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_build_feature_sets_generates_desired_binary_features_for_cp_like():
"""Binary feature sets can be correctly generated for heat capacity-like features"""
YS = symengine.Symbol("YS")
Z = symengine.Symbol("Z")
temp_features = [v.T, v.T**2, 1 / v.T, v.T**3]
excess_features = [YS, YS * Z, YS * Z**2, YS * Z**3]
feat_sets = build_feature_sets(temp_features, excess_features)
assert len(feat_sets) == 340
assert feat_sets[0] == [v.T * YS]
assert feat_sets[5] == [v.T * YS, v.T * YS * Z, v.T**2 * YS * Z]
assert feat_sets[-1] == [
v.T * YS,
v.T**2 * YS,
1 / v.T * YS,
v.T**3 * YS,
v.T * YS * Z,
v.T**2 * YS * Z,
1 / v.T * YS * Z,
v.T**3 * YS * Z,
v.T * YS * Z**2,
v.T**2 * YS * Z**2,
1 / v.T * YS * Z**2,
v.T**3 * YS * Z**2,
v.T * YS * Z**3,
v.T**2 * YS * Z**3,
1 / v.T * YS * Z**3,
v.T**3 * YS * Z**3,
]
def test_substitute_helpers(self):
backend = NumbaBackend()
a = se.Symbol("a")
b = se.Symbol("b")
y = se.Symbol("y")
HELPERS = [(a, se.exp(-12 * y))]
DERIVATIVES = [-b * a + y, y**2]
result = backend._substitute_helpers(DERIVATIVES, HELPERS)
self.assertListEqual(result, [-b * se.exp(-12 * y) + y, y**2])
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 qubit_op_to_expr(qubit_op, angle_folds=0):
qubit_op.compress()
dict_op = qubit_op.terms
expr = 0
for key in dict_op:
term = dict_op[key]
for var in key:
num, char = var
if char == 'X':
term *= se.cos(se.Symbol('phi' + str(num))) * se.sin(
se.Symbol('the' + str(num)))
if angle_folds == 3:
term *= se.Symbol('W' + str(num))
if char == 'Y':
term *= se.sin(se.Symbol('phi' + str(num))) * se.sin(
se.Symbol('the' + str(num)))
if angle_folds > 1:
term *= se.Symbol('Q' + str(num))
if char == 'Z':
term *= se.cos(se.Symbol('the' + str(num)))
if angle_folds > 0:
term *= se.Symbol('Z' + str(num))
expr += term
return expr
def get_coherent_state(bloch_angles, n):
coherent_state = 1
for i in range(n):
try:
phi = bloch_angles[se.Symbol('phi' + str(i))]
except KeyError:
phi = 0
the = bloch_angles[se.Symbol('the' + str(i))]
psi = np.cos(the / 2) * np.array([1, 0]) + np.exp(1j * phi) * np.sin(
the / 2) * np.array([0, 1])
coherent_state = np.kron(coherent_state, psi)
coherent_state = np.reshape(coherent_state, (-1, 1))
return coherent_state
def QMF(qubit_H,
angle_folds,
sampler,
num_cycles=5,
num_samples=1000,
strength=1e3,
verbose=False):
n = count_qubits(qubit_H)
expr = qubit_op_to_expr(qubit_H, angle_folds=angle_folds)
QMF_energy, cont_dict, disc_dict = minimize_expr(expr,
angle_folds,
0,
sampler,
max_cycles=num_cycles,
num_samples=num_samples,
strength=strength,
verbose=verbose)
for key in cont_dict:
num = str(key)[3:]
if str(key)[:3] == 'phi':
if angle_folds == 3:
try:
W = disc_dict[se.Symbol('W' + str(num))]
if W == -1:
cont_dict[key] = np.pi - cont_dict[key]
except KeyError:
pass
if angle_folds >= 2:
try:
Q = disc_dict[se.Symbol('Q' + str(num))]
if Q == -1:
cont_dict[key] = 2 * np.pi - cont_dict[key]
except KeyError:
pass
elif str(key)[:3] == 'the':
if angle_folds >= 1:
try:
Z = disc_dict[se.Symbol('Z' + str(num))]
if Z == -1:
cont_dict[key] = np.pi - cont_dict[key]
except KeyError:
pass
return QMF_energy, cont_dict
def subs(self, parameter_map: Dict) -> "ParameterExpression":
"""Returns a new Expression with replacement Parameters.
