def log(expr):
"""Logarithm"""
if type(expr) == GC:
return GC(se.log(expr.expr),
{s: d / expr.expr
for s, d in expr.gradients.items()})
return se.log(expr)
def test_ternary_candidate_models_are_constructed_correctly():
"""Candidate models should be generated for all valid combinations of possible models in the ternary case"""
features = OrderedDict([("CPM_FORM", (v.T * symengine.log(v.T), v.T**2)),
("SM_FORM", (v.T, )),
("HM_FORM", (symengine.S.One, ))])
YS = symengine.Symbol('YS')
V_I, V_J, V_K = symengine.Symbol('V_I'), symengine.Symbol(
'V_J'), symengine.Symbol('V_K')
candidate_models = build_candidate_models((('A', 'B', 'C'), 'A'), features)
assert candidate_models == OrderedDict([
('CPM_FORM', [
[v.T * YS * symengine.log(v.T)],
[v.T * YS * symengine.log(v.T), v.T**2 * YS],
[
v.T * V_I * YS * symengine.log(v.T),
v.T * V_J * YS * symengine.log(v.T),
v.T * V_K * YS * symengine.log(v.T)
],
[
v.T * V_I * YS * symengine.log(v.T), v.T**2 * V_I * YS,
v.T * V_J * YS * symengine.log(v.T), v.T**2 * V_J * YS,
v.T * V_K * YS * symengine.log(v.T), v.T**2 * V_K * YS
],
]),
('SM_FORM', [[v.T * YS],
[v.T * V_I * YS, v.T * V_J * YS, v.T * V_K * YS]]),
('HM_FORM', [[YS], [V_I * YS, V_J * YS, V_K * YS]])
])
def test_log():
x = Symbol("x")
x1 = sympy.Symbol("x")
assert log(x) == log(x1)
assert log(x)._sympy_() == sympy.log(x1)
assert sympify(sympy.log(x1)) == log(x)
y = Symbol("y")
y1 = sympy.Symbol("y")
assert log(x, y) == log(x, y1)
assert log(x1, y) == log(x1, y1)
assert log(x, y)._sympy_() == sympy.log(x1, y1)
assert sympify(sympy.log(x1, y1)) == log(x, y)
def test_log():
x = Symbol("x")
x1 = sympy.Symbol("x")
assert log(x) == log(x1)
assert log(x)._sympy_() == sympy.log(x1)
assert sympify(sympy.log(x1)) == log(x)
y = Symbol("y")
y1 = sympy.Symbol("y")
assert log(x, y) == log(x, y1)
assert log(x1, y) == log(x1, y1)
assert log(x, y)._sympy_() == sympy.log(x1, y1)
assert sympify(sympy.log(x1, y1)) == log(x, y)
def test_loggamma():
assert loggamma(-1) == oo
assert loggamma(-2) == oo
assert loggamma(0) == oo
assert loggamma(1) == 0
assert loggamma(2) == 0
assert loggamma(3) == log(2)
def test_FunctionWrapper():
import sympy
n, m, theta, phi = sympy.symbols("n, m, theta, phi")
r = sympy.Ynm(n, m, theta, phi)
s = Integer(2) * r
assert isinstance(s, Mul)
assert isinstance(s.args[1]._sympy_(), sympy.Ynm)
x = symbols("x")
e = x + sympy.loggamma(x)
assert str(e) == "x + loggamma(x)"
assert isinstance(e, Add)
assert e + sympy.loggamma(x) == x + 2 * sympy.loggamma(x)
f = e.subs({x: 10})
assert f == 10 + log(362880)
f = e.subs({x: 2})
assert f == 2
f = e.subs({x: 100})
v = f.n(53, real=True)
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x)
assert f == 1 + sympy.polygamma(0, x)
def test_FunctionWrapper():
import sympy
n, m, theta, phi = sympy.symbols("n, m, theta, phi")
r = sympy.Ynm(n, m, theta, phi)
s = Integer(2)*r
assert isinstance(s, Mul)
assert isinstance(s.args[1]._sympy_(), sympy.Ynm)
x = symbols("x")
e = x + sympy.loggamma(x)
assert str(e) == "x + loggamma(x)"
assert isinstance(e, Add)
assert e + sympy.loggamma(x) == x + 2*sympy.loggamma(x)
f = e.subs({x : 10})
assert f == 10 + log(362880)
f = e.subs({x : 2})
assert f == 2
f = e.subs({x : 100});
v = f.n(53, real=True);
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x)
assert f == 1 + sympy.polygamma(0, x)
def _get_array():
X, Y, Z = inp = array.array('d', [1, 2, 3])
args = x, y, z = se.symbols('x y z')
exprs = [x+y+z, se.sin(x)*se.log(y)*se.exp(z)]
ref = [X+Y+Z, math.sin(X)*math.log(Y)*math.exp(Z)]
def check(arr):
assert all([abs(x1-x2) < 1e-13 for x1, x2 in zip(ref, arr)])
return args, exprs, inp, check
def _get_array():
X, Y, Z = inp = array.array('d', [1, 2, 3])
args = x, y, z = se.symbols('x y z')
exprs = [x+y+z, se.sin(x)*se.log(y)*se.exp(z)]
ref = [X+Y+Z, math.sin(X)*math.log(Y)*math.exp(Z)]
def check(arr):
assert all([abs(x1-x2) < 1e-13 for x1, x2 in zip(ref, arr)])
return args, exprs, inp, check
def __pow__(self, other):
if type(other) == GradientContainer:
gradients = {
s: d * other.expr * (self.expr**(other.expr - 1))
for s, d in self.gradients.items()
}
for s, d in other.gradients.items():
if s in gradients:
gradients[s] += d * self.expr * se.log(
self.expr) * (self.expr**(other.expr - 1))
else:
gradients[s] = se.log(self.expr) * d * (self.expr**
other.expr)
return GradientContainer(self.expr**other.expr, gradients)
return GradientContainer(
self.expr**other, {
s: d * other * (self.expr**(other - 1))
for s, d in self.gradients.items()
})
def LLF_sym(self, hazard, covariate_data):
# x = b, b1, b2, b2 = symengine.symbols('b b1 b2 b3')
x = symengine.symbols(f'x:{self.numSymbols}')
second = []
prodlist = []
for i in range(self.n):
sum1 = 1
sum2 = 1
TempTerm1 = 1
for j in range(self.numParameters, self.numSymbols):
TempTerm1 = TempTerm1 * symengine.exp(
covariate_data[j - self.numParameters][i] * x[j])
sum1 = 1 - ((1 -
(hazard(i + 1, x[:self.numParameters])))**(TempTerm1))
for k in range(i):
TempTerm2 = 1
for j in range(self.numParameters, self.numSymbols):
TempTerm2 = TempTerm2 * symengine.exp(
covariate_data[j - self.numParameters][k] * x[j])
sum2 = sum2 * (
(1 - (hazard(i + 1, x[:self.numParameters])))**(TempTerm2))
second.append(sum2)
prodlist.append(sum1 * sum2)
firstTerm = -sum(self.failures) #Verified
secondTerm = sum(self.failures) * symengine.log(
sum(self.failures) / sum(prodlist))
logTerm = [] #Verified
for i in range(self.n):
logTerm.append(self.failures[i] * symengine.log(prodlist[i]))
thirdTerm = sum(logTerm)
factTerm = [] #Verified
for i in range(self.n):
factTerm.append(symengine.log(math.factorial(self.failures[i])))
fourthTerm = sum(factTerm)
f = firstTerm + secondTerm + thirdTerm - fourthTerm
return f, x
def solve_chi_saddlepoint(mu, Sigma):
"""Compute the saddlepoint approximation for the generalized chi square distribution given a mean and a covariance matrix. Currently has two different ways of solving:
1. If the mean is close to zero, the system can be solved symbolically."""
P = None
eigenvalues, eigenvectors = np.linalg.eig(Sigma)
if (eigenvectors == np.diag(eigenvalues)).all():
P = np.eye(len(mu))
else:
P = eigenvectors.T
Sigma_12 = np.linalg.cholesky(Sigma)
b = P @ Sigma_12 @ mu
x = sym.Symbol("x")
t = sym.Symbol("t")
# Cumulant function
K = 0
for i, l in enumerate(eigenvalues):
K += (t * b[i]**2 * l) / (1 - 2 * t * l) - 1 / 2 * sym.log(1 -
2 * l * t)
Kp = sym.diff(K, t).simplify()
Kpp = sym.diff(K, t, t).simplify()
roots = sym.lib.symengine_wrapper.solve(sym.Eq(Kp, x), t).args
if len(roots) > 1:
for expr in roots:
trial = Kpp.subs(t, expr).subs(x, np.dot(b, b))
if trial >= 0.0:
s_hat = expr
else:
s_hat = roots[0]
f = 1 / sym.sqrt(2 * sym.pi * Kpp.subs(
t, s_hat)) * sym.exp(K.subs(t, s_hat) - s_hat * x)
fp = sym.Lambdify(x, f.simplify())
c = integrate.quad(fp, 0, np.inf)[0]
return lambda x: 1 / c * fp(x)
def test_get_data_quantities_AL_NI_VA_interaction():
"""Test that an interaction with a VA produces the correct data quantities
We just have a template database that has the phase defined. We then hot
patch the Model object to have the GM from the fixed model we printed out
and the data we printed out. The hot patch is needed because this is
formation enthalpy data and the model needs to have the lower order terms
in composition.
