Eigen (C++ library): Difference between revisions
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Eigen is a template header-only C++ linear algebra library. | Eigen is a template header-only C++ linear algebra library. You can think of it as as [[numpy]] for C++. | ||
[http://eigen.tuxfamily.org/index.php?title=Main_Page Website] | [http://eigen.tuxfamily.org/index.php?title=Main_Page Website] | ||
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For optimal performance, I recommend using the following flags when compiling.<br> | For optimal performance, I recommend using the following flags when compiling.<br> | ||
====GCC==== | ====GCC==== | ||
*<code>-mfma</code> Enable fused multiply add | *<code>-march=native</code> and <code>-mtune=native</code> if running only locally or <code>-march=skylake</code> if distributing to relatively modern (since ~2015) cpus. | ||
*<code>-mavx2</code> Enable avx2 vector instructions | **Otherwise, at a minimum | ||
**<code>-mfma</code> Enable fused multiply add | |||
**<code>-mavx2</code> Enable avx2 vector instructions | |||
*<code>-DEIGEN_NO_DEBUG</code> Set preprocessor define for eigen optimizations | *<code>-DEIGEN_NO_DEBUG</code> Set preprocessor define for eigen optimizations | ||
*<code>-fopenmp</code> OpenMP parallel execution | *<code>-fopenmp</code> OpenMP parallel execution | ||
*<code>-O3</code> to enable optimizations | |||
===Data to Eigen=== | |||
You can use [https://eigen.tuxfamily.org/dox/classEigen_1_1Map.html <code>Eigen::Map</code>] to create an eigen view for your existing data. | |||
This works with aligned or unaligned data, row-order or column-order, and different strides.<br> | |||
See [https://eigen.tuxfamily.org/dox/group__TutorialMapClass.html Eigen: Interfacing with raw buffers] for an example. | |||
==Math== | |||
===SVD=== | |||
Eigen comes with a few SVD implementations in its [https://eigen.tuxfamily.org/dox/group__SVD__Module.html SVD Module].<br> | |||
If you only need low-rank approximations then you may be interested in randomized SVD.<br> | |||
This can be 10-20x faster when calculating low-rank approximations on large matrices.<br> | |||
[https://github.com/kazuotani14/RandomizedSvd Github Implementation]<br> | |||
[https://arxiv.org/abs/0909.4061 Finding structure with randomness paper]<br> | |||
[https://research.fb.com/blog/2014/09/fast-randomized-svd/ Facebook Blog post] | |||
==Unsupported== | |||
===FFT=== | |||
https://eigen.tuxfamily.org/dox/unsupported/group__FFT__Module.html<br> | |||
https://gitlab.com/libeigen/eigen/-/blob/master/unsupported/Eigen/FFT?ref_type=heads<br> | |||
https://eigen.tuxfamily.org/index.php?title=EigenFFT<br> | |||
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: | |||
<syntaxhighlight lang="cpp"> | |||
// 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); | |||
</syntaxhighlight> | |||
'''Notes''' | |||
* Alternative backend implementations can be set with <code>EIGEN_FFTW_DEFAULT</code>, <code>EIGEN_MKL_DEFAULT</code>, <code>EIGEN_POCKETFFT_DEFAULT</code> | |||
* <code>fwd2</code> and <code>inv2</code> is available on the non-default backends. | |||
Latest revision as of 20:38, 16 April 2024
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=nativeand-mtune=nativeif running only locally or-march=skylakeif distributing to relatively modern (since ~2015) cpus.- Otherwise, at a minimum
-mfmaEnable fused multiply add-mavx2Enable avx2 vector instructions
-DEIGEN_NO_DEBUGSet preprocessor define for eigen optimizations-fopenmpOpenMP parallel execution-O3to 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 fwd2andinv2is available on the non-default backends.