def test_unbiased_aug_grad():
# Test using linear 2D system eps
N = 100
z = np.random.normal(0.0, 1.0, (N, 4)).astype(DTYPE)
log_q_z = np.random.normal(2.0, 3.0, (N, )).astype(DTYPE)
mu = np.array([0.0, 0.1, 2 * np.pi, 0.1 * np.pi]).astype(DTYPE)
lb = np.NINF
ub = np.PINF
a11 = Parameter("a11", 1, lb, ub)
a12 = Parameter("a12", 1, lb, ub)
a21 = Parameter("a21", 1, lb, ub)
a22 = Parameter("a22", 1, lb, ub)
params = [a11, a12, a21, a22]
M = Model("lds", params)
M.set_eps(linear2D_freq)
nf = NormalizingFlow(arch_type="autoregressive",
D=4,
num_stages=1,
num_layers=2,
num_units=15)
with tf.GradientTape(persistent=True) as tape:
z, log_q_z = nf(N)
params = nf.trainable_variables
nparams = len(params)
tape.watch(params)
_, _, R1s, R2 = aug_lag_vars(z, log_q_z, M.eps, mu, N)
aug_grad = unbiased_aug_grad(R1s, R2, params, tape)
T_x_grads = [[[None for i in range(N // 2)] for i in range(4)]
for i in range(nparams)]
T_x = M.eps(z)
for i in range(N // 2):
T_x_i_grads = []
for j in range(4):
_grads = tape.gradient(T_x[i, j] - mu[j], params)
for k in range(nparams):
T_x_grads[k][j][i] = _grads[k]
del tape
# Average across the first half of samples
for k in range(nparams):
T_x_grads[k] = np.mean(np.array(T_x_grads[k]), axis=1)
R2_np = np.mean(T_x[N // 2:, :], 0) - mu
aug_grad_np = []
for k in range(nparams):
aug_grad_np.append(np.tensordot(T_x_grads[k], R2_np, axes=(0, 0)))
for i in range(nparams):
assert np.isclose(aug_grad_np[i], aug_grad[i], rtol=1e-3).all()
return None
def test_aug_lag_vars():
# Test using linear 2D system eps
N = 100
z = np.random.normal(0.0, 1.0, (N, 4)).astype(DTYPE)
log_q_z = np.random.normal(2.0, 3.0, (N, )).astype(DTYPE)
mu = np.array([0.0, 0.1, 2 * np.pi, 0.1 * np.pi]).astype(DTYPE)
lb = np.NINF
ub = np.PINF
a11 = Parameter("a11", 1, lb, ub)
a12 = Parameter("a12", 1, lb, ub)
a21 = Parameter("a21", 1, lb, ub)
a22 = Parameter("a22", 1, lb, ub)
params = [a11, a12, a21, a22]
M = Model("lds", params)
M.set_eps(linear2D_freq)
H, R, R1s, R2 = aug_lag_vars(z, log_q_z, M.eps, mu, N)
alphas = np.zeros((N, ))
omegas = np.zeros((N, ))
for i in range(N):
alphas[i], omegas[i] = linear2D_freq_np(z[i, 0], z[i, 1], z[i, 2],
z[i, 3])
# mean_alphas = np.mean(alphas)
# mean_omegas = np.mean(omegas)
mean_alphas = 0.0
mean_omegas = 2.0 * np.pi
T_x_np = np.stack(
(
alphas,
np.square(alphas - mean_alphas),
omegas,
np.square(omegas - mean_omegas),
),
axis=1,
)
H_np = np.mean(-log_q_z)
R_np = np.mean(T_x_np, 0) - mu
R1_np = np.mean(T_x_np[:N // 2, :], 0) - mu
R2_np = np.mean(T_x_np[N // 2:, :], 0) - mu
R1s_np = list(R1_np)
rtol = 1e-3
assert np.isclose(H, H_np, rtol=rtol)
assert np.isclose(R, R_np, rtol=rtol).all()
assert np.isclose(R1s, R1s_np, rtol=rtol).all()
assert np.isclose(R2, R2_np, rtol=rtol).all()
return None
def LRRNN_setup(N, g, K):
D = int(N * RANK)
lb = -np.ones((D, ))
ub = np.ones((D, ))
U = Parameter("U", D, lb=lb, ub=ub)
V = Parameter("V", D, lb=lb, ub=ub)
parameters = [U, V]
model = Model("Rank2Net_g=%.4f_K=%d" % (g, K), parameters)
W_eigs = get_W_eigs_tf(g, K)
def stable_amp(U, V):
U = tf.reshape(U, (-1, N, RANK))
V = tf.reshape(V, (-1, N, RANK))
T_x = W_eigs(U, V)
return T_x
model.set_eps(stable_amp)
return model
def test_check_convergence():
