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https://github.com/bluescarni/heyoka
C++ library for ODE integration via Taylor's method and LLVM
https://github.com/bluescarni/heyoka
astrodynamics astronomy astrophysics celestial-mechanics cpp cpp17 differential-equations extended-precision just-in-time llvm multiprecision n-body nbody ode ode-solver simd
Last synced: 1 day ago
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C++ library for ODE integration via Taylor's method and LLVM
- Host: GitHub
- URL: https://github.com/bluescarni/heyoka
- Owner: bluescarni
- License: mpl-2.0
- Created: 2020-07-01T08:22:45.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2025-01-07T16:40:32.000Z (16 days ago)
- Last Synced: 2025-01-15T11:35:11.135Z (8 days ago)
- Topics: astrodynamics, astronomy, astrophysics, celestial-mechanics, cpp, cpp17, differential-equations, extended-precision, just-in-time, llvm, multiprecision, n-body, nbody, ode, ode-solver, simd
- Language: C++
- Homepage: https://bluescarni.github.io/heyoka/
- Size: 449 MB
- Stars: 207
- Watchers: 7
- Forks: 12
- Open Issues: 4
-
Metadata Files:
- Readme: README.md
- License: COPYING
Awesome Lists containing this project
README
heyoka
======
[](https://circleci.com/gh/bluescarni/heyoka)
[](https://github.com/bluescarni/heyoka/actions?query=workflow%3A%22GitHub+CI%22)
[](https://codecov.io/github/bluescarni/heyoka?branch=master)
[](https://anaconda.org/conda-forge/heyoka)
Modern Taylor's method via just-in-time compilation
Explore the docs »
Report bug
·
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Discuss
> The [heyókȟa](https://en.wikipedia.org/wiki/Heyoka>) [...] is a kind of
> sacred clown in the culture of the Sioux (Lakota and Dakota people)
> of the Great Plains of North America. The heyoka is a contrarian, jester,
> and satirist, who speaks, moves and reacts in an opposite fashion to the
> people around them.
heyoka is a C++ library for the integration of ordinary differential equations
(ODEs) via Taylor's method, based on automatic differentiation techniques and aggressive just-in-time
compilation via [LLVM](https://llvm.org/). Notable features include:
* support for single-precision, double-precision, extended-precision (80-bit and 128-bit),
and arbitrary-precision floating-point types,
* high-precision zero-cost dense output,
* accurate and reliable event detection,
* builtin support for analytical mechanics - bring your own Lagrangians/Hamiltonians
and let heyoka formulate and solve the equations of motion,
* builtin support for high-order variational equations - compute not only the solution,
but also its partial derivatives,
* builtin support for machine learning applications via neural network models,
* the ability to maintain machine precision accuracy over
tens of billions of timesteps,
* batch mode integration to harness the power of modern
[SIMD](https://en.wikipedia.org/wiki/SIMD) instruction sets
(including AVX/AVX2/AVX-512/Neon/VSX),
* ensemble simulations and automatic parallelisation.
If you prefer using Python rather than C++, heyoka can be used from Python via
[heyoka.py](https://github.com/bluescarni/heyoka.py), its Python bindings.
If you are using heyoka as part of your research, teaching, or other activities, we would be grateful if you could star
the repository and/or cite our work. For citation purposes, you can use the following BibTex entry, which refers
to the heyoka paper ([arXiv preprint](https://arxiv.org/abs/2105.00800)):
```bibtex
@article{10.1093/mnras/stab1032,
author = {Biscani, Francesco and Izzo, Dario},
title = "{Revisiting high-order Taylor methods for astrodynamics and celestial mechanics}",
journal = {Monthly Notices of the Royal Astronomical Society},
volume = {504},
number = {2},
pages = {2614-2628},
year = {2021},
month = {04},
issn = {0035-8711},
doi = {10.1093/mnras/stab1032},
url = {https://doi.org/10.1093/mnras/stab1032},
eprint = {https://academic.oup.com/mnras/article-pdf/504/2/2614/37750349/stab1032.pdf}
}
```
heyoka's novel event detection system is described in the following paper ([arXiv preprint](https://arxiv.org/abs/2204.09948)):
```bibtex
@article{10.1093/mnras/stac1092,
author = {Biscani, Francesco and Izzo, Dario},
title = "{Reliable event detection for Taylor methods in astrodynamics}",
journal = {Monthly Notices of the Royal Astronomical Society},
volume = {513},
number = {4},
pages = {4833-4844},
year = {2022},
month = {04},
issn = {0035-8711},
doi = {10.1093/mnras/stac1092},
url = {https://doi.org/10.1093/mnras/stac1092},
eprint = {https://academic.oup.com/mnras/article-pdf/513/4/4833/43796551/stac1092.pdf}
}
```
Quick example
-------------
As a simple example, here's how the ODE system of the
[pendulum](https://en.wikipedia.org/wiki/Pendulum_(mathematics))
is defined and numerically integrated
in heyoka:
```c++
#include
#include
using namespace heyoka;
int main()
{
// Create the symbolic variables x and v.
auto [x, v] = make_vars("x", "v");
// Create the integrator object
// in double precision.
auto ta = taylor_adaptive{// Definition of the ODE system:
// x' = v
// v' = -9.8 * sin(x)
{prime(x) = v, prime(v) = -9.8 * sin(x)},
// Initial conditions
// for x and v.
{0.05, 0.025}};
// Integrate for 10 time units.
ta.propagate_for(10.);
// Print the state vector.
std::cout << "x(10) = " << ta.get_state()[0] << '\n';
std::cout << "v(10) = " << ta.get_state()[1] << '\n';
}
```
Output:
```console
x(10) = 0.0487397
y(10) = 0.0429423
```
Documentation
-------------
The full documentation can be found [here](https://bluescarni.github.io/heyoka/).
Authors
-------
* Francesco Biscani (European Space Agency)
* Dario Izzo (European Space Agency)
License
-------
heyoka is released under the [MPL-2.0](https://www.mozilla.org/en-US/MPL/2.0/FAQ/)
license.