dft.c File Reference

All routines related with discrete fourier transformations. More...

#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <fftw3.h>
#include "cdr.h"
#include "cstream.h"
#include "grid.h"
#include "parameters.h"
#include "proto.h"
#include "rz_array.h"
#include "species.h"

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Macros
#define	AM   (1.0 / RAND_MAX)

Functions
static void	renormalize (cdr_grid_t *grid, rz_array_t *var)
	Renormalize var for some cases.
static double	rnd_gauss (double mu, double sigma)
	Returns a random number with a gaussian distribution centered around mu with width sigma.
static double	ranf (void)
	Returns a random number uniformly distributed in [0, 1].
void	dft_transform (rz_array_t *in, rz_array_t *out, int sign)
	Transform the discrete fourier transformations ????
void	dft_diff (grid_t *grid, rz_array_t *f)
	Calculates the Fourier transform of the derivative of a function given its Fourier transform.
void	dft_weight (cdr_grid_t *cdr, rz_array_t *var, double weights[], double power)
	Calculates the weight for a given cdr grid and a variable ???
void	dft_out_weights (cdr_grid_t *grid, const char *prefix, double t)
	Outputs to a file 'weights.tsv' the results of dft_weight.
void	dft_perturb (cdr_grid_t *cdr, rz_array_t *var, double *epsilon_k)
	Perturbs a FFT-transformed variable.
void	dft_dens_perturb_r (cdr_grid_t *grid, int species, double *epsilon_k)
	Takes a density in real space, transforms it to Fourier space, perturbs it and then transforms back to real space.

Detailed Description

All routines related with discrete fourier transformations.

We make intensive use of the fftw library.
FFTW, the Fastest Fourier Transform in the West, is a collection of fast C routines to compute the discrete Fourier transform. See http://www.fftw.org/doc/ for the manual documents of FFTW version 3.3.3.

Note: All calls to FFTW should be made here, so

1. If we decide to change our FFT library, we only have to make changes in this module.
2. We can compile a 2d version of the code that does not depend on fftw. by eliminating this module.

Definition in file dft.c.

Macro Definition Documentation

#define AM   (1.0 / RAND_MAX)

Definition at line 366 of file dft.c.

Function Documentation

static void renormalize ( cdr_grid_t *  grid, rz_array_t *  var  )

static

Renormalize var for some cases.

FFTW does not normalize the Fourier transform, so after transforming forth and back, the original values are multiplied by max_ntheta. We use this routine to renormalize var in those cases.

Note that this is taken care of when calculating the charge, so in most cases you do not need to call this function.

Definition at line 319 of file dft.c.

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static double rnd_gauss ( double  mu, double  sigma  )

static

Returns a random number with a gaussian distribution centered around mu with width sigma.

Definition at line 339 of file dft.c.

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static double ranf ( void  )

static

Returns a random number uniformly distributed in [0, 1].

Definition at line 370 of file dft.c.

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void dft_transform	(	rz_array_t *	in,
		rz_array_t *	out,
		int	sign
	)

Transform the discrete fourier transformations ????

Definition at line 37 of file dft.c.

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void dft_diff	(	grid_t *	grid,
		rz_array_t *	f
	)

Calculates the Fourier transform of the derivative of a function given its Fourier transform.

Definition at line 97 of file dft.c.

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void dft_weight	(	cdr_grid_t *	cdr,
		rz_array_t *	var,
		double	weights[],
		double	power
	)

Calculates the weight for a given cdr grid and a variable ???

For a given cdr grid and a variable, calculates its "weight": the integral of the variable raised to power for each Fourier mode. weights[] must be able to contain at least cdr->ntheta values.

Definition at line 143 of file dft.c.

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void dft_out_weights	(	cdr_grid_t *	grid,
		const char *	prefix,
		double	t
	)

Outputs to a file 'weights.tsv' the results of dft_weight.

Assumes that grid->charge is calculated but in real space then it transforms it to Fourier space and leaves it like that: so do not assume that grid->charge is unchanged.

grid->dens[electrons], on the other hand, is transformed forth and back.

Definition at line 177 of file dft.c.

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void dft_perturb	(	cdr_grid_t *	cdr,
		rz_array_t *	var,
		double *	epsilon_k
	)

Perturbs a FFT-transformed variable.

Assumes that the unperturbed variable is axi-symmetrical and hence all modes are zero except k=0. The perturbation is then selected as a Gaussian random number epsilon_k times the zero-mode value of the variable. epsilon_k is distributed as epsilon_k = N(0, perturb_epsilon).

Definition at line 246 of file dft.c.

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void dft_dens_perturb_r	(	cdr_grid_t *	grid,
		int	species,
		double *	epsilon_k
	)

Takes a density in real space, transforms it to Fourier space, perturbs it and then transforms back to real space.

Definition at line 270 of file dft.c.

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