How to solve matrix differential equations in Python?

Question

dx/dt = Ax where A, x belongs to n x n array. I have tried using solve_ivp and odeint features in scipy.integrate, but both these work only with n x 1 arrays.

Answer 1

The integrators expect that the ODE function consumes a flat, one-dimensional array as the state variable and returns an equally flat derivatives vector. This input array contains the entries of the matrix. To perform matrix operations on it, you need to build a matrix from the flat input array, and in the end reverse that for the output of the derivatives function

x0 = x0.reshape(-1);         # make data 1-dimensional
def odefun(t,x):
    x=x.reshape([n,n]);      # restore to matrix form
    dx=A.dot(x);             # perform matrix operations
    return dx.reshape(-1);   # return 1-dimensional vector

sol = solve_ivp(odefun, [t0, tf], x0)