Modern Taylor's method via just-in-time compilation
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The heyókȟa [...] 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. Notable features include:
- support for both double-precision and extended-precision floating-point types (80-bit and 128-bit),
- the ability to maintain machine precision accuracy over tens of billions of timesteps,
- high-precision zero-cost dense output,
- accurate and reliable event detection,
- batch mode integration to harness the power of modern SIMD instruction sets,
- a high-performance implementation of Taylor's method based on automatic differentiation techniques and aggressive just-in-time compilation via LLVM.
If you prefer using Python rather than C++, heyoka can be used from Python via heyoka.py, its Python bindings.
As a simple example, here's how the ODE system of the pendulum is defined and numerically integrated in heyoka:
#include <iostream>
#include <heyoka/heyoka.hpp>
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<double>{// 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';
}The full documentation can be found here.
- Francesco Biscani (Max Planck Institute for Astronomy)
- Dario Izzo (European Space Agency)
heyoka is released under the MPL-2.0 license.