N = 500
nu = 0.1
M_test = 200
N_test = int(nu * N)
mu = np.array([0.0, 0.1, 2 * np.pi, 0.1 * np.pi], dtype=np.float32)
lb_a12 = 0.0
ub_a12 = 10.0
lb_a21 = -10.0
ub_a21 = 0.0
a11 = Parameter("a11", 1, 0.0)
a12 = Parameter("a12", 1, lb_a12, ub_a12)
a21 = Parameter("a21", 1, lb_a21, ub_a21)
a22 = Parameter("a22", 1, ub=0.0)
params = [a11, a12, a21, a22]
M = Model("lds_2D", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, epi_path, failed = M.epi(
mu,
num_iters=1000,
K=10,
N=N,
stop_early=True,
save_movie_data=False,
random_seed=1,
)
assert not failed
assert (opt_data["converged"] == True).sum() > 0
epi_df = M.get_epi_df()
epi_df_row = epi_df[epi_df["iteration"] == epi_df["iteration"].max()].iloc[0]
init = epi_df_row["init"]
init_params = {"mu": init["mu"], "Sigma": init["Sigma"]}
nf = M._df_row_to_nf(epi_df_row)
aug_lag_hps = M._df_row_to_al_hps(epi_df_row)
best_k, converged, best_H = M.get_convergence_epoch(
init_params, nf, mu, aug_lag_hps, alpha=0.05, nu=0.1,
)
assert converged
return None
def lds_2D_model_fixture():
# 1. Define the model.
lb, ub = -10.0, 10.0
a11 = Parameter("a11", 1, lb=lb, ub=ub)
a12 = Parameter("a12", 1, lb=lb, ub=ub)
a21 = Parameter("a21", 1, lb=lb, ub=ub)
a22 = Parameter("a22", 1, lb=lb, ub=ub)
name = "lds_2D"
params = [a11, a12, a21, a22]
M = Model(name, params)
# 2. Define the emergent property.
def linear2D_eig(a11, a12, a21, a22):
tau = 1.0
c11 = a11 / tau
c12 = a12 / tau
c21 = a21 / tau
c22 = a22 / tau
# Quadratic formula.
real_term = 0.5 * (c11 + c22)
complex_term = 0.5 * tf.sqrt(
tf.complex(
tf.square(c11 + c22) - 4.0 * (c11 * c22 - c12 * c21), 0.0))
real_lambda = real_term + tf.math.real(complex_term)
imag_lambda = tf.math.imag(complex_term)
T_x = tf.concat(
(
real_lambda,
imag_lambda,
tf.square(real_lambda - 0.0),
tf.square(imag_lambda - (2.0 * np.pi)),
),
axis=1,
)
return T_x
M.set_eps(linear2D_eig)
return M
def test_Model_init():
"""Test Model initialization."""
p1 = Parameter("a", 1, 0, 1)
p2 = Parameter("b", 1)
params = [p1, p2]
M = Model("foo", params)
assert M.name == "foo"
for i, p in enumerate(M.parameters):
assert p == params[i]
with raises(TypeError):
Model(1, params)
params = [p1, "bar"]
with raises(TypeError):
Model("foo", params)
with raises(TypeError):
Model("foo", "bar")
p3 = Parameter("c", 1, 1, 4)
p3.lb = np.array([1])
p3.ub = np.array([-1])
params = [p1, p2, p3]
with raises(ValueError):
Model("foo", params)
p3.lb = np.array([1])
p3.ub = np.array([1])
with raises(ValueError):
Model("foo", params)
p3 = Parameter("a", 1, 1, 4)
params = [p1, p2, p3]
with raises(ValueError):
Model("foo", params)
return None
args = parser.parse_args()
print(
'Running epi for matrix determinant with hyper parameter random seed %d.' %
args.seed)
d = args.d
# 1. Define model: dxd matrix
D = int(d * (d + 1) / 2)
# Set up the bound vectors.
lb = -2. * np.ones((D, ))
ub = 2. * np.ones((D, ))
# Define the parameter A.
A = Parameter("A", D, lb=lb, ub=ub)
parameters = [A]
# Define the model matrix.
M = Model("matrix", parameters)
# 2. Define the emergent property: E[det(A)] = 100, std(det(A)) = 5
mu = np.array([d, 0., 1., 1.], dtype=DTYPE)
def trace_det(A):
diag_div = tf.expand_dims(tf.eye(d), 0) + 1.
