def compare(dynamics, dynamics_ij, dynamics_beta, c, arguments, N, sigma, low, high, transition_to_high):
t = np.arange(0, 100, 0.01)
num_col = int(np.sqrt(N))
A = network_ensemble_grid(9, 3)
xs_l, xs_h = stable_state(A, degree, dynamics, c, low, high, arguments)
A = network_ensemble_grid(N, num_col)
if transition_to_high == 1:
x_initial = np.mean(xs_l) * np.ones(N)
else:
x_initial = np.mean(xs_h) * np.ones(N)
index = np.where(A!=0)
A_interaction = A[index].reshape(N, degree)
local_state = np.random.RandomState(1) # avoid same random process.
noise= local_state.normal(0, np.sqrt(dt), (np.size(t)-1, N)) * sigma
dyn = main.sdesolver(main.close(dynamics, *(N, index, degree, A_interaction, c, arguments)), x_initial, t, dW = noise)
transition_first = np.where(dyn > (xs_l[0] + xs_h[0])/2)[1][0]
# transition_first = 8
first_neighbor = index[1][transition_first * c : (transition_first+1) * c]
noise_beta = np.zeros((np.size(t)-1, 2))
noise_beta[:, 0] = noise[:, transition_first]
noise_beta[:, 1] = np.mean(np.take(noise, first_neighbor, axis=1), -1)
# noise_beta[:, 2] = np.mean(noise, -1)
dyn_ij = main.sdesolver(main.close(dynamics_ij, *(c,arguments[:-1])), x_initial[:2], t, dW = noise_beta)
'''
des = '../data/' + 'mutual' + str(4) + f'/size1/c{c}/'
xy_relation = np.array(pd.read_csv(des + 'xy_relation.csv', header=None).iloc[:, :])
f = interp1d(xy_relation[0], xy_relation[1])
xj_stable = np.zeros((np.size(dyn_ij[:, 0])))
plt.plot(t, xj_stable)
for xi, i in zip(dyn_ij[:, 0], range(np.size(dyn_ij[:, 0]))):
if xi < xy_relation[0, 0]:
xj = xy_relation[1, 0]
elif xi > xy_relation[0, -1]:
xj = xy_relation[1, -1]
else:
xj = f(xi)
xj_stable[i] = xj
dyn_beta = main.sdesolver(main.close(dynamics_beta, *(c,arguments[:-1]), f, xy_relation[0, 0], xy_relation[0, -1]), x_initial[:1], t, dW = noise_beta[:, 0].reshape(np.size(noise_beta[:,0]), 1))
plt.plot(t, dyn_beta, label='beta')
'''
plt.plot(t, dyn[:, transition_first], label='first_original')
plt.plot(t, np.mean(np.take(dyn, first_neighbor, axis=1), -1), label='neighbor_original')
plt.plot(t, dyn_ij[:, 0], label='first_reduction')
plt.plot(t, dyn_ij[:, 1], label='neighbor_reduction')
#plt.plot(t, np.mean(dyn, -1))
plt.xlabel('t', fontsize=fs)
plt.ylabel('x', fontsize=fs)
# plt.title(f'$c=${c}_$N=${N}_$\\sigma=${sigma}', fontsize=fs)
plt.xticks(fontsize=15)
plt.yticks(fontsize=15)
plt.subplots_adjust(left=0.15, right=0.99, wspace=0.25, hspace=0.25, bottom=0.13, top=0.99)
plt.legend(fontsize=14)
plt.xlim(right=40)
plt.show()
return index, dyn, xs_l, xs_h
def system_collect(store_index, N, index, degree, A_interaction, strength, x_initial, T_start, T_end, t, dt, des_evolution, des_ave, des_high, dynamics, c, arguments, transition_to_high, criteria, remove, initial_noise):
"""one realization to run sdeint and save dynamics
"""
evolution_file = des_evolution + f'realization{store_index}_T_{T_start}_{T_end}'
# local_state = np.random.RandomState(store_index + T_start * int(parallel_size_all/T_every) ) # avoid same random process.
