def test_adjacencies(self):
network = MAS.Network(*generate_uniform(4))
reachable_1 = np.array([[0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0]])
reachable_2 = np.array([[0, 1, 1, 1], [1, 0, 1, 1], [1, 1, 0, 1], [1, 1, 1, 0]])
network.adjacency_1 = reachable_1
self.assertTrue(is_equal(reachable_1.flatten(), network.get_adjacencies(1).flatten()))
self.assertTrue(is_equal(reachable_2.flatten(), network.get_adjacencies(2).flatten()))
def test_throughputs(self):
# compute and check throughputs for uniform network
network = MAS.Network(*generate_uniform())
# check throughputs
self.assertTrue(is_equal(network.throughputs(), (1.0 / 3) * np.ones((3,))))
# check availabilities
self.assertTrue(is_equal(network.availabilities(), np.ones((3,))))
def test_throughputs(self):
# compute and check throughputs for uniform network
network = MAS.Network(*generate_uniform())
# check throughputs
self.assertTrue(
is_equal(network.throughputs(), (1. / 3) * np.ones((3, ))))
# check availabilities
self.assertTrue(is_equal(network.availabilities(), np.ones((3, ))))
def test_balance(self):
# test if the balance strategy effectively balance the network
network = MAS.Network(*generate_asymmetric())
tmp = np.array([0.5, 0.5, 1.0])
self.assertTrue(is_equal(network.new_availabilities(), tmp))
opt_rates, opt_routing = network.balance()
tmp = np.array([1.0, 1.0, 1.0])
self.assertTrue(is_equal(network.new_availabilities(), tmp))
def test_balance(self):
# test if the balance strategy effectively balance the network
network = MAS.Network(*generate_asymmetric())
tmp = np.array([.5, .5, 1.])
self.assertTrue(is_equal(network.new_availabilities(), tmp))
opt_rates, opt_routing = network.balance()
tmp = np.array([1., 1., 1.])
self.assertTrue(is_equal(network.new_availabilities(), tmp))
def test_min_attack_solver(self):
# generate asymmetric network
network = MAS.Network(*generate_asymmetric())
target = np.ones((3,))
cost = np.ones((3,3))
opt_rates, opt_routing = MinAttackSolver(network, target, cost).solve()
self.assertTrue(is_equal(opt_rates, np.array([0.,0.,1.])))
tmp = .5 * np.ones((3, 3))
tmp[range(3), range(3)] = 0.0
self.assertTrue(is_equal(opt_routing, tmp))
def test_adjacencies(self):
network = MAS.Network(*generate_uniform(4))
reachable_1 = np.array([[0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1],
[0, 1, 1, 0]])
reachable_2 = np.array([[0, 1, 1, 1], [1, 0, 1, 1], [1, 1, 0, 1],
[1, 1, 1, 0]])
network.adjacency_1 = reachable_1
self.assertTrue(
is_equal(reachable_1.flatten(),
network.get_adjacencies(1).flatten()))
self.assertTrue(
is_equal(reachable_2.flatten(),
network.get_adjacencies(2).flatten()))
def test_min_cost_flow_init(self):
# generate asymmetric network
network = MAS.Network(*generate_asymmetric())
# target for the availabilities
target = np.array([.5, 1., 1.])
# cost is uniform
cost = np.ones((3,3))
coeff, sources = MinAttackSolver(network, target, cost).min_cost_flow_init()
# check coefficients
tmp = np.ones((3,3))
tmp[0,:] = np.array([2., 2., 2.])
self.assertTrue(is_equal(coeff, tmp))
# check sources
self.assertTrue(is_equal(sources, np.array([.0, .5, -.5])))
def test_availabilities(self):
# compute and check availabilities for asymmetric network
rates, routing, travel_times = generate_asymmetric()
rates[0] = 2.
network = MAS.Network(rates, routing, travel_times)
self.assertTrue(
is_equal(network.availabilities(), np.array([.25, .5, 1.])))
def test_flow_to_rates_routing(self):
network = MAS.Network(*generate_asymmetric())
flow = np.zeros((3, 3))
flow[0,1] = .25
flow[0,2] = .25
flow[1,0] = .5
flow[1,2] = .5
cost = np.ones((3,3))
target = np.array([.5, 1., 1.])
rates, routing = MinAttackSolver(network, target, cost).flow_to_rates_routing(flow)
# check rates
self.assertTrue(is_equal(rates, np.array([1., 1., 0.])))
