In NumPy, I'm trying to represent differential equations of the form: y' = p(t)y + g(t), where p(t) is an nxn matrix and and g(t) is an nx1 matrix. Something like:
y' = [[1,5], [2,1]] + [[e^t], [1]]
I know how to represent matrices in NumPy, but how would I represent matrices that contain variables (for example, 2t or e^t)?
A 'variable' in this sense (as in, y is a function of t) should probably be represented by a 1d array of that variable's domain. This would increase the dimension of your array (making it (n, n, m) where m is the size of your domain (length of t).
If you plan on using a scipy ode solver, then you write it as a function, so instead of
t = np.arange(0, 10, .1)
y' = [[1,5]*len(t), [2,1]*len(t)] + [[np.exp(t)], [1]*len(t)]
you need to do something like:
def yderiv(t):
return [[1,5], [2,1]] + [[np.exp(t)], [1]]
e^t does what you expect it to. Did you mean something like np.exp(t)?