local_state = np.random.RandomState(store_index)
if initial_noise == 'metastable' and T_start == 0:
pre_t = np.arange(0, 50, dt)
dynamics_pre = globals()[dynamics.__name__[: dynamics.__name__.find('_')] + '_preprocess']
noise= local_state.normal(0, np.sqrt(dt), (np.size(pre_t)-1, N)) * strength
x_initial = main.sdesolver(main.close(dynamics_pre, *(N, index, degree, A_interaction, c, arguments)), x_initial, pre_t, dW = noise)[-1]
for i in range(int(T_start/T_every)+1):
noise= local_state.normal(0, np.sqrt(dt), (np.size(t)-1, N)) * strength
if N == 1:
dynamics = globals()[dynamics.__name__[: dynamics.__name__.find('_')] + '_1D']
dyn_all = main.sdesolver(main.close(dynamics, *(c, arguments[:-1])), x_initial, t, dW=noise.reshape(np.size(noise), 1) )
'''
des = '../data/' + 'mutual' + str(4) + f'/size1/c{c}/'
xy_relation = np.array(pd.read_csv(des + 'xy_relation.csv', header=None).iloc[:, :])
f = interp1d(xy_relation[0], xy_relation[1])
dynamics = globals()[dynamics.__name__[: dynamics.__name__.find('_')] + '_beta']
dyn_all = main.sdesolver(main.close(dynamics, *(c, arguments[:-1], f, xy_relation[0, 0], xy_relation[0, -1] )), x_initial, t, dW=noise.reshape(np.size(noise), 1) )
'''
dyn_ave = np.mean(dyn_all, -1)
x_high = np.mean(dyn_all[-1])
elif N == 2:
dynamics = globals()[dynamics.__name__[: dynamics.__name__.find('_')] + '_ij']
noise[:, 1] = noise[:, 1] / 2
dyn_all = main.sdesolver(main.close(dynamics, *(c, arguments)), x_initial, t, dW=noise )
x_high = dyn_all[-1, 0]
dyn_ave = dyn_all[:, 0]
else:
dyn_all = main.sdesolver(main.close(dynamics, *(N, index, degree, A_interaction, c, arguments)), x_initial, t, dW = noise)
dyn_ave = np.mean(dyn_all, -1)
x_high = np.mean(dyn_all[-1])
x_high_df = pd.DataFrame(np.ones((1, 1)) * x_high)
x_high_df.to_csv(des_high + f'realization{store_index}.csv', mode='a', index=False, header=False)
if (transition_to_high == 1 and x_high > criteria) or (transition_to_high == 0 and x_high < criteria):
ave_file = des_ave + f'realization{store_index}_T_{T_start}_{T_end}'
np.save(ave_file, dyn_ave)
if remove == 0:
np.save(evolution_file, dyn_all)
else:
np.save(evolution_file, dyn_all)
del noise, dyn_all, x_high, dyn_ave
return None
def system_collect(store_index, N, index, degree, A_interaction, strength,
x_initial, T_start, T_end, t, dt, des_evolution, des_ave,
des_high, c):
"""one realization to run sdeint and save dynamics
"""
local_state = np.random.RandomState(store_index +
T_start) # avoid same random process.
noise = local_state.normal(0, np.sqrt(dt), (np.size(t) - 1, N)) * strength
dyn_all = main.sdesolver(main.close(harvest_lattice,
*(N, index, degree, A_interaction, c)),
x_initial,
t,
dW=noise)
evolution_file = des_evolution + f'realization{store_index}_T_{T_start}_{T_end}'
np.save(evolution_file, dyn_all)
x_high = np.mean(dyn_all[-1])
x_high_df = pd.DataFrame(np.ones((1, 1)) * x_high)
x_high_df.to_csv(des_high + f'realization{store_index}.csv',
mode='a',
index=False,
header=False)
if x_high > K / 2:
ave_file = des_ave + f'realization{store_index}_T_{T_start}_{T_end}'
np.save(ave_file, np.mean(dyn_all, -1))
return None
def tg_from_one_transition(dynamics, c, arguments, N, sigma, low, high, transition_to_high):
"""TODO: Docstring for tg_from_one_transition.
:N: TODO
:sigma: TODO
:returns: TODO
"""
t = np.arange(0, 100, 0.01)
num_col = int(np.sqrt(N))
A = network_ensemble_grid(9, 3)
xs_l, xs_h = stable_state(A, degree, dynamics, c, low, high, arguments)
A = network_ensemble_grid(N, num_col)
if transition_to_high == 1:
x_initial = np.mean(xs_l) * np.ones(N)
else:
x_initial = np.mean(xs_h) * np.ones(N)
x_half = (np.mean(xs_l) + np.mean(xs_h))/2
x_initial[int(num_col/2)] = np.mean(xs_h)
index = np.where(A!=0)
A_interaction = A[index].reshape(N, degree)
local_state = np.random.RandomState(5) # avoid same random process.
noise= np.random.normal(0, np.sqrt(dt), (np.size(t)-1, N)) * sigma
dyn = main.sdesolver(main.close(dynamics, *(N, index, degree, A_interaction, c, arguments)), x_initial, t, dW = noise)
rho = np.mean(dyn, -1)
tg = next(x for x, y in enumerate(rho) if y > x_half) * 0.01
return tg
def example():
N = 100
num_col = int(np.sqrt(N))
x_initial = np.ones(N) * 1
A = network_ensemble_grid(N, num_col)
N = np.size(A, -1)
index = np.where(A != 0)
A_interaction = A[index].reshape(N, degree)
local_state = np.random.RandomState(0) # avoid same random process.
noise = local_state.normal(0, np.sqrt(dt), (np.size(t) - 1, N)) * strength
dyn = main.sdesolver(main.close(harvest_lattice,
*(N, index, degree, A_interaction, c)),
x_initial,
t,
dW=noise)
def example(dynamics, c, arguments, N, sigma, low, high, transition_to_high):
t = np.arange(0, 1000, 0.01)
num_col = int(np.sqrt(N))
A = network_ensemble_grid(9, 3)
xs_l, xs_h = stable_state(A, degree, dynamics, c, low, high, arguments)
A = network_ensemble_grid(N, num_col)
if transition_to_high == 1:
x_initial = np.mean(xs_l) * np.ones(N)
else:
x_initial = np.mean(xs_h) * np.ones(N)
index = np.where(A!=0)
A_interaction = A[index].reshape(N, degree)
local_state = np.random.RandomState(5) # avoid same random process.
noise= local_state.normal(0, np.sqrt(dt), (np.size(t)-1, N)) * sigma
dyn = main.sdesolver(main.close(dynamics, *(N, index, degree, A_interaction, c, arguments)), x_initial, t, dW = noise)
#plt.plot(t, np.mean(dyn, -1))
plt.plot(t, dyn)
plt.xlabel('t', fontsize=fs)
plt.ylabel('x', fontsize=fs)
plt.title(f'$c=${c}_$N=${N}_$\\sigma=${sigma}', fontsize=fs)
plt.show()
return index, dyn, xs_l, xs_h