def hermite(x0, x1, v0, v1, t):
a = array([1, t, t**2, t**3])
M = array([[1, 0, 0, 0],
[1, 1, 1, 1],
[0, 1, 0, 0],
[0, 1, 2, 3]])
p = transpose([[x0, x1, v0, v1]])
return dot(dot(a, inverse(M)), p)
def bezier2(x0, p1, p2, x1, t):
a = array([1, t, t**2, t**3])
M = array([[1, 0, 0, 0],
[1, 1, 1, 1],
[0, 1, 0, 0],
[0, 1, 2, 3]])
B = array([[1, 0, 0, 0],
[0, 0, 0, 1],
[-3, 3, 0, 0],
[0, 0, -3, 3]])
p = transpose([[x0, p1, p2, x1]])
C = dot(inverse(M), B)
return dot(dot(a, C), p)
def covariance(xs: List[float], ys: List[float]) -> float:
assert len(xs) == len(ys), "xs and ys must have same number of elements"
return dot(de_mean(xs), de_mean(ys)) / (len(xs) - 1)