One possible issue is that the new GM in the fixed model does not have any
individual contributions, so it cannot be used to test excluded model
contributions. The only excluded model contributions in this data are
idmix, but the property we are testing is HM_FORM, so the feature transform
of the idmix property should be zero.
"""
# Hack the namespace to make the copy-pasted Gibbs energy function work
from symengine import log, Piecewise, And
T = v.T
data = [{
'components': ['AL', 'NI', 'VA'],
'phases': ['BCC_B2'],
'solver': {
'mode':
'manual',
'sublattice_occupancies': [[1.0, [0.5, 0.5], 1.0],
[1.0, [0.75, 0.25], 1.0]],
'sublattice_site_ratios': [0.5, 0.5, 1.0],
'sublattice_configurations':
(('AL', ('NI', 'VA'), 'VA'), ('AL', ('NI', 'VA'), 'VA')),
'comment':
'BCC_B2 sublattice configuration (2SL)'
},
'conditions': {
'P': 101325.0,
'T': np.array([300.])
},
'reference_state': 'SGTE91',
'output': 'HM_FORM',
'values': np.array([[[-40316.61077, -56361.58554]]]),
'reference': 'C. Jiang 2009 (constrained SQS)',
'excluded_model_contributions': ['idmix']
}, {
'components': ['AL', 'NI', 'VA'],
'phases': ['BCC_B2'],
'solver': {
'mode':
'manual',
'sublattice_occupancies': [[1.0, [0.5, 0.5], 1.0],
[1.0, [0.75, 0.25], 1.0]],
'sublattice_site_ratios': [0.5, 0.5, 1.0],
'sublattice_configurations':
(('AL', ('NI', 'VA'), 'VA'), ('AL', ('NI', 'VA'), 'VA')),
'comment':
'BCC_B2 sublattice configuration (2SL)'
},
'conditions': {
'P': 101325.0,
'T': np.array([300.])
},
'reference_state': 'SGTE91',
'output': 'HM_FORM',
'values': np.array([[[-41921.43363, -57769.49473]]]),
'reference': 'C. Jiang 2009 (relaxed SQS)',
'excluded_model_contributions': ['idmix']
}]
NEW_GM = 8.3145 * T * (
0.5 * Piecewise((v.SiteFraction("BCC_B2", 0, "AL") *
log(v.SiteFraction("BCC_B2", 0, "AL")),
v.SiteFraction("BCC_B2", 0, "AL") > 1.0e-16),
(0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")) + 0.5 * Piecewise(
(v.SiteFraction("BCC_B2", 0, "NI") *
log(v.SiteFraction("BCC_B2", 0, "NI")),
v.SiteFraction("BCC_B2", 0, "NI") > 1.0e-16), (0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")) + 0.5 * Piecewise(
(v.SiteFraction("BCC_B2", 0, "VA") *
log(v.SiteFraction("BCC_B2", 0, "VA")),
v.SiteFraction("BCC_B2", 0, "VA") > 1.0e-16), (0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")) + 0.5 * Piecewise(
(v.SiteFraction("BCC_B2", 1, "AL") *
log(v.SiteFraction("BCC_B2", 1, "AL")),
v.SiteFraction("BCC_B2", 1, "AL") > 1.0e-16), (0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")) + 0.5 * Piecewise(
(v.SiteFraction("BCC_B2", 1, "NI") *
log(v.SiteFraction("BCC_B2", 1, "NI")),
v.SiteFraction("BCC_B2", 1, "NI") > 1.0e-16), (0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")) + 0.5 * Piecewise(
(v.SiteFraction("BCC_B2", 1, "VA") *
log(v.SiteFraction("BCC_B2", 1, "VA")),
v.SiteFraction("BCC_B2", 1, "VA") > 1.0e-16), (0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")) + Piecewise(
(v.SiteFraction("BCC_B2", 2, "VA") *
log(v.SiteFraction("BCC_B2", 2, "VA")),
v.SiteFraction("BCC_B2", 2, "VA") > 1.0e-16), (0, True)) /
(0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI"))
) + (
45262.9 * v.SiteFraction("BCC_B2", 0, "AL") *
v.SiteFraction("BCC_B2", 0, "NI") * v.SiteFraction("BCC_B2", 1, "AL") *
v.SiteFraction("BCC_B2", 2, "VA") +
45262.9 * v.SiteFraction("BCC_B2", 0, "AL") *
v.SiteFraction("BCC_B2", 1, "AL") * v.SiteFraction("BCC_B2", 1, "NI") *
v.SiteFraction("BCC_B2", 2, "VA")) / (
0.5 * v.SiteFraction("BCC_B2", 0, "AL") + 0.5 * v.SiteFraction(
"BCC_B2", 0, "NI") + 0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI")
) + (1.0 * v.SiteFraction("BCC_B2", 0, "AL") * v.SiteFraction(
"BCC_B2", 1, "AL") * v.SiteFraction("BCC_B2", 2, "VA") * Piecewise(
(10083 - 4.813 * T, And((T >= 298.15),
(T < 2900.0))), (0, True)) +
v.SiteFraction("BCC_B2", 0, "AL") * v.SiteFraction(
"BCC_B2", 1, "NI") * v.SiteFraction("BCC_B2", 2, "VA") *
(9.52839e-8 * T**3 + 0.00123463 * T**2 +
0.000871898 * T * log(T) + 1.31471 * T - 64435.3 + 23095.2 / T) +
v.SiteFraction("BCC_B2", 0, "AL") * v.SiteFraction(
"BCC_B2", 1, "VA") * v.SiteFraction("BCC_B2", 2, "VA") *
(10.0 * T + 16432.5) +
v.SiteFraction("BCC_B2", 0, "NI") * v.SiteFraction(
"BCC_B2", 1, "AL") * v.SiteFraction("BCC_B2", 2, "VA") *
(9.52839e-8 * T**3 + 0.00123463 * T**2 + 0.000871898 * T * log(T)
+ 1.31471 * T - 64435.3 + 23095.2 / T) + 1.0 * v.SiteFraction(
"BCC_B2", 0, "NI") * v.SiteFraction("BCC_B2", 1, "NI") *
v.SiteFraction("BCC_B2", 2, "VA") * Piecewise(
(8715.084 - 3.556 * T, And((T >= 298.15),
(T < 3000.0))), (0, True)) +
32790.6 * v.SiteFraction("BCC_B2", 0, "NI") * v.SiteFraction(
"BCC_B2", 1, "VA") * v.SiteFraction("BCC_B2", 2, "VA") +
v.SiteFraction("BCC_B2", 0, "VA") * v.SiteFraction(
"BCC_B2", 1, "AL") * v.SiteFraction("BCC_B2", 2, "VA") *
(10.0 * T + 16432.5) +
32790.6 * v.SiteFraction("BCC_B2", 0, "VA") * v.SiteFraction(
"BCC_B2", 1, "NI") * v.SiteFraction("BCC_B2", 2, "VA")) / (
0.5 * v.SiteFraction("BCC_B2", 0, "AL") +
0.5 * v.SiteFraction("BCC_B2", 0, "NI") +
0.5 * v.SiteFraction("BCC_B2", 1, "AL") +
0.5 * v.SiteFraction("BCC_B2", 1, "NI"))
dbf = Database(
"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ Date: 2019-12-08 18:05
$ Components: AL, NI, VA
$ Phases: BCC_B2
$ Generated by brandon (pycalphad 0.8.1.post1)
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
ELEMENT AL FCC_A1 26.982 4577.3 28.322 !
ELEMENT NI FCC_A1 58.69 4787.0 29.796 !
ELEMENT VA VACUUM 0.0 0.0 0.0 !
TYPE_DEFINITION % SEQ * !
DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
DEFAULT_COMMAND DEFINE_SYSTEM_ELEMENT VA !
PHASE BCC_B2 % 3 0.5 0.5 1 !
CONSTITUENT BCC_B2 :AL,NI,VA:AL,NI,VA:VA: !