Args:
parameter_map: Mapping from Parameters in self to the ParameterExpression
instances with which they should be replaced.
Raises:
CircuitError:
- If parameter_map contains Parameters outside those in self.
- If the replacement Parameters in parameter_map would result in
a name conflict in the generated expression.
Returns:
A new expression with the specified parameters replaced.
"""
inbound_parameters = set()
inbound_names = {}
for replacement_expr in parameter_map.values():
for p in replacement_expr.parameters:
inbound_parameters.add(p)
inbound_names[p.name] = p
self._raise_if_passed_unknown_parameters(parameter_map.keys())
self._raise_if_parameter_names_conflict(inbound_names,
parameter_map.keys())
if _optionals.HAS_SYMENGINE:
import symengine
new_parameter_symbols = {
p: symengine.Symbol(p.name)
for p in inbound_parameters
}
else:
from sympy import Symbol
new_parameter_symbols = {
p: Symbol(p.name)
for p in inbound_parameters
}
# Include existing parameters in self not set to be replaced.
new_parameter_symbols.update({
p: s
for p, s in self._parameter_symbols.items()
if p not in parameter_map
})
# If new_param is an expr, we'll need to construct a matching sympy expr
# but with our sympy symbols instead of theirs.
symbol_map = {
self._parameter_symbols[old_param]: new_param._symbol_expr
for old_param, new_param in parameter_map.items()
}
substituted_symbol_expr = self._symbol_expr.subs(symbol_map)
return ParameterExpression(new_parameter_symbols,
substituted_symbol_expr)
def __init__(self, params, seed=None):
"""
:param params: parameters of the neural mass
:type params: dict
:param seed: seed for random number generator
:type seed: int|None
"""
assert isinstance(params, dict)
self.params = deepcopy(params)
self.seed = seed
# used in determining portion of the full system's state vector
self.idx_state_var = None
self.initialised = False
# initialise possible helpers
self.helper_symbols = {
symbol: se.Symbol(symbol)
for symbol in self.helper_variables
}
# initialise possible callback functions
self.callback_functions = {
function: se.Function(function)
for function in self.python_callbacks
}
self._validate_params()
def test_numeric(self):
t = symengine.Symbol("t")
for method in ["gauss", "midpoint"]:
with self.subTest(method=method):
result = quadrature(t**2, t, 0, 1, nsteps=100, method=method)
self.assertAlmostEqual(float(result.n().real_part()),
1 / 3,
places=3)
def __setstate__(self, state):
self._name = state["name"]
if not HAS_SYMENGINE:
from sympy import Symbol
symbol = Symbol(self._name)
else:
symbol = symengine.Symbol(self._name)
super().__init__(symbol_map={self: symbol}, expr=symbol)
def validate_parameters(self, parameter_values, use_cache=False):
"""Validate a dict or Series of parameter values
Currently checks that all covariance matrices are posdef
use_cache for using symengine cached matrices
"""
if use_cache and not hasattr(self, '_cached_sigmas'):
self._cached_sigmas = {}
for rvs, dist in self.distributions():
if len(rvs) > 1:
sigma = dist.sigma
a = [
[symengine.Symbol(e.name) for e in sigma.row(i)] for i in range(sigma.rows)
]
A = symengine.Matrix(a)
self._cached_sigmas[rvs[0]] = A
for rvs, dist in self.distributions():
if len(rvs) > 1:
if not use_cache:
sigma = dist.sigma.subs(dict(parameter_values))
# Switch to numpy here. Sympy posdef check is problematic
# see https://github.com/sympy/sympy/issues/18955
if not sigma.free_symbols:
a = np.array(sigma).astype(np.float64)
if not pharmpy.math.is_posdef(a):
return False
else:
sigma = self._cached_sigmas[rvs[0]]
replacement = {}
# Following because https://github.com/symengine/symengine/issues/1660
for param in dict(parameter_values):
replacement[symengine.Symbol(param)] = parameter_values[param]
sigma = sigma.subs(replacement)
