\(
\newcommand{\P}[]{\unicode{xB6}}
\newcommand{\AA}[]{\unicode{x212B}}
\newcommand{\empty}[]{\emptyset}
\newcommand{\O}[]{\emptyset}
\newcommand{\Alpha}[]{Α}
\newcommand{\Beta}[]{Β}
\newcommand{\Epsilon}[]{Ε}
\newcommand{\Iota}[]{Ι}
\newcommand{\Kappa}[]{Κ}
\newcommand{\Rho}[]{Ρ}
\newcommand{\Tau}[]{Τ}
\newcommand{\Zeta}[]{Ζ}
\newcommand{\Mu}[]{\unicode{x039C}}
\newcommand{\Chi}[]{Χ}
\newcommand{\Eta}[]{\unicode{x0397}}
\newcommand{\Nu}[]{\unicode{x039D}}
\newcommand{\Omicron}[]{\unicode{x039F}}
\DeclareMathOperator{\sgn}{sgn}
\def\oiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x222F}\,}{\unicode{x222F}}{\unicode{x222F}}{\unicode{x222F}}}\,}\nolimits}
\def\oiiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x2230}\,}{\unicode{x2230}}{\unicode{x2230}}{\unicode{x2230}}}\,}\nolimits}
\)
Eigen is a template header-only C++ linear algebra library. It is one of the fastest and most popular.
Website
Usage
Compilation
Reference
For optimal performance, I recommend using the following flags when compiling.
GCC
-mfma
Enable fused multiply add
-mavx2
Enable avx2 vector instructions
-DEIGEN_NO_DEBUG
Set preprocessor define for eigen optimizations
-fopenmp
OpenMP parallel execution
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