Functions to calculate the numerical derivatives. More...

#include <fftw3.h>

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Functions
void	complex_mult_vec (fftw_complex a, fftw_complex b, fftw_complex *c, int len)
	Multiply two arrays of complex numbers element-wise.

void	init_diff_shift_op (double delta, fftw_complex *Dk, int N)
	Initialise the coefficients required to simultaneously perform differentiation and shifting by amount delta, using a forward and backward FFT.

void	first_derivative (fftw_complex in_pb_pf, fftw_complex out_pb_pf, fftw_complex *Dk, int N, fftw_plan pf, fftw_plan pb)
	Calculate the first derivative of a sampled function.

Detailed Description

Functions to calculate the numerical derivatives.

This code is the main dependency on FFTW3.

Function Documentation

◆ complex_mult_vec()

void complex_mult_vec	(	fftw_complex *	a,
		fftw_complex *	b,
		fftw_complex *	c,
		int	len
	)

Multiply two arrays of complex numbers element-wise.

Performs element-wise complex multiplication of the array a with the array b. a and b must be must be of equal length. Stores the result in c. Internally used by first_derivative.

Parameters

[in]	a	Array of complex numbers to multiply with those in b.
[in]	b	Array of complex numbers to multiply with those in a.
[out]	c	The results of the element-wise multiplications a .* b.
[in]	len	The length of the arrays.

◆ first_derivative()

void first_derivative	(	fftw_complex *	in_pb_pf,
		fftw_complex *	out_pb_pf,
		fftw_complex *	Dk,
		int	N,
		fftw_plan	pf,
		fftw_plan	pb
	)

Calculate the first derivative of a sampled function.

Note: in_pb_pf must be the buffer which is the input for both plans pf and pb. Likewise, out_pb_pf must be the output for both plans pf and pb.

Parameters

[in] in_pb_pf The buffer containing the data to be differentiated.

Warning: This buffer will be overwritten as part of the computation.

Parameters

[out]	out_pb_pf	The buffer which will contain the computed derivative.
[in,out]	Dk	Buffer to write the coefficients for performing differentiation and shifting in Fourier space.
[in]	N	Number of elements in buffers.
[in]	pf	The plan for forward FFT.
[in]	pb	The plan for backward FFT.

◆ init_diff_shift_op()

void init_diff_shift_op	(	double	delta,
		fftw_complex *	Dk,
		int	N
	)

Initialise the coefficients required to simultaneously perform differentiation and shifting by amount delta, using a forward and backward FFT.

Parameters

[in]	delta	The fraction of the spatial step.
[out]	Dk	Buffer to write the coefficients to.
[in]	N	The number of elements in Dk.