def samplepH_onlyone(size, one, Temp=298, pHrange=[7,12], salttype='nom',
uniquefix=None, fn_preamble=''):
"""
Get power supplies from a sample with fixed T at Temp and a flat
distribution across pHrange, for salt level salttype.
This specifically only samples across one other variable, named by
the attribute one.
"""
if one=='all':
return samplepH(size, Temp=Temp, pHrange=pHrange, salttype=salttype)
cd_preamble = 'E21data/pH_samples/ind_variance/'
thissamplename = cd_preamble+fn_preamble+one+'_pH_'+str(size)+'_'+str(Temp)+'_'+salttype+'.npy'
try:
xvals, PS = np.load(thissamplename, allow_pickle=True)
return xvals, PS
except:
fixed = {}
if uniquefix == None:
fixed = deepcopy(EG.default_nomdict)
else:
fixed=uniquefix
fixed['T'] = Temp
fixed['pH'] = None
fixed[one] = None
sigmas = EG.getsigmas(size, fixed=fixed, pHlims=pHrange, dummyvals=True)
PS, xvals = np.empty(size), np.empty(size)
for i, s in enumerate(sigmas):
PS[i] = EG.getPSfromSigmas(s, dummyvals=True, salttype=salttype)
xvals[i] = s[-1]
np.save(thissamplename, np.array([xvals, PS]))
return xvals, PS
def samplepH(size, Temp=298, pHrange=[7,12], salttype='nom',
fixupdate={}, fn_preamble=''):
"""
Get power supplies from a sample with fixed T at Temp and a flat
distribution across pHrange, for salt level salttype.
If you want to update the fix dictionary (e.g. to only sample select
parameters), send them via fixupdate.
"""
f = {'T':Temp, 'pH':None}
f.update(fixupdate)
cd_preamble = 'E21data/pH_samples/'
thissamplename = cd_preamble+fn_preamble+'pH_'+str(size)+'_'+str(Temp)+'_'+salttype+'.npy'
try:
xvals, PS = np.load(thissamplename, allow_pickle=True)
return xvals, PS
except:
sigmas = EG.getsigmas(size, fixed=f, pHlims=pHrange, dummyvals=True)
PS, xvals = np.empty(size), np.empty(size)
for i, s in enumerate(sigmas):
PS[i] = EG.getPSfromSigmas(s, dummyvals=True, salttype=salttype)
xvals[i] = s[-1]
np.save(thissamplename, np.array([xvals, PS]))
return xvals, PS
def ATPEnergyContourPlot(ax,
CO2origin='pH',
pHrange=np.linspace(7, 14, num=11),
Trange=np.linspace(273, 473, num=11)):
plotkey = 'ATPGibbs'
Meshes = EnceladusGrids.getMesh(Trange, pHrange, params=[plotkey])
XX = Meshes['pH']
YY = Meshes['T']
ZZ = Meshes[plotkey]
contf = ax.contourf(XX,
YY,
ZZ[0],
levels=np.arange(55000, 68000, 1000),
cmap='cool_r',
vmin=55000,
vmax=68000)
cont = ax.contour(XX,
YY,
ZZ[0],
levels=5,
colors=['k'],
vmin=55000,
vmax=68000)
ax.clabel(cont, inline=1, fontsize=12, fmt='%d') # add label
return ax, contf
def plot_sigmas(sample):
"""
Plot and show the distribution given by a sample size of `sample'.
"""
sig = EG.getsigmas(sample, fixed={'T':330, 'pH':8.5}, dummyvals=True)
a, b, c, d, e, f = [],[],[],[], [],[]
for i in sig:
a.append(i[0])
b.append(i[1])
c.append(i[2])
d.append(i[3])
e.append(i[4])
f.append(i[5])
fig, axs = plt.subplots(nrows=3, ncols=2)
axs = axs.flatten()
axs[0].scatter(a,b, alpha=0.2, marker='.')
axs[1].scatter(a,c, alpha=0.2, marker='.')
axs[2].scatter(a, d, alpha=0.2, marker='.')
axs[3].scatter(a, e, alpha=0.2, marker='.')
axs[4].scatter(a, f, alpha=0.2, marker='.')
axs[5].scatter(e, f, alpha=0.2, marker='.')
plt.show()
def nominal_pH(Temp, pHlims=[7,12], num=100, salttype='nom', zeroed=False,
fixupdate={}, fn_preamble=''):
"""
Get power supplies from the nominal case with fixed T at Temp and a uniform distribution across pHrange of length num, for salt level salttype.
