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 xfit(mobile, target, mobile_state=-1, target_state=-1, load_b=0,
cycles=10, match='align', guide=1, seed=0, quiet=1,
bfit=0, distribution='student', _self=cmd):
'''
DESCRIPTION
Weighted superposition of the model in the first selection on to the model
in the second selection. The weights are estimated with maximum likelihood.
The result should be very similar to "theseus".
Requires CSB, https://github.com/csb-toolbox/CSB
ARGUMENTS
mobile = string: atom selection
target = string: atom selection
mobile_state = int: object state of mobile selection {default: current}
target_state = int: object state of target selection {default: current}
load_b = 0 or 1: save -log(weights) into B-factor column {default: 0}
SEE ALSO
intra_xfit, align, super, fit, cealign, theseus
'''
from numpy import asarray, identity, log, dot, zeros
from csb.bio.utils import distance_sq, wfit, fit
from . import querying
cycles, quiet = int(cycles), int(quiet)
mobile_state, target_state = int(mobile_state), int(target_state)
mobile_obj = querying.get_object_name(mobile, 1)
if mobile_state < 1: mobile_state = querying.get_object_state(mobile_obj)
if target_state < 1: target_state = querying.get_selection_state(target)
if int(guide):
mobile = '(%s) and guide' % (mobile)
target = '(%s) and guide' % (target)
mm = MatchMaker(mobile, target, match)
Y = asarray(querying.get_coords(mm.mobile, mobile_state))
X = asarray(querying.get_coords(mm.target, target_state))
if int(seed):
R, t = identity(3), zeros(3)
else:
R, t = fit(X, Y)
if int(bfit):
# adapted from csb.apps.bfit
from csb.bio.utils import distance, probabilistic_fit
from csb.statistics.scalemixture import ScaleMixture
mixture = ScaleMixture(scales=X.shape[0],
prior=_bfit_get_prior(distribution), d=3)
for _ in range(cycles):
data = distance(Y, dot(X - t, R))
mixture.estimate(data)
R, t = probabilistic_fit(X, Y, mixture.scales)
scales = mixture.scales
else:
for _ in range(cycles):
data = distance_sq(Y, dot(X - t, R))
scales = 1.0 / data.clip(1e-3)
R, t = wfit(X, Y, scales)
m = identity(4)
m[0:3,0:3] = R
m[0:3,3] = t
cmd.transform_object(mobile_obj, list(m.flat))
if int(load_b):
b_iter = iter(-log(scales))
cmd.alter(mm.mobile, 'b = next(b_iter)', space={'b_iter': b_iter, 'next': next})
if not quiet:
print(' xfit: %d atoms aligned' % (len(X)))
def xfit(mobile, target, mobile_state=-1, target_state=-1, load_b=0,
cycles=10, match='align', guide=1, seed=0, quiet=1,
bfit=0, distribution='student', _self=cmd):
'''
DESCRIPTION
Weighted superposition of the model in the first selection on to the model
in the second selection. The weights are estimated with maximum likelihood.
The result should be very similar to "theseus".
Requires CSB, https://github.com/csb-toolbox/CSB
ARGUMENTS
mobile = string: atom selection
target = string: atom selection
mobile_state = int: object state of mobile selection {default: current}
target_state = int: object state of target selection {default: current}
load_b = 0 or 1: save -log(weights) into B-factor column {default: 0}
SEE ALSO
intra_xfit, align, super, fit, cealign, theseus
'''
from numpy import asarray, identity, log, dot, zeros
from csb.bio.utils import distance_sq, wfit, fit
from . import querying
cycles, quiet = int(cycles), int(quiet)
mobile_state, target_state = int(mobile_state), int(target_state)
mobile_obj = querying.get_object_name(mobile, 1, _self=_self)
if mobile_state < 1: mobile_state = querying.get_object_state(mobile_obj, _self=_self)
if target_state < 1: target_state = querying.get_selection_state(target, _self=_self)
if int(guide):
mobile = '(%s) and guide' % (mobile)
target = '(%s) and guide' % (target)
mm = MatchMaker(mobile, target, match, _self=_self)
Y = asarray(_self.get_coords(mm.mobile, mobile_state))
X = asarray(_self.get_coords(mm.target, target_state))
if int(seed):
R, t = identity(3), zeros(3)
else:
R, t = fit(X, Y)
if int(bfit):
# adapted from csb.apps.bfit
from csb.bio.utils import distance, probabilistic_fit
from csb.statistics.scalemixture import ScaleMixture
mixture = ScaleMixture(scales=X.shape[0],
prior=_bfit_get_prior(distribution), d=3)
for _ in range(cycles):
data = distance(Y, dot(X - t, R))
mixture.estimate(data)
R, t = probabilistic_fit(X, Y, mixture.scales)
scales = mixture.scales
else:
for _ in range(cycles):
data = distance_sq(Y, dot(X - t, R))
scales = 1.0 / data.clip(1e-3)
R, t = wfit(X, Y, scales)
m = identity(4)
m[0:3,0:3] = R
m[0:3,3] = t
_self.transform_object(mobile_obj, list(m.flat))
if int(load_b):
b_iter = iter(-log(scales))
_self.alter(mm.mobile, 'b = next(b_iter)', space={'b_iter': b_iter, 'next': next})
if not quiet:
print(' xfit: %d atoms aligned' % (len(X)))