/usr/lib/python2.7/dist-packages/csb/test/cases/statistics/scalemixture.py is in python-csb 1.2.3+dfsg-3.
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import csb.test as test
import csb.statistics.pdf
from csb.bio.io.wwpdb import LegacyStructureParser
from csb.bio.utils import probabilistic_fit, average_structure
from csb.statistics.scalemixture import ScaleMixture, GammaPrior, InvGammaPrior
from csb.statistics.scalemixture import GammaPosteriorMAP, InvGammaPosteriorMAP
@test.functional
class TestScaleMixture(test.Case):
def testRandom(self):
mixture = ScaleMixture(scales=[1., 1., 1., 1.],
prior=GammaPrior(), d=3)
mixture.random()
samples = mixture.random(10000)
mu = numpy.mean(samples)
var = numpy.var(samples)
self.assertAlmostEqual(0.0, mu, delta=1e-1)
self.assertAlmostEqual(1., var, delta=1e-1)
def testLogProb(self):
x = numpy.linspace(-5, 5, 1000)
normal = csb.statistics.pdf.Normal()
mixture = ScaleMixture(scales=[1., 1., 1., 1.],
prior=None, d=1)
px = mixture(x)
gx = normal(x)
for i in range(len(px)):
self.assertAlmostEqual(px[i], 4 * gx[i], delta=1e-1)
def testGamma(self):
"""
The posterior of a gaussian scale mixture with gamma prior
is a Student's t distribution, with parameters alpha and beta.
Give enough samples, we shoud be able to estimate these parameters
"""
pdbfile = self.config.getTestFile('ake-xray-ensemble-ca.pdb')
ensemble = LegacyStructureParser(pdbfile).parse_models()
X = numpy.array(ensemble[0].get_coordinates(['CA'], True))
Y = numpy.array(ensemble[13].get_coordinates(['CA'], True))
mixture = ScaleMixture(scales=X.shape[0],
prior=GammaPrior(), d=3)
from csb.bio.utils import fit
R, t = fit(X, Y)
#numpy.random.seed(100)
# gibbs sampling cycle
for i in range(200):
# apply rotation
data = numpy.sum((X - numpy.dot(Y, numpy.transpose(R)) - t) ** 2, axis= -1) ** (1. / 2)
# sample scales
mixture.estimate(data)
# sample rotations
R, t = probabilistic_fit(X, Y, mixture.scales)
self.assertEqual(mixture.scales.shape, (211,))
R_opt = numpy.eye(3)
t_opt = numpy.zeros((3,))
for i in range(3):
self.assertAlmostEqual(t[i], t_opt[i], delta=2.)
for j in range(3):
self.assertAlmostEqual(R_opt[i, j], R[i, j], delta=1e-1)
def testGammaMAP(self):
"""
The posterior of a gaussian scale mixture with gamma prior
is a Student's t distribution, with parameters alpha and beta.
Give enough samples, we shoud be able to estimate these parameters
"""
pdbfile = self.config.getTestFile('ake-xray-ensemble-ca.pdb')
ensemble = LegacyStructureParser(pdbfile).parse_models()
X = numpy.array(ensemble[0].get_coordinates(['CA'], True))
Y = numpy.array(ensemble[13].get_coordinates(['CA'], True))
prior = GammaPrior()
prior.estimator = GammaPosteriorMAP()
mixture = ScaleMixture(scales=X.shape[0],
prior=prior, d=3)
from csb.bio.utils import fit, wfit
R, t = fit(X, Y)
#numpy.random.seed(100)
# gibbs sampling cycle
for i in range(200):
# apply rotation
data = numpy.sum((X - numpy.dot(Y, numpy.transpose(R)) - t) ** 2, axis= -1) ** (1. / 2)
# sample scales
mixture.estimate(data)
# sample rotations
R, t = wfit(X, Y, mixture.scales)
self.assertEqual(mixture.scales.shape, (211,))
R_opt = numpy.eye(3)
t_opt = numpy.zeros((3,))
for i in range(3):
self.assertAlmostEqual(t[i], t_opt[i], delta=2.)
for j in range(3):
self.assertAlmostEqual(R_opt[i, j], R[i, j], delta=1e-1)
def testInvGamma(self):
"""
The posterior of a gaussian scale mixture with gamma prior
is a Student's t distribution, with parameters alpha and beta.
