def GetdG0(self, nH, z, nMg, T=default_T):
key = self._MakeKey(nH, z, nMg)
if key not in self.dgs:
return None
dG0_list = self.dgs[key]
return -(R*T) * log_sum_exp([x/(-R*T) for x in dG0_list])
def Squeeze(self, T=default_T):
"""Groups together all pseudoisomers that have the same key"""
squeezed_dgs = {}
for k, dG0_list in self.dgs.iteritems():
squeezed_dG0 = -(R*T) * log_sum_exp([x/(-R*T) for x in dG0_list])
squeezed_dgs[k] = [squeezed_dG0]
self.dgs = squeezed_dgs
def log_det(X):
if (X.shape[0] != X.shape[1]):
raise Exception("X is not a square matrix so its determinant cannot be calculated")
if (X.shape[0] == 1):
return X[0,0]
if (X.shape[0] == 2): # X is a 2x2 matrix
return(log_subt_exp(X[0,0]+X[1,1], X[1,0]+X[0,1]))
if (X.shape[0] == 3):
s_plus = log_sum_exp([X[0,0]+X[1,1]+X[2,2], X[0,2]+X[1,0]+X[2,1], X[0,1]+X[1,2]+X[2,0]])
s_minus = log_sum_exp([X[0,1]+X[1,0]+X[2,2], X[0,2]+X[1,1]+X[2,0], X[0,0]+X[1,2]+X[2,1]])
return log_subt_exp(s_plus, s_minus)
raise Exception("log_det is only implemented for matrices of size < 4")
def log_dot(X,Y):
if (X.shape[1] != Y.shape[0]):
raise Exception("The dimensions of the matrices do not match: (%d,%d) and (%d,%d)" % (X.shape[0], X.shape[1], Y.shape[0], Y.shape[1]))
R = zeros((X.shape[0], Y.shape[1]))
for i in range(X.shape[0]):
for j in range(Y.shape[1]):
R[i,j] = log_sum_exp([(X[i,k] + Y[k,j]) for k in range(X.shape[1])])
return R
def array_transform(dG0, nH, z, nMg, pH, pMg, I, T):
"""
dG0, nH and z - are the species parameters (can be vectors)
pH and I - are the conditions, must be scalars
returns the transformed gibbs energy: dG0'
"""
from toolbox.util import log_sum_exp
ddG0 = correction_function(nH, z, nMg, pH, pMg, I, T)
dG0_tag = dG0 + ddG0
return -R * T * log_sum_exp(dG0_tag / (-R * T))
def Transform(self, pH, pMg, I, T):
"""
Transform this set of pseudoisomers to a dG value at the
specified conditions.
"""
if not self.dgs:
raise ValueError("Cannot run Transform on an empty pseudoisomer map")
_v_dG0, v_dG0_tag, _v_nH, _v_z, _v_nMg = self._Transform(pH, pMg, I, T)
return -R * T * log_sum_exp(v_dG0_tag / (-R*T))
def array_transform(dG0, nH, z, nMg, pH, pMg, I, T):
"""
dG0, nH and z - are the species parameters (can be vectors)
pH and I - are the conditions, must be scalars
returns the transformed gibbs energy: dG0'
"""
from toolbox.util import log_sum_exp
ddG0 = correction_function(nH, z, nMg, pH, pMg, I, T)
dG0_tag = dG0 + ddG0
return -R * T * log_sum_exp(dG0_tag / (-R*T))
def log_dot(X, Y):
if (X.shape[1] != Y.shape[0]):
raise Exception(
"The dimensions of the matrices do not match: (%d,%d) and (%d,%d)"
% (X.shape[0], X.shape[1], Y.shape[0], Y.shape[1]))
R = zeros((X.shape[0], Y.shape[1]))
for i in range(X.shape[0]):
for j in range(Y.shape[1]):
R[i, j] = log_sum_exp([(X[i, k] + Y[k, j])
for k in range(X.shape[1])])
return R
def log_det(X):
if (X.shape[0] != X.shape[1]):
raise Exception(
"X is not a square matrix so its determinant cannot be calculated")
if (X.shape[0] == 1):
return X[0, 0]
if (X.shape[0] == 2): # X is a 2x2 matrix
return (log_subt_exp(X[0, 0] + X[1, 1], X[1, 0] + X[0, 1]))
if (X.shape[0] == 3):
s_plus = log_sum_exp([
X[0, 0] + X[1, 1] + X[2, 2], X[0, 2] + X[1, 0] + X[2, 1],
X[0, 1] + X[1, 2] + X[2, 0]
])
s_minus = log_sum_exp([
X[0, 1] + X[1, 0] + X[2, 2], X[0, 2] + X[1, 1] + X[2, 0],
X[0, 0] + X[1, 2] + X[2, 1]
])
return log_subt_exp(s_plus, s_minus)
raise Exception("log_det is only implemented for matrices of size < 4")
def GetDeltaDeltaG0(self, pH, I, pMg, T, nH=None, nMg=0):
"""
Return:
the transformed ddG0 = dG0'_f - dG0_f
Note:
assume that the dG0_f of one of the psuedoisomers
(according to the given nH) is 0
"""
if nH is None:
nH = self.min_nH
pseudoisomer_matrix = self.GetTransformedDeltaGs(pH, I, pMg, T, nH=nH, nMg=nMg)
ddG0_f = -R * T * log_sum_exp([dG0_tag / (-R*T) for (_nH, _z, _nMg, dG0_tag) in pseudoisomer_matrix])
return ddG0_f
def _Bolzmann(self, pH, pMg, I, T):
"""
Returns a dictionary with the same keys as self.dgs, but the
values are the relative abundance of that species at the
specified conditions
"""
_v_dG0, v_dG0_tag, v_nH, v_z, v_nMg = self._Transform(pH, pMg, I, T)
minus_E_over_RT = [-E / (R*T) for E in v_dG0_tag]
total = log_sum_exp(minus_E_over_RT)
species2abundance = {}
for i in xrange(len(v_dG0_tag)):
key = PseudoisomerMap._MakeKey(v_nH[i], v_z[i], v_nMg[i])
abundance = pylab.exp(minus_E_over_RT[i] - total)
species2abundance[key] = species2abundance.get(key, 0.0) + abundance
return species2abundance
def GetDeltaDeltaG0(self, pH, I, pMg, T, nH=None, nMg=0):
"""
Return:
the transformed ddG0 = dG0'_f - dG0_f
Note:
assume that the dG0_f of one of the psuedoisomers
(according to the given nH) is 0
"""
if nH is None:
nH = self.min_nH
pseudoisomer_matrix = self.GetTransformedDeltaGs(pH,
I,
pMg,
T,
nH=nH,
nMg=nMg)
ddG0_f = -R * T * log_sum_exp([
dG0_tag / (-R * T)
for (_nH, _z, _nMg, dG0_tag) in pseudoisomer_matrix
])
return ddG0_f