You can change the nominal parameter space values by passing them in
fixupdate. Pass zeroed as True if you want the Power supplies that NutMEG
couldn't calculate removed, otherwise ther will be 1e-50 W/cell.
"""
cd_preamble = 'E21data/nominalPS/'
thisnominalname = cd_preamble+fn_preamble+'T_'+str(Temp)+'_pHs_'+str(pHlims[0])+'_'+str(pHlims[1])+'_'+salttype+'.npy'
try:
xvals, PS = np.load(thisnominalname, allow_pickle=True)
if zeroed:
zeroes = (np.log10(PS) != -50.)
PS = np.log10(PS)[zeroes]
xvals = xvals[zeroes]
return xvals, PS
except:
pHnoms = np.linspace(pHlims[0],pHlims[1],num=num)
fix=deepcopy(EG.default_nomdict)
fix.update(fixupdate)
PSnoms=[]
for pHnom in pHnoms:
PSnoms.append(EG.getPSfromSigmas(
[fix['CO2'],fix['H2'],fix['CH4'],fix['nATP'],fix['k_corr'],
Temp,pHnom],
dummyvals=True, salttype=salttype))
np.save(thisnominalname, np.array([pHnoms, PSnoms]))
if zeroed:
zeroes = (np.log10(PSnoms) != -50.)
PSnoms = np.log10(PSnoms)[zeroes]
pHnoms = pHnoms[zeroes]
return pHnoms, PSnoms
def uniform_samplepH(size, Temp=298, pHrange=[8,12], pHnum=50, k_corr=0.0):
thissamplename = '2_uniform_data_samples/pH_'+str(size)+'_'+str(Temp)+'.npy'
try:
xvals, PS = np.load(thissamplename, allow_pickle=True)
return xvals, PS
except:
PS, xvals = np.empty(size), np.empty(size)
ix=0
for pH in np.linspace(8,12, num=pHnum):
sigmas = EG.getsigmas(int(size/pHnum), fixed={'T':Temp, 'pH':pH}, pHlims=pHrange, dummyvals=True)
for s in sigmas:
PS[ix] = EG.getPSfromSigmas(s, dummyvals=True)
xvals[ix] = s[-1]
ix += 1
np.save(thissamplename, np.array([xvals, PS]))
return xvals, PS
def total_varianceplot(Ts = [300]):
samplesize=2500
pHnum=100
fig, ax = plt.subplots(figsize=(10,5), ncols=2, nrows=1)
# cmaps=[transparent_cmap(238/360), transparent_cmap(120/360), 'Reds']
cmaps=[transparent_cmap2(blue_to_a), transparent_cmap2(green_to_a), transparent_cmap2(red_to_a)]
colors = ['blue', 'green','red']
Tresults = []
pHresults = []
minpH, maxpH = 7,12
pHnoms = np.linspace(minpH,maxpH,num=int(pHnum))
Tnoms = np.linspace(273, 400, num=int(pHnum))
for i, T in enumerate(Ts):
pHvals, PS = samplepH(samplesize, Temp=T, pHrange=[7,12])#, pHnum=pHnum) #random sample
PSnoms=[]
for pHnom in pHnoms:
PSnoms.append(EG.getPSfromSigmas([0,0,0,1,0,T,pHnom], dummyvals=True))
logPSnoms = np.log10(PSnoms)
zeroes = (np.log10(PS) != -50.)
