ShiftConvolveFFTW

ShiftConvolve is a R package which uses exponential shifting and the Fast Fourier Transformations (FFT) to compute the (right) tail of the Poisson Binomial Distribution. This package makes use of the Fastest Fourier Transform in the West (FFTW) library to perform the necessary DFT and Inverse DFT computations.

For the ShiftConvolve implementation which uses minFFT to perform the Fourier Transformations please go to https://github.com/andrew12678/ShiftConvolve.

In the interest of speed we all significant computational aspects of our procedure are executed by code written in C and the R code mainly acts as a wrapper around that compiled C code.

We have successfully installed ShiftConvolveFFTW on Windows 10: Professional Version 1909, macOS: Mojave 10.14.6/Catalina 10.15.4 and Linux: Ubuntu 18.04/Manjaro 19.02 KDE Plasma. A full installation guide will be provided below for all 3 Operating Systems.

ShiftConvolveFFTW has also been installed on both AMD and Intel CPU systems. Specifically, a Intel Core i7 MacMini with 32GB of RAM, AMD Ryzen 5 2600 with 16GB of RAM and a Macbook Pro i7 with 16GB of RAM

Dependencies

As eluded to above, FFTW will be a necessary dependency.

Linux

This package was originally compiled in an Ubuntu 18.04 Linux operating system using R 3.5.1 and FFTW 3.3.5 but was later recompiled (without any modification of the configurations) in a Manjaro 19.02 KDE Plasma Linux operating system with inbuilt FFTW 3.3.8 and R 3.6.3. Since the FFTW came along with the Manjaro installation, we will only outline installations on the Ubuntu and macOS system which does not automatically install FFTW.

For Ubuntu the steps included:

wget http://fftw.org/fftw-3.3.5.tar.gz
tar -xzf fftw-3.3.5.tar.gz
cd fftw-3.3.5
./configure --enable-shared
make
sudo make install

Since the Manjaro distribution came with FFTW 3.3.8, later versions of FFTW should be able to be installed as well.

macOS

FFTW should be first installed in the same manner as the Linux distributions with the macOS terminal. For emphasis we repeat it below.

wget http://fftw.org/fftw-3.3.5.tar.gz
tar -xzf fftw-3.3.5.tar.gz
cd fftw-3.3.5
./configure --enable-shared
make
sudo make install

To use wget, the user may have to install Homebrew, which can be installed with the following command.

/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install.sh)"

To avoid a further pkg-config error later down the track, we shall install it with brew

brew install pkg-config

If the above throws an error then it should prompt you make the following 2 changes and then try the installation again.

sudo chown -R $(whoami) /usr/local/lib/pkgconfig /usr/local/share/info
chmod u+w /usr/local/lib/pkgconfig /usr/local/share/info
brew install pkg-config

Windows

Before installation, get to see if you have Rtools installed on your system already (via Add or remove programs). If not we wish to download and install here: https://cran.r-project.org/bin/windows/Rtools/

We will not be installing FFTW in the conventional way for Windows, instead we will use the precompiled binary called fftw-3.3.5-dll64.zip found here: http://www.fftw.org/install/windows.html.

After unzipping fftw-3.3.5-dll64.zip, we want to copy the files fftw3.h and libfftw3-3.dll to a directory C:\fftw (to create this directory simply open any Windows File Explorer, click This PC on the left panel and enter Local Disk (C:) and just make a new folder called fftw)

Then in the Windows search bar we want to type environment and then click: Edit the system environment variables.

We then want to click Environment Variables in the following pop-up:

Then under System Variables click New to add a variable for LIB_FFTW with value C:\fftw:

Then back to System Variables we want to find the entry called Path, click once on it to highlight it and then click Edit:

Here we want to make sure the C:\Rtools\bin and C:\fftw are both entries are in Path, otherwise we add then by clicking New:

That should conclude all the installation of FFTW dependencies on Windows.

Alternatively, one could attempt to build FFTW from source using MinGW as outlined on http://www.fftw.org/install/windows.html using the commands in the MinGW terminal in the directory of the zip file downloaded earlier:

./configure --with-our-malloc16 --with-windows-f77-mangling --enable-shared --disable-static --enable-threads --with-combined-threads --enable-portable-binary --enable-sse2 --with-incoming-stack-boundary=2
make
make install

However, we have not (and do not intend to) try this.

Installation

The most simple installation involves installing devtools in R and using the install_github() function.

install.packages('devtools') # If you have not installed devtools
devtools::install_github('https://github.com/andrew12678/ShiftConvolveFFTW.git')

An alternative installation procedure involves cloning the repository, creating a RStudio project and then building.

Examples

An simple example with the uniform distribution

library(ShiftConvolvePoibin)
set.seed(18)
n=1000
probs <- runif(n)
x <- c(200, 500, 800)
p <- seq(0, 1, 0.01)
dpoisbin(x,probs,method="ShiftConvolve",log.p=FALSE)
ppoisbin(x,probs,method="ShiftConvolve",lower.tail=FALSE,log.p=TRUE)
qpoisbin(p,probs,method="ShiftConvolve",lower.tail=TRUE,log.p=FALSE)
rpoisbin(n,probs)

References

[1] Peres, N., Lee, A., and Keich, U. (2020). Exactly computing the tail of the Poisson-Binomial Distribution. arXiv:2004.07429