def test_lpdf_matrix_N_components(self):
llval = GMM1_lpdf(
[
[1.0, 0.0, 0.0],
[0, 0, 1],
[0, 0, 1000],
],
[0.25, 0.25, .5], # weights
[0.0, 1.0, 2.0], # mu
[1.0, 2.0, 5.0], # sigma
)
print llval
assert llval.shape == (3, 3)
a = (.25 / np.sqrt(2 * np.pi * 1.0**2) * np.exp(-.5 * (1.0)**2))
a += (.25 / np.sqrt(2 * np.pi * 2.0**2))
a += (.5 / np.sqrt(2 * np.pi * 5.0**2) * np.exp(-.5 * (1.0 / 5.0)**2))
assert np.allclose(llval[0, 0], np.log(a))
assert np.allclose(llval[1, 2], np.log(a))
# case x = 0.0
a = (.25 / np.sqrt(2 * np.pi * 1.0**2))
a += (.25 / np.sqrt(2 * np.pi * 2.0**2) * np.exp(-.5 * (1.0 / 2.0)**2))
a += (.5 / np.sqrt(2 * np.pi * 5.0**2) * np.exp(-.5 * (2.0 / 5.0)**2))
assert np.allclose(llval[0, 1], np.log(a))
assert np.allclose(llval[0, 2], np.log(a))
assert np.allclose(llval[1, 0], np.log(a))
assert np.allclose(llval[1, 1], np.log(a))
assert np.allclose(llval[2, 0], np.log(a))
assert np.allclose(llval[2, 1], np.log(a))
assert np.isfinite(llval[2, 2])
def work(self):
self.worked = True
kwargs = dict(
weights=self.weights,
mus=self.mus,
sigmas=self.sigmas,
low=self.low,
high=self.high,
q=self.q,
)
samples = GMM1(rng=self.rng, size=(self.n_samples, ), **kwargs)
samples = np.sort(samples)
edges = samples[::self.samples_per_bin]
#print samples
pdf = np.exp(GMM1_lpdf(edges[:-1], **kwargs))
dx = edges[1:] - edges[:-1]
y = 1 / dx / len(dx)
if self.show:
plt.scatter(edges[:-1], y)
plt.plot(edges[:-1], pdf)
plt.show()
err = (pdf - y)**2
print np.max(err)
print np.mean(err)
print np.median(err)
if not self.show:
assert np.max(err) < .1
assert np.mean(err) < .01
assert np.median(err) < .01
def test_lpdf_vector_N_components(self):
llval = GMM1_lpdf(
[1.0, 0.0], # x
[0.25, 0.25, 0.5], # weights
[0.0, 1.0, 2.0], # mu
[1.0, 2.0, 5.0], # sigma
)
# case x = 1.0
a = 0.25 / np.sqrt(2 * np.pi * 1.0 ** 2) * np.exp(-0.5 * (1.0) ** 2)
a += old_div(0.25, np.sqrt(2 * np.pi * 2.0 ** 2))
a += (
0.5
/ np.sqrt(2 * np.pi * 5.0 ** 2)
* np.exp(-0.5 * (old_div(1.0, 5.0)) ** 2)
)
assert llval.shape == (2,)
assert np.allclose(llval[0], np.log(a))
# case x = 0.0
a = old_div(0.25, np.sqrt(2 * np.pi * 1.0 ** 2))
a += (
0.25
/ np.sqrt(2 * np.pi * 2.0 ** 2)
* np.exp(-0.5 * (old_div(1.0, 2.0)) ** 2)
)
a += (
0.5
/ np.sqrt(2 * np.pi * 5.0 ** 2)
* np.exp(-0.5 * (old_div(2.0, 5.0)) ** 2)
)
assert np.allclose(llval[1], np.log(a))
def test_lpdf_scalar_one_component(self):
llval = GMM1_lpdf(
1.0, # x
[1.], # weights
[1.0], # mu
[2.0], # sigma
)
assert llval.shape == ()
assert np.allclose(llval, np.log(1.0 / np.sqrt(2 * np.pi * 2.0**2)))
def test_lpdf_scalar_N_components(self):
llval = GMM1_lpdf(
1.0, # x
[0.25, 0.25, .5], # weights
[0.0, 1.0, 2.0], # mu
[1.0, 2.0, 5.0], # sigma
)
a = (.25 / np.sqrt(2 * np.pi * 1.0**2) * np.exp(-.5 * (1.0)**2))