# check routing
tmp = .5 * np.ones((3, 3))
tmp[range(3), range(3)] = 0.0
self.assertTrue(is_equal(routing, tmp))
def test_cplex_attack_routing_small_network(self):
# trying with CPLEX, see test_attack_routing_2() above for more details
network = MAS.Network(*generate_uniform())
attack_rates = np.array([1.0, 1.0, 0.0])
k = 2
a, routing = network.opt_attack_routing(attack_rates, k, cplex=True)
self.assertTrue(is_equal(a, network.new_availabilities()))
self.assertTrue(abs(np.sum(a) - 5.0 / 3))
def test_cplex_attack_routing_small_network(self):
# trying with CPLEX, see test_attack_routing_2() above for more details
network = MAS.Network(*generate_uniform())
attack_rates = np.array([1., 1., 0.])
k = 2
a, routing = network.opt_attack_routing(attack_rates, k, cplex=True)
self.assertTrue(is_equal(a, network.new_availabilities()))
self.assertTrue(abs(np.sum(a) - 5. / 3))
def test_cplex_attack_routing_full_network(self):
network = MAS.load_network("data/queueing_params.mat")
k = np.where(network.new_availabilities() - 1.0 == 0.0)[0][0]
print "availabilities before attacks", np.sum(network.new_availabilities())
attack_rates = 5.0 * np.ones((network.size,))
a, routing = network.opt_attack_routing(attack_rates, k, cplex=True)
self.assertTrue(is_equal(a, network.new_availabilities()))
print "availabilities after attacks", np.sum(network.new_availabilities())
def test_cplex_attack_routing_full_network(self):
network = MAS.load_network('data/queueing_params.mat')
k = np.where(network.new_availabilities() - 1. == 0.0)[0][0]
print 'availabilities before attacks', np.sum(
network.new_availabilities())
attack_rates = 5. * np.ones((network.size, ))
a, routing = network.opt_attack_routing(attack_rates, k, cplex=True)
self.assertTrue(is_equal(a, network.new_availabilities()))
print 'availabilities after attacks', np.sum(
network.new_availabilities())
def check(self):
# check if the attack_routing 'kappa' is valid
assert self.kappa.shape[0] == self.N, \
'attack_routing has {} rows but N = {}'.format(self.kappa.shape[0], self.N)
assert self.kappa.shape[1] == self.N, \
'attack_routing has {} rows but N = {}'.format(self.kappa.shape[1], self.N)
assert np.min(self.kappa) >= 0.0
assert is_equal(np.sum(self.kappa, axis=1), 1.0, self.eps), \
'attack_routing not stochastic {}'.format(np.sum(self.kappa, axis=1))
self.check_nu(self.nu)
def check(self):
# check if the attack_routing 'kappa' is valid
assert self.kappa.shape[0] == self.N, \
'attack_routing has {} rows but N = {}'.format(self.kappa.shape[0], self.N)
assert self.kappa.shape[1] == self.N, \
'attack_routing has {} rows but N = {}'.format(self.kappa.shape[1], self.N)
assert np.min(self.kappa) >= 0.0
assert is_equal(np.sum(self.kappa, axis=1), 1.0, self.eps), \
'attack_routing not stochastic {}'.format(np.sum(self.kappa, axis=1))
self.check_nu(self.nu)
def test_single_destination_attack(self):
# generate asymmetric MAS_network with availabilities [0.5 0.5 1.0]
# and attack on station 2 with budget = 1.0 (default)
network = MAS.Network(*generate_asymmetric())
sol = SingleDestinationAttack(network, 2).apply()
attack_rates, attack_routing = sol['attack_rates'], sol['attack_routing']
network.update(attack_rates, attack_routing)
self.assertTrue(is_equal(network.new_availabilities(), np.array([1./3, 1./3, 1.])))
