def _MakeDrivingForceConstraints(self, ln_conc, driving_force_lb=0):
"""
driving_force_lb can either be a cvxpy variable use later in the optimization
or a scalar, which sets it as a constraint. By default the lower bound is 0.
"""
constraints = []
S = cvxpy.matrix(self.S)
dg0r_primes = cvxpy.matrix(self.dG0_r_prime)
for i in xrange(self.Nr):
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(self.dG0_r_prime[0, i]):
continue
curr_dgr = dg0r_primes[0, i] + RT * ln_conc * S[:, i]
if self.fluxes[0, i] == 0:
constraints += cvxpy.eq(curr_dgr, 0)
else:
if self.normalization == DeltaGNormalization.DIVIDE_BY_FLUX:
motive_force = -curr_dgr * (1.0 / self.fluxes[0, i])
elif self.normalization == DeltaGNormalization.TIMES_FLUX:
motive_force = -curr_dgr * self.fluxes[0, i]
elif self.normalization == DeltaGNormalization.SIGN_FLUX:
motive_force = -curr_dgr * np.sign(self.fluxes[0, i])
else:
raise ValueError("bad value for normalization method: " +
str(self.normalization))
constraints += [cvxpy.geq(motive_force, driving_force_lb)]
return constraints
def _MakeDrivingForceConstraints(self, ln_conc, driving_force_lb=0):
"""
driving_force_lb can either be a cvxpy variable use later in the optimization
or a scalar, which sets it as a constraint. By default the lower bound is 0.
"""
constraints = []
S = cvxpy.matrix(self.S)
dg0r_primes = cvxpy.matrix(self.dG0_r_prime)
for i in xrange(self.Nr):
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(self.dG0_r_prime[0, i]):
continue
curr_dgr = dg0r_primes[0, i] + RT * ln_conc * S[:, i]
if self.fluxes[0, i] == 0:
constraints += cvxpy.eq(curr_dgr, 0)
else:
if self.normalization == DeltaGNormalization.DIVIDE_BY_FLUX:
motive_force = -curr_dgr * (1.0 / self.fluxes[0, i])
elif self.normalization == DeltaGNormalization.TIMES_FLUX:
motive_force = -curr_dgr * self.fluxes[0, i]
elif self.normalization == DeltaGNormalization.SIGN_FLUX:
motive_force = -curr_dgr * np.sign(self.fluxes[0, i])
else:
raise ValueError("bad value for normalization method: "
+ str(self.normalization))
constraints += [cvxpy.geq(motive_force, driving_force_lb)]
return constraints
def _MakeMinimalFeasbileConcentrationProblem(self, bounds=None, c_range=(1e-6, 1e-2)):
# Define and apply the constraints on the concentrations
constraints = []
# Define and apply the constraints on the concentrations
ln_conc = cvxpy.variable(1, self.Nc, name='lnC')
constraints += self._MakeLnConcentratonBounds(ln_conc, bounds=bounds,
c_range=c_range)
# find the row vector describing the overall stoichiometry
S = cvxpy.matrix(self.S)
dg0r_primes = cvxpy.matrix(self.dG0_r_prime)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
for i in xrange(self.Nr):
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(self.dG0_r_prime[0, i]):
continue
curr_dgr = dg0r_primes[0, i] + RT * ln_conc * S[:, i]
if self.fluxes[0, i] != 0:
constraints.append(cvxpy.leq(curr_dgr * np.sign(self.fluxes[0, i]),
self.DEFAULT_REACTION_UB))
constraints.append(cvxpy.geq(curr_dgr * np.sign(self.fluxes[0, i]),
self.DEFAULT_REACTION_LB))
else:
constraints.append(cvxpy.eq(curr_dgr, 0))
# Set the constraints
return ln_conc, constraints
def _cqp(D, o, k, m, N):
''' solves using cvxpy '''
# cast to object.
D = cvxpy.matrix(D)
N = cvxpy.matrix(N)
o = cvxpy.matrix(o)
# create variables.
f = cvxpy.variable(k, 1, name='f')
x=cvxpy.variable(m, 1, name='x')
y=cvxpy.variable(m, 1, name='y')
# create constraints.
geqs = cvxpy.greater_equals(f,0.0)
#TO DO: Sum of all f = sum of observed reads classes (and not equal to 1)
sum1 = cvxpy.equals(cvxpy.sum(f), 1.0)
#sum1 = cvxpy.equals(cvxpy.sum(f), sum_obs_freq)
#3
#dev = cvxpy.equals(D*f-o-x,0.0)
#4. matrix N (m x m) * x - y = 0
sizeConstr = cvxpy.equals(N*x-y,0.0)
#Check now to do N^2
#sizeConstr = cvxpy.equals(N^2*x-y,0.0)
#This might not work but try
#sizeConstr = cvxpy.equals(x/N-y,0.0)
#constrs = [geqs, sum1, dev, sizeConstr]
constrs = [geqs, sum1]
log.debug('\tin _cqp function: \n\t\tPrint matrices shapes:')
log.debug('\t\t\t%s', D.shape)
log.debug('\t\t\t%s', f.shape)
log.debug('\t\t\t%s', o.shape)