if not sigma.free_symbols: # Cannot validate since missing params
a = np.array(sigma).astype(np.float64)
if not pharmpy.math.is_posdef(a):
return False
return True
def test_comparison(self):
interval = (-3, 10)
t = symengine.Symbol("t")
spline = CubicHermiteSpline(n=2)
spline.from_function(
[symengine.sin(t), symengine.cos(t)],
times_of_interest=interval,
max_anchors=100,
)
times = np.linspace(*interval, 100)
evaluation = spline.get_state(times)
control = np.vstack((np.sin(times), np.cos(times))).T
assert_allclose(evaluation, control, atol=0.01)
def test_simple_polynomial(self):
T = symengine.Symbol("T")
poly = 2 * T**3 - 3 * T**2 - 36 * T + 17
arg_extremes = [-2, 3]
arrify = lambda expr, t: np.atleast_1d(float(expr.subs({T: t})))
spline = CubicHermiteSpline(
1, [(t, arrify(poly, t), arrify(poly.diff(T), t))
for t in arg_extremes])
result = extrema_from_anchors(spline)
assert_allclose(result.minima, arrify(poly, arg_extremes[1]))
assert_allclose(result.maxima, arrify(poly, arg_extremes[0]))
assert_allclose(result.arg_min, arg_extremes[1])
assert_allclose(result.arg_max, arg_extremes[0])
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 __init__(
self,
f,
g,
y,
t=0.0,
f_helpers=(),
g_helpers=(),
control_pars=(),
seed=None,
additive=False,
do_cse=False,
):
self.state = y
self.n = len(self.state)
self.t = t
self.parameters = []
self.noises = []
self.noise_index = None
self.new_y = None
self.new_t = None
self.RNG = np.random.RandomState(seed)
self.additive = additive
from jitcsde import t, y
f_subs = list(reversed(f_helpers))
g_subs = list(reversed(g_helpers))
lambda_args = [t]
for i in range(self.n):
symbol = symengine.Symbol("dummy_argument_%i" % i)
lambda_args.append(symbol)
f_subs.append((y(i), symbol))
g_subs.append((y(i), symbol))
lambda_args.extend(control_pars)
f_wc = list(
ordered_subs(entry, f_subs).simplify(ratio=1) for entry in f())
g_wc = list(
ordered_subs(entry, g_subs).simplify(ratio=1) for entry in g())
lambdify = symengine.LambdifyCSE if do_cse else symengine.Lambdify
core_f = lambdify(lambda_args, f_wc)
self.f = lambda t, Y: core_f(np.hstack([t, Y, self.parameters]))
if self.additive:
core_g = lambdify([t] + list(control_pars), g_wc)
self.g = lambda t: core_g(np.hstack([t, self.parameters]))
else:
core_g = lambdify(lambda_args, g_wc)
self.g = lambda t, Y: core_g(np.hstack([t, Y, self.parameters]))
def __init__(self, name: str):
"""Create a new named :class:`Parameter`.
Args:
name: name of the ``Parameter``, used for visual representation. This can
be any unicode string, e.g. "ϕ".
"""
self._name = name
if not HAS_SYMENGINE:
from sympy import Symbol
symbol = Symbol(name)
else:
symbol = symengine.Symbol(name)
super().__init__(symbol_map={self: symbol}, expr=symbol)
def _prepare_lambdas(self):
if not hasattr(self, "_lambda_subs") or not hasattr(
self, "_lambda_args"):
if self.helpers:
warn(
"Lambdification handles helpers by plugging them in. This may be very inefficient"
)
self._lambda_subs = list(reversed(self.helpers))
self._lambda_args = [t]
for i in range(self.n):
symbol = symengine.Symbol("dummy_argument_%i" % i)
self._lambda_args.append(symbol)
self._lambda_subs.append((y(i), symbol))
self._lambda_args.extend(self.control_pars)
def dict_to_func(dictionary):
expr = 0
for key in dictionary:
term = dictionary[key]
for var in key:
term *= se.Symbol(var)
expr += term
if type(expr) == float:
f = expr
else:
var_list = list(expr.free_symbols)
var_list.sort(key=sort_disc_func)
f = se.lambdify(var_list, (expr, ))
return f
def var(self, name, shape, lower_bound, upper_bound, vtype, obj):
"""Add a variable to the model
This method will create a matrix with dimensions `shape` that is filled
with SymPy symbols of name `name_{i,j}`, where `i` and `j` are indices
along the rows and columns, respectively. This is the return value.