logy = np.log10(PS)[zeroes]
y = PS[zeroes]
x = pHvals[zeroes]
logvariance = np.empty(len(logy))
variance = np.empty(len(y))
ic = 0
for xi, yi, logyi in zip(x, y, logy):
close_nom = int((xi-minpH) / (maxpH-minpH) * pHnum)
logvariance[ic] = logyi - logPSnoms[close_nom]
variance[ic] = yi - PSnoms[close_nom]
ic+=1
# ax[0].hexbin(x, y, gridsize=(int(pHnum/2), int(pHnum/8)), cmap=cmaps[i])
ax[0].hist2d(x,logvariance, bins=[45,45], range=[[8, 12], [-5, 5]], cmap=cmaps[i], edgecolor=None, label='T = 300 K')
ax[0].set_ylabel('log10( variance in power supply [W/cell])')
ax[1].hist2d(x,variance, bins=[45,45], range=[[8, 12], [-1e-15,1e-15]], cmap=cmaps[i], edgecolor=None, label='T = 300 K')
ax[1].set_ylabel('Variance in power supply [Wcell]')
ax[0].legend(bbox_to_anchor=(0., 1.05, 1.0, .102), loc='center',
ncol=3, mode="expand", borderaxespad=0., fontsize=12)
ax[1].legend(bbox_to_anchor=(0., 1.05, 1.0, .102), loc='center',
ncol=3, mode="expand", borderaxespad=0., fontsize=12)
plt.tight_layout()
plt.savefig('totvariance_logvslin.pdf')
def PSContourPlot(ax,
CO2origin='pH',
pHrange=np.linspace(7, 14, num=11),
Trange=np.linspace(273, 473, num=21),
cmap='PuBu',
maincont=0,
mesh=False,
k_corr=0.0,
nATP=1.0):
plotkey = 'PowerSupply'
Meshes = EnceladusGrids.getMesh(Trange,
pHrange,
params=[plotkey],
CO2origin=CO2origin,
k_corr=k_corr,
nATP=nATP)
XX = Meshes['pH']
YY = Meshes['T']
ZZ = Meshes[plotkey]
contourlevels = [-25, -15, -10, -5]
cmap = plt.cm.get_cmap(cmap, 15)
if mesh:
contf = ax.pcolormesh(XX,
YY,
np.log10(ZZ[maincont]),
vmin=-25,
vmax=-5,
shading='nearest',
cmap=cmap,
edgecolor='slategray',
linewidth=1)
else:
contf = ax.contourf(XX,
YY,
np.log10(ZZ[maincont]),
levels=np.arange(-25, -4, 1),
cmap=cmap,
vmin=-25,
vmax=-5,
extend='both')
return ax, contf
def PShabitabilityPlot(Trange=np.linspace(273, 403, num=14),
pHrange=np.linspace(7, 12, num=11),
nATP=1.0):
mpl.rcParams['xtick.labelsize'] = 13
mpl.rcParams['ytick.labelsize'] = 13
mpl.rcParams['font.size'] = 13
nomcols = plt.get_cmap('YlOrRd', 6)
cmaplist = [nomcols(i) for i in range(nomcols.N)]
# force the first color entry to be grey
cmaplist[0] = (.95, .95, .95, 1.0)
# create the new map
nomcols = mpl.colors.LinearSegmentedColormap.from_list(
'Custom cmap', cmaplist, nomcols.N)
# get a mesh for the 5 cases.
fn_preamble = ''
if nATP == 1:
fn_preamble = 'E21data/PSgrids/'
else:
fn_preamble = 'E21data/PSgrids/' + str(nATP) + '_'
# for generating and saving
# noms = EnceladusGrids.getMesh(Trange, pHrange, params=['PowerSupply'], nATP=nATP, quotienttype='salty_endmember')
# np.save(fn_preamble+'noms.npy', noms['PowerSupply'][0])
# np.save(fn_preamble+'pHgrid.npy', noms['pH'])
# np.save(fn_preamble+'Tgrid.npy', noms['T'])
#
# nomhigh = EnceladusGrids.getMesh(Trange, pHrange, params=['PowerSupply'], nATP=nATP, k_corr=1., quotienttype='salty_high')['PowerSupply'][0]
# highest = EnceladusGrids.getMesh(Trange, pHrange, params=['PowerSupply'], nATP=nATP, k_corr=1., quotienttype='salty_high')['PowerSupply'][2]
#
# nomlow = EnceladusGrids.getMesh(Trange, pHrange, params=['PowerSupply'], nATP=nATP, k_corr=-1., quotienttype='salty_low')['PowerSupply'][0]
# lowest = EnceladusGrids.getMesh(Trange, pHrange, params=['PowerSupply'], nATP=nATP, k_corr=-1., quotienttype='salty_low')['PowerSupply'][1]
#
# np.save(fn_preamble+'nomhigh.npy', nomhigh)
# np.save(fn_preamble+'highest.npy', highest)
# np.save(fn_preamble+'nomlow.npy', nomlow)
# np.save(fn_preamble+'lowest.npy', lowest)
noms = np.load(fn_preamble + 'noms.npy')
