def test_newton_4(self):
# convergence relies heavily on x0
n, s = (40, 35)
# n, s = (5, 35)
A = mg.random_weighted_matrix_generator_dense(n,
sup_ext=100,
sym=False,
seed=s,
intweights=True)
A[0, :] = 0
bA = np.array([[1 if aa != 0 else 0 for aa in a] for a in A])
k_out = np.sum(bA, axis=1)
k_in = np.sum(bA, axis=0)
s_out = np.sum(A, axis=1)
s_in = np.sum(A, axis=0)
x0 = 0.1 * np.ones(4 * n)
# x0 = np.concatenate((-1*np.ones(2*n), np.ones(2*n)))
args = (k_out, k_in, s_out, s_in)
x0[np.concatenate(args) == 0] = 1e3
fun = lambda x: -mof.loglikelihood_prime_decm_exp(x, args)
fun_jac = lambda x: -mof.loglikelihood_hessian_decm_exp(x, args)
step_fun = lambda x: -mof.loglikelihood_decm_exp(x, args)
lin_fun = lambda x: mof.linsearch_fun_DECM_exp(x, (step_fun, ))
hes_reg = sof.matrix_regulariser_function
sol = sof.solver(
x0,
fun=fun,
step_fun=step_fun,
fun_jac=fun_jac,
linsearch_fun=lin_fun,
tol=1e-6,
eps=1e-5,
max_steps=100,
method="newton",
verbose=False,
regularise=True,
full_return=False,
linsearch=True,
hessian_regulariser=hes_reg,
)
sol = np.exp(-sol)
ek = mof.expected_decm(sol)
k = np.concatenate((k_out, k_in, s_out, s_in))
err = np.max(np.abs(ek - k))
# debug
# print(ek)
# print(k)
# print('\ntest 4: error = {}'.format(err))
# print('method: {}, matrix {}x{} with zeros'.format('newton', n,n))
# test result
self.assertTrue(err < 1e-1)
def test_quasinewton_1(self):
n, s = (4, 25)
A = mg.random_weighted_matrix_generator_dense(n,
sup_ext=10,
sym=False,
seed=s,
intweights=True)
A[0, :] = 0
bA = np.array([[1 if aa != 0 else 0 for aa in a] for a in A])
k_out = np.sum(bA, axis=1)
k_in = np.sum(bA, axis=0)
s_out = np.sum(A, axis=1)
s_in = np.sum(A, axis=0)
x0 = 0.9 * np.ones(n * 4)
args = (k_out, k_in, s_out, s_in)
fun = lambda x: -mof.loglikelihood_prime_decm_exp(x, args)
fun_jac = lambda x: -mof.loglikelihood_hessian_diag_decm_exp(x, args)
step_fun = lambda x: -mof.loglikelihood_decm_exp(x, args)
lin_fun = lambda x: mof.linsearch_fun_DECM_exp(x, (
mof.loglikelihood_decm_exp, args))
hes_reg = sof.matrix_regulariser_function
sol = sof.solver(
x0,
fun=fun,
step_fun=step_fun,
fun_jac=fun_jac,
linsearch_fun=lin_fun,
tol=1e-6,
eps=1e-10,
max_steps=300,
method="quasinewton",
verbose=False,
regularise=True,
full_return=False,
linsearch=True,
hessian_regulariser=hes_reg,
)
sol = np.exp(-sol)
ek = mof.expected_decm(sol)
k = np.concatenate((k_out, k_in, s_out, s_in))
err = np.max(np.abs(ek - k))
# debug
# print(ek)
# print(k)
# print('\ntest 0: error = {}'.format(err))
# print('method = {}, matrix {}x{}'.format('quasinewton', n, n))
# test result
self.assertTrue(err < 1e-1)
def test_iterative_3(self):
n, s = (40, 35)
# n, s = (5, 35)
A = mg.random_weighted_matrix_generator_dense(n,
sup_ext=100,
sym=False,
seed=s,
intweights=True)
A[0, :] = 0
bA = np.array([[1 if aa != 0 else 0 for aa in a] for a in A])
k_out = np.sum(bA, axis=1)
k_in = np.sum(bA, axis=0)
s_out = np.sum(A, axis=1)
s_in = np.sum(A, axis=0)
x0 = 0.1 * np.ones(n * 4)
args = (k_out, k_in, s_out, s_in)
x0[np.concatenate(args) == 0] = 1e3
fun = lambda x: mof.iterative_decm_exp(x, args)
step_fun = lambda x: -mof.loglikelihood_decm_exp(x, args)
lin_fun = lambda x: mof.linsearch_fun_DECM_exp(x, (step_fun, ))
hes_reg = sof.matrix_regulariser_function
sol = sof.solver(
