def fe_dd(comp, pose, mode, lambdas, weights, dd_type, rest_file, temperature):
kB = 1.381e-23 * 6.022e23 / (4.184 * 1000.0
) # Boltzmann constant in kJ/mol/K
beta = 1 / (kB * temperature) # beta
N_max = 20000 # Max frames for any simulation window, you should check this if you did some long runs
os.chdir('fe')
os.chdir(pose)
os.chdir('dd')
if comp == 'f' or comp == 'w':
os.chdir('bulk')
elif comp == 'v' or comp == 'e':
os.chdir('site')
if not os.path.exists('data'):
os.makedirs('data')
# Define log file
sys.stdout = open('./data/' + dd_type + '-' + comp + '-' + mode + '.dat',
'w')
### Determine Number of windows
K = 0
filename = './' + comp + '%02.0f/%s' % (K, rest_file)
while os.path.isfile(filename):
K = K + 1
filename = './' + comp + '%02.0f/%s' % (K, rest_file)
if dd_type == 'ti':
deltag = 0
dvdl = []
for k in range(K):
data = []
# Read in Values for restrained variables for each simulation
filename = './' + comp + '%02.0f/%s' % (k, rest_file)
infile = open(filename, 'r')
restdat = infile.readlines(
) # slice off first 20 lines readlines()[20:]
infile.close()
# Parse Data
for line in restdat:
data.append(float(line.split()[1]))
dvdl.append(float(sum(data) / len(data)))
for i in range(0, len(dvdl)):
print('%-10s%6.5f, %-8s%9.5f' %
('lambda =', float(lambdas[i]), 'dvdl =', float(dvdl[i])))
for i in range(K):
deltag = deltag + dvdl[i] * weights[i]
print('\n%-8s %9.5f' % ('deltaG ', float(deltag)))
elif dd_type == 'mbar':
### Allocate storage for simulation data
N = np.zeros(
[K], np.int32
) # N_k[k] is the number of snapshots to be used from umbrella simulation k
Neff = np.zeros([K], np.int32)
Nind = np.zeros([K], np.int32)
val = np.zeros(
[N_max, K, K],
np.float64) # value of the restrained variable at each frame n
g = np.zeros([K], np.float64)
u = np.zeros([N_max], np.float64)
### Calculate Statistical Inefficiency (g)
def calcg(data):
sum = 0
randnum = ("%05.0f" % (int(100000 * np.random.random())))
datafn = '/dev/shm/series.' + randnum + '.dat'
acffn = '/dev/shm/acf.' + randnum + '.dat'
cppfn = '/dev/shm/pt-acf.' + randnum + '.in'
np.savetxt(datafn, data)
cpptin = open(cppfn, 'w')
cpptin.write("readdata " + datafn + " name " + randnum +
"\nautocorr " + randnum + " out " + acffn +
" noheader\n")
cpptin.close()
FNULL = open(os.devnull, 'w')
sp.call(['cpptraj', '-i', cppfn], stdout=FNULL, stderr=sp.STDOUT)
with open(acffn, 'r') as acf:
for line in acf:
col = line.split()
t = float(col[0]) - 1.0
T = t
with open(acffn, 'r') as acf:
for line in acf:
col = line.split()
t = float(col[0]) - 1.0
v = float(col[1])
if t == 0:
continue
if v < 0.0:
break
sum += (1 - (t / T)) * (v)
sp.call(['rm', datafn, acffn, cppfn])
return 1 + (2 * sum)
for k in range(K):
# Read in Values for restrained variables for each simulation
filename = './' + comp + '%02.0f/%s' % (k, rest_file)
infile = open(filename, 'r')
restdat = infile.readlines(
) # slice off first 20 lines readlines()[20:]
infile.close()
# Parse Data
n = 0
lambdas = []
for line in restdat:
cols = line.split()
if len(cols) >= 1:
lambdas.append(float(cols[1]))
if len(cols) == 0:
break
for line in restdat:
cols = line.split()
if len(cols) >= 1:
if '**' not in cols[2]:
lamb = float(cols[1].strip())
val[n, k, lambdas.index(lamb)] = cols[2]
if len(cols) == 0:
n += 1
N[k] = n
# Calculate reduced potential
u[0:N[k]] = beta * (val[0:N[k], k, k])
# Subsample or not
if mode == 'sub':
g[k] = calcg(u[0:N[k]])
subs = timeseries.subsampleCorrelatedData(np.zeros([N[k]]),
g=g[k])
Nind[k] = len(subs)
Neff[k] = Nind[k]
else:
g[k] = 1.00
Neff[k] = N[k]
print "Processed Window %5.0f. N= %12.0f. g= %10.3f Neff= %12.0f" % (
k, N[k], g[k], Neff[k])
# Calculate decoupling energy
Upot = np.zeros([K, K, np.max(Neff)], np.float64)
for k in range(K):
for l in range(K):
Upot[k, l, 0:Neff[k]] = beta * (val[0:Neff[k], k, l])
val = []
print "\nRunning MBAR... "
mbar = pymbar.MBAR(Upot,
Neff,
verbose=True,
method='adaptive',
initialize='BAR')
print "Calculate Free Energy Differences Between States"
[Deltaf, dDeltaf] = mbar.getFreeEnergyDifferences()
min = np.argmin(Deltaf[0])
# Write to file
print "\nFree Energy Differences (in units of kcal/mol)"
print "%9s %8s %8s" % ('lambda', 'f', 'df')
for k in range(K):
print "%10.5f %10.5f %10.5f" % (lambdas[k], Deltaf[0, k] / beta,
dDeltaf[0, k] / beta)
print "\n\n"
os.chdir('../../../../')
def get(self, mvals, AGrad=True, AHess=True):
"""
Fitting of lipid bulk properties. This is the current major
direction of development for ForceBalance. Basically, fitting
the QM energies / forces alone does not always give us the
best simulation behavior. In many cases it makes more sense
to try and reproduce some experimentally known data as well.
In order to reproduce experimentally known data, we need to
run a simulation and compare the simulation result to
experiment. The main challenge here is that the simulations
are computationally intensive (i.e. they require energy and
force evaluations), and furthermore the results are noisy. We
need to run the simulations automatically and remotely
(i.e. on clusters) and a good way to calculate the derivatives
of the simulation results with respect to the parameter values.
This function contains some experimentally known values of the
density and enthalpy of vaporization (Hvap) of lipid water.
It launches the density and Hvap calculations on the cluster,
and gathers the results / derivatives. The actual calculation
of results / derivatives is done in a separate file.
After the results come back, they are gathered together to form
an objective function.
@param[in] mvals Mathematical parameter values
@param[in] AGrad Switch to turn on analytic gradient
@param[in] AHess Switch to turn on analytic Hessian
@return Answer Contribution to the objective function
"""
mbar_verbose = False
Answer = {}
Results = {}
Points = [] # These are the phase points for which data exists.