# create the program.
#p = cvxpy.program(cvxpy.minimize(cvxpy.norm2(y)),constraints=constrs)
p = cvxpy.program(cvxpy.minimize(cvxpy.norm2(D*f-o)),constraints=constrs)
p.options['abstol'] = 1e-6 ## 'abstol' - Absolute accuracy Default: 1e-7
p.options['reltol'] = 1e-5 ## 'reltol' - Relative accuracy Default: 1e-6
p.options['feastol'] = 1e-5 ## 'feastol' - Tolerance for feasibility conditions Default: 1e-6
p.options['maxiters'] = 500 ## 'maxiters' - Maximum number of iterations Default: 100
# solve the program.
p.solve(quiet=True)
# return results.
#print np.around(f.value, decimals=20)
#print "Print using loop"
getcontext().prec = 20
#for i in f.value:
# temp_fi=str(i).strip('[]')
# print temp_fi
return f.value
def _GetTotalReactionEnergy(self, c_range=(1e-6, 1e-2), bounds=None, min_driving_force=0):
constraints = []
# Define and apply the constraints on the concentrations
ln_conc = cvxpy.variable(1, self.Nc, name='lnC')
constraints += self._MakeLnConcentratonBounds(ln_conc, bounds=bounds,
c_range=c_range)
# find the row vector describing the overall stoichiometry
S = cvxpy.matrix(self.S)
f = cvxpy.matrix(self.fluxes)
g0 = cvxpy.matrix(self.dG0_r_prime)
g = g0 + RT * ln_conc * S
total_g = f * g.T
constraints += self._MakeDrivingForceConstraints(ln_conc, min_driving_force)
return ln_conc, constraints, total_g
def _MakeMinimumFeasbileConcentrationsProblem(self,
bounds=None,
c_range=(1e-6, 1e-2)):
"""Creates the CVXOPT problem for finding minimum total concentrations.
Returns:
Two tuple (ln_concentrations var, problem).
"""
assert self.dG0_f_prime is not None
constraints = []
# Define and apply the constraints on the concentrations
ln_conc = cvxpy.variable(1, self.Nc, name='lnC')
constraints += self._MakeLnConcentratonBounds(ln_conc,
bounds=bounds,
c_range=c_range)
# Make the objective and problem.
S = cvxpy.matrix(self.S)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
dgf_primes = RT * ln_conc + cvxpy.matrix(self.dG0_f_prime)
for i in xrange(self.Nr):
if self.fluxes[0, i] > 0:
constraints.append(
cvxpy.leq(S[i, :] * dgf_primes, self.DEFAULT_REACTION_UB))
constraints.append(
cvxpy.geq(S[i, :] * dgf_primes, self.DEFAULT_REACTION_LB))
elif self.fluxes[0, i] == 0:
constraints.append(cvxpy.eq(S[i, :] * dgf_primes, 0))
else:
constraints.append(
cvxpy.geq(S[i, :] * dgf_primes, -self.DEFAULT_REACTION_UB))
constraints.append(
cvxpy.leq(S[i, :] * dgf_primes, -self.DEFAULT_REACTION_LB))
return ln_conc, constraints
def _MakeMinimumFeasbileConcentrationsProblem(self, bounds=None,
c_range=(1e-6, 1e-2)):
"""Creates the CVXOPT problem for finding minimum total concentrations.
Returns:
Two tuple (ln_concentrations var, problem).
"""
assert self.dG0_f_prime is not None
constraints = []
# Define and apply the constraints on the concentrations
ln_conc = cvxpy.variable(1, self.Nc, name='lnC')
constraints += self._MakeLnConcentratonBounds(ln_conc, bounds=bounds,
c_range=c_range)