Give enough samples, we shoud be able to estimate these parameters
"""
pdbfile = self.config.getTestFile('ake-xray-ensemble-ca.pdb')
ensemble = LegacyStructureParser(pdbfile).parse_models()
X = numpy.array(ensemble[0].get_coordinates(['CA'], True))
Y = numpy.array(ensemble[13].get_coordinates(['CA'], True))
mixture = ScaleMixture(scales=X.shape[0],
prior=InvGammaPrior(), d=3)
from csb.bio.utils import fit
R, t = fit(X, Y)
#numpy.random.seed(100)
# gibbs sampling cycle
for i in range(200):
# apply rotation
data = numpy.sum((X - numpy.dot(Y, numpy.transpose(R)) - t) ** 2, axis= -1) ** (1. / 2)
# sample scales
mixture.estimate(data)
# sample rotations
R, t = probabilistic_fit(X, Y, mixture.scales)
self.assertEqual(mixture.scales.shape, (211,))
R_opt = numpy.eye(3)
t_opt = numpy.zeros((3,))
for i in range(3):
self.assertAlmostEqual(t[i], t_opt[i], delta=2.)
for j in range(3):
self.assertAlmostEqual(R_opt[i, j], R[i, j], delta=1e-1)
def testInvGammaMAP(self):
"""
The posterior of a gaussian scale mixture with gamma prior
is a Student's t distribution, with parameters alpha and beta.
Give enough samples, we shoud be able to estimate these parameters
"""
pdbfile = self.config.getTestFile('ake-xray-ensemble-ca.pdb')
ensemble = LegacyStructureParser(pdbfile).parse_models()
X = numpy.array(ensemble[0].get_coordinates(['CA'], True))
Y = numpy.array(ensemble[13].get_coordinates(['CA'], True))
prior = InvGammaPrior()
prior.estimator = InvGammaPosteriorMAP()
mixture = ScaleMixture(scales=X.shape[0],
prior=prior, d=3)
from csb.bio.utils import fit, wfit
R, t = fit(X, Y)
#numpy.random.seed(100)
# gibbs sampling cycle
for i in range(200):
# apply rotation
data = numpy.sum((X - numpy.dot(Y, numpy.transpose(R)) - t) ** 2, axis= -1) ** (1. / 2)
# sample scales
mixture.estimate(data)
# sample rotations
R, t = wfit(X, Y, mixture.scales)
self.assertEqual(mixture.scales.shape, (211,))
R_opt = numpy.eye(3)
t_opt = numpy.zeros((3,))
for i in range(3):
self.assertAlmostEqual(t[i], t_opt[i], delta=2.)
for j in range(3):
self.assertAlmostEqual(R_opt[i, j], R[i, j], delta=1e-1)
def testEnsemble(self):
"""
The posterior of a gaussian scale mixture with gamma prior
is a Student's t distribution, with parameters alpha and beta.
Give enough samples, we shoud be able to estimate these parameters
"""
pdbfile = self.config.getTestFile('ake-xray-ensemble-ca.pdb')
ensemble = LegacyStructureParser(pdbfile).parse_models()
X = numpy.array([model.get_coordinates(['CA'], True) for model in ensemble])
x_mu = average_structure(X)
n =X.shape[1]
m =X.shape[0]
R = numpy.zeros((m,3,3))
t = numpy.ones((m,3))
prior = GammaPrior()
mixture = ScaleMixture(scales=n, prior = prior, d=3)
from csb.bio.utils import fit, wfit
for i in range(m):
R[i,:,:], t[i,:] = fit(x_mu, X[i])
# gibbs sampling cycle
for j in range(200):
# apply rotation
data = numpy.array([numpy.sum((x_mu - numpy.dot(X[i], numpy.transpose(R[i])) - t[i]) **2, -1)**0.5
for i in range(m)]).T
# sample scales
mixture.estimate(data)
# sample rotations
for i in range(m):
R[i,:,:], t[i,:] = wfit(x_mu, X[i], mixture.scales)
self.assertEqual(mixture.scales.shape, (211,))
R_opt = numpy.eye(3)
t_opt = numpy.zeros((3,))
for k in range(m):
for i in range(3):
self.assertAlmostEqual(t[k,i], t_opt[i], delta=2.)
for j in range(3):
self.assertAlmostEqual(abs(R[k,i, j]), R_opt[i, j], delta=0.15)
if __name__ == '__main__':
test.Console()
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