def test_cost(self):
self.assertAlmostEqual(
compute_cost(self.val[0], self.val[1], self.val[2]),
65591548106.457443, 6)
self.assertAlmostEqual(
compute_cost(self.val[0], np.array(self.best_theta), self.val[2]),
2062961418.085968, 6)
def test_normal_eq_and_gradient_descent(self):
self.assertAlmostEqual(
compute_cost(self.val[0], self.super_best_theta, self.val[2]),
compute_cost(self.val[0], normal_equation(self.val[0],
self.val[2]),
self.val[2]), 5)
X = np.vstack(data[:, 0]) # convert to vertical array ... column vector
y = np.vstack(data[:, 1])
m = len(y)
# plot the data
kit.plot_data(X, y, 'Price (x $10k)', 'Population (x 10k)')
# cost function
one_v = np.reshape(np.ones(m), (m, 1)) # alternative to vstack
X1 = np.concatenate((one_v, X), axis=1) # two columns
theta = np.array([[0.0], [0.0]])
# compute and display initial cost :: ans = 32.07
import linear_regression as lr
J = lr.compute_cost(X1, y, theta)
print("With theta = [0 ; 0] ... Cost computed = {:7.3f}".format(J))
# further testing of the cost function :: ans = 54.24
J = lr.compute_cost(X1, y, [[-1.0], [2.0]])
print("With theta = [-1 ; 2] ... Cost computed = {:7.3f}".format(J))
# Some gradient descent settings
iterations = 1500
alpha = 0.01
# run gradient descent :: ans = [ [-3.6303], [1.1664] ]
theta, J_history = lr.gradient_descent(X1, y, theta, alpha, iterations)
print("Calculated theta = \n", theta)
# predict values for population sizes of 35,000 and 70,000
def main():
#load sample data
#mengisi contoh data
data = multivariasi.load_data_single()
X_, y = data[:, 0], data[:, 1]
X = np.ones([y.size, 2])
X[:, 1] = X_
#compute theta
#menghitung theta
m, dim = X.shape
theta = np.zeros([dim, 1])
alpha, max_iter = 0.01, 300
theta = linear_regression.gradient_descent(theta, X, y, alpha, max_iter)
print theta
#plot sample data and predicted line
#contoh plot data dan melakukan prediksi garis
plt.subplot(2, 1, 1)
plt.scatter(data[:, 0], data[:, 1], color='r', marker='x')
xx = np.linspace(-10, 10)
yy = theta[0] + theta[1] * xx
plt.plot(xx, yy, 'k-')
#plot contour
#bentuk permukaan plot
theta0_vals = np.linspace(-10, 10, 100)
theta1_vals = np.linspace(-1, 4, 100)
#initialize J_vals to a matrix of 0's
#mengenalkan J_vals pada sebuah matrix dari 0
J_vals = np.zeros(shape=(theta0_vals.size, theta1_vals.size))
#fill out J_vals
#mengisi hasil keluaran J_vals
for t1, element in enumerate(theta0_vals):
for t2, element2 in enumerate(theta1_vals):
thetaT = np.zeros(shape=(2, 1))
thetaT[0][0] = element
thetaT[1][0] = element2
J_vals[t1, t2] = linear_regression.compute_cost(thetaT, X, y)
#contour plot
#bentuk permukaan plot
J_vals = J_vals.T
#plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
#plot J_vals pada 15 bentuk permukaan yang terisi secara logaritma diantara 0.01 dan 100
plt.subplot(2, 1, 2)
plt.contour(theta0_vals, theta1_vals, J_vals, np.logspace(-2, 3, 40))
plt.xlabel('theta_0')
plt.ylabel('theta_1')
plt.scatter(theta[0][0], theta[1][0])
#3D contour and scatter plot
#bentuk permukaan 3D dan plot yang betebaran
theta0_vals, theta1_vals = np.meshgrid(theta0_vals, theta1_vals)
fig = plt.figure()
ax = fig.gca(projection='3d')
plt.hold(True)
ax.plot_surface(theta0_vals, theta1_vals, J_vals,
cmap=cm.coolwarm, rstride=3, cstride=3,
antialiased=True)
ax.view_init(elev=60, azim=50)
ax.dist = 8
x_sct, y_sct = theta[0][0], theta[1][0]
thetaT_sct = np.zeros(shape=(2, 1))
thetaT_sct[0][0] = theta[0][0]
thetaT_sct[1][0] = theta[1][0]
z_sct = linear_regression.compute_cost(thetaT_sct, X, y)
ax.scatter(x_sct, y_sct, z_sct)
plt.show()
def main():
# load sample data
data = multivariate_normal.load_data_single()
X_, y = data[:, 0], data[:, 1]
X = np.ones([y.size, 2])
X[:, 1] = X_
# compute theta
m, dim = X.shape
theta = np.zeros([dim, 1])
alpha, max_iter = 0.01, 300
theta = linear_regression.gradient_descent(theta, X, y, alpha, max_iter)
print theta
# plot sample data and predicted line
plt.subplot(2, 1, 1)
plt.scatter(data[:, 0], data[:, 1], color='r', marker='x')
xx = np.linspace(-10, 10)
yy = theta[0] + theta[1] * xx
plt.plot(xx, yy, 'k-')
# plot contour
theta0_vals = np.linspace(-10, 10, 100)
theta1_vals = np.linspace(-1, 4, 100)
# initialize J_vals to a matrix of 0's
J_vals = np.zeros(shape=(theta0_vals.size, theta1_vals.size))
# Fill out J_vals
for t1, element in enumerate(theta0_vals):
for t2, element2 in enumerate(theta1_vals):
thetaT = np.zeros(shape=(2, 1))
thetaT[0][0] = element
thetaT[1][0] = element2
J_vals[t1, t2] = linear_regression.compute_cost(thetaT, X, y)
# Contour plot
J_vals = J_vals.T
# Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
plt.subplot(2, 1, 2)
plt.contour(theta0_vals, theta1_vals, J_vals, np.logspace(-2, 3, 40))
plt.xlabel('theta_0')
plt.ylabel('theta_1')
plt.scatter(theta[0][0], theta[1][0])
# 3D contour and scatter plot
theta0_vals, theta1_vals = np.meshgrid(theta0_vals, theta1_vals)
fig = plt.figure()
ax = fig.gca(projection='3d')
plt.hold(True)
ax.plot_surface(theta0_vals, theta1_vals, J_vals,
cmap=cm.coolwarm, rstride=3, cstride=3,
antialiased=True)
ax.view_init(elev=60, azim=50)
ax.dist = 8
x_sct, y_sct = theta[0][0], theta[1][0]
thetaT_sct = np.zeros(shape=(2, 1))
thetaT_sct[0][0] = theta[0][0]
thetaT_sct[1][0] = theta[1][0]
z_sct = linear_regression.compute_cost(thetaT_sct, X, y)
ax.scatter(x_sct, y_sct, z_sct)
plt.show()