def __call__(self, fitted_model):
# We want to use the fitted model
self.hf0 = fitted_model.hf0
self.w = fitted_model.w
self.nu = fitted_model.nu
self.pi = fitted_model.pi
X_ = fitted_model.X.copy()
for j in fitted_model.applythreshold:
X_[:, j] = threshold.u_v(X_[:, j], self.nu)
self.history_evaluation(X_, fitted_model.r, (0.75, .55))
out = [Likelihood_and_Slope_Collector(fitted_model)] #0,1,2
out.append([self.vdifficult]) # 3
out.append([self.veasy]) # 4
out.append([self.phist]) # 5
out.append([self.pstim]) # 6
out.append([self.pSH]) # 7
out.append([self.peasy]) # 8
out.append(fitted_model.pi) # 9,10,11
# out.append ( fitted_model.w[1:self.hf0] ) # 12,...,12+hf0
out.append(
self.get_thres(fitted_model.w[:self.hf0], fitted_model.nu,
fitted_model.pi, .75)) # 12,...,12+hf0
out.append(
self.get_thres(fitted_model.w[:self.hf0], fitted_model.nu,
fitted_model.pi, .85)) # 12+hf0,...,12+2*hf0
out.append(fitted_model.nu) #
out.append(fitted_model.w) #
out.append(np.ravel(self.stimuli))
out.append(np.ravel(self.conditions))
out.append(np.ravel(self.variance_explained))
return np.concatenate(out)
def pmfplot(d, results, infodict, ax, errors=True):
"""Generate the pmf plot"""
for i, c in enumerate(infodict['conditions']):
c = int(c)
d_ = d.getsummary(c)
x = pl.mgrid[infodict['xmin']:infodict['xmax']:100j]
if len(d.th_features) > 0:
# d_[:,0] = u_v ( d_[:,0], results['model_w_hist'].nu )
# x = u_v ( x, results['model_w_hist'].nu )
d_[:, 0] = u_v(d_[:, 0], results['model_nohist'].nu)
x = u_v(x, results['model_nohist'].nu)
if errors:
graphics.plot_data_summary(d_, ax, infodict['colors'][i],
infodict['labels'][i])
else:
# AEU: change the marker to make datapoints small. What goes wrong in the plot here?
ax.plot(d_[:, 0],
d_[:, 1] / d_[:, 2],
'.',
color=infodict['colors'][i],
label=infodict['labels'][i])
# wfit = results['model_w_hist'].w[infodict['indices'][c]]
wfit = results['model_nohist'].w[infodict['indices'][i]]
w0fit = results['model_w_hist'].w0[infodict['indices'][i]]
pfit = results['model_w_hist'].pi
p0fit = results['model_nohist'].pi
if not d.ground_truth is None:
wgfit = d.ground_truth['w'][infodict['indices'][i]]
pgfit = d.ground_truth['pi']
gt = graphics.plot_pmf(pgfit, wgfit, x, ax,
(np.array([255, 240, 240], 'd') / 255 +
infodict['colors'][i]) / 2.)
