def _generate_matrix(self):
"""Generate A matrix if required"""
k = self.k
n = self.n
m = self.m
dim = self.dim
self._calculate_orders()
self.A = sparse.dok_matrix((self.order_idx[k],dim))
self.row_counter = 0
for ordi in xrange(k):
self.nterms = m**(n - (ordi+1))
self.terms = dec2base(np.c_[0:self.nterms,], m, n-(ordi+1))
self._recloop((ordi+1), 1, [], [], n, m)
print "Order " + str(ordi+1) + " complete. Time: " + time.ctime()
# save matrix to file
self.A = self.A.tocsc()
savedict = {'A':self.A, 'order_idx':self.order_idx}
sio.savemat(self.filename, savedict)
def order1direct(p,a):
"""Compute first order solution directly for testing"""
if p.size != a.fdim:
raise ValueError, "Probability vector doesn't match a.fdim"
# 1st order marginals
marg = a.eta_from_p(p)[:a.order_idx[1]]
# output
p1 = np.zeros(a.fdim)
the1pos = lambda x,v: ((v-1)*a.n)+x
# loop over all probabilities (not p(0))
for i in range(1,a.fdim):
Pword = dec2base(np.atleast_2d(i).T,a.m,a.n)
# loop over each variable
for j in range(a.n):
# this value
x = Pword[0][j]
if x!=0:
# this is a normal non-zero marginal
factor = marg[the1pos(j,x)]
else:
# this is a zero-value marginal
factor = 1 - marg[the1pos(j,np.r_[1:a.m])].sum()
if p1[i]==0:
# first entry
p1[i] = factor
else:
p1[i] *= factor
# normalise
p1[0] = 1.0 - p1.sum()
return p1
def order1direct(p,a):
"""Compute first order solution directly for testing"""
if p.size != a.fdim:
raise ValueError, "Probability vector doesn't match a.fdim"
# 1st order marginals
marg = a.eta_from_p(p)[:a.order_idx[1]]
# output
p1 = np.zeros(a.fdim)
the1pos = lambda x,v: ((v-1)*a.n)+x
# loop over all probabilities (not p(0))
for i in range(1,a.fdim):
Pword = dec2base(np.atleast_2d(i).T,a.m,a.n)
# loop over each variable
for j in range(a.n):
# this value
x = Pword[0][j]
if x!=0:
# this is a normal non-zero marginal
factor = marg[the1pos(j,x)]
else:
# this is a zero-value marginal
factor = 1 - marg[the1pos(j,np.r_[1:a.m])].sum()
if p1[i]==0:
# first entry
p1[i] = factor
else:
p1[i] *= factor
# normalise
p1[0] = 1.0 - p1.sum()
return p1
def _sample(self, method='naive'):
"""Sample probabilities of system.
Parameters
----------
method : {'naive', 'beta:x', 'kt'}, optional
Sampling method to use. 'naive' is the standard histrogram method.
'beta:x' is for an add-constant beta estimator, with beta value
following the colon eg 'beta:0.01' [1]_. 'kt' is for the
Krichevsky-Trofimov estimator [2]_, which is equivalent to
'beta:0.5'.
References
----------
.. [1] T. Schurmann and P. Grassberger, "Entropy estimation of
symbol sequences," Chaos,vol. 6, no. 3, pp. 414--427, 1996.
.. [2] R. Krichevsky and V. Trofimov, "The performance of universal
encoding," IEEE Trans. Information Theory, vol. 27, no. 2,
pp. 199--207, Mar. 1981.
