C06 Chapter Contents
C06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentC06GBF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

C06GBF forms the complex conjugate of a Hermitian sequence of $n$ data values.

## 2  Specification

 SUBROUTINE C06GBF ( X, N, IFAIL)
 INTEGER N, IFAIL REAL (KIND=nag_wp) X(N)

## 3  Description

This is a utility routine for use in conjunction with C06EAF, C06EBF, C06FAF or C06FBF to calculate inverse discrete Fourier transforms (see the C06 Chapter Introduction).

None.

## 5  Parameters

1:     X(N) – REAL (KIND=nag_wp) arrayInput/Output
On entry: if the data values ${z}_{j}$ are written as ${x}_{j}+i{y}_{j}$ and if X is declared with bounds $\left(0:{\mathbf{N}}-1\right)$ in the subroutine from which C06GBF is called, then for $0\le j\le n/2$, ${\mathbf{X}}\left(j\right)$ must contain ${x}_{j}$ ($\text{}={x}_{n-j}$), while for $n/2, ${\mathbf{X}}\left(j\right)$ must contain ${-y}_{j}$ ($\text{}={y}_{n-j}$). In other words, X must contain the Hermitian sequence in Hermitian form. (See also Section 2.1.2 in the C06 Chapter Introduction.)
On exit: the imaginary parts ${y}_{j}$ are negated. The real parts ${x}_{j}$ are not referenced.
2:     N – INTEGERInput
On entry: $n$, the number of data values.
Constraint: ${\mathbf{N}}\ge 1$.
3:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
 On entry, ${\mathbf{N}}<1$.

## 7  Accuracy

Exact.

The time taken by C06GBF is negligible.

## 9  Example

This example reads in a sequence of real data values, calls C06EAF followed by C06GBF to compute their inverse discrete Fourier transform, and prints this after expanding it from Hermitian form into a full complex sequence.

### 9.1  Program Text

Program Text (c06gbfe.f90)

### 9.2  Program Data

Program Data (c06gbfe.d)

### 9.3  Program Results

Program Results (c06gbfe.r)