A_lower = tfp.math.fill_triangular(A)
A = (A_lower + tf.transpose(A_lower, [0, 2, 1]))
e, v = tf.linalg.eigh(A)
trace = tf.reduce_sum(e, axis=1)
freq = args.freq
mu_std = args.mu_std
beta = args.beta
c0 = 10.0**args.logc0
random_seed = args.random_seed
g_el_lb = 4.0
sigma_I = 1.0e-12
# sleep_dur = np.abs(args.logc0) + random_seed/5. + beta/3.
# print('short stagger sleep of', sleep_dur, flush=True)
# time.sleep(sleep_dur)
# 1. Specify the V1 model for EPI.
D = 2
g_el = Parameter("g_el", 1, lb=g_el_lb, ub=8.0)
g_synA = Parameter("g_synA", 1, lb=0.01, ub=4.0)
# Define model
name = "STG_sigmaI=%.2E" % sigma_I
parameters = [g_el, g_synA]
model = Model(name, parameters)
# Emergent property values.
mu = np.array([freq, mu_std**2])
init_type = "abc"
abc_std = mu_std
init_params = {
"num_keep": 500,
"means": np.array([freq]),
p = args.p
AL_beta = args.beta
elemwise_fn = args.elemwise_fn
c0 = 10.0**args.logc0
mu_std = args.mu_std
random_seed = args.random_seed
M = 100
N = 200
# 1. Specify the V1 model for EPI.
lb = -5.0
ub = 5.0
sW = Parameter("sW", 1, lb=lb, ub=ub)
vW = Parameter("vW", 1, lb=lb, ub=ub)
dW = Parameter("dW", 1, lb=lb, ub=ub)
hW = Parameter("hW", 1, lb=lb, ub=ub)
parameters = [sW, vW, dW, hW]
model = Model("SC_Circuit_var", parameters)
# EP values
mu = np.array([p, 1.0 - p, mu_std**2, mu_std**2])
model.set_eps(SC_acc_var(p))
# 3. Run EPI.
q_theta, opt_data, epi_path, failed = model.epi(
def test_epi():
mu = np.array([0.0, 0.1, 2 * np.pi, 0.1 * np.pi])
lb_a12 = 0.0
ub_a12 = 10.0
lb_a21 = -10.0
ub_a21 = 0.0
a11 = Parameter("a11", 1, 0.0)
a12 = Parameter("a12", 1, lb_a12, ub_a12)
a21 = Parameter("a21", 1, lb_a21, ub_a21)
a22 = Parameter("a22", 1, ub=0.0)
params = [a11, a12, a21, a22]
M = Model("lds", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, save_path, _ = M.epi(
mu, num_iters=100, K=1, save_movie_data=True
)
g = q_theta.plot_dist()
M.epi_opt_movie(save_path)
params = [a11, a12, a21, a22]
M = Model("lds_2D", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, save_path, _ = M.epi(
mu, num_iters=100, K=1, save_movie_data=True
)
q_theta = M.load_epi_dist(mu, k=1)
M.epi_opt_movie(save_path)
q_theta, opt_data, save_path, _ = M.epi(
mu, num_units=31, num_iters=100, K=1, save_movie_data=True
)
M.plot_epi_hpsearch(mu)
opt_data_filename = save_path + "opt_data.csv"
opt_data_cols = ["k", "iteration", "H", "converged"] + [
"R%d" % i for i in range(1, M.m + 1)
]
for x, y in zip(opt_data.columns, opt_data_cols):
assert x == y
# opt_data_df = pd.read_csv(opt_data_filename)
# opt_data_df['iteration'] = 2*opt_data_df['iteration']
# opt_data_df.to_csv(opt_data_filename)
# with raises(IOError):
# M.epi_opt_movie(save_path)
# os.remove(opt_data_filename)
# with raises(IOError):
# M.epi_opt_movie(save_path)
assert q_theta is not None
with raises(ValueError):
q_theta = M.load_epi_dist(mu, k=20)
with raises(TypeError):
q_theta = M.load_epi_dist(mu, k="foo")
with raises(ValueError):
q_theta = M.load_epi_dist(mu, k=-1)
M = Model("foo", params)
with raises(ValueError):
q_theta = M.load_epi_dist(mu, k=-1)
z = q_theta(1000)
log_q_z = q_theta.log_prob(z)
