store function values for future integration

Question

I have a function H(t) returning a float. I then want to numerically compute several integrals involving this function. However, one of the integrals basically invokes the previous integral, e.g.

from scipy.integrate import quad

def H(t):
    return t

def G1(t):
    return quad(lambda x: H(x)*H(t-x),0,1)[0]

def G2(t):
    return quad(lambda x: G1(x)*H(t-x),0,1)[0]

res = quad(G1,0,1) + quad(G2,0,1)

I will need to do this for a large number of functions (i.e. continue like this with G3, G4… Gn) and my end-result will depend on all of them. Since I have to compute G1 for many values of t anyway in order to perform quad(G1,0,1), is it possible to store those computed values and use them when computing quad(G2,0,1)? I could maybe try to write my own simplistic integration function, but how would I go about storing and re-using these values?

Asked By: Shinja

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Answer 1

I guess it’s exactly same as lru_cache, but since I already wrote it, might as well share:

def store_result(func):
    def remember(t):
        if t not in func.results:
            func.results[t]  = func(t)
        return func.results[t]
    setattr(func, 'results', {}) # make dictionary to store results
    return remember

This is decorator that modifies function to store results to dictionary and retrieve those when they are called with the same arguments. You can modify it to suit your needs.

usage:

@store_result
def G1(t):
    return quad(lambda x: H(x)*H(t-x),0,1)[0]

Answered By: user1308345

store function values for future integration

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