Is it possible to solve delay differential equation?

Modeling
21

Not really. The repo above contains a modified DDSolve in which I use complex-step derivative approximation. This is equivalent to forward-sensitivity calculation. That’s why complex number support is needed.

1 Like
22

Building statically compiled functions will be really hard for this, since this is using staged compilation. This is why I was looking for a way to do dynamic linking to link into libjulia.

23

Ah I see. I’ve done something like this with Python. The Stan model declares but doesn’t implement a function

functions {
    real userfunc2(vector theta);
}

then implements it in C++


template <> var userfunc2(const Eigen::Matrix<var, -1, 1>& theta, std::ostream* pstream__) {
    const Eigen::Matrix<double, -1, 1> theta_val = value_of(theta);
    double fa;
    double *ga = new double[theta.rows()];
    callpy::foo(theta.rows(), theta_val.data(), &fa, ga);
    std::vector<double> std_ga(theta.rows());
    std_ga.assign(ga, ga + theta.rows());
    delete ga;
    vector<var> theta_std(theta.data(), theta.data() + theta.rows());
    return precomputed_gradients(fa, theta_std, std_ga);
}

which is just calling a C function using the Python C API

PyObject *lp = PyObject_GetAttrString(main, "lp");
PyArrayObject *lp_val = (PyArrayObject*)
PyObject_CallFunctionObjArgs(lp, np_x, NULL);
PyArray_ScalarAsCtype((PyObject*) lp_val, (void*) &c_lp);
Py_DECREF(lp);
Py_DECREF(lp_val);

which is just calling a Python function

def lp(x):
    return np.sum(-x**2)

where the autograd package is used to compute gradients. The working example is over here:

I’m less familiar with Julia C API, but something equivalent should be possible.

3 Likes
24

Thanks. Yes, that route should be possible. I’m bookmarking this for a rainy day.