def test_get_factorial_term(self):
"""
Given the tuples of integers a and b,
Then, the "factorial term" should be exactly "a_result" and "b_result", respectively
:return:
"""
a = (2, 3, 4)
b = (0, 1, 6)
a_expected = sp.S(1) / (sp.factorial(2) * sp.factorial(3) * sp.factorial(4))
b_expected = sp.S(1) / (sp.factorial(6))
a_result = get_one_over_n_factorial(a)
b_result = get_one_over_n_factorial(b)
self.assertEqual(a_expected, a_result)
self.assertEqual(b_expected, b_result)
def generate_dmu_over_dt(species, propensity, n_counter, stoichiometry_matrix):
r"""
Calculate :math:`\frac{d\mu_i}{dt}` in eq. 6 (see Ale et al. 2013).
.. math::
\frac{d\mu_i}{dt} = S \begin{bmatrix} \sum_{l} \sum_{n_1=0}^{\infty} ...
\sum_{n_d=0}^{\infty}
\frac{1}{\mathbf{n!}}
\frac{\partial^n \mathbf{n}a_l(\mathbf{x})}{\partial \mathbf{x^n}} |_{x=\mu}
\mathbf{M_{x^n}} \end{bmatrix}
:param species: the name of the species/variables (typically `['y_0', 'y_1', ..., 'y_n']`)
:type species: list[`sympy.Symbol`]
:param propensity: the reactions describes by the model
:param n_counter: a list of :class:`~means.core.descriptors.Moment`\s representing central moments
:type n_counter: list[:class:`~means.core.descriptors.Moment`]
:param stoichiometry_matrix: the stoichiometry matrix
:type stoichiometry_matrix: `sympy.Matrix`
:return: a matrix in which each row corresponds to a reaction, and each column to an element of counter.
"""
# compute derivatives :math:`\frac{\partial^n \mathbf{n}a_l(\mathbf{x})}{\partial \mathbf{x^n}}`
# for EACH REACTION and EACH entry in COUNTER
derives =[derive_expr_from_counter_entry(reac, species, c.n_vector) for (reac, c) in itertools.product(propensity, n_counter)]
# Computes the factorial terms (:math:`\frac{1}{\mathbf{n!}}`) for EACH REACTION and EACH entry in COUNTER
# this does not depend of the reaction, so we just repeat the result for each reaction
factorial_terms = [get_one_over_n_factorial(tuple(c.n_vector)) for c in n_counter] * len(propensity)
# we make a matrix in which every element is the entry-wise multiplication of `derives` and factorial_terms
taylor_exp_matrix = sp.Matrix(len(propensity), len(n_counter), [d*f for (d, f) in zip(derives, factorial_terms)])
# dmu_over_dt is the product of the stoichiometry matrix by the taylor expansion matrix
return stoichiometry_matrix * taylor_exp_matrix
def _make_f_expectation(self, expr):
"""
Calculates :math:`<F>` in eq. 12 (see Ale et al. 2013) to calculate :math:`<F>` for EACH VARIABLE combination.
:param expr: an expression
:return: a column vector. Each row correspond to an element of counter.
:rtype: :class:`sympy.Matrix`
"""
# compute derivatives for EACH ENTRY in COUNTER
derives = sp.Matrix([
derive_expr_from_counter_entry(expr, self.__species,
tuple(c.n_vector))
for c in self.__n_counter
])
# Computes the factorial terms for EACH entry in COUNTER
factorial_terms = sp.Matrix([
get_one_over_n_factorial(tuple(c.n_vector))
for c in self.__n_counter
])
# Element wise product of the two vectors
te_vector = derives.multiply_elementwise(factorial_terms)
return te_vector
def _make_f_expectation(self, expr):
"""
Calculates :math:`<F>` in eq. 12 (see Ale et al. 2013) to calculate :math:`<F>` for EACH VARIABLE combination.
:param expr: an expression
:return: a column vector. Each row correspond to an element of counter.
:rtype: :class:`sympy.Matrix`
"""
# compute derivatives for EACH ENTRY in COUNTER
derives = sp.Matrix([derive_expr_from_counter_entry(expr, self.__species, tuple(c.n_vector))
for c in self.__n_counter])
# Computes the factorial terms for EACH entry in COUNTER
factorial_terms = sp.Matrix([get_one_over_n_factorial(tuple(c.n_vector)) for c in self.__n_counter])
# Element wise product of the two vectors
te_vector= derives.multiply_elementwise(factorial_terms)
return te_vector
def generate_dmu_over_dt(species, propensity, n_counter, stoichiometry_matrix):
r"""
Calculate :math:`\frac{d\mu_i}{dt}` in eq. 6 (see Ale et al. 2013).
.. math::
\frac{d\mu_i}{dt} = S \begin{bmatrix} \sum_{l} \sum_{n_1=0}^{\infty} ...
\sum_{n_d=0}^{\infty}
\frac{1}{\mathbf{n!}}
\frac{\partial^n \mathbf{n}a_l(\mathbf{x})}{\partial \mathbf{x^n}} |_{x=\mu}
\mathbf{M_{x^n}} \end{bmatrix}
:param species: the name of the species/variables (typically `['y_0', 'y_1', ..., 'y_n']`)
:type species: list[`sympy.Symbol`]
:param propensity: the reactions describes by the model
:param n_counter: a list of :class:`~means.core.descriptors.Moment`\s representing central moments
:type n_counter: list[:class:`~means.core.descriptors.Moment`]
:param stoichiometry_matrix: the stoichiometry matrix
:type stoichiometry_matrix: `sympy.Matrix`
:return: a matrix in which each row corresponds to a reaction, and each column to an element of counter.
"""
# compute derivatives :math:`\frac{\partial^n \mathbf{n}a_l(\mathbf{x})}{\partial \mathbf{x^n}}`
# for EACH REACTION and EACH entry in COUNTER
derives = [
derive_expr_from_counter_entry(reac, species, c.n_vector)
for (reac, c) in itertools.product(propensity, n_counter)
]
# Computes the factorial terms (:math:`\frac{1}{\mathbf{n!}}`) for EACH REACTION and EACH entry in COUNTER
# this does not depend of the reaction, so we just repeat the result for each reaction
factorial_terms = [
get_one_over_n_factorial(tuple(c.n_vector)) for c in n_counter
] * len(propensity)
# we make a matrix in which every element is the entry-wise multiplication of `derives` and factorial_terms
taylor_exp_matrix = sp.Matrix(
len(propensity), len(n_counter),
[d * f for (d, f) in zip(derives, factorial_terms)])
# dmu_over_dt is the product of the stoichiometry matrix by the taylor expansion matrix
return stoichiometry_matrix * taylor_exp_matrix
