def test_initialisation_of_propensities_as_matrix(self):
"""
The model constructor should accept propensities as a sympy matrix
e.g. sympy.Matrix(['y_0+y_1', 'y_1+y_2'])
and return them as sympy (column) Matrix of equations
i.e. sympy.Matrix(['y_0+y_1', 'y_1+y_2'])
"""
answer = to_sympy_matrix([['c_0*y_0*(y_0 + y_1 - 181)'],
['c_1*(-y_0 - y_1 + 301)'],
['c_2*(-y_0 - y_1 + 301)']])
# Column
m = Model(self.SAMPLE_VARIABLES,
self.SAMPLE_CONSTANTS,
to_sympy_matrix(['c_0*y_0*(y_0 + y_1 - 181)',
'c_1*(-y_0 - y_1 + 301)',
'c_2*(-y_0 - y_1 + 301)']),
self.SAMPLE_STOICHIOMETRY_MATRIX)
self.assertEqual(m.propensities, answer)
# Row matrix
m = Model(
self.SAMPLE_VARIABLES,
self.SAMPLE_CONSTANTS,
[['c_0*y_0*(y_0 + y_1 - 181)',
'c_1*(-y_0 - y_1 + 301)',
'c_2*(-y_0 - y_1 + 301)']],
self.SAMPLE_STOICHIOMETRY_MATRIX)
self.assertEqual(m.propensities, answer)
def test_initialisation_of_propensities_as_matrix(self):
"""
The model constructor should accept propensities as a sympy matrix
e.g. sympy.Matrix(['y_0+y_1', 'y_1+y_2'])
and return them as sympy (column) Matrix of equations
i.e. sympy.Matrix(['y_0+y_1', 'y_1+y_2'])
"""
answer = to_sympy_matrix([['c_0*y_0*(y_0 + y_1 - 181)'],
['c_1*(-y_0 - y_1 + 301)'],
['c_2*(-y_0 - y_1 + 301)']])
# Column
m = Model(
self.SAMPLE_VARIABLES, self.SAMPLE_CONSTANTS,
to_sympy_matrix([
'c_0*y_0*(y_0 + y_1 - 181)', 'c_1*(-y_0 - y_1 + 301)',
'c_2*(-y_0 - y_1 + 301)'
]), self.SAMPLE_STOICHIOMETRY_MATRIX)
self.assertEqual(m.propensities, answer)
# Row matrix
m = Model(self.SAMPLE_VARIABLES, self.SAMPLE_CONSTANTS, [[
'c_0*y_0*(y_0 + y_1 - 181)', 'c_1*(-y_0 - y_1 + 301)',
'c_2*(-y_0 - y_1 + 301)'
]], self.SAMPLE_STOICHIOMETRY_MATRIX)
self.assertEqual(m.propensities, answer)
def test_TaylorExpansion(self):
"""
Given the number of moments is 3, the number of species is 2,
Given the propensities of the 3 reactions in `a_strings`,
And Given the combination of derivative order in counter,
Then results of `TaylorExpansion()` should produce a matrix exactly equal to
exactly equal to the the expected one (`expected_te_matrix`).
:return:
"""
mea = MomentExpansionApproximation(None, 3)
species = ["a", "b", "c"]
propensities = to_sympy_matrix(["a*2 +w * b**3", "b - a*x /c", "c + a*b /32"])
stoichiometry_matrix = sp.Matrix([
[1, 0, 1],
[-1, -1, 0],
[0, 1, -1]
])
counter = [
Moment([0, 0, 2], sp.Symbol("q1")),
Moment([0, 2, 0], sp.Symbol("q2")),
Moment([0, 0, 2], sp.Symbol("q3")),
Moment([2, 0, 0], sp.Symbol("q4")),
Moment([1, 1, 0], sp.Symbol("q5")),
Moment([0, 1, 1], sp.Symbol("q6")),
Moment([1, 0, 1], sp.Symbol("q7"))]
result = generate_dmu_over_dt(species, propensities, counter, stoichiometry_matrix)
expected = stoichiometry_matrix * to_sympy_matrix([[" 0", "3*b*w", "0", "0", "0", "0", "0"],
["-a*x/c**3", "0", "-a*x/c**3", "0", "0", "0", "x/c**2"],
["0", "0", "0", "0", "1/32", "0", "0"]])
self.assertEqual(result, expected)
def test_TaylorExpansion(self):
"""
Given the number of moments is 3, the number of species is 2,
Given the propensities of the 3 reactions in `a_strings`,
And Given the combination of derivative order in counter,
Then results of `TaylorExpansion()` should produce a matrix exactly equal to
exactly equal to the the expected one (`expected_te_matrix`).
:return:
"""
mea = MomentExpansionApproximation(None, 3)
species = ["a", "b", "c"]
propensities = to_sympy_matrix(
["a*2 +w * b**3", "b - a*x /c", "c + a*b /32"])
stoichiometry_matrix = sp.Matrix([[1, 0, 1], [-1, -1, 0], [0, 1, -1]])
counter = [
Moment([0, 0, 2], sp.Symbol("q1")),
Moment([0, 2, 0], sp.Symbol("q2")),
Moment([0, 0, 2], sp.Symbol("q3")),
Moment([2, 0, 0], sp.Symbol("q4")),
Moment([1, 1, 0], sp.Symbol("q5")),
Moment([0, 1, 1], sp.Symbol("q6")),
Moment([1, 0, 1], sp.Symbol("q7"))
]
result = generate_dmu_over_dt(species, propensities, counter,
stoichiometry_matrix)
expected = stoichiometry_matrix * to_sympy_matrix(
[[" 0", "3*b*w", "0", "0", "0", "0", "0"],
["-a*x/c**3", "0", "-a*x/c**3", "0", "0", "0", "x/c**2"],
["0", "0", "0", "0", "1/32", "0", "0"]])
self.assertEqual(result, expected)
def test_get_log_covariance(self):
log_variance_mat =to_sympy_matrix([
["log(1+yx7/y_0**2)", "0", "0"],
["0", "log(1+yx4/y_1**2)", "0"],
["0", "0", "log(1+yx2/y_2**2)"]
])
log_expectation_symbols = to_sympy_matrix([
["log(y_0)-log(1+yx7/y_0**2)/2"],
["log(y_1)-log(1+yx4/y_1**2)/2"],
["log(y_2)-log(1+yx2/y_2**2)/2"]
])
covariance_matrix = to_sympy_matrix([
["yx7","yx6","yx5"],
["yx6","yx4","yx3"],
["yx5","yx3","yx2"]])
expected = sympy.sympify("log(1 + yx6/(y_0*y_1))")
closer = LogNormalClosure(2, multivariate=True)
answer = closer._get_log_covariance(log_variance_mat, log_expectation_symbols, covariance_matrix, 0,1)
self.assertEqual(answer, expected)
answer1 = closer._get_log_covariance(log_variance_mat, log_expectation_symbols, covariance_matrix, 1,2)
answer2 = closer._get_log_covariance(log_variance_mat, log_expectation_symbols, covariance_matrix, 1,2)
#logcovariance between species 1 and 2 == covariance between sp. 2 and 1
self.assertEqual(answer1, answer2)
def test_ode_rhs_as_function_cache_does_not_persist_between_instances(self):
"""
Given two ODEProblems, the cache should not persist between these objects.
:return:
"""
p1_lhs = [Moment(np.ones(4), i) for i in sympy.Matrix(['y_1', 'y_2', 'y_3', 'y_4'])]
p1_rhs = to_sympy_matrix(['y_1+y_2+c_2', 'y_2+y_3+c_3', 'y_3+c_1', 'y_1*2'])
p2_lhs = [Moment(np.ones(3), i) for i in sympy.Matrix(['y_1', 'y_2', 'y_3'])]
p2_rhs = to_sympy_matrix(['y_1', 'c_1', 'y_2+y_3'])
p1 = ODEProblem('MEA', p1_lhs, p1_rhs, parameters=sympy.symbols(['c_1', 'c_2', 'c_3']))
p1_rhs_as_function = p1.right_hand_side_as_function
p2 = ODEProblem('MEA', p2_lhs, p2_rhs, parameters=sympy.symbols(['c_1', 'c_2', 'c_3']))
p2_rhs_as_function = p2.right_hand_side_as_function
constants = [1, 2, 3]
values_p1 = [4, 5, 6, 5] # y_1, y_2, y_3, y_4 in that order
values_p2 = [4, 5, 6] # y_1, y_2, y_3 in that order
p1_expected_ans = np.array([11, 14, 7, 8])
p2_expected_ans = np.array([4, 1, 6+5])
p1_actual_ans = np.array(p1_rhs_as_function(values_p1, constants))
p2_actual_ans = np.array(p2_rhs_as_function(values_p2, constants))
# This checks if by any means p2 is able to "override" the p1 result
p1_ans_after_p2 = np.array(p1_rhs_as_function(values_p1, constants))
assert_array_equal(p1_actual_ans, p1_expected_ans)
assert_array_equal(p2_actual_ans, p2_expected_ans)
assert_array_equal(p1_ans_after_p2, p1_expected_ans)
def test_get_log_covariance(self):
log_variance_mat = to_sympy_matrix([["log(1+yx7/y_0**2)", "0", "0"],
["0", "log(1+yx4/y_1**2)", "0"],
["0", "0", "log(1+yx2/y_2**2)"]])
log_expectation_symbols = to_sympy_matrix([[
"log(y_0)-log(1+yx7/y_0**2)/2"
], ["log(y_1)-log(1+yx4/y_1**2)/2"], ["log(y_2)-log(1+yx2/y_2**2)/2"]])
covariance_matrix = to_sympy_matrix([["yx7", "yx6", "yx5"],
["yx6", "yx4", "yx3"],
["yx5", "yx3", "yx2"]])
expected = sympy.sympify("log(1 + yx6/(y_0*y_1))")
closer = LogNormalClosure(2, multivariate=True)
answer = closer._get_log_covariance(log_variance_mat,
log_expectation_symbols,
covariance_matrix, 0, 1)
self.assertEqual(answer, expected)
answer1 = closer._get_log_covariance(log_variance_mat,
log_expectation_symbols,
covariance_matrix, 1, 2)
answer2 = closer._get_log_covariance(log_variance_mat,
log_expectation_symbols,
covariance_matrix, 1, 2)
#logcovariance between species 1 and 2 == covariance between sp. 2 and 1
self.assertEqual(answer1, answer2)
def test_transcription_model(self):
#use simple production and degradation of mRNA and protein for testing
# mRNA production rate is k1, degradation rate is g1
# protein production rate is k2, degradation rate is g2
stoichiometry_matrix = sympy.Matrix([[1, -1, 0, 0],
[0, 0, 1, -1]])
propensities = to_sympy_matrix(['k1',
'g1*x',
'k2*x',
'g2*y'])
species = to_sympy_matrix(['x', 'y'])
correct_rhs = to_sympy_matrix(
["k1 - g1 * x",
"k2 * x - g2 * y",
"k1 + g1 * x - 2 * g1 * V_0_0",
"k2 * V_0_0 - (g1 + g2) * V_0_1",
"k2 * x + g2 * y + k2 * V_0_1 + k2 * V_0_1 - 2 * g2 * V_1_1"])
correct_lhs = to_sympy_matrix(['x','y','V_0_0', 'V_0_1', 'V_1_1'])
constants = ["k1","k2","g1","g2"]
model = Model(species, constants, propensities, stoichiometry_matrix)
lna = LinearNoiseApproximation(model)
problem = lna.run()
answer_rhs = problem.right_hand_side
answer_lhs = problem.left_hand_side
assert_sympy_expressions_equal(correct_rhs, answer_rhs)
self.assertEqual(correct_lhs, answer_lhs)
def test_substitute_all_on_expression(self):
to_substitute = sympy.sympify("a*b + c*d + d*e + e*f")
pairs = zip(to_sympy_matrix(["a", "d", "e", "c", "b"]),
to_sympy_matrix(["z", "w", "v", "x", "y"]))
expected = sympy.sympify("z*y + x*w + w*v + v*f")
answer = substitute_all(to_substitute, pairs)
self.assertEqual(answer, expected)
def test_substitute_all_on_expression(self):
to_substitute = sympy.sympify("a*b + c*d + d*e + e*f")
pairs = zip(to_sympy_matrix(["a","d","e","c","b"]),
to_sympy_matrix(["z","w","v","x","y"]))
expected = sympy.sympify("z*y + x*w + w*v + v*f")
answer = substitute_all(to_substitute, pairs)
self.assertEqual(answer, expected)
def test_substitute_all_on_matrix(self):
to_substitute = to_sympy_matrix(["a*b", "c*d", "d*e", "e*f"])
pairs = zip(to_sympy_matrix(["a", "d", "e", "c", "b"]),
to_sympy_matrix(["z", "w", "v", "x", "y"]))
expected = sympy.Matrix(["z*y", "x*w", "w*v", "v*f"])
answer = substitute_all(to_substitute, pairs)
self.assertEqual(answer, expected)
def test_substitute_all_on_matrix(self):
to_substitute = to_sympy_matrix(["a*b","c*d","d*e","e*f"])
pairs = zip(to_sympy_matrix(["a","d","e","c","b"]),
to_sympy_matrix(["z","w","v","x","y"]))
expected = sympy.Matrix(["z*y","x*w","w*v","v*f"])
answer = substitute_all(to_substitute, pairs)
self.assertEqual(answer, expected)
def __init__(self, species, parameters, propensities, stoichiometry_matrix):
r"""
Creates a `Model` object that stores the model of reactions we want to analyse
:param species: variables of the model, as `sympy.Symbol`s, i.e. species
:param parameters: parameters of the model, as `sympy` symbols
:param propensities: a matrix of propensities for each of the reaction in the model.
:param stoichiometry_matrix: stoichiometry matrix for the model
"""
self.__parameters = to_list_of_symbols(parameters)
self.__species = to_list_of_symbols(species)
self.__propensities = to_sympy_column_matrix(to_sympy_matrix(propensities))
self.__stoichiometry_matrix = to_sympy_matrix(stoichiometry_matrix)
self.validate()
def test_ode_moment_getting_n_vector_from_dict_and_key(self):
"""
Given a list of descriptor and a list of symbols used to create Moment,
Then problem descriptor_for_symbol function should return the correct
descriptor for each corresponding symbol
:return:
"""
symbs = to_sympy_matrix(['y_1', 'y_2', 'y_3'])
desc = [[0, 0, 1], [1, 0, 432], [21, 43, 34]]
lhs = [Moment(d, s) for d, s in zip(desc, symbs)]
rhs = to_sympy_matrix(['y_1+y_2+c_2', 'y_2+y_3+c_3', 'y_3+c_1'])
p = ODEProblem('MEA', lhs, rhs, parameters=sympy.symbols(['c_1', 'c_2', 'c_3']))
for i, l in enumerate(lhs):
self.assertEqual(p.descriptor_for_symbol(l.symbol), l)
def __init__(self, species, parameters, propensities,
stoichiometry_matrix):
r"""
Creates a `Model` object that stores the model of reactions we want to analyse
:param species: variables of the model, as `sympy.Symbol`s, i.e. species
:param parameters: parameters of the model, as `sympy` symbols
:param propensities: a matrix of propensities for each of the reaction in the model.
