def test_normalize():
np.random.seed(123)
npar = 2
k = 3
x = np.linspace(-k*np.pi, k*np.pi, 21)
vnm = mixvn.VonMisesMixture(x)
for k_dist in range(1, 5):
nparams = npar * k_dist + k_dist - 1
for _ in range(10):
params = np.random.uniform(-5, 5, size=nparams)
params[npar * k_dist:] /= 10
pdf1 = vnm.pdf_mix(params)
params2 = mixvn.normalize_params(params)
#most params are changed
#print np.max(np.abs(params - params2)) > 0.001,
pdf2 = vnm.pdf_mix(params2)
assert_almost_equal(pdf2, pdf1, decimal=14)
Created on Fri Oct 26 21:57:48 2012
Author: Josef Perktold
"""
import numpy as np
from scipy import stats, interpolate, integrate
from dist_mixtures.mixture_von_mises import (VonMisesMixture,
normalize_params, shift_loc)
from numpy.testing import assert_almost_equal, assert_
p = [-4, -2.5*np.pi, -4, 1*np.pi, 5, 3.5*np.pi, 0, 0]
p_transformed = [4, 0.5*np.pi, 4, 0, 5, -0.5*np.pi, 0, 0]
assert_almost_equal(normalize_params(p), p_transformed, 13)
loc1 = shift_loc(np.linspace(-5, 5, 21) * np.pi)[:-1]
loc2 = np.tile(np.linspace(-1, 0.5, 4) * np.pi, 5)
assert_almost_equal(loc1, loc2, 13)
res2_params = np.array([ 1.90886275, -2.99882496, 0.38442792, -0.86952549,
0.33013396])
res3_params = np.array([ 0.27505697, -1.27358384, 2.38037407, -2.90256257,
-4.29683974, -0.48736552, 2.08776124, 1.9212298 ])
res4_params = np.array([ 1.56354196, -2.95987588, -1.19876203, -2.94677148,
-4.76746645, 1.87938641, 9.89761038, -0.49076411,
3.97260961, 2.50826187, 1.29319052])
alpha=0.7,
label='data')
plt.plot(data[:, 0],
res.model.pdf_mix(res.params, data[:, 0]) * rad_diff,
color='r',
lw=2,
alpha=0.7,
label='estimated')
plt.title('Length distribution - data and estimate')
plt.legend()
count_endog = data_raw[:, 1] / 100.
bins_exog = np.linspace(-np.pi, np.pi, 180 + 1)
modb = mixvn.VonMisesMixtureBinned(count_endog, bins_exog)
resb = modb.fit(start_params=res.params, method='bfgs')
resb.params = mixvn.normalize_params(resb.params)
resb2 = modb.fit(start_params=start_params, method='bfgs')
resb2.params = mixvn.normalize_params(resb2.params)
print 'res.params ', res.params
print 'resb.params ', resb.params
print 'resb2.params', resb2.params
#TODO: need to standardize sequence of components in params
print 'gof chisquare', resb.model.gof_chisquare(resb.params)
#LS is more sensitive to start_params ?
resbls = modb.fit_ls(start_params=res.params)
resbls_params = mixvn.normalize_params(resbls[0])
print 'resbls params ', resbls_params
plt.figure()
plt.plot(data[:, 0],
def test_vonmisesmixture():
#np.random.seed(987789) #TODO: add seed later, random failure without
#values of initialization not used
mod2 = mixvn.VonMisesMixture(np.random.uniform(-np.pi, np.pi, size=10))
params = [2., -0.75 * np.pi, 4., np.pi/2, 0.4]
nobs = 50000
rvs = mod2.rvs_mix(params, size=nobs, shuffle=True)
assert_equal(len(rvs), nobs)
#check withing bounds
above = (rvs > np.pi).sum()
below = (rvs < -np.pi).sum()
assert_equal(above, 0)
assert_equal(below, 0)
#gof tests
bins = 180
bins = np.linspace(-np.pi, np.pi, bins+1)
#count, bins_ = np.histogram(rvs, bins=bins, normed=True)
#freq = count * np.diff(bins_)
count, bins_ = np.histogram(rvs, bins=bins)
freq = count / count.sum()
assert_equal(count.sum(), len(rvs))
ks = stats.kstest(rvs, lambda x: mod2.cdf_mix(params, x))
assert_array_less(0.1, ks[1])
c1 = mod2.cdf_mix(params, bins)
p0 = np.diff(c1)
chi2 = stats.chisquare(count, p0 * nobs)
assert_array_less(0.1, chi2[1])
mse = ((freq - p0)**2).mean()
assert_array_less(mse, 1e-4)
#bin_center = bins[:-1] + np.diff(bins) / 2
#more pdf, cdf checks
p2 = mod2.pdf_mix(params, bins)
from scipy import integrate
c2 = integrate.cumtrapz(p2, dx=bins[1]-bins[0])
assert_almost_equal(c2, c1[1:], decimal=4) #approximation error
#check wrapping to [-np.pi, np.pi] #TODO: open interval ?
