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 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.]))
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)
#
# Hint: By using the 'hold(True)' 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 = zeros(3)
theta, J_history = gradientDescentMulti(X_data, y, theta, alpha, num_iters);
# Plot the convergence graph
fig = figure()
plot(J_history, '-b', linewidth=2)
xlabel('Number of iterations')
ylabel('Cost J')
fig.show()
# Display gradient descent's result
print 'Theta computed from gradient descent:'
for t in theta: print t
print
# Estimate the price of a 1650 sq-ft, 3 br house
# ====================== YOUR CODE HERE ======================
