def GradientDescentRegular(x, y, w_init):
#添加正则项的梯度下降算法
lamda = 0.001 # 设置正则系数
w = np.mat(w_init.copy()).T #将数据转化为矩阵
Y = np.mat(y).T
step = 0.05 #设置布长为0.05
X = np.mat(np.zeros((x.size, w_init.size))) #范德蒙德矩阵的计算
for i in range(x.size):
for j in range(w_init.size):
X[i, j] = pow(x[i], j)
loss_function = 1.0 #初始设置损失函数值
iteratornNum = 0 #迭代次数极为0
while (loss_function > 0.001 and iteratornNum < 200000):
#迭代终止条件为loss_function > 0.001 and iteratornNum < 200000
iteratornNum = iteratornNum + 1
w -= step * (np.dot(X.T, (np.dot(X, w) - Y)) + lamda * w
) #更新w，并设置惩罚系数为0.001
loss_function = 0.0
for i in range(x.size):
loss_function += pow(
poly.polynomial(x[i],
np.array(w.T)[0]) - y[i], 2)
loss_function /= (2 * x.size) #计算损失函数值
W = np.zeros(w_init.size)
for i in range(w_init.size):
W[i] = w[i, 0]
print("loss_function:", loss_function)
print("The iteratorNum times is:", iteratornNum)
return W
w_init = np.random.randn(power)
print("x", x)
print("y", y)
print("w_init:", w_init)
plot.title("Least Square")
plot.plot(x_points,
np.sin(2 * np.pi * x_points),
label='$sin(2*pi*x)$',
color="red")
for i in range(size):
plot.scatter(x[i], y[i], color="green", linewidths=0.01)
w_LS1 = LS.leastSqure(x, y, w_init)
print("w_LS1:", w_LS1)
plot.plot(x_points,
poly.polynomial(x_points, w_LS1),
label='$LS$',
color="green")
w_LS2 = LS.leastSqureRegular(x, y, w_init)
print("w_LS2:", w_LS2)
plot.plot(x_points,
poly.polynomial(x_points, w_LS2),
label='$LS+Regular$',
color="blue")
plot.legend()
plot.show()
w_init = np.random.randn(power)
print("x", x)
print("y", y)
print("w_init:", w_init)
plot.title("Conjungate Gradient")
plot.plot(x_points,
np.sin(2 * np.pi * x_points),
label='$sin(2*pi*x)$',
color="red")
for i in range(size):
plot.scatter(x[i], y[i], color="green", linewidths=0.01)
w_FR1 = CG.ConjungateGradient(x, y, w_init)
print("w_FR1:", w_FR1)
plot.plot(x_points,
poly.polynomial(x_points, w_FR1),
label='$CG$',
color="green")
w_FR2 = CG.ConjungateGradientRegular(x, y, w_init)
print("w_FR2:", w_FR2)
plot.plot(x_points,
poly.polynomial(x_points, w_FR2),
label='$CG+Regular$',
color="blue")
plot.legend()
plot.show()
w_init = np.random.randn(power)
print("x", x)
print("y", y)
print("w_init:", w_init)
plot.title("Gradient Descent")
plot.plot(x_points,
np.sin(2 * np.pi * x_points),
label='$sin(2*pi*x)$',
color="red")
for i in range(size):
plot.scatter(x[i], y[i], color="green", linewidths=0.01)
w_GD1 = GD.GradientDescent(x, y, w_init)
print("w_GD1:", w_GD1)
plot.plot(x_points,
poly.polynomial(x_points, w_GD1),
label='$GD$',
color="blue")
w_GD2 = GD.GradientDescentRegular(x, y, w_init)
print("w_GD2:", w_GD2)
plot.plot(x_points,
poly.polynomial(x_points, w_GD2),
label='$GD+Regular$',
color="green")
plot.legend()
plot.show()
print("y", y)
print("w_init:", w_init)
plot.title("sin function")
plot.plot(x_points,
np.sin(2 * np.pi * x_points),
label='$sin(2*pi*x)$',
color="red")
for i in range(size):
plot.scatter(x[i], y[i], color="green", linewidths=0.01)
w_LS1 = LS.leastSqure(x, y, w_init)
print("w_LS1:", w_LS1)
plot.plot(x_points,
poly.polynomial(x_points, w_LS1),
label='$LS$',
color="green")
w_LS2 = LS.leastSqureRegular(x, y, w_init)
print("w_LS2:", w_LS2)
plot.plot(x_points,
poly.polynomial(x_points, w_LS2),
label='$LS+Regular$',
color="blue")
w_GD1 = GD.GradientDescent(x, y, w_init)
print("w_GD1:", w_GD1)
plot.plot(x_points,
poly.polynomial(x_points, w_GD1),
label='$GD$',