assert_almost_equal(mod2.cdf_mix(params, -np.pi), 0, decimal=13)
assert_almost_equal(mod2.cdf_mix(params, np.pi), 1, decimal=13)
c3 = mod2.cdf_mix(params, bins + 2 * np.pi)
assert_almost_equal(c3 - 1, c1, decimal=13)
c3 = mod2.cdf_mix(params, bins - 2 * np.pi)
assert_almost_equal(c3 + 1, c1, decimal=13)
p1 = mod2.pdf_mix(params, bins)
p3 = mod2.pdf_mix(params, bins + 2 * np.pi)
assert_almost_equal(p3, p1, decimal=13)
p3 = mod2.pdf_mix(params, bins - 2 * np.pi)
assert_almost_equal(p3, p1, decimal=13)
#check standalone functions
p4 = mod2.pdf_mix(params, bins * 4)
pf1 = mixvn.pdf_mix(params, bins * 4)
assert_almost_equal(pf1, p4, decimal=13)
pvn = mixvn.pdf_vn(bins * 4, params[0], params[1])
psp = stats.vonmises.pdf(bins * 4, params[0], params[1])
assert_almost_equal(pvn, psp, decimal=13)
#periodicity of cdf with trend, origin not fixed
cvn = mixvn.cdf_vn(bins, params[0], params[1])
cvn3 = mixvn.cdf_vn(bins + 2 * np.pi, params[0], params[1])
assert_almost_equal(cvn3 - 1, cvn, decimal=13)
cvn3 = mixvn.cdf_vn(bins - 2 * np.pi, params[0], params[1])
assert_almost_equal(cvn3 + 1, cvn, decimal=13)
assert_almost_equal(pvn, psp, decimal=13)
#test fit
mod3 = mixvn.VonMisesMixture(rvs[:2000])
#good starting values
res3 = mod3.fit(start_params=np.array(params)*1.1)
res3.params = mixvn.normalize_params(res3.params)
assert_almost_equal(res3.params, params, decimal=1)
#simple starting values, refit same model instance
res3 = mod3.fit(start_params=0.5*np.ones(len(params)))
res3.params = mixvn.normalize_params(res3.params)
assert_almost_equal(res3.params, params, decimal=1)
##fit is not much better with full sample (but slower)
#mod4 = mixvn.VonMisesMixture(rvs)
#res4 = mod4.fit(start_params=0.5*np.ones(len(params)))
#res4.params = mixvn.normalize_params(res4.params)
#assert_almost_equal(res4.params, params, decimal=1)
#fit with binned data, full sample, 180 bins on (-pi, pi)
mod5 = mixvn.VonMisesMixtureBinned(count, bins)
#good starting values
res5 = mod5.fit(start_params=np.array(params)*1.1)
res5.params = mixvn.normalize_params(res5.params)
assert_almost_equal(res5.params, params, decimal=1)
assert_almost_equal(res5.params, res3.params, decimal=1)
#LSfit with binned data, full sample, 180 bins on (-pi, pi)
#mod5 = mixvn.VonMisesMixtureBinned(count.astype(float), bins)
#good starting values
res6 = mod5.fit_ls(start_params=np.array(params)*1.1)
res6_params = mixvn.normalize_params(res6[0])
assert_almost_equal(res6_params, params, decimal=1)
assert_almost_equal(res6_params, res5.params, decimal=2)
#simple starting values
start_params=0.5*np.ones(len(params))
start_params[-1] = 0.05
#TODO: optimize.leastsq can fail with maxfev, scipy cdf with ZeroDivision
start_params = [-2.5, 4, 0.1, 4, 0.1]
res6a = mod5.fit_ls(start_params=start_params)
res6a_params = mixvn.normalize_params(res6a[0])
assert_almost_equal(res6a_params, params, decimal=1)
assert_almost_equal(res6_params, res6_params, decimal=4)
Created on Fri Oct 26 21:57:48 2012
Author: Josef Perktold
"""
import numpy as np
from scipy import stats, interpolate, integrate
from dist_mixtures.mixture_von_mises import (VonMisesMixture, normalize_params,
shift_loc)
from numpy.testing import assert_almost_equal, assert_
p = [-4, -2.5 * np.pi, -4, 1 * np.pi, 5, 3.5 * np.pi, 0, 0]
p_transformed = [4, 0.5 * np.pi, 4, 0, 5, -0.5 * np.pi, 0, 0]
assert_almost_equal(normalize_params(p), p_transformed, 13)
loc1 = shift_loc(np.linspace(-5, 5, 21) * np.pi)[:-1]
loc2 = np.tile(np.linspace(-1, 0.5, 4) * np.pi, 5)
assert_almost_equal(loc1, loc2, 13)
res2_params = np.array(
[1.90886275, -2.99882496, 0.38442792, -0.86952549, 0.33013396])
res3_params = np.array([
0.27505697, -1.27358384, 2.38037407, -2.90256257, -4.29683974, -0.48736552,
2.08776124, 1.9212298
])
res4_params = np.array([
1.56354196, -2.95987588, -1.19876203, -2.94677148, -4.76746645, 1.87938641,