:param stoichiometry_matrix: stoichiometry matrix for the model
"""
self.__parameters = to_list_of_symbols(parameters)
self.__species = to_list_of_symbols(species)
self.__propensities = to_sympy_column_matrix(
to_sympy_matrix(propensities))
self.__stoichiometry_matrix = to_sympy_matrix(stoichiometry_matrix)
self.validate()
def test_creation_from_matrix_returns_itself(self):
"""
Given a `sympy.Matrix`, `to_sympy_matrix` should return the said matrix.
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
assert_sympy_expressions_equal(m, to_sympy_matrix(m))
def test_creation_from_matrix_returns_itself(self):
"""
Given a `sympy.Matrix`, `to_sympy_matrix` should return the said matrix.
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
assert_sympy_expressions_equal(m, to_sympy_matrix(m))
def test_compute_raw_moments(self):
expected = to_sympy_matrix([
["y_2**2+yx2"], ["y_1*y_2+yx3"], ["y_1**2+yx4"], ["y_0*y_2+yx5"],
["y_0*y_1+yx6"], ["y_0**2+yx7"],
["y_2**3+3*y_2*yx2+3*yx2**2/y_2+yx2**3/y_2**3"],
[
"y_1*y_2**2+y_1*yx2+2*y_2*yx3+2*yx2*yx3/y_2+yx3**2/y_1+yx2*yx3**2/(y_1*y_2**2)"
],
[
"y_1**2*y_2+2*y_1*yx3+y_2*yx4+yx3**2/y_2+2*yx3*yx4/y_1+yx3**2*yx4/(y_1**2*y_2)"
], ["y_1**3+3*y_1*yx4+3*yx4**2/y_1+yx4**3/y_1**3"],
[
"y_0*y_2**2+y_0*yx2+2*y_2*yx5+2*yx2*yx5/y_2+yx5**2/y_0+yx2*yx5**2/(y_0*y_2**2)"
],
[
"y_0*y_1*y_2+y_0*yx3+y_1*yx5+y_2*yx6+yx3*yx5/y_2+yx3*yx6/y_1+yx5*yx6/y_0+yx3*yx5*yx6/(y_0*y_1*y_2)"
],
[
"y_0*y_1**2+y_0*yx4+2*y_1*yx6+2*yx4*yx6/y_1+yx6**2/y_0+yx4*yx6**2/(y_0*y_1**2)"
],
[
"y_0**2*y_2+2*y_0*yx5+y_2*yx7+yx5**2/y_2+2*yx5*yx7/y_0+yx5**2*yx7/(y_0**2*y_2)"
],
[
"y_0**2*y_1+2*y_0*yx6+y_1*yx7+yx6**2/y_1+2*yx6*yx7/y_0+yx6**2*yx7/(y_0**2*y_1)"
], ["y_0**3+3*y_0*yx7+3*yx7**2/y_0+yx7**3/y_0**3"]
])
closer = LogNormalClosure(2, multivariate=True)
answer = closer._compute_raw_moments(
self.__n_counter,
self.__k_counter,
)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_for_p53(self):
"""
Given the preopensities,
Given the soichiometry matrix,
Given the counter (list of Moments),
Given the species list,
Given k_vector and
Given ek_counter (list of moment)
The answer should match exactly the expected result
:return:
"""
stoichio = sympy.Matrix([
[1, -1, -1, 0, 0, 0],
[0, 0, 0, 1, -1, 0],
[0, 0, 0, 0, 1, -1]
])
propensities = to_sympy_matrix([
[" c_0"],
[" c_1*y_0"],
["c_2*y_0*y_2/(c_6 + y_0)"],
[" c_3*y_0"],
[" c_4*y_1"],
[" c_5*y_2"]])
counter = [
Moment([0, 0, 0], 1),
Moment([0, 0, 2], sympy.Symbol("yx1")),
Moment([0, 1, 1], sympy.Symbol("yx2")),
Moment([0, 2, 0], sympy.Symbol("yx3")),
Moment([1, 0, 1], sympy.Symbol("yx4")),
Moment([1, 1, 0], sympy.Symbol("yx5")),
Moment([2, 0, 0], sympy.Symbol("yx6"))
]
species = sympy.Matrix(["y_0", "y_1", "y_2"])
dbdt_calc = DBetaOverDtCalculator(propensities, counter,stoichio, species)
k_vec = [1, 0, 0]
ek_counter = [Moment([1, 0, 0], sympy.Symbol("y_0"))]
answer = dbdt_calc.get(k_vec,ek_counter).T
result = to_sympy_matrix(["c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)"," 0"," 0"," 0"," c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0)"," 0"," -c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2"])
assert_sympy_expressions_equal(answer, result)
def test_creation_from_list_of_integers_returns_matrix(self):
"""
Given a list of integers, to_sympy_matrix should be able to convert it to a matrix of these integers
:return:
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
m_as_list = [[1, 2, 3], [4, 5, 6]]
assert_sympy_expressions_equal(m, to_sympy_matrix(m_as_list))
def test_creation_from_list_of_integers_returns_matrix(self):
"""
Given a list of integers, to_sympy_matrix should be able to convert it to a matrix of these integers
:return:
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
m_as_list = [[1, 2, 3], [4, 5, 6]]
assert_sympy_expressions_equal(m, to_sympy_matrix(m_as_list))
def test_log_normal_closer_wrapper(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"],
["x_0_1_1-y_1*y_2"],
["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"],
["x_1_1_0-y_0*y_1"],
["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]
])
max_order = 2
expected = to_sympy_matrix([
["c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3+(c_2*c_6*yx5*(yx5*y_0 ** 2+2*y_2*yx7*y_0+yx5*yx7))/(y_0 ** 2*y_2*(c_6+y_0) ** 3)-(c_2*c_6*y_2*yx7 ** 2*(3*y_0 ** 2+yx7))/(y_0 ** 3*(c_6+y_0) ** 4)"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["-(c_2*y_0 ** 5*y_2 ** 2*yx2+c_1*y_0 ** 5*y_2 ** 2*yx5-c_4*y_0 ** 5*y_2 ** 2*yx6+c_5*y_0 ** 5*y_2 ** 2*yx5+2*c_2*c_6*y_0 ** 4*y_2 ** 2*yx2+3*c_1*c_6*y_0 ** 4*y_2 ** 2*yx5+c_2*c_6*y_0 ** 3*y_2 ** 3*yx5-3*c_4*c_6*y_0 ** 4*y_2 ** 2*yx6+3*c_5*c_6*y_0 ** 4*y_2 ** 2*yx5+c_2*c_6*y_0 ** 2*yx2*yx5 ** 2+c_2*c_6 ** 2*y_0*yx2*yx5 ** 2-c_2*c_6*y_2 ** 2*yx5 ** 2*yx7+c_2*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx2+3*c_1*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx5+c_1*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx5+c_2*c_6 ** 2*y_0*y_2 ** 2*yx5 ** 2+c_2*c_6 ** 2*y_0 ** 2*y_2 ** 3*yx5-3*c_4*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx6-c_4*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx6+3*c_5*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx5+c_5*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx5+2*c_2*c_6*y_0 ** 3*y_2*yx2*yx5-2*c_2*c_6*y_0*y_2 ** 3*yx5*yx7+2*c_2*c_6 ** 2*y_0 ** 2*y_2*yx2*yx5)/(y_0 ** 2*y_2 ** 2*(c_6+y_0) ** 3)"],
["-(c_2*y_0 ** 5*y_1*y_2*yx3+c_1*y_0 ** 5*y_1*y_2*yx6-c_3*y_0 ** 5*y_1*y_2*yx7+c_4*y_0 ** 5*y_1*y_2*yx6-c_2*c_6*y_2 ** 2*yx6 ** 2*yx7-c_2*c_6*y_0 ** 2*y_2 ** 2*yx6 ** 2+c_2*c_6 ** 2*y_0 ** 2*y_1*y_2 ** 2*yx6+2*c_2*c_6*y_0 ** 4*y_1*y_2*yx3+3*c_1*c_6*y_0 ** 4*y_1*y_2*yx6-3*c_3*c_6*y_0 ** 4*y_1*y_2*yx7+3*c_4*c_6*y_0 ** 4*y_1*y_2*yx6+c_2*c_6*y_0 ** 3*y_1*yx3*yx5+c_2*c_6*y_0 ** 3*y_2*yx3*yx6+c_2*c_6*y_0 ** 2*yx3*yx5*yx6+c_2*c_6 ** 2*y_0*yx3*yx5*yx6+c_2*c_6 ** 2*y_0 ** 3*y_1*y_2*yx3+3*c_1*c_6 ** 2*y_0 ** 3*y_1*y_2*yx6+c_1*c_6 ** 3*y_0 ** 2*y_1*y_2*yx6+c_2*c_6*y_0 ** 3*y_1*y_2 ** 2*yx6-3*c_3*c_6 ** 2*y_0 ** 3*y_1*y_2*yx7-c_3*c_6 ** 3*y_0 ** 2*y_1*y_2*yx7+3*c_4*c_6 ** 2*y_0 ** 3*y_1*y_2*yx6+c_4*c_6 ** 3*y_0 ** 2*y_1*y_2*yx6+c_2*c_6 ** 2*y_0 ** 2*y_1*yx3*yx5+c_2*c_6 ** 2*y_0 ** 2*y_2*yx3*yx6+c_2*c_6*y_0 ** 2*y_1*y_2*yx5*yx6+c_2*c_6 ** 2*y_0*y_1*y_2*yx5*yx6-2*c_2*c_6*y_0*y_1*y_2 ** 2*yx6*yx7)/(y_0 ** 2*y_1*y_2*(c_6+y_0) ** 3)"],
["-(-c_1*c_6 ** 4*y_0 ** 4*y_2+2*c_1*c_6 ** 4*y_0 ** 3*y_2*yx7-c_0*c_6 ** 4*y_0 ** 3*y_2-4*c_1*c_6 ** 3*y_0 ** 5*y_2-c_2*c_6 ** 3*y_0 ** 4*y_2 ** 2+2*c_2*c_6 ** 3*y_0 ** 4*y_2*yx5+8*c_1*c_6 ** 3*y_0 ** 4*y_2*yx7-4*c_0*c_6 ** 3*y_0 ** 4*y_2+2*c_2*c_6 ** 3*y_0 ** 3*y_2 ** 2*yx7-c_2*c_6 ** 3*y_0 ** 3*y_2*yx5+2*c_2*c_6 ** 3*y_0 ** 3*yx5 ** 2+4*c_2*c_6 ** 3*y_0 ** 2*y_2*yx5*yx7+2*c_2*c_6 ** 3*y_0*yx5 ** 2*yx7-6*c_1*c_6 ** 2*y_0 ** 6*y_2-3*c_2*c_6 ** 2*y_0 ** 5*y_2 ** 2+6*c_2*c_6 ** 2*y_0 ** 5*y_2*yx5+12*c_1*c_6 ** 2*y_0 ** 5*y_2*yx7-6*c_0*c_6 ** 2*y_0 ** 5*y_2+4*c_2*c_6 ** 2*y_0 ** 4*y_2 ** 2*yx7-2*c_2*c_6 ** 2*y_0 ** 4*y_2*yx5+4*c_2*c_6 ** 2*y_0 ** 4*yx5 ** 2+c_2*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx7+8*c_2*c_6 ** 2*y_0 ** 3*y_2*yx5*yx7+c_2*c_6 ** 2*y_0 ** 3*yx5 ** 2-6*c_2*c_6 ** 2*y_0 ** 2*y_2 ** 2*yx7 ** 2+2*c_2*c_6 ** 2*y_0 ** 2*y_2*yx5*yx7+4*c_2*c_6 ** 2*y_0 ** 2*yx5 ** 2*yx7+c_2*c_6 ** 2*y_0*yx5 ** 2*yx7-2*c_2*c_6 ** 2*y_2 ** 2*yx7 ** 3-4*c_1*c_6*y_0 ** 7*y_2-3*c_2*c_6*y_0 ** 6*y_2 ** 2+6*c_2*c_6*y_0 ** 6*y_2*yx5+8*c_1*c_6*y_0 ** 6*y_2*yx7-4*c_0*c_6*y_0 ** 6*y_2+2*c_2*c_6*y_0 ** 5*y_2 ** 2*yx7-c_2*c_6*y_0 ** 5*y_2*yx5+2*c_2*c_6*y_0 ** 5*yx5 ** 2+c_2*c_6*y_0 ** 4*y_2 ** 2*yx7+4*c_2*c_6*y_0 ** 4*y_2*yx5*yx7+c_2*c_6*y_0 ** 4*yx5 ** 2-6*c_2*c_6*y_0 ** 3*y_2 ** 2*yx7 ** 2+2*c_2*c_6*y_0 ** 3*y_2*yx5*yx7+2*c_2*c_6*y_0 ** 3*yx5 ** 2*yx7-3*c_2*c_6*y_0 ** 2*y_2 ** 2*yx7 ** 2+c_2*c_6*y_0 ** 2*yx5 ** 2*yx7-2*c_2*c_6*y_0*y_2 ** 2*yx7 ** 3-c_2*c_6*y_2 ** 2*yx7 ** 3-c_1*y_0 ** 8*y_2-c_2*y_0 ** 7*y_2 ** 2+2*c_2*y_0 ** 7*y_2*yx5+2*c_1*y_0 ** 7*y_2*yx7-c_0*y_0 ** 7*y_2)/(y_0 ** 3*y_2*(c_6+y_0) ** 4)"]
])
closer = LogNormalClosure(max_order,multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs, self.__n_counter, self.__k_counter)
#print (answer -expected).applyfunc(sympy.simplify)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_creation_from_list_of_strings_returns_matrix(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a matrix of expressions.
