def main():
np.seterr(all='warn')
K = 50
ks = np.linspace(0, K - 1, K)
f_mean = lambda k: np.exp(-k * 0.2)
noise_eff = 0.05
true_stats = np.ndarray(K, fit_dtype)
true_stats['mean'] = f_mean(ks)
true_stats['lower'] = true_stats['mean'] - noise_eff
true_stats['upper'] = true_stats['mean'] + noise_eff
simulate = lambda: simulate_distribution(true_stats)
# two realizations
X1 = simulate()
X1_order = scale_score(X1)
X2 = simulate()
X2_order = scale_score(X2)
# Now estimate upper and lower bounds by simulations
observed_stats = estimate_bounds_by_simulations(simulate, N=100)
order_est = estimate_order_by_resimulating(observed_stats, N=1000)
print('Simulating distribution...')
orders = compute_order_samples(simulate, N=10000)
print('..done')
r = Report('orderdemo')
f = r.figure('figures', cols=3)
z = 0.6
figparams = dict(figsize=(4 * z, 3 * z), mime=MIME_PDF)
from matplotlib import rc
rc('font', **{'family':'serif',
'serif':['Times', 'Times New Roman', 'Palatino'],
'size': 7.0})
rc('text', usetex=True)
with f.plot('true', caption='True distribution', **figparams) as pl:
plot_rate_bars(pl, ks, true_stats, 'b', label='$p(X^k)$')
#pl.plot(ks, true_stats['mean'], 'b.')
pl.xlabel('$k$')
pl.ylabel('$X^k$')
pl.legend()
#pl.title('Distribution of the random variables $X^k$')
with f.plot('meanorder', caption='True distribution', **figparams) as pl:
pl.plot(ks, scale_score(true_stats['mean']), 'r.',
label='$\\mathsf{order}(\\mathsf{mean}(X^k))$')
pl.xlabel('$k$')
pl.ylabel('$\\mathsf{order}(\\mathsf{mean}(X^k))$')
pl.legend()
#pl.title('Order of the means of $X^k$')
with f.plot('realizations', caption='Realizations', **figparams) as pl:
pl.plot(X1, 'bx', label='$x_1$')
pl.plot(X2, 'g.', label='$x_2$')
pl.xlabel('$k$')
pl.ylabel('$x_i$')
pl.legend()
#pl.title('Two realizations of the process')
with f.plot('orders', caption='orders', **figparams) as pl:
pl.plot(X1_order, 'rx', label='$\\mathsf{order}(x_1)$')
pl.plot(X2_order, 'm.', label='$\\mathsf{order}(x_2)$')
pl.xlabel('$k$')
pl.ylabel('$\\mathsf{order}(x_i)$')
pl.legend()
#pl.title('Computed order from realizations of the process')
with f.plot('estorder', caption='Estimated order', **figparams) as pl:
plot_rate_bars(pl, ks, order_est, 'r', label='$p(\\mathsf{order}(X^k))$')
#pl.plot(ks, order_est['mean'], 'r.')
pl.xlabel('$k$')
pl.ylabel('$\\mathsf{order}(X)$')
pl.legend()
#pl.title('Estimated confidence bounds order from resimulating')
with f.plot('observed', caption='Observed statistics', **figparams) as pl:
plot_rate_bars(pl, ks, observed_stats, 'b')
pl.xlabel('$k$')
pl.ylabel('$X^k$')
def plot_histogram(k, pylab, color, label):
dist = orders[k, :]
values, _ = np.histogram(dist, bins=range(K + 1), normed=True)
left = ks
pylab.bar(left, values, width=1, color=color, label=label)
with f.plot('ordersex', caption='Some examples', **figparams) as pl:
plot_histogram(10, pl, 'r', '$\\mathsf{order}(X^{10})$')
plot_histogram(15, pl, 'g', '$\\mathsf{order}(X^{15})$')
plot_histogram(40, pl, 'b', '$\\mathsf{order}(X^{40})$')
pl.xlabel('$\\mathsf{order}$')
pl.ylabel('probability')
pl.legend(loc='upper left')
rd = 'order_estimation_test2'
filename = os.path.join(rd, 'index.html')
print('Writing to %r.' % filename)
r.to_html(filename, resources_dir=rd)
def main():
np.seterr(all='warn')
n = 100
z = np.linspace(-1, 1, n)
z_order = np.array(range(n))
alpha = 0.1
base = 0.3
noise_eff = 0.05
noise_est = noise_eff
f_L = lambda z: np.exp(-np.abs(+1 - np.maximum(z, 0)) / alpha) + base
f_R = lambda z: np.exp(-np.abs(-1 - np.minimum(z, 0)) / alpha) + base
rate_L0 = f_L(z)
rate_R0 = f_R(z)
simulate_L = lambda: f_L(z) + np.random.uniform(-1, 1, n) * noise_eff
