def find_excitability_region(P, El, Gl, Cm, pp=low_rate_fluct_domain, discret=40, print_domain=False):
"""
P are the coefficients of the firing rate response fit
the other parameters set the default boundaries of
the numerical evaluation of the relevant firing rate domain
here all in SI units
"""
sV0 = np.linspace(pp["sV_min"], pp["sV_max"], discret)
TvN0 = np.linspace(pp["Ts_ratio"] + 1.0 / pp["muG_max"], pp["Ts_ratio"] + 1.0 / pp["muG_min"], discret)
muV0 = np.linspace(pp["muV_min"], pp["muV_max"], 5 * discret) # high discret
muV, sV, TvN = np.meshgrid(muV0, sV0, TvN0)
Vthre = final_threshold_func(P, muV, sV, TvN, Gl, El)
Fout = erfc_func(muV, sV, TvN, Vthre, Gl, Cm)
dmuV, dsV, dTvN = derivatives_template(P, muV, sV, TvN, Gl * np.ones(muV.shape), El, Gl, Cm)
ok = (Fout < pp["max_Fout"]) & (Fout > pp["min_Fout"]) & (dmuV > 0) & (dsV > 0) # desired conditions
if print_domain:
print "muV domain :", round(1e3 * muV[ok].min()), round(1e3 * muV[ok].max())
print "sV domain :", round(1e3 * sV[ok].min()), round(1e3 * sV[ok].max())
print "TvN domain :", round(1e2 * TvN[ok].min()), round(1e2 * TvN[ok].max())
return Fout[ok], Vthre[ok], muV[ok], sV[ok], TvN[ok]
def make_3d_and_2d_figs(P, Fout, s_Fout, muV, sV, Tv_ratio,\
muGn, Gl, Cm, El, cell_id, vthre_lim=None,\
FONTSIZE=18):
font = {'size' : FONTSIZE}
mpl.rc('font', **font)
Tv_ratio = np.round(1000.*Tv_ratio)/10
sV, muV = np.round(sV), np.round(muV)
Tv_levels = np.unique(Tv_ratio)
muV_levels = np.unique(muV)
DISCRET_muV = len(muV_levels)
# 3d view - Fout
fig1 = plt.figure(figsize=(5,3))
plt.subplots_adjust(left=.3, bottom=.3)
ax = plt.subplot(111, projection='3d')
ax.set_title(cell_id)
ax.view_init(elev=20., azim=210.)
plt.xlabel('\n\n $\mu_V$ (mV)')
plt.ylabel('\n\n $\sigma_V$ (mV)')
ax.set_zlabel('\n\n $\\nu_\mathrm{out}$ (Hz)')
# the colorbar to index the autocorrelation
fig3 = plt.figure(figsize=(1.7,4.))
plt.subplots_adjust(right=.25)
Tv_levels = np.unique(Tv_ratio)
# levels no more than 5
mymap = mpl.colors.LinearSegmentedColormap.from_list(\
'mycolors',['red','blue'])
bounds= np.linspace(Tv_levels.min()-10, Tv_levels.max()+10, len(Tv_levels)+1)
norm = mpl.colors.BoundaryNorm(bounds, mymap.N)
cb = mpl.colorbar.ColorbarBase(plt.subplot(111), cmap=mymap, norm=norm,
orientation='vertical')
cb.set_ticks(np.round(Tv_levels))
cb.set_label('$\\tau_V / \\tau_\mathrm{m}^0$ (%)', fontsize=16)
for TvN in Tv_levels:
i_repet_Tv = np.where(Tv_ratio==TvN)[0]
# setting color
if len(Tv_levels)>1:
r = np.min([1,(TvN-bounds.min())/(bounds.max()-bounds.min())])
else:
r=1
muV2, sV2 = muV[i_repet_Tv], sV[i_repet_Tv]
Fout2, s_Fout2 = Fout[i_repet_Tv], s_Fout[i_repet_Tv]
for muV3 in np.unique(muV2):
i_repet_muV = np.where(muV2==muV3)[0]
i_muV = np.where(muV3==muV_levels)[0]
sV3 = sV2[i_repet_muV]
Fout3, s_Fout3 = Fout2[i_repet_muV], s_Fout2[i_repet_muV]
ax.plot(muV3*np.ones(len(sV3)), sV3, Fout3,\
'D', color=mymap(r,1), ms=6, lw=0)
sv_th = np.linspace(0, sV3.max())
muGn3 =np.ones(len(sv_th))
Vthre_th = final_threshold_func(P,\
1e-3*muV3, 1e-3*sv_th, TvN/100., muGn3, El)
Fout_th = erfc_func(1e-3*muV3, 1e-3*sv_th,\
TvN/100., Vthre_th, Gl, Cm)
ax.plot(muV3*np.ones(len(sv_th)), sv_th,\
Fout_th, color=mymap(r,1), alpha=.7, lw=3)
for ii in range(len(Fout3)): # then errobar manually
