-by-n
               upper triangular part of array a must contain the upper
               triangular part of the Hermitian matrix.  The strictly lower
               triangular part of a is not referenced.  On exit, the upper
               triangular part of the updated matrix overwrites the upper
               triangular part of array a.

               Before entry with uplo = 'L' or 'l', the leading n-by-n
               lower triangular part of array a must contain the lower
               triangular part of the Hermitian matrix.  The strictly upper
               triangular part of a is not referenced.  On exit, the lower
               triangular part of the updated matrix overwrites the lower
               triangular part of array a.

               The imaginary parts of the diagonal elements need not be
               set.  They are assumed to be 0; on exit, they are set to 0.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  lda >= MAX(1,n).

NOTES
     CHER2/ZHER2 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
     SYR2(3F)