# NAG C Library Function Document

## 1Purpose

nag_multiple_conjugate_hermitian (c06gqc) forms the complex conjugates of $m$ Hermitian sequences, each containing $n$ data values.

## 2Specification

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

## 3Description

This is a utility function for use in conjunction with nag_fft_multiple_real (c06fpc) and nag_fft_multiple_hermitian (c06fqc) to calculate inverse discrete Fourier transforms.
None.

## 5Arguments

1:    $\mathbf{m}$IntegerInput
On entry: the number of Hermitian sequences to be conjugated, $m$.
Constraint: ${\mathbf{m}}\ge 1$.
2:    $\mathbf{n}$IntegerInput
On entry: the number of data values in each Hermitian sequence, $n$.
Constraint: ${\mathbf{n}}\ge 1$.
3:    $\mathbf{x}\left[{\mathbf{m}}×{\mathbf{n}}\right]$doubleInput/Output
On entry: the $m$ data sequences must be stored in x consecutively. If the $n$ data values ${z}_{j}^{p}$ are written as ${x}_{j}^{p}+{iy}_{j}^{p}$, $p=1,2,\dots ,m$, then for $0\le j\le n/2$, ${x}_{j}^{p}$ is contained in ${\mathbf{x}}\left[\left(p-1\right)×n+j\right]$, and for $1\le j\le \left(n-1\right)/2$, ${y}_{j}^{p}$ is contained in ${\mathbf{x}}\left[\left(p-1\right)×n+n-j\right]$.
On exit: the imaginary parts ${y}_{j}^{p}$ are negated. The real parts ${x}_{j}^{p}$ are not referenced.
4:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error Indicators and Warnings

NE_INT_ARG_LT
On entry, ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m}}\ge 1$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.

Exact.

## 8Parallelism and Performance

nag_multiple_conjugate_hermitian (c06gqc) is not threaded in any implementation.

None.

## 10Example

This program reads in sequences of real data values which are assumed to be Hermitian sequences of complex data stored in Hermitian form. The sequences are expanded into full complex form using nag_multiple_hermitian_to_complex (c06gsc) and printed. The sequences are then conjugated (using nag_multiple_conjugate_hermitian (c06gqc)) and the conjugated sequences are expanded into complex form using nag_multiple_hermitian_to_complex (c06gsc) and printed out.

### 10.1Program Text

Program Text (c06gqce.c)

### 10.2Program Data

Program Data (c06gqce.d)

### 10.3Program Results

Program Results (c06gqce.r)