a += (.25 / np.sqrt(2 * np.pi * 2.0**2))
a += (.5 / np.sqrt(2 * np.pi * 5.0**2) * np.exp(-.5 * (1.0 / 5.0)**2))
def test_lpdf_scalar_N_components(self):
llval = GMM1_lpdf(
1.0, # x
[0.25, 0.25, 0.5], # weights
[0.0, 1.0, 2.0], # mu
[1.0, 2.0, 5.0], # sigma
)
print(llval)
a = 0.25 / np.sqrt(2 * np.pi * 1.0**2) * np.exp(-0.5 * (1.0)**2)
a += old_div(0.25, np.sqrt(2 * np.pi * 2.0**2))
a += (0.5 / np.sqrt(2 * np.pi * 5.0**2) *
np.exp(-0.5 * (old_div(1.0, 5.0))**2))
def work(self, **kwargs):
self.__dict__.update(kwargs)
del kwargs
self.worked = True
gkwargs = dict(
weights=self.weights,
mus=self.mus,
sigmas=self.sigmas,
low=self.low,
high=self.high,
q=self.q,
)
samples = GMM1(rng=self.rng, size=(self.n_samples, ), **
gkwargs) / self.q
print 'drew', len(samples), 'samples'
assert np.all(samples == samples.astype('int'))
min_max = int(samples.min()), int(samples.max())
counts = np.bincount(samples.astype('int') - min_max[0])
print counts
xcoords = np.arange(min_max[0], min_max[1] + 1) * self.q
prob = np.exp(GMM1_lpdf(xcoords, **gkwargs))
assert counts.sum() == self.n_samples
y = counts / float(self.n_samples)
if self.show:
import matplotlib.pyplot as plt
plt.scatter(xcoords, y, c='r', label='empirical')
plt.scatter(xcoords, prob, c='b', label='predicted')
plt.legend()
plt.title(str(self.show))
plt.show()
err = (prob - y)**2
print np.max(err)
print np.mean(err)
print np.median(err)
if self.show:
raise nose.SkipTest()
else:
assert np.max(err) < .1
assert np.mean(err) < .01
assert np.median(err) < .01
def work(self, **kwargs):
self.__dict__.update(kwargs)
del kwargs
self.worked = True
gkwargs = dict(
weights=self.weights,
mus=self.mus,
sigmas=self.sigmas,
low=self.low,
high=self.high,
q=self.q,
)
samples = old_div(
GMM1(rng=self.rng, size=(self.n_samples, ), **gkwargs), self.q)
print("drew", len(samples), "samples")
assert np.all(samples == samples.astype("int"))
min_max = int(samples.min()), int(samples.max())
counts = np.bincount(samples.astype("int") - min_max[0])
print(counts)
xcoords = np.arange(min_max[0], min_max[1] + 1) * self.q
prob = np.exp(GMM1_lpdf(xcoords, **gkwargs))
assert counts.sum() == self.n_samples
y = old_div(counts, float(self.n_samples))
if self.show:
plt.scatter(xcoords, y, c="r", label="empirical")
plt.scatter(xcoords, prob, c="b", label="predicted")
plt.legend()
plt.title(str(self.show))
plt.show()
err = (prob - y)**2
print(np.max(err))
print(np.mean(err))
print(np.median(err))
if self.show:
raise nose.SkipTest()
else:
assert np.max(err) < 0.1
assert np.mean(err) < 0.01
assert np.median(err) < 0.01
def test_lpdf_scalar_one_component(self):
# x # weights # mu # sigma
llval = GMM1_lpdf(1.0, [1.0], [1.0], [2.0])
assert llval.shape == ()
assert np.allclose(llval,
np.log(old_div(1.0, np.sqrt(2 * np.pi * 2.0**2))))