pHgrid = np.load(fn_preamble + 'pHgrid.npy')
Tgrid = np.load(fn_preamble + 'Tgrid.npy')
nomhigh = np.load(fn_preamble + 'nomhigh.npy')
highest = np.load(fn_preamble + 'highest.npy')
nomlow = np.load(fn_preamble + 'nomlow.npy')
lowest = np.load(fn_preamble + 'lowest.npy')
# get the maintenance dictionaries
HC, Ti, L, B = EnceladusGrids.maintenancemesh(Trange, pHrange, nATP=nATP)
Bpass = np.ndarray((len(Trange), len(pHrange)))
Lpass = np.ndarray((len(Trange), len(pHrange)))
Tipass = np.ndarray((len(Trange), len(pHrange)))
HCpass = np.ndarray((len(Trange), len(pHrange)))
# print(HCpass)
yindex = 0
for T in Trange:
xindex = 0
for pH in pHrange:
for mp, mppass in zip([HC, Ti, L, B],
[HCpass, Tipass, Lpass, Bpass]):
mppass[yindex][xindex] = 0
if lowest[yindex][xindex] > mp[yindex][xindex]:
mppass[yindex][xindex] = 1
elif nomlow[yindex][xindex] > mp[yindex][xindex]:
mppass[yindex][xindex] = 2
elif noms[yindex][xindex] > mp[yindex][xindex]:
mppass[yindex][xindex] = 3
elif nomhigh[yindex][xindex] > mp[yindex][xindex]:
mppass[yindex][xindex] = 4
elif highest[yindex][xindex] > mp[yindex][xindex]:
mppass[yindex][xindex] = 5
xindex += 1
yindex += 1
fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(10, 11))
contf = ax[0][0].pcolormesh(pHgrid,
Tgrid,
HCpass,
vmin=0,
vmax=5,
shading='nearest',
cmap=nomcols,
edgecolor='slategray',
linewidth=1)
contf = ax[0][1].pcolormesh(pHgrid,
Tgrid,
Tipass,
vmin=0,
vmax=5,
shading='nearest',
cmap=nomcols,
edgecolor='slategray',
linewidth=1)
contf = ax[1][0].pcolormesh(pHgrid,
Tgrid,
Lpass,
vmin=0,
vmax=5,
shading='nearest',
cmap=nomcols,
edgecolor='slategray',
linewidth=1)
contf = ax[1][1].pcolormesh(pHgrid,
Tgrid,
Bpass,
vmin=0,
vmax=5,
shading='nearest',
cmap=nomcols,
edgecolor='slategray',
linewidth=1)
# fig.colorbar(contf)
ax[0][0].plot([0], [0],
c=cmaplist[0],
label='Not enough power available in any configuration',
linewidth=10)
ax[0][0].plot(
[0], [0],
c=cmaplist[1],
label='Enough power available in the worst-case low-salt scenario',
linewidth=10)
ax[0][0].plot(
[0], [0],
c=cmaplist[2],
label='Enough power available in the nominal low-salt scenario',
linewidth=10)
ax[0][0].plot([0], [0],
c=cmaplist[3],
label='Enough power available in the nominal scenario',
linewidth=10)
ax[0][0].plot(
[0], [0],
c=cmaplist[4],
label='Enough power available in the nominal high-salt scenario',
linewidth=10)
ax[0][0].plot(
[0], [0],
c=cmaplist[5],
label='Enough power available in the best-case high-salt scenario',
linewidth=10)
ax[0][0].set_title(
'To exceed maximum optimal maintenance \n (Higgins & Cockell 2020)',
fontsize=13)
ax[0][1].set_title(
'To exceed empirical maintenance for anaerobes \n (Tijhuis+ 1993)',
fontsize=13)
ax[1][0].set_title('To exceed minimal maintenance power \n (Lever+ 2015)',
fontsize=13)
ax[1][1].set_title(
'To exceed minimal Earth subsurface power supplies \n (Bradley+ 2020)',
fontsize=12)
for aa in ax:
for a in aa:
a.set_xlim(6.75, 12.25)
a.set_ylim(268, 408)
a.set_xlabel('Bulk ocean pH (at 273 K)')
a.set_ylabel('Seawater temperature [K]')
plt.subplots_adjust(wspace=0.2,
hspace=0.33,
left=0.08,
right=0.98,
bottom=0.05,
top=0.78)
ax[0][0].legend(bbox_to_anchor=(0., 1.18, 2.15, .102),
loc=3,
ncol=1,
mode="expand",
borderaxespad=0.)