"""
calc = self.calc
# decimalise
if any([c in calc for c in ['HXY', 'HX']]):
if self.X_n > 1:
d_X = decimalise(self.X, self.X_n, self.X_m)
else:
# make 1D
d_X = self.X.reshape(self.X.size)
# unconditional probabilities
if ('HX' in calc) or ('ChiX' in calc):
self.PX = prob(d_X, self.X_dim, method=method)
if any([c in calc for c in ['HXY', 'HiX', 'HiXY', 'HY']]):
self.PY = _probcount(self.Ny, self.N, method)
if 'SiHXi' in calc:
for i in xrange(self.X_n):
self.PXi[:, i] = prob(self.X[i, :], self.X_m, method=method)
# conditional probabilities
if any([c in calc for c in ['HiXY', 'HXY', 'HshXY']]):
sstart = 0
for i in xrange(self.Y_dim):
send = sstart + self.Ny[i]
indx = slice(sstart, send)
sstart = send
if 'HXY' in calc:
# output conditional ensemble
oce = d_X[indx]
if oce.size == 0:
print 'Warning: Null output conditional ensemble for ' + \
'output : ' + str(i)
else:
self.PXY[:, i] = prob(oce, self.X_dim, method=method)
if any([c in calc for c in ['HiX', 'HiXY', 'HshXY']]):
for j in xrange(self.X_n):
# output conditional ensemble for a single variable
oce = self.X[j, indx]
if oce.size == 0:
print 'Warning: Null independent output conditional ensemble for ' + \
'output : ' + str(i) + ', variable : ' + str(j)
else:
self.PXiY[:, j, i] = prob(oce,
self.X_m,
method=method)
if 'HshXY' in calc:
# shuffle
#np.random.shuffle(oce)
shfoce = np.random.permutation(oce)
self.Xsh[j, indx] = shfoce
# Pind(X) = <Pind(X|Y)>_y
if ('HiX' in calc) or ('ChiX' in calc):
# construct joint distribution
words = dec2base(
np.atleast_2d(np.r_[0:self.X_dim]).T, self.X_m, self.X_n)
PiXY = np.zeros((self.X_dim, self.Y_dim))
PiXY = self.PXiY[words, np.r_[0:self.X_n]].prod(axis=1)
# average over Y
self.PiX = np.dot(PiXY, self.PY)
self.sampled = True
def _sample(self, method='naive'):
"""Sample probabilities of system.
Parameters
----------
method : {'naive', 'beta:x', 'kt'}, optional
Sampling method to use. 'naive' is the standard histrogram method.
'beta:x' is for an add-constant beta estimator, with beta value
following the colon eg 'beta:0.01' [1]_. 'kt' is for the
Krichevsky-Trofimov estimator [2]_, which is equivalent to
'beta:0.5'.
References
----------
.. [1] T. Schurmann and P. Grassberger, "Entropy estimation of
symbol sequences," Chaos,vol. 6, no. 3, pp. 414--427, 1996.
.. [2] R. Krichevsky and V. Trofimov, "The performance of universal
encoding," IEEE Trans. Information Theory, vol. 27, no. 2,
pp. 199--207, Mar. 1981.
"""
calc = self.calc
# decimalise
if any([c in calc for c in ['HXY','HX']]):
if self.X_n > 1:
d_X = decimalise(self.X, self.X_n, self.X_m)
else:
# make 1D
d_X = self.X.reshape(self.X.size)
# unconditional probabilities
if ('HX' in calc) or ('ChiX' in calc):
self.PX = prob(d_X, self.X_dim, method=method)
if any([c in calc for c in ['HXY','HiX','HiXY','HY']]):
self.PY = _probcount(self.Ny,self.N,method)
if 'SiHXi' in calc:
for i in xrange(self.X_n):
self.PXi[:,i] = prob(self.X[i,:], self.X_m, method=method)
# conditional probabilities
if any([c in calc for c in ['HiXY','HXY','HshXY']]):
sstart=0
for i in xrange(self.Y_dim):
send = sstart+self.Ny[i]
indx = slice(sstart,send)
sstart = send
if 'HXY' in calc:
# output conditional ensemble
oce = d_X[indx]
if oce.size == 0:
print 'Warning: Null output conditional ensemble for ' + \
'output : ' + str(i)
else:
self.PXY[:,i] = prob(oce, self.X_dim, method=method)
if any([c in calc for c in ['HiX','HiXY','HshXY']]):
for j in xrange(self.X_n):
# output conditional ensemble for a single variable
oce = self.X[j,indx]
if oce.size == 0:
print 'Warning: Null independent output conditional ensemble for ' + \
'output : ' + str(i) + ', variable : ' + str(j)
else:
self.PXiY[:,j,i] = prob(oce, self.X_m, method=method)
if 'HshXY' in calc:
# shuffle
#np.random.shuffle(oce)
shfoce = np.random.permutation(oce)
self.Xsh[j,indx] = shfoce
# Pind(X) = <Pind(X|Y)>_y
if ('HiX' in calc) or ('ChiX' in calc):
# construct joint distribution
words = dec2base(np.atleast_2d(np.r_[0:self.X_dim]).T,self.X_m,self.X_n)
PiXY = np.zeros((self.X_dim, self.Y_dim))
PiXY = self.PXiY[words,np.r_[0:self.X_n]].prod(axis=1)
# average over Y
self.PiX = np.dot(PiXY,self.PY)
self.sampled = True
