def test_jackknife_results():
np.random.seed(0)
x = np.random.normal(0, 1, 100)
mu1, sig1 = jackknife(x, np.mean, kwargs=dict(axis=1))
mu2, sig2 = jackknife(x, np.std, kwargs=dict(axis=1))
assert_allclose([mu1, sig1, mu2, sig2], [0.0598080155345, 0.100288031685, 1.01510470168, 0.0649020337599])
def test_jackknife_pass_indices():
np.random.seed(0)
x = np.random.normal(0, 1, 100)
res1 = jackknife(x, np.mean, kwargs=dict(axis=1))
res2 = jackknife(x, lambda i: np.mean(x[i], axis=1), pass_indices=True)
assert_allclose(res1, res2)
def test_jackknife_pass_indices():
np.random.seed(0)
x = np.random.normal(0, 1, 100)
res1 = jackknife(x, np.mean, kwargs=dict(axis=1))
res2 = jackknife(x, lambda i: np.mean(x[i], axis=1), pass_indices=True)
assert_allclose(res1, res2)
def test_jackknife_results():
np.random.seed(0)
x = np.random.normal(0, 1, 100)
mu1, sig1 = jackknife(x, np.mean, kwargs=dict(axis=1))
mu2, sig2 = jackknife(x, np.std, kwargs=dict(axis=1))
assert_allclose(
[mu1, sig1, mu2, sig2],
[0.0598080155345, 0.100288031685, 1.01510470168, 0.0649020337599])
def test_jackknife_multiple():
np.random.seed(0)
x = np.random.normal(0, 1, 100)
mu1, sig1 = jackknife(x, np.mean, kwargs=dict(axis=1))
mu2, sig2 = jackknife(x, np.std, kwargs=dict(axis=1))
res = jackknife(x, mean_sigma, kwargs=dict(axis=1))
assert_allclose(res[0], (mu1, sig1))
assert_allclose(res[1], (mu2, sig2))
def test_jackknife_multiple():
np.random.seed(0)
x = np.random.normal(0, 1, 100)
mu1, sig1 = jackknife(x, np.mean, kwargs=dict(axis=1))
mu2, sig2 = jackknife(x, np.std, kwargs=dict(axis=1))
res = jackknife(x, mean_sigma, kwargs=dict(axis=1))
assert_allclose(res[0], (mu1, sig1))
assert_allclose(res[1], (mu2, sig2))
def median_value(x,y, nbin=6, xmin= None, xmax = None, err=1 ):
if xmin==None: xmin = x.min()
if xmax==None: xmax = x.max()
step = (xmax - xmin)/nbin
bin_ = np.linspace(xmin-step/1.99, xmax+step/1.99, nbin+2)
mid_bin = (bin_+step/2.)[:nbin+1]
dig = np.digitize(x,bin_)
if not err: return mid_bin, np.array([np.median(y[dig==i+1]) for i in xrange(len(mid_bin))])
yout = np.zeros(len(mid_bin))
yerr = np.zeros(len(mid_bin))
std = np.zeros(len(mid_bin))
for i in xrange(len(mid_bin)):
s = y[dig==i+1]
s = s[(~np.isnan(s))&(np.isfinite(s))]
if not len(s):continue
mu, sig = jackknife(s, np.mean, kwargs=dict(axis=1))
yerr[i] = sig
yout[i] = mu
std[i] = np.std(s)
return mid_bin, yout, yerr, std #np.array([np.mean(y[dig==i+1]) for i in xrange(len(mid_bin))])
setup_text_plots(fontsize=8, usetex=True)
#------------------------------------------------------------
# sample values from a normal distribution
np.random.seed(123)
m = 1000 # number of points
data = norm(0, 1).rvs(m)
#------------------------------------------------------------
# Compute jackknife resamplings of data
from astroML.resample import jackknife
from astroML.stats import sigmaG
# mu1 is the mean of the standard-deviation-based width
mu1, sigma_mu1, mu1_raw = jackknife(data,
np.std,
kwargs=dict(axis=1, ddof=1),
return_raw_distribution=True)
pdf1_theory = norm(1, 1. / np.sqrt(2 * (m - 1)))
pdf1_jackknife = norm(mu1, sigma_mu1)
# mu2 is the mean of the interquartile-based width
# WARNING: do not use the following in practice. This example
# shows that jackknife fails for rank-based statistics.
mu2, sigma_mu2, mu2_raw = jackknife(data,
sigmaG,
kwargs=dict(axis=1),
return_raw_distribution=True)
pdf2_theory = norm(data.std(), 1.06 / np.sqrt(m))
pdf2_jackknife = norm(mu2, sigma_mu2)
print(mu2, sigma_mu2)
from matplotlib import pyplot as plt
#------------------------------------------------------------
# sample values from a normal distribution
np.random.seed(123)
m = 1000 # number of points
data = norm(0, 1).rvs(m)
#------------------------------------------------------------
# Compute jackknife resamplings of data
from astroML.resample import jackknife
from astroML.stats import sigmaG
# mu1 is the mean of the standard-deviation-based width
mu1, sigma_mu1, mu1_raw = jackknife(data, np.std,
kwargs=dict(axis=1, ddof=1),
return_raw_distribution=True)
pdf1_theory = norm(1, 1. / np.sqrt(2 * (m - 1)))
pdf1_jackknife = norm(mu1, sigma_mu1)
# mu2 is the mean of the interquartile-based width
# WARNING: do not use the following in practice. This example
# shows that jackknife fails for rank-based statistics.
mu2, sigma_mu2, mu2_raw = jackknife(data, sigmaG,
kwargs=dict(axis=1),
return_raw_distribution=True)
pdf2_theory = norm(data.std(), 1.06 / np.sqrt(m))
pdf2_jackknife = norm(mu2, sigma_mu2)
print mu2, sigma_mu2