def test_bootstrap_pd_stats():
'''
Notes
-----
create a population of 3d data points
with a known mean and certain spread
take a sample of n points from that population
get the mean and std error of that sample
use bootstrap_pd_stats to get kappa
95% of time, real mean pd should lie within kappa of sample means
'''
n_trials = 100
pop_size = 1e6
smp_size = 40
alpha = 0.05 # used to be 0.95 here
pds = [[0., 0., 1.], [0.,1.,0.], [1.,0.,0.]]
sss = [[0.1, 0.1, 0.1], [0.25, 0.25, 0.25], [0.5, 0.5, 0.5]]
for pd in pds:
for ss in sss:
print "--------------------"
print "pd: ", pd
print "ss: ", ss
failures = 0
for i in range(n_trials):
pop = np.random.standard_normal(size=(pop_size,3)) * ss + pd
smp_inds = np.random.randint(pop_size, size=smp_size)
smp = pop[smp_inds]
smp_mean = np.mean(smp, axis=0)
smp_k = np.sqrt(np.sum(smp_mean**2))
smp_pd = smp_mean / smp_k
smp_stderr = np.std(smp, axis=0, ddof=1) / np.sqrt(smp_size)
# estimate k_s, kappa using bootstrap_pd_stats
k_s, kappa, R = cpd.bootstrap_pd_stats( \
smp_pd, smp_stderr, smp_k, n_samp=smp_size)
interangle = np.arccos(np.dot(pd, smp_pd))
theta = sphere_stat.measure_percentile_angle_ex_kappa( \
kappa)
print "%2d- interangle: %6.4f theta %6.4f" % \
(i, interangle, theta),
if interangle > theta:
failures += 1
print '*'
else:
print '-'
print "failures: %.2f" % (failures / float(n_trials))
assert failures < (alpha * n_trials)