pl.setp(gt, linestyle='--')
# graphics.plot_pmf ( pfit, w0fit, x, ax, [.9,.9,.9], alpha=0.1 )
graphics.plot_pmf(p0fit, wfit, x, ax, infodict['colors'][i])
graphics.label_axes(title="(A) psychometric function",
xlabel=r"transduced stimulus $u_\nu(s\tilde{z})$",
ylabel=r"probability for $r=1$",
nxticks=5,
ax=ax)
def plot_nonlinearity(nu, x=None, ax=None, color='k'):
"""Plot a threshold nonlinearity"""
from threshold import u_v
if ax is None:
ax = pl.gca()
ax = prepare_axes(ax)
if x is None:
xmin, xmax = ax.get_xlim()
x = pl.mgrid[xmin:xmax:100j]
return ax.plot(x, u_v(x, nu), color=color)
def pcorrect(self, x, pleft=0.5, pright=0.5, ind=[0, 1]):
"""Get probability of a correct response rather than probability of left/right response
:Parameters:
*x* stimulus intensities
*pleft* probability that the stimulus is on the left (or number of stimuli on the left)
*pright* probability that the stimulus is on the right
"""
Z = pleft + pright
if Z > 1:
pleft /= Z
pright /= Z
s = threshold.u_v(x, self.nu)
psi_p = self.pi[1] + self.pi[2] * logistic(self.w[ind[0]] +
self.w[ind[1]] * s)
psi_m = self.pi[0] + self.pi[2] * (
1 - logistic(self.w[ind[0]] - self.w[ind[1]] * s))
return pleft * psi_m + pright * psi_p, s
def e(x):
p1 = pi[1] + pi[2] * model.logistic(w[0] + w[i] *
threshold.u_v(x, nu))
p2 = 1 - (pi[1] + pi[2] *
model.logistic(w[0] + w[i] * threshold.u_v(-x, nu)))
return abs(.5 * p1 + .5 * p2 - p)
def history_evaluation(self, X, r, p):
"""Determine variance explained by history
:Parameters:
*X*
design matrix
*r*
responses
*p*
probability correct that is considered the border between
easy and difficult
"""
difficult, easy = performance_filter(r, X, p, hf0=self.hf0)
assert np.shape(
np.shape(difficult))[0] == 1, 'difficult is not a vectors'
assert np.shape(np.shape(easy))[0] == 1, 'easy is not a vectors'
# AEU: get both output args from performance_filter
#easy = np.logical_not ( difficult )
X_ = X.copy()
for j in self.applythreshold:
X_[:, j] = threshold.u_v(X[:, j], self.nu)
current_stimulus = np.dot(X_[:, 1:self.hf0], self.w[1:self.hf0])
history_features = np.dot(X_[:, self.hf0:], self.w[self.hf0:])
self.vdifficult = np.var ( history_features[difficult] ) / \
(np.var (history_features[difficult]) + np.var(current_stimulus[difficult]))
self.veasy = np.var ( history_features[easy] ) / \
(np.var (history_features[easy]) + np.var(current_stimulus[easy]))
S = []
V = []
C = []
for condition in xrange(1, self.hf0):
stimuli = np.unique(abs(X_[:, condition]))
S_ = []
V_ = []
for s in stimuli:
if abs(s) < 1e-10:
continue
i = abs(X_[:, condition]) == s
S_.append(s)
V_.append(
np.var(history_features[i]) /
(np.var(history_features[i]) +
np.var(current_stimulus[i])))
S.append(S_)
V.append(V_)
C.append([condition] * len(S_))
self.stimuli = np.concatenate(S)
self.conditions = np.concatenate(C)
self.variance_explained = np.concatenate(V)
# c = -self.w[0]
c = 0.
self.phist = np.mean((history_features[difficult] > c) == r[difficult])
self.pstim = np.mean((current_stimulus[difficult] > c) == r[difficult])
self.pSH = np.mean(((history_features[difficult] +
current_stimulus[difficult]) > c) == r)
self.peasy = np.mean((history_features[easy] > c) == r[easy])
return np.var(current_stimulus), np.var(history_features), (S, V)
def __em(self, X, r):
"""Optimize parameters using expectation maximation
:Parameters:
*X*
design matrix
*r*
response vector
"""
w = self.w
p = self.pi
nu = self.nu
# w = np.array ( [.01,.8,-.8,.5] )
if self.verbose:
print "Starting values:"
print "nu:", nu
print "w: ", w
print "p: ", p
X_ = X.copy()
for j in self.applythreshold:
X_[:, j] = threshold.u_v(X[:, j], nu)
# Expectation
gwx = history_model.__combine_features(X_, w)
q = history_model.__determine_single_trial_lapses(r, gwx, p)
p = history_model.__optimize_p(q, self.pprior)
l = history_model.__likelihood(gwx, r, p)
for i in xrange(self.emiter):
# Maximization
nu_ = nu
nu = threshold.optimize_nu(X,
r,
q[:, -1],
w,
nu,
self.applythreshold,
niter=self.nuiter,
stop=self.nustop)
if np.isnan(nu):
sys.exit(2)
for j in self.applythreshold:
X_[:, j] = threshold.u_v(X[:, j], nu)
# if len ( self.applythreshold ) == 1:
# nu = threshold.optimize_nu ( X, r, q[:,-1], w, nu, niter=self.nuiter, stop=self.nustop )
# if np.isnan(nu):
# sys.exit ( 2 )
# for j in self.applythreshold:
# X_[:,j] = threshold.u_v ( X[:,j], nu )
# elif len ( self.applythreshold ) > 1:
# raise NotImplementedError, "optimization of the threshold nu is not implemented for this case"
w_ = w
p_ = p
w = glm.optimize_w(X_,
r,
q[:, -1],
w,
niter=self.glmiter,
stop=self.glmstop,
lm=self.lmprior)
p = history_model.__optimize_p(q, self.pprior)
if np.isnan(p).any():
print i, p
sys.exit(1)
# Expectation
gwx = history_model.__combine_features(X_, w)
q = history_model.__determine_single_trial_lapses(r, gwx, p)
l_ = history_model.__likelihood(gwx, r, p)
