def test_get_B_matrix_nes_on_gap():
x = np.array([0, 2, 3, 5])
period = 3
B_nes = mu.get_B_matrix_nes(x, period)
expected_matrix = [[1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 0, 1]]
expected_result = cvxopt.sparse(cvxopt.matrix(expected_matrix).T)
assert max(B_nes - expected_result) < 1e-13
def l1_fit(index, y, beta_d2=1.0, beta_d1=1.0, beta_seasonal=1.0,
beta_step=5.0, period=12, growth=0.0, step_permissives=None):
assert isinstance(y, np.ndarray)
assert isinstance(index, np.ndarray)
#x must be integer type for seasonality to make sense
assert index.dtype.kind == 'i'
n = len(y)
m = n-2
p = period
ys, y_min, y_max = mu.scale_numpy(y)
D1 = mu.get_first_derivative_matrix_nes(index)
D2 = mu.get_second_derivative_matrix_nes(index)
H = mu.get_step_function_matrix(n)
T = mu.get_T_matrix(p)
B = mu.get_B_matrix_nes(index, p)
Q = B*T
#define F_matrix from blocks like in paper
zero = mu.zero_spmatrix
ident = mu.identity_spmatrix
gvec = spmatrix(growth, range(m), [0]*m)
zero_m = spmatrix(0.0, range(m), [0]*m)
zero_p = spmatrix(0.0, range(p), [0]*p)
zero_n = spmatrix(0.0, range(n), [0]*n)
step_reg = mu.get_step_function_reg(n, beta_step, permissives=step_permissives)
F_matrix = sparse([
[ident(n), -beta_d1*D1, -beta_d2*D2, zero(p, n), zero(n)],
[Q, zero(m, p-1), zero(m, p-1), -beta_seasonal*T, zero(n, p-1)],
[H, zero(m, n), zero(m, n), zero(p, n), step_reg]
])
w_vector = sparse([
mu.np2spmatrix(ys), gvec, zero_m, zero_p, zero_n
])
solution_vector = np.asarray(l1.l1(matrix(F_matrix), matrix(w_vector))).squeeze()
#separate
xbase = solution_vector[0:n]
s = solution_vector[n:n+p-1]
h = solution_vector[n+p-1:]
#scale back to original
if y_max > y_min:
scaling = y_max - y_min
else:
scaling = 1.0
xbase = xbase*scaling + y_min
s = s*scaling
h = h*scaling
seas = np.asarray(Q*matrix(s)).squeeze()
steps = np.asarray(H*matrix(h)).squeeze()
x = xbase + seas + steps
solution = {'xbase': xbase, 'seas': seas, 'steps': steps, 'x': x, 'h': h, 's': s}
return solution
def test_get_B_matrix_nes_aggrees_with_es():
n = 27
period = 5
B_nes = mu.get_B_matrix_nes(np.arange(n), period)
B_es = mu.get_B_matrix(n, period)
diff = B_nes - B_es
max_diff = max(abs(diff))
assert max_diff < 1e-13