self.assertTrue(is_equal(sol['alpha'], 1.5))
# now attack on station 1
sol = SingleDestinationAttack(network, 1).apply()
attack_rates, attack_routing = sol['attack_rates'], sol['attack_routing']
network.update(attack_rates, attack_routing)
self.assertTrue(is_equal(network.new_availabilities(), np.array([1./3, 1., 2./3])))
self.assertTrue(is_equal(sol['alpha'], 1.5))
# now attack on station 1 with 0.49 budget -> inefficient attack
network.budget = 0.49
sol = SingleDestinationAttack(network, 1).apply()
attack_rates, attack_routing = sol['attack_rates'], sol['attack_routing']
network.update(attack_rates, attack_routing)
self.assertTrue(is_equal(network.new_availabilities(), np.array([.5, .5, 1.])))
def test_attack_routing_2(self):
# test if the routing of attacks works given fixed attack rates
network = MAS.Network(*generate_uniform())
# attack rates are fixed
attack_rates = np.array([1.0, 1.0, 0.0])
# find routing minimizing the weighted sum of availabilities
# fix the availability at station 2 to be equal to 1
k = 2
# get the availabilities 'a' and routing that led to 'a'
a, routing = network.opt_attack_routing(attack_rates, k)
self.assertTrue(is_equal(a, network.new_availabilities(), 1e-7))
self.assertTrue(abs(np.sum(a) - 5.0 / 3))
def test_attack_routing_2(self):
# test if the routing of attacks works given fixed attack rates
network = MAS.Network(*generate_uniform())
# attack rates are fixed
attack_rates = np.array([1., 1., 0.])
# find routing minimizing the weighted sum of availabilities
# fix the availability at station 2 to be equal to 1
k = 2
# get the availabilities 'a' and routing that led to 'a'
a, routing = network.opt_attack_routing(attack_rates, k)
self.assertTrue(is_equal(a, network.new_availabilities(), 1e-7))
self.assertTrue(abs(np.sum(a) - 5. / 3))
def check(self, eps=1e-8):
assert eps > 0., "eps too small"
# check that dimensions match
assert self.routing.shape == (self.size, self.size), \
"sizes of rates and routing do not match"
assert self.travel_times.shape == (self.size, self.size), \
"sizes of rates and travel_times don't match"
# check that we have probabilities for routing
assert np.min(self.routing) >= 0.0, "negative probabilities"
assert np.sum(self.routing.diagonal()) == 0.0, \
"diagonal of routing matrix not null"
assert is_equal(np.sum(self.routing, axis=1), 1.0, eps), \
"routing matrix are not probabilities"
# make sure that the Jackson network is not ill-defined
assert np.min(self.rates) > eps, "rates too small"
assert float(np.min(self.rates)) / np.max(self.rates) > eps, \
"ratio min(rates) / max(rates) too small"
# check travel times
tmp = self.travel_times
tmp[range(self.size), range(self.size)] = np.max(self.travel_times)
assert np.sum(tmp > eps) == self.size * self.size, \
"travel times too small"
assert float(np.min(tmp)) / np.max(tmp) > eps, \
"ratio min(travel_times) / max(travel_times) too small"
# check the weights
assert len(self.weights) == self.size, 'weights wrong size'
assert np.sum(self.weights > eps) == self.size, 'weights not positive'
# check the adjacency matrix
if self.adjacency is not None:
assert self.adjacency.shape == (self.size, self.size)
tmp = (self.adjacency == 0.) + (self.adjacency == 1.)
