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import numpy as np
import matplotlib.pyplot as plt
n = 50
N = 1000
x = np.linspace(-3, 3, n).reshape(n, 1)
X = np.linspace(-3, 3, N).reshape(N, 1)
pix = np.pi * x
y = (np.sin(pix) / pix + 0.1 * x) + 0.2 * np.random.randn(n, 1)
x2 = x * x
xx = x2 + x2.T - 2 * x.dot(x.T)
hhs = np.asarray([0.03, 0.3, 3])
hhs = 2 * hhs ** 2
ls = np.asarray([0.0001, 0.1, 100])
m = 5
u = []
for i in range(n):
temp = int(m * (i - 1) / n)
u.append(temp)
u = np.asarray(u)
u = np.random.permutation(u)
g = np.zeros((3, 3, 5))
# 对hhs，ls数组中的值进行交叉验证
for hk in range(len(hhs)):
hh = hhs[hk]
k = np.exp(-xx / hh)
# 划分4个用于学习(ki,yi==>40*50, 40*1)，1个用于验证(kc, yc==>10*50, 10 * 1)
for i in range(m):
ki = k[u != i, :]
kc = k[u == i, :]
yi = y[u != i]
yc = y[u == i]
for lk in range(len(ls)):
l = ls[lk]
t = np.linalg.lstsq((ki.T.dot(ki) + l * np.eye(n)), ki.T.dot(yi), rcond=-1)[0]
fc = kc.dot(t)
# 将所有的平方残差存储进数组g
g[hk, lk, i] = ((fc - yc) ** 2).mean()
# 根据数组g，取能得到最小残差和的h->HH值和l->L值
temp = g.mean(axis=2)
gl = temp.min(axis=1)
ggl = temp.argmin(axis=1)
ghl = gl.min()
gghl = gl.argmin()
L = ls[ggl[gghl]]
HH = hhs[gghl]
K = np.exp(-((X ** 2) + x2.T - 2 * X.dot(x.T)) / HH)
k = np.exp(-xx / HH)
# t = np.linalg.lstsq(k.dot(k.T) + L * np.eye(n), k.dot(y), rcond=-1)[0]
t = np.linalg.inv((k.T.dot(k) + L * np.eye(n))).dot(k.T).dot(y)
F = K.dot(t)
plt.plot(x, y, 'bo')
plt.plot(X, F, 'g-')
plt.axis([-2.8, 2.8, -0.7, 1.7])
plt.show()
from sklearn.linear_model import Ridge
from sklearn.model_selection import cross_val_score