simulate_R = lambda: f_R(z) + np.random.uniform(-1, 1, n) * noise_eff
rate_L = simulate_L()
rate_R = simulate_R()
T = 100
ord1 = np.zeros((n, T))
for k in range(T):
ord1[:, k] = scale_score(simulate_L())
order_L_sim = np.ndarray(n, fit_dtype)
for i in range(n):
order_L_sim[i]['mean'] = np.mean(ord1[i, :])
l, u = np.percentile(ord1[i, :], [5, 95])
order_L_sim[i]['upper'] = u
order_L_sim[i]['lower'] = l
rate_L_est = np.ndarray(n, fit_dtype)
rate_L_est['upper'] = rate_L + noise_est
rate_L_est['lower'] = rate_L - noise_est
rate_R_est = np.ndarray(n, fit_dtype)
rate_R_est['upper'] = rate_R + noise_est
rate_R_est['lower'] = rate_R - noise_est
# estimate according to naive procedure
z_naive = estimate_stimulus_naive(rate_L, rate_R)
res = estimate_stimulus(rate_L_est, rate_R_est)
L_order = res.L_order
R_order = res.R_order
scale_rate = max(rate_L.max(), rate_R.max()) * 1.2
cL = 'r'
cR = 'b'
r = Report()
f = r.figure(cols=3)
with r.plot('noiseless') as pylab:
pylab.plot(z, rate_L0, '%s-' % cL)
pylab.plot(z, rate_R0, '%s-' % cR)
pylab.axis((-1, 1, 0.0, scale_rate))
r.last().add_to(f, caption='noiseless rates')
with r.plot('observed_rates') as pylab:
pylab.plot(z, rate_R0, '%s-' % cR)
pylab.plot(z, rate_L0, '%s-' % cL)
plot_rate_bars(pylab, z, rate_L_est, '%s' % cL)
plot_rate_bars(pylab, z, rate_R_est, '%s' % cR)
pylab.axis((-1, 1, 0.0, scale_rate))
r.last().add_to(f, caption='true_rates')
with r.plot('M') as pylab:
pylab.plot(z, rate_L0, '%s-' % cL)
pylab.plot(z, rate_R0, '%s-' % cR)
pylab.axis((-1, 1, 0.0, scale_rate))
with r.plot('z_naive') as pylab:
pylab.plot(z_naive, rate_L, '%s.' % cL)
pylab.plot(z_naive, rate_R, '%s.' % cR)
pylab.axis((-1, 1, 0.0, scale_rate))
r.last().add_to(f, caption='Stimulus estimated in naive way.')
with r.plot('simulated_order_stats') as pylab:
pylab.plot([0, 0], [n, n], 'k-')
pylab.plot([0, n], [n, 0], 'k-')
pylab.plot(z_order, order_L_sim['mean'], '%s.' % cL)
plot_rate_bars(pylab, z_order, order_L_sim, '%s' % cL)
pylab.axis((0, n, -n / 10, n * 1.1))
pylab.axis('equal')
r.last().add_to(f, caption='Orders as found by simulation')
with r.plot('estimated_order') as pylab:
pylab.plot(z, L_order['mean'], '%s.' % cL)
pylab.plot(z, R_order['mean'], '%s.' % cR)
pylab.axis((-1, 1, -n / 2, n * 3 / 2))
r.last().add_to(f, caption='estimated_order')
with r.plot('estimated_order_order') as pylab:
pylab.plot([0, 0], [n, n], 'k-')
plot_rate_bars(pylab, z_order, L_order, '%s' % cL)
plot_rate_bars(pylab, z_order, R_order, '%s' % cR)
pylab.plot([0, 0], [n, n], 'k-')
pylab.axis((0, n, -n / 10, n * 1.1))
pylab.axis('equal')
r.last().add_to(f, caption='estimated_order_order')
with r.plot('estimated_order_bar') as pylab:
pylab.plot(z, L_order['mean'], '%s.' % cL)
pylab.plot(z, R_order['mean'], '%s.' % cR)
plot_rate_bars(pylab, z, L_order, '%s' % cL)
plot_rate_bars(pylab, z, R_order, '%s' % cR)
pylab.axis((-1, 1, -n / 2, n * 3 / 2))
r.last().add_to(f, caption='estimated_order_bar')
with r.plot('estimated_order_both') as pylab:
pylab.plot([0, 0], [n, n], 'g-')
pylab.plot(z_order, res.order['mean'], 'k.')
plot_rate_bars(pylab, z_order, res.order, 'k')
pylab.axis((0, n, -n / 10, n * 1.1))
pylab.axis('equal')
r.last().add_to(f, caption='estimated_order_order')
with r.plot('z_better') as pylab:
pylab.plot(res.z['mean'], rate_L, '%s.' % cL)
pylab.plot(res.z['mean'], rate_R, '%s.' % cR)
pylab.axis((-1, 1, 0.0, scale_rate))
r.last().add_to(f, caption='Stimulus estimated in a better way.')
filename = 'order_estimation.html'
print('Writing to %r.' % filename)
r.to_html(filename)
def compute_order(samples):
order = np.zeros(samples.shape)
for t in range(samples.shape[1]):
order[:, t] = scale_score(samples[:, t])
return order