It will also create convert CPlex-structured variables for the names,
upper- and lower bounds, types, and **obj? and add them to the CPlex model
it is derived from.
name -- The name of the variable; will be indexed as "name_{i,j}"
shape -- A tuple with the dimension lengths [rows x columns]
lower_bound -- The lower value limit a variable can take
upper_bound -- The upper value limit a variable can take
vtype -- Type of the variable; 'I' integer, 'B' binary; 'C' count (I>=0)
obj --
return -- A numpy matrix with shape `shape` filled with SymPy symbols `name_{i,j}`
"""
if name in self._shape.keys():
raise ("Variable with name {} already added".format(name))
else:
self._shape[name] = shape
#TODO: this should reference species name, not index
ijstr = lambda i, j: sympy.Symbol(name + "_{" + str(int(i)) + "," +
str(int(j)) + "}")
matrix = np.array(np.fromfunction(np.vectorize(ijstr), shape))
names = [str(e) for e in matrix.flatten().tolist()]
nvars = len(self._idx)
ntup = zip(names, range(nvars, nvars + len(names)))
self._idx.update({k: v for k, v in ntup})
var = {}
var['names'] = names
var['ub'] = [upper_bound] * matrix.size
var['lb'] = [lower_bound] * matrix.size
var['types'] = [vtype] * matrix.size
if np.isscalar(obj):
var['obj'] = [obj] * matrix.size
else:
var['obj'] = np.array(obj).flatten().tolist()
#TODO: check if non-scalar args have the right length
self.variables.add(**var)
return np.matrix(matrix)
def init_node(self, **kwargs):
"""
Initialise node and all the masses within.
:kwargs: optional keyword arguments to init_mass
"""
# we need to have the index already assigned
assert self.index is not None
# initialise possible sync variables
self.sync_symbols = {
f"{symbol}_{self.index}": se.Symbol(f"{symbol}_{self.index}") for symbol in self.sync_variables
}
for mass in self:
mass.init_mass(**kwargs)
assert all(mass.initialised for mass in self)
self.initialised = True
def init_network(self, **kwargs):
"""
Initialise network and the nodes within.
:kwargs: optional keyword arguments to init_node
"""
# create symbol for each node for input
self.sync_symbols = {
f"{symbol}_{node_idx}": se.Symbol(f"{symbol}_{node_idx}")
for symbol in self.sync_variables
for node_idx in range(self.num_nodes)
}
for node_idx, node in enumerate(self.nodes):
node.init_node(start_idx_for_noise=node_idx * node.num_noise_variables)
assert all(node.initialised for node in self)
self.initialised = True
def validate_parameters(self, parameter_values):
"""Validate a dict or Series of parameter values
Currently checks that all covariance matrices are posdef
use_cache for using symengine cached matrices
"""
for rvs, dist in self.distributions():
if len(rvs) > 1:
sigma = rvs[0]._symengine_variance
replacement = {}
for param in dict(parameter_values):
replacement[symengine.Symbol(
param)] = parameter_values[param]
sigma = sigma.subs(replacement)
if not sigma.free_symbols: # Cannot validate since missing params
a = np.array(sigma).astype(np.float64)
if not pharmpy.math.is_posdef(a):
return False
return True
def __init__(
self,
f_sym=(),
*,
helpers=None,
wants_jacobian=False,
n=None,
control_pars=(),
callback_functions=(),
verbose=True,
module_location=None,
):
jitcxde.__init__(self, n, verbose, module_location)
self.f_sym = self._handle_input(f_sym)
self._f_C_source = False
self._jac_C_source = False
self._helper_C_source = False
self.helpers = sort_helpers(sympify_helpers(helpers or []))
self.control_pars = control_pars
self.control_par_values = ()
self.callback_functions = callback_functions
self._wants_jacobian = wants_jacobian
self.integrator = empty_integrator()
if self.jitced is None:
self._initialise = None
self.f = None
self.jac = None
else:
# Load derivative and Jacobian if a compiled module has been provided
self._initialise = self.jitced.initialise
self.f = self.jitced.f
self.jac = self.jitced.jac if hasattr(self.jitced, "jac") else None
self._number_of_jac_helpers = None
self._number_of_f_helpers = None
self.general_subs = {
control_par: symengine.Symbol("parameter_" + control_par.name)
for control_par in self.control_pars
}
def _prepare_lambdas(self):
if self.callback_functions:
raise NotImplementedError(
"Callbacks do not work with lambdification. You must use the C backend."