# Make the objective and problem.
S = cvxpy.matrix(self.S)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
dgf_primes = RT * ln_conc + cvxpy.matrix(self.dG0_f_prime)
for i in xrange(self.Nr):
if self.fluxes[0, i] > 0:
constraints.append(cvxpy.leq(S[i, :] * dgf_primes,
self.DEFAULT_REACTION_UB))
constraints.append(cvxpy.geq(S[i, :] * dgf_primes,
self.DEFAULT_REACTION_LB))
elif self.fluxes[0, i] == 0:
constraints.append(cvxpy.eq(S[i, :] * dgf_primes,
0))
else:
constraints.append(cvxpy.geq(S[i, :] * dgf_primes,
-self.DEFAULT_REACTION_UB))
constraints.append(cvxpy.leq(S[i, :] * dgf_primes,
-self.DEFAULT_REACTION_LB))
return ln_conc, constraints
def _MakeMinimalFeasbileConcentrationProblem(self,
bounds=None,
c_range=(1e-6, 1e-2)):
# Define and apply the constraints on the concentrations
constraints = []
# Define and apply the constraints on the concentrations
ln_conc = cvxpy.variable(1, self.Nc, name='lnC')
constraints += self._MakeLnConcentratonBounds(ln_conc,
bounds=bounds,
c_range=c_range)
# find the row vector describing the overall stoichiometry
S = cvxpy.matrix(self.S)
dg0r_primes = cvxpy.matrix(self.dG0_r_prime)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
for i in xrange(self.Nr):
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(self.dG0_r_prime[0, i]):
continue
curr_dgr = dg0r_primes[0, i] + RT * ln_conc * S[:, i]
if self.fluxes[0, i] != 0:
constraints.append(
cvxpy.leq(curr_dgr * np.sign(self.fluxes[0, i]),
self.DEFAULT_REACTION_UB))
constraints.append(
cvxpy.geq(curr_dgr * np.sign(self.fluxes[0, i]),
self.DEFAULT_REACTION_LB))
else:
constraints.append(cvxpy.eq(curr_dgr, 0))
# Set the constraints
return ln_conc, constraints
def _MakeLnConcentratonBounds(self, ln_conc, bounds=None, c_range=None):
"""Make bounds on logarithmic concentrations."""
_c_range = c_range or self.DEFAULT_C_RANGE
c_lower, c_upper = c_range
ln_conc_lb = np.ones((1, self.Nc)) * np.log(c_lower)
ln_conc_ub = np.ones((1, self.Nc)) * np.log(c_upper)
if bounds:
for i, bound in enumerate(bounds):
lb, ub = bound
log_lb = np.log(lb or c_lower)
log_ub = np.log(ub or c_upper)
if log_lb > log_ub:
raise Exception("Lower bound is greater than upper bound: "
"%d > %d" % (log_lb, log_ub))
elif abs(log_lb - log_ub) < 1e-2:
log_lb = log_ub - 1e-2
ln_conc_lb[0, i] = log_lb
ln_conc_ub[0, i] = log_ub
return [cvxpy.geq(ln_conc, cvxpy.matrix(ln_conc_lb)) + \
cvxpy.leq(ln_conc, cvxpy.matrix(ln_conc_ub))]
def _GetTotalReactionEnergy(self,
c_range=(1e-6, 1e-2),
bounds=None,
min_driving_force=0):
constraints = []
# Define and apply the constraints on the concentrations
ln_conc = cvxpy.variable(1, self.Nc, name='lnC')
constraints += self._MakeLnConcentratonBounds(ln_conc,
bounds=bounds,
c_range=c_range)
# find the row vector describing the overall stoichiometry
S = cvxpy.matrix(self.S)
f = cvxpy.matrix(self.fluxes)
g0 = cvxpy.matrix(self.dG0_r_prime)
g = g0 + RT * ln_conc * S
total_g = f * g.T
constraints += self._MakeDrivingForceConstraints(
ln_conc, min_driving_force)
return ln_conc, constraints, total_g
def _MakeLnConcentratonBounds(self, ln_conc, bounds=None, c_range=None):
"""Make bounds on logarithmic concentrations."""