BPoints = [
] # These are the phase points for which we are doing MBAR for the condensed phase.
tt = 0
for label, PT in zip(self.Labels, self.PhasePoints):
if os.path.exists('./%s/npt_result.p' % label):
logger.info('Reading information from ./%s/npt_result.p\n' %
label)
Points.append(PT)
Results[tt] = lp_load('./%s/npt_result.p' % label)
tt += 1
else:
logger.warning(
'The file ./%s/npt_result.p does not exist so we cannot read it\n'
% label)
pass
# for obs in self.RefData:
# del self.RefData[obs][PT]
if len(Points) == 0:
logger.error(
'The lipid simulations have terminated with \x1b[1;91mno readable data\x1b[0m - this is a problem!\n'
)
raise RuntimeError
# Assign variable names to all the stuff in npt_result.p
Rhos, Vols, Potentials, Energies, Dips, Grads, GDips, \
Rho_errs, Alpha_errs, Kappa_errs, Cp_errs, Eps0_errs, NMols, Als, Al_errs, Scds, Scd_errs = ([Results[t][i] for t in range(len(Points))] for i in range(17))
# Determine the number of molecules
if len(set(NMols)) != 1:
logger.error(str(NMols))
logger.error(
'The above list should only contain one number - the number of molecules\n'
)
raise RuntimeError
else:
NMol = list(set(NMols))[0]
R = np.array(list(itertools.chain(*list(Rhos))))
V = np.array(list(itertools.chain(*list(Vols))))
E = np.array(list(itertools.chain(*list(Energies))))
Dx = np.array(list(itertools.chain(*list(d[:, 0] for d in Dips))))
Dy = np.array(list(itertools.chain(*list(d[:, 1] for d in Dips))))
Dz = np.array(list(itertools.chain(*list(d[:, 2] for d in Dips))))
G = np.hstack(tuple(Grads))
GDx = np.hstack(tuple(gd[0] for gd in GDips))
GDy = np.hstack(tuple(gd[1] for gd in GDips))
GDz = np.hstack(tuple(gd[2] for gd in GDips))
A = np.array(list(itertools.chain(*list(Als))))
S = np.array(list(itertools.chain(*list(Scds))))
Rho_calc = OrderedDict([])
Rho_grad = OrderedDict([])
Rho_std = OrderedDict([])
Alpha_calc = OrderedDict([])
Alpha_grad = OrderedDict([])
Alpha_std = OrderedDict([])
Kappa_calc = OrderedDict([])
Kappa_grad = OrderedDict([])
Kappa_std = OrderedDict([])
Cp_calc = OrderedDict([])
Cp_grad = OrderedDict([])
Cp_std = OrderedDict([])
Eps0_calc = OrderedDict([])
Eps0_grad = OrderedDict([])
Eps0_std = OrderedDict([])
Al_calc = OrderedDict([])
Al_grad = OrderedDict([])
Al_std = OrderedDict([])
Scd_calc = OrderedDict([])
Scd_grad = OrderedDict([])
Scd_std = OrderedDict([])
# The unit that converts atmospheres * nm**3 into kj/mol :)
pvkj = 0.061019351687175
# Run MBAR using the total energies. Required for estimates that use the kinetic energy.
BSims = len(BPoints)
Shots = len(Energies[0])
N_k = np.ones(BSims) * Shots
# Use the value of the energy for snapshot t from simulation k at potential m
U_kln = np.zeros([BSims, BSims, Shots])
for m, PT in enumerate(BPoints):
T = PT[0]
P = PT[1] / 1.01325 if PT[2] == 'bar' else PT[1]
beta = 1. / (kb * T)
for k in range(BSims):
# The correct Boltzmann factors include PV.
# Note that because the Boltzmann factors are computed from the conditions at simulation "m",
# the pV terms must be rescaled to the pressure at simulation "m".
kk = Points.index(BPoints[k])
U_kln[k, m, :] = Energies[kk] + P * Vols[kk] * pvkj
U_kln[k, m, :] *= beta
W1 = None
if len(BPoints) > 1:
logger.info("Running MBAR analysis on %i states...\n" %
len(BPoints))
mbar = pymbar.MBAR(U_kln,
N_k,
verbose=mbar_verbose,
relative_tolerance=5.0e-8)
W1 = mbar.getWeights()
logger.info("Done\n")
elif len(BPoints) == 1:
W1 = np.ones((BPoints * Shots, BPoints))
W1 /= BPoints * Shots
def fill_weights(weights, phase_points, mbar_points, snapshots):
""" Fill in the weight matrix with MBAR weights where MBAR was run,
and equal weights otherwise. """
new_weights = np.zeros(
[len(phase_points) * snapshots,
len(phase_points)])
for m, PT in enumerate(phase_points):
if PT in mbar_points:
mm = mbar_points.index(PT)
for kk, PT1 in enumerate(mbar_points):
k = phase_points.index(PT1)
logger.debug(
"Will fill W2[%i:%i,%i] with W1[%i:%i,%i]\n" %
(k * snapshots, k * snapshots + snapshots, m,
kk * snapshots, kk * snapshots + snapshots, mm))
new_weights[k * snapshots:(k + 1) * snapshots,
m] = weights[kk * snapshots:(kk + 1) *
snapshots, mm]
else:
logger.debug(
"Will fill W2[%i:%i,%i] with equal weights\n" %
(m * snapshots, (m + 1) * snapshots, m))
new_weights[m * snapshots:(m + 1) * snapshots,
m] = 1.0 / snapshots
return new_weights
W2 = fill_weights(W1, Points, BPoints, Shots)
if self.do_self_pol:
EPol = self.polarization_correction(mvals)
GEPol = np.array([
(f12d3p(fdwrap(self.polarization_correction, mvals, p),
h=self.h,
f0=EPol)[0] if p in self.pgrad else 0.0)
for p in range(self.FF.np)
])
bar = printcool(
"Self-polarization correction to \nenthalpy of vaporization is % .3f kJ/mol%s"
% (EPol, ", Derivative:" if AGrad else ""))
if AGrad:
self.FF.print_map(vals=GEPol)
logger.info(bar)
for i, PT in enumerate(Points):
T = PT[0]
P = PT[1] / 1.01325 if PT[2] == 'bar' else PT[1]
PV = P * V * pvkj
H = E + PV
# The weights that we want are the last ones.
W = flat(W2[:, i])
C = weight_info(W,
PT,
np.ones(len(Points)) * Shots,
verbose=mbar_verbose)
Gbar = flat(np.mat(G) * col(W))
mBeta = -1 / kb / T
Beta = 1 / kb / T
kT = kb * T
# Define some things to make the analytic derivatives easier.
def avg(vec):
return np.dot(W, vec)
def covde(vec):
return flat(np.mat(G) * col(W * vec)) - avg(vec) * Gbar
def deprod(vec):
return flat(np.mat(G) * col(W * vec))
## Density.
Rho_calc[PT] = np.dot(W, R)
Rho_grad[PT] = mBeta * (flat(np.mat(G) * col(W * R)) -
np.dot(W, R) * Gbar)
