def cost(p, x, y):
"""Cost function for LM least-squares fit"""
mu, sigma, A = p
return A * g(mu, sigma, x) - y
mvi2mot[(mviname, framei0)] = mot[recname]
allmotion = np.hstack(list(mvi2mot.values()))
allmotion = np.hstack([allmotion, -allmotion]) # make it symmetric around 0
motionbins = np.arange(-300, 300+MOTIONBINW, MOTIONBINW) # deg/s, symmetric around 0
midbins = motionbins[:-1] + MOTIONBINW / 2
motioncount = np.histogram(allmotion, bins=motionbins)[0]
k = kurtosis(allmotion)
# kurtosistest() seems to use the method of Anscombe & Glynn (1983),
# http://biomet.oxfordjournals.org/content/70/1/227
z, p = kurtosistest(allmotion)
pstring = 'p < %g' % ceilsigfig(p)
# normally distributed signal with same std as data, to check that its kurtosis is 0:
#nsamples = 10000000
#normal = scipy.random.normal(0, allmotion.std(), nsamples)
#normalcount = np.histogram(normal, bins=motionbins)[0]
normalcount = core.g(0, allmotion.std(), midbins) # generate normal distrib directly
# normalize to get same probability mass:
normalcount = normalcount / normalcount.sum() * motioncount.sum()
plot(midbins, normalcount, marker=None, ls='-', c='0.7', lw=2)
plot(midbins, motioncount, marker=None, ls='-', c='k', lw=2)
text(0.98, 0.98, 'k = %.1f' % k, # kurtosis
horizontalalignment='right', verticalalignment='top',
transform=gca().transAxes, color='k')
text(0.98, 0.90, '%s' % pstring, # p-value of null (normal) hypothesis of kurtosis test
horizontalalignment='right', verticalalignment='top',
transform=gca().transAxes, color='k')
#k = kurtosis(normal)
#z, p = kurtosistest(normal)
#text(0.98, 0.82, 'k=%.1f' % k, # kurtosis
# horizontalalignment='right', verticalalignment='top',
# transform=gca().transAxes, color='e')
edges = np.logspace(logstart, logend, nbins+1) # nbins+1 points in log space
y = hist(allrates, bins=edges, color='k')[0]
logx = np.log10(edges)[:-1] # left bin edges
logx = logx + (logx[1] - logx[0]) / 2 # middle of bins
# do least-squares LM fit of a lognormal distribution to the data:
modellogmean = -1
modellogsigma = 1
A = max(y)
p = modellogmean, modellogsigma, A
result = leastsq(cost, p, args=(logx, y), full_output=True)
p, cov_p, infodict, mesg, ier = result
mu, sigma, A = p
modelx = np.logspace(logstart, logend, 200) # 200 points in log space
modely = A*g(mu, sigma, np.log10(modelx))
# Figure 2: plot lognormal model in magenta:
plot(modelx, modely, 'm-', linewidth=3)
# Figure 2: finish up
axvline(x=MINRATE, c='e', ls='--', marker=None) # plot threshold
xscale('log')
xlabel('mean firing rate (Hz)')
ylabel('neuron count')
# arrow doesn't display correctly on log axis, use annotate instead:
#arrow(10**logmean, 30, 0, -4, head_width=0.1, head_length=2, length_includes_head=True)
annotate('', xy=(10**logmean, 26), xycoords='data',
xytext=(10**logmean, 29), textcoords='data',
arrowprops=dict(fc='k', ec='none', width=1, frac=0.5))
annotate('', xy=(10**mu, 26), xycoords='data',
sp = slogmean, slogstd, sA # parameter list
dp = dlogmean, dlogstd, dA
def cost(p, x, y):
"""Cost function for LM least-squares fit"""
mu, sigma, A = p
return A * g(mu, sigma, x) - y
# fit the 3 parameters for both synched and desynched distribs:
sresult = leastsq(cost, sp, args=(logmidbins, shist), full_output=True)
dresult = leastsq(cost, dp, args=(logmidbins, dhist), full_output=True)
sp, cov_p, infodict, mesg, ier = sresult
dp, cov_p, infodict, mesg, ier = dresult
smu, ssigma, sA = sp
dmu, dsigma, dA = dp
# generate fit distributions from fit parameters
modelx = np.logspace(logmin, logmax, 200) # 200 points in log space
smodel = sA*g(smu, ssigma, log10(modelx))
dmodel = dA*g(dmu, dsigma, log10(modelx))
# plot the fit distributions:
plot(modelx, smodel, 'r--', lw=1, alpha=0.5)
plot(modelx, dmodel, 'b--', lw=1, alpha=0.5)
# display geometric means and percentages of response events with <= 1 spike/trial:
text(0.02, 0.984, '$\mu$ = %.1f' % smean, # synched
horizontalalignment='left', verticalalignment='top',
transform=gca().transAxes, color='r')
text(0.02, 0.904, '$\mu$ = %.1f' % dmean, # desynched
horizontalalignment='left', verticalalignment='top',