_c_range = c_range or self.DEFAULT_C_RANGE
c_lower, c_upper = c_range
ln_conc_lb = np.ones((1, self.Nc)) * np.log(c_lower)
ln_conc_ub = np.ones((1, self.Nc)) * np.log(c_upper)
if bounds:
for i, bound in enumerate(bounds):
lb, ub = bound
log_lb = np.log(lb or c_lower)
log_ub = np.log(ub or c_upper)
if log_lb > log_ub:
raise Exception("Lower bound is greater than upper bound: "
"%d > %d" % (log_lb, log_ub))
elif abs(log_lb - log_ub) < 1e-2:
log_lb = log_ub - 1e-2
ln_conc_lb[0, i] = log_lb
ln_conc_ub[0, i] = log_ub
return [cvxpy.geq(ln_conc, cvxpy.matrix(ln_conc_lb)) + \
cvxpy.leq(ln_conc, cvxpy.matrix(ln_conc_ub))]
def fit_ellipse_eps_insensitive(x, y):
"""
fit ellipoid using epsilon-insensitive loss
"""
x = numpy.array(x)
y = numpy.array(y)
print "shapes", x.shape, y.shape
assert len(x) == len(y)
N = len(x)
D = 5
dat = numpy.zeros((N, D))
dat[:,0] = x*x
dat[:,1] = y*y
#dat[:,2] = y*x
dat[:,2] = x
dat[:,3] = y
dat[:,4] = numpy.ones(N)
print dat.shape
dat = cvxpy.matrix(dat)
#### parameters
# data
X = cvxpy.parameter(N, D, name="X")
# parameter for eps-insensitive loss
eps = cvxpy.parameter(1, name="eps")
#### varibales
# parameter vector
theta = cvxpy.variable(D, name="theta")
# dim = (N x 1)
s = cvxpy.variable(N, name="s")
t = cvxpy.variable(N, name="t")
# simple objective
objective = cvxpy.sum(t)
# create problem
p = cvxpy.program(cvxpy.minimize(objective))
# add constraints
# (N x D) * (D X 1) = (N X 1)
p.constraints.append(X*theta <= s)
p.constraints.append(-X*theta <= s)
p.constraints.append(s - eps <= t)
p.constraints.append(0 <= t)
#p.constraints.append(theta[4] == 1)
# trace constraint
p.constraints.append(theta[0] + theta[1] == 1)
###### set values
X.value = dat
eps.value = 0.0
#solver = "mosek"
#p.solve(lpsolver=solver)
p.solve()
cvxpy.printval(theta)
w = numpy.array(cvxpy.value(theta))
#cvxpy.printval(s)
#cvxpy.printval(t)
## For clarity, fill in the quadratic form variables
A = numpy.zeros((2,2))
A[0,0] = w[0]
A.ravel()[1:3] = 0#w[2]
A[1,1] = w[1]
bv = w[2:4]
c = w[4]
## find parameters
z, a, b, alpha = util.conic2parametric(A, bv, c)
return z, a, b, alpha
def MinimizeConcentration(self,
metabolite_index=None,
concentration_bounds=None):
"""Finds feasible concentrations minimizing the concentration
of metabolite i.
Args:
metabolite_index: the index of the metabolite to minimize.
if == None, minimize the sum of all concentrations.
concentration_bounds: the Bounds objects setting concentration bounds.
"""
my_bounds = concentration_bounds or self.DefaultConcentrationBounds()
ln_conc = cvxpy.variable(m=1, n=self.Ncompounds, name='lnC')
ln_conc_lb, ln_conc_ub = my_bounds.GetLnBounds(self.compounds)
constr = [
cvxpy.geq(ln_conc, cvxpy.matrix(ln_conc_lb)),
cvxpy.leq(ln_conc, cvxpy.matrix(ln_conc_ub))
]
my_dG0_r_primes = np.matrix(self.dG0_r_prime)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
S = np.matrix(self.S)
for i, flux in enumerate(self.fluxes):
curr_dg0 = my_dG0_r_primes[0, i]
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(curr_dg0):
continue
rcol = cvxpy.matrix(S[:, i])
curr_dgr = curr_dg0 + RT * ln_conc * rcol
if flux == 0:
constr.append(cvxpy.eq(curr_dgr, 0.0))
else:
constr.append(cvxpy.leq(curr_dgr, 0.0))
objective = None
if metabolite_index is not None:
my_conc = ln_conc[0, metabolite_index]
objective = cvxpy.minimize(cvxpy.exp(my_conc))
else:
objective = cvxpy.minimize(cvxpy.sum(cvxpy.exp(ln_conc)))
name = 'CONC_OPT'
if metabolite_index:
name = 'CONC_%d_OPT' % metabolite_index
problem = cvxpy.program(objective, constr, name=name)
optimum = problem.solve(quiet=True)
"""
status = problem.solve(quiet=True)
if status != 'optimal':
status = optimized_pathway.OptimizationStatus.Infeasible(
'Pathway infeasible given bounds.')
return ConcentrationOptimizedPathway(
self._model, self._thermo,
my_bounds, optimization_status=status)
"""
opt_ln_conc = np.matrix(np.array(ln_conc.value))
result = ConcentrationOptimizedPathway(
self._model,
self._thermo,
my_bounds,
optimal_value=optimum,
optimal_ln_metabolite_concentrations=opt_ln_conc)
return result
# Add noise to signal
rSig = signal + noise
rSig = abs(rSig) #phase is not used in MRI
# Choose regularization parameter
# lambda > lambda_max -> zero solution
lambda_max = 2*norm(dot(nA.T, rSig.T), np.inf)
lamb = 1.0e-8*lambda_max
print('Solving L1 penalized system with cvxpy...')