""")
mod = Model(dbf, ['AL', 'NI', 'VA'], 'BCC_B2')
dd = {ky: 0.0 for ky in mod.models.keys()}
dd['GM'] = NEW_GM
mod.models = dd
print(mod.HM)
config_tup = (('AL', ), ('NI', 'VA'), ('VA', ))
calculate_dict = get_prop_samples(data, config_tup)
sample_condition_dicts = _get_sample_condition_dicts(
calculate_dict, list(map(len, config_tup)))
qty = get_data_quantities('HM_FORM', mod, [0], data,
sample_condition_dicts)
print(qty)
assert np.all(
np.isclose(
[-6254.7802775, -5126.1206475, -7458.3974225, -6358.04118875],
qty))
def test_log():
x = Symbol("x")
y = Symbol("y")
assert log(E) == 1
assert log(x, x) == 1
assert log(x, y) == log(x) / log(y)
def Paci2018(tDrugApplication, INaFRedMed, ICaLRedMed, IKrRedMed, IKsRedMed):
dY = [None] * 23
VmaxUp = 0.5113 # millimolar_per_second (in calcium_dynamics)
g_irel_max = 62.5434 # millimolar_per_second (in calcium_dynamics)
RyRa1 = 0.05354 # uM
RyRa2 = 0.0488 # uM
RyRahalf = 0.02427 # uM
RyRohalf = 0.01042 # uM
RyRchalf = 0.00144 # uM
kNaCa = 3917.0463 # A_per_F (in i_NaCa)
PNaK = 2.6351 # A_per_F (in i_NaK)
Kup = 3.1928e-4 # millimolar (in calcium_dynamics)
V_leak = 4.7279e-4 # per_second (in calcium_dynamics)
alpha = 2.5371 # dimensionless (in i_NaCa)
## Constants
F = 96485.3415 # coulomb_per_mole (in model_parameters)
R = 8.314472 # joule_per_mole_kelvin (in model_parameters)
T = 310.0 # kelvin (in model_parameters)
## Cell geometry
V_SR = 583.73 # micrometre_cube (in model_parameters)
Vc = 8800.0 # micrometre_cube (in model_parameters)
Cm = 9.87109e-11 # farad (in model_parameters)
## Extracellular concentrations
Nao = 151.0 # millimolar (in model_parameters)
Ko = 5.4 # millimolar (in model_parameters)
Cao = 1.8 #3#5#1.8 # millimolar (in model_parameters)
## Intracellular concentrations
# Naio = 10 mM y(17)
Ki = 150.0 # millimolar (in model_parameters)
# Cai = 0.0002 mM y(2)
# caSR = 0.3 mM y(1)
# time (second)
## Nernst potential
E_Na = R * T / F * symengine.log(Nao / y(17))
E_Ca = 0.5 * R * T / F * symengine.log(Cao / y(2))
E_K = R * T / F * log(Ko / Ki)
PkNa = 0.03 # dimensionless (in electric_potentials)
E_Ks = R * T / F * symengine.log((Ko + PkNa * Nao) / (Ki + PkNa * y(17)))
## INa
g_Na = 3671.2302 # S_per_F (in i_Na)
drug_no_drug_na = [
g_Na * y(13)**3.0 * y(11) * y(12) * (y(0) - E_Na),
INaFRedMed * g_Na * y(13)**3.0 * y(11) * y(12) * (y(0) - E_Na)
]
i_Na = drug_no_drug_na[0]
h_inf = 1.0 / symengine.sqrt(1.0 +
symengine.exp((y(0) * 1000.0 + 72.1) / 5.7))
alpha_h = 0.057 * symengine.exp(-(y(0) * 1000.0 + 80.0) / 6.8)
beta_h = 2.7 * symengine.exp(
0.079 * y(0) * 1000.0) + 3.1 * 10.0**5.0 * symengine.exp(
0.3485 * y(0) * 1000.0)
tau_h = sigmoid_generator(y(0), -0.0385, -1) * (1.5 / (
(alpha_h + beta_h) * 1000.0)) + sigmoid_generator(
y(0), -0.0385, 1) * (1.5 * 1.6947 / 1000.0)
dY[11] = (h_inf - y(11)) / tau_h
j_inf = 1.0 / symengine.sqrt(1.0 +
symengine.exp((y(0) * 1000.0 + 72.1) / 5.7))
alpha_j = sigmoid_generator(y(0), -0.04, -1) * (
-25428.0 * symengine.exp(0.2444 * y(0) * 1000.0) - 6.948 * 10.0**-6.0 *
symengine.exp(-0.04391 * y(0) * 1000.0)) * (y(0) * 1000.0 + 37.78) / (
1.0 + symengine.exp(0.311 *
(y(0) * 1000.0 + 79.23))) + sigmoid_generator(
y(0), -0.04, 1) * 0
beta_j = sigmoid_generator(y(0), -0.04, -1) * (
(0.02424 * symengine.exp(-0.01052 * y(0) * 1000) /
(1 + symengine.exp(-0.1378 *
(y(0) * 1000 + 40.14))))) + sigmoid_generator(
y(0), -0.04, 1) * (
(0.6 * symengine.exp(
(0.057) * y(0) * 1000) /
(1 + symengine.exp(-0.1 *
(y(0) * 1000 + 32)))))
tau_j = 7.0 / ((alpha_j + beta_j) * 1000.0)
dY[12] = (j_inf - y(12)) / tau_j
m_inf = 1.0 / (1.0 + symengine.exp(
(-y(0) * 1000.0 - 34.1) / 5.9))**(1.0 / 3.0)
alpha_m = 1.0 / (1.0 + symengine.exp((-y(0) * 1000.0 - 60.0) / 5.0))
beta_m = 0.1 / (1.0 + symengine.exp(
(y(0) * 1000.0 + 35.0) / 5.0)) + 0.1 / (1.0 + symengine.exp(
(y(0) * 1000.0 - 50.0) / 200.0))
tau_m = 1.0 * alpha_m * beta_m / 1000.0
dY[13] = (m_inf - y(13)) / tau_m
## INaL
myCoefTauM = 1
tauINaL = 200 #ms
GNaLmax = 2.3 * 7.5 #(S/F)
Vh_hLate = 87.61
i_NaL = GNaLmax * y(18)**(3) * y(19) * (y(0) - E_Na)
m_inf_L = 1 / (1 + symengine.exp(-(y(0) * 1000 + 42.85) / (5.264)))
alpha_m_L = 1 / (1 + symengine.exp((-60 - y(0) * 1000) / 5))
beta_m_L = 0.1 / (1 + symengine.exp(
(y(0) * 1000 + 35) / 5)) + 0.1 / (1 + symengine.exp(
(y(0) * 1000 - 50) / 200))
tau_m_L = 1 / 1000 * myCoefTauM * alpha_m_L * beta_m_L
dY[18] = (m_inf_L - y(18)) / tau_m_L
h_inf_L = 1 / (1 + symengine.exp((y(0) * 1000 + Vh_hLate) / (7.488)))
tau_h_L = 1 / 1000 * tauINaL
dY[19] = (h_inf_L - y(19)) / tau_h_L
## If
E_f = -0.017 # volt (in i_f)
g_f = 30.10312 # S_per_F (in i_f)
i_f = g_f * y(14) * (y(0) - E_f)
i_fNa = 0.42 * g_f * y(14) * (y(0) - E_Na)
Xf_infinity = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 77.85) / 5.0))
tau_Xf = 1900.0 / (1.0 + symengine.exp(
(y(0) * 1000.0 + 15.0) / 10.0)) / 1000.0
dY[14] = (Xf_infinity - y(14)) / tau_Xf
## ICaL
g_CaL = 8.635702e-5 # metre_cube_per_F_per_s (in i_CaL)
drug_no_drug_CaL = [
g_CaL * 4.0 * y(0) * F**2.0 / (R * T) *
(y(2) * symengine.exp(2.0 * y(0) * F / (R * T)) - 0.341 * Cao) /
(symengine.exp(2.0 * y(0) * F / (R * T)) - 1.0) * y(4) * y(5) * y(6) *
y(7), ICaLRedMed * g_CaL * 4.0 * y(0) * F**2.0 / (R * T) *
(y(2) * symengine.exp(2.0 * y(0) * F / (R * T)) - 0.341 * Cao) /
(symengine.exp(2.0 * y(0) * F /
(R * T)) - 1.0) * y(4) * y(5) * y(6) * y(7)
]
i_CaL = drug_no_drug_CaL[0]
d_infinity = 1.0 / (1.0 + symengine.exp(-(y(0) * 1000.0 + 9.1) / 7.0))
alpha_d = 0.25 + 1.4 / (1.0 + symengine.exp(
(-y(0) * 1000.0 - 35.0) / 13.0))
beta_d = 1.4 / (1.0 + symengine.exp((y(0) * 1000.0 + 5.0) / 5.0))
gamma_d = 1.0 / (1.0 + symengine.exp((-y(0) * 1000.0 + 50.0) / 20.0))
tau_d = (alpha_d * beta_d + gamma_d) * 1.0 / 1000.0
dY[4] = (d_infinity - y(4)) / tau_d
f1_inf = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 26.0) / 3.0))
