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 = 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] = 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])
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 = 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] = 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])
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()
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()