assert np.sum(
tmp) == self.size * self.size, "entries in adj not in 0, 1"
assert np.sum(self.adjacency.diagonal()) == 0.0, \
"diagonal of routing matrix not null"
def check(self, eps=1e-8):
assert eps > 0., "eps too small"
# check that dimensions match
assert self.routing.shape == (self.size, self.size), \
"sizes of rates and routing do not match"
assert self.travel_times.shape == (self.size, self.size), \
"sizes of rates and travel_times don't match"
# check that we have probabilities for routing
assert np.min(self.routing) >= 0.0, "negative probabilities"
assert np.sum(self.routing.diagonal()) == 0.0, \
"diagonal of routing matrix not null"
assert is_equal(np.sum(self.routing, axis=1), 1.0, eps), \
"routing matrix are not probabilities"
# make sure that the Jackson network is not ill-defined
assert np.min(self.rates) > eps, "rates too small"
assert float(np.min(self.rates)) / np.max(self.rates) > eps, \
"ratio min(rates) / max(rates) too small"
# check travel times
tmp = self.travel_times
tmp[range(self.size), range(self.size)] = np.max(self.travel_times)
assert np.sum(tmp > eps) == self.size * self.size, \
"travel times too small"
assert float(np.min(tmp)) / np.max(tmp) > eps, \
"ratio min(travel_times) / max(travel_times) too small"
# check the weights
assert len(self.weights) == self.size, 'weights wrong size'
assert np.sum(self.weights > eps) == self.size, 'weights not positive'
# check the adjacency matrix
if self.adjacency is not None:
assert self.adjacency.shape == (self.size, self.size)
tmp = (self.adjacency == 0.) + (self.adjacency == 1.)
assert np.sum(tmp) == self.size * self.size, "entries in adj not in 0, 1"
assert np.sum(self.adjacency.diagonal()) == 0.0, \
"diagonal of routing matrix not null"
def test_simplex_projection(self):
v = np.array([1, 0, 0, 0, 0, 0])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([0.1, 0.2, 0.3, 0.4])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([10, 10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, -10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, 10])
w = np.array([0, 1])
self.assertTrue(is_equal(simplex_projection(v), w))
for _ in range(20):
v = (np.random.rand(20) - np.ones(20) * 0.5) * 100
self.assertTrue(is_equal(np.sum(simplex_projection(v)), 1))
self.assertTrue(is_equal(np.sum(simplex_projection(v, 5)), 5))
def test_simplex_projection(self):
v = np.array([1, 0, 0, 0, 0, 0])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([0.1, 0.2, 0.3, 0.4])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([10, 10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, -10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, 10])
w = np.array([0, 1])
self.assertTrue(is_equal(simplex_projection(v), w))
for _ in range(20):
v = (np.random.rand(20) - np.ones(20) * 0.5) * 100
self.assertTrue(is_equal(np.sum(simplex_projection(v)), 1))
self.assertTrue(is_equal(np.sum(simplex_projection(v, 5)), 5))
def test_objective(self):
obj, a = self.generate_solver().objective(nu = np.array([1., 0., 0.]))
self.assertTrue(is_equal(obj, 1.75))
self.assertTrue(is_equal(a, np.array([.25, .5, 1.])))
def test_cplex_balance_small_network(self):
network = MAS.Network(*generate_asymmetric())
tmp = np.array([.5, .5, 1.])
self.assertTrue(is_equal(network.new_availabilities(), tmp))
network.balance(cplex=True)
self.assertTrue(is_equal(network.new_availabilities(), np.ones((3, ))))
def test_cplex_balance_full_network(self):
# loading the full network
network = MAS.load_network('data/queueing_params.mat')
network.balance(cplex=True)
self.assertTrue(
is_equal(network.new_availabilities(), np.ones((network.size, ))))
def test_single_destination_attack(self):
network = MAS.Network(*generate_asymmetric())
network.single_destination_attack(2)
self.assertTrue(
is_equal(network.new_availabilities(),
np.array([1. / 3, 1. / 3, 1.])))
def test_throughputs_2(self):
# compute and check throughputs for asymmetric network
network = MAS.Network(*generate_asymmetric())
self.assertTrue(
is_equal(network.throughputs(), np.array([.25, .25, .5])))
def test_min_attack(self):
# test if the attacks affectively achieve the target availabilities
target = np.array([.25, .5, 1.])