## Ignore enthalpy.
## Thermal expansion coefficient.
Alpha_calc[PT] = 1e4 * (avg(H * V) -
avg(H) * avg(V)) / avg(V) / (kT * T)
GAlpha1 = -1 * Beta * deprod(H * V) * avg(V) / avg(V)**2
GAlpha2 = +1 * Beta * avg(H * V) * deprod(V) / avg(V)**2
GAlpha3 = deprod(V) / avg(V) - Gbar
GAlpha4 = Beta * covde(H)
Alpha_grad[PT] = 1e4 * (GAlpha1 + GAlpha2 + GAlpha3 +
GAlpha4) / (kT * T)
## Isothermal compressibility.
bar_unit = 0.06022141793 * 1e6
Kappa_calc[PT] = bar_unit / kT * (avg(V**2) - avg(V)**2) / avg(V)
GKappa1 = +1 * Beta**2 * avg(V**2) * deprod(V) / avg(V)**2
GKappa2 = -1 * Beta**2 * avg(V) * deprod(V**2) / avg(V)**2
GKappa3 = +1 * Beta**2 * covde(V)
Kappa_grad[PT] = bar_unit * (GKappa1 + GKappa2 + GKappa3)
## Isobaric heat capacity.
Cp_calc[PT] = 1000 / (4.184 * NMol * kT * T) * (avg(H**2) -
avg(H)**2)
if hasattr(self, 'use_cvib_intra') and self.use_cvib_intra:
logger.debug("Adding " + str(self.RefData['devib_intra'][PT]) +
" to the heat capacity\n")
Cp_calc[PT] += self.RefData['devib_intra'][PT]
if hasattr(self, 'use_cvib_inter') and self.use_cvib_inter:
logger.debug("Adding " + str(self.RefData['devib_inter'][PT]) +
" to the heat capacity\n")
Cp_calc[PT] += self.RefData['devib_inter'][PT]
GCp1 = 2 * covde(H) * 1000 / 4.184 / (NMol * kT * T)
GCp2 = mBeta * covde(H**2) * 1000 / 4.184 / (NMol * kT * T)
GCp3 = 2 * Beta * avg(H) * covde(H) * 1000 / 4.184 / (NMol * kT *
T)
Cp_grad[PT] = GCp1 + GCp2 + GCp3
## Static dielectric constant.
prefactor = 30.348705333964077
D2 = avg(Dx**2) + avg(Dy**2) + avg(
Dz**2) - avg(Dx)**2 - avg(Dy)**2 - avg(Dz)**2
Eps0_calc[PT] = 1.0 + prefactor * (D2 / avg(V)) / T
GD2 = 2 * (flat(np.mat(GDx) * col(W * Dx)) -
avg(Dx) * flat(np.mat(GDx) * col(W))) - Beta * (
covde(Dx**2) - 2 * avg(Dx) * covde(Dx))
GD2 += 2 * (flat(np.mat(GDy) * col(W * Dy)) -
avg(Dy) * flat(np.mat(GDy) * col(W))) - Beta * (
covde(Dy**2) - 2 * avg(Dy) * covde(Dy))
GD2 += 2 * (flat(np.mat(GDz) * col(W * Dz)) -
avg(Dz) * flat(np.mat(GDz) * col(W))) - Beta * (
covde(Dz**2) - 2 * avg(Dz) * covde(Dz))
Eps0_grad[PT] = prefactor * (GD2 / avg(V) -
mBeta * covde(V) * D2 / avg(V)**2) / T
## Average area per lipid
Al_calc[PT] = np.dot(W, A)
Al_grad[PT] = mBeta * (flat(np.mat(G) * col(W * A)) -
np.dot(W, A) * Gbar)
## Deuterium order parameter
Scd_calc[PT] = np.dot(W, S)
Scd_grad[PT] = mBeta * (
flat(np.average(np.mat(G) * (S * W[:, np.newaxis]), axis=1)) -
np.average(np.average(S * W[:, np.newaxis], axis=0), axis=0) *
Gbar)
## Estimation of errors.
Rho_std[PT] = np.sqrt(sum(C**2 * np.array(Rho_errs)**2))
Alpha_std[PT] = np.sqrt(sum(C**2 * np.array(Alpha_errs)**2)) * 1e4
Kappa_std[PT] = np.sqrt(sum(C**2 * np.array(Kappa_errs)**2)) * 1e6
Cp_std[PT] = np.sqrt(sum(C**2 * np.array(Cp_errs)**2))
Eps0_std[PT] = np.sqrt(sum(C**2 * np.array(Eps0_errs)**2))
Al_std[PT] = np.sqrt(sum(C**2 * np.array(Al_errs)**2))
Scd_std[PT] = np.sqrt(sum(np.mat(C**2) * np.array(Scd_errs)**2))
# Get contributions to the objective function
X_Rho, G_Rho, H_Rho, RhoPrint = self.objective_term(Points,
'rho',
Rho_calc,
Rho_std,
Rho_grad,
name="Density")
X_Alpha, G_Alpha, H_Alpha, AlphaPrint = self.objective_term(
Points,
'alpha',
Alpha_calc,
Alpha_std,
Alpha_grad,
name="Thermal Expansion")
X_Kappa, G_Kappa, H_Kappa, KappaPrint = self.objective_term(
Points,
'kappa',
Kappa_calc,
Kappa_std,
Kappa_grad,
name="Compressibility")
X_Cp, G_Cp, H_Cp, CpPrint = self.objective_term(Points,
'cp',
Cp_calc,
Cp_std,
Cp_grad,
name="Heat Capacity")
X_Eps0, G_Eps0, H_Eps0, Eps0Print = self.objective_term(
Points,
'eps0',
Eps0_calc,
Eps0_std,
Eps0_grad,
name="Dielectric Constant")
X_Al, G_Al, H_Al, AlPrint = self.objective_term(
Points, 'al', Al_calc, Al_std, Al_grad, name="Avg Area per Lipid")
X_Scd, G_Scd, H_Scd, ScdPrint = self.objective_term(
Points,
'scd',
Scd_calc,
Scd_std,
Scd_grad,
name="Deuterium Order Parameter")
Gradient = np.zeros(self.FF.np)
Hessian = np.zeros((self.FF.np, self.FF.np))
if X_Rho == 0: self.w_rho = 0.0
if X_Alpha == 0: self.w_alpha = 0.0
if X_Kappa == 0: self.w_kappa = 0.0
if X_Cp == 0: self.w_cp = 0.0
if X_Eps0 == 0: self.w_eps0 = 0.0
if X_Al == 0: self.w_al = 0.0
if X_Scd == 0: self.w_scd = 0.0
w_tot = self.w_rho + self.w_alpha + self.w_kappa + self.w_cp + self.w_eps0 + self.w_al + self.w_scd
w_1 = self.w_rho / w_tot
w_3 = self.w_alpha / w_tot
w_4 = self.w_kappa / w_tot
w_5 = self.w_cp / w_tot
w_6 = self.w_eps0 / w_tot
w_7 = self.w_al / w_tot
w_8 = self.w_scd / w_tot
Objective = w_1 * X_Rho + w_3 * X_Alpha + w_4 * X_Kappa + w_5 * X_Cp + w_6 * X_Eps0 + w_7 * X_Al + w_8 * X_Scd
if AGrad:
Gradient = w_1 * G_Rho + w_3 * G_Alpha + w_4 * G_Kappa + w_5 * G_Cp + w_6 * G_Eps0 + w_7 * G_Al + w_8 * G_Scd
if AHess:
Hessian = w_1 * H_Rho + w_3 * H_Alpha + w_4 * H_Kappa + w_5 * H_Cp + w_6 * H_Eps0 + w_7 * H_Al + w_8 * H_Scd
