fastrk 0.0.4

FastRK, a generator of fast jit-compiled code for ODE propagation by ERK methods with adaptive step and events

FastRK

• developed as fast alternative for subset of scipy.integrate.ode methods (i.e. DOP853);
• is a python code generator for Ordinary Differential Equations (ODE) propagation;
• uses explicit embedded Runge-Kutta (ERK) methods with adaptive step technique;
• calculates events using event functions (like scipy.integrate.solve_ivp);
• is jit-compiled by numba;
  • compiled code cached on SSD/HDD to prevent unnecessary recompilation;
• reentry, i.e. can be used in multithreaded applications;
• OS-independent (to the same extent as numba);
• contains Butcher Tables for several ERK methods:
  • Dormand and Prince 6(5)8M;
  • Dormand and Prince 8(7)13M;
    • >2x faster than DOP853 from scipy.integrate.ode
  • Verner's 8(9)16;
• user-defined Butcher Tables also supported;
• generated code is open and user-modifiable;

Butcher Tables was adapted from TrackerComponentLibrary.

Installation

pip install fastrk

Fast example

import numpy as np
import matplotlib.pyplot as plt
from fastrk import BT8713M, RKCodeGen

# CRTBP ODE, https://github.com/BoberSA/fastrk/tree/master/examples/model_crtbp.py
from model_crtbp import crtbp

rk_module = RKCodeGen(BT8713M, autonomous=True).save_and_import()
rk_prop = rk_module.rk_prop

t0, t1 = 0., 3 * np.pi
# initial state for halo orbit
s0 = np.zeros(6)
s0[[0, 2, 4]] = 9.949942666080747733e-01, 4.732924802139452415e-03, -1.973768492871211949e-02
mc = np.array([3.001348389698916e-06])  # CRTBP constant
rtol, atol = 1e-12, 1e-12

# integrate CRTBP ODE from t0, s0 to t1
arr = rk_prop(crtbp, s0, t0, t1, np.inf, rtol, atol, mc)

plt.plot(arr[:, 1], arr[:, 2], 'r')
plt.axis('equal')
plt.show()

Detailed examples

Example 0: Propagate spacecraft motion in Circular Restricted Three Body Problem

Example 1: Calculate events in Circular Restricted Three Body Problem

Required modules:

• model_crtbp.py

Parallel (OpenMP) example

Required modules:

• model_crtbp.py
• map_vy_funcs.py

Output for Ryzen 7 4700U CPU

    compiling sequential...
    compiling parallel...
    states count: 2500
    sequential calculation started (Ms)
    map calculation time: 46.31 s
    parallel calculation started (Mp)
    map calculation time: 22.19 s
    speedup x 2.09
    ||Ms - Mp|| = 0.0

Core Developer

Stanislav Bober, MIEM NRU HSE, IKI RAS