constf1 = sigmoid_generator(f1_inf - y(5), 0, 1) * 1.0 + 1433.0 * (
y(2) - 50.0 * 1.0e-6) + sigmoid_generator(f1_inf - y(5), 0, -1) * 1.0
tau_f1 = (20.0 + 1102.5 * symengine.exp(-(
(y(0) * 1000.0 + 27.0)**2.0 / 15.0)**2.0) + 200.0 /
(1.0 + symengine.exp((13.0 - y(0) * 1000.0) / 10.0)) + 180.0 /
(1.0 + symengine.exp(
(30.0 + y(0) * 1000.0) / 10.0))) * constf1 / 1000.0
dY[5] = (f1_inf - y(5)) / tau_f1
f2_inf = 0.33 + 0.67 / (1.0 + symengine.exp((y(0) * 1000.0 + 32.0) / 4.0))
constf2 = 1.0
tau_f2 = (600.0 * symengine.exp(-(y(0) * 1000.0 + 25.0)**2.0 / 170.0) +
31.0 / (1.0 + symengine.exp(
(25.0 - y(0) * 1000.0) / 10.0)) + 16.0 /
(1.0 + symengine.exp(
(30.0 + y(0) * 1000.0) / 10.0))) * constf2 / 1000.0
dY[6] = (f2_inf - y(6)) / tau_f2
alpha_fCa = 1.0 / (1.0 + (y(2) / 0.0006)**8.0)
beta_fCa = 0.1 / (1.0 + symengine.exp((y(2) - 0.0009) / 0.0001))
gamma_fCa = 0.3 / (1.0 + symengine.exp((y(2) - 0.00075) / 0.0008))
fCa_inf = (alpha_fCa + beta_fCa + gamma_fCa) / 1.3156
constfCa = sigmoid_generator(y(0), -0.06, 1) * sigmoid_generator(
fCa_inf, y(7), 1) * 0 + (sigmoid_generator(y(0), -0.06, -1) +
sigmoid_generator(fCa_inf, y(7), -1)) * 1.0
tau_fCa = 0.002 # second (in i_CaL_fCa_gate)
dY[7] = constfCa * (fCa_inf - y(7)) / tau_fCa
## Ito
g_to = 29.9038 # S_per_F (in i_to)
i_to = g_to * (y(0) - E_K) * y(15) * y(16)
q_inf = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 53.0) / 13.0))
tau_q = (6.06 + 39.102 /
(0.57 * symengine.exp(-0.08 * (y(0) * 1000.0 + 44.0)) +
0.065 * symengine.exp(0.1 * (y(0) * 1000.0 + 45.93)))) / 1000.0
dY[15] = (q_inf - y(15)) / tau_q
r_inf = 1.0 / (1.0 + symengine.exp(-(y(0) * 1000.0 - 22.3) / 18.75))
tau_r = (2.75352 + 14.40516 /
(1.037 * symengine.exp(0.09 * (y(0) * 1000.0 + 30.61)) +
0.369 * symengine.exp(-0.12 * (y(0) * 1000.0 + 23.84)))) / 1000.0
dY[16] = (r_inf - y(16)) / tau_r
## IKs
g_Ks = 2.041 # S_per_F (in i_Ks)
drug_no_drug_Ks = [
g_Ks * (y(0) - E_Ks) * y(10)**2.0 *
(1.0 + 0.6 / (1.0 + (3.8 * 0.00001 / y(2))**1.4)),
IKsRedMed * g_Ks * (y(0) - E_Ks) * y(10)**2.0 *
(1.0 + 0.6 / (1.0 + (3.8 * 0.00001 / y(2))**1.4))
]
i_Ks = drug_no_drug_Ks[0]
Xs_infinity = 1.0 / (1.0 + symengine.exp((-y(0) * 1000.0 - 20.0) / 16.0))
alpha_Xs = 1100.0 / symengine.sqrt(1.0 + symengine.exp(
(-10.0 - y(0) * 1000.0) / 6.0))
beta_Xs = 1.0 / (1.0 + symengine.exp((-60.0 + y(0) * 1000.0) / 20.0))
tau_Xs = 1.0 * alpha_Xs * beta_Xs / 1000.0
dY[10] = (Xs_infinity - y(10)) / tau_Xs
## IKr
L0 = 0.025 # dimensionless (in i_Kr_Xr1_gate)
Q = 2.3 # dimensionless (in i_Kr_Xr1_gate)
g_Kr = 29.8667 # S_per_F (in i_Kr)
drug_no_drug_Kr = [
g_Kr * (y(0) - E_K) * y(8) * y(9) * sqrt(Ko / 5.4),
IKrRedMed * g_Kr * (y(0) - E_K) * y(8) * y(9) * sqrt(Ko / 5.4)
]
i_Kr = drug_no_drug_Kr[0]
V_half = 1000.0 * (-R * T / (F * Q) * log(
(1.0 + Cao / 2.6)**4.0 / (L0 * (1.0 + Cao / 0.58)**4.0)) - 0.019)
Xr1_inf = 1.0 / (1.0 + symengine.exp((V_half - y(0) * 1000.0) / 4.9))
alpha_Xr1 = 450.0 / (1.0 + symengine.exp((-45.0 - y(0) * 1000.0) / 10.0))
beta_Xr1 = 6.0 / (1.0 + symengine.exp((30.0 + y(0) * 1000.0) / 11.5))
tau_Xr1 = 1.0 * alpha_Xr1 * beta_Xr1 / 1000.0
dY[8] = (Xr1_inf - y(8)) / tau_Xr1
Xr2_infinity = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 88.0) / 50.0))
alpha_Xr2 = 3.0 / (1.0 + symengine.exp((-60.0 - y(0) * 1000.0) / 20.0))
beta_Xr2 = 1.12 / (1.0 + symengine.exp((-60.0 + y(0) * 1000.0) / 20.0))
tau_Xr2 = 1.0 * alpha_Xr2 * beta_Xr2 / 1000.0
dY[9] = (Xr2_infinity - y(9)) / tau_Xr2
## IK1
alpha_K1 = 3.91 / (1.0 +
symengine.exp(0.5942 *
(y(0) * 1000.0 - E_K * 1000.0 - 200.0)))
beta_K1 = (-1.509 * symengine.exp(0.0002 *
(y(0) * 1000.0 - E_K * 1000.0 + 100.0)) +
symengine.exp(0.5886 * (y(0) * 1000.0 - E_K * 1000.0 - 10.0))
) / (1.0 + symengine.exp(0.4547 *
(y(0) * 1000.0 - E_K * 1000.0)))
XK1_inf = alpha_K1 / (alpha_K1 + beta_K1)
g_K1 = 28.1492 # S_per_F (in i_K1)
i_K1 = g_K1 * XK1_inf * (y(0) - E_K) * sqrt(Ko / 5.4)
## INaCa
KmCa = 1.38 # millimolar (in i_NaCa)
KmNai = 87.5 # millimolar (in i_NaCa)
Ksat = 0.1 # dimensionless (in i_NaCa)
gamma = 0.35 # dimensionless (in i_NaCa)
kNaCa1 = kNaCa # A_per_F (in i_NaCa)
i_NaCa = kNaCa1 * (symengine.exp(gamma * y(0) * F /
(R * T)) * y(17)**3.0 * Cao -
symengine.exp(
(gamma - 1.0) * y(0) * F /
(R * T)) * Nao**3.0 * y(2) * alpha) / (
(KmNai**3.0 + Nao**3.0) * (KmCa + Cao) *
(1.0 + Ksat * symengine.exp(
(gamma - 1.0) * y(0) * F / (R * T))))
## INaK
Km_K = 1.0 # millimolar (in i_NaK)
Km_Na = 40.0 # millimolar (in i_NaK)
PNaK1 = PNaK # A_per_F (in i_NaK)
i_NaK = PNaK1 * Ko / (Ko + Km_K) * y(17) / (y(17) + Km_Na) / (
1.0 + 0.1245 * symengine.exp(-0.1 * y(0) * F / (R * T)) +
0.0353 * symengine.exp(-y(0) * F / (R * T)))
## IpCa
KPCa = 0.0005 # millimolar (in i_PCa)
g_PCa = 0.4125 # A_per_F (in i_PCa)
i_PCa = g_PCa * y(2) / (y(2) + KPCa)
## Background currents
g_b_Na = 0.95 # S_per_F (in i_b_Na)
i_b_Na = g_b_Na * (y(0) - E_Na)
g_b_Ca = 0.727272 # S_per_F (in i_b_Ca)
i_b_Ca = g_b_Ca * (y(0) - E_Ca)
## Sarcoplasmic reticulum
i_up = VmaxUp / (1.0 + Kup**2.0 / y(2)**2.0)
i_leak = (y(1) - y(2)) * V_leak
dY[3] = 0
# RyR
RyRSRCass = (1 - 1 / (1 + symengine.exp((y(1) - 0.3) / 0.1)))
i_rel = g_irel_max * RyRSRCass * y(21) * y(22) * (y(1) - y(2))
RyRainfss = RyRa1 - RyRa2 / (1 + symengine.exp(
(1000 * y(2) - (RyRahalf)) / 0.0082))
RyRtauadapt = 1 #s
dY[20] = (RyRainfss - y(20)) / RyRtauadapt
RyRoinfss = (1 - 1 / (1 + symengine.exp(
(1000 * y(2) - (y(20) + RyRohalf)) / 0.003)))
RyRtauact = sigmoid_generator(
RyRoinfss, y(21), 1) * 18.75e-3 + 0.1 * 18.75e-3 * sigmoid_generator(
RyRoinfss, y(21), -1)
dY[21] = (RyRoinfss - y(21)) / RyRtauact
RyRcinfss = (1 / (1 + symengine.exp(
(1000 * y(2) - (y(20) + RyRchalf)) / 0.001)))
RyRtauinact = sigmoid_generator(RyRcinfss, y(22),
1) * 2 * 87.5e-3 + sigmoid_generator(
RyRcinfss, y(22), -1) * 87.5e-3
dY[22] = (RyRcinfss - y(22)) / RyRtauinact
