def huber_small(self, solver):
# Solve the Huber regression problem
x = Variable(3)
objective = sum(huber(x))
# Solve problem with QP
p = Problem(Minimize(objective), [x[2] >= 3])
self.solve_QP(p, solver)
self.assertAlmostEqual(3, x.value[2], places=4)
self.assertAlmostEqual(5, objective.value, places=4)
def huber(self, solver):
# Generate problem data
np.random.seed(2)
n = 3
m = 5
A = sp.random(m, n, density=0.8, format='csc')
x_true = np.random.randn(n) / np.sqrt(n)
ind95 = (np.random.rand(m) < 0.95).astype(float)
b = A.dot(x_true) + np.multiply(0.5*np.random.randn(m), ind95) \
+ np.multiply(10.*np.random.rand(m), 1. - ind95)
# Solve the Huber regression problem
x = Variable(n)
objective = sum(huber(A * x - b))
# Solve problem with QP
p = Problem(Minimize(objective))
self.solve_QP(p, solver)
self.assertAlmostEqual(1.327429461061672, objective.value, places=3)
self.assertItemsAlmostEqual(x.value,
[-1.03751745, 0.86657204, -0.9649172],
places=3)