fftw bindings for the xtensor C++ multi-dimensional array library.

Example

Calculate the derivative of a field a in Fourier space, e.g. a sine shaped field:

#include <xtensor-fftw/basic.hpp>   // rfft, irfft
#include <xtensor-fftw/helper.hpp>  // rfftscale 
#include <xtensor/xarray.hpp>
#include <xtensor/xbuilder.hpp>     // xt::arange
#include <xtensor/xmath.hpp>        // xt::sin, cos
#include <complex>
#include <xtensor/xio.hpp>

// generate a sinusoid field
double dx = M_PI/100;
xt::xarray<double> x = xt::arange(0., 2*M_PI, dx);
xt::xarray<double> sin = xt::sin(x);

// transform to Fourier space
auto sin_fs = xt::fftw::rfft(sin);

// multiply by i*k
std::complex<double> i {0, 1};
auto k = xt::fftw::rfftscale<double>(sin.shape()[0], dx);
xt::xarray< std::complex<double> > sin_derivative_fs = xt::eval(i * k * sin_fs);

// transform back to normal space
auto sin_derivative = xt::fftw::irfft(sin_derivative_fs);

std::cout << "x:              " << x << std::endl;
std::cout << "sin:            " << sin << std::endl;
std::cout << "cos:            " << xt::cos(x) << std::endl;
std::cout << "sin_derivative: " << sin_derivative << std::endl;

Installation

Using conda:

conda install xtensor-fftw -c conda-forge

This automatically installs dependencies as well (see list of dependencies below).

Installing from source into $PREFIX (for instance $CONDA_PREFIX when in a conda environment, or $HOME/.local) after manually installing the dependencies:

git clone https://github.com/egpbos/xtensor-fftw
cd xtensor-fftw
mkdir build
cd build
cmake .. -DCMAKE_INSTALL_PREFIX=$PREFIX
make install

Dependencies

• xtensor
• xtl
• FFTW version 3
• A compiler supporting C++14

Usage

xtensor-fftw is a header-only library. To use, include one of the header files in the include directory, e.g. xtensor-fftw/basic.hpp, in your c++ code. To compile, one should also include the paths to the FFTW header and libraries and link to the appropriate FFTW library.

Note that xtensor-fftw on Windows does not support long double precision. The long double precision version of the FFTW library requires that sizeof(long double) == 12. In recent versions of Visual Studio, long double is an alias of double and has size 8.

Building and running tests

What follows are instructions for compiling and running the xtensor-fftw tests. These also serve as an example of how to do build your own code using xtensor-fftw (excluding the GoogleTest specific parts).

Dependencies for building tests

The main dependency is a version of FFTW 3. For the tests, we need the floating point version which is enabled in the FFTW configuration step using:

./configure --enable-float

CMake and xtensor must also be installed in order to compile the xtensor-fftw tests. Both can either be installed through Conda or built/installed manually. When using a non-Conda xtensor-install, make sure that the CMake find_package command can find xtensor, e.g. by passing something like -DCMAKE_MODULE_PATH="path_to_xtensorConfig.cmake" to CMake. If xtensor was installed in a default location, CMake should be able to find it without any command line options.

Optionally, a GoogleTest installation can be used. However, it is recommended to use the built-in option to download GoogleTest automatically (see below).

Configure tests

Inside the xtensor-fftw source directory, create a build directory and cd into it:

mkdir build
cd build

If pkg-config is present on your system and your FFTW installation can be found by it, then CMake can configure your build with command:

cmake .. -DBUILD_TESTS=ON -DDOWNLOAD_GTEST=ON

If you do not use pkg-config, the FFTW prefix, i.e. the base directory under which FFTW is installed, must be passed to CMake. Either set the FFTWDIR environment variable to the prefix path, or use the FFTW_ROOT CMake option variable. For instance, if FFTW was installed using ./configure --prefix=/home/username/.local; make; make install, then either set the an environment variable in your shell before running CMake:

export FFTWDIR=/home/username/.local
cmake ..  -DBUILD_TESTS=ON -DDOWNLOAD_GTEST=ON [other options]

or pass the path to CMake directly as such:

cmake .. -DFFTW_ROOT=/home/username/.local  -DBUILD_TESTS=ON -DDOWNLOAD_GTEST=ON [other options]

Compile tests

After successful CMake configuration, run inside the build directory:

make

Run tests

From the build directory, change to the test directory and run the tests:

cd test
./test_xtensor-fftw

License

We use a shared copyright model that enables all contributors to maintain the copyright on their contributions.

This software is licensed under the BSD-3-Clause license. See the LICENSE file for details.