带参数的sigmoid

$y=\frac{1}{1+e^{-(\alpha\times x+\beta)}}$
alpha越大，曲线越陡峭，beta控制平移

import numpy as np
import pylab as plt

x = np.linspace(-7, 7, 100)
alpha_range = [-1, 0, 1, 2, 1]
beta_range = [-1, 0, 0, 0, 1]
pairs = []
for alpha, beta in zip(alpha_range, beta_range):
    y = 1 / (1 + np.exp(- (alpha * x + beta)))
    plt.plot(x, y)
    pairs.append("alpha=%s,beta=%s" % (alpha, beta))
plt.legend(pairs)
plt.title("y=1/[1+e^(-(alpha*x+beta))]")
plt.show()