Eigen (C++ library)

Eigen is a template header-only C++ linear algebra library. You can think of it as as numpy for C++.

Usage

Compilation

Reference
For optimal performance, I recommend using the following flags when compiling.

GCC

-march=native and -mtune=native if running only locally or -march=skylake if distributing to relatively modern (since ~2015) cpus.
- Otherwise, at a minimum
- -mfma Enable fused multiply add
- -mavx2 Enable avx2 vector instructions
-DEIGEN_NO_DEBUG Set preprocessor define for eigen optimizations
-fopenmp OpenMP parallel execution
-O3 to enable optimizations

Data to Eigen

You can use Eigen::Map to create an eigen view for your existing data. This works with aligned or unaligned data, row-order or column-order, and different strides.
See Eigen: Interfacing with raw buffers for an example.

Math

SVD

Eigen comes with a few SVD implementations in its SVD Module.
If you only need low-rank approximations then you may be interested in randomized SVD.
This can be 10-20x faster when calculating low-rank approximations on large matrices.
Github Implementation
Finding structure with randomness paper
Facebook Blog post

Unsupported

FFT

https://eigen.tuxfamily.org/dox/unsupported/group__FFT__Module.html
https://gitlab.com/libeigen/eigen/-/blob/master/unsupported/Eigen/FFT?ref_type=heads
https://eigen.tuxfamily.org/index.php?title=EigenFFT

This uses either kissfft (default), FFTW (GPL), Intel oneMKL, or pocketFFT under the hood. There is very little documentation on this so it's easier to just read the code:

// Initialize standard FFT.
Eigen::FFT<double> fft;

// Initialize RFFT
Eigen::FFT<double> fft(Eigen::FFT<double>::impl_type(), Eigen::FFT<double>::HalfSpectrum);

// Do the actual FFT or RFFT.
std::vector<double> my_data = {1.0, 2.0, 3.0, 4.0};
std::vector<std::complex<double>> fft_result;
fft.fwd(fft_result, my_data);

// Inverse
fft.inv(my_data, fft_result);

Notes

Alternative backend implementations can be set with EIGEN_FFTW_DEFAULT, EIGEN_MKL_DEFAULT, EIGEN_POCKETFFT_DEFAULT
fwd2 and inv2 is available on the non-default backends.