coefs = cvx.variable(n_qpnts,1)
A = cvx.matrix(nA)
rhs = cvx.matrix(rSig).T
objective = cvx.minimize(cvx.norm2(A*coefs - rhs) +
lamb*cvx.norm1(coefs) )
constraints = [cvx.geq(coefs,0.0)]
prob = cvx.program(objective, constraints)
# Call the solver
prob.solve(quiet=True) #Use quiet=True to suppress output
# Convert the cvxmod objects to plain numpy arrays for further processing
nd_coefs_l1 = np.array(coefs.value).squeeze()
# Cutoff those coefficients that are less than cutoff
def _cqp(D, o, k, m, N):
''' solves using cvxpy '''
# cast to object.
D = cvxpy.matrix(D)
N = cvxpy.matrix(N)
o = cvxpy.matrix(o)
# create variables.
f = cvxpy.variable(k, 1, name='f')
x = cvxpy.variable(m, 1, name='x')
y = cvxpy.variable(m, 1, name='y')
# create constraints.
geqs = cvxpy.greater_equals(f, 0.0)
#TO DO: Sum of all f = sum of observed reads classes (and not equal to 1)
sum1 = cvxpy.equals(cvxpy.sum(f), 1.0)
#sum1 = cvxpy.equals(cvxpy.sum(f), sum_obs_freq)
#3
#dev = cvxpy.equals(D*f-o-x,0.0)
#4. matrix N (m x m) * x - y = 0
sizeConstr = cvxpy.equals(N * x - y, 0.0)
#Check now to do N^2
#sizeConstr = cvxpy.equals(N^2*x-y,0.0)
#This might not work but try
#sizeConstr = cvxpy.equals(x/N-y,0.0)
#constrs = [geqs, sum1, dev, sizeConstr]
constrs = [geqs, sum1]
log.debug('\tin _cqp function: \n\t\tPrint matrices shapes:')
log.debug('\t\t\t%s', D.shape)
log.debug('\t\t\t%s', f.shape)
log.debug('\t\t\t%s', o.shape)
# create the program.
#p = cvxpy.program(cvxpy.minimize(cvxpy.norm2(y)),constraints=constrs)
p = cvxpy.program(cvxpy.minimize(cvxpy.norm2(D * f - o)),
constraints=constrs)
p.options['abstol'] = 1e-6 ## 'abstol' - Absolute accuracy Default: 1e-7
p.options['reltol'] = 1e-5 ## 'reltol' - Relative accuracy Default: 1e-6
p.options[
'feastol'] = 1e-5 ## 'feastol' - Tolerance for feasibility conditions Default: 1e-6
p.options[
'maxiters'] = 500 ## 'maxiters' - Maximum number of iterations Default: 100
# solve the program.
p.solve(quiet=True)
# return results.
#print np.around(f.value, decimals=20)
#print "Print using loop"
getcontext().prec = 20
#for i in f.value:
# temp_fi=str(i).strip('[]')
# print temp_fi
return f.value
#!/usr/bin/python
import cvxpy
import numpy
S = cvxpy.matrix([[-1, 1, 0],
[0, -1, 1]])
Km = cvxpy.matrix([[1e-4, 0, 0],
[0, 1e-4, 0]])
kcat = cvxpy.matrix([[100],[100]])
m_plus = numpy.abs(numpy.clip(S, -1000, 0))
c = cvxpy.variable(3, 1, name='concentrations')
opt = cvxpy.minimize()
#!/usr/bin/python import cvxpy import numpy S = cvxpy.matrix([[-1, 1, 0], [0, -1, 1]]) Km = cvxpy.matrix([[1e-4, 0, 0], [0, 1e-4, 0]]) kcat = cvxpy.matrix([[100], [100]]) m_plus = numpy.abs(numpy.clip(S, -1000, 0)) c = cvxpy.variable(3, 1, name='concentrations') opt = cvxpy.minimize()
def FindMTDF(self, concentration_bounds=None, normalization=None):
"""Finds the MTDF.
Args:
bounds: the Bounds objects setting concentration bounds.
"""
my_bounds = concentration_bounds or self.DefaultConcentrationBounds()
normalization = normalization or self.DeltaGNormalization.DEFAULT
# Constrain concentrations
ln_conc = cvxpy.variable(m=1, n=self.Ncompounds, name='lnC')
ln_conc_lb, ln_conc_ub = my_bounds.GetLnBounds(self.compounds)
constr = [cvxpy.geq(ln_conc, cvxpy.matrix(ln_conc_lb)),
cvxpy.leq(ln_conc, cvxpy.matrix(ln_conc_ub))]
# Make the objective
motive_force_lb = cvxpy.variable(name='B')
my_dG0_r_primes = np.matrix(self.dG0_r_prime)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
S = np.matrix(self.S)
for i, flux in enumerate(self.fluxes):
curr_dg0 = my_dG0_r_primes[0, i]
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(curr_dg0):
continue
rcol = cvxpy.matrix(S[:, i])
curr_dgr = curr_dg0 + RT * ln_conc * rcol
if flux == 0:
constr.append(cvxpy.eq(curr_dgr, 0))
else:
motive_force = self.DeltaGNormalization.NormalizeDGByFlux(
curr_dgr, flux, normalization)
constr.append(cvxpy.geq(motive_force, motive_force_lb))
objective = cvxpy.maximize(motive_force_lb)
problem = cvxpy.program(objective, constr, name='MTDF_OPT')
problem.solve(quiet=True)
"""
if status != 'optimal':
status = optimized_pathway.OptimizationStatus.Infeasible(
'Pathway infeasible given bounds.')