"""
m = sympy.Matrix([[sympy.sympify('x+y+3'), sympy.sympify('x+3')],
[sympy.sympify('y-x'), sympy.sympify('x+y+166')]])
m_as_string = [['x+y+3', 'x+3'], ['y-x', 'x+y+166']]
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_creation_of_column_matrix_from_list_of_strings(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a column matrix of expresions
"""
m = sympy.Matrix([sympy.sympify('x+y+3'), sympy.sympify('x+3'), sympy.sympify('y-x'),
sympy.sympify('x+y+166')])
m_as_string = ['x+y+3', 'x+3', 'y-x', 'x+y+166']
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_log_normal_closer_wrapper(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"], ["x_0_1_1-y_1*y_2"], ["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"], ["x_1_1_0-y_0*y_1"], ["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]])
max_order = 2
expected = to_sympy_matrix([
[
"c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3+(c_2*c_6*yx5*(yx5*y_0 ** 2+2*y_2*yx7*y_0+yx5*yx7))/(y_0 ** 2*y_2*(c_6+y_0) ** 3)-(c_2*c_6*y_2*yx7 ** 2*(3*y_0 ** 2+yx7))/(y_0 ** 3*(c_6+y_0) ** 4)"
], ["c_3*y_0-c_4*y_1"], ["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
[
"-(c_2*y_0 ** 5*y_2 ** 2*yx2+c_1*y_0 ** 5*y_2 ** 2*yx5-c_4*y_0 ** 5*y_2 ** 2*yx6+c_5*y_0 ** 5*y_2 ** 2*yx5+2*c_2*c_6*y_0 ** 4*y_2 ** 2*yx2+3*c_1*c_6*y_0 ** 4*y_2 ** 2*yx5+c_2*c_6*y_0 ** 3*y_2 ** 3*yx5-3*c_4*c_6*y_0 ** 4*y_2 ** 2*yx6+3*c_5*c_6*y_0 ** 4*y_2 ** 2*yx5+c_2*c_6*y_0 ** 2*yx2*yx5 ** 2+c_2*c_6 ** 2*y_0*yx2*yx5 ** 2-c_2*c_6*y_2 ** 2*yx5 ** 2*yx7+c_2*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx2+3*c_1*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx5+c_1*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx5+c_2*c_6 ** 2*y_0*y_2 ** 2*yx5 ** 2+c_2*c_6 ** 2*y_0 ** 2*y_2 ** 3*yx5-3*c_4*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx6-c_4*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx6+3*c_5*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx5+c_5*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx5+2*c_2*c_6*y_0 ** 3*y_2*yx2*yx5-2*c_2*c_6*y_0*y_2 ** 3*yx5*yx7+2*c_2*c_6 ** 2*y_0 ** 2*y_2*yx2*yx5)/(y_0 ** 2*y_2 ** 2*(c_6+y_0) ** 3)"
],
[
"-(c_2*y_0 ** 5*y_1*y_2*yx3+c_1*y_0 ** 5*y_1*y_2*yx6-c_3*y_0 ** 5*y_1*y_2*yx7+c_4*y_0 ** 5*y_1*y_2*yx6-c_2*c_6*y_2 ** 2*yx6 ** 2*yx7-c_2*c_6*y_0 ** 2*y_2 ** 2*yx6 ** 2+c_2*c_6 ** 2*y_0 ** 2*y_1*y_2 ** 2*yx6+2*c_2*c_6*y_0 ** 4*y_1*y_2*yx3+3*c_1*c_6*y_0 ** 4*y_1*y_2*yx6-3*c_3*c_6*y_0 ** 4*y_1*y_2*yx7+3*c_4*c_6*y_0 ** 4*y_1*y_2*yx6+c_2*c_6*y_0 ** 3*y_1*yx3*yx5+c_2*c_6*y_0 ** 3*y_2*yx3*yx6+c_2*c_6*y_0 ** 2*yx3*yx5*yx6+c_2*c_6 ** 2*y_0*yx3*yx5*yx6+c_2*c_6 ** 2*y_0 ** 3*y_1*y_2*yx3+3*c_1*c_6 ** 2*y_0 ** 3*y_1*y_2*yx6+c_1*c_6 ** 3*y_0 ** 2*y_1*y_2*yx6+c_2*c_6*y_0 ** 3*y_1*y_2 ** 2*yx6-3*c_3*c_6 ** 2*y_0 ** 3*y_1*y_2*yx7-c_3*c_6 ** 3*y_0 ** 2*y_1*y_2*yx7+3*c_4*c_6 ** 2*y_0 ** 3*y_1*y_2*yx6+c_4*c_6 ** 3*y_0 ** 2*y_1*y_2*yx6+c_2*c_6 ** 2*y_0 ** 2*y_1*yx3*yx5+c_2*c_6 ** 2*y_0 ** 2*y_2*yx3*yx6+c_2*c_6*y_0 ** 2*y_1*y_2*yx5*yx6+c_2*c_6 ** 2*y_0*y_1*y_2*yx5*yx6-2*c_2*c_6*y_0*y_1*y_2 ** 2*yx6*yx7)/(y_0 ** 2*y_1*y_2*(c_6+y_0) ** 3)"
],
[
"-(-c_1*c_6 ** 4*y_0 ** 4*y_2+2*c_1*c_6 ** 4*y_0 ** 3*y_2*yx7-c_0*c_6 ** 4*y_0 ** 3*y_2-4*c_1*c_6 ** 3*y_0 ** 5*y_2-c_2*c_6 ** 3*y_0 ** 4*y_2 ** 2+2*c_2*c_6 ** 3*y_0 ** 4*y_2*yx5+8*c_1*c_6 ** 3*y_0 ** 4*y_2*yx7-4*c_0*c_6 ** 3*y_0 ** 4*y_2+2*c_2*c_6 ** 3*y_0 ** 3*y_2 ** 2*yx7-c_2*c_6 ** 3*y_0 ** 3*y_2*yx5+2*c_2*c_6 ** 3*y_0 ** 3*yx5 ** 2+4*c_2*c_6 ** 3*y_0 ** 2*y_2*yx5*yx7+2*c_2*c_6 ** 3*y_0*yx5 ** 2*yx7-6*c_1*c_6 ** 2*y_0 ** 6*y_2-3*c_2*c_6 ** 2*y_0 ** 5*y_2 ** 2+6*c_2*c_6 ** 2*y_0 ** 5*y_2*yx5+12*c_1*c_6 ** 2*y_0 ** 5*y_2*yx7-6*c_0*c_6 ** 2*y_0 ** 5*y_2+4*c_2*c_6 ** 2*y_0 ** 4*y_2 ** 2*yx7-2*c_2*c_6 ** 2*y_0 ** 4*y_2*yx5+4*c_2*c_6 ** 2*y_0 ** 4*yx5 ** 2+c_2*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx7+8*c_2*c_6 ** 2*y_0 ** 3*y_2*yx5*yx7+c_2*c_6 ** 2*y_0 ** 3*yx5 ** 2-6*c_2*c_6 ** 2*y_0 ** 2*y_2 ** 2*yx7 ** 2+2*c_2*c_6 ** 2*y_0 ** 2*y_2*yx5*yx7+4*c_2*c_6 ** 2*y_0 ** 2*yx5 ** 2*yx7+c_2*c_6 ** 2*y_0*yx5 ** 2*yx7-2*c_2*c_6 ** 2*y_2 ** 2*yx7 ** 3-4*c_1*c_6*y_0 ** 7*y_2-3*c_2*c_6*y_0 ** 6*y_2 ** 2+6*c_2*c_6*y_0 ** 6*y_2*yx5+8*c_1*c_6*y_0 ** 6*y_2*yx7-4*c_0*c_6*y_0 ** 6*y_2+2*c_2*c_6*y_0 ** 5*y_2 ** 2*yx7-c_2*c_6*y_0 ** 5*y_2*yx5+2*c_2*c_6*y_0 ** 5*yx5 ** 2+c_2*c_6*y_0 ** 4*y_2 ** 2*yx7+4*c_2*c_6*y_0 ** 4*y_2*yx5*yx7+c_2*c_6*y_0 ** 4*yx5 ** 2-6*c_2*c_6*y_0 ** 3*y_2 ** 2*yx7 ** 2+2*c_2*c_6*y_0 ** 3*y_2*yx5*yx7+2*c_2*c_6*y_0 ** 3*yx5 ** 2*yx7-3*c_2*c_6*y_0 ** 2*y_2 ** 2*yx7 ** 2+c_2*c_6*y_0 ** 2*yx5 ** 2*yx7-2*c_2*c_6*y_0*y_2 ** 2*yx7 ** 3-c_2*c_6*y_2 ** 2*yx7 ** 3-c_1*y_0 ** 8*y_2-c_2*y_0 ** 7*y_2 ** 2+2*c_2*y_0 ** 7*y_2*yx5+2*c_1*y_0 ** 7*y_2*yx7-c_0*y_0 ** 7*y_2)/(y_0 ** 3*y_2*(c_6+y_0) ** 4)"
]
])
closer = LogNormalClosure(max_order, multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs,
self.__n_counter, self.__k_counter)
#print (answer -expected).applyfunc(sympy.simplify)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_centralmoments_using_MM_model(self):
"""
Given the MM model hard codded bellow,the result of central moment should match exactly the expected one
:return:
"""
counter_nvecs = [[0, 0], [0, 2], [1, 1], [2, 0]]
mcounter_nvecs = [[0, 0], [0, 1], [1, 0], [0, 2], [1, 1], [2, 0]]
counter = [Moment(c,sympy.Symbol("YU{0}".format(i))) for i,c in enumerate(counter_nvecs)]
mcounter = [Moment(c,sympy.Symbol("y_{0}".format(i))) for i,c in enumerate(mcounter_nvecs)]
m = to_sympy_matrix([
['-c_0*y_0*(y_0 + y_1 - 181) + c_1*(-y_0 - y_1 + 301)',
0,
'-c_0',
'-c_0'],
[
'c_2*(-y_0 - y_1 + 301)',
0,
0,
0]
])
species = sympy.Matrix(map(sympy.var, ['y_0', 'y_1']))
propensities = to_sympy_matrix(['c_0*y_0*(y_0 + y_1 - 181)',
'c_1*(-y_0 - y_1 + 301)',
'c_2*(-y_0 - y_1 + 301)'])
stoichiometry_matrix = sympy.Matrix([[-1, 1, 0],
[0, 0, 1]])
expected = to_sympy_matrix([
["c_2*(-y_0 - y_1 + 301)"," -2*c_2"," -2*c_2"," 0"],
["-c_0*y_0*y_1*(y_0 + y_1 - 181) + c_1*y_1*(-y_0 - y_1 + 301) + c_2*y_0*(-y_0 - y_1 + 301) - c_2*y_2*(-y_0 - y_1 + 301) - y_1*(-c_0*y_0*(y_0 + y_1 - 181) + c_1*(-y_0 - y_1 + 301))"," -c_0*y_0 - c_1"," -c_0*y_0 - c_0*(y_0 + y_1 - 181) - c_1 - c_2"," -c_2"],
["-2*c_0*y_0**2*(y_0 + y_1 - 181) + c_0*y_0*(y_0 + y_1 - 181) + 2*c_1*y_0*(-y_0 - y_1 + 301) + c_1*(-y_0 - y_1 + 301) - 2*y_2*(-c_0*y_0*(y_0 + y_1 - 181) + c_1*(-y_0 - y_1 + 301))"," 0"," -4*c_0*y_0 + 2*c_0*y_2 + c_0 - 2*c_1"," -4*c_0*y_0 + 2*c_0*y_2 - 2*c_0*(y_0 + y_1 - 181) + c_0 - 2*c_1"]
])
answer = eq_central_moments(counter, mcounter, m, species, propensities, stoichiometry_matrix, 2)
assert_sympy_expressions_equal(answer, expected)
def test_ode_moment_no_description_from_variance_terms(self):
"""
Given Variance terms as left hand side terms, the generated descriptions
dict should have nones
for each of the symbols
"""
lhs = [VarianceTerm(pos, term) for term, pos in [('V34', (3, 4)), ('V32', (3, 2)), ('V11', (1, 1))]]
rhs = to_sympy_matrix(['y_1+y_2+c_2', 'y_2+y_3+c_3', 'y_3+c_1'])
p = ODEProblem('LNA', lhs, rhs, parameters=sympy.symbols(['c_1', 'c_2', 'c_3']))
for i,l in enumerate(lhs):
self.assertIsNone(p._descriptions_dict[l.symbol].descriptor)
def test_log_normal_closer_wrapper_univariate(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"], ["x_0_1_1-y_1*y_2"], ["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"], ["x_1_1_0-y_0*y_1"], ["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]])
max_order = 2
expected = to_sympy_matrix([
[
"c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3-(c_2*c_6*y_2*yx7 ** 2*(3*y_0 ** 2+yx7))/(y_0 ** 3*(c_6+y_0) ** 4)"
], ["c_3*y_0-c_4*y_1"], ["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
[
"c_4*yx6-c_1*yx5-c_5*yx5-(c_2*y_0*yx2)/(c_6+y_0)-(c_2*y_2*yx5)/(c_6+y_0)+(c_2*y_0*y_2*yx5)/(c_6+y_0) ** 2"
],
[
"c_3*yx7-c_1*yx6-c_4*yx6-(c_2*y_0*yx3)/(c_6+y_0)-(c_2*y_2*yx6)/(c_6+y_0)+(c_2*y_0*y_2*yx6)/(c_6+y_0) ** 2"
],
[
"(c_0*y_0 ** 7+c_1*y_0 ** 8+c_2*y_0 ** 7*y_2-2*c_2*y_0 ** 7*yx5-2*c_1*y_0 ** 7*yx7+6*c_0*c_6 ** 2*y_0 ** 5+4*c_0*c_6 ** 3*y_0 ** 4+c_0*c_6 ** 4*y_0 ** 3+6*c_1*c_6 ** 2*y_0 ** 6+4*c_1*c_6 ** 3*y_0 ** 5+c_1*c_6 ** 4*y_0 ** 4+4*c_0*c_6*y_0 ** 6+4*c_1*c_6*y_0 ** 7+3*c_2*c_6*y_0 ** 6*y_2+c_2*c_6*y_0 ** 5*yx5-6*c_2*c_6*y_0 ** 6*yx5-8*c_1*c_6*y_0 ** 6*yx7+c_2*c_6*y_2*yx7 ** 3+3*c_2*c_6 ** 2*y_0 ** 5*y_2+c_2*c_6 ** 3*y_0 ** 4*y_2+2*c_2*c_6 ** 2*y_0 ** 4*yx5+c_2*c_6 ** 3*y_0 ** 3*yx5-6*c_2*c_6 ** 2*y_0 ** 5*yx5-2*c_2*c_6 ** 3*y_0 ** 4*yx5-12*c_1*c_6 ** 2*y_0 ** 5*yx7-8*c_1*c_6 ** 3*y_0 ** 4*yx7-2*c_1*c_6 ** 4*y_0 ** 3*yx7+2*c_2*c_6 ** 2*y_2*yx7 ** 3+3*c_2*c_6*y_0 ** 2*y_2*yx7 ** 2+6*c_2*c_6*y_0 ** 3*y_2*yx7 ** 2-c_2*c_6 ** 2*y_0 ** 3*y_2*yx7-4*c_2*c_6 ** 2*y_0 ** 4*y_2*yx7-2*c_2*c_6 ** 3*y_0 ** 3*y_2*yx7+6*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7 ** 2+2*c_2*c_6*y_0*y_2*yx7 ** 3-c_2*c_6*y_0 ** 4*y_2*yx7-2*c_2*c_6*y_0 ** 5*y_2*yx7)/(y_0 ** 3*(c_6+y_0) ** 4)"
]
])
#here, we set univariate!
closer = LogNormalClosure(max_order, multivariate=False)
answer = closer.close(self.__mfk, central_from_raw_exprs,
self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_creation_from_list_of_strings_returns_matrix(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a matrix of expressions.
