nag_sum_fft_sine (c06rec) (PDF version)
c06 Chapter Contents
c06 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_sum_fft_sine (c06rec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_sum_fft_sine (c06rec) computes the discrete Fourier sine transforms of m sequences of real data values. The elements of each sequence and its transform are stored contiguously.

2  Specification

#include <nag.h>
#include <nagc06.h>
void  nag_sum_fft_sine (Integer m, Integer n, double x[], NagError *fail)

3  Description

Given m sequences of n-1 real data values xjp , for j=1,2,,n-1 and p=1,2,,m, nag_sum_fft_sine (c06rec) simultaneously calculates the Fourier sine transforms of all the sequences defined by
x^ k p = 2n j=1 n-1 xjp × sin jk πn ,   k= 1, 2, , n-1 ​ and ​ p= 1, 2, , m .
(Note the scale factor 2n  in this definition.)
This transform is also known as type-I DST.
Since the Fourier sine transform defined above is its own inverse, two consecutive calls of nag_sum_fft_sine (c06rec) will restore the original data.
The transform calculated by this function can be used to solve Poisson's equation when the solution is specified at both left and right boundaries (see Swarztrauber (1977)).

4  References


5  Arguments

1:     mIntegerInput
Constraint: m1.
2:     nIntegerInput
Constraint: n1.
3:     x[n-1×m]doubleInput/Output
On entry: the pth sequence to be transformed, denoted by xjp, for j=1,2,,n-1 and p=1,2,,m, must be stored in x[p-1×n-1+j-1].
On exit: the m Fourier sine transforms, overwriting the corresponding original sequences. The n-1 components of the pth Fourier sine transform, denoted by x^kp, for k=1,2,,n-1 and p=1,2,,m, are stored in x[p-1×n-1+k-1].
4:     failNagError *Input/Output

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, m=value.
Constraint: m1.
On entry, n=value.
Constraint: n1.

7  Accuracy


8  Parallelism and Performance

nag_sum_fft_sine (c06rec) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

9  Further Comments

The time taken by nag_sum_fft_sine (c06rec) is approximately proportional to nm logn, but also depends on the factors of n. nag_sum_fft_sine (c06rec) is fastest if the only prime factors of n are 2, 3 and 5, and is particularly slow if n is a large prime, or has large prime factors. Workspace is internally allocated by this function. The total amount of memory allocated is On double values.

10  Example

This example reads in sequences of real data values and prints their Fourier sine transforms (as computed by nag_sum_fft_sine (c06rec)). It then calls nag_sum_fft_sine (c06rec) again and prints the results which may be compared with the original sequence.

10.1  Program Text

Program Text (c06rece.c)

10.2  Program Data

Program Data (c06rece.d)

10.3  Program Results

Program Results (c06rece.r)

nag_sum_fft_sine (c06rec) (PDF version)
c06 Chapter Contents
c06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014