# File fft.hxx#

FFT routines

Copyright 2010 B.D.Dudson, S.Farley, M.V.Umansky, X.Q.Xu

Contact: Ben Dudson, bd512@york.ac.uk

This file is part of BOUT++.

BOUT++ is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

BOUT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with BOUT++. If not, see http://www.gnu.org/licenses/.

Functions

BOUT_ENUM_CLASS(FFT_MEASUREMENT_FLAG, estimate, measure, exhaustive)#
inline void rfft(const BoutReal *in, int length, dcomplex *out)#

Returns the fft of a real signal using fftw_forward

The fftw_forward returns out_k = sum_{j=0}^(length-1) in_j*exp(-2*pi*j*k*sqrt(-1)/length)

Thus, out_k must be divided by ‘length’ in order for DFT[IDFT[in]] = in where IDFT is the inverse fourier transform. See the the fftw user manual for details.

Parameters:
• in[in] Pointer to the 1D array to take the fourier transform of

• length[in] Number of points in the input array

• out[out] Pointer to the complex 1D array which is the FFT of in

inline void irfft(const dcomplex *in, int length, BoutReal *out)#

Take the inverse fft of signal where the outputs are only reals.

This is done through a call to fftw_plan_dft_c2r_1d which is calling fftw_backwards.

That is out_k = sum_{j=0}^(length-1) in_j*exp(2*pi*j*k*sqrt(-1)/length)

See the the fftw user manual for details.

Parameters:
• in[in] Pointer to the 1D array to take the inverse fourier transform of

• length[in] Number of points in the input array

• out[out] Pointer to the complex 1D array which is IFFTed

inline void DST(const BoutReal *in, int length, dcomplex *out)#

Discrete Sine Transform

`in` and `out` arrays must both be of the same `length`

inline void DST_rev(dcomplex *in, int length, BoutReal *out)#

Inverse Discrete Sine Transform

`in` and `out` arrays must both be of the same `length`

namespace bout

Usage

#include <bout/hyprelib.hxx>

class MyClass { public:

private: HypreLib lib; };

This will then automatically initialise Hypre the first time an object is created, and finalise it when the last object is destroyed.

Copyright 2012 B.D.Dudson, S.Farley, M.V.Umansky, X.Q.Xu

Contact: Ben Dudson, bd512@york.ac.uk

This file is part of BOUT++.

BOUT++ is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

BOUT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with BOUT++. If not, see http://www.gnu.org/licenses/.

Information about the version of BOUT++

The build system will update this file on every commit, which may result in files that include it getting rebuilt. Therefore it should be included in as few places as possible

Information about the version of BOUT++

The build system will update this file at configure-time

SNB model

namespace fft#

Functions

inline void rfft(const BoutReal *in, int length, dcomplex *out)#

Returns the fft of a real signal using fftw_forward

The fftw_forward returns out_k = sum_{j=0}^(length-1) in_j*exp(-2*pi*j*k*sqrt(-1)/length)

Thus, out_k must be divided by ‘length’ in order for DFT[IDFT[in]] = in where IDFT is the inverse fourier transform. See the the fftw user manual for details.

Parameters:
• in[in] Pointer to the 1D array to take the fourier transform of

• length[in] Number of points in the input array

• out[out] Pointer to the complex 1D array which is the FFT of in

inline void irfft(const dcomplex *in, int length, BoutReal *out)#

Take the inverse fft of signal where the outputs are only reals.

This is done through a call to fftw_plan_dft_c2r_1d which is calling fftw_backwards.

That is out_k = sum_{j=0}^(length-1) in_j*exp(2*pi*j*k*sqrt(-1)/length)

See the the fftw user manual for details.

Parameters:
• in[in] Pointer to the 1D array to take the inverse fourier transform of

• length[in] Number of points in the input array

• out[out] Pointer to the complex 1D array which is IFFTed

inline void DST(const BoutReal *in, int length, dcomplex *out)#

Discrete Sine Transform

`in` and `out` arrays must both be of the same `length`

inline void DST_rev(dcomplex *in, int length, BoutReal *out)#

Inverse Discrete Sine Transform

`in` and `out` arrays must both be of the same `length`

void fft_init(bool fft_measure)#

Should the FFT functions find and use an optimised plan?

void fft_init(FFT_MEASUREMENT_FLAG fft_flag)#

Should the FFT functions find and use an optimised plan?

void fft_init(Options *options = nullptr)#

Should the FFT functions find and use an optimised plan?

If `options` is not nullptr, it should contain a bool called “fftw_measure”. If it is nullptr, use the global `Options` root

Array<dcomplex> rfft(const Array<BoutReal> &in)#

Returns the fft of a real signal `in` using fftw_forward.

Array<BoutReal> irfft(const Array<dcomplex> &in, int length)#

Take the inverse fft of signal `in` where the outputs are only reals. Requires the `length` of the original real signal

`length` is required because input signals to the forward transform of length `n` and `n + 1` both produce ffts of length `(n / 2) + 1` &#8212; i.e. it’s not possible to recover the length of the original signal from the fft alone.

Expects that `in.size() == (length / 2) + 1`