"""
m = sympy.Matrix([[sympy.sympify('x+y+3'),
sympy.sympify('x+3')],
[sympy.sympify('y-x'),
sympy.sympify('x+y+166')]])
m_as_string = [['x+y+3', 'x+3'], ['y-x', 'x+y+166']]
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_close_type_one(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"],
["x_0_1_1-y_1*y_2"],
["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"],
["x_1_1_0-y_0*y_1"],
["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]
])
max_order = 2
expected = to_sympy_matrix([
["yx5*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0)) + yx7*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2) + c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0) + (-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2)*(2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2)) + (c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3)*(2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["-yx2*c_2*y_0/(c_6 + y_0) + yx5*(-c_1 + 2*c_2*y_0*y_2/(c_6 + y_0)**2 - 2*c_2*y_2/(c_6 + y_0) - c_5 - y_2*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))) + yx6*c_4 + yx7*(-c_2*y_0*y_2**2/(c_6 + y_0)**3 + c_2*y_2**2/(c_6 + y_0)**2 - y_2*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)) + c_0*y_2 - c_1*y_0*y_2 - c_2*y_0*y_2**2/(c_6 + y_0) + c_4*y_0*y_1 - c_5*y_0*y_2 - y_0*(c_4*y_1 - c_5*y_2) - y_2*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + (c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))*(2*yx2*yx5/y_2 + yx2*y_0 + 2*yx5*y_2 + 3*y_0*y_2**2 - y_0*(yx2 + y_2**2) - 2*y_2*(yx5 + y_0*y_2)) + (-2*c_2*y_0*y_2/(c_6 + y_0)**3 + 2*c_2*y_2/(c_6 + y_0)**2 - y_2*(-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2))*(2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2)) + (c_2*y_0*y_2**2/(c_6 + y_0)**4 - c_2*y_2**2/(c_6 + y_0)**3 - y_2*(c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3))*(2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))"],
["-yx3*c_2*y_0/(c_6 + y_0) + yx5*(c_2*y_0*y_1/(c_6 + y_0)**2 - c_2*y_1/(c_6 + y_0) - y_1*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))) + yx6*(-c_1 + c_2*y_0*y_2/(c_6 + y_0)**2 - c_2*y_2/(c_6 + y_0) - c_4) + yx7*(-c_2*y_0*y_1*y_2/(c_6 + y_0)**3 + c_2*y_1*y_2/(c_6 + y_0)**2 + c_3 - y_1*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)) + c_0*y_1 - c_1*y_0*y_1 - c_2*y_0*y_1*y_2/(c_6 + y_0) + c_3*y_0**2 - c_4*y_0*y_1 - y_0*(c_3*y_0 - c_4*y_1) - y_1*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + (c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))*(yx3*y_0 + yx5*y_1 + yx6*y_2 + 3*y_0*y_1*y_2 - y_0*(yx3 + y_1*y_2) - y_1*(yx5 + y_0*y_2) - y_2*(yx6 + y_0*y_1)) + (-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)*(2*yx6*yx7/y_0 + 2*yx6*y_0 + yx7*y_1 + 3*y_0**2*y_1 - 2*y_0*(yx6 + y_0*y_1) - y_1*(yx7 + y_0**2)) + (-c_2*y_0*y_1/(c_6 + y_0)**3 + c_2*y_1/(c_6 + y_0)**2 - y_1*(-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2))*(2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2)) + (c_2*y_0*y_1*y_2/(c_6 + y_0)**4 - c_2*y_1*y_2/(c_6 + y_0)**3 - y_1*(c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3))*(2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))"],
["yx5*(2*c_2*y_0**2/(c_6 + y_0)**2 - 4*c_2*y_0/(c_6 + y_0) - c_2*y_0/(c_6 + y_0)**2 + c_2/(c_6 + y_0) - 2*y_0*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))) + yx7*(-2*c_1 - 2*c_2*y_0**2*y_2/(c_6 + y_0)**3 + 4*c_2*y_0*y_2/(c_6 + y_0)**2 + c_2*y_0*y_2/(c_6 + y_0)**3 - 2*c_2*y_2/(c_6 + y_0) - c_2*y_2/(c_6 + y_0)**2 - 2*y_0*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)) + 2*c_0*y_0 + c_0 - 2*c_1*y_0**2 + c_1*y_0 - 2*c_2*y_0**2*y_2/(c_6 + y_0) + c_2*y_0*y_2/(c_6 + y_0) - 2*y_0*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + (2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))*(2*c_2*y_0**2*y_2/(c_6 + y_0)**4 - 4*c_2*y_0*y_2/(c_6 + y_0)**3 - c_2*y_0*y_2/(c_6 + y_0)**4 + 2*c_2*y_2/(c_6 + y_0)**2 + c_2*y_2/(c_6 + y_0)**3 - 2*y_0*(c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3)) + (2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2))*(-2*c_2*y_0**2/(c_6 + y_0)**3 + 4*c_2*y_0/(c_6 + y_0)**2 + c_2*y_0/(c_6 + y_0)**3 - 2*c_2/(c_6 + y_0) - c_2/(c_6 + y_0)**2 - 2*y_0*(-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2))"]
])
closer = GammaClosure(max_order, multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs, self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_log_normal_closer_wrapper_univariate(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"],
["x_0_1_1-y_1*y_2"],
["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"],
["x_1_1_0-y_0*y_1"],
["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]
])
max_order = 2
expected = to_sympy_matrix([
["c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3-(c_2*c_6*y_2*yx7 ** 2*(3*y_0 ** 2+yx7))/(y_0 ** 3*(c_6+y_0) ** 4)"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["c_4*yx6-c_1*yx5-c_5*yx5-(c_2*y_0*yx2)/(c_6+y_0)-(c_2*y_2*yx5)/(c_6+y_0)+(c_2*y_0*y_2*yx5)/(c_6+y_0) ** 2"],
["c_3*yx7-c_1*yx6-c_4*yx6-(c_2*y_0*yx3)/(c_6+y_0)-(c_2*y_2*yx6)/(c_6+y_0)+(c_2*y_0*y_2*yx6)/(c_6+y_0) ** 2"],
["(c_0*y_0 ** 7+c_1*y_0 ** 8+c_2*y_0 ** 7*y_2-2*c_2*y_0 ** 7*yx5-2*c_1*y_0 ** 7*yx7+6*c_0*c_6 ** 2*y_0 ** 5+4*c_0*c_6 ** 3*y_0 ** 4+c_0*c_6 ** 4*y_0 ** 3+6*c_1*c_6 ** 2*y_0 ** 6+4*c_1*c_6 ** 3*y_0 ** 5+c_1*c_6 ** 4*y_0 ** 4+4*c_0*c_6*y_0 ** 6+4*c_1*c_6*y_0 ** 7+3*c_2*c_6*y_0 ** 6*y_2+c_2*c_6*y_0 ** 5*yx5-6*c_2*c_6*y_0 ** 6*yx5-8*c_1*c_6*y_0 ** 6*yx7+c_2*c_6*y_2*yx7 ** 3+3*c_2*c_6 ** 2*y_0 ** 5*y_2+c_2*c_6 ** 3*y_0 ** 4*y_2+2*c_2*c_6 ** 2*y_0 ** 4*yx5+c_2*c_6 ** 3*y_0 ** 3*yx5-6*c_2*c_6 ** 2*y_0 ** 5*yx5-2*c_2*c_6 ** 3*y_0 ** 4*yx5-12*c_1*c_6 ** 2*y_0 ** 5*yx7-8*c_1*c_6 ** 3*y_0 ** 4*yx7-2*c_1*c_6 ** 4*y_0 ** 3*yx7+2*c_2*c_6 ** 2*y_2*yx7 ** 3+3*c_2*c_6*y_0 ** 2*y_2*yx7 ** 2+6*c_2*c_6*y_0 ** 3*y_2*yx7 ** 2-c_2*c_6 ** 2*y_0 ** 3*y_2*yx7-4*c_2*c_6 ** 2*y_0 ** 4*y_2*yx7-2*c_2*c_6 ** 3*y_0 ** 3*y_2*yx7+6*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7 ** 2+2*c_2*c_6*y_0*y_2*yx7 ** 3-c_2*c_6*y_0 ** 4*y_2*yx7-2*c_2*c_6*y_0 ** 5*y_2*yx7)/(y_0 ** 3*(c_6+y_0) ** 4)"]
])
#here, we set univariate!
closer = LogNormalClosure(max_order, multivariate=False)
answer = closer.close(self.__mfk, central_from_raw_exprs, self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_close_type_zero(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"],
["x_0_1_1-y_1*y_2"],
["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"],
["x_1_1_0-y_0*y_1"],
["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]
])
max_order = 2
expected = to_sympy_matrix([
["c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3-(2*c_2*c_6*y_2*yx7 ** 2)/(y_0*(c_6+y_0) ** 4)"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["c_4*yx6-c_1*yx5-c_5*yx5-(c_2*y_0*yx2)/(c_6+y_0)-(c_2*y_2*yx5)/(c_6+y_0)+(c_2*y_0*y_2*yx5)/(c_6+y_0) ** 2"],
["c_3*yx7-c_1*yx6-c_4*yx6-(c_2*y_0*yx3)/(c_6+y_0)-(c_2*y_2*yx6)/(c_6+y_0)+(c_2*y_0*y_2*yx6)/(c_6+y_0) ** 2"],
["(c_0*y_0 ** 5+c_1*y_0 ** 6+c_2*y_0 ** 5*y_2-2*c_2*y_0 ** 5*yx5-2*c_1*y_0 ** 5*yx7+6*c_0*c_6 ** 2*y_0 ** 3+4*c_0*c_6 ** 3*y_0 ** 2+6*c_1*c_6 ** 2*y_0 ** 4+4*c_1*c_6 ** 3*y_0 ** 3+c_1*c_6 ** 4*y_0 ** 2+4*c_0*c_6*y_0 ** 4+c_0*c_6 ** 4*y_0+4*c_1*c_6*y_0 ** 5+3*c_2*c_6*y_0 ** 4*y_2+c_2*c_6*y_0 ** 3*yx5+c_2*c_6 ** 3*y_0*yx5-6*c_2*c_6*y_0 ** 4*yx5-8*c_1*c_6*y_0 ** 4*yx7-2*c_1*c_6 ** 4*y_0*yx7+2*c_2*c_6*y_2*yx7 ** 2+3*c_2*c_6 ** 2*y_0 ** 3*y_2+c_2*c_6 ** 3*y_0 ** 2*y_2+2*c_2*c_6 ** 2*y_0 ** 2*yx5-6*c_2*c_6 ** 2*y_0 ** 3*yx5-2*c_2*c_6 ** 3*y_0 ** 2*yx5-12*c_1*c_6 ** 2*y_0 ** 3*yx7-8*c_1*c_6 ** 3*y_0 ** 2*yx7+4*c_2*c_6 ** 2*y_2*yx7 ** 2-4*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7+4*c_2*c_6*y_0*y_2*yx7 ** 2-c_2*c_6*y_0 ** 2*y_2*yx7-c_2*c_6 ** 2*y_0*y_2*yx7-2*c_2*c_6*y_0 ** 3*y_2*yx7-2*c_2*c_6 ** 3*y_0*y_2*yx7)/(y_0*(c_6+y_0) ** 4)"]
])
closer = GammaClosure(max_order, multivariate=False)
answer = closer.close(self.__mfk, central_from_raw_exprs, self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_creation_of_column_matrix_from_list_of_strings(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a column matrix of expresions
"""
m = sympy.Matrix([
sympy.sympify('x+y+3'),
sympy.sympify('x+3'),
sympy.sympify('y-x'),
sympy.sympify('x+y+166')
])
m_as_string = ['x+y+3', 'x+3', 'y-x', 'x+y+166']
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def __init__(self, method, left_hand_side_descriptors, right_hand_side, parameters):
"""
:param method: a string describing the method used to generate the problem.
Currently, 'MEA' and 'LNA' are supported"
:param left_hand_side_descriptors: the left hand side of equations as a list of
:class:`~means.core.descriptors.Descriptor` objects (such as :class:`~means.core.descriptors.Moment`)
:param right_hand_side: the right hand side of equations
:param parameters: the parameters of the model
"""
self.__left_hand_side_descriptors = left_hand_side_descriptors
self.__left_hand_side = to_sympy_column_matrix(to_sympy_matrix(
[plhs.symbol for plhs in left_hand_side_descriptors])
)
self.__right_hand_side = to_sympy_column_matrix(right_hand_side)
self.__parameters = to_list_of_symbols(parameters)
self.__method = method
def test_ode_rhs_as_function(self):
"""
Given an ODEProblem with well specified LHS, RHS expressions as well as list of constants,
the value of rhs_as_function given the appropriate params should be the same as the value of
rhs evaluated for these params. The returned answer should also be an one-dimensional numpy array.