if not in_fd():
self.Xp = {
"Rho": X_Rho,
"Alpha": X_Alpha,
"Kappa": X_Kappa,
"Cp": X_Cp,
"Eps0": X_Eps0,
"Al": X_Al,
"Scd": X_Scd
}
self.Wp = {
"Rho": w_1,
"Alpha": w_3,
"Kappa": w_4,
"Cp": w_5,
"Eps0": w_6,
"Al": w_7,
"Scd": w_8
}
self.Pp = {
"Rho": RhoPrint,
"Alpha": AlphaPrint,
"Kappa": KappaPrint,
"Cp": CpPrint,
"Eps0": Eps0Print,
"Al": AlPrint,
"Scd": ScdPrint
}
if AGrad:
self.Gp = {
"Rho": G_Rho,
"Alpha": G_Alpha,
"Kappa": G_Kappa,
"Cp": G_Cp,
"Eps0": G_Eps0,
"Al": G_Al,
"Scd": G_Scd
}
self.Objective = Objective
Answer = {'X': Objective, 'G': Gradient, 'H': Hessian}
return Answer
def fe_mbar(comp, pose, mode, rest_file, temperature):
kB = 1.381e-23 * 6.022e23 / (4.184 * 1000.0
) # Boltzmann constant in kJ/mol/K
beta = 1 / (kB * temperature) # beta
N_max = 20000 # Max frames for any simulation window, you should check this if you did some long runs
### Change to pose directory
os.chdir('fe')
os.chdir(pose)
if comp != 'u':
os.chdir('rest')
else:
os.chdir('pmf')
if not os.path.exists('data'):
os.makedirs('data')
# Define log file
sys.stdout = open('./data/mbar-' + comp + '-' + mode + '.log', 'w')
### Determine Number of windows
K = 0
filename = './' + comp + '%02.0f/%s' % (K, rest_file)
while os.path.isfile(filename):
K = K + 1
filename = './' + comp + '%02.0f/%s' % (K, rest_file)
## Determine Number of restraints
infile = open('./' + comp + '00/disang.rest', 'r')
disang = infile.readlines()
infile.close()
R = 0
if (comp == 't' or comp == 'u'):
for line in disang:
cols = line.split()
if len(cols) != 0 and (cols[-1] == "#Lig_TR"):
R += 1
elif (comp == 'l' or comp == 'c'):
for line in disang:
cols = line.split()
if len(cols) != 0 and (cols[-1] == "#Lig_C"
or cols[-1] == "#Lig_D"):
R += 1
elif (comp == 'a' or comp == 'r'):
for line in disang:
cols = line.split()
if len(cols) != 0 and (cols[-1] == "#Rec_C"
or cols[-1] == "#Rec_D"):
R += 1
print "K= %5.0f R= %5.0f" % (K, R)
### Calculate Statistical Inefficiency (g)
def calcg(data):
sum = 0
randnum = ("%05.0f" % (int(100000 * np.random.random())))
datafn = '/dev/shm/series.' + randnum + '.dat'
acffn = '/dev/shm/acf.' + randnum + '.dat'
cppfn = '/dev/shm/pt-acf.' + randnum + '.in'
np.savetxt(datafn, data)
cpptin = open(cppfn, 'w')
cpptin.write("readdata " + datafn + " name " + randnum +
"\nautocorr " + randnum + " out " + acffn + " noheader\n")
cpptin.close()
FNULL = open(os.devnull, 'w')
sp.call(['cpptraj', '-i', cppfn], stdout=FNULL, stderr=sp.STDOUT)
with open(acffn, 'r') as acf:
for line in acf:
col = line.split()
t = float(col[0]) - 1.0
T = t
with open(acffn, 'r') as acf:
for line in acf:
col = line.split()
t = float(col[0]) - 1.0
v = float(col[1])
if t == 0:
continue
if v < 0.0:
break
sum += (1 - (t / T)) * (v)
sp.call(['rm', datafn, acffn, cppfn])
return 1 + (2 * sum)
### Allocate storage for simulation data
N = np.zeros(
[K], np.int32
) # N_k[k] is the number of snapshots to be used from umbrella simulation k
Neff = np.zeros([K], np.int32)
Nind = np.zeros([K], np.int32)
rty = ['d'] * R # restraint type (distance or angle)
rfc = np.zeros([K, R], np.float64) # restraint force constant
req = np.zeros([K, R], np.float64) # restraint target value
val = np.zeros(
[N_max, K, R],
np.float64) # value of the restrained variable at each frame n
g = np.zeros([K], np.float64)
u = np.zeros([N_max], np.float64)
### Read the simulation data
for k in range(K):
# Read Equilibrium Value and Force Constant
filename = './' + comp + '%02.0f/disang.rest' % k
infile = open(filename, 'r')
disang = infile.readlines()
infile.close()
r = 0
for line in disang:
cols = line.split()
if (comp == 't' or comp == 'u'):
if len(cols) != 0 and (cols[-1] == "#Lig_TR"):
natms = len(cols[2].split(',')) - 1
req[k, r] = float(cols[6].replace(",", ""))
if natms == 2:
rty[r] = 'd'
rfc[k, r] = float(cols[12].replace(",", ""))
elif natms == 3:
rty[r] = 'a'
rfc[k, r] = float(cols[12].replace(
",", "")) * (np.pi / 180.0) * (
np.pi / 180.0) ### Convert to degrees
elif natms == 4:
rty[r] = 't'
rfc[k, r] = float(cols[12].replace(
",", "")) * (np.pi / 180.0) * (
np.pi / 180.0) ### Convert to degrees
else:
sys.exit("not sure about restraint type!")
r += 1
elif (comp == 'l' or comp == 'c'):
if len(cols) != 0 and (cols[-1] == "#Lig_C"
or cols[-1] == "#Lig_D"):
natms = len(cols[2].split(',')) - 1
req[k, r] = float(cols[6].replace(",", ""))
if natms == 2:
rty[r] = 'd'
rfc[k, r] = float(cols[12].replace(",", ""))
elif natms == 3:
rty[r] = 'a'
rfc[k, r] = float(cols[12].replace(
",", "")) * (np.pi / 180.0) * (
np.pi / 180.0) ### Convert to degrees
elif natms == 4:
rty[r] = 't'
rfc[k, r] = float(cols[12].replace(
",", "")) * (np.pi / 180.0) * (
np.pi / 180.0) ### Convert to degrees
else:
sys.exit("not sure about restraint type!")
