Imitate ode45 function from MATLAB in Python

Question

I am wondering how to export MATLAB function ode45 to python. According to the documentation is should be as follows:

 MATLAB:  [t,y]=ode45(@vdp1,[0 20],[2 0]);

 Python:  import numpy as np
          def  vdp1(t,y):
              dydt= np.array([y[1], (1-y[0]**2)*y[1]-y[0]])
              return dydt
          import scipy integrate 
          l=scipy.integrate.ode(vdp1([0,20],[2,0])).set_integrator("dopri5")

The results are completely different, Matlab returns different dimensions than Python.

Solution 1

As @LutzL mentioned, you can use the newer API, solve_ivp.

results = solve_ivp(obj_func, t_span, y0, t_eval = time_series)

If t_eval is not specified, then you won't have one record per one timestamp, which is mostly the cases I assume.

Another side note is that for odeint and often other integrators, the output array is a ndarray of a shape of [len(time), len(states)], however for solve_ivp, the output is a list(length of state vector) of 1-dimension ndarray(which length is equal to t_eval).

So you have to merge it if you want the same order. You can do so by:

Y =results
merged = np.hstack([i.reshape(-1,1) for i in Y.y])

First you need to reshape to make it a [n,1] array, and merge it horizontally. Hope this helps!

Solution 2

The function scipy.integrate.solve_ivp uses the method RK45 by default, similar the method used by Matlab's function ODE45 as both use the Dormand-Pierce formulas with fourth-order method accuracy.

vdp1 = @(T,Y) [Y(2); (1 - Y(1)^2) * Y(2) - Y(1)];
[T,Y] = ode45 (vdp1, [0, 20], [2, 0]);

from scipy.integrate import solve_ivp

vdp1 = lambda T,Y: [Y[1], (1 - Y[0]**2) * Y[1] - Y[0]]
sol = solve_ivp (vdp1, [0, 20], [2, 0])

T = sol.t
Y = sol.y

Ordinary Differential Equations (solve_ivp)

Comments

[extraymond]

Thx for cleanup.

[crobar]

Does this do variable step sizes like ode45?

[Lin]

don't you hate when someone come, ask a question and do not pick one as correct? (also when someone resurrect an old post)

[Lutz Lehmann]

Note that Matlab's ode45 has a "Refine" option that defaults to 4. That is, per computed point it adds 3 additional interpolated points from the segment to the return vectors. There is no such option in python solve_ivp, so that with the same tolerances leading to approximately the same work ode45 will return more points that give smoother looking plots.