def output(partId):
# Random Test Cases
X1 = np.column_stack(
(np.ones(20), np.exp(1) + np.exp(2) * np.linspace(0.1, 2, 20)))
Y1 = X1[:, 1] + np.sin(X1[:, 0]) + np.cos(X1[:, 1])
X2 = np.column_stack((X1, X1[:, 1]**0.5, X1[:, 1]**0.25))
Y2 = np.power(Y1, 0.5) + Y1
if partId == '1':
out = formatter('%0.5f ', warmUpExercise())
elif partId == '2':
out = formatter('%0.5f ', computeCost(X1, Y1, np.array([0.5, -0.5])))
elif partId == '3':
out = formatter(
'%0.5f ', gradientDescent(X1, Y1, np.array([0.5, -0.5]), 0.01, 10))
elif partId == '4':
out = formatter('%0.5f ', featureNormalize(X2[:, 1:4]))
elif partId == '5':
out = formatter(
'%0.5f ', computeCostMulti(X2, Y2, np.array([0.1, 0.2, 0.3, 0.4])))
elif partId == '6':
out = formatter(
'%0.5f ',
gradientDescentMulti(X2, Y2, np.array([-0.1, -0.2, -0.3, -0.4]),
0.01, 10))
elif partId == '7':
out = formatter('%0.5f ', normalEqn(X2, Y2))
return out
def output(partId):
# Random Test Cases
X1 = column_stack((ones(20), exp(1) + dot(exp(2), arange(0.1, 2.1, 0.1))))
Y1 = X1[:,1] + sin(X1[:,0]) + cos(X1[:,1])
X2 = column_stack((X1, X1[:,1]**0.5, X1[:,1]**0.25))
Y2 = Y1**0.5 + Y1
if partId == '1':
return sprintf('%0.5f ', warmUpExercise())
elif partId == '2':
return sprintf('%0.5f ', computeCost(X1, Y1, array([0.5, -0.5])))
elif partId == '3':
return sprintf('%0.5f ', gradientDescent(X1, Y1, array([0.5, -0.5]), 0.01, 10))
elif partId == '4':
return sprintf('%0.5f ', featureNormalize(X2[:,1:3]));
elif partId == '5':
return sprintf('%0.5f ', computeCostMulti(X2, Y2, array([0.1, 0.2, 0.3, 0.4])))
elif partId == '6':
return sprintf('%0.5f ', gradientDescentMulti(X2, Y2, array([-0.1, -0.2, -0.3, -0.4]), 0.01, 10))
elif partId == '7':
return sprintf('%0.5f ', normalEqn(X2, Y2))
# Add intercept term to X
X_padded = np.column_stack((np.ones(
(m, 1)), X_norm)) # Add a column of ones to x
## ================ Part 2: Gradient Descent ================
print('Running gradient descent...')
# Choose some alpha value
alpha = 0.01
num_iters = 400
# Init Theta and Run Gradient Descent
theta = np.zeros((3, 1))
theta, J_history = gdm.gradientDescentMulti(X_padded, y, theta, alpha,
num_iters)
# Plot the convergence graph
plt.plot(range(J_history.size), J_history, "-b", linewidth=2)
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
plt.show(block=False)
# Display gradient descent's result
print('Theta computed from gradient descent: ')
print("{:f}, {:f}, {:f}".format(theta[0, 0], theta[1, 0], theta[2, 0]))
print("")
# Estimate the price of a 1650 sq-ft, 3 br house
# ====================== YOUR CODE HERE ======================
# Recall that the first column of X is all-ones. Thus, it does
ones = np.ones((len(x), 1))
X = np.hstack((ones, X))
#print(np.hstack((ones, X)))
# Gradient Descent
# 1) Try different values of alpha
# 2) prediction (With feature normalisation)
alpha = 0.009
#0.009, try 0.01, 0.009.