# Stop?
rel_e = np.abs((l_ - l) / l)
abs_e = max(max(np.abs(w - w_).max(),
np.abs(p - p_).max()), abs(nu - nu_))
if i > self.miniter:
if rel_e < self.emstop and abs_e < self.emabs:
if self.verbose:
sys.stderr.write(
"Converged after %d iterations\n relative error: %g\n absolute error: %g\n"
% (i, rel_e, abs_e))
break
if self.storeopt:
self.opt.append([l_, rel_e, abs_e] + [pp for pp in p] +
[ww for ww in w] + [float(nu)])
if self.verbose:
print l_, rel_e, abs_e
l = l_
else:
if self.verbose:
sys.stderr.write(
"No convergence after %d iterations\nrelative error: %g\n"
% (i, rel_e))
return w, p, q, l, nu
def figure3 ( ):
w,h = 25,8.5
fig = pl.figure ( figsize=(fullwidth,h*fullwidth/w) )
# a,b,c,d = place_axes ( fig, 1.5,2, [9,9,5,5],[6]*4,
# [True]*2+[False]*2, [1.8,1.8,.5,.5], (w,h) )
a,b,c = place_axes ( fig, 1.5,2, [9,9,5],[6]*3,
[True]*2+[False], [1.8,1.8,.5], (w,h) )
d = fig.add_axes ( [10,10,1,1] )
a.text ( .05, laby, r"\textbf{a}", transform=a.transAxes )
b.text ( .05, laby, r"\textbf{b}", transform=b.transAxes )
c.text ( .05, laby, r"\textbf{c}", transform=c.transAxes )
d.text ( .05, laby, r"\textbf{d}", transform=d.transAxes )
M = results['model_w_hist']
# Figures 3 A,B
for condition in plotinfo['conditions']:
condition = int ( condition )
print "c",condition
d_ = data.getsummary ( condition )
# x = pl.mgrid[0:plotinfo['xmax']:100j]
x = pl.mgrid[0:30:100j]
# if len(data.th_features)>0:
# x = threshold.u_v ( x, results['model_w_hist'].nu )
wfit = results['model_w_hist'].w[plotinfo['indices'][condition]]
w0fit = results['model_nohist'].w[plotinfo['indices'][condition]]
pfit = results['model_w_hist'].pi
p0fit = results['model_nohist'].pi
x_ = threshold.u_v ( x, results['model_w_hist'].nu )
x0 = threshold.u_v ( x, results['model_nohist'].nu )
col = plotinfo['colors'][condition]
pmf = 0.5*(pfit[1]+pfit[2]*model.logistic ( wfit[0]+wfit[1]*x_ )) + \
0.5*(1-(pfit[1]+pfit[2]*model.logistic ( wfit[0]-wfit[1]*x_ )))
p0f = 0.5*(p0fit[1]+p0fit[2]*model.logistic ( w0fit[0]+w0fit[1]*x0 )) + \
0.5*(1-(p0fit[1]+p0fit[2]*model.logistic ( w0fit[0]-w0fit[1]*x0 )))
print p0fit
perror = (1-p0f-(1-pmf))/(1-p0f)
a.plot ( x, pmf, color = col )
a.plot ( x, p0f, color = col, linestyle='--' )
b.plot ( x, pl.clip(perror,0,1e5), color = col )
a.yaxis.set_major_formatter ( prcformatter )
a.xaxis.set_major_formatter ( myformatter )
a.set_xticks ( (0,10,20,30) )
pl.setp ( (a,b), xlabel='Stimulus intensity' )
a.set_ylabel ( 'Probability correct [\%]' )
b.set_ylabel ( 'Error rate exp. [\%]' )
