def test_sampling_bias1(self):
from spikecount.shannon import entropy1, bootstrap
from numpy import pi, e, log2
from numpy import array, polyfit
print
print "Sampling bias 1d"
x = generate_gaussian(sigma = 10, N=30000)
N = x.size
N = array([N/2**i for i in xrange(5)])
print N, '\n'
ss = []
for i, n in enumerate(N):
y = x[:n*(2**i)].reshape((2**i, n))
smean = array([entropy1(z) for z in y]).mean()
ss.append(smean)
print n, smean, smean - log2(x.std()), log2(2*pi*e)/2
# pl.plot(1.0/N, ss)
# pl.show()
sr = polyfit(1.0/N, ss, 1)
s0 = sr[-1]
print s0, s0-log2(x.std()), log2(2*pi*e)/2
scompare = bootstrap(entropy1, x, debug=False)['predict']
print scompare, scompare - log2(x.std()), log2(2*pi*e)/2
def test_entropy1(self): from spikecount.shannon import entropy1 from numpy import pi, e, log2 print print "Test 1d entroy." x = generate_gaussian(sigma = 5) print entropy1(x), entropy1(x)-log2(x.std()), log2(2*pi*e)/2 x = generate_gaussian(sigma = 30) print entropy1(x), entropy1(x)-log2(x.std()), log2(2*pi*e)/2 x = generate_gaussian(sigma = 75) print entropy1(x), entropy1(x)-log2(x.std()), log2(2*pi*e)/2
def test_mix_samples(self): from spikecount.shannon import mix_samples, entropy2, entropy1, log2, bootstrap from numpy import hstack print "\nTest mixing samples." c = 0.3 x1, y1 = generate_correlated_gaussian(sigma=5, N=100000, c = c) x2, y2 = generate_correlated_gaussian(sigma=10, N=100000, c = c) print "Well mixed samples" z1 = mix_samples([x1,x2]) z2 = mix_samples([y1,y2]) print entropy1(z1) + entropy1(z2) - entropy2(z1, z2), -log2(1-c**2)/2 print "Datasets pasted side by side" z1 = hstack((x1, x2)) z2 = hstack((y1, y2)) print entropy1(z1) + entropy1(z2) - entropy2(z1, z2), -log2(1-c**2)/2 print "Now testing shifting and mixing samples" x1, y1 = generate_correlated_gaussian(sigma=4, N=100000, c = c) x2, y2 = generate_correlated_gaussian(sigma=4, N=100000, c = c) z1 = mix_samples((x1,x2+1000)) z2 = mix_samples((y1,y2+1000)) print bootstrap(entropy1, z1)['predict'] + bootstrap(entropy1, z2)['predict'] - bootstrap(entropy2, z1, z2)['predict'], -log2(1-c**2)/2 print bootstrap(entropy1, x2)['predict'] + bootstrap(entropy1, y2)['predict'] - bootstrap(entropy2, x2, y2)['predict'], -log2(1-c**2)/2