num_iters = 350
# Init Theta and Run Gradient Descent
theta = np.zeros((3, 1))
[theta, J_History] = gdm.gradientDescentMulti(X, y, theta, alpha, num_iters)
print('Values of theta:')
print(theta)
plot.plot(J_History)
plot.title('Convergence Graph')
plot.xlabel('No Of Iterations')
plot.ylabel('Cost J')
'''
iteration = np.zeros((num_iters, 1))
for i in range(num_iters):
iteration[i, :] = i
plot.plot(iteration, J_History)
'''
# Prediction
from featureNormalize import featureNormalize
from computeCostMulti import computeCostMulti, computeCostMulti2
from gradientDescentMulti import gradientDescentMulti
#3
data = pd.read_csv('ex1data2.txt', header=None) #read from dataset
X = data.iloc[:, 0:2] # read first 2column
y = data.iloc[:, 2] # read third column
m = len(y) # number of training example
data_top = data.head() # view first few rows of the data
print(data_top)
#3.1
X = featureNormalize(X)
#3.2
ones = np.ones((m, 1))
y = y[:, np.newaxis]
X = np.hstack((ones, X)) # adding the intercept term
theta = np.zeros([3, 1])
iterations = 400
alpha = 0.01
J = computeCostMulti(X, y, theta)
print('CostFunction: ', J)
J1 = computeCostMulti2(X, y, theta)
print('CostFunction2: ', J1)
theta = gradientDescentMulti(X, y, theta, alpha, iterations)
print('Theta from gradientDescent: ', theta)
def testGradientDescentMulti1():
X = array([[1.,0.]])
y = array([0.])
theta = array([0.,0.])
th = gradientDescentMulti(X, y, theta, 0, 0)[0]
assert_array_equal(th, theta)
def testGradientDescentMulti8():
X = column_stack((ones(10), sin(arange(10)), cos(arange(10)), linspace(0.3,0.7,10)))
y = arange(10)
theta = array([1.,2.,3.,4.])
th = gradientDescentMulti(X, y, theta, 0.05, 100)[0]
assert_array_almost_equal(th, array([1.6225, 0.39764, -0.39422, 5.7765]), decimal=3)
def ex1_multi():
# Initialization
# ================ Part 1: Feature Normalization ================
# Clear and Close Figures
#clear ; close all; clc
print('Loading data ...')
# Load Data
data = np.loadtxt('ex1data2.txt', delimiter=',')
X = np.reshape(data[:, 0:2], (data.shape[0], 2))
y = np.reshape(data[:, 2], (data.shape[0], 1))
m = y.shape[0]
# Print out some data points
print('First 10 examples from the dataset: ')
print(np.c_[X[0:10, :], y[0:10, :]].T)
print('Program paused. Press enter to continue.')
#input()
# Scale features and set them to zero mean
print('Normalizing Features ...')
X, mu, sigma = featureNormalize(X)
# Add intercept term to X
X = np.c_[np.ones((m, 1)), X]
# ================ Part 2: Gradient Descent ================
# ====================== YOUR CODE HERE ======================
# Instructions: We have provided you with the following starter
# code that runs gradient descent with a particular
# learning rate (alpha).
#
# Your task is to first make sure that your functions -
# computeCost and gradientDescent already work with
# this starter code and support multiple variables.
#
# After that, try running gradient descent with
# different values of alpha and see which one gives
# you the best result.
#
# Finally, you should complete the code at the end
# to predict the price of a 1650 sq-ft, 3 br house.
#
# Hint: By using the 'hold on' command, you can plot multiple
# graphs on the same figure.
# Hint: At prediction, make sure you do the same feature normalization.
# Begin: My code plotting for different learning rates
alphas = [0.3, 0.1, 0.03, 0.01]
colors = ['r', 'g', 'b', 'k']
short_iters = 50
fig = plt.figure()
#hold on;
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
for i in range(len(alphas)):
_, J = gradientDescentMulti(X, y, np.reshape(np.zeros((3, 1)), (3, 1)), alphas[i], short_iters)
plt.plot(range(len(J)), J, colors[i], markersize=2)
plt.savefig('figure1.multi.png')
# End: My code plotting for different learning rates
print('Running gradient descent ...')
# Choose some alpha value
alpha = 0.01
num_iters = 400
# Init Theta and Run Gradient Descent
theta = np.reshape(np.zeros((3, 1)), (3, 1))
theta, J_history = gradientDescentMulti(X, y, theta, alpha, num_iters)
# Plot the convergence graph
fig = plt.figure()
plt.plot(range(len(J_history)), J_history, '-b', markersize=2)
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
plt.savefig('figure2.multi.png')
# Display gradient descent's result
print('Theta computed from gradient descent: ')
print(theta)
print()
# Estimate the price of a 1650 sq-ft, 3 br house
# ====================== YOUR CODE HERE ======================
# Recall that the first column of X is all-ones. Thus, it does
# not need to be normalized.
#price = 0; % You should change this
price = np.dot(np.r_[1, np.divide(np.subtract([1650, 3], mu), sigma)], theta)
# ============================================================
print('Predicted price of a 1650 sq-ft, 3 br house (using gradient descent):\n $%f' % price)
print('Program paused. Press enter to continue.')
