c06 Chapter Contents
c06 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_conjugate_hermitian (c06gbc)

## 1  Purpose

nag_conjugate_hermitian (c06gbc) forms the complex conjugate of a Hermitian sequence of $n$ data values.

## 2  Specification

 #include #include
 void nag_conjugate_hermitian (Integer n, double x[], NagError *fail)

## 3  Description

This is a utility function for use in conjunction with nag_fft_real (c06eac) and nag_fft_hermitian (c06ebc), to calculate inverse discrete Fourier transforms.

None.

## 5  Arguments

1:     nIntegerInput
On entry: the number of data values, $n$.
Constraint: ${\mathbf{n}}\ge 1$.
2:     x[n]doubleInput/Output
On entry: if the data values ${z}_{j}$ are written as ${x}_{j}+i{y}_{j}$, then for $0\le j\le n/2$, ${\mathbf{x}}\left[j\right]$ must contain ${x}_{j}\left(={x}_{n-j}\right)$, while for $n/2, ${\mathbf{x}}\left[j\right]$ must contain $-{y}_{j}\left(={y}_{n-j}\right)$. In other words, x must contain the Hermitian sequence in Hermitian form.
On exit: the imaginary parts ${y}_{j}$ are negated. The real parts ${x}_{j}$ are not referenced.
3:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_INT_ARG_LT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 1$.

Exact.

## 8  Parallelism and Performance

Not applicable.

The time taken is negligible.

## 10  Example

This program reads in a sequence of real data values, calls nag_fft_real (c06eac) followed by nag_conjugate_hermitian (c06gbc) to compute their inverse discrete Fourier transform, and prints this after expanding it from Hermitian form into a full complex sequence.

### 10.1  Program Text

Program Text (c06gbce.c)

### 10.2  Program Data

Program Data (c06gbce.d)

### 10.3  Program Results

Program Results (c06gbce.r)