assert np.sum(z[:, 0] < 0.0) == 0
assert np.sum(z[:, 1] < lb_a12) == 0
assert np.sum(z[:, 1] > ub_a12) == 0
assert np.sum(z[:, 2] < lb_a21) == 0
assert np.sum(z[:, 2] > ub_a21) == 0
assert np.sum(z[:, 3] > 0.0) == 0
assert np.sum(1 - np.isfinite(z)) == 0
assert np.sum(1 - np.isfinite(log_q_z)) == 0
# Intentionally swap order in list to insure proper handling.
params = [a22, a21, a12, a11]
M = Model("lds2", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, save_path, _ = M.epi(
mu, K=2, num_iters=100, stop_early=True, verbose=True
)
with raises(IOError):
M.epi_opt_movie(save_path)
z = q_theta(1000)
log_q_z = q_theta.log_prob(z)
assert np.sum(z[:, 0] < 0.0) == 0
assert np.sum(z[:, 1] < lb_a12) == 0
assert np.sum(z[:, 1] > ub_a12) == 0
assert np.sum(z[:, 2] < lb_a21) == 0
assert np.sum(z[:, 2] > ub_a21) == 0
assert np.sum(z[:, 3] > 0.0) == 0
assert np.sum(1 - np.isfinite(z)) == 0
assert np.sum(1 - np.isfinite(log_q_z)) == 0
for x, y in zip(opt_data.columns, opt_data_cols):
assert x == y
with raises(ValueError):
def bad_f(a11, a12, a21, a22):
return tf.expand_dims(a11 + a12 + a21 + a22, 0)
M.set_eps(bad_f)
params = [a22, a21, a12, a11]
M = Model("lds2", params)
nf = NormalizingFlow("autoregressive", 4, 1, 2, 10)
al_hps = AugLagHPs()
with raises(AttributeError):
save_path = M.get_save_path(mu, nf, al_hps, None)
save_path = M.get_save_path(mu, nf, al_hps, eps_name="foo")
return None
def test_Parameter_init():
"""Test Parameter initialization."""
p = Parameter("foo", 1, -0.1, 1.2)
assert p.name == "foo"
assert p.D == 1
assert p.lb[0] == -0.1
assert p.ub[0] == 1.2
p = Parameter("foo", 4, -np.random.rand(4), np.random.rand(4) + 1)
assert p.name == "foo"
assert p.D == 4
with raises(TypeError):
p = Parameter(20, 1)
with raises(TypeError):
p = Parameter("foo", "bar")
with raises(TypeError):
p = Parameter("foo", 1, "bar")
with raises(TypeError):
p = Parameter("foo", 1, 0.0, "bar")
with raises(ValueError):
p = Parameter("foo", -1)
with raises(ValueError):
p = Parameter("foo", 1, 1.0, 0.0)
with raises(ValueError):
p = Parameter("foo", 1, 0.0, 0.0)
with raises(ValueError):
p = Parameter("foo", 2, lb=np.random.rand(3))
with raises(ValueError):
p = Parameter("foo", 2, lb=np.random.rand(2, 2))
with raises(ValueError):
p = Parameter("foo", 2, ub=np.random.rand(3))
with raises(ValueError):
p = Parameter("foo", 2, ub=np.random.rand(2, 2))
return None
num_neurons = args.n
T = args.T
if (args.traj==1):
full_traj = True
elif (args.traj==0):
full_traj = False
else:
raise ValueError('--traj must be 0 or 1')
print(num_neurons, T, full_traj)
# 1. Define model: dxd matrix
D = num_neurons**2
lb = -2.*np.ones((D,), np.float32)
ub = 2.*np.ones((D,), np.float32)
J = Parameter("J", D=D, lb=lb, ub=ub)
params = [J]
M = Model('RNN_n=%d_T=%d' % (num_neurons, T), params)
# 2. Define the emergent property:
x0 = tf.constant(np.random.normal(0., 1., (1, num_neurons,1)), dtype=tf.float32)
w = tf.constant(np.random.normal(0., 1., (num_neurons,)), tf.float32)
if (full_traj):
targ = np.expand_dims(np.sin(4*np.pi*np.arange(T+1)/T), 0)
def sim(J):
J_shape = tf.shape(J)
N = J_shape[0]
J = tf.reshape(J, (N, num_neurons, num_neurons))
contrast = 0.5
W_mat = load_SSSN_variable("W", ind=ind)
hb = load_SSSN_variable("hb", ind=ind).numpy()
hc = load_SSSN_variable("hc", ind=ind).numpy()
h = hb[None, :] + contrast * hc[None, :]
neuron_inds = {"E": 0, "P": 1, "S": 2, "V": 3}
neuron_ind = neuron_inds[alpha]