#input()
# ================ Part 3: Normal Equations ================
print('Solving with normal equations...')
# ====================== YOUR CODE HERE ======================
# Instructions: The following code computes the closed form
# solution for linear regression using the normal
# equations. You should complete the code in
# normalEqn.m
#
# After doing so, you should complete this code
# to predict the price of a 1650 sq-ft, 3 br house.
#
# Load Data
data = np.loadtxt('ex1data2.txt', delimiter=',')
X = np.reshape(data[:, 0:2], (data.shape[0], 2))
y = np.reshape(data[:, 2], (data.shape[0], 1))
m = y.shape[0]
# Add intercept term to X
X = np.c_[np.ones((m, 1)), X]
# Calculate the parameters from the normal equation
theta = normalEqn(X, y)
# Display normal equation's result
print('Theta computed from the normal equations: ')
print(theta)
print('')
# Estimate the price of a 1650 sq-ft, 3 br house
# ====================== YOUR CODE HERE ======================
price = np.dot([1, 1650, 3], theta) # You should change this
# ============================================================
print('Predicted price of a 1650 sq-ft, 3 br house (using normal equations):\n $%f' % price)
# http://scikit-learn.org/stable/auto_examples/linear_model/plot_ridge_coeffs.html
# Using sklearn
X = np.reshape(data[:, 0:2], (data.shape[0], 2))
y = np.reshape(data[:, 2], (data.shape[0], 1))
model = linear_model.Ridge(max_iter=num_iters, solver='lsqr')
count = 200
alphas = np.logspace(-3, 1, count)
coefs = np.zeros((count, 2))
errors = np.zeros((count, 1))
for i, alpha in enumerate(alphas):
model.set_params(alpha=alpha)
model.fit(X, y)
coefs[i, :] = model.coef_
errors[i, 0] = metrics.mean_squared_error(model.predict(X), y)
results = [(r'$\theta_1$', coefs[:, 0]), (r'$\theta_2$', coefs[:, 1]), ('MSE', errors)]
for i, result in enumerate(results):
label, values = result
plt.figure()
ax = plt.gca()
ax.set_xscale('log')
ax.plot(alphas, values)
plt.xlabel(r'$\alpha$')
plt.ylabel(label)
plt.savefig('figure%d.multi.sklearn.png' % (i + 1))
#model = linear_model.LinearRegression()
model = linear_model.Ridge(alpha=alpha, max_iter=num_iters, solver='lsqr')
model.fit(X, y)
print('Theta found: ')
print('%f %f %f' % (model.intercept_[0], model.coef_[0, 0], model.coef_[0, 1]))
print('Predicted price of a 1650 sq-ft, 3 br house (using sklearn):\n $%f' % model.predict([[1650, 3]]))
def testGradientDescentMulti5():
X = column_stack((ones(101), linspace(0,10,101)))
y = sin(linspace(0,10,101))
theta = array([1.,-1.])
th = gradientDescentMulti(X, y, theta, 0.05, 100)[0]
assert_array_almost_equal(th, array([0.5132, -0.0545]), decimal=3)
def testGradientDescentMulti4():
X = column_stack((ones(10), arange(10)))
y = arange(10)*2
theta = array([1.,2.])
th = gradientDescentMulti(X, y, theta, 0.05, 100)[0]
assert_array_almost_equal(th, array([0.2353, 1.9625]), decimal=3)
X, mu, sigma = featureNormalize(X)
X = np.array(X)
X = np.insert(X, 0, 1, axis=1)
y = np.array(y).reshape(m, 1)
##================ Part 2: Gradient Descent ================##
print('Running Gradient Descent...')
alpha = 0.01
iterations = 400
theta = np.zeros([3, 1])
theta, J_history = gradientDescentMulti(X, y, theta, alpha, iterations)
#Plot the convergence plot
plt.plot(J_history)
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
plt.show()
print('Theta computed from gradient descent: \n', theta)
X_pred = np.array([1650, 3])
X_predn = (X_pred - mu) / sigma
X_predn = np.insert(X_predn, 0, 1)
y_pred = X_predn.dot(theta)
print(
#
# Hint: By using the 'hold on' command, you can plot multiple
# graphs on the same figure.
#
# Hint: At prediction, make sure you do the same feature normalization.
#
print 'Running gradient descent ...'