r += 1
elif (comp == 'a' or comp == 'r'):
if len(cols) != 0 and (cols[-1] == "#Rec_C"
or cols[-1] == "#Rec_D"):
natms = len(cols[2].split(',')) - 1
req[k, r] = float(cols[6].replace(",", ""))
if natms == 2:
rty[r] = 'd'
rfc[k, r] = float(cols[12].replace(",", ""))
elif natms == 3:
rty[r] = 'a'
rfc[k, r] = float(cols[12].replace(
",", "")) * (np.pi / 180.0) * (
np.pi / 180.0) ### Convert to degrees
elif natms == 4:
rty[r] = 't'
rfc[k, r] = float(cols[12].replace(
",", "")) * (np.pi / 180.0) * (
np.pi / 180.0) ### Convert to degrees
else:
sys.exit("not sure about restraint type!")
r += 1
# Read in Values for restrained variables for each simulation
filename = './' + comp + '%02.0f/%s' % (k, rest_file)
infile = open(filename, 'r')
restdat = infile.readlines(
) # slice off first 20 lines readlines()[20:]
infile.close()
# Parse Data
n = 0
for line in restdat:
if line[0] != '#' and line[0] != '@' and n < N_max:
cols = line.split()
for r in range(R):
if rty[r] == 't': # Do phase corrections
tmp = float(cols[r + 1])
if tmp < req[k, r] - 180.0:
val[n, k, r] = tmp + 360
elif tmp > req[k, r] + 180.0:
val[n, k, r] = tmp - 360
else:
val[n, k, r] = tmp
else:
val[n, k, r] = float(cols[r + 1])
n += 1
N[k] = n
# Calculate Reduced Potential
if comp != 'u': ### Attach/Release Restraints
if rfc[k, 0] == 0:
tmp = np.ones(
[R], np.float64
) * 0.001 ########## CHECK THIS!! might interfere on protein attach
u[0:N[k]] = np.sum(beta * tmp[0:R] *
((val[0:N[k], k, 0:R] - req[k, 0:R])**2),
axis=1)
else:
u[0:N[k]] = np.sum(beta * rfc[k, 0:R] *
((val[0:N[k], k, 0:R] - req[k, 0:R])**2),
axis=1)
else: ### Umbrella/Translation
u[0:N[k]] = (beta * rfc[k, 0] *
((val[0:N[k], k, 0] - req[k, 0])**2))
if mode == 'sub':
g[k] = calcg(u[0:N[k]])
subs = timeseries.subsampleCorrelatedData(np.zeros([N[k]]), g=g[k])
Nind[k] = len(subs)
Neff[k] = Nind[k]
else:
g[k] = 1.00
Neff[k] = N[k]
print "Processed Window %5.0f. N= %12.0f. g= %10.3f Neff= %12.0f" % (
k, N[k], g[k], Neff[k])
Upot = np.zeros([K, K, np.max(Neff)], np.float64)
# Calculate Restraint Energy
for k in range(K):
if mode == 'sub': #subsampling
subs = timeseries.subsampleCorrelatedData(np.zeros([N[k]]), g=g[k])
for l in range(K):
if comp != 'u': # Attach Restraints
Upot[k, l, 0:Neff[k]] = np.sum(
beta * rfc[l, 0:R] *
((val[subs[0:Neff[k]], k, 0:R] - req[l, 0:R])**2),
axis=1)
else: # Umbrella/Translation
Upot[k, l, 0:Neff[k]] = (beta * rfc[l, 0] * (
(val[subs[0:Neff[k]], k, 0] - req[l, 0])**2))
else:
Neff[k] = N[k]
for l in range(K): # all samples
if comp != 'u': # Attach Restraints
Upot[k, l, 0:Neff[k]] = np.sum(
beta * rfc[l, 0:R] *
((val[0:Neff[k], k, 0:R] - req[l, 0:R])**2),
axis=1)
else: # Umbrella/Translation
Upot[k, l,
0:Neff[k]] = (beta * rfc[l, 0] *
((val[0:Neff[k], k, 0] - req[l, 0])**2))
val = []
print "Running MBAR... "
mbar = pymbar.MBAR(Upot,
Neff,
verbose=True,
method='adaptive',
initialize='BAR')
print "Calculate Free Energy Differences Between States"
[Deltaf, dDeltaf] = mbar.getFreeEnergyDifferences()
min = np.argmin(Deltaf[0])
# Write to file
print "Free Energy Differences (in units of kcal/mol)"
print "%9s %8s %8s %12s %12s" % ('bin', 'f', 'df', 'deq', 'dfc')
datfile = open('./data/mbar-' + comp + '-' + mode + '.dat', 'w')
for k in range(K):
if comp != 'u': # Attach/release
print "%10.5f %10.5f %10.5f %12.7f %12.7f" % (
rfc[k, 0] / rfc[-1, 0], Deltaf[0, k] / beta,
dDeltaf[0, k] / beta, req[k, 0], rfc[k, 0])
datfile.write("%10.5f %10.5f %10.5f %12.7f %12.7f\n" %
(rfc[k, 0] / rfc[-1, 0], Deltaf[0, k] / beta,
dDeltaf[0, k] / beta, req[k, 0], rfc[k, 0]))
else: # Umbrella/Translation
print "%10.5f %10.5f %10.5f %12.7f %12.7f" % (
req[k, 0], Deltaf[0, k] / beta, dDeltaf[0, k] / beta,
req[k, 0], rfc[k, 0])
datfile.write("%10.5f %10.5f %10.5f %12.7f %12.7f\n" %
(req[k, 0], Deltaf[0, k] / beta,
dDeltaf[0, k] / beta, req[k, 0], rfc[k, 0]))
datfile.close()
print "\n\n"
os.chdir('../../../')
def get(self, mvals, AGrad=True, AHess=True):
"""
Fitting of liquid bulk properties. This is the current major
direction of development for ForceBalance. Basically, fitting
the QM energies / forces alone does not always give us the
best simulation behavior. In many cases it makes more sense
to try and reproduce some experimentally known data as well.
In order to reproduce experimentally known data, we need to
run a simulation and compare the simulation result to
experiment. The main challenge here is that the simulations
are computationally intensive (i.e. they require energy and
force evaluations), and furthermore the results are noisy. We
need to run the simulations automatically and remotely
(i.e. on clusters) and a good way to calculate the derivatives
of the simulation results with respect to the parameter values.
This function contains some experimentally known values of the
density and enthalpy of vaporization (Hvap) of liquid water.
It launches the density and Hvap calculations on the cluster,
and gathers the results / derivatives. The actual calculation
of results / derivatives is done in a separate file.
After the results come back, they are gathered together to form
an objective function.
@param[in] mvals Mathematical parameter values
@param[in] AGrad Switch to turn on analytic gradient
@param[in] AHess Switch to turn on analytic Hessian
@return Answer Contribution to the objective function
"""
unpack = forcebalance.nifty.lp_load('forcebalance.p')
mvals1 = unpack[1]
if (np.max(np.abs(mvals1 - mvals)) > 1e-3):
warn_press_key("mvals from forcebalance.p does not match up with internal values! (Are you reading data from a previous run?)\nmvals(call)=%s mvals(disk)=%s" % (mvals, mvals1))
mbar_verbose = False
Answer = {}
Results = {}
Points = [] # These are the phase points for which data exists.