M = 100
# 1. Specify the V1 model for EPI.
D = 4
lb = np.zeros((D, ))
ub = lim * np.ones((D, ))
sigma_eps = Parameter("sigma_eps", D, lb=lb, ub=ub)
# Define model
name = "SSSN_stddev_sigma_%s_%.2E_%.2E_ind=%d" % (alpha, sE_mean, sE_std, ind)
parameters = [sigma_eps]
model = Model(name, parameters)
dt = 0.0005
T = 150
N = 100
stddev = get_stddev_sigma(alpha,
W_mat,
h,
N=N,
dt=dt,
args = parser.parse_args()
alpha = args.alpha
beta = args.beta
inc_val = args.inc_val
inc_std = args.inc_std
num_stages = args.num_stages
num_units = args.num_units
c0 = 10.**args.logc0
random_seed = args.random_seed
# 1. Specify the V1 model for EPI.
D = 4
lb = -5. * np.ones((D, ))
ub = 5. * np.ones((D, ))
dh = Parameter("dh", D, lb=lb, ub=ub)
parameters = [dh]
beta_str = ''
if beta == '':
b = np.array([1., 1., 1., 1.25])
elif beta == 'P':
b = np.array([1., -5., 1., 1.25])
beta_str += '_P'
elif beta == 'S':
b = np.array([1., 1., -5., 1.25])
beta_str += '_S'
else:
raise (NotImplentedError("Error: beta = %s ?" % beta))
name = "V1Circuit_%s%s" % (alpha, beta_str)
def test_epi():
mu = np.array([0.0, 0.1, 2 * np.pi, 0.1 * np.pi])
lb_a12 = 0.0
ub_a12 = 10.0
lb_a21 = -10.0
ub_a21 = 0.0
a11 = Parameter("a11", 1, 0.0)
a12 = Parameter("a12", 1, lb_a12, ub_a12)
a21 = Parameter("a21", 1, lb_a21, ub_a21)
a22 = Parameter("a22", 1, ub=0.0)
params = [a11, a12, a21, a22]
M = Model("lds_2D", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, epi_path, failed = M.epi(
mu, num_iters=100, K=1, save_movie_data=True, log_rate=10,
)
z = q_theta(50)
g = q_theta.plot_dist(z)
M.epi_opt_movie(epi_path)
params = [a11, a12, a21, a22]
# should load from prev epi
M = Model("lds_2D", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, epi_path, failed = M.epi(
mu, num_iters=100, K=1, save_movie_data=True
)
print("epi_path", epi_path)
epi_df = M.get_epi_df()
epi_df_row = epi_df[epi_df["iteration"] == 100].iloc[0]
q_theta = M.get_epi_dist(epi_df_row)
opt_data_filename = os.path.join(epi_path, "opt_data.csv")
M.set_eps(linear2D_freq)
q_theta, opt_data, epi_path, failed = M.epi(
mu, num_iters=100, K=1, save_movie_data=True, log_rate=10,
)
opt_data_cols = ["k", "iteration", "H", "cost", "converged"] + [
"R%d" % i for i in range(1, M.m + 1)
]
for x, y in zip(opt_data.columns, opt_data_cols):
assert x == y
assert q_theta is not None
z = q_theta(1000)
log_q_z = q_theta.log_prob(z)
