def cost(w, x, y, N):
result = 0
for n in range(0, N):
val = polynomial(w, x[n]) - y[n]
val = val * val
result = result + val
return 0.5 * result / N
def gradient(w, x, y, N):
grad = w * 0.
I = len(w) - 1
pw = range(I + 1)
for n in range(0, N):
val = polynomial(w, x[n]) - y[n]
phi = np.power(x[n], pw)
grad = grad + phi * val
return grad / N
def step(w, x, y, g, N):
grad = w * 0.
I = len(w) - 1
pw = range(I + 1)
alpha1 = 0
alpha2 = 0
for n in range(0, N):
val = polynomial(w, x[n]) - y[n]
phi = np.power(x[n], pw)
dot = np.dot(phi, g)
alpha1 = alpha1 + val * dot
alpha2 = alpha2 + dot * dot
return alpha1 / alpha2