Eigen (C++ library)

Eigen is a template header-only C++ linear algebra library. It is one of the fastest and most popular.

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