## Ca2+ buffering
Buf_C = 0.25 # millimolar (in calcium_dynamics)
Buf_SR = 10.0 # millimolar (in calcium_dynamics)
Kbuf_C = 0.001 # millimolar (in calcium_dynamics)
Kbuf_SR = 0.3 # millimolar (in calcium_dynamics)
Cai_bufc = 1.0 / (1.0 + Buf_C * Kbuf_C / (y(2) + Kbuf_C)**2.0)
Ca_SR_bufSR = 1.0 / (1.0 + Buf_SR * Kbuf_SR / (y(1) + Kbuf_SR)**2.0)
## Ionic concentrations
#Nai
dY[17] = -Cm * (i_Na + i_NaL + i_b_Na + 3.0 * i_NaK + 3.0 * i_NaCa +
i_fNa) / (F * Vc * 1.0e-18)
#caSR
dY[2] = Cai_bufc * (i_leak - i_up + i_rel -
(i_CaL + i_b_Ca + i_PCa - 2.0 * i_NaCa) * Cm /
(2.0 * Vc * F * 1.0e-18))
#Cai
dY[1] = Ca_SR_bufSR * Vc / V_SR * (i_up - (i_rel + i_leak))
## Stimulation
i_stim_Amplitude = 7.5e-10 # ampere (in stim_mode)
i_stim_End = 1000.0 # second (in stim_mode)
i_stim_PulseDuration = 0.005 # second (in stim_mode)
i_stim_Start = 0.0 # second (in stim_mode)
i_stim_frequency = 60.0 # per_second (in stim_mode)
stim_flag = 0.0 # dimensionless (in stim_mode)
i_stim_Period = 60.0 / i_stim_frequency
i_stim = 0 #(sigmoid_generator(time, i_stim_Start, 1) * sigmoid_generator(time, i_stim_End, -1) * (sigmoid_generator(time-i_stim_Start-symengine.floor((time-i_stim_Start)/i_stim_Period)*i_stim_Period, i_stim_PulseDuration, -1) ))*stim_flag*i_stim_Amplitude/Cm+0.0
## Membrane potential
dY[0] = -(i_K1 + i_to + i_Kr + i_Ks + i_CaL + i_NaK + i_Na + i_NaL +
i_NaCa + i_PCa + i_f + i_b_Na + i_b_Ca - i_stim)
## Output variables
IK1 = i_K1
Ito = i_to
IKr = i_Kr
IKs = i_Ks
ICaL = i_CaL
INaK = i_NaK
INa = i_Na
INaCa = i_NaCa
IpCa = i_PCa
If = i_f
IbNa = i_b_Na
IbCa = i_b_Ca
Irel = i_rel
Iup = i_up
Ileak = i_leak
Istim = i_stim
INaL = i_NaL
dati = [
INa, If, ICaL, Ito, IKs, IKr, IK1, INaCa, INaK, IpCa, IbNa, IbCa, Irel,
Iup, Ileak, Istim, E_K, E_Na, INaL
]
return dY
# 1 - evaluate function at Y...
# 2 - loop over Y, perturb each element by a small percent of its total
# 3 - during each loop, find dY/dt, given the perturbation
# 4 - find the change in Y as a function of the change in the perturbation
# Conditionals
# tau_h = 1.5*1.6947/1000.0
# alpha_j = 0.0
# beta_j = ((0.6*exp((0.057)*Y[0]*1000)/(1+exp(-0.1*(Y[0]*1000+32)))))
# constf1 = 1.0
# constfCa = 1.0
# RyRtauact = 0.1*18.75e-3 #s
# RyRtauinact = 87.5e-3 #s
# i_stim = 0.0
'''
def test_dirichlet_eta():
assert dirichlet_eta(0) == Rational(1, 2)
assert dirichlet_eta(-1) == Rational(1, 4)
assert dirichlet_eta(1) == log(2)
assert dirichlet_eta(2) == pi**2 / 12
assert dirichlet_eta(4) == pi**4 * Rational(7, 720)
def Paci2018(tDrugApplication, INaFRedMed,ICaLRedMed, IKrRedMed, IKsRedMed):
dY = [None]*23
'''
Parameters from optimizer
VmaxUp = param(1)
g_irel_max = param(2)
RyRa1 = param(3)
RyRa2 = param(4)
RyRahalf = param(5)
RyRohalf = param(6)
RyRchalf = param(7)
kNaCa = param(8)
PNaK = param(9)
Kup = param(10)
V_leak = param(11)
alpha = param(12)
'''
VmaxUp = 0.5113 # millimolar_per_second (in calcium_dynamics)
g_irel_max = 62.5434 # millimolar_per_second (in calcium_dynamics)
RyRa1 = 0.05354 # uM
RyRa2 = 0.0488 # uM
RyRahalf = 0.02427 # uM
RyRohalf = 0.01042 # uM
RyRchalf = 0.00144 # uM
kNaCa = 3917.0463 # A_per_F (in i_NaCa)
PNaK = 2.6351 # A_per_F (in i_NaK)
Kup = 3.1928e-4 # millimolar (in calcium_dynamics)
V_leak = 4.7279e-4 # per_second (in calcium_dynamics)
alpha = 2.5371 # dimensionless (in i_NaCa)
## Constants
F = 96485.3415 # coulomb_per_mole (in model_parameters)
R = 8.314472 # joule_per_mole_kelvin (in model_parameters)
T = 310 # kelvin (in model_parameters)
## Cell geometry
V_SR = 583.73 # micrometre_cube (in model_parameters)
Vc = 8800 # micrometre_cube (in model_parameters)
Cm = 9.87109e-11 # farad (in model_parameters)
## Extracellular concentrations
Nao = 151 # millimolar (in model_parameters)
Ko = 5.4 # millimolar (in model_parameters)
Cao = 1.8 #3#5#1.8 # millimolar (in model_parameters)
## Intracellular concentrations
# Naio = 10 mM y(17)
Ki = 150 # millimolar (in model_parameters)
# Cai = 0.0002 mM y(2)
# caSR = 0.3 mM y(1)
## Nernst potential
E_Na = R*T/F*log(Nao/y(17))
E_Ca = 0.5*R*T/F*log(Cao/y(2))
E_K = R*T/F*log(Ko/Ki)
PkNa = 0.03 # dimensionless (in electric_potentials)
E_Ks = R*T/F*log((Ko+PkNa*Nao)/(Ki+PkNa*y(17)))
## INa
g_Na = 3671.2302 # S_per_F (in i_Na)
i_Na = g_Na*y(13)**3*y(11)*y(12)*(y(0)-E_Na)
h_inf = 1/sqrt(1+exp((y(0)*1000+72.1)/5.7))
alpha_h = 0.057*exp(-(y(0)*1000+80)/6.8)
beta_h = 2.7*exp(0.079*y(0)*1000)+3.1*10**5*exp(0.3485*y(0)*1000)
tau_h = conditional(y(0),-0.0385,1.5/((alpha_h+beta_h)*1000),1.5*1.6947/1000)
dY[11] = (h_inf-y(11))/tau_h
j_inf = 1/sqrt(1+exp((y(0)*1000+72.1)/5.7))
alpha_j = conditional(y(0),-0.04,(-25428*exp(0.2444*y(0)*1000)-6.948*10**-6*exp(-0.04391*y(0)*1000))*(y(0)*1000+37.78)/(1+exp(0.311*(y(0)*1000+79.23))),0)
beta_j = conditional(
y(0),-0.04,
0.02424*exp(-0.01052*y(0)*1000)/(1+exp(-0.1378*(y(0)*1000+40.14))),
0.6*exp((0.057)*y(0)*1000)/(1+exp(-0.1*(y(0)*1000+32))),
)
tau_j = 7/((alpha_j+beta_j)*1000)
dY[12] = (j_inf-y(12))/tau_j
m_inf = 1/(1+exp((-y(0)*1000-34.1)/5.9))**(1/3)
alpha_m = 1/(1+exp((-y(0)*1000-60)/5))
beta_m = 0.1/(1+exp((y(0)*1000+35)/5))+0.1/(1+exp((y(0)*1000-50)/200))
tau_m = 1*alpha_m*beta_m/1000
dY[13] = (m_inf-y(13))/tau_m
## INaL
myCoefTauM = 1
tauINaL = 200 #ms
GNaLmax = 2.3*7.5 #(S/F)
Vh_hLate = 87.61
i_NaL = GNaLmax* y(18)**(3)*y(19)*(y(0)-E_Na)
m_inf_L = 1/(1+exp(-(y(0)*1000+42.85)/(5.264)))
alpha_m_L = 1/(1+exp((-60-y(0)*1000)/5))
beta_m_L = 0.1/(1+exp((y(0)*1000+35)/5))+0.1/(1+exp((y(0)*1000-50)/200))
tau_m_L = 1/1000 * myCoefTauM*alpha_m_L*beta_m_L
dY[18] = (m_inf_L-y(18))/tau_m_L
h_inf_L = 1/(1+exp((y(0)*1000+Vh_hLate)/(7.488)))
tau_h_L = 1/1000 * tauINaL
dY[19] = (h_inf_L-y(19))/tau_h_L
## If
E_f = -0.017 # volt (in i_f)
g_f = 30.10312 # S_per_F (in i_f)
i_f = g_f*y(14)*(y(0)-E_f)
i_fNa = 0.42*g_f*y(14)*(y(0)-E_Na)
