human
I am working on the file "OODE/.ipynb_checkpoints/introduction_hints-checkpoint.ipynb".
The first task is:
Solving an initial value problems with scipy.integrate
Initial value problems as considered in the lecture are of the form
$$ \dot x(t) = f(t, x(t), p), \quad x(t_0) = x_0 $$
where $ p $ is a parameter.
Scipy provides with ODE a class to solve ordinary differential equations.
The following function provides a convenience interface to solve an initial value problem as specified above:
Can you write Python program for it?

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Write me a the Python program you requested?
assistant
#Here is the Python program you requested.

import scipy.integrate

class IVPResult:
    pass

def solve_ivp(f, ts, x0, p=None, integrator='dopri5', store_trajectory=False):
    """
    Solve initial value problem
        d/dt x = f(t, x, p);  x(t0) = x0.

    Evaluate Solution at time points specified in ts, with ts[0] = t0.
    """

    ivp = scipy.integrate.ode(f)
    ivp.set_integrator(integrator)

    if store_trajectory:
        times = []
        points = []
        def solout(t, x):
            if len(times) == 0 or t != times[-1]:
                times.append(t)
                points.append(np.copy(x[:x0.shape[0]]))
        ivp.set_solout(solout)

    ivp.set_initial_value(x0, ts[0])
    ivp.set_f_params(p)

    result = IVPResult()
    result.ts = ts
    result.xs = np.zeros([ts.shape[0], x0.shape[0]])
    result.success = True

    result.xs[0,:] = x0
    for ii in range(1,ts.shape[0]):
        ivp.integrate(ts[ii])
        result.xs[ii,:] = ivp.y[:x0.shape[0]]
        if not ivp.successful():
            result.success = False
            break

    if store_trajectory:
        result.trajectory_t = np.array(times)
        result.trajectory_x = np.array(points)

    return result