if nATP == 1.0:
plt.savefig('figs/habgrid.pdf')
else:
plt.savefig('suppfigs/habgrid_' + str(nATP) + '.pdf')
def MethanogenesisEnergyContourPlot(ax,
CO2origin='pH',
pHrange=np.linspace(7, 14, num=11),
Trange=np.linspace(273, 473, num=11),
maincont=0,
quotienttype='salty_nominal'):
plotkey = 'Gibbs_Methanogenesis'
Meshes = EnceladusGrids.getMesh(Trange,
pHrange,
params=[plotkey],
CO2origin=CO2origin,
quotienttype=quotienttype)
XX = Meshes['pH']
YY = Meshes['T']
ZZ = Meshes[plotkey]
levels = [-150, -75, 0, 75]
# contf = ax.contourf(XX, YY, ZZ[maincont], levels=np.arange(-150000, 150000, 3000), cmap=energycolormap(), vmin=-150000, vmax=150000, extend='both')
contf = ax.contourf(XX,
YY,
ZZ[maincont] / 1000,
levels=np.arange(-160, 80, 2.5),
cmap=energycolormap(),
vmin=-160,
vmax=80,
extend='both')
contourcolor = 'k' #'dimgray'
cont = ax.contour(XX,
YY,
ZZ[0] / 1000,
levels=levels,
colors=[contourcolor],
vmin=-150000,
vmax=80000,
linewidths=2.5)
ax.clabel(cont, inline=1, fontsize=16, fmt='%d') # add label
ax.contour(XX,
YY,
ZZ[1] / 1000,
levels=levels,
linestyles='dotted',
colors=[contourcolor],
vmin=-150,
vmax=80,
linewidths=2.5)
ax.contour(XX,
YY,
ZZ[2] / 1000,
levels=levels,
linestyles='dotted',
colors=[contourcolor],
vmin=-150,
vmax=80,
linewidths=2.5)
ax.plot([0, 0], [0, 0],
c=contourcolor,
label='Uncertainty bounds on Gibbs free energy contour',
linestyle='dotted',
linewidth=2.5)
return ax, contf
def ones_varianceplot(T=300, pH=None, samplesize=100, nominals=True, save=True, show=True):
xnum=100
fig, ax = plt.subplots(figsize=(8,12), ncols=2, nrows=3)
ax = ax.flatten()
# cmaps=[transparent_cmap(238/360), transparent_cmap(120/360), 'Reds']
cmaps=[transparent_cmap2(blue_to_a), transparent_cmap2(green_to_a), transparent_cmap2(red_to_a)]
colors = ['blue', 'green','red']
Tresults = []
pHresults = []
minpH, maxpH = 7,12
minT, maxT = 273,400
minx,maxx = 0, 0
xnoms =[]
if pH == None:
minx, maxx = minpH, maxpH
xnoms = np.linspace(minpH,maxpH,num=int(xnum))
elif T== None:
minx, maxx = minT, maxT
xnoms = np.linspace(minT, maxT, num=int(xnum))
if nominals:
PSnoms=[]
for xnom in xnoms:
if pH == None:
PSnoms.append(EG.getPSfromSigmas([0,0,0,1,0,T,xnom], dummyvals=True))
elif T == None:
PSnoms.append(EG.getPSfromSigmas([0,0,0,1,0,xnom,pH], dummyvals=True))
logPSnoms = np.log10(PSnoms)
ind = ['all', 'CH4', 'CO2','H2','nATP', 'k_corr']
for i, v in enumerate(ind):
xvals, PS = [],[]
if pH == None:
xvals, PS = samplepH_onlyone(samplesize, one=v, Temp=T, pHrange=[minx,maxx])#, pHnum=pHnum) #random sample
ax[i].set_xlabel('pH')
elif T == None:
xvals, PS = sampleT_onlyone(samplesize, one=v, Trange=[minx,maxx], pH=pH)#, pHnum=pHnum) #random sample
ax[i].set_xlabel('Temperature [K]')
if save or show:
_logy = np.log10(PS)
zeroes = (_logy != -50.)