Xf_infinity = 1/(1+exp((y(0)*1000+77.85)/5))
tau_Xf = 1900/(1+exp((y(0)*1000+15)/10))/1000
dY[14] = (Xf_infinity-y(14))/tau_Xf
## ICaL
g_CaL = 8.635702e-5 # metre_cube_per_F_per_s (in i_CaL)
i_CaL = g_CaL*4*y(0)*F**2/(R*T)*(y(2)*exp(2*y(0)*F/(R*T))-0.341*Cao)/(exp(2*y(0)*F/(R*T))-1)*y(4)*y(5)*y(6)*y(7)
d_infinity = 1/(1+exp(-(y(0)*1000+9.1)/7))
alpha_d = 0.25+1.4/(1+exp((-y(0)*1000-35)/13))
beta_d = 1.4/(1+exp((y(0)*1000+5)/5))
gamma_d = 1/(1+exp((-y(0)*1000+50)/20))
tau_d = (alpha_d*beta_d+gamma_d)*1/1000
dY[4] = (d_infinity-y(4))/tau_d
f1_inf = 1/(1+exp((y(0)*1000+26)/3))
constf1 = 1 + 1433*(y(2)-50*1e-6)
tau_f1 = (20+1102.5*exp(-((y(0)*1000+27)**2/15)**2)+200/(1+exp((13-y(0)*1000)/10))+180/(1+exp((30+y(0)*1000)/10)))*constf1/1000
dY[5] = (f1_inf-y(5))/tau_f1
f2_inf = 0.33+0.67/(1+exp((y(0)*1000+32)/4))
constf2 = 1
tau_f2 = (600*exp(-(y(0)*1000+25)**2/170)+31/(1+exp((25-y(0)*1000)/10))+16/(1+exp((30+y(0)*1000)/10)))*constf2/1000
dY[6] = (f2_inf-y(6))/tau_f2
alpha_fCa = 1/(1+(y(2)/0.0006)**8)
beta_fCa = 0.1/(1+exp((y(2)-0.0009)/0.0001))
gamma_fCa = 0.3/(1+exp((y(2)-0.00075)/0.0008))
fCa_inf = (alpha_fCa+beta_fCa+gamma_fCa)/1.3156
constfCa = conditional( y(0), -0.06, 1, conditional(fCa_inf,y(7),1,0) )
tau_fCa = 0.002 # second (in i_CaL_fCa_gate)
dY[7] = constfCa*(fCa_inf-y(7))/tau_fCa
## Ito
g_to = 29.9038 # S_per_F (in i_to)
i_to = g_to*(y(0)-E_K)*y(15)*y(16)
q_inf = 1/(1+exp((y(0)*1000+53)/13))
tau_q = (6.06+39.102/(0.57*exp(-0.08*(y(0)*1000+44))+0.065*exp(0.1*(y(0)*1000+45.93))))/1000
dY[15] = (q_inf-y(15))/tau_q
r_inf = 1/(1+exp(-(y(0)*1000-22.3)/18.75))
tau_r = (2.75352+14.40516/(1.037*exp(0.09*(y(0)*1000+30.61))+0.369*exp(-0.12*(y(0)*1000+23.84))))/1000
dY[16] = (r_inf-y(16))/tau_r
## IKs
g_Ks = 2.041 # S_per_F (in i_Ks)
i_Ks = g_Ks*(y(0)-E_Ks)*y(10)**2*(1+0.6/(1+(3.8*0.00001/y(2))**1.4))
Xs_infinity = 1/(1+exp((-y(0)*1000-20)/16))
alpha_Xs = 1100/sqrt(1+exp((-10-y(0)*1000)/6))
beta_Xs = 1/(1+exp((-60+y(0)*1000)/20))
tau_Xs = 1*alpha_Xs*beta_Xs/1000
dY[10] = (Xs_infinity-y(10))/tau_Xs
## IKr
L0 = 0.025 # dimensionless (in i_Kr_Xr1_gate)
Q = 2.3 # dimensionless (in i_Kr_Xr1_gate)
g_Kr = 29.8667 # S_per_F (in i_Kr)
i_Kr = g_Kr*(y(0)-E_K)*y(8)*y(9)*sqrt(Ko/5.4)
V_half = 1000*(-R*T/(F*Q)*log((1+Cao/2.6)**4/(L0*(1+Cao/0.58)**4))-0.019)
Xr1_inf = 1/(1+exp((V_half-y(0)*1000)/4.9))
alpha_Xr1 = 450/(1+exp((-45-y(0)*1000)/10))
beta_Xr1 = 6/(1+exp((30+y(0)*1000)/11.5))
tau_Xr1 = 1*alpha_Xr1*beta_Xr1/1000
dY[8] = (Xr1_inf-y(8))/tau_Xr1
Xr2_infinity = 1/(1+exp((y(0)*1000+88)/50))
alpha_Xr2 = 3/(1+exp((-60-y(0)*1000)/20))
beta_Xr2 = 1.12/(1+exp((-60+y(0)*1000)/20))
tau_Xr2 = 1*alpha_Xr2*beta_Xr2/1000
dY[9] = (Xr2_infinity-y(9))/tau_Xr2
## IK1
alpha_K1 = 3.91/(1+exp(0.5942*(y(0)*1000-E_K*1000-200)))
beta_K1 = (-1.509*exp(0.0002*(y(0)*1000-E_K*1000+100))+exp(0.5886*(y(0)*1000-E_K*1000-10)))/(1+exp(0.4547*(y(0)*1000-E_K*1000)))
XK1_inf = alpha_K1/(alpha_K1+beta_K1)
g_K1 = 28.1492 # S_per_F (in i_K1)
i_K1 = g_K1*XK1_inf*(y(0)-E_K)*sqrt(Ko/5.4)
## INaCa
KmCa = 1.38 # millimolar (in i_NaCa)
KmNai = 87.5 # millimolar (in i_NaCa)
Ksat = 0.1 # dimensionless (in i_NaCa)
gamma = 0.35 # dimensionless (in i_NaCa)
kNaCa1 = kNaCa # A_per_F (in i_NaCa)
i_NaCa = kNaCa1*(exp(gamma*y(0)*F/(R*T))*y(17)**3*Cao-exp((gamma-1)*y(0)*F/(R*T))*Nao**3*y(2)*alpha)/((KmNai**3+Nao**3)*(KmCa+Cao)*(1+Ksat*exp((gamma-1)*y(0)*F/(R*T))))
## INaK
Km_K = 1 # millimolar (in i_NaK)
Km_Na = 40 # millimolar (in i_NaK)
PNaK1 = PNaK # A_per_F (in i_NaK)
i_NaK = PNaK1*Ko/(Ko+Km_K)*y(17)/(y(17)+Km_Na)/(1+0.1245*exp(-0.1*y(0)*F/(R*T))+0.0353*exp(-y(0)*F/(R*T)))
## IpCa
KPCa = 0.0005 # millimolar (in i_PCa)
g_PCa = 0.4125 # A_per_F (in i_PCa)
i_PCa = g_PCa*y(2)/(y(2)+KPCa)
## Background currents
g_b_Na = 0.95 # S_per_F (in i_b_Na)
i_b_Na = g_b_Na*(y(0)-E_Na)
g_b_Ca = 0.727272 # S_per_F (in i_b_Ca)
i_b_Ca = g_b_Ca*(y(0)-E_Ca)
## Sarcoplasmic reticulum
i_up = VmaxUp/(1+Kup**2/y(2)**2)
i_leak = (y(1)-y(2))*V_leak
dY[3] = 0
# RyR
RyRSRCass = (1 - 1/(1 + exp((y(1)-0.3)/0.1)))
i_rel = g_irel_max*RyRSRCass*y(21)*y(22)*(y(1)-y(2))
RyRainfss = RyRa1-RyRa2/(1 + exp((1000*y(2)-(RyRahalf))/0.0082))
RyRtauadapt = 1 #s
dY[20] = (RyRainfss- y(20))/RyRtauadapt
RyRoinfss = (1 - 1/(1 + exp((1000*y(2)-(y(20)+ RyRohalf))/0.003)))
RyRtauact = conditional(RyRoinfss,y(21),0.1,1)*18.75e-3
dY[21] = (RyRoinfss- y(21))/RyRtauact
RyRcinfss = (1/(1 + exp((1000*y(2)-(y(20)+RyRchalf))/0.001)))
RyRtauinact = conditional(RyRcinfss,y(22),1,2)*87.5e-3
dY[22] = (RyRcinfss- y(22))/RyRtauinact
## Ca2+ buffering
Buf_C = 0.25 # millimolar (in calcium_dynamics)
Buf_SR = 10 # millimolar (in calcium_dynamics)
Kbuf_C = 0.001 # millimolar (in calcium_dynamics)
Kbuf_SR = 0.3 # millimolar (in calcium_dynamics)
Cai_bufc = 1/(1+Buf_C*Kbuf_C/(y(2)+Kbuf_C)**2)
Ca_SR_bufSR = 1/(1+Buf_SR*Kbuf_SR/(y(1)+Kbuf_SR)**2)
## Ionic concentrations
#Nai
dY[17] = -Cm*(i_Na+i_NaL+i_b_Na+3*i_NaK+3*i_NaCa+i_fNa)/(F*Vc*1e-18)
#caSR
dY[2] = Cai_bufc*(i_leak-i_up+i_rel-(i_CaL+i_b_Ca+i_PCa-2*i_NaCa)*Cm/(2*Vc*F*1e-18))
#Cai
dY[1] = Ca_SR_bufSR*Vc/V_SR*(i_up-(i_rel+i_leak))
i_stim = 0
## Membrane potential
dY[0] = -(i_K1+i_to+i_Kr+i_Ks+i_CaL+i_NaK+i_Na+i_NaL+i_NaCa+i_PCa+i_f+i_b_Na+i_b_Ca-i_stim)
return dY
def test_lambertw():
assert LambertW(0) == 0
assert LambertW(E) == 1
assert LambertW(-1 / E) == -1
assert LambertW(-log(2) / 2) == -log(2)
def test_log():
x = Symbol("x")
y = Symbol("y")
assert log(E) == 1
assert log(x, x) == 1
assert log(x, y) == log(x) / log(y)
def test_sage_conversions():
x, y = sage.SR.var('x y')
x1, y1 = symbols('x, y')
# Symbol
assert x1._sage_() == x
assert x1 == sympify(x)
# Integer
assert Integer(12)._sage_() == sage.Integer(12)
assert Integer(12) == sympify(sage.Integer(12))
# Rational
assert (Integer(1) / 2)._sage_() == sage.Integer(1) / 2
assert Integer(1) / 2 == sympify(sage.Integer(1) / 2)
