from numpy import sqrt import timeit # created by Yu Hu ([email protected]), Aug 2020 plt.rcParams.update({'font.size': 18}) # compare simulation and iid Gaussian theory g_ls = [0.5] N_ls = [100, 400, 800] ifig = 0 for g in g_ls: for N in N_ls: ifig += 1 J = g * randn(N, N) / sqrt(N) C = J2C(J) eig_C = eigvalsh(C) x, px = pdf_g(g, nx=1000) fig = plt.figure(figsize=(8, 6)) plt.plot(x, px, linewidth=1.5, label='theory') plt.hist(eig_C, 40, density=True, label='N=' + str(N)) plt.plot([x[0], x[-1]], [0, 0], '.', markersize=10) plt.xlabel('cov eigenvalues') plt.ylabel('probabilty') plt.legend() plt.title('g=' + str(g)) plt.tight_layout() fig.savefig('./figure/figure1a_' + str(ifig) + '.png', dpi=600) # different g
print('0.995 quantile r:', r_quantile)
J = randn(N,N)/sqrt(N)*g
# kdivh = 0.25 # squared root of the kappa notations in text
kdivh = 0.45 # squared root of the kappa notations in text
kdiv = sqrt(kdivh**2/(1-kdivh**2)*(g**2/N)) # g is after removing div motifs
print('b entry var b/sqrt(N): ', kdiv*sqrt(N))
print('xuv, x=', N*kdiv)
b = randn(N) * kdiv # squared root of the kappa notations in text
print('check', np.linalg.norm(b)*np.linalg.norm(ones(N)))
print('outlier theory:', J_uv_outlier(g,N*kdiv))
print('outlier theory:', J_uv_outlier(g,np.linalg.norm(b)*np.linalg.norm(ones(N))))
Jm = J + np.outer(ones(N),b)
x,px = pdf_g(g)
C = J2C(J)
Cm = J2C(Jm)
eig_C = eigvalsh(C)
eig_Cm = eigvalsh(Cm)
fig = plt.figure(figsize=(8,4))
plt.hist(eig_C, 40, density=True, label='N='+str(N));
plt.plot(x,px, linewidth=1.5, label='g='+str(g))
x_lim = plt.xlim()
plt.xlabel('cov eigenvalues')
plt.ylabel('probability')
plt.legend()
plt.title(r'Cov spectrum with $J$')
plt.tight_layout()
fig.savefig('./figure/figure3a_1_cov_J.png', dpi=600)
eig_J = eigvals(J)
plt.legend()
plt.xlabel('cov eigenvalues')
plt.ylabel('probabilty')
plt.title('Random antisymmetric connectivity')
plt.tight_layout()
yline = linspace(0, 9, 400)
plt.plot(x[-1] * ones(400), yline, color='grey', linestyle='--', linewidth='3')
plt.ylim(0, 9)
fig.savefig('./figure/figure5a.png', dpi=600)
# example bimodal
g = 1.1
kre = -0.99
N = 400
J = J_g_kre(N, g, kre)
C = J2C(J)
eig_C = eigvalsh(C)
x, px = pdf_g_kre(g, kre, nx=10000)
fig = plt.figure(figsize=(8, 6))
plt.hist(eig_C, 40, density=True, color='orange', label='N=' + str(N))
t0 = timeit.default_timer()
ipeaks, _ = find_peaks(px)
t1 = timeit.default_timer()
print('finding peaks:', t1 - t0)
line = plt.plot(x,
px,
'b',
linewidth=2,
label='$g=' + str(g) + ',\;\hat{\kappa}_{re}=' + str(kre) +
'$')
plt.plot([x[0], x[-1]], [0, 0], '.', color=line[0].get_color(), markersize=10)
# wi = 1.5*p*w0
# x1 = -wi*n + p*n*w0
n_ls = np.array([400, 800, 1200, 1600, 2000])
nn = len(n_ls)
ntrial = 400
x1p_ls = zeros((ntrial, nn))
t0 = timeit.default_timer()
for i, n in enumerate(n_ls):
p = 4 * x1**2 / (4 * x1**2 + n * g**2)
w0 = g / sqrt(n * p * (1 - p))
wi = 1.5 * p * w0
for t in range(ntrial):
J = np.random.binomial(1, p, (n, n))
J = J * w0
J = J - wi * ones((n, n))
C = J2C(J)
eig_C = np.sort(eigvalsh(C))
x1p_ls[t, i] = eig_C[0]
t1 = timeit.default_timer()
t01 = t1 - t0
print('simulation time: ', t01)
with open('./data/figure_outlier_ER_subI_MSE_' + str(plot_id) + '.npz',
'wb') as file1:
np.savez(file1, g, x1, n_ls, ntrial, x1p_ls, t01)
else:
with np.load('./data/figure_outlier_ER_subI_MSE_' + str(plot_id) +
'.npz') as file1:
g = file1['arr_0']
x1 = file1['arr_1']
n_ls = file1['arr_2']
ntrial = file1['arr_3']