How to do a polynomial fit with fixed points

Question

I have been doing some fitting in python using numpy (which uses least squares).

I was wondering if there was a way of getting it to fit data while forcing it throug

Answer 1

If you use curve_fit(), you can use sigma argument to give every point a weight. The following example gives the first , middle, last point very small sigma, so the fitting result will be very close to these three points:

N = 20
x = np.linspace(0, 2, N)
np.random.seed(1)
noise = np.random.randn(N)*0.2
sigma =np.ones(N)
sigma[[0, N//2, -1]] = 0.01
pr = (-2, 3, 0, 1)
y = 1+3.0*x**2-2*x**3+0.3*x**4 + noise

def f(x, *p):
    return np.poly1d(p)(x)

p1, _ = optimize.curve_fit(f, x, y, (0, 0, 0, 0, 0), sigma=sigma)
p2, _ = optimize.curve_fit(f, x, y, (0, 0, 0, 0, 0))

x2 = np.linspace(0, 2, 100)
y2 = np.poly1d(p)(x2)
plot(x, y, "o")
plot(x2, f(x2, *p1), "r", label=u"fix three points")
plot(x2, f(x2, *p2), "b", label=u"no fix")
legend(loc="best")