ax.plot([muV3, muV3], [sV3[ii], sV3[ii]],\
[Fout3[ii]+s_Fout3[ii], Fout3[ii]-s_Fout3[ii]],\
marker='_', color=mymap(r,1))
ax.set_zlim([0., Fout.max()])
ax.xaxis.set_major_locator( MaxNLocator(nbins = 4,prune='both') )
ax.yaxis.set_major_locator( MaxNLocator(nbins = 4) )
ax.zaxis.set_major_locator( MaxNLocator(nbins = 4,prune='lower'))
fig1.tight_layout()
ax.set_zlim([0., max([1,Fout.max()])])
ax.xaxis.set_major_locator( MaxNLocator(nbins = 4,prune='both') )
ax.yaxis.set_major_locator( MaxNLocator(nbins = 4) )
ax.zaxis.set_major_locator( MaxNLocator(nbins = 4,prune='lower') )
return fig1
def make_3d_fig(P, Fout, s_Fout, muV, sV, Tv_ratio,\
muGn, Gl, Cm, El, cell_id, vthre_lim=None,\
FONTSIZE=18):
font = {'size': FONTSIZE}
mpl.rc('font', **font)
Tv_ratio = np.round(1000. * Tv_ratio) / 10
sV, muV = np.round(sV), np.round(muV)
Tv_levels = np.unique(Tv_ratio)
muV_levels = np.unique(muV)
DISCRET_muV = len(muV_levels)
# 3d view - Fout
fig1 = plt.figure(figsize=(7, 4))
plt.subplots_adjust(left=.1, bottom=.2, right=.78, top=0.95)
ax = plt.subplot(111, projection='3d')
ax.set_title(cell_id)
ax.view_init(elev=20., azim=210.)
plt.xlabel('\n\n $\mu_V$ (mV)')
plt.ylabel('\n\n $\sigma_V$ (mV)')
ax.set_zlabel('\n\n $\\nu_\mathrm{out}$ (Hz)')
# the colorbar to index the autocorrelation
ax2 = plt.axes([.82, .1, .02, .8])
Tv_levels = np.unique(Tv_ratio)
# levels no more than 5
mymap = mpl.colors.LinearSegmentedColormap.from_list(\
'mycolors',['red','blue'])
bounds = np.linspace(Tv_levels.min() - 10,
Tv_levels.max() + 10,
len(Tv_levels) + 1)
norm = mpl.colors.BoundaryNorm(bounds, mymap.N)
cb = mpl.colorbar.ColorbarBase(ax2,
cmap=mymap,
norm=norm,
orientation='vertical')
cb.set_ticks(np.round(Tv_levels))
cb.set_label('$\\tau_V / \\tau_\mathrm{m}^0$ (%)', fontsize=16)
for TvN in Tv_levels:
i_repet_Tv = np.where(Tv_ratio == TvN)[0]
# setting color
if len(Tv_levels) > 1:
r = np.min(
[1, (TvN - bounds.min()) / (bounds.max() - bounds.min())])
else:
r = 1
muV2, sV2 = muV[i_repet_Tv], sV[i_repet_Tv]
Fout2, s_Fout2 = Fout[i_repet_Tv], s_Fout[i_repet_Tv]
for muV3 in np.unique(muV2):
i_repet_muV = np.where(muV2 == muV3)[0]
i_muV = np.where(muV3 == muV_levels)[0]
sV3 = sV2[i_repet_muV]
Fout3, s_Fout3 = Fout2[i_repet_muV], s_Fout2[i_repet_muV]
ax.plot(muV3*np.ones(len(sV3)), sV3, Fout3,\
'D', color=mymap(r,1), ms=6, lw=0)
sv_th = np.linspace(0, sV3.max())
muGn3 = np.ones(len(sv_th))
Vthre_th = final_threshold_func(P,\
1e-3*muV3, 1e-3*sv_th, TvN/100., muGn3, El)
Fout_th = erfc_func(1e-3*muV3, 1e-3*sv_th,\
TvN/100., Vthre_th, Gl, Cm)
ax.plot(muV3*np.ones(len(sv_th)), sv_th,\
Fout_th, color=mymap(r,1), alpha=.7, lw=3)
for ii in range(len(Fout3)): # then errobar manually
ax.plot([muV3, muV3], [sV3[ii], sV3[ii]],\
[Fout3[ii]+s_Fout3[ii], Fout3[ii]-s_Fout3[ii]],\
marker='_', color=mymap(r,1))
ax.set_zlim([0., Fout.max()])
ax.xaxis.set_major_locator(MaxNLocator(nbins=4, prune='both'))
ax.yaxis.set_major_locator(MaxNLocator(nbins=4))
ax.zaxis.set_major_locator(MaxNLocator(nbins=4, prune='lower'))
ax.set_zlim([0., max([1, Fout.max()])])
ax.xaxis.set_major_locator(MaxNLocator(nbins=4, prune='both'))
ax.yaxis.set_major_locator(MaxNLocator(nbins=4))
ax.zaxis.set_major_locator(MaxNLocator(nbins=4, prune='lower'))
return fig1
