def test_trunc_exp():
x = np.linspace(0, 10, 100)
k = 0.25
xlim = [3, 5]
# replaced with from astroML.stats.random import trunc_exp
# trunc_exp = trunc_exp_gen(name="trunc_exp", shapes='a, b, k')
myfunc = trunc_exp(xlim[0], xlim[1], k)
y = myfunc.pdf(x)
zeros = np.zeros(len(y))
# Test that the function is zero outside of defined limits
assert_array_equal(y[x < xlim[0]], zeros[x < xlim[0]])
assert_array_equal(y[x > xlim[1]], zeros[x > xlim[1]])
inlims = (x < xlim[1]) & (x > xlim[0])
C = k / (np.exp(k * xlim[1]) - np.exp(k * xlim[0]))
# Test that within defined limits, function is exponential
assert_array_equal(y[inlims], C*np.exp(k * x[inlims]))
# Test that the PDF integrates to just about 1
dx = x[1] - x[0]
integral = np.sum(y * dx)
assert np.round(integral, 1) == 1
# Author: Jake VanderPlas <*****@*****.**> # License: BSD # The figure produced by this code is published in the textbook # "Statistics, Data Mining, and Machine Learning in Astronomy" (2013) # For more information, see http://astroML.github.com import numpy as np from matplotlib import pyplot as plt from astroML.stats.random import trunc_exp #------------------------------------------------------------ # Sample from a truncated exponential distribution N = 1E6 hmin = 4.3 hmax = 5.7 k = 0.6 * np.log(10) true_dist = trunc_exp(hmin - 1.4, hmax + 3.4, 0.6 * np.log(10)) # draw the true distributions and heteroscedastic noise np.random.seed(0) h_true = true_dist.rvs(N) dh = 0.5 * (1 + np.random.random(N)) h_obs = np.random.normal(h_true, dh) # create observational cuts cut = (h_obs < hmax) & (h_obs > hmin) # select a random (not observationally cut) subsample rand = np.arange(len(h_obs)) np.random.shuffle(rand) rand = rand[:cut.sum()]
#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX. This may
# result in an error if LaTeX is not installed on your system. In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)
#------------------------------------------------------------
# Sample from a truncated exponential distribution
N = 1E6
hmin = 4.3
hmax = 5.7
k = 0.6 * np.log(10)
true_dist = trunc_exp(hmin - 1.4,
hmax + 3.4,
0.6 * np.log(10))
# draw the true distributions and heteroscedastic noise
np.random.seed(0)
h_true = true_dist.rvs(N)
dh = 0.5 * (1 + np.random.random(N))
h_obs = np.random.normal(h_true, dh)
# create observational cuts
cut = (h_obs < hmax) & (h_obs > hmin)
# select a random (not observationally cut) subsample
rand = np.arange(len(h_obs))
np.random.shuffle(rand)
rand = rand[:cut.sum()]
