numpp

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numpp is an open source, template only, numerical library aimed at maximizing runtime efficiency by performing every calculation during the compilation step.

Currently it consists of:

• three differentiation ways (symbolic, automatic, finite difference),
• linear algebra structures (matrix dense, sparse, vector)
• root finding methods (bisection, newton, halley)
• krylov subspace methods (conjugate gradient, preconditioned conjugate gradient)

It trims the runtime by using cutting edge C++17 features, template metaprogramming, numerical ideas seen in recent numerical research papers and many others.

Usage Example:

1. Differentiating cos(x1)*sin(x2) two times with respect to x1 and y2.

#include"numpp/differentiation/symbolic.hpp"
namespace nds = numpp::differentiation::symbolic; //Removes redundant namespace

using Function = decltype(cos(nds::x<0>{})*sin(nds::x<1>{})); //Create function type
using Derivative = differentiate<Function, 2>::with_respect_to<0,1>; //Differentiate type

int main(){
  std::cout << Derivative::calculate(std::array<double, 2>{3, 5}; //Evaluate derivative at point x1 = 3, x2 = 5
  return 0;
}

How does it compare?

1. Most promising module

Best looking part is, without a doubt, symbolic differentiation.

Thanks to researchers from this paper and some improvements of mine, it seems, that it can achieve around 10x speedup or more in derivative evaluations against SymPy which approaches efficiency of hand-coded derivatives. When it comes to memory it should use 0b as it's only type based.

For thorough compilation times comparison, I urge you to check their scientific paper!

Credits for the squeezer idea and being first to publish it go to academics mentioned above.

2. Overall Runtime speedup

30 x speedups in matrix multiplication is not uncommon (compared to Eigen), and binaries created are shorter by about the same amount. In other areas, for example numerical differentiation, speed up over GNU Scientific Library can exceed 50x.

3. Compilation times

I'm not going to lie, this is the place, where some modules loses to the competition. In the case of matrix multiplication, memory bandwith and lack of parallelism during compilation may slow the matrix operations even by a few seconds.

Installation:

1. Normal installation

Just clone this repository into your /usr/include/ path or other performing the same functionality. It needs GCC7.0 or more for it to work. It should work for Clang as well, but it wasn't thoroughly tests

2. Dockerized installation

If your distro doesn't have GCC7.0 just run the Docker image provided in the banner at the top via command:

$ docker run -i -t vyzyv/numpp:latest /bin/bash

to enter the container, which has everything you need to run your applications based on numpp.

Documentation:

For more specific informations about what the library has to offer check below:

Documentation

For in-depth dissertation of provided functionality check the paper below and others linked inside:

Contributions:

Currently looking for contributors with interesting numerical ideas and all those willing to perform additional testing, expand documentation or implement their/someones (with permission and credits)