assert np.sum(z[:, 0] < 0.0) == 0
assert np.sum(z[:, 1] < lb_a12) == 0
assert np.sum(z[:, 1] > ub_a12) == 0
assert np.sum(z[:, 2] < lb_a21) == 0
assert np.sum(z[:, 2] > ub_a21) == 0
assert np.sum(z[:, 3] > 0.0) == 0
assert np.sum(1 - np.isfinite(z)) == 0
# Intentionally swap order in list to insure proper handling.
params = [a22, a21, a12, a11]
M = Model("lds", params)
M.set_eps(linear2D_freq)
q_theta, opt_data, epi_path, _ = M.epi(
mu,
K=2,
num_iters=100,
stop_early=True,
verbose=True,
save_movie_data=True,
log_rate=10,
)
M.epi_opt_movie(epi_path)
z = q_theta(1000)
log_q_z = q_theta.log_prob(z)
assert np.sum(z[:, 0] < 0.0) == 0
assert np.sum(z[:, 1] < lb_a12) == 0
assert np.sum(z[:, 1] > ub_a12) == 0
assert np.sum(z[:, 2] < lb_a21) == 0
assert np.sum(z[:, 2] > ub_a21) == 0
assert np.sum(z[:, 3] > 0.0) == 0
assert np.sum(1 - np.isfinite(z)) == 0
print("DOING ABC NOW")
# Need finite support for ABC
a11 = Parameter("a11", 1, -10.0, 10.0)
a12 = Parameter("a12", 1, -10.0, 10.0)
a21 = Parameter("a21", 1, -10.0, 10.0)
a22 = Parameter("a22", 1, -10.0, 10.0)
params = [a11, a12, a21, a22]
M = Model("lds_2D", params)
M.set_eps(linear2D_freq)
init_type = "abc"
init_params = {"num_keep": 50, "mean": mu[:2], "std": np.sqrt(mu[2:])}
q_theta, opt_data, epi_path, failed = M.epi(
mu,
num_iters=100,
K=1,
init_type=init_type,
init_params=init_params,
save_movie_data=True,
log_rate=10,
)
params = [a11, a12, a21, a22]
M = Model("lds2", params)
M.set_eps(linear2D_freq)
# This should cause opt to fail with nan since c0=1e20 is too high.
q_theta, opt_data, epi_path, _ = M.epi(
mu,
K=3,
num_iters=1000,
c0=1e20,
stop_early=True,
verbose=True,
save_movie_data=False,
log_rate=10,
)
with raises(IOError):
M.epi_opt_movie(epi_path)
for x, y in zip(opt_data.columns, opt_data_cols):
assert x == y
with raises(ValueError):
def bad_f(a11, a12, a21, a22):
return tf.expand_dims(a11 + a12 + a21 + a22, 0)
M.set_eps(bad_f)
params = [a11, a12, a21, a22]
M = Model("lds2", params)
init_params = {"mu": 2 * np.zeros((4,)), "Sigma": np.eye(4)}
nf = NormalizingFlow("autoregressive", 4, 1, 2, 10)
al_hps = AugLagHPs()
epi_path, exists = M.get_epi_path(init_params, nf, mu, al_hps, eps_name="foo")
assert not exists
return None
from epi.util import sample_aug_lag_hps
import numpy as np
import argparse
# Get random seed.
parser = argparse.ArgumentParser()
parser.add_argument('--seed', type=int)
args = parser.parse_args()
print('Running epi on 2D-LDS with hyper parameter random seed %d.' % args.seed)
# Define the 2D LDS model parameters.
# The four entries of the dynamics matrix will be bounded.
lb = -10.
ub = 10.
a11 = Parameter("a11", 1, lb=lb, ub=ub)
a12 = Parameter("a12", 1, lb=lb, ub=ub)
a21 = Parameter("a21", 1, lb=lb, ub=ub)
a22 = Parameter("a22", 1, lb=lb, ub=ub)
params = [a11, a12, a21, a22]
M = Model("lds_2D", params)
# Set the emergent property statistics to frequency.
M.set_eps(linear2D_freq)
# Set the mergent property values
mu = np.array([0.0, 0.5**2, 2 * np.pi, (0.1 * 2 * np.pi)**2])
np.random.seed(args.seed)
num_stages = 3
num_layers = np.random.randint(1, 3)
c0 = 10**(args.c0)
rs = args.rs
r = 2 # rank-2 networks
num_epochs = 1
# 1. Define model: dxd matrix
D = int(N * r)
# Set up the bound vectors.
lb = -np.ones((D, ))
ub = np.ones((D, ))
# Define the parameter A.
U = Parameter("U", D, lb=lb, ub=ub)
V = Parameter("V", D, lb=lb, ub=ub)
parameters = [U, V]
# Define the model matrix.
M = Model("Rank2Net_g=%.4f_K=%d" % (g, K), parameters)
# 2. Define the emergent property:
J_eig_realmax_mean = 0.5
Js_eig_max_mean = 1.5
eig_std = 0.25
mu = np.array([J_eig_realmax_mean, Js_eig_max_mean, eig_std**2, eig_std**2],
dtype=DTYPE)
W_eigs = get_W_eigs_tf(g, K)