logy = _logy[zeroes]
# y = PS[zeroes]
x = xvals[zeroes]
logvariance = np.empty(len(logy))
# variance = np.empty(len(y))
ic = 0
for xi, logyi in zip(x, logy):
close_nom = int((xi-minx) / (maxx-minx) * xnum)
logvariance[ic] = logyi - logPSnoms[close_nom]
ic+=1
ax[i].hist2d(x,logvariance, bins=[45,45], range=[[minx, maxx], [-4, 4]], cmap=cmaps[0], edgecolor=None)
ax[i].set_title(v)
ax[i].set_ylabel('Variance in log10 (power supply)')
if pH == None:
plt.suptitle('Variance with pH when T = '+str(T))
elif T == None:
plt.suptitle('Variance with T when pH = '+str(pH))
plt.tight_layout()
if save:
plt.savefig('2_totvariance_independents_T_'+str(T)+'_pH_'+str(pH)+'.pdf')
if show:
plt.show()
plt.close()
def sampleplot3(Ts=[400, 350,300], pHs=[8,9,10]):
"""For testing different plot types, with nominal line """
samplesize=1500
pHnum=100
fig, ax = plt.subplots(figsize=(10,5), ncols=2, nrows=1)
# cmaps=[transparent_cmap(238/360), transparent_cmap(120/360), 'Reds']
cmaps=[transparent_cmap2(blue_to_a), transparent_cmap2(green_to_a), transparent_cmap2(red_to_a)]
colors = ['blue', 'green','red']
Tresults = []
pHresults = []
pHnoms = np.linspace(7,12,num=int(pHnum))
Tnoms = np.linspace(273, 400, num=int(pHnum))
for i, T in enumerate(Ts):
pHvals, PS = samplepH(samplesize, Temp=T, pHrange=[7,12])#, pHnum=pHnum) #random sample
PSnoms=[]
for pHnom in pHnoms:
PSnoms.append(EG.getPSfromSigmas([0,0,0,1,0,T,pHnom], dummyvals=True))
zeroes = (np.log10(PS) != -50.)
y = np.log10(PS)[zeroes]
x = pHvals[zeroes]
# ax[0].hexbin(x, y, gridsize=(int(pHnum/2), int(pHnum/8)), cmap=cmaps[i])
ax[0].hist2d(x,y, bins=[45,45], range=[[7, 12], [-35, -5]], cmap=cmaps[i], edgecolor=None)
nomzeroes = (np.log10(PSnoms) != -50.)
nomy = np.log10(PSnoms)[nomzeroes]
nomx = pHnoms[nomzeroes]
ax[0].plot(nomx, nomy, c=colors[i], linewidth=2, label='T = '+ str(T))
for i, pH in enumerate(pHs):
Tvals, PS = sampleT(samplesize, pH=pH)
PSnoms=[]
for Tnom in Tnoms:
PSnoms.append(EG.getPSfromSigmas([0,0,0,1,0,Tnom,pH], dummyvals=True))
zeroes = (np.log10(PS) != -50.)
y = np.log10(PS)[zeroes]
x = Tvals[zeroes]
# ax[0].hexbin(x, y, gridsize=(int(pHnum/2), int(pHnum/8)), cmap=cmaps[i])
ax[1].hist2d(x,y, bins=[45,45], range=[[273, 400], [-35, -5]], cmap=cmaps[i], edgecolor=None)
nomzeroes = (np.log10(PSnoms) != -50.)
nomy = np.log10(PSnoms)[nomzeroes]
nomx = Tnoms[nomzeroes]
ax[1].plot(nomx, nomy, c=colors[i], linewidth=2, label='pH = '+str(pH))
for a in ax:
a.set_ylabel('log10 (Power Supply [W/cell])')
a.set_ylim(-35,-5)
# EPS.add_maintnenace_lines(a)
ax[0].set_xlabel('pH')
ax[1].set_xlabel('Temperature [K]')
ax[0].set_xlim(7,12)
ax[1].set_xlim(273,400)
ax[0].legend(bbox_to_anchor=(0., 1.05, 1.0, .102), loc='center',
ncol=3, mode="expand", borderaxespad=0., fontsize=12)
ax[1].legend(bbox_to_anchor=(0., 1.05, 1.0, .102), loc='center',
ncol=3, mode="expand", borderaxespad=0., fontsize=12)
plt.tight_layout()
plt.savefig('2_binline.pdf')