# Operators
assert x1 + y == x1 + y1
assert x1 * y == x1 * y1
assert x1**y == x1**y1
assert x1 - y == x1 - y1
assert x1 / y == x1 / y1
assert x + y1 == x + y
assert x * y1 == x * y
# Doesn't work in Sage 6.1.1ubuntu2
# assert x ** y1 == x ** y
assert x - y1 == x - y
assert x / y1 == x / y
# Conversions
assert (x1 + y1)._sage_() == x + y
assert (x1 * y1)._sage_() == x * y
assert (x1**y1)._sage_() == x**y
assert (x1 - y1)._sage_() == x - y
assert (x1 / y1)._sage_() == x / y
assert x1 + y1 == sympify(x + y)
assert x1 * y1 == sympify(x * y)
assert x1**y1 == sympify(x**y)
assert x1 - y1 == sympify(x - y)
assert x1 / y1 == sympify(x / y)
# Functions
assert sin(x1) == sin(x)
assert sin(x1)._sage_() == sage.sin(x)
assert sin(x1) == sympify(sage.sin(x))
assert cos(x1) == cos(x)
assert cos(x1)._sage_() == sage.cos(x)
assert cos(x1) == sympify(sage.cos(x))
assert function_symbol('f', x1, y1)._sage_() == sage.function('f')(x, y)
assert (function_symbol('f', 2 * x1,
x1 + y1).diff(x1)._sage_() == sage.function('f')(
2 * x, x + y).diff(x))
assert LambertW(x1) == LambertW(x)
assert LambertW(x1)._sage_() == sage.lambert_w(x)
assert KroneckerDelta(x1, y1) == KroneckerDelta(x, y)
assert KroneckerDelta(x1, y1)._sage_() == sage.kronecker_delta(x, y)
assert erf(x1) == erf(x)
assert erf(x1)._sage_() == sage.erf(x)
assert lowergamma(x1, y1) == lowergamma(x, y)
assert lowergamma(x1, y1)._sage_() == sage.gamma_inc_lower(x, y)
assert uppergamma(x1, y1) == uppergamma(x, y)
assert uppergamma(x1, y1)._sage_() == sage.gamma_inc(x, y)
assert loggamma(x1) == loggamma(x)
assert loggamma(x1)._sage_() == sage.log_gamma(x)
assert beta(x1, y1) == beta(x, y)
assert beta(x1, y1)._sage_() == sage.beta(x, y)
assert floor(x1) == floor(x)
assert floor(x1)._sage_() == sage.floor(x)
assert ceiling(x1) == ceiling(x)
assert ceiling(x1)._sage_() == sage.ceil(x)
assert conjugate(x1) == conjugate(x)
assert conjugate(x1)._sage_() == sage.conjugate(x)
# For the following test, sage needs to be modified
# assert sage.sin(x) == sage.sin(x1)
# Constants and Booleans
assert pi._sage_() == sage.pi
assert E._sage_() == sage.e
assert I._sage_() == sage.I
assert GoldenRatio._sage_() == sage.golden_ratio
assert Catalan._sage_() == sage.catalan
assert EulerGamma._sage_() == sage.euler_gamma
assert oo._sage_() == sage.oo
assert zoo._sage_() == sage.unsigned_infinity
assert nan._sage_() == sage.NaN
assert true._sage_() == True
assert false._sage_() == False
assert pi == sympify(sage.pi)
assert E == sympify(sage.e)
assert GoldenRatio == sympify(sage.golden_ratio)
assert Catalan == sympify(sage.catalan)
assert EulerGamma == sympify(sage.euler_gamma)
assert oo == sympify(sage.oo)
assert zoo == sympify(sage.unsigned_infinity)
assert nan == sympify(sage.NaN)
# SympyConverter does not support converting the following
# assert I == sympify(sage.I)
# Matrix
assert DenseMatrix(1, 2, [x1, y1])._sage_() == sage.matrix([[x, y]])
# SympyConverter does not support converting the following
# assert DenseMatrix(1, 2, [x1, y1]) == sympify(sage.matrix([[x, y]]))
# Sage Number
a = sage.Mod(2, 7)
b = PyNumber(a, sage_module)
a = a + 8
b = b + 8
assert isinstance(b, PyNumber)
assert b._sage_() == a
assert str(a) == str(b)
# Sage Function
e = x1 + wrap_sage_function(sage.log_gamma(x))
assert str(e) == "x + log_gamma(x)"
assert isinstance(e, Add)
assert (e + wrap_sage_function(sage.log_gamma(x)) == x1 +
2 * wrap_sage_function(sage.log_gamma(x)))
f = e.subs({x1: 10})
assert f == 10 + log(362880)
f = e.subs({x1: 2})
assert f == 2
f = e.subs({x1: 100})
v = f.n(53, real=True)
assert abs(float(v) - 459.13420537) < 1e-7
f = e.diff(x1)
def test_binary_candidate_models_are_constructed_correctly():
"""Candidate models should be generated for all valid combinations of possible models in the binary case"""
features = OrderedDict([("CPM_FORM", (v.T * symengine.log(v.T), v.T**2)),
("SM_FORM", (v.T, )),
("HM_FORM", (symengine.S.One, ))])
YS = symengine.Symbol('YS')
Z = symengine.Symbol('Z')
candidate_models = build_candidate_models((('A', 'B'), 'A'), features)
assert candidate_models == OrderedDict([
('CPM_FORM',
[[v.T * YS * symengine.log(v.T)],
[v.T * YS * symengine.log(v.T), v.T**2 * YS],
[v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T)],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z, v.T * YS * Z**2 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z, v.T * YS * Z**2 * symengine.log(v.T),
v.T**2 * YS * Z**2
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z,
v.T * YS * Z**2 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z,
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2,
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2,
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z, v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z, v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z, v.T * YS * Z**2 * symengine.log(v.T),
v.T**2 * YS * Z**2, v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T * YS * Z * symengine.log(v.T),
v.T**2 * YS * Z, v.T * YS * Z**2 * symengine.log(v.T),
v.T**2 * YS * Z**2, v.T * YS * Z**3 * symengine.log(v.T),
v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2,
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T),
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2,
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z,
v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z,
v.T * YS * Z**2 * symengine.log(v.T),
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z,
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2,
v.T * YS * Z**3 * symengine.log(v.T)
],
[
v.T * YS * symengine.log(v.T), v.T**2 * YS,
v.T * YS * Z * symengine.log(v.T), v.T**2 * YS * Z,
v.T * YS * Z**2 * symengine.log(v.T), v.T**2 * YS * Z**2,
v.T * YS * Z**3 * symengine.log(v.T), v.T**2 * YS * Z**3
]]),
('SM_FORM',
