# -*- coding: utf-8 -*-
"""
Created on Tue Jun 30 16:41:10 2020
@author: cheetah023
"""
import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as opt
#函数定义
def sigmoid(X):
return 1 /(1 + np.exp(-X))
def costFunction(theta, X, y, lamda):
theta = np.reshape(theta,(X.shape[1],1))
sig = sigmoid(np.dot(X,theta))
m = X.shape[0]
#不能用theta[0]=0来算，会出错
#theta[0] = 0
cost = (np.dot(-y.T,np.log(sig)) - np.dot(1-y.T,np.log(1-sig))) / m
cost = cost + np.dot(theta.T[0,1:],theta[1:,0]) * lamda / (2 * m)
return cost
def gradient(theta, X, y, lamda):
theta = np.reshape(theta,(X.shape[1],1))
m = X.shape[0]
sig = sigmoid(np.dot(X,theta))
#这里不reshape的话，执行opt.minimize
#会报错ValueError: tnc: invalid gradient vector from minimized function.
#sig = np.reshape(sig,(m,1))
theta[0] = 0
grad = np.zeros([X.shape[1],1])
grad = np.dot(X.T,(sig - y)) / m
grad = grad + theta * lamda / m
return grad
def plotDecisionBoundary(theta, X, y):
x1_min = np.min(X[:,1])
x1_max = np.max(X[:,1])
x1 = np.arange(x1_min, x1_max,0.5)
x2 = -(theta[0] + theta[1] * x1) / theta[2]
plt.plot(x1,x2,'-')
plt.legend(['decision boundary','Admitted','not Admitted'],loc='upper right')
def plotdata(X, y):
postive = np.where(y > 0.5)
negtive = np.where(y < 0.5)
#postive和negtive包含两个元组，取第一个元组postive[0]和negtive[0]
plt.scatter(X[postive[0],0],X[postive[0],1],marker='o',c='g')
plt.scatter(X[negtive[0],0],X[negtive[0],1],marker='x',c='r')
#Part 1: Plotting
data = np.loadtxt('ex2data1.txt',delimiter=',')
X = data[:,0:2]
y = data[:,2:3]
print('X:',X.shape)
print('y:',y.shape)
plotdata(X, y)
plt.xlabel('exam 1 score')
plt.ylabel('exam 2 score')
plt.legend(['Admitted','not Admitted'],loc='upper right')
#Part 2: Compute Cost and Gradient
[m,n] = X.shape
ones = np.ones((m,1))
X = np.column_stack((ones,X))
initial_theta = np.zeros((n+1,1))
lamda = 0
cost = costFunction(initial_theta, X, y,lamda)
grad = gradient(initial_theta, X, y,lamda)
print("Cost at initial theta (zeros):",cost)
print('Expected cost (approx): 0.693')
print('Gradient at initial theta (zeros):\n',grad)
print('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628')
test_theta =[[-24],[0.2],[0.2]]
cost = costFunction(test_theta, X, y, lamda)
grad = gradient(test_theta, X, y, lamda)
print('Cost at test theta:',cost)
print('Expected cost (approx): 0.218')
print('Gradient at test theta:\n',grad)
print('Expected gradients (approx):\n 0.043\n 2.566\n 2.647')
#Part 3: Optimizing using fminunc
result = opt.minimize(fun=costFunction,
x0=initial_theta,
args=(X,y,lamda),
method='TNC',
jac=gradient)
print('Cost at theta found by fminunc:',result.fun)
print('Expected cost (approx): 0.203')
print('theta:',result.x)
print('Expected theta (approx):')
print('-25.161\n 0.206\n 0.201')
#Plot Boundary
theta = result.x
plotDecisionBoundary(theta, X, y)
plt.legend(['decision boundary','Admitted','not Admitted'],loc='upper right')
#Part 4: Predict and Accuracies
prob = sigmoid(np.dot([1,45,85],theta))
print('For a student with scores 45 and 85, we predict an admission')
print('probability of',prob)
h = sigmoid(np.dot(X,theta))
index = np.where(h >= 0.5)
p = np.zeros([m,1])
p[index] = 1
prob = np.mean(np.double(p==y)) * 100
print('Train Accuracy:',prob)
print('Expected accuracy (approx): 89.0')
运行结果：
X: (100, 2) y: (100, 1) Cost at initial theta (zeros): [[0.69314718]] Expected cost (approx): 0.693 Gradient at initial theta (zeros): [[ -0.1 ] [-12.00921659] [-11.26284221]] Expected gradients (approx): -0.1000 -12.0092 -11.2628 Cost at test theta: [[0.21833019]] Expected cost (approx): 0.218 Gradient at test theta: [[0.04290299] [2.56623412] [2.64679737]] Expected gradients (approx): 0.043 2.566 2.647 Cost at theta found by fminunc: [[0.2034977]] Expected cost (approx): 0.203 theta: [-25.16131857 0.20623159 0.20147149] Expected theta (approx): -25.161 0.206 0.201 For a student with scores 45 and 85, we predict an admission probability of 0.7762906213164001 Train Accuracy: 89.0 Expected accuracy (approx): 89.0
参考资料：
https://blog.csdn.net/lccflccf/category_8379707.html
https://blog.csdn.net/Cowry5/article/details/83302646
https://blog.csdn.net/weixin_44027820/category_9754493.html
总结：
1、遇到的最大的坑是opt.minimize报错ValueError: tnc: invalid gradient vector from minimized function.通过reshape解决
2、cost的计算结果错误，theta[0]=0带进去计算导致的，
