def autocor(PSTH,N=None,T=20*br.ms,bin=None):
if bin is None:
bin = br.defaultclock.dt
p = int(T/ bin)
SAC = br.zeros(p)
if N is None:
SAC[0] = br.mean(PSTH * PSTH)
else: # correction to exclude self-coincidences
PSTHnoself = br.clip(PSTH - 1. / (bin * N), 0*br.kHz, br.Inf*br.kHz)
SAC[0] = br.mean(PSTH * PSTHnoself) * N / (N - 1.)
SAC[1:] = [br.mean(PSTH[:-i] * PSTH[i:]) for i in range(1,p)]
SAC = br.hstack((SAC[::-1], SAC[1:]))
out = (br.arange(len(SAC)) - len(SAC) / 2) * bin
return out, SAC
def plot_average_membrane_potential(axes,
population='E_non',
group='non-selective',
tmin=None,
tmax=None,
legend=True,
title=True,
namespace=namespace):
# using formula:
V_L = namespace['V_L']
V_thr = namespace['V_thr']
V_reset = namespace['V_reset']
tau_m_E = namespace['tau_m_E']
g_m_E = namespace['g_m_E']
V_SS = V_L - net['st_' + population].I_syn.mean(axis=0) / (g_m_E)
nu = net['r_' + population].smooth_rate('gaussian', 5 * b2.ms)
V_avg = V_SS - (V_thr - V_reset) * nu * tau_m_E
# using data:
v_mean = b2.mean(net['st_' + population].v, axis=0)
v_std = b2.std(net['st_' + population].v, axis=0)
if tmin is None:
tmin = net['r_' + population].t[0]
if tmax is None:
tmax = net['r_' + population].t[-1]
mask = (net['r_I'].t >= tmin) & (net['r_I'].t <= tmax)
true_line = axes.plot(net['r_' + population].t[mask] / b2.ms,
v_mean[mask] / b2.mV,
label='true avg.',
ls='--')
colour = true_line[0].get_color()
axes.fill_between(net['r_' + population].t[mask] / b2.ms,
(v_mean - v_std)[mask] / b2.mV,
(v_mean + v_std)[mask] / b2.mV,
alpha=0.6,
label=r'$\pm 1$ std',
color=colour)
axes.fill_between(net['r_' + population].t[mask] / b2.ms,
(v_mean - 2 * v_std)[mask] / b2.mV,
(v_mean - v_std)[mask] / b2.mV,
alpha=0.3,
label=r'$\pm 2$ std',
color=colour)
axes.fill_between(net['r_' + population].t[mask] / b2.ms,
(v_mean + 2 * v_std)[mask] / b2.mV,
(v_mean + v_std)[mask] / b2.mV,
alpha=0.3,
color=colour)
axes.plot(net['r_' + population].t[mask] / b2.ms,
V_avg[mask] / b2.mV,
label='computed',
color='darkorange',
lw=1)
if legend:
axes.legend()
axes.grid(alpha=0.5)
if title:
axes.set_title(r'Comparison of $\langle V \rangle$' +
f'\nGroup: {group}')
return None