b.set_xticks ( (0,10,20,30) )
b.yaxis.set_major_locator ( tckr ( density=2, figure=fig, which=1 ) )
b.yaxis.set_major_formatter ( prcformatter )
b.xaxis.set_major_formatter ( myformatter )
if observer in ['KP','sim_KP','sim_KP_nh']:
b.set_ylim ( 0, .35 )
if observer in ['pk']:
pl.setp ( (a,b), xlim=(-.1,30.1) )
# figure 3 C
textfile.write ( "Figure 3C:\n" )
z0 = 0
C = statistics.EvaluationCollector ( M )
ewh = C(results['model_w_hist'])
enh = C(results['model_nohist'])
hf0 = M.hf0
# perm = results['permutation_wh']
# # TODO: These indices have to be adapted to the revised collector
# thresholds_wh = pl.array([C.get_thres ( perm[i,13+hf0:13+2*hf0], perm[i,12+hf0], perm[i,9:12], p=0.75 ) \
# for i in xrange ( 2000 )])
# perm = results['permutation_nh']
# thresholds_nh = pl.array([C.get_thres ( perm[i,13+hf0:13+2*hf0], perm[i,12+hf0], perm[i,9:12], p=0.75 ) \
# for i in xrange ( 2000 )])
if thlev == .75:
thind = 11
elif thlev == .85:
thind = 10+hf0
else:
raise ValueError
for condition in xrange ( 1, M.hf0 ):
s_wh = results['permutation_wh'][:,thind+condition]
s_nh = results['permutation_nh'][:,thind+condition]
# s_wh = thresholds_wh[:,condition]
# s_nh = thresholds_nh[:,condition]
s_ratio = s_wh/s_nh
s_ratio_obs = ewh[thind+condition]/enh[thind+condition]
# s_ratio_obs = results['model_w_hist'].w[condition]/results['model_nohist'].w[condition]
z = (s_ratio_obs-pl.mean(s_ratio))/pl.std(s_ratio)
cpe = pl.mean ( s_ratio < s_ratio_obs )
ci = pl.prctile ( s_ratio, (2.5,97.5) )
if z < z0 and ci[1]-ci[0] > 0:
c0 = condition
s_ratio_ = s_ratio
s_ratio_obs_ = s_ratio_obs
ci_ = ci
textfile.write (
"Condition %d\n th75_ratio = %g\n cpe = %g\n percentiles of Null-Distribution: %g, %g\n" % \
(condition,s_ratio_obs,cpe,ci[0],ci[1]) )
try:
print "Using condition %d for figure 3C" % (c0,)
except:
c0 = 1
s_ratio_ = s_ratio
s_ratio_obs_ = s_ratio_obs
ci_ = ci
hist,bins = pl.histogram ( s_ratio_ )
c.bar ( bins[:-1], hist, pl.diff ( bins ),
edgecolor=graphics.histogram_color, facecolor=graphics.histogram_color )
yrange = c.get_ylim ()
# c.plot ( [1]*2, yrange, 'k:' )
if s_ratio_obs<ci_[0]:
c.plot ( [s_ratio_obs_]*2, (yrange[0],yrange[0]+0.85*(yrange[1]-yrange[0])), linewidth=2,
color=graphics.observed_color )
c.plot ( [s_ratio_obs_], [yrange[0]+0.95*(yrange[1]-yrange[0])], '*', color=graphics.observed_color )
else:
c.plot ( [s_ratio_obs_]*2, yrange, linewidth=2, color=graphics.observed_color )
c.plot ( [ci_[0]]*2, yrange, color=graphics.C95_color )
c.plot ( [ci_[1]]*2, yrange, color=graphics.C95_color )