:return:
"""
lhs = [Moment(np.ones(3),i) for i in sympy.Matrix(['y_1', 'y_2', 'y_3'])]
rhs = to_sympy_matrix(['y_1+y_2+c_2', 'y_2+y_3+c_3', 'y_3+c_1'])
p = ODEProblem('MEA', lhs, rhs, parameters=sympy.symbols(['c_1', 'c_2', 'c_3']))
rhs_as_function = p.right_hand_side_as_function
values = [4, 5, 6] # y_1, y_2, y_3 in that order
expected_ans = np.array([11, 14, 7])
actual_ans = np.array(rhs_as_function(values, [1, 2, 3]))
self.assertEqual(actual_ans.ndim, 1) # Returned answer must be an one-dimensional array,
# otherwise ExplicitEuler solver would fail.
assert_array_equal(actual_ans, expected_ans)
def test_compute_raw_moments(self):
expected = to_sympy_matrix([
["y_2**2+yx2"],
["y_1*y_2+yx3"],
["y_1**2+yx4"],
["y_0*y_2+yx5"],
["y_0*y_1+yx6"],
["y_0**2+yx7"],
["y_2**3+3*y_2*yx2+3*yx2**2/y_2+yx2**3/y_2**3"],
["y_1*y_2**2+y_1*yx2+2*y_2*yx3+2*yx2*yx3/y_2+yx3**2/y_1+yx2*yx3**2/(y_1*y_2**2)"],
["y_1**2*y_2+2*y_1*yx3+y_2*yx4+yx3**2/y_2+2*yx3*yx4/y_1+yx3**2*yx4/(y_1**2*y_2)"],
["y_1**3+3*y_1*yx4+3*yx4**2/y_1+yx4**3/y_1**3"],
["y_0*y_2**2+y_0*yx2+2*y_2*yx5+2*yx2*yx5/y_2+yx5**2/y_0+yx2*yx5**2/(y_0*y_2**2)"],
["y_0*y_1*y_2+y_0*yx3+y_1*yx5+y_2*yx6+yx3*yx5/y_2+yx3*yx6/y_1+yx5*yx6/y_0+yx3*yx5*yx6/(y_0*y_1*y_2)"],
["y_0*y_1**2+y_0*yx4+2*y_1*yx6+2*yx4*yx6/y_1+yx6**2/y_0+yx4*yx6**2/(y_0*y_1**2)"],
["y_0**2*y_2+2*y_0*yx5+y_2*yx7+yx5**2/y_2+2*yx5*yx7/y_0+yx5**2*yx7/(y_0**2*y_2)"],
["y_0**2*y_1+2*y_0*yx6+y_1*yx7+yx6**2/y_1+2*yx6*yx7/y_0+yx6**2*yx7/(y_0**2*y_1)"],
["y_0**3+3*y_0*yx7+3*yx7**2/y_0+yx7**3/y_0**3"]
])
closer = LogNormalClosure(2,multivariate=True)
answer = closer._compute_raw_moments(self.__n_counter, self.__k_counter,)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_normal_closer_wrapper(self):
central_from_raw_exprs = to_sympy_matrix([
["x_0_0_2 - y_2**2"],
["x_0_1_1 - y_1*y_2"],
["x_0_2_0 - y_1**2"],
["x_1_0_1 - y_0*y_2"],
["x_1_1_0 - y_0*y_1"],
["x_2_0_0 - y_0**2"],
["-3*x_0_0_2*y_2 + x_0_0_3 + 2*y_2**3"],
["-x_0_0_2*y_1 - 2*x_0_1_1*y_2 + x_0_1_2 + 2*y_1*y_2**2"],
["-2*x_0_1_1*y_1 - x_0_2_0*y_2 + x_0_2_1 + 2*y_1**2*y_2"],
["-3*x_0_2_0*y_1 + x_0_3_0 + 2*y_1**3"],
["-x_0_0_2*y_0 - 2*x_1_0_1*y_2 + x_1_0_2 + 2*y_0*y_2**2"],
["-x_0_1_1*y_0 - x_1_0_1*y_1 - x_1_1_0*y_2 + x_1_1_1 + 2*y_0*y_1*y_2"],
["-x_0_2_0*y_0 - 2*x_1_1_0*y_1 + x_1_2_0 + 2*y_0*y_1**2"],
["-2*x_1_0_1*y_0 - x_2_0_0*y_2 + x_2_0_1 + 2*y_0**2*y_2"],
["-2*x_1_1_0*y_0 - x_2_0_0*y_1 + x_2_1_0 + 2*y_0**2*y_1"],
["-3*x_2_0_0*y_0 + x_3_0_0 + 2*y_0**3"]
])
k_counter = [
Moment([0, 0, 0], symbol=sympy.Integer(1)),
Moment([1, 0, 0], symbol=sympy.Symbol("y_0")),
Moment([0, 1, 0], symbol=sympy.Symbol("y_1")),
Moment([0, 0, 1], symbol=sympy.Symbol("y_2")),
Moment([0, 0, 2], symbol=sympy.Symbol("x_0_0_2")),
Moment([0, 1, 1], symbol=sympy.Symbol("x_0_1_1")),
Moment([0, 2, 0], symbol=sympy.Symbol("x_0_2_0")),
Moment([1, 0, 1], symbol=sympy.Symbol("x_1_0_1")),
Moment([1, 1, 0], symbol=sympy.Symbol("x_1_1_0")),
Moment([2, 0, 0], symbol=sympy.Symbol("x_2_0_0")),
Moment([0, 0, 3], symbol=sympy.Symbol("x_0_0_3")),
Moment([0, 1, 2], symbol=sympy.Symbol("x_0_1_2")),
Moment([0, 2, 1], symbol=sympy.Symbol("x_0_2_1")),
Moment([0, 3, 0], symbol=sympy.Symbol("x_0_3_0")),
Moment([1, 0, 2], symbol=sympy.Symbol("x_1_0_2")),
Moment([1, 1, 1], symbol=sympy.Symbol("x_1_1_1")),
Moment([1, 2, 0], symbol=sympy.Symbol("x_1_2_0")),
Moment([2, 0, 1], symbol=sympy.Symbol("x_2_0_1")),
Moment([2, 1, 0], symbol=sympy.Symbol("x_2_1_0")),
Moment([3, 0, 0], symbol=sympy.Symbol("x_3_0_0"))
]
max_order = 2
prob_moments = self.__problem_moments
expected = to_sympy_matrix([
["c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["c_4*yx6-c_1*yx5-c_5*yx5-(c_2*y_0*yx2)/(c_6+y_0)-(c_2*y_2*yx5)/(c_6+y_0)+(c_2*y_0*y_2*yx5)/(c_6+y_0) ** 2"],
["c_3*yx7-c_1*yx6-c_4*yx6-(c_2*y_0*yx3)/(c_6+y_0)-(c_2*y_2*yx6)/(c_6+y_0)+(c_2*y_0*y_2*yx6)/(c_6+y_0) ** 2"],
["(c_0*c_6 ** 3+c_0*y_0 ** 3+c_1*y_0 ** 4+c_2*y_0 ** 3*y_2-2*c_2*y_0 ** 3*yx5-2*c_1*y_0 ** 3*yx7+3*c_1*c_6 ** 2*y_0 ** 2+3*c_0*c_6*y_0 ** 2+3*c_0*c_6 ** 2*y_0+3*c_1*c_6*y_0 ** 3+c_1*c_6 ** 3*y_0+c_2*c_6 ** 2*yx5-2*c_1*c_6 ** 3*yx7+c_2*c_6*y_0*yx5-c_2*c_6*y_2*yx7+2*c_2*c_6*y_0 ** 2*y_2+c_2*c_6 ** 2*y_0*y_2-4*c_2*c_6*y_0 ** 2*yx5-2*c_2*c_6 ** 2*y_0*yx5-6*c_1*c_6*y_0 ** 2*yx7-6*c_1*c_6 ** 2*y_0*yx7-2*c_2*c_6 ** 2*y_2*yx7-2*c_2*c_6*y_0*y_2*yx7)/(c_6+y_0) ** 3"]
])
closer = NormalClosure(max_order, multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs,self.__n_counter, k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
class TestLogNormalCloser(unittest.TestCase):
__n_counter = [
Moment([0, 0, 0], symbol=sympy.Integer(0)),
Moment([0, 0, 2], symbol=sympy.Symbol("yx2")),
Moment([0, 1, 1], symbol=sympy.Symbol("yx3")),
Moment([0, 2, 0], symbol=sympy.Symbol("yx4")),
Moment([1, 0, 1], symbol=sympy.Symbol("yx5")),
Moment([1, 1, 0], symbol=sympy.Symbol("yx6")),
Moment([2, 0, 0], symbol=sympy.Symbol("yx7")),
Moment([0, 0, 3], symbol=sympy.Symbol("yx8")),
Moment([0, 1, 2], symbol=sympy.Symbol("yx9")),
Moment([0, 2, 1], symbol=sympy.Symbol("yx10")),
Moment([0, 3, 0], symbol=sympy.Symbol("yx11")),
Moment([1, 0, 2], symbol=sympy.Symbol("yx12")),
Moment([1, 1, 1], symbol=sympy.Symbol("yx13")),
Moment([1, 2, 0], symbol=sympy.Symbol("yx14")),
Moment([2, 0, 1], symbol=sympy.Symbol("yx15")),
Moment([2, 1, 0], symbol=sympy.Symbol("yx16")),
Moment([3, 0, 0], symbol=sympy.Symbol("yx17")),
]
__k_counter = [
Moment([0, 0, 0], symbol=sympy.Integer(1)),
Moment([1, 0, 0], symbol=sympy.Symbol("y_0")),
Moment([0, 1, 0], symbol=sympy.Symbol("y_1")),
Moment([0, 0, 1], symbol=sympy.Symbol("y_2")),
Moment([0, 0, 2], symbol=sympy.Symbol("x_0_0_2")),
Moment([0, 1, 1], symbol=sympy.Symbol("x_0_1_1")),
Moment([0, 2, 0], symbol=sympy.Symbol("x_0_2_0")),
Moment([1, 0, 1], symbol=sympy.Symbol("x_1_0_1")),
Moment([1, 1, 0], symbol=sympy.Symbol("x_1_1_0")),
Moment([2, 0, 0], symbol=sympy.Symbol("x_2_0_0")),
Moment([0, 0, 3], symbol=sympy.Symbol("x_0_0_3")),
Moment([0, 1, 2], symbol=sympy.Symbol("x_0_1_2")),
Moment([0, 2, 1], symbol=sympy.Symbol("x_0_2_1")),
Moment([0, 3, 0], symbol=sympy.Symbol("x_0_3_0")),
Moment([1, 0, 2], symbol=sympy.Symbol("x_1_0_2")),
Moment([1, 1, 1], symbol=sympy.Symbol("x_1_1_1")),
Moment([1, 2, 0], symbol=sympy.Symbol("x_1_2_0")),
Moment([2, 0, 1], symbol=sympy.Symbol("x_2_0_1")),
Moment([2, 1, 0], symbol=sympy.Symbol("x_2_1_0")),
Moment([3, 0, 0], symbol=sympy.Symbol("x_3_0_0"))
]
__mfk = to_sympy_matrix([
["c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0) - c_2*y_2*yx17*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)**3 - c_2*y_2*yx7*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx15*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx5*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)"],
["c_3*y_0 - c_4*y_1"],
["c_4*y_1 - c_5*y_2"],
["2*c_4*y_1*y_2 + c_4*y_1 + 2*c_4*yx3 - 2*c_5*y_2**2 + c_5*y_2 - 2*c_5*yx2 - 2*y_2*(c_4*y_1 - c_5*y_2)"],
["c_3*y_0*y_2 + c_3*yx5 + c_4*y_1**2 - c_4*y_1*y_2 - c_4*y_1 + c_4*yx4 - c_5*y_1*y_2 - y_1*(c_4*y_1 - c_5*y_2) - y_2*(c_3*y_0 - c_4*y_1) + yx3*(-c_4 - c_5)"],
["2*c_3*y_0*y_1 + c_3*y_0 + 2*c_3*yx6 - 2*c_4*y_1**2 + c_4*y_1 - 2*c_4*yx4 - 2*y_1*(c_3*y_0 - c_4*y_1)"],
["c_0*y_2 - c_1*y_0*y_2 - c_2*y_0*y_2**2/(c_6 + y_0) - c_2*y_0*yx2/(c_6 + y_0) - c_2*y_2*yx15*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx12*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_4*y_0*y_1 + c_4*yx6 - c_5*y_0*y_2 - y_0*(c_4*y_1 - c_5*y_2) - y_2*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + yx5*(-c_1 - c_2*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) - c_5)"],
["c_0*y_1 - c_1*y_0*y_1 - c_2*y_0*y_1*y_2/(c_6 + y_0) - c_2*y_0*yx3/(c_6 + y_0) - c_2*y_2*yx16*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx13*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_3*y_0**2 + c_3*yx7 - c_4*y_0*y_1 - y_0*(c_3*y_0 - c_4*y_1) - y_1*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + yx6*(-c_1 - c_2*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) - c_4)"],
["2*c_0*y_0 + c_0 - 2*c_1*y_0**2 + c_1*y_0 - 2*c_2*y_0**2*y_2/(c_6 + y_0) + c_2*y_0*y_2/(c_6 + y_0) - 2*y_0*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + yx15*(2*c_2*y_0*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - 2*c_2*(y_0**2/(c_6 + y_0)**2 - 2*y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_2*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2) + yx17*(2*c_2*y_0*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)**3 - 2*c_2*y_2*(-y_0**2/(c_6 + y_0)**2 + 2*y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 + c_2*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)**3) + yx5*(2*c_2*y_0*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) - 2*c_2*y_0*(-y_0/(c_6 + y_0) + 2)/(c_6 + y_0) + c_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)) + yx7*(-2*c_1 + 2*c_2*y_0*y_2*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - 2*c_2*y_2*(y_0**2/(c_6 + y_0)**2 - 2*y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_2*y_2*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2)"]
])
def test_close_type_one(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"],
["x_0_1_1-y_1*y_2"],
["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"],
["x_1_1_0-y_0*y_1"],
["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]
])
max_order = 2
expected = to_sympy_matrix([