return MTDFOptimizedPathway(
self._model, self._thermo,
my_bounds, optimization_status=status)
"""
mtdf = float(motive_force_lb.value)
opt_ln_conc = np.matrix(np.array(ln_conc.value))
result = MTDFOptimizedPathway(
self._model, self._thermo,
my_bounds, optimal_value=mtdf,
optimal_ln_metabolite_concentrations=opt_ln_conc)
result.SetNormalization(normalization)
return result
def fit_ellipse_stack2(dx, dy, dz, di, norm_type="l2"):
"""
fit ellipoid using squared loss
idea to learn all stacks together including smoothness
"""
#TODO create flag for norm1 vs norm2
assert norm_type in ["l1", "l2", "huber"]
# sanity check
assert len(dx) == len(dy)
assert len(dx) == len(dz)
assert len(dx) == len(di)
# unique zs
dat = defaultdict(list)
# resort data
for idx in range(len(dx)):
dat[dz[idx]].append( [dx[idx], dy[idx], di[idx]] )
# init ret
ellipse_stack = []
for idx in range(max(dz)):
ellipse_stack.append(Ellipse(0, 0, idx, 1, 1, 0))
total_N = len(dx)
M = len(dat.keys())
#D = 5
D = 4
X_matrix = []
thetas = []
slacks = []
eps_slacks = []
mean_di = float(numpy.mean(di))
for z in dat.keys():
x = numpy.array(dat[z])[:,0]
y = numpy.array(dat[z])[:,1]
# intensities
i = numpy.array(dat[z])[:,2]
ity = numpy.diag(i) / mean_di
# dimensionality
N = len(x)
d = numpy.zeros((N, D))
d[:,0] = x*x
d[:,1] = y*y
#d[:,2] = x*y
d[:,2] = x
d[:,3] = y
#d[:,4] = numpy.ones(N)
#d[:,0] = x*x
#d[:,1] = y*y
#d[:,2] = x*y
#d[:,3] = x
#d[:,4] = y
#d[:,5] = numpy.ones(N)
# consider intensities
old_shape = d.shape
#d = numpy.dot(ity, d)
assert d.shape == old_shape
print d.shape
d = cvxpy.matrix(d)
#### parameters
# da
X = cvxpy.parameter(N, D, name="X" + str(z))
X.value = d
X_matrix.append(X)
#### varibales
# parameter vector
theta = cvxpy.variable(D, name="theta" + str(z))
thetas.append(theta)
# construct obj
objective = 0
print "norm type", norm_type
for i in xrange(M):
if norm_type == "l1":
objective += cvxpy.norm1(X_matrix[i] * thetas[i] + 1.0)
if norm_type == "l2":
objective += cvxpy.norm2(X_matrix[i] * thetas[i] + 1.0)
#TODO these need to be summed
#objective += cvxpy.huber(X_matrix[i] * thetas[i], 1)
#objective += cvxpy.deadzone(X_matrix[i] * thetas[i], 1)
# add smoothness regularization
reg_const = float(total_N) / float(M-1)
for i in xrange(M-1):
objective += reg_const * cvxpy.norm2(thetas[i] - thetas[i+1])
# create problem
p = cvxpy.program(cvxpy.minimize(objective))
prob = p
import ipdb
ipdb.set_trace()
# add constraints
#for i in xrange(M):
# #p.constraints.append(cvxpy.eq(thetas[i][0,:] + thetas[i][1,:], 1))
# p.constraints.append(cvxpy.eq(thetas[i][4,:], 1))
# set solver settings
p.options['reltol'] = 1e-1
p.options['abstol'] = 1e-1
#p.options['feastol'] = 1e-1
# invoke solver
p.solve()
# wrap up result
ellipse_stack = {}
active_layers = dat.keys()
assert len(active_layers) == M
for i in xrange(M):
w = numpy.array(thetas[i].value)
## For clarity, fill in the quadratic form variables
#A = numpy.zeros((2,2))
#A[0,0] = w[0]
#A.ravel()[1:3] = w[2]
#A[1,1] = w[1]
#bv = w[3:5]
#c = w[5]
A = numpy.zeros((2,2))
A[0,0] = w[0]
A.ravel()[1:3] = 0 #w[2]
A[1,1] = w[1]
#bv = w[2:4]
bv = w[2:]
#c = w[4]
c = 1.0
## find parameters
z, a, b, alpha = util.conic2parametric(A, bv, c)
print "layer (i,z,a,b,alpha):", i, z, a, b, alpha
layer = active_layers[i]
ellipse_stack[layer] = Ellipse(z[0], z[1], layer, a, b, alpha)
return ellipse_stack
def FindMTDF(self, concentration_bounds=None, normalization=None):
"""Finds the MTDF.