network = MAS.Network(*generate_asymmetric())
opt_rates, opt_routing = network.min_attack(target)
self.assertTrue(is_equal(network.new_availabilities(), target))
def test_min_attack(self):
# test if the attacks affectively achieve the target availabilities
target = np.array([0.25, 0.5, 1.0])
network = MAS.Network(*generate_asymmetric())
opt_rates, opt_routing = network.min_attack(target)
self.assertTrue(is_equal(network.new_availabilities(), target))
def test_cplex_balance_small_network(self):
network = MAS.Network(*generate_asymmetric())
tmp = np.array([0.5, 0.5, 1.0])
self.assertTrue(is_equal(network.new_availabilities(), tmp))
network.balance(cplex=True)
self.assertTrue(is_equal(network.new_availabilities(), np.ones((3,))))
def test_cplex_balance_full_network(self):
# loading the full network
network = MAS.load_network("data/queueing_params.mat")
network.balance(cplex=True)
self.assertTrue(is_equal(network.new_availabilities(), np.ones((network.size,))))
def test_availabilities(self):
# compute and check availabilities for asymmetric network
rates, routing, travel_times = generate_asymmetric()
rates[0] = 2.0
network = MAS.Network(rates, routing, travel_times)
self.assertTrue(is_equal(network.availabilities(), np.array([0.25, 0.5, 1.0])))
def test_throughputs_2(self):
# compute and check throughputs for asymmetric network
network = MAS.Network(*generate_asymmetric())
self.assertTrue(is_equal(network.throughputs(), np.array([0.25, 0.25, 0.5])))
def test_gradient_computation(self):
g = self.generate_solver().gradient()
self.assertTrue(is_equal(g, np.array([-.125, -.375, .75])))
def get_question_by_id(id):
if id <= 2:
a = np.random.randint(1, 51)
b = np.random.randint(1, 51)
if id == 2:
a = get_str_value(np.random.randint(1, 100) / 10)
b = get_str_value(np.random.randint(1, 100) / 10)
all = ['{} - {}'.format(a, b),
'-{} - {}'.format(a, b),
'-{} + {}'.format(a, b),
'-{} + (-{})'.format(a, b),
'{} + (-{})'.format(a, b),
'-{} - (-{})'.format(a, b),
'{} - (-{})'.format(a, b),
'-{} - (-{})'.format(a, b),
'-(-{}) + {}'.format(a, b),
'-(-{}) - {}'.format(a, b),
'-(-{}) + (-{})'.format(a, b),
'-(-{}) - (-{})'.format(a, b)]
res = np.random.choice(all, 1)[0]
return 'Вычисли: {}'.format(res), '{}'.format(get_str_value(eval(res), n=5))
elif id <= 4:
l, r = -9, 10
if id == 4:
l, r = -5, 5
def get_coefficient():
if np.random.rand() < 0.2:
return np.random.choice([-1, 1])
return np.random.randint(l, r)
a = [get_coefficient(), get_coefficient(), np.random.randint(l, r)]
while a[0] == 0:
a[0] = get_coefficient()
res = get_square_equation(a)
if id == 3:
return 'Последовательно выпиши три числа: коэффициенты <b>a, b, c</b> квадратного уравнения.\n\n{} = 0'.format(res), \
'{}, {}, {}'.format(get_str_value(a[0], n=5), get_str_value(a[1], n=5), get_str_value(a[2], n=5))
else:
D = a[1] ** 2 - 4 * a[0] * a[2]
roots = 2
if D == 0:
roots = 1
elif D < 0:
roots = 0
return 'Последовательно выпиши два числа: дискриминант и количество различных корней квадратного уравнения.\n\n{} = 0'.format(res), \
'{}, {}'.format(get_str_value(D, n=5), get_str_value(roots, n=5))
elif id == 5:
max_sqrt_d = 15
if np.random.random() < 0.15:
while True:
a = [np.random.randint(-5, 6), np.random.randint(-15, 16), np.random.randint(-20, 20)]
D = a[1] * a[1] - 4 * a[0] * a[2]
if D < 0:
break
else:
while True:
