def testComputeCost1():
X = array([[1., 0.]])
y = array([0.])
theta = array([0., 0.])
assert_equal(computeCost(X, y, theta), 0)
def testComputeCost2():
X = column_stack((ones(10), arange(10)))
y = arange(10)*2
theta = array([1., 2.])
assert_almost_equal(computeCost(X, y, theta), 0.5)
def testComputeCost3():
X = column_stack((ones(101), linspace(0,10,101)))
y = sin(linspace(0,10,101))
theta = array([0., 0.])
assert_almost_equal(computeCost(X, y, theta), 0.23699618)
raw_input()
## =================== Part 3: Gradient descent ===================
print 'Running Gradient Descent ...'
X_design = column_stack((ones(m), data[:,0])) # Add a column of ones to x
theta = zeros(2) # initialize fitting parameters
# Some gradient descent settings
iterations = 1500
alpha = 0.01
# compute and display initial cost
print computeCost(X_design, y, theta)
# run gradient descent
(theta, J_history) = gradientDescent(X_design, y, theta, alpha, iterations)
#pdb.set_trace()
# print theta to screen
print 'Theta found by gradient descent: '
print '%f %f \n' % (theta[0], theta[1])
# Plot the linear fit
hold(True); # keep previous plot visible
plot(X_design[:,1], X_design.dot(theta), '-')
legend(('Training data', 'Linear regression'))
firstPlot.show()
# not sure how to avoid overlaying any more plots on this figure - call figure()?