This is a python adaptor for the fortan-based Bulirsch-Stoer integrator. The integrator is written in fortran, from Numerical Recipies. An example implementation is included in the file pythagorean_threebody.py. After installing, run this file from the command-line, and examine output.dat and output.png to see the results.
This module requires Numpy. If you have Numpy installed and accessible, it should work. To install this module, use:
$ sudo python setup.py install
If this works proprely, you will have a bsint module with a bsintegrate method that you can use to carry out Bulirsch-Stoer integrations.
To run the example program, try
$ ./pythagorean_threebody.py
and look at output.png!
To use the bsintegrate() function, you'll need to write a function which calculates the derivatives of your system of equations. The signature of your derivatives function should be derivs(t,Ys,*args) where args are any extra arguments you wish to pass through the integrator to the derivatives function. Derivatives should return an array dYsdt, the derivatives of Ys, which should be the same shape as Ys. Ys and dYsdt should be Numpy arrays.
The bsintegrate function itself:
yout,tout = bsintegrate(derivs,y,t0,t1,[tacc,h0,mxstep,args])
derivs : call-back function. Should take the current timestep and position. derivs(t,y)
y : input array of variables for integration at t0.
t0 : float, starting time for integration
t1 : float, ending point for integration
args: input tuple, optional- Default:
() tacc: input float, optional- Default:
1e-14 h0: input float, optional- Default:
1e-3 mxstep: input int, optional- Default:
1e4
yout : rank-2 array() with bounds (steps,nes)
tout : rank-1 array() with bounds (steps)
Call-back functions:
def derivs(x,y): return dydx
Required arguments:
x : input float
y : input rank-1 array('d') with bounds (n)
Return objects:
dydx : rank-1 array('d') with bounds (n)