errorsFig = plt.figure()
ax = errorsFig.add_subplot(111)
ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.4f'))
ax.plot(range((len(errors))), errors)
ax.set_xlabel('Number of iterations')
ax.set_ylabel('Cost J')
plt.show()
size = 100
theta0Vals = np.linspace(-10, 10, size)
theta1Vals = np.linspace(-2, 4, size)
JVals = np.zeros((size, size))
for i in range(size):
for j in range(size):
col = np.matrix([[theta0Vals[i]], [theta1Vals[j]]])
JVals[i, j] = re.J(col, X, y)
theta0Vals, theta1Vals = np.meshgrid(theta0Vals, theta1Vals)
JVals = JVals.T
contourSurf = plt.figure()
ax = contourSurf.gca(projection='3d')
ax.plot_surface(theta0Vals, theta1Vals, JVals, rstride=2, cstride=2, alpha=0.3,
cmap='rainbow', linewidth=0, antialiased=False)
ax.plot(thetas[0], thetas[1], 'rx')
ax.set_xlabel(r'$\theta_0$')
ax.set_ylabel(r'$\theta_1$')
ax.set_zlabel(r'$J(\theta)$')
plt.show()
ax.plot(range(len(errors)), errors)
ax.set_xlabel('Number of iterations')
ax.set_ylabel('Cost J')
plt.show()
# 3D cost function
size = 100
theta0Vals = np.linspace(-10, 10, size)
theta1Vals = np.linspace(-2, 4, size)
JVals = np.zeros((size, size))
for i in range(size):
for j in range(size):
col = np.matrix([[theta0Vals[i]], [theta1Vals[j]]])
JVals[i, j] = regression.J(col, X, y)
theta0Vals, theta1Vals = np.meshgrid(theta0Vals, theta1Vals)
JVals = JVals.T
contourSurf = plt.figure()
ax = contourSurf.gca(projection='3d')
ax.plot_surface(theta0Vals,
theta1Vals,
JVals,
rstride=2,
cstride=2,
alpha=0.3,
cmap=cm.rainbow,
linewidth=0,
antialiased=False)
fittingLine, = ax.plot(xCopy[:,1], yHat, color='g')
ax.set_xlabel('Population of City in 10,000s')
ax.set_ylabel('Profit in $10,000s')
plt.legend([trainingSet, fittingLine], ['Training Set', 'Linear Regression'])
plt.show()
# 绘制能量函数的轮廓
theta1Vals = np.linspace(min(thetas[1]), max(thetas[1]), 100)
theta2Vals = np.linspace(min(thetas[2]), max(thetas[2]), 100)
JVals = np.zeros((100, 100))
for i in range(100):
for j in range(100):
theta = np.matrix([[0], [theta1Vals[i]], [theta2Vals[j]]])
JVals[i,j] = regression.J(theta, X, y)
contourFig = plt.figure()
ax = contourFig.add_subplot(111)
ax.contour(theta1Vals, theta2Vals, JVals, np.logspace(-2,3,20))
plt.show()
# 打印误差曲线
errorsFig = plt.figure()
ax = errorsFig.add_subplot(111)
ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.4f'))
ax.plot(range(len(errors)), errors)
ax.set_xlabel('Number of iterations')
ax.set_ylabel('Cost J')