)
if not hasattr(self, "_lambda_subs") or not hasattr(
self, "_lambda_args"):
if self.helpers:
warn(
"Lambdification handles helpers by plugging them in. This may be very inefficient"
)
self._lambda_subs = list(reversed(self.helpers))
self._lambda_args = [t]
for i in range(self.n):
symbol = symengine.Symbol("dummy_argument_%i" % i)
self._lambda_args.append(symbol)
self._lambda_subs.append((y(i), symbol))
self._lambda_args.extend(self.control_pars)
def setUp(self):
interval = (-3, 2)
self.times = np.linspace(*interval, 10)
t = symengine.Symbol("t")
self.sin_spline = CubicHermiteSpline(n=1)
self.sin_spline.from_function(
[symengine.sin(t)],
times_of_interest=interval,
max_anchors=100,
)
self.sin_evaluation = self.sin_spline.get_state(self.times)
self.exp_spline = CubicHermiteSpline(n=1)
self.exp_spline.from_function(
[symengine.exp(t)],
times_of_interest=interval,
max_anchors=100,
)
self.exp_evaluation = self.exp_spline.get_state(self.times)
def point_estimate(self):
# self.isomer_percents = [sympy.Symbol("P" + str(isomer_id)) for isomer_id in range(self.num_of_isomers)]
self.isomer_percents = [symengine.Symbol("P" + str(isomer_id)) for isomer_id in range(self.num_of_isomers)]
logger.info("Generating the likelihood function .. ")
self.pe_neg_loglike_function = self.get_neg_likelihood_of_iso_freq(
within_isomer_ids=set(self.traversome.represent_for_isomers))\
.loglike_func
logger.info("Maximizing the likelihood function .. ")
success_run = self.minimize_neg_likelihood(
neg_loglike_func=self.pe_neg_loglike_function,
num_variables=self.num_of_isomers,
verbose=self.traversome.loglevel in ("TRACE", "ALL"))
if success_run:
# for run_res in sorted(success_runs, key=lambda x: x.fun):
# logger.info(str(run_res.fun) + str([round(m, 8) for m in run_res.x]))
self.pe_best_proportions, echo_prop = self.__summarize_run_prop(success_run)
logger.info("Proportions: " + ", ".join(["%s:%.4f" % (_id, _p) for _id, _p, in echo_prop.items()]))
logger.info("Log-likelihood: %s" % (-success_run.fun))
return self.pe_best_proportions
else:
raise Exception("Likelihood maximization failed.")
def test_random_function(self):
roots = np.sort(np.random.normal(size=5))
value = np.random.normal()
t = symengine.Symbol("t")
function = np.prod([t - root for root in roots]) + value
i = 1
spline = CubicHermiteSpline(n=3)
spline.from_function(
[10, function, 10],
times_of_interest=(min(roots) - 0.01, max(roots) + 0.01),
max_anchors=1000,
tol=7,
)
solutions = spline.solve(i=i, value=value)
sol_times = [sol[0] for sol in solutions]
assert_allclose(spline.get_state(sol_times)[:, i], value)
assert_allclose([sol[0] for sol in solutions], roots, atol=1e-3)
for time, diff in solutions:
true_diff = float(function.diff(t).subs({t: time}))
self.assertAlmostEqual(true_diff, diff, places=5)
def kmc_test(dt, runner, ks):
Y = symengine.Symbol("Y")
F = scenario["F"].subs(y(0), Y)
G = scenario["G"].subs(y(0), Y)
Fd = F.diff(Y)
Gd = G.diff(Y)
Fdd = Fd.diff(Y)
Gdd = Gd.diff(Y)
# Theoretical expectation
M = [
symengine.Lambdify([Y], F + (F * Fd + G**2 * Fdd / 2) * dt / 2),
symengine.Lambdify([Y], G**2 + (2 * F * (F + G * Gd) + G**2 *
(2 * Fd + Gd**2 + G * Gdd)) * dt / 2),
symengine.Lambdify([Y], 3 * G**2 * (F + G * Gd) * dt),
symengine.Lambdify([Y], 3 * G**4 * dt),
symengine.Lambdify([Y], 15 * G**4 * (F + 2 * G * Gd) * dt**2),
symengine.Lambdify([Y], 15 * G**6 * dt**2)
]
# Numerical estimate
bins, *kmcs = KMC(runner(), dt, kmax=kmax, nbins=nbins)
# Comparing the two
i = 0
while i < len(ks):
k = ks[i]
good = 0
for X, value, error in zip(bins, *kmcs[k]):
theory = M[k](X)
if value - error < theory < value + error:
good += 1
if good < thresholds[k] * len(bins):
i += 1
else:
ks.pop(i)
return ks
def test_no_method(self):
t = symengine.Symbol("t")
with self.assertRaises(NotImplementedError):
quadrature(t**2,t,0,1,method="tai")