prescaledFastAdj

Extended version of the FastAdjacency package of Dominik Bünger.

Python extension to compute fast approximate evaluations of the Gaussian kernel, the Matérn(1/2) kernel and their derivative kernels for our paper "Fast Evaluation of Additive Kernels: Feature Arrangement, Fourier Methods and Kernel Derivatives".

Different to the original FastAdjacency, this package additionally enables to evaluate the Gaussian derivative kernel matrix, the Matérn(1/2) kernel and its derivative kernel. Moreover, the data is prescaled with scaling parameters based on the scaled data in order to be scaled equally in all dimensions for a transparent global sensitivity analysis and to achieve a better approximation.

This package provides a Python interface to a part of the NFFT3 library to quickly approximate adjacency matrices of fully connected graphs with Gaussian edge weights. See test/showcase.ipynb for an overview of the method.

Installation

• This software has been tested with Python 3.7.

• This software currently depends on the Julia interface of the NFFT3 library.

  • Download the NFFT3 source from https://github.com/NFFT/nfft.
  • When building the prerequesite FFTW3, make sure to call the configure script with --enable-shared --enable-openmp --enable-threads.
  • Configure, build and install NFFT3 following the instructions on the homepage. Make sure to configure the library with --enable-julia.

• Call echo $LD_LIBRARY_PATH to make sure that it contains /usr/local/lib, where the shared libraries of FFTW and NFFT are installed. If not, add the line export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib to your ~/.bashrc file and run source ~/.bashrc.

• Navigate to the prescaledFastAdj folder.

• Export the path to your NFFT3 installation folder as the NFFT_BASE environment variable via export NFFT_BASE=/path/to/your/NFFT/base/directory.

• From the same terminal, run make and make install. Optionally run make check to test your installation.

• To rebuild, run make clean before make.

Usage

This package mainly consists of the following three classes:

• AccuracySetup stores setup parameters for the NFFT Fastsum algorithm. You can load one of three presets via AccuracySetup(preset='name'). Available preset names are 'default', 'fine', and 'rough'.

• AdjacencyCore is the core type of fastadj, implemented in C. It serves as a wrapper for the NFFT fastsum type. Although it can be instantiated directly, we advise against it.

• AdjacencyMatrix is a convenient wrapper for AdjacencyCore, written in Python. This is the recommended way to use this package.

See test/showcase.ipynb and test/test.py for an example.