Python - how to write this in vector form [closed]

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def compute(c, r):
    s = 0;
    l = len(c);
    for i in range(l):
        s = s + c[i]*f(r[i]);
    return s

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I don't know what you mean by vector form (unless you are using numpy?), but I would write your function like this:

def compute(c, r):
  return sum(x*f(y) for x,y in zip(c,r))

If you are using numpy you can use whole-array expressions instead of generator expressions, but in that case c and r must be numpy arrays:

def compute(c, r):
  return (c*f(r)).sum()