BPoints = [] # These are the phase points for which we are doing MBAR for the condensed phase.
mBPoints = [] # These are the phase points for which we are doing MBAR for the monomers.
mPoints = [] # These are the phase points to use for enthalpy of vaporization; if we're scanning pressure then set hvap_wt for higher pressures to zero.
tt = 0
for label, PT in zip(self.Labels, self.PhasePoints):
if os.path.exists('./%s/npt_result.p' % label):
logger.info('Reading information from ./%s/npt_result.p\n' % label)
Points.append(PT)
Results[tt] = lp_load('./%s/npt_result.p' % label)
if 'hvap' in self.RefData and PT[0] not in [i[0] for i in mPoints]:
mPoints.append(PT)
if 'mbar' in self.RefData and PT in self.RefData['mbar'] and self.RefData['mbar'][PT]:
BPoints.append(PT)
if 'hvap' in self.RefData and PT[0] not in [i[0] for i in mBPoints]:
mBPoints.append(PT)
tt += 1
else:
logger.warning('In %s :\n' % os.getcwd())
logger.warning('The file ./%s/npt_result.p does not exist so we cannot read it\n' % label)
pass
if len(Points) == 0:
logger.error('The liquid simulations have terminated with \x1b[1;91mno readable data\x1b[0m - this is a problem!\n')
raise RuntimeError
# Assign variable names to all the stuff in npt_result.p
Rhos, Vols, Potentials, Energies, Dips, Grads, GDips, mPotentials, mEnergies, mGrads, \
Rho_errs, Hvap_errs, Alpha_errs, Kappa_errs, Cp_errs, Eps0_errs, NMols = ([Results[t][i] for t in range(len(Points))] for i in range(17))
# Determine the number of molecules
if len(set(NMols)) != 1:
logger.error(str(NMols))
logger.error('The above list should only contain one number - the number of molecules\n')
raise RuntimeError
else:
NMol = list(set(NMols))[0]
if not self.adapt_errors:
self.AllResults = defaultdict(lambda:defaultdict(list))
astrm = astr(mvals)
if len(Points) != len(self.Labels):
logger.info("Data sets is not full, will not use for concatenation.")
astrm += "_"*(Counter()+1)
self.AllResults[astrm]['Pts'].append(Points)
self.AllResults[astrm]['mPts'].append(Points)
self.AllResults[astrm]['E'].append(np.array(Energies))
self.AllResults[astrm]['V'].append(np.array(Vols))
self.AllResults[astrm]['R'].append(np.array(Rhos))
self.AllResults[astrm]['Dx'].append(np.array([d[:,0] for d in Dips]))
self.AllResults[astrm]['Dy'].append(np.array([d[:,1] for d in Dips]))
self.AllResults[astrm]['Dz'].append(np.array([d[:,2] for d in Dips]))
self.AllResults[astrm]['G'].append(np.array(Grads))
self.AllResults[astrm]['GDx'].append(np.array([gd[0] for gd in GDips]))
self.AllResults[astrm]['GDy'].append(np.array([gd[1] for gd in GDips]))
self.AllResults[astrm]['GDz'].append(np.array([gd[2] for gd in GDips]))
self.AllResults[astrm]['L'].append(len(Energies[0]))
self.AllResults[astrm]['Steps'].append(self.liquid_md_steps)
if len(mPoints) > 0:
self.AllResults[astrm]['mE'].append(np.array([i for pt, i in zip(Points,mEnergies) if pt in mPoints]))
self.AllResults[astrm]['mG'].append(np.array([i for pt, i in zip(Points,mGrads) if pt in mPoints]))
# Number of data sets belonging to this value of the parameters.
Nrpt = len(self.AllResults[astrm]['R'])
sumsteps = sum(self.AllResults[astrm]['Steps'])
if self.liquid_md_steps != sumsteps:
printcool("This objective function evaluation combines %i datasets\n" \
"Increasing simulation length: %i -> %i steps" % \
(Nrpt, self.liquid_md_steps, sumsteps), color=6)
if self.liquid_md_steps * 2 != sumsteps:
logger.error("Spoo!\n")
raise RuntimeError
self.liquid_eq_steps *= 2
self.liquid_md_steps *= 2
self.gas_eq_steps *= 2
self.gas_md_steps *= 2
# Concatenate along the data-set axis (more than 1 element if we've returned to these parameters.)
E, V, R, Dx, Dy, Dz = \
(np.hstack(tuple(self.AllResults[astrm][i])) for i in \
['E', 'V', 'R', 'Dx', 'Dy', 'Dz'])
G, GDx, GDy, GDz = \
(np.hstack((np.concatenate(tuple(self.AllResults[astrm][i]), axis=2))) for i in ['G', 'GDx', 'GDy', 'GDz'])
if len(mPoints) > 0:
mE = np.hstack(tuple(self.AllResults[astrm]['mE']))
mG = np.hstack((np.concatenate(tuple(self.AllResults[astrm]['mG']), axis=2)))
Rho_calc = OrderedDict([])
Rho_grad = OrderedDict([])
Rho_std = OrderedDict([])
Hvap_calc = OrderedDict([])
Hvap_grad = OrderedDict([])
Hvap_std = OrderedDict([])
Alpha_calc = OrderedDict([])
Alpha_grad = OrderedDict([])
Alpha_std = OrderedDict([])
Kappa_calc = OrderedDict([])
Kappa_grad = OrderedDict([])
Kappa_std = OrderedDict([])
Cp_calc = OrderedDict([])
Cp_grad = OrderedDict([])
Cp_std = OrderedDict([])
Eps0_calc = OrderedDict([])
Eps0_grad = OrderedDict([])
Eps0_std = OrderedDict([])
# The unit that converts atmospheres * nm**3 into kj/mol :)
pvkj=0.061019351687175
# Run MBAR using the total energies. Required for estimates that use the kinetic energy.
BSims = len(BPoints)
Shots = len(E[0])
N_k = np.ones(BSims)*Shots
# Use the value of the energy for snapshot t from simulation k at potential m
U_kln = np.zeros([BSims,BSims,Shots])
for m, PT in enumerate(BPoints):
T = PT[0]
P = PT[1] / 1.01325 if PT[2] == 'bar' else PT[1]
beta = 1. / (kb * T)
for k in range(BSims):