x0,
fun=fun,
step_fun=step_fun,
linsearch_fun=lin_fun,
tol=1e-6,
eps=1e-10,
max_steps=7000,
method="fixed-point",
verbose=False,
regularise=True,
full_return=False,
linsearch=True,
hessian_regulariser=hes_reg,
)
sol = np.exp(-sol)
ek = mof.expected_decm(sol)
k = np.concatenate((k_out, k_in, s_out, s_in))
err = np.max(np.abs(ek - k))
# debug
# print(ek)
# print(k)
# print('\ntest 6: error = {}'.format(err))
# print('method: {}, matrix {}x{} '.format('iterative', n,n))
# test result
self.assertTrue(err < 1)
def test_iterative_1(self):
n, seed = (4, 22)
a = mg.random_binary_matrix_generator_dense(n, sym=False, seed=seed)
a[0, :] = 0
k_out = np.sum(a, 1)
k_in = np.sum(a, 0)
g = sample.DirectedGraph(a)
g.degree_reduction()
g.initial_guess = "random"
g.full_return = False
g._set_initial_guess("dcm")
g._set_args("dcm")
x0 = g.x0
x0[x0 == 0] = 100
args = g.args
fun = lambda x: iterative_dcm_exp(x, args)
step_fun = lambda x: -loglikelihood_dcm_exp(x, args)
lin_fun = lambda x: linsearch_fun_DCM_exp(x, (step_fun, ))
hes_reg = sof.matrix_regulariser_function
f = fun(x0)
norm = np.linalg.norm(f)
theta_sol = sof.solver(
x0,
fun=fun,
step_fun=step_fun,
linsearch_fun=lin_fun,
tol=1e-6,
eps=1e-10,
max_steps=700,
method="fixed-point",
verbose=False,
regularise=True,
full_return=False,
linsearch=False,
hessian_regulariser=hes_reg,
)
g._set_solved_problem_dcm(theta_sol)
theta_sol_full = np.concatenate((g.x, g.y))
sol = np.exp(-theta_sol_full)
sol[np.isnan(sol)] = 0
ek = np.concatenate((
expected_out_degree_dcm(sol),
expected_in_degree_dcm(sol),
))
k = np.concatenate((k_out, k_in))
err = np.max(abs(ek - k))
# debug
# print(ek)
# print(k)
# print('\ntest 0: error = {}'.format(err))
# test result
self.assertTrue(err < 1e-2)
def test_quasinewton_2(self):
n, seed = (40, 26)
a = mg.random_binary_matrix_generator_dense(n, sym=False, seed=seed)
k_out = np.sum(a, 1)
k_in = np.sum(a, 0)
"""
nz_index_out = np.array([0,1,2])
nz_index_in = np.array([0,1,2,3])
c = np.array([2,1,1])
"""
g = sample.DirectedGraph(a)
g.degree_reduction()
g.initial_guess = "random"
g.full_return = False
g._set_initial_guess("dcm")
g._set_args("dcm")
x0 = g.x0
x0[x0 == 0] = np.infty
args = g.args
fun = lambda x: -loglikelihood_prime_dcm_exp(x, args)
step_fun = lambda x: -loglikelihood_dcm_exp(x, args)
fun_jac = lambda x: -loglikelihood_hessian_diag_dcm_exp(x, args)
lin_fun = lambda x: linsearch_fun_DCM_exp(x, (step_fun, ))
hes_reg = sof.matrix_regulariser_function
f = fun(x0)
norm = np.linalg.norm(f)
theta_sol = sof.solver(
x0,
fun=fun,
step_fun=step_fun,
fun_jac=fun_jac,
linsearch_fun=lin_fun,
tol=1e-6,
eps=1e-1,
max_steps=100,
method="quasinewton",
verbose=False,
regularise=True,
full_return=False,
linsearch=True,
hessian_regulariser=hes_reg,
)
g._set_solved_problem_dcm(theta_sol)
theta_sol_full = np.concatenate((g.x, g.y))
sol = np.exp(-theta_sol_full)
sol[np.isnan(sol)] = 0
ek = np.concatenate((
expected_out_degree_dcm(sol),
expected_in_degree_dcm(sol),
))
k = np.concatenate((k_out, k_in))
err = np.max(abs(ek - k))
# debug
# print(ek)
# print(k)
# print('\ntest 6: error = {}'.format(err))
# test result
self.assertTrue(err < 1e-2)
# debug
# print(ek)
# print(k)
# print('\ntest 7: error = {}'.format(err))
# test result
self.assertTrue(err < 1e-2)