["yx5*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0)) + yx7*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2) + c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0) + (-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2)*(2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2)) + (c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3)*(2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["-yx2*c_2*y_0/(c_6 + y_0) + yx5*(-c_1 + 2*c_2*y_0*y_2/(c_6 + y_0)**2 - 2*c_2*y_2/(c_6 + y_0) - c_5 - y_2*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))) + yx6*c_4 + yx7*(-c_2*y_0*y_2**2/(c_6 + y_0)**3 + c_2*y_2**2/(c_6 + y_0)**2 - y_2*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)) + c_0*y_2 - c_1*y_0*y_2 - c_2*y_0*y_2**2/(c_6 + y_0) + c_4*y_0*y_1 - c_5*y_0*y_2 - y_0*(c_4*y_1 - c_5*y_2) - y_2*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + (c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))*(2*yx2*yx5/y_2 + yx2*y_0 + 2*yx5*y_2 + 3*y_0*y_2**2 - y_0*(yx2 + y_2**2) - 2*y_2*(yx5 + y_0*y_2)) + (-2*c_2*y_0*y_2/(c_6 + y_0)**3 + 2*c_2*y_2/(c_6 + y_0)**2 - y_2*(-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2))*(2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2)) + (c_2*y_0*y_2**2/(c_6 + y_0)**4 - c_2*y_2**2/(c_6 + y_0)**3 - y_2*(c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3))*(2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))"],
["-yx3*c_2*y_0/(c_6 + y_0) + yx5*(c_2*y_0*y_1/(c_6 + y_0)**2 - c_2*y_1/(c_6 + y_0) - y_1*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))) + yx6*(-c_1 + c_2*y_0*y_2/(c_6 + y_0)**2 - c_2*y_2/(c_6 + y_0) - c_4) + yx7*(-c_2*y_0*y_1*y_2/(c_6 + y_0)**3 + c_2*y_1*y_2/(c_6 + y_0)**2 + c_3 - y_1*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)) + c_0*y_1 - c_1*y_0*y_1 - c_2*y_0*y_1*y_2/(c_6 + y_0) + c_3*y_0**2 - c_4*y_0*y_1 - y_0*(c_3*y_0 - c_4*y_1) - y_1*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + (c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))*(yx3*y_0 + yx5*y_1 + yx6*y_2 + 3*y_0*y_1*y_2 - y_0*(yx3 + y_1*y_2) - y_1*(yx5 + y_0*y_2) - y_2*(yx6 + y_0*y_1)) + (-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)*(2*yx6*yx7/y_0 + 2*yx6*y_0 + yx7*y_1 + 3*y_0**2*y_1 - 2*y_0*(yx6 + y_0*y_1) - y_1*(yx7 + y_0**2)) + (-c_2*y_0*y_1/(c_6 + y_0)**3 + c_2*y_1/(c_6 + y_0)**2 - y_1*(-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2))*(2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2)) + (c_2*y_0*y_1*y_2/(c_6 + y_0)**4 - c_2*y_1*y_2/(c_6 + y_0)**3 - y_1*(c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3))*(2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))"],
["yx5*(2*c_2*y_0**2/(c_6 + y_0)**2 - 4*c_2*y_0/(c_6 + y_0) - c_2*y_0/(c_6 + y_0)**2 + c_2/(c_6 + y_0) - 2*y_0*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))) + yx7*(-2*c_1 - 2*c_2*y_0**2*y_2/(c_6 + y_0)**3 + 4*c_2*y_0*y_2/(c_6 + y_0)**2 + c_2*y_0*y_2/(c_6 + y_0)**3 - 2*c_2*y_2/(c_6 + y_0) - c_2*y_2/(c_6 + y_0)**2 - 2*y_0*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)) + 2*c_0*y_0 + c_0 - 2*c_1*y_0**2 + c_1*y_0 - 2*c_2*y_0**2*y_2/(c_6 + y_0) + c_2*y_0*y_2/(c_6 + y_0) - 2*y_0*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + (2*yx7**2/y_0 + 3*yx7*y_0 + 3*y_0**3 - 3*y_0*(yx7 + y_0**2))*(2*c_2*y_0**2*y_2/(c_6 + y_0)**4 - 4*c_2*y_0*y_2/(c_6 + y_0)**3 - c_2*y_0*y_2/(c_6 + y_0)**4 + 2*c_2*y_2/(c_6 + y_0)**2 + c_2*y_2/(c_6 + y_0)**3 - 2*y_0*(c_2*y_0*y_2/(c_6 + y_0)**4 - c_2*y_2/(c_6 + y_0)**3)) + (2*yx5*yx7/y_0 + 2*yx5*y_0 + yx7*y_2 + 3*y_0**2*y_2 - 2*y_0*(yx5 + y_0*y_2) - y_2*(yx7 + y_0**2))*(-2*c_2*y_0**2/(c_6 + y_0)**3 + 4*c_2*y_0/(c_6 + y_0)**2 + c_2*y_0/(c_6 + y_0)**3 - 2*c_2/(c_6 + y_0) - c_2/(c_6 + y_0)**2 - 2*y_0*(-c_2*y_0/(c_6 + y_0)**3 + c_2/(c_6 + y_0)**2))"]
])
closer = GammaClosure(max_order, multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs, self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_close_type_zero(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"],
["x_0_1_1-y_1*y_2"],
["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"],
["x_1_1_0-y_0*y_1"],
["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]
])
max_order = 2
expected = to_sympy_matrix([
["c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3-(2*c_2*c_6*y_2*yx7 ** 2)/(y_0*(c_6+y_0) ** 4)"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["c_4*yx6-c_1*yx5-c_5*yx5-(c_2*y_0*yx2)/(c_6+y_0)-(c_2*y_2*yx5)/(c_6+y_0)+(c_2*y_0*y_2*yx5)/(c_6+y_0) ** 2"],
["c_3*yx7-c_1*yx6-c_4*yx6-(c_2*y_0*yx3)/(c_6+y_0)-(c_2*y_2*yx6)/(c_6+y_0)+(c_2*y_0*y_2*yx6)/(c_6+y_0) ** 2"],
["(c_0*y_0 ** 5+c_1*y_0 ** 6+c_2*y_0 ** 5*y_2-2*c_2*y_0 ** 5*yx5-2*c_1*y_0 ** 5*yx7+6*c_0*c_6 ** 2*y_0 ** 3+4*c_0*c_6 ** 3*y_0 ** 2+6*c_1*c_6 ** 2*y_0 ** 4+4*c_1*c_6 ** 3*y_0 ** 3+c_1*c_6 ** 4*y_0 ** 2+4*c_0*c_6*y_0 ** 4+c_0*c_6 ** 4*y_0+4*c_1*c_6*y_0 ** 5+3*c_2*c_6*y_0 ** 4*y_2+c_2*c_6*y_0 ** 3*yx5+c_2*c_6 ** 3*y_0*yx5-6*c_2*c_6*y_0 ** 4*yx5-8*c_1*c_6*y_0 ** 4*yx7-2*c_1*c_6 ** 4*y_0*yx7+2*c_2*c_6*y_2*yx7 ** 2+3*c_2*c_6 ** 2*y_0 ** 3*y_2+c_2*c_6 ** 3*y_0 ** 2*y_2+2*c_2*c_6 ** 2*y_0 ** 2*yx5-6*c_2*c_6 ** 2*y_0 ** 3*yx5-2*c_2*c_6 ** 3*y_0 ** 2*yx5-12*c_1*c_6 ** 2*y_0 ** 3*yx7-8*c_1*c_6 ** 3*y_0 ** 2*yx7+4*c_2*c_6 ** 2*y_2*yx7 ** 2-4*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7+4*c_2*c_6*y_0*y_2*yx7 ** 2-c_2*c_6*y_0 ** 2*y_2*yx7-c_2*c_6 ** 2*y_0*y_2*yx7-2*c_2*c_6*y_0 ** 3*y_2*yx7-2*c_2*c_6 ** 3*y_0*y_2*yx7)/(y_0*(c_6+y_0) ** 4)"]
])
closer = GammaClosure(max_order, multivariate=False)
answer = closer.close(self.__mfk, central_from_raw_exprs, self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
class TestLogNormalCloser(unittest.TestCase):
__n_counter = [
Moment([0, 0, 0], symbol=sympy.Integer(0)),
Moment([0, 0, 2], symbol=sympy.Symbol("yx2")),
Moment([0, 1, 1], symbol=sympy.Symbol("yx3")),
Moment([0, 2, 0], symbol=sympy.Symbol("yx4")),
Moment([1, 0, 1], symbol=sympy.Symbol("yx5")),
Moment([1, 1, 0], symbol=sympy.Symbol("yx6")),
Moment([2, 0, 0], symbol=sympy.Symbol("yx7")),
Moment([0, 0, 3], symbol=sympy.Symbol("yx8")),
Moment([0, 1, 2], symbol=sympy.Symbol("yx9")),
Moment([0, 2, 1], symbol=sympy.Symbol("yx10")),
Moment([0, 3, 0], symbol=sympy.Symbol("yx11")),
Moment([1, 0, 2], symbol=sympy.Symbol("yx12")),
Moment([1, 1, 1], symbol=sympy.Symbol("yx13")),
Moment([1, 2, 0], symbol=sympy.Symbol("yx14")),
Moment([2, 0, 1], symbol=sympy.Symbol("yx15")),
Moment([2, 1, 0], symbol=sympy.Symbol("yx16")),
Moment([3, 0, 0], symbol=sympy.Symbol("yx17")),
]
__k_counter = [
Moment([0, 0, 0], symbol=sympy.Integer(1)),
Moment([1, 0, 0], symbol=sympy.Symbol("y_0")),
Moment([0, 1, 0], symbol=sympy.Symbol("y_1")),
Moment([0, 0, 1], symbol=sympy.Symbol("y_2")),
Moment([0, 0, 2], symbol=sympy.Symbol("x_0_0_2")),
Moment([0, 1, 1], symbol=sympy.Symbol("x_0_1_1")),
Moment([0, 2, 0], symbol=sympy.Symbol("x_0_2_0")),
Moment([1, 0, 1], symbol=sympy.Symbol("x_1_0_1")),
Moment([1, 1, 0], symbol=sympy.Symbol("x_1_1_0")),
Moment([2, 0, 0], symbol=sympy.Symbol("x_2_0_0")),
Moment([0, 0, 3], symbol=sympy.Symbol("x_0_0_3")),
Moment([0, 1, 2], symbol=sympy.Symbol("x_0_1_2")),
Moment([0, 2, 1], symbol=sympy.Symbol("x_0_2_1")),
Moment([0, 3, 0], symbol=sympy.Symbol("x_0_3_0")),
Moment([1, 0, 2], symbol=sympy.Symbol("x_1_0_2")),
Moment([1, 1, 1], symbol=sympy.Symbol("x_1_1_1")),
Moment([1, 2, 0], symbol=sympy.Symbol("x_1_2_0")),
Moment([2, 0, 1], symbol=sympy.Symbol("x_2_0_1")),
Moment([2, 1, 0], symbol=sympy.Symbol("x_2_1_0")),
Moment([3, 0, 0], symbol=sympy.Symbol("x_3_0_0"))
]
__mfk = to_sympy_matrix([
[
"c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0) - c_2*y_2*yx17*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)**3 - c_2*y_2*yx7*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx15*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx5*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)"
], ["c_3*y_0 - c_4*y_1"], ["c_4*y_1 - c_5*y_2"],
[
"2*c_4*y_1*y_2 + c_4*y_1 + 2*c_4*yx3 - 2*c_5*y_2**2 + c_5*y_2 - 2*c_5*yx2 - 2*y_2*(c_4*y_1 - c_5*y_2)"
],
[
"c_3*y_0*y_2 + c_3*yx5 + c_4*y_1**2 - c_4*y_1*y_2 - c_4*y_1 + c_4*yx4 - c_5*y_1*y_2 - y_1*(c_4*y_1 - c_5*y_2) - y_2*(c_3*y_0 - c_4*y_1) + yx3*(-c_4 - c_5)"
],
[
"2*c_3*y_0*y_1 + c_3*y_0 + 2*c_3*yx6 - 2*c_4*y_1**2 + c_4*y_1 - 2*c_4*yx4 - 2*y_1*(c_3*y_0 - c_4*y_1)"
],
[
"c_0*y_2 - c_1*y_0*y_2 - c_2*y_0*y_2**2/(c_6 + y_0) - c_2*y_0*yx2/(c_6 + y_0) - c_2*y_2*yx15*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx12*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_4*y_0*y_1 + c_4*yx6 - c_5*y_0*y_2 - y_0*(c_4*y_1 - c_5*y_2) - y_2*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + yx5*(-c_1 - c_2*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) - c_5)"
],
[
"c_0*y_1 - c_1*y_0*y_1 - c_2*y_0*y_1*y_2/(c_6 + y_0) - c_2*y_0*yx3/(c_6 + y_0) - c_2*y_2*yx16*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - c_2*yx13*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_3*y_0**2 + c_3*yx7 - c_4*y_0*y_1 - y_0*(c_3*y_0 - c_4*y_1) - y_1*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + yx6*(-c_1 - c_2*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) - c_4)"
],
[
"2*c_0*y_0 + c_0 - 2*c_1*y_0**2 + c_1*y_0 - 2*c_2*y_0**2*y_2/(c_6 + y_0) + c_2*y_0*y_2/(c_6 + y_0) - 2*y_0*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) + yx15*(2*c_2*y_0*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - 2*c_2*(y_0**2/(c_6 + y_0)**2 - 2*y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_2*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2) + yx17*(2*c_2*y_0*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)**3 - 2*c_2*y_2*(-y_0**2/(c_6 + y_0)**2 + 2*y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 + c_2*y_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)**3) + yx5*(2*c_2*y_0*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0) - 2*c_2*y_0*(-y_0/(c_6 + y_0) + 2)/(c_6 + y_0) + c_2*(-y_0/(c_6 + y_0) + 1)/(c_6 + y_0)) + yx7*(-2*c_1 + 2*c_2*y_0*y_2*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2 - 2*c_2*y_2*(y_0**2/(c_6 + y_0)**2 - 2*y_0/(c_6 + y_0) + 1)/(c_6 + y_0) + c_2*y_2*(y_0/(c_6 + y_0) - 1)/(c_6 + y_0)**2)"