Args:
bounds: the Bounds objects setting concentration bounds.
"""
my_bounds = concentration_bounds or self.DefaultConcentrationBounds()
normalization = normalization or self.DeltaGNormalization.DEFAULT
# Constrain concentrations
ln_conc = cvxpy.variable(m=1, n=self.Ncompounds, name='lnC')
ln_conc_lb, ln_conc_ub = my_bounds.GetLnBounds(self.compounds)
constr = [
cvxpy.geq(ln_conc, cvxpy.matrix(ln_conc_lb)),
cvxpy.leq(ln_conc, cvxpy.matrix(ln_conc_ub))
]
# Make the objective
motive_force_lb = cvxpy.variable(name='B')
my_dG0_r_primes = np.matrix(self.dG0_r_prime)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
S = np.matrix(self.S)
for i, flux in enumerate(self.fluxes):
curr_dg0 = my_dG0_r_primes[0, i]
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(curr_dg0):
continue
rcol = cvxpy.matrix(S[:, i])
curr_dgr = curr_dg0 + RT * ln_conc * rcol
if flux == 0:
constr.append(cvxpy.eq(curr_dgr, 0))
else:
motive_force = self.DeltaGNormalization.NormalizeDGByFlux(
curr_dgr, flux, normalization)
constr.append(cvxpy.geq(motive_force, motive_force_lb))
objective = cvxpy.maximize(motive_force_lb)
problem = cvxpy.program(objective, constr, name='MTDF_OPT')
problem.solve(quiet=True)
"""
if status != 'optimal':
status = optimized_pathway.OptimizationStatus.Infeasible(
'Pathway infeasible given bounds.')
return MTDFOptimizedPathway(
self._model, self._thermo,
my_bounds, optimization_status=status)
"""
mtdf = float(motive_force_lb.value)
opt_ln_conc = np.matrix(np.array(ln_conc.value))
result = MTDFOptimizedPathway(
self._model,
self._thermo,
my_bounds,
optimal_value=mtdf,
optimal_ln_metabolite_concentrations=opt_ln_conc)
result.SetNormalization(normalization)
return result
def MinimizeConcentration(self, metabolite_index=None,
concentration_bounds=None):
"""Finds feasible concentrations minimizing the concentration
of metabolite i.
Args:
metabolite_index: the index of the metabolite to minimize.
if == None, minimize the sum of all concentrations.
concentration_bounds: the Bounds objects setting concentration bounds.
"""
my_bounds = concentration_bounds or self.DefaultConcentrationBounds()
ln_conc = cvxpy.variable(m=1, n=self.Ncompounds, name='lnC')
ln_conc_lb, ln_conc_ub = my_bounds.GetLnBounds(self.compounds)
constr = [cvxpy.geq(ln_conc, cvxpy.matrix(ln_conc_lb)),
cvxpy.leq(ln_conc, cvxpy.matrix(ln_conc_ub))]
my_dG0_r_primes = np.matrix(self.dG0_r_prime)
# Make flux-based constraints on reaction free energies.
# All reactions must have negative dGr in the direction of the flux.
# Reactions with a flux of 0 must be in equilibrium.
S = np.matrix(self.S)
for i, flux in enumerate(self.fluxes):
curr_dg0 = my_dG0_r_primes[0, i]
# if the dG0 is unknown, this reaction imposes no new constraints
if np.isnan(curr_dg0):
continue
rcol = cvxpy.matrix(S[:, i])
curr_dgr = curr_dg0 + RT * ln_conc * rcol
if flux == 0:
constr.append(cvxpy.eq(curr_dgr, 0.0))
else:
constr.append(cvxpy.leq(curr_dgr, 0.0))
objective = None
if metabolite_index is not None:
my_conc = ln_conc[0, metabolite_index]
objective = cvxpy.minimize(cvxpy.exp(my_conc))
else:
objective = cvxpy.minimize(
cvxpy.sum(cvxpy.exp(ln_conc)))
name = 'CONC_OPT'
if metabolite_index:
name = 'CONC_%d_OPT' % metabolite_index
problem = cvxpy.program(objective, constr, name=name)
optimum = problem.solve(quiet=True)
"""
status = problem.solve(quiet=True)
if status != 'optimal':
status = optimized_pathway.OptimizationStatus.Infeasible(
'Pathway infeasible given bounds.')