# Choose some alpha value
alpha = 0.01
num_iters = 400
# Init Theta and Run Gradient Descent
theta = np.zeros(3)
theta, theta_history, J_history = gradientDescentMulti(Xnorm, y, theta, alpha,
num_iters)
# Plot the convergence graph
plotConvergence(J_history, num_iters)
#dummy = plt.ylim([4,7])
plt.show(block=False)
# Display gradient descent's result
print 'Theta computed from gradient descent: '
print theta
# Estimate the price of a 1650 sq-ft, 3 br house
#We did: Xnorm, mu, sigma = featureNormalize(X)
test = np.array([1650, 3])
scaled = (test - mu[1:]) / sigma[1:]
# Add intercept term to X
X_padded = np.column_stack((np.ones((m,1)), X_norm)) # Add a column of ones to x
## ================ Part 2: Gradient Descent ================
print('Running gradient descent...')
# Choose some alpha value
alpha = 0.01
num_iters = 400
# Init Theta and Run Gradient Descent
theta = np.zeros((3, 1))
theta, J_history = gdm.gradientDescentMulti(X_padded, y, theta, alpha, num_iters)
# Plot the convergence graph
plt.plot(xrange(J_history.size), J_history, "-b", linewidth=2 )
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
plt.show(block=False)
# Display gradient descent's result
print('Theta computed from gradient descent: ')
print("{:f}, {:f}, {:f}".format(theta[0,0], theta[1,0], theta[2,0]))
print("")
# Estimate the price of a 1650 sq-ft, 3 br house
# ====================== YOUR CODE HERE ======================
# Recall that the first column of X is all-ones. Thus, it does
# Add intercept term to X
X = np.hstack((np.ones((m, 1)), X))
# ================ Part 2: Gradient Descent ================
# ====================== YOUR CODE HERE ====================
print('Running gradient descent ...')
# Choose some alpha value
alpha = 0.01
num_iters = 400
# Init Theta and Run Gradient Descent
theta = np.zeros((3, 1))
theta, J_history = gradientDescentMulti(X, y, theta, alpha, num_iters)
# Plot the convergence graph
plt.plot(range(len(J_history)), J_history, '-b')
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
plt.show()
# Display gradient descent's result
print('Theta computed from gradient descent:')
print(theta)
# Estimate the price of a 1650 sq-ft, 3 br house
# ====================== YOUR CODE HERE ======================
price = 0 # You should change this
def testGradientDescentMulti7():
X = column_stack((ones(10), arange(10), arange(10)))
y = arange(10)*2
theta = array([0.,0.,0.])
th = gradientDescentMulti(X, y, theta, 1, 1)[0]
assert_array_almost_equal(th, array([9.,57.,57.]))
X, mu, sigma = featureNormalize(X)
# Add intercept term to X
X = np.vstack((np.ones(m), X.T)).T
## ================ Part 2: Gradient Descent ================
print('Running gradient descent ...\n')
# Choose some alpha value
alpha = 0.01
num_iters = 400
# Init Theta and Run Gradient Descent
theta = np.zeros((3, 1))
theta, J_history = gradientDescentMulti(X, y, theta, alpha, num_iters)
# Plot the convergence graph
plt.ion()
plt.figure()
plt.plot(np.arange(0, J_history.size, 1), J_history, '-g')
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
# Display gradient descent's result
print('Theta computed from gradient descent: \n')
print(theta)
print('\n')
temp = np.array([[1.0, 1650.0, 3.0]])
temp[0, 1:3] = (temp[0, 1:3] - mu) / sigma
## ================ Part 2: Gradient Descent ================
print('Running gradient descent ...')
# perform linear regression on the data set
alpha1 = 0.001
alpha2 = 0.01
alpha3 = 0.05
num_iters = 400
# Initialize Theta and run Gradient Descent
theta = np.zeros((3, 1))
theta_1 = np.zeros((2, 1))
theta1, J_history1 = gradientDescentMulti(X_padded, y, theta, alpha1,
num_iters)
theta2, J_history2 = gradientDescentMulti(X_padded, y, theta, alpha2,
num_iters)
theta3, J_history3 = gradientDescentMulti(X_padded, y, theta, alpha3,
num_iters)
theta4, J_history4 = gradientDescentMulti(X_norm, y, theta_1, alpha2,
num_iters)
theta5, J_history5 = gradientDescentMulti(X, y, theta_1, alpha2, num_iters)
print 'Theta 5 is:'
print theta5
#get the cost (error) of the model
#computeCostMulti(X, y, theta)