]
])
def test_get_log_covariance(self):
log_variance_mat = to_sympy_matrix([["log(1+yx7/y_0**2)", "0", "0"],
["0", "log(1+yx4/y_1**2)", "0"],
["0", "0", "log(1+yx2/y_2**2)"]])
log_expectation_symbols = to_sympy_matrix([[
"log(y_0)-log(1+yx7/y_0**2)/2"
], ["log(y_1)-log(1+yx4/y_1**2)/2"], ["log(y_2)-log(1+yx2/y_2**2)/2"]])
covariance_matrix = to_sympy_matrix([["yx7", "yx6", "yx5"],
["yx6", "yx4", "yx3"],
["yx5", "yx3", "yx2"]])
expected = sympy.sympify("log(1 + yx6/(y_0*y_1))")
closer = LogNormalClosure(2, multivariate=True)
answer = closer._get_log_covariance(log_variance_mat,
log_expectation_symbols,
covariance_matrix, 0, 1)
self.assertEqual(answer, expected)
answer1 = closer._get_log_covariance(log_variance_mat,
log_expectation_symbols,
covariance_matrix, 1, 2)
answer2 = closer._get_log_covariance(log_variance_mat,
log_expectation_symbols,
covariance_matrix, 1, 2)
#logcovariance between species 1 and 2 == covariance between sp. 2 and 1
self.assertEqual(answer1, answer2)
def test_get_covariance_symbol(self):
closer = LogNormalClosure(3, multivariate=True)
expected = sympy.Symbol("yx3")
answer = closer._get_covariance_symbol(self.__n_counter, 1, 2)
self.assertEqual(answer, expected)
def test_get_covariance_symbol2(self):
closer = LogNormalClosure(3, multivariate=True)
expected = sympy.Symbol("yx6")
answer = closer._get_covariance_symbol(self.__n_counter, 1, 0)
self.assertEqual(answer, expected)
def test_get_covariance_symbol_is_triangular(self):
closer = LogNormalClosure(3, multivariate=True)
#covariance between species 1 and 2 == covariance between sp. 2 and 1
answer1 = closer._get_covariance_symbol(self.__n_counter, 1, 0)
answer2 = closer._get_covariance_symbol(self.__n_counter, 0, 1)
self.assertEqual(answer1, answer2)
def test_compute_raw_moments(self):
expected = to_sympy_matrix([
["y_2**2+yx2"], ["y_1*y_2+yx3"], ["y_1**2+yx4"], ["y_0*y_2+yx5"],
["y_0*y_1+yx6"], ["y_0**2+yx7"],
["y_2**3+3*y_2*yx2+3*yx2**2/y_2+yx2**3/y_2**3"],
[
"y_1*y_2**2+y_1*yx2+2*y_2*yx3+2*yx2*yx3/y_2+yx3**2/y_1+yx2*yx3**2/(y_1*y_2**2)"
],
[
"y_1**2*y_2+2*y_1*yx3+y_2*yx4+yx3**2/y_2+2*yx3*yx4/y_1+yx3**2*yx4/(y_1**2*y_2)"
], ["y_1**3+3*y_1*yx4+3*yx4**2/y_1+yx4**3/y_1**3"],
[
"y_0*y_2**2+y_0*yx2+2*y_2*yx5+2*yx2*yx5/y_2+yx5**2/y_0+yx2*yx5**2/(y_0*y_2**2)"
],
[
"y_0*y_1*y_2+y_0*yx3+y_1*yx5+y_2*yx6+yx3*yx5/y_2+yx3*yx6/y_1+yx5*yx6/y_0+yx3*yx5*yx6/(y_0*y_1*y_2)"
],
[
"y_0*y_1**2+y_0*yx4+2*y_1*yx6+2*yx4*yx6/y_1+yx6**2/y_0+yx4*yx6**2/(y_0*y_1**2)"
],
[
"y_0**2*y_2+2*y_0*yx5+y_2*yx7+yx5**2/y_2+2*yx5*yx7/y_0+yx5**2*yx7/(y_0**2*y_2)"
],
[
"y_0**2*y_1+2*y_0*yx6+y_1*yx7+yx6**2/y_1+2*yx6*yx7/y_0+yx6**2*yx7/(y_0**2*y_1)"
], ["y_0**3+3*y_0*yx7+3*yx7**2/y_0+yx7**3/y_0**3"]
])
closer = LogNormalClosure(2, multivariate=True)
answer = closer._compute_raw_moments(
self.__n_counter,
self.__k_counter,
)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_log_normal_closer_wrapper(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"], ["x_0_1_1-y_1*y_2"], ["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"], ["x_1_1_0-y_0*y_1"], ["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]])
max_order = 2
expected = to_sympy_matrix([
[
"c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3+(c_2*c_6*yx5*(yx5*y_0 ** 2+2*y_2*yx7*y_0+yx5*yx7))/(y_0 ** 2*y_2*(c_6+y_0) ** 3)-(c_2*c_6*y_2*yx7 ** 2*(3*y_0 ** 2+yx7))/(y_0 ** 3*(c_6+y_0) ** 4)"
], ["c_3*y_0-c_4*y_1"], ["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
[
"-(c_2*y_0 ** 5*y_2 ** 2*yx2+c_1*y_0 ** 5*y_2 ** 2*yx5-c_4*y_0 ** 5*y_2 ** 2*yx6+c_5*y_0 ** 5*y_2 ** 2*yx5+2*c_2*c_6*y_0 ** 4*y_2 ** 2*yx2+3*c_1*c_6*y_0 ** 4*y_2 ** 2*yx5+c_2*c_6*y_0 ** 3*y_2 ** 3*yx5-3*c_4*c_6*y_0 ** 4*y_2 ** 2*yx6+3*c_5*c_6*y_0 ** 4*y_2 ** 2*yx5+c_2*c_6*y_0 ** 2*yx2*yx5 ** 2+c_2*c_6 ** 2*y_0*yx2*yx5 ** 2-c_2*c_6*y_2 ** 2*yx5 ** 2*yx7+c_2*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx2+3*c_1*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx5+c_1*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx5+c_2*c_6 ** 2*y_0*y_2 ** 2*yx5 ** 2+c_2*c_6 ** 2*y_0 ** 2*y_2 ** 3*yx5-3*c_4*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx6-c_4*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx6+3*c_5*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx5+c_5*c_6 ** 3*y_0 ** 2*y_2 ** 2*yx5+2*c_2*c_6*y_0 ** 3*y_2*yx2*yx5-2*c_2*c_6*y_0*y_2 ** 3*yx5*yx7+2*c_2*c_6 ** 2*y_0 ** 2*y_2*yx2*yx5)/(y_0 ** 2*y_2 ** 2*(c_6+y_0) ** 3)"
],
[
"-(c_2*y_0 ** 5*y_1*y_2*yx3+c_1*y_0 ** 5*y_1*y_2*yx6-c_3*y_0 ** 5*y_1*y_2*yx7+c_4*y_0 ** 5*y_1*y_2*yx6-c_2*c_6*y_2 ** 2*yx6 ** 2*yx7-c_2*c_6*y_0 ** 2*y_2 ** 2*yx6 ** 2+c_2*c_6 ** 2*y_0 ** 2*y_1*y_2 ** 2*yx6+2*c_2*c_6*y_0 ** 4*y_1*y_2*yx3+3*c_1*c_6*y_0 ** 4*y_1*y_2*yx6-3*c_3*c_6*y_0 ** 4*y_1*y_2*yx7+3*c_4*c_6*y_0 ** 4*y_1*y_2*yx6+c_2*c_6*y_0 ** 3*y_1*yx3*yx5+c_2*c_6*y_0 ** 3*y_2*yx3*yx6+c_2*c_6*y_0 ** 2*yx3*yx5*yx6+c_2*c_6 ** 2*y_0*yx3*yx5*yx6+c_2*c_6 ** 2*y_0 ** 3*y_1*y_2*yx3+3*c_1*c_6 ** 2*y_0 ** 3*y_1*y_2*yx6+c_1*c_6 ** 3*y_0 ** 2*y_1*y_2*yx6+c_2*c_6*y_0 ** 3*y_1*y_2 ** 2*yx6-3*c_3*c_6 ** 2*y_0 ** 3*y_1*y_2*yx7-c_3*c_6 ** 3*y_0 ** 2*y_1*y_2*yx7+3*c_4*c_6 ** 2*y_0 ** 3*y_1*y_2*yx6+c_4*c_6 ** 3*y_0 ** 2*y_1*y_2*yx6+c_2*c_6 ** 2*y_0 ** 2*y_1*yx3*yx5+c_2*c_6 ** 2*y_0 ** 2*y_2*yx3*yx6+c_2*c_6*y_0 ** 2*y_1*y_2*yx5*yx6+c_2*c_6 ** 2*y_0*y_1*y_2*yx5*yx6-2*c_2*c_6*y_0*y_1*y_2 ** 2*yx6*yx7)/(y_0 ** 2*y_1*y_2*(c_6+y_0) ** 3)"
],
[
"-(-c_1*c_6 ** 4*y_0 ** 4*y_2+2*c_1*c_6 ** 4*y_0 ** 3*y_2*yx7-c_0*c_6 ** 4*y_0 ** 3*y_2-4*c_1*c_6 ** 3*y_0 ** 5*y_2-c_2*c_6 ** 3*y_0 ** 4*y_2 ** 2+2*c_2*c_6 ** 3*y_0 ** 4*y_2*yx5+8*c_1*c_6 ** 3*y_0 ** 4*y_2*yx7-4*c_0*c_6 ** 3*y_0 ** 4*y_2+2*c_2*c_6 ** 3*y_0 ** 3*y_2 ** 2*yx7-c_2*c_6 ** 3*y_0 ** 3*y_2*yx5+2*c_2*c_6 ** 3*y_0 ** 3*yx5 ** 2+4*c_2*c_6 ** 3*y_0 ** 2*y_2*yx5*yx7+2*c_2*c_6 ** 3*y_0*yx5 ** 2*yx7-6*c_1*c_6 ** 2*y_0 ** 6*y_2-3*c_2*c_6 ** 2*y_0 ** 5*y_2 ** 2+6*c_2*c_6 ** 2*y_0 ** 5*y_2*yx5+12*c_1*c_6 ** 2*y_0 ** 5*y_2*yx7-6*c_0*c_6 ** 2*y_0 ** 5*y_2+4*c_2*c_6 ** 2*y_0 ** 4*y_2 ** 2*yx7-2*c_2*c_6 ** 2*y_0 ** 4*y_2*yx5+4*c_2*c_6 ** 2*y_0 ** 4*yx5 ** 2+c_2*c_6 ** 2*y_0 ** 3*y_2 ** 2*yx7+8*c_2*c_6 ** 2*y_0 ** 3*y_2*yx5*yx7+c_2*c_6 ** 2*y_0 ** 3*yx5 ** 2-6*c_2*c_6 ** 2*y_0 ** 2*y_2 ** 2*yx7 ** 2+2*c_2*c_6 ** 2*y_0 ** 2*y_2*yx5*yx7+4*c_2*c_6 ** 2*y_0 ** 2*yx5 ** 2*yx7+c_2*c_6 ** 2*y_0*yx5 ** 2*yx7-2*c_2*c_6 ** 2*y_2 ** 2*yx7 ** 3-4*c_1*c_6*y_0 ** 7*y_2-3*c_2*c_6*y_0 ** 6*y_2 ** 2+6*c_2*c_6*y_0 ** 6*y_2*yx5+8*c_1*c_6*y_0 ** 6*y_2*yx7-4*c_0*c_6*y_0 ** 6*y_2+2*c_2*c_6*y_0 ** 5*y_2 ** 2*yx7-c_2*c_6*y_0 ** 5*y_2*yx5+2*c_2*c_6*y_0 ** 5*yx5 ** 2+c_2*c_6*y_0 ** 4*y_2 ** 2*yx7+4*c_2*c_6*y_0 ** 4*y_2*yx5*yx7+c_2*c_6*y_0 ** 4*yx5 ** 2-6*c_2*c_6*y_0 ** 3*y_2 ** 2*yx7 ** 2+2*c_2*c_6*y_0 ** 3*y_2*yx5*yx7+2*c_2*c_6*y_0 ** 3*yx5 ** 2*yx7-3*c_2*c_6*y_0 ** 2*y_2 ** 2*yx7 ** 2+c_2*c_6*y_0 ** 2*yx5 ** 2*yx7-2*c_2*c_6*y_0*y_2 ** 2*yx7 ** 3-c_2*c_6*y_2 ** 2*yx7 ** 3-c_1*y_0 ** 8*y_2-c_2*y_0 ** 7*y_2 ** 2+2*c_2*y_0 ** 7*y_2*yx5+2*c_1*y_0 ** 7*y_2*yx7-c_0*y_0 ** 7*y_2)/(y_0 ** 3*y_2*(c_6+y_0) ** 4)"
]
])
closer = LogNormalClosure(max_order, multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs,
self.__n_counter, self.__k_counter)
#print (answer -expected).applyfunc(sympy.simplify)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_log_normal_closer_wrapper_univariate(self):
central_from_raw_exprs = to_sympy_matrix(
[["x_0_0_2-y_2**2"], ["x_0_1_1-y_1*y_2"], ["x_0_2_0-y_1**2"],
["x_1_0_1-y_0*y_2"], ["x_1_1_0-y_0*y_1"], ["x_2_0_0-y_0**2"],
["-3*x_0_0_2*y_2+x_0_0_3+2*y_2**3"],
["-x_0_0_2*y_1-2*x_0_1_1*y_2+x_0_1_2+2*y_1*y_2**2"],
["-2*x_0_1_1*y_1-x_0_2_0*y_2+x_0_2_1+2*y_1**2*y_2"],
["-3*x_0_2_0*y_1+x_0_3_0+2*y_1**3"],
["-x_0_0_2*y_0-2*x_1_0_1*y_2+x_1_0_2+2*y_0*y_2**2"],
["-x_0_1_1*y_0-x_1_0_1*y_1-x_1_1_0*y_2+x_1_1_1+2*y_0*y_1*y_2"],
["-x_0_2_0*y_0-2*x_1_1_0*y_1+x_1_2_0+2*y_0*y_1**2"],
["-2*x_1_0_1*y_0-x_2_0_0*y_2+x_2_0_1+2*y_0**2*y_2"],
["-2*x_1_1_0*y_0-x_2_0_0*y_1+x_2_1_0+2*y_0**2*y_1"],
["-3*x_2_0_0*y_0+x_3_0_0+2*y_0**3"]])
max_order = 2
expected = to_sympy_matrix([
[
"c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2-(c_2*y_0*y_2)/(c_6+y_0)+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3-(c_2*c_6*y_2*yx7 ** 2*(3*y_0 ** 2+yx7))/(y_0 ** 3*(c_6+y_0) ** 4)"
], ["c_3*y_0-c_4*y_1"], ["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
[
"c_4*yx6-c_1*yx5-c_5*yx5-(c_2*y_0*yx2)/(c_6+y_0)-(c_2*y_2*yx5)/(c_6+y_0)+(c_2*y_0*y_2*yx5)/(c_6+y_0) ** 2"
],
[
"c_3*yx7-c_1*yx6-c_4*yx6-(c_2*y_0*yx3)/(c_6+y_0)-(c_2*y_2*yx6)/(c_6+y_0)+(c_2*y_0*y_2*yx6)/(c_6+y_0) ** 2"
],
[
"(c_0*y_0 ** 7+c_1*y_0 ** 8+c_2*y_0 ** 7*y_2-2*c_2*y_0 ** 7*yx5-2*c_1*y_0 ** 7*yx7+6*c_0*c_6 ** 2*y_0 ** 5+4*c_0*c_6 ** 3*y_0 ** 4+c_0*c_6 ** 4*y_0 ** 3+6*c_1*c_6 ** 2*y_0 ** 6+4*c_1*c_6 ** 3*y_0 ** 5+c_1*c_6 ** 4*y_0 ** 4+4*c_0*c_6*y_0 ** 6+4*c_1*c_6*y_0 ** 7+3*c_2*c_6*y_0 ** 6*y_2+c_2*c_6*y_0 ** 5*yx5-6*c_2*c_6*y_0 ** 6*yx5-8*c_1*c_6*y_0 ** 6*yx7+c_2*c_6*y_2*yx7 ** 3+3*c_2*c_6 ** 2*y_0 ** 5*y_2+c_2*c_6 ** 3*y_0 ** 4*y_2+2*c_2*c_6 ** 2*y_0 ** 4*yx5+c_2*c_6 ** 3*y_0 ** 3*yx5-6*c_2*c_6 ** 2*y_0 ** 5*yx5-2*c_2*c_6 ** 3*y_0 ** 4*yx5-12*c_1*c_6 ** 2*y_0 ** 5*yx7-8*c_1*c_6 ** 3*y_0 ** 4*yx7-2*c_1*c_6 ** 4*y_0 ** 3*yx7+2*c_2*c_6 ** 2*y_2*yx7 ** 3+3*c_2*c_6*y_0 ** 2*y_2*yx7 ** 2+6*c_2*c_6*y_0 ** 3*y_2*yx7 ** 2-c_2*c_6 ** 2*y_0 ** 3*y_2*yx7-4*c_2*c_6 ** 2*y_0 ** 4*y_2*yx7-2*c_2*c_6 ** 3*y_0 ** 3*y_2*yx7+6*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7 ** 2+2*c_2*c_6*y_0*y_2*yx7 ** 3-c_2*c_6*y_0 ** 4*y_2*yx7-2*c_2*c_6*y_0 ** 5*y_2*yx7)/(y_0 ** 3*(c_6+y_0) ** 4)"
]
])
#here, we set univariate!