# The correct Boltzmann factors include PV.
# Note that because the Boltzmann factors are computed from the conditions at simulation "m",
# the pV terms must be rescaled to the pressure at simulation "m".
kk = Points.index(BPoints[k])
U_kln[k, m, :] = E[kk] + P*V[kk]*pvkj
U_kln[k, m, :] *= beta
W1 = None
if len(BPoints) > 1:
logger.info("Running MBAR analysis on %i states...\n" % len(BPoints))
mbar = pymbar.MBAR(U_kln, N_k, verbose=mbar_verbose, relative_tolerance=5.0e-8)
W1 = mbar.getWeights()
logger.info("Done\n")
elif len(BPoints) == 1:
W1 = np.ones((BPoints*Shots,BPoints))
W1 /= BPoints*Shots
def fill_weights(weights, phase_points, mbar_points, snapshots):
""" Fill in the weight matrix with MBAR weights where MBAR was run,
and equal weights otherwise. """
new_weights = np.zeros([len(phase_points)*snapshots,len(phase_points)])
for m, PT in enumerate(phase_points):
if PT in mbar_points:
mm = mbar_points.index(PT)
for kk, PT1 in enumerate(mbar_points):
k = phase_points.index(PT1)
logger.debug("Will fill W2[%i:%i,%i] with W1[%i:%i,%i]\n" % (k*snapshots,k*snapshots+snapshots,m,kk*snapshots,kk*snapshots+snapshots,mm))
new_weights[k*snapshots:(k+1)*snapshots,m] = weights[kk*snapshots:(kk+1)*snapshots,mm]
else:
logger.debug("Will fill W2[%i:%i,%i] with equal weights\n" % (m*snapshots,(m+1)*snapshots,m))
new_weights[m*snapshots:(m+1)*snapshots,m] = 1.0/snapshots
return new_weights
W2 = fill_weights(W1, Points, BPoints, Shots)
if len(mPoints) > 0:
# Run MBAR on the monomers. This is barely necessary.
mW1 = None
mShots = len(mE[0])
if len(mBPoints) > 0:
mBSims = len(mBPoints)
mN_k = np.ones(mBSims)*mShots
mU_kln = np.zeros([mBSims,mBSims,mShots])
for m, PT in enumerate(mBPoints):
T = PT[0]
beta = 1. / (kb * T)
for k in range(mBSims):
kk = Points.index(mBPoints[k])
mU_kln[k, m, :] = mE[kk]
mU_kln[k, m, :] *= beta
if np.abs(np.std(mE)) > 1e-6 and mBSims > 1:
mmbar = pymbar.MBAR(mU_kln, mN_k, verbose=False, relative_tolerance=5.0e-8, method='self-consistent-iteration')
mW1 = mmbar.getWeights()
elif len(mBPoints) == 1:
mW1 = np.ones((mBSims*mShots,mSims))
mW1 /= mBSims*mShots
mW2 = fill_weights(mW1, mPoints, mBPoints, mShots)
if self.do_self_pol:
EPol = self.polarization_correction(mvals)
GEPol = np.array([(f12d3p(fdwrap(self.polarization_correction, mvals, p), h = self.h, f0 = EPol)[0] if p in self.pgrad else 0.0) for p in range(self.FF.np)])
bar = printcool("Self-polarization correction to \nenthalpy of vaporization is % .3f kJ/mol%s" % (EPol, ", Derivative:" if AGrad else ""))
if AGrad:
self.FF.print_map(vals=GEPol)
logger.info(bar)
# Arrays must be flattened now for calculation of properties.
E = E.flatten()
V = V.flatten()
R = R.flatten()
Dx = Dx.flatten()
Dy = Dy.flatten()
Dz = Dz.flatten()
if len(mPoints) > 0: mE = mE.flatten()
for i, PT in enumerate(Points):
T = PT[0]
P = PT[1] / 1.01325 if PT[2] == 'bar' else PT[1]
PV = P*V*pvkj
H = E + PV
# The weights that we want are the last ones.
W = flat(W2[:,i])
C = weight_info(W, PT, np.ones(len(Points))*Shots, verbose=mbar_verbose)
Gbar = flat(np.matrix(G)*col(W))
mBeta = -1/kb/T
Beta = 1/kb/T
kT = kb*T
# Define some things to make the analytic derivatives easier.
def avg(vec):
return np.dot(W,vec)
def covde(vec):
return flat(np.matrix(G)*col(W*vec)) - avg(vec)*Gbar
def deprod(vec):
return flat(np.matrix(G)*col(W*vec))
## Density.
Rho_calc[PT] = np.dot(W,R)
Rho_grad[PT] = mBeta*(flat(np.matrix(G)*col(W*R)) - np.dot(W,R)*Gbar)
## Enthalpy of vaporization.
if PT in mPoints:
ii = mPoints.index(PT)
mW = flat(mW2[:,ii])
mGbar = flat(np.matrix(mG)*col(mW))
Hvap_calc[PT] = np.dot(mW,mE) - np.dot(W,E)/NMol + kb*T - np.dot(W, PV)/NMol
Hvap_grad[PT] = mGbar + mBeta*(flat(np.matrix(mG)*col(mW*mE)) - np.dot(mW,mE)*mGbar)
Hvap_grad[PT] -= (Gbar + mBeta*(flat(np.matrix(G)*col(W*E)) - np.dot(W,E)*Gbar)) / NMol
Hvap_grad[PT] -= (mBeta*(flat(np.matrix(G)*col(W*PV)) - np.dot(W,PV)*Gbar)) / NMol
if self.do_self_pol:
Hvap_calc[PT] -= EPol
Hvap_grad[PT] -= GEPol
if hasattr(self,'use_cni') and self.use_cni:
if not ('cni' in self.RefData and self.RefData['cni'][PT]):
logger.error('Asked for a nonideality correction but not provided in reference data (data.csv). Either disable the option in data.csv or add data.\n')
raise RuntimeError
logger.debug("Adding % .3f to enthalpy of vaporization at " % self.RefData['cni'][PT] + str(PT) + '\n')
Hvap_calc[PT] += self.RefData['cni'][PT]
if hasattr(self,'use_cvib_intra') and self.use_cvib_intra:
if not ('cvib_intra' in self.RefData and self.RefData['cvib_intra'][PT]):
logger.error('Asked for a quantum intramolecular vibrational correction but not provided in reference data (data.csv). Either disable the option in data.csv or add data.\n')
raise RuntimeError
logger.debug("Adding % .3f to enthalpy of vaporization at " % self.RefData['cvib_intra'][PT] + str(PT) + '\n')
Hvap_calc[PT] += self.RefData['cvib_intra'][PT]
if hasattr(self,'use_cvib_inter') and self.use_cvib_inter:
if not ('cvib_inter' in self.RefData and self.RefData['cvib_inter'][PT]):
logger.error('Asked for a quantum intermolecular vibrational correction but not provided in reference data (data.csv). Either disable the option in data.csv or add data.\n')
raise RuntimeError
logger.debug("Adding % .3f to enthalpy of vaporization at " % self.RefData['cvib_inter'][PT] + str(PT) + '\n')
Hvap_calc[PT] += self.RefData['cvib_inter'][PT]
else:
Hvap_calc[PT] = 0.0
Hvap_grad[PT] = np.zeros(self.FF.np)
## Thermal expansion coefficient.
Alpha_calc[PT] = 1e4 * (avg(H*V)-avg(H)*avg(V))/avg(V)/(kT*T)
GAlpha1 = -1 * Beta * deprod(H*V) * avg(V) / avg(V)**2
GAlpha2 = +1 * Beta * avg(H*V) * deprod(V) / avg(V)**2
GAlpha3 = deprod(V)/avg(V) - Gbar
GAlpha4 = Beta * covde(H)
Alpha_grad[PT] = 1e4 * (GAlpha1 + GAlpha2 + GAlpha3 + GAlpha4)/(kT*T)
## Isothermal compressibility.
bar_unit = 0.06022141793 * 1e6
Kappa_calc[PT] = bar_unit / kT * (avg(V**2)-avg(V)**2)/avg(V)
GKappa1 = +1 * Beta**2 * avg(V**2) * deprod(V) / avg(V)**2
GKappa2 = -1 * Beta**2 * avg(V) * deprod(V**2) / avg(V)**2
GKappa3 = +1 * Beta**2 * covde(V)
Kappa_grad[PT] = bar_unit*(GKappa1 + GKappa2 + GKappa3)
