Allow for intermediate results to be stored during integration

[jrenaud90]

In the current implementation of CyRK the only variables that are stored during integration are the dependent-y variables. For example,

# y = dy(t, y0)
t, y, success, message = nbrk_ode(dy, time_span, y0)

However, it is often useful to a user for additional parameters to be stored. For instance, a and b below.

def dy(t, y):
    dy_ = np.empty(2, dtype=np.complex128)
    a = g(t, y)  # Some function of time and y
    b = h(t, y)  # Some function of time and y
    dy_[0] = a * y[0]
    dy_[1] = b * y[1]
    return dy_

The values of a and b are lost after the integration is completed. The user would then need to make separate calls to the g and h function to retrieve their values. This is duplicating calculations and forcing the user to write additional code.

Propose CyRK stores these intermediate results during integration and returns them to the user.

One way this could be done is by having the user define the differential equation like,

def dy(t, y):
    dy_ = np.empty(2, dtype=np.complex128)
    a = g(t, y)  # Some function of time and y
    b = h(t, y)  # Some function of time and y
    dy_[0] = a * y[0]
    dy_[1] = b * y[1]
    return dy_, (a, b)

Then both cyrk_ode and nbrk_ode would store the result (probably best as a np.array) and return the result to the user.

To-Do

• Implement intermediate saving for cyrk_ode
  • Implement basic saving
  • Implement interpolation for t_eval
  • Create tests
• Implement intermediate saving for nbrk_ode
  • Implement basic saving
  • Implement interpolation for t_eval
  • Create tests

[jrenaud90]

This feature has been added, along with tests, with PR #18 in CyRK v0.4.0.