transform=gca().transAxes, color='b')
'''
text(0.98, 0.82, 'p < %.1g' % ceilsigfig(p, 1),
horizontalalignment='right', verticalalignment='top',
transform=gca().transAxes, color='k')
def cost(p, x, y):
"""Cost function for LM least-squares fit"""
mu, sigma, A = p
return A * g(mu, sigma, x) - y
def model(self, p, ts):
"""Temporal sum of Gaussians"""
#try:
V0, V1, s0, s1, Voff = p
return V0*g(self.t0, s0, ts) + V1*g(self.t1, s1, ts) + Voff
edges = np.logspace(logstart, logend, nbins + 1) # nbins+1 points in log space
y = hist(allrates, bins=edges, color='k')[0]
logx = np.log10(edges)[:-1] # left bin edges
logx = logx + (logx[1] - logx[0]) / 2 # middle of bins
# do least-squares LM fit of a lognormal distribution to the data:
modellogmean = -1
modellogsigma = 1
A = max(y)
p = modellogmean, modellogsigma, A
result = leastsq(cost, p, args=(logx, y), full_output=True)
p, cov_p, infodict, mesg, ier = result
mu, sigma, A = p
modelx = np.logspace(logstart, logend, 200) # 200 points in log space
modely = A * g(mu, sigma, np.log10(modelx))
# Figure 2: plot lognormal model in magenta:
plot(modelx, modely, 'm-', linewidth=3)
# Figure 2: finish up
axvline(x=MINRATE, c='e', ls='--', marker=None) # plot threshold
xscale('log')
xlabel('mean firing rate (Hz)')
ylabel('neuron count')
# arrow doesn't display correctly on log axis, use annotate instead:
#arrow(10**logmean, 30, 0, -4, head_width=0.1, head_length=2, length_includes_head=True)
annotate('',
xy=(10**logmean, 26),
xycoords='data',
xytext=(10**logmean, 29),
allmotion = np.hstack(list(mvi2mot.values()))
allmotion = np.hstack([allmotion, -allmotion]) # make it symmetric around 0
motionbins = np.arange(-300, 300 + MOTIONBINW,
MOTIONBINW) # deg/s, symmetric around 0
midbins = motionbins[:-1] + MOTIONBINW / 2
motioncount = np.histogram(allmotion, bins=motionbins)[0]
k = kurtosis(allmotion)
# kurtosistest() seems to use the method of Anscombe & Glynn (1983),
# http://biomet.oxfordjournals.org/content/70/1/227
z, p = kurtosistest(allmotion)
pstring = 'p < %g' % ceilsigfig(p)
# normally distributed signal with same std as data, to check that its kurtosis is 0:
#nsamples = 10000000
#normal = scipy.random.normal(0, allmotion.std(), nsamples)
#normalcount = np.histogram(normal, bins=motionbins)[0]
normalcount = core.g(0, allmotion.std(),
midbins) # generate normal distrib directly
# normalize to get same probability mass:
normalcount = normalcount / normalcount.sum() * motioncount.sum()
plot(midbins, normalcount, marker=None, ls='-', c='0.7', lw=2)
plot(midbins, motioncount, marker=None, ls='-', c='k', lw=2)
text(
0.98,
0.98,
'k = %.1f' % k, # kurtosis
horizontalalignment='right',
verticalalignment='top',
transform=gca().transAxes,
color='k')
text(
0.98,
0.90,
# Do least-squares LM fit of a lognormal distribution to the data.
# Everything is done in log space:
# set initial parameters:
sA, dA = max(shist), max(dhist) # Gaussian amplitude
sp = slogmean, slogstd, sA # parameter list
dp = dlogmean, dlogstd, dA
# fit the 3 parameters for both synched and desynched distribs:
sresult = leastsq(cost, sp, args=(logmidbins, shist), full_output=True)
dresult = leastsq(cost, dp, args=(logmidbins, dhist), full_output=True)
sp, cov_p, infodict, mesg, ier = sresult
dp, cov_p, infodict, mesg, ier = dresult
smu, ssigma, sA = sp
dmu, dsigma, dA = dp
# generate fit distributions from fit parameters
modelx = np.logspace(logmin, logmax, 200) # 200 points in log space
smodel = sA * g(smu, ssigma, log10(modelx))
dmodel = dA * g(dmu, dsigma, log10(modelx))
# plot the fit distributions:
plot(modelx, smodel, 'r--', lw=1, alpha=0.5)
plot(modelx, dmodel, 'b--', lw=1, alpha=0.5)
xscale('log')
xlim(xmin=10**logmin, xmax=10**logmax)
ylim(ymax=ymax)
xticks(ticks)
yticks(range(0, 40 + 10, 10))
xlabel('mean firing rate (Hz)')
ylabel('unit count')
# display geometric means and p value:
text(
0.02,
0.98,
def model(self, p, ts):
"""Temporal sum of Gaussians"""
#try:
V0, V1, s0, s1, Voff = p
return V0 * g(self.t0, s0, ts) + V1 * g(self.t1, s1, ts) + Voff
def cost(p, x, y):
mu, sigma, A = p
return A * g(mu, sigma, x) - y