## Isobaric heat capacity.
Cp_calc[PT] = 1000/(4.184*NMol*kT*T) * (avg(H**2) - avg(H)**2)
if hasattr(self,'use_cvib_intra') and self.use_cvib_intra:
logger.debug("Adding " + str(self.RefData['devib_intra'][PT]) + " to the heat capacity\n")
Cp_calc[PT] += self.RefData['devib_intra'][PT]
if hasattr(self,'use_cvib_inter') and self.use_cvib_inter:
logger.debug("Adding " + str(self.RefData['devib_inter'][PT]) + " to the heat capacity\n")
Cp_calc[PT] += self.RefData['devib_inter'][PT]
GCp1 = 2*covde(H) * 1000 / 4.184 / (NMol*kT*T)
GCp2 = mBeta*covde(H**2) * 1000 / 4.184 / (NMol*kT*T)
GCp3 = 2*Beta*avg(H)*covde(H) * 1000 / 4.184 / (NMol*kT*T)
Cp_grad[PT] = GCp1 + GCp2 + GCp3
## Static dielectric constant.
prefactor = 30.348705333964077
D2 = avg(Dx**2)+avg(Dy**2)+avg(Dz**2)-avg(Dx)**2-avg(Dy)**2-avg(Dz)**2
Eps0_calc[PT] = 1.0 + prefactor*(D2/avg(V))/T
GD2 = 2*(flat(np.matrix(GDx)*col(W*Dx)) - avg(Dx)*flat(np.matrix(GDx)*col(W))) - Beta*(covde(Dx**2) - 2*avg(Dx)*covde(Dx))
GD2 += 2*(flat(np.matrix(GDy)*col(W*Dy)) - avg(Dy)*flat(np.matrix(GDy)*col(W))) - Beta*(covde(Dy**2) - 2*avg(Dy)*covde(Dy))
GD2 += 2*(flat(np.matrix(GDz)*col(W*Dz)) - avg(Dz)*flat(np.matrix(GDz)*col(W))) - Beta*(covde(Dz**2) - 2*avg(Dz)*covde(Dz))
Eps0_grad[PT] = prefactor*(GD2/avg(V) - mBeta*covde(V)*D2/avg(V)**2)/T
## Estimation of errors.
Rho_std[PT] = np.sqrt(sum(C**2 * np.array(Rho_errs)**2))
if PT in mPoints:
Hvap_std[PT] = np.sqrt(sum(C**2 * np.array(Hvap_errs)**2))
else:
Hvap_std[PT] = 0.0
Alpha_std[PT] = np.sqrt(sum(C**2 * np.array(Alpha_errs)**2)) * 1e4
Kappa_std[PT] = np.sqrt(sum(C**2 * np.array(Kappa_errs)**2)) * 1e6
Cp_std[PT] = np.sqrt(sum(C**2 * np.array(Cp_errs)**2))
Eps0_std[PT] = np.sqrt(sum(C**2 * np.array(Eps0_errs)**2))
# Get contributions to the objective function
X_Rho, G_Rho, H_Rho, RhoPrint = self.objective_term(Points, 'rho', Rho_calc, Rho_std, Rho_grad, name="Density")
X_Hvap, G_Hvap, H_Hvap, HvapPrint = self.objective_term(Points, 'hvap', Hvap_calc, Hvap_std, Hvap_grad, name="H_vap", SubAverage=self.hvap_subaverage)
X_Alpha, G_Alpha, H_Alpha, AlphaPrint = self.objective_term(Points, 'alpha', Alpha_calc, Alpha_std, Alpha_grad, name="Thermal Expansion")
X_Kappa, G_Kappa, H_Kappa, KappaPrint = self.objective_term(Points, 'kappa', Kappa_calc, Kappa_std, Kappa_grad, name="Compressibility")
X_Cp, G_Cp, H_Cp, CpPrint = self.objective_term(Points, 'cp', Cp_calc, Cp_std, Cp_grad, name="Heat Capacity")
X_Eps0, G_Eps0, H_Eps0, Eps0Print = self.objective_term(Points, 'eps0', Eps0_calc, Eps0_std, Eps0_grad, name="Dielectric Constant")
Gradient = np.zeros(self.FF.np)
Hessian = np.zeros((self.FF.np,self.FF.np))
if X_Rho == 0: self.w_rho = 0.0
if X_Hvap == 0: self.w_hvap = 0.0
if X_Alpha == 0: self.w_alpha = 0.0
if X_Kappa == 0: self.w_kappa = 0.0
if X_Cp == 0: self.w_cp = 0.0
if X_Eps0 == 0: self.w_eps0 = 0.0
if self.w_normalize:
w_tot = self.w_rho + self.w_hvap + self.w_alpha + self.w_kappa + self.w_cp + self.w_eps0
else:
w_tot = 1.0
w_1 = self.w_rho / w_tot
w_2 = self.w_hvap / w_tot
w_3 = self.w_alpha / w_tot
w_4 = self.w_kappa / w_tot
w_5 = self.w_cp / w_tot
w_6 = self.w_eps0 / w_tot
Objective = w_1 * X_Rho + w_2 * X_Hvap + w_3 * X_Alpha + w_4 * X_Kappa + w_5 * X_Cp + w_6 * X_Eps0
if AGrad:
Gradient = w_1 * G_Rho + w_2 * G_Hvap + w_3 * G_Alpha + w_4 * G_Kappa + w_5 * G_Cp + w_6 * G_Eps0
if AHess:
Hessian = w_1 * H_Rho + w_2 * H_Hvap + w_3 * H_Alpha + w_4 * H_Kappa + w_5 * H_Cp + w_6 * H_Eps0
if not in_fd():
self.Xp = {"Rho" : X_Rho, "Hvap" : X_Hvap, "Alpha" : X_Alpha,
"Kappa" : X_Kappa, "Cp" : X_Cp, "Eps0" : X_Eps0}
self.Wp = {"Rho" : w_1, "Hvap" : w_2, "Alpha" : w_3,
"Kappa" : w_4, "Cp" : w_5, "Eps0" : w_6}
self.Pp = {"Rho" : RhoPrint, "Hvap" : HvapPrint, "Alpha" : AlphaPrint,
"Kappa" : KappaPrint, "Cp" : CpPrint, "Eps0" : Eps0Print}
if AGrad:
self.Gp = {"Rho" : G_Rho, "Hvap" : G_Hvap, "Alpha" : G_Alpha,
"Kappa" : G_Kappa, "Cp" : G_Cp, "Eps0" : G_Eps0}
self.Objective = Objective
Answer = {'X':Objective, 'G':Gradient, 'H':Hessian}
return Answer