[[v.T * YS], [v.T * YS, v.T * YS * Z],
[v.T * YS, v.T * YS * Z, v.T * YS * Z**2],
[v.T * YS, v.T * YS * Z, v.T * YS * Z**2, v.T * YS * Z**3]]),
('HM_FORM', [[YS], [YS, YS * Z], [YS, YS * Z, YS * Z**2],
[YS, YS * Z, YS * Z**2, YS * Z**3]])
])
def fit_formation_energy(dbf,
comps,
phase_name,
configuration,
symmetry,
datasets,
ridge_alpha=None,
aicc_phase_penalty=None,
features=None):
"""
Find suitable linear model parameters for the given phase.
We do this by successively fitting heat capacities, entropies and
enthalpies of formation, and selecting against criteria to prevent
overfitting. The "best" set of parameters minimizes the error
without overfitting.
Parameters
----------
dbf : Database
pycalphad Database. Partially complete, so we know what degrees of freedom to fix.
comps : [str]
Names of the relevant components.
phase_name : str
Name of the desired phase for which the parameters will be found.
configuration : ndarray
Configuration of the sublattices for the fitting procedure.
symmetry : [[int]]
Symmetry of the sublattice configuration.
datasets : PickleableTinyDB
All the datasets desired to fit to.
ridge_alpha : float
Value of the :math:`\\alpha` hyperparameter used in ridge regression. Defaults to 1.0e-100, which should be degenerate
with ordinary least squares regression. For now, the parameter is applied to all features.
aicc_feature_factors : dict
Map of phase name to feature to a multiplication factor for the AICc's parameter penalty.
features : dict
Maps "property" to a list of features for the linear model.
These will be transformed from "GM" coefficients
e.g., {"CPM_FORM": (v.T*symengine.log(v.T), v.T**2, v.T**-1, v.T**3)} (Default value = None)
Returns
-------
dict
{feature: estimated_value}
"""
aicc_feature_factors = aicc_phase_penalty if aicc_phase_penalty is not None else {}
if interaction_test(configuration):
_log.debug('ENDMEMBERS FROM INTERACTION: %s',
endmembers_from_interaction(configuration))
fitting_steps = (["CPM_FORM",
"CPM_MIX"], ["SM_FORM",
"SM_MIX"], ["HM_FORM", "HM_MIX"])
else:
# We are only fitting an endmember; no mixing data needed
fitting_steps = (["CPM_FORM"], ["SM_FORM"], ["HM_FORM"])
# create the candidate models and fitting steps
if features is None:
features = OrderedDict([
("CPM_FORM", (v.T * symengine.log(v.T), v.T**2, v.T**-1, v.T**3)),
("SM_FORM", (v.T, )),
("HM_FORM", (symengine.S.One, )),
])
# dict of {feature, [candidate_models]}
candidate_models_features = build_candidate_models(configuration, features)
# All possible parameter values that could be taken on. This is some legacy
# code from before there were many candidate models built. For very large
# sets of candidate models, this could be quite slow.
# TODO: we might be able to remove this initialization for clarity, depends on fixed poritions
parameters = {}
for candidate_models in candidate_models_features.values():
for model in candidate_models:
for coef in model:
parameters[coef] = 0
# These is our previously fit partial model from previous steps
# Subtract out all of these contributions (zero out reference state because these are formation properties)
fixed_model = None # Profiling suggests we delay instantiation
fixed_portions = [0]
for desired_props in fitting_steps:
feature_type = desired_props[0].split('_')[0] # HM_FORM -> HM
aicc_factor = aicc_feature_factors.get(feature_type, 1.0)
solver_qry = (where('solver').test(
symmetry_filter, configuration,
recursive_tuplify(symmetry) if symmetry else symmetry))
desired_data = get_prop_data(comps,
phase_name,
desired_props,
datasets,
additional_query=solver_qry)
desired_data = filter_configurations(desired_data, configuration,
symmetry)
desired_data = filter_temperatures(desired_data)
_log.trace('%s: datasets found: %s', desired_props, len(desired_data))
if len(desired_data) > 0:
if fixed_model is None:
fixed_model = Model(dbf,
comps,
phase_name,
parameters={
'GHSER' + (c.upper() * 2)[:2]: 0
for c in comps
})
config_tup = tuple(map(tuplify, configuration))
calculate_dict = get_prop_samples(desired_data, config_tup)
sample_condition_dicts = _get_sample_condition_dicts(
calculate_dict, list(map(len, config_tup)))
weights = calculate_dict['weights']
assert len(sample_condition_dicts) == len(weights)
# We assume all properties in the same fitting step have the same
# features (all CPM, all HM, etc., but different ref states).
# data quantities are the same for each candidate model and can be computed up front
data_qtys = get_data_quantities(feature_type, fixed_model,
fixed_portions, desired_data,
sample_condition_dicts)
# build the candidate model transformation matrix and response vector (A, b in Ax=b)
feature_matricies = []
data_quantities = []
for candidate_coefficients in candidate_models_features[
desired_props[0]]:
# Map coeffiecients in G to coefficients in the feature_type (H, S, CP)
transformed_coefficients = list(
map(feature_transforms[feature_type],
candidate_coefficients))
if interaction_test(configuration, 3):
feature_matricies.append(
_build_feature_matrix(sample_condition_dicts,
transformed_coefficients))
else:
feature_matricies.append(
_build_feature_matrix(sample_condition_dicts,
transformed_coefficients))
data_quantities.append(data_qtys)
# provide candidate models and get back a selected model.
selected_model = select_model(zip(
candidate_models_features[desired_props[0]], feature_matricies,
data_quantities),
ridge_alpha,
weights=weights,
aicc_factor=aicc_factor)
selected_features, selected_values = selected_model
parameters.update(zip(*(selected_features, selected_values)))
# Add these parameters to be fixed for the next fitting step
fixed_portion = np.array(selected_features, dtype=np.object_)
fixed_portion = np.dot(fixed_portion, selected_values)
fixed_portions.append(fixed_portion)
return parameters