# ?her

Performs a rank-1 update of a Hermitian matrix.

## Syntax

FORTRAN 77:

call cher(uplo, n, alpha, x, incx, a, lda )

call zher(uplo, n, alpha, x, incx, a, lda )

Fortran 95:

call her(a, x [,uplo] [, alpha])

## Description

The ?her routines perform a matrix-vector operation defined as
`A := alpha*x*conjg(x') + A,`

where:

alpha is a real scalar,

x is an n-element vector,

A is an n-by-n Hermitian matrix.

## Input Parameters

uplo

  CHARACTER*1. Specifies whether the upper or lower triangular part of the array a is used.

  If `uplo = 'U'` or 'u', then the upper triangular of the array a is used.

  If `uplo = 'L'` or 'l', then the low triangular of the array a is is used.

n

  INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

alpha

  REAL for cher

  DOUBLE PRECISION for zher

  Specifies the scalar alpha.

x

  COMPLEX for cher

  DOUBLE COMPLEX for zher

  Array, dimension at least `(1 + (n - 1)*abs(incx))`. Before entry, the incremented array x must contain the n-element vector x.

incx

  INTEGER. Specifies the increment for the elements of x.

  The value of incx must not be zero.

a

  COMPLEX for cher

  DOUBLE COMPLEX for zher

  Array, DIMENSION `(lda, n)`.

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

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

  The imaginary parts of the diagonal elements need not be set and are assumed to be zero.

lda

  INTEGER. Specifies the first dimension of a as declared in the calling (sub)program. The value of lda must be at least `max(1, n)`.

## Output Parameters

a

  With `uplo = 'U'` or 'u', the upper triangular part of the array a is overwritten by the upper triangular part of the updated matrix.

  With `uplo = 'L'` or 'l', the lower triangular part of the array a is overwritten by the lower triangular part of the updated matrix.

  The imaginary parts of the diagonal elements are set to zero.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine her interface are the following:

a

  Holds the matrix A of size (n,n).

x

  Holds the vector of length (n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

alpha

  The default value is 1.

Parent topic: BLAS Level 2 Routines