# NAG C Library Function Document

## 1Purpose

nag_fft_init_trig (c06gzc) calculates the trigonometric coefficients required for the computation of discrete Fourier transforms.

## 2Specification

 #include #include
 void nag_fft_init_trig (Integer n, double trig[], NagError *fail)

## 3Description

This is a utility function for use in conjunction with nag_fft_multiple_real (c06fpc) and nag_fft_multiple_hermitian (c06fqc). nag_fft_init_trig (c06gzc) initializes the array trig with trigonometric coefficients according to the value of n and must be called prior to the first call of one of the above listed functions.

None.

## 5Arguments

1:    $\mathbf{n}$IntegerInput
On entry: the value of $n$ in the Fourier transform function being called.
Constraint: ${\mathbf{n}}\ge 1$.
2:    $\mathbf{trig}\left[2×{\mathbf{n}}\right]$doubleOutput
On exit: the trigonometric coefficients are stored in trig.
3:    $\mathbf{fail}$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, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.

Exact.

## 8Parallelism and Performance

nag_fft_init_trig (c06gzc) is not threaded in any implementation.

None.

## 10Example

The program reads in 3 real data sequences and prints their discrete Fourier transforms in Hermitian format as calculated by nag_fft_multiple_real (c06fpc). A call is made to nag_fft_init_trig (c06gzc) to initialize the array trig prior to calling nag_fft_multiple_real (c06fpc). The transforms are then printed out in full complex form after a call to nag_multiple_hermitian_to_complex (c06gsc).

### 10.1Program Text

Program Text (c06gzce.c)

### 10.2Program Data

Program Data (c06gzce.d)

### 10.3Program Results

Program Results (c06gzce.r)