c.set_ylim ( *yrange )
c.set_xlabel ( r'Threshold ratio' )
c.xaxis.set_major_formatter ( myformatter )
c.xaxis.set_major_formatter ( myformatter )
# c.text ( .7, 0.7, r"$\frac{\theta_\mathrm{h}}{\theta_0}$",
# transform=c.transAxes )
# c.set_xlim ( trimmed_hlim ( s_ratio_, s_ratio_obs_ ) )
# c.xaxis.set_major_locator ( tckr ( density=0.4, figure=fig, which=0 ) )
c.set_xlim ( .99, 1.01 )
# c.xaxis.set_ticks ( (.95,1) )
# c.set_xlim ( .85, 1.05 )
c.xaxis.set_ticks ( (.99,1.,1.01) )
# figure 3 D
l_wh = 0.5*results['permutation_wh'][:,[9,10]].sum(1)
l_nh = 0.5*results['permutation_nh'][:,[9,10]].sum(1)
l_ratio = l_wh-l_nh
l_ratio_obs = results['model_w_hist'].pi[[0,1]].sum()-results['model_nohist'].pi[[0,1]].sum()
cpe = pl.mean ( l_ratio < l_ratio_obs )
ci = pl.prctile ( l_ratio, (2.5,97.5) )
textfile.write (
"Figure 3D:\n lapse_ratio = %g\n cpe = %g\n percentiles of Null-distribution: %g, %g\n lapse_rate (w hist) = %g\n lapse_rate (no hist) = %g\n" % \
(l_ratio_obs,cpe,ci[0],ci[1],results['model_w_hist'].pi[[0,1]].sum(),results['model_nohist'].pi[[0,1]].sum()) )
d = graphics.prepare_axes ( d, haveon=('bottom',) )
# hist,bins = pl.histogram ( l_ratio )
hist,bins = pl.histogram ( l_ratio, bins=good_lapse_bins ( l_ratio ) )
# hist,bins = pl.histogram ( l_ratio, bins=pl.mgrid[-.0001:.0001:20j] )
d.bar ( bins[:-1], hist, pl.diff(bins),
edgecolor=graphics.histogram_color, facecolor=graphics.histogram_color, zorder=0 )
yrange = d.get_ylim ()
# d.plot ( [1]*2, yrange, 'k:' )
if l_ratio_obs < ci[0] or l_ratio_obs > ci[1]:
d.plot ( [l_ratio_obs]*2, [yrange[0], yrange[0]+0.85*(yrange[1]-yrange[0])],
linewidth=2, color=graphics.observed_color)
d.plot ( [l_ratio_obs], [yrange[0]+0.95*(yrange[1]-yrange[0])], '*', color=graphics.observed_color)
else:
print "lrobs",l_ratio_obs
d.plot ( [l_ratio_obs]*2, yrange, color=graphics.observed_color, zorder=2)
d.plot ([ci[0]]*2, yrange, color=graphics.C95_color, zorder=1 )
d.plot ([ci[1]]*2, yrange, color=graphics.C95_color, zorder=1 )
d.set_ylim ( yrange )
d.set_xlabel ( r'Asymptote difference' )
# d.text ( .7, 0.7, r"$\frac{\lambda_\mathrm{h}}{\lambda_0}$",
# transform=d.transAxes )
# d.set_xlim ( trimmed_hlim ( l_ratio, l_ratio_obs, (0,5) ) )
d.set_xlim ( -.003, .001 )
d.xaxis.set_major_locator ( tckr ( density=0.4, figure=fig, which=0 ) )
d.xaxis.set_ticks ( (-.002,0) )
# d.set_xlim ( (.75, 1.25) )
d.xaxis.set_major_formatter ( myformatter )
a.set_ylim ( .49, 1.01 )
pl.savefig ( "figures/%s3.pdf" % ( figname, ) )
pl.savefig ( "figures/%s3.eps" % ( figname, ) )