return ConcentrationOptimizedPathway(
self._model, self._thermo,
my_bounds, optimization_status=status)
"""
opt_ln_conc = np.matrix(np.array(ln_conc.value))
result = ConcentrationOptimizedPathway(
self._model, self._thermo,
my_bounds, optimal_value=optimum,
optimal_ln_metabolite_concentrations=opt_ln_conc)
return result
def ACT2Corrected(self,gene,num_iterations=5):
"""
Next steps: Some way to preserve flows at divergence nodes
One way could be reallocate flows at all divergence nodes in the original ratio and fix it
Iterate 10 times
"""
inwgs=self.wgsdict[gene]
outwgs=inwgs
component1=1.0
for iteri in range(num_iterations):
component1=1.0-iteri*1.0/num_iterations
wgs=addwgs(inwgs,outwgs,component1)
A,B,X=self.wgs2problem(wgs)
Xvar = cvx.variable(len(X),1)
A=cvx.matrix(A)
B=cvx.matrix(B)
B=B.T
p = cvx.program(cvx.minimize(cvx.norm2(A*Xvar-B)),[cvx.geq(Xvar,0.0)])
try:
p.solve(quiet=1)
except:
message='Could not solve for %s'%(gene)
common.printstatus(message,'W',common.func_name(),1)
return (outwgs,100.0)
if iteri==0: # Get optimal value
err=cvx.norm2(A*Xvar-B)
#print err.value/len(X)
Xval=Xvar.T.value.tolist()[0]
X_corr= [a[:] for a in X]
for i in range(len(Xval)):
X_corr[i][3]=int(Xval[i]*100)/100.0
#print X_corr
exonlist=[[a[1],a[2]] for a in X_corr if a[0]==2]
exonwtlist=[a[3] for a in X_corr if a[0]==2]
#print 'E',exonlist
intronlist=[]
intronwtlist=[]
splicelist=[[a[1],a[2]] for a in X_corr if a[0]==3]
splicewtlist=[a[3] for a in X_corr if a[0]==3]
removelist=[]
for i in range(len(exonlist)):
exon=exonlist[i]
if exon in splicelist:
exonwt=exonwtlist[i]
intronlist.append([exon[0]+1,exon[1]-1])
intronwtlist.append(exonwt)
removelist.append(i)
removelist.reverse()
for i in removelist:
exonlist.pop(i)
exonwtlist.pop(i)
#print 'E',exonlist
startnodelist=[a[1]for a in X_corr if a[0]==1]
endnodelist=[a[1]for a in X_corr if a[0]==-1]
novelnodelist=wgs[5]
#print exonlist
#print wgs[0]
#print intronlist
#print wgs[1]
exonwtlist1=[exonwtlist[i] for i in range(len(exonwtlist)) if exonlist[i] in wgs[0]]
intronwtlist1=[exonwtlist[i] for i in range(len(exonwtlist)) if exonlist[i] in wgs[1]]
#wgrstuple=(exonlist,intronlist,splicelist,startnodelist,endnodelist,novelnodelist,exonwtlist,intronwtlist,splicewtlist)
outwgs=(wgs[0],wgs[1],splicelist,wgs[3],wgs[4],novelnodelist,exonwtlist1,intronwtlist1,splicewtlist)
return (outwgs,err.value/len(X))
def fit_ellipse(x, y):
"""
fit ellipoid using squared loss and abs loss
"""
#TODO introduce flag for switching between losses
assert len(x) == len(y)
N = len(x)
D = 5
dat = numpy.zeros((N, D))
dat[:,0] = x*x
dat[:,1] = y*y
#dat[:,2] = x*y
dat[:,2] = x
dat[:,3] = y
dat[:,4] = numpy.ones(N)
print dat.shape
dat = cvxpy.matrix(dat)
#### parameters
# data
X = cvxpy.parameter(N, D, name="X")
#### varibales
# parameter vector
theta = cvxpy.variable(D, name="theta")
# simple objective
objective = cvxpy.norm1(X*theta)
# create problem
p = cvxpy.program(cvxpy.minimize(objective))
p.constraints.append(cvxpy.eq(theta[0,:] + theta[1,:], 1))
###### set values
X.value = dat
p.solve()
w = numpy.array(theta.value)
#print weights
## For clarity, fill in the quadratic form variables
A = numpy.zeros((2,2))
A[0,0] = w[0]
A.ravel()[1:3] = 0 #w[2]
A[1,1] = w[1]
bv = w[2:4]
c = w[4]
## find parameters
z, a, b, alpha = util.conic2parametric(A, bv, c)
print "XXX", z, a, b, alpha
return z, a, b, alpha