x1 = np.random.randint(-15, 16)
x2 = np.random.randint(-15, 16)
if abs(x1 - x2) <= max_sqrt_d:
break
a = [1, -x1 - x2, x1 * x2]
D = a[1] * a[1] - 4 * a[0] * a[2]
while True:
coef = np.random.choice([0.1, 0.5, 1, 2, 3, 4, 5, -0.1, -0.5, -1, -2, -3, -4, -5])
if is_equal(abs(coef), 0.5) and D % 4 != 0 and D * 25 > max_sqrt_d * max_sqrt_d:
continue
if abs(a[1] * coef) <= 100 and D * coef * coef <= max_sqrt_d * max_sqrt_d:
break
a[0] *= coef
a[1] *= coef
a[2] *= coef
D *= coef * coef
res = get_square_equation(a)
ans = 's '
if D < 0:
ans += '0 корней'
elif D == 0:
ans += '1 корень, x = {}'.format(get_str_value(x1))
else:
if x1 > x2:
x1, x2 = x2, x1
ans += '2 корня, x₁ = {}, x₂ = {}'.format(get_str_value(x1), get_str_value(x2))
return 'Последовательно выпиши количество различных корней квадратного уравнения и сами корни.\n\n{} = 0\n\nИспользуй тот факт, что дискриминант D = {}'.format(res, get_str_value(D)), ans
elif 6 <= id and id <= 11:
def get_all_primes(n):
is_prime = [True for i in range(n)]
res = []
for i in range(2, n):
if is_prime[i]:
res.append(i)
for j in range(2 * i, n, i):
is_prime[j] = False
return res
if id == 6:
mods = get_all_primes(51)
probs = np.array(mods) ** 0.5
probs /= np.sum(probs)
mod = np.random.choice(mods, p=probs)
a = np.random.randint(mod)
b = np.random.randint(mod)
return f'Вычисли {a} + {b} в поле по модулю {mod}', (a + b) % mod
elif id == 7:
mods = get_all_primes(51)
probs = np.array(mods) ** 0.5
probs /= np.sum(probs)
mod = np.random.choice(mods, p=probs)
if np.random.rand() < 0.1:
a = np.random.randint(1, mod)
return f'Вычисли {-a} в поле по модулю {mod}', (-a) % mod
a = np.random.randint(mod)
b = np.random.randint(mod)
return f'Вычисли {a} - {b} в поле по модулю {mod}', (a - b) % mod
elif id == 8:
mods = get_all_primes(14)
probs = np.array(mods) ** 0.5
probs /= np.sum(probs)
mod = np.random.choice(mods, p=probs)
a = np.random.randint(mod)
b = np.random.randint(mod)
return f'Вычисли {a} * {b} в поле по модулю {mod}', (a * b) % mod
else:
def inverse(x, mod):
def power(x, n, mod):
res = 1
while n > 0:
if n % 2 == 1:
res = (res * x) % mod
x = (x * x) % mod
n //= 2
return res
return power(x, mod - 2, mod)
mods = get_all_primes(12)
probs = np.array(mods) ** 1.0
probs /= np.sum(probs)
mod = np.random.choice(mods, p=probs)
if id == 9:
a = np.random.randint(1, mod)
return f'Вычисли обратный элемент к числу {a} в поле по модулю {mod}', inverse(a, mod)
elif id == 10:
a = np.random.randint(mod)
b = np.random.randint(1, mod)
return f'Вычисли {a} / {b} в поле по модулю {mod}', (a * inverse(b, mod)) % mod
else:
a = np.random.randint(mod)
b = np.random.randint(1, mod)
c = np.random.randint(mod)
d = np.random.randint(1, mod)
sign = np.random.choice(['+', '-'])
return f'Вычисли {a}/{b} {sign} {c}/{d} в поле по модулю {mod}', eval(f'a * inverse(b, mod) {sign} c * inverse(d, mod)') % mod
def test_init_solver(self):
ars_solver = self.generate_solver()
ars_solver.init_solver()
self.assertTrue(is_equal(ars_solver.obj_values[0], 1.75))
self.assertTrue(is_equal(ars_solver.a, np.array([.25, .5, 1.])))
self.assertTrue(ars_solver.iter == 0)
def test_single_destination_attack(self):
network = MAS.Network(*generate_asymmetric())
network.single_destination_attack(2)
self.assertTrue(is_equal(network.new_availabilities(), np.array([1.0 / 3, 1.0 / 3, 1.0])))