closer = LogNormalClosure(max_order, multivariate=False)
answer = closer.close(self.__mfk, central_from_raw_exprs,
self.__n_counter, self.__k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_normal_closer_wrapper(self):
central_from_raw_exprs = to_sympy_matrix([
["x_0_0_2 - y_2**2"],
["x_0_1_1 - y_1*y_2"],
["x_0_2_0 - y_1**2"],
["x_1_0_1 - y_0*y_2"],
["x_1_1_0 - y_0*y_1"],
["x_2_0_0 - y_0**2"],
["-3*x_0_0_2*y_2 + x_0_0_3 + 2*y_2**3"],
["-x_0_0_2*y_1 - 2*x_0_1_1*y_2 + x_0_1_2 + 2*y_1*y_2**2"],
["-2*x_0_1_1*y_1 - x_0_2_0*y_2 + x_0_2_1 + 2*y_1**2*y_2"],
["-3*x_0_2_0*y_1 + x_0_3_0 + 2*y_1**3"],
["-x_0_0_2*y_0 - 2*x_1_0_1*y_2 + x_1_0_2 + 2*y_0*y_2**2"],
["-x_0_1_1*y_0 - x_1_0_1*y_1 - x_1_1_0*y_2 + x_1_1_1 + 2*y_0*y_1*y_2"],
["-x_0_2_0*y_0 - 2*x_1_1_0*y_1 + x_1_2_0 + 2*y_0*y_1**2"],
["-2*x_1_0_1*y_0 - x_2_0_0*y_2 + x_2_0_1 + 2*y_0**2*y_2"],
["-2*x_1_1_0*y_0 - x_2_0_0*y_1 + x_2_1_0 + 2*y_0**2*y_1"],
["-3*x_2_0_0*y_0 + x_3_0_0 + 2*y_0**3"],
["6*x_0_0_2*y_2**2 - 4*x_0_0_3*y_2 + x_0_0_4 - 3*y_2**4"],
["3*x_0_0_2*y_1*y_2 - x_0_0_3*y_1 + 3*x_0_1_1*y_2**2 - 3*x_0_1_2*y_2 + x_0_1_3 - 3*y_1*y_2**3"],
["x_0_0_2*y_1**2 + 4*x_0_1_1*y_1*y_2 - 2*x_0_1_2*y_1 + x_0_2_0*y_2**2 - 2*x_0_2_1*y_2 + x_0_2_2 - 3*y_1**2*y_2**2"],
["3*x_0_1_1*y_1**2 + 3*x_0_2_0*y_1*y_2 - 3*x_0_2_1*y_1 - x_0_3_0*y_2 + x_0_3_1 - 3*y_1**3*y_2"],
["6*x_0_2_0*y_1**2 - 4*x_0_3_0*y_1 + x_0_4_0 - 3*y_1**4"],
["3*x_0_0_2*y_0*y_2 - x_0_0_3*y_0 + 3*x_1_0_1*y_2**2 - 3*x_1_0_2*y_2 + x_1_0_3 - 3*y_0*y_2**3"],
["x_0_0_2*y_0*y_1 + 2*x_0_1_1*y_0*y_2 - x_0_1_2*y_0 + 2*x_1_0_1*y_1*y_2 - x_1_0_2*y_1 + x_1_1_0*y_2**2 - 2*x_1_1_1*y_2 + x_1_1_2 - 3*y_0*y_1*y_2**2"],
["2*x_0_1_1*y_0*y_1 + x_0_2_0*y_0*y_2 - x_0_2_1*y_0 + x_1_0_1*y_1**2 + 2*x_1_1_0*y_1*y_2 - 2*x_1_1_1*y_1 - x_1_2_0*y_2 + x_1_2_1 - 3*y_0*y_1**2*y_2"],
["3*x_0_2_0*y_0*y_1 - x_0_3_0*y_0 + 3*x_1_1_0*y_1**2 - 3*x_1_2_0*y_1 + x_1_3_0 - 3*y_0*y_1**3"],
["x_0_0_2*y_0**2 + 4*x_1_0_1*y_0*y_2 - 2*x_1_0_2*y_0 + x_2_0_0*y_2**2 - 2*x_2_0_1*y_2 + x_2_0_2 - 3*y_0**2*y_2**2"],
["x_0_1_1*y_0**2 + 2*x_1_0_1*y_0*y_1 + 2*x_1_1_0*y_0*y_2 - 2*x_1_1_1*y_0 + x_2_0_0*y_1*y_2 - x_2_0_1*y_1 - x_2_1_0*y_2 + x_2_1_1 - 3*y_0**2*y_1*y_2"],
["x_0_2_0*y_0**2 + 4*x_1_1_0*y_0*y_1 - 2*x_1_2_0*y_0 + x_2_0_0*y_1**2 - 2*x_2_1_0*y_1 + x_2_2_0 - 3*y_0**2*y_1**2"],
["3*x_1_0_1*y_0**2 + 3*x_2_0_0*y_0*y_2 - 3*x_2_0_1*y_0 - x_3_0_0*y_2 + x_3_0_1 - 3*y_0**3*y_2"],
["3*x_1_1_0*y_0**2 + 3*x_2_0_0*y_0*y_1 - 3*x_2_1_0*y_0 - x_3_0_0*y_1 + x_3_1_0 - 3*y_0**3*y_1"],
["6*x_2_0_0*y_0**2 - 4*x_3_0_0*y_0 + x_4_0_0 - 3*y_0**4"]
])
k_counter = [
Moment([0, 0, 0], symbol=sympy.Symbol("1")),
Moment([1, 0, 0], symbol=sympy.Symbol("y_0")),
Moment([0, 1, 0], symbol=sympy.Symbol("y_1")),
Moment([0, 0, 1], symbol=sympy.Symbol("y_2")),
Moment([0, 0, 2], symbol=sympy.Symbol("x_0_0_2")),
Moment([0, 1, 1], symbol=sympy.Symbol("x_0_1_1")),
Moment([0, 2, 0], symbol=sympy.Symbol("x_0_2_0")),
Moment([1, 0, 1], symbol=sympy.Symbol("x_1_0_1")),
Moment([1, 1, 0], symbol=sympy.Symbol("x_1_1_0")),
Moment([2, 0, 0], symbol=sympy.Symbol("x_2_0_0")),
Moment([0, 0, 3], symbol=sympy.Symbol("x_0_0_3")),
Moment([0, 1, 2], symbol=sympy.Symbol("x_0_1_2")),
Moment([0, 2, 1], symbol=sympy.Symbol("x_0_2_1")),
Moment([0, 3, 0], symbol=sympy.Symbol("x_0_3_0")),
Moment([1, 0, 2], symbol=sympy.Symbol("x_1_0_2")),
Moment([1, 1, 1], symbol=sympy.Symbol("x_1_1_1")),
Moment([1, 2, 0], symbol=sympy.Symbol("x_1_2_0")),
Moment([2, 0, 1], symbol=sympy.Symbol("x_2_0_1")),
Moment([2, 1, 0], symbol=sympy.Symbol("x_2_1_0")),
Moment([3, 0, 0], symbol=sympy.Symbol("x_3_0_0")),
Moment([0, 0, 4], symbol=sympy.Symbol("x_0_0_4")),
Moment([0, 1, 3], symbol=sympy.Symbol("x_0_1_3")),
Moment([0, 2, 2], symbol=sympy.Symbol("x_0_2_2")),
Moment([0, 3, 1], symbol=sympy.Symbol("x_0_3_1")),
Moment([0, 4, 0], symbol=sympy.Symbol("x_0_4_0")),
Moment([1, 0, 3], symbol=sympy.Symbol("x_1_0_3")),
Moment([1, 1, 2], symbol=sympy.Symbol("x_1_1_2")),
Moment([1, 2, 1], symbol=sympy.Symbol("x_1_2_1")),
Moment([1, 3, 0], symbol=sympy.Symbol("x_1_3_0")),
Moment([2, 0, 2], symbol=sympy.Symbol("x_2_0_2")),
Moment([2, 1, 1], symbol=sympy.Symbol("x_2_1_1")),
Moment([2, 2, 0], symbol=sympy.Symbol("x_2_2_0")),
Moment([3, 0, 1], symbol=sympy.Symbol("x_3_0_1")),
Moment([3, 1, 0], symbol=sympy.Symbol("x_3_1_0")),
Moment([4, 0, 0], symbol=sympy.Symbol("x_4_0_0"))
]
max_order = 3
expected = to_sympy_matrix([
["c_0-c_1*y_0-(c_2*c_6*yx5)/(c_6+y_0) ** 2+(c_2*c_6*yx15)/(c_6+y_0) ** 3-(c_2*y_0*y_2)/(c_6+y_0)+(3*c_2*c_6*y_2*yx7 ** 2)/(c_6+y_0) ** 5+(c_2*c_6*y_2*yx7)/(c_6+y_0) ** 3-(c_2*c_6*y_2*yx17)/(c_6+y_0) ** 4-(3*c_2*c_6*yx5*yx7)/(c_6+y_0) ** 4"],
["c_3*y_0-c_4*y_1"],
["c_4*y_1-c_5*y_2"],
["c_4*y_1+c_5*y_2+2*c_4*yx3-2*c_5*yx2"],
["c_3*yx5-c_4*yx3-c_4*y_1+c_4*yx4-c_5*yx3"],
["c_3*y_0+c_4*y_1-2*c_4*yx4+2*c_3*yx6"],
["-(c_2*y_0 ** 4*yx2+c_1*y_0 ** 4*yx5-c_4*y_0 ** 4*yx6+c_5*y_0 ** 4*yx5-2*c_2*c_6 ** 2*yx5 ** 2+c_1*c_6 ** 4*yx5-c_4*c_6 ** 4*yx6+c_5*c_6 ** 4*yx5+c_2*c_6 ** 3*yx12+3*c_2*c_6*y_0 ** 3*yx2+c_2*c_6 ** 3*y_0*yx2+4*c_1*c_6*y_0 ** 3*yx5+4*c_1*c_6 ** 3*y_0*yx5-2*c_2*c_6*y_0*yx5 ** 2+c_2*c_6 ** 3*y_2*yx5-4*c_4*c_6*y_0 ** 3*yx6-4*c_4*c_6 ** 3*y_0*yx6+4*c_5*c_6*y_0 ** 3*yx5+4*c_5*c_6 ** 3*y_0*yx5+c_2*c_6*y_0 ** 2*yx12+2*c_2*c_6 ** 2*y_0*yx12-c_2*c_6 ** 2*y_2*yx15-c_2*c_6 ** 2*yx2*yx7+3*c_2*c_6 ** 2*y_0 ** 2*yx2+6*c_1*c_6 ** 2*y_0 ** 2*yx5-6*c_4*c_6 ** 2*y_0 ** 2*yx6+6*c_5*c_6 ** 2*y_0 ** 2*yx5-c_2*c_6*y_0*y_2*yx15-c_2*c_6*y_0*yx2*yx7+3*c_2*c_6*y_2*yx5*yx7+c_2*c_6*y_0 ** 2*y_2*yx5+2*c_2*c_6 ** 2*y_0*y_2*yx5)/(c_6+y_0) ** 4"],
["-(c_2*y_0 ** 4*yx3+c_1*y_0 ** 4*yx6-c_3*y_0 ** 4*yx7+c_4*y_0 ** 4*yx6+c_1*c_6 ** 4*yx6-c_3*c_6 ** 4*yx7+c_4*c_6 ** 4*yx6+c_2*c_6 ** 3*yx13+3*c_2*c_6*y_0 ** 3*yx3+c_2*c_6 ** 3*y_0*yx3+4*c_1*c_6*y_0 ** 3*yx6+4*c_1*c_6 ** 3*y_0*yx6+c_2*c_6 ** 3*y_2*yx6-4*c_3*c_6*y_0 ** 3*yx7-4*c_3*c_6 ** 3*y_0*yx7+4*c_4*c_6*y_0 ** 3*yx6+4*c_4*c_6 ** 3*y_0*yx6+c_2*c_6*y_0 ** 2*yx13+2*c_2*c_6 ** 2*y_0*yx13-c_2*c_6 ** 2*y_2*yx16-c_2*c_6 ** 2*yx3*yx7-2*c_2*c_6 ** 2*yx5*yx6+3*c_2*c_6 ** 2*y_0 ** 2*yx3+6*c_1*c_6 ** 2*y_0 ** 2*yx6-6*c_3*c_6 ** 2*y_0 ** 2*yx7+6*c_4*c_6 ** 2*y_0 ** 2*yx6-c_2*c_6*y_0*y_2*yx16-c_2*c_6*y_0*yx3*yx7-2*c_2*c_6*y_0*yx5*yx6+3*c_2*c_6*y_2*yx6*yx7+c_2*c_6*y_0 ** 2*y_2*yx6+2*c_2*c_6 ** 2*y_0*y_2*yx6)/(c_6+y_0) ** 4"],
["(c_0*c_6 ** 5+c_0*y_0 ** 5+c_1*y_0 ** 6+c_2*y_0 ** 5*y_2-2*c_2*y_0 ** 5*yx5-2*c_1*y_0 ** 5*yx7+10*c_0*c_6 ** 2*y_0 ** 3+10*c_0*c_6 ** 3*y_0 ** 2+10*c_1*c_6 ** 2*y_0 ** 4+10*c_1*c_6 ** 3*y_0 ** 3+5*c_1*c_6 ** 4*y_0 ** 2+5*c_0*c_6*y_0 ** 4+5*c_0*c_6 ** 4*y_0+5*c_1*c_6*y_0 ** 5+c_1*c_6 ** 5*y_0+c_2*c_6 ** 4*yx5-2*c_1*c_6 ** 5*yx7-c_2*c_6 ** 3*yx15-2*c_2*c_6 ** 4*yx15+4*c_2*c_6*y_0 ** 4*y_2+c_2*c_6 ** 4*y_0*y_2+c_2*c_6*y_0 ** 3*yx5+3*c_2*c_6 ** 3*y_0*yx5-8*c_2*c_6*y_0 ** 4*yx5-2*c_2*c_6 ** 4*y_0*yx5-10*c_1*c_6*y_0 ** 4*yx7-10*c_1*c_6 ** 4*y_0*yx7-3*c_2*c_6*y_2*yx7 ** 2-c_2*c_6 ** 3*y_2*yx7-2*c_2*c_6 ** 4*y_2*yx7-c_2*c_6*y_0 ** 2*yx15-2*c_2*c_6 ** 2*y_0*yx15-2*c_2*c_6*y_0 ** 3*yx15-6*c_2*c_6 ** 3*y_0*yx15+c_2*c_6 ** 2*y_2*yx17+2*c_2*c_6 ** 3*y_2*yx17+3*c_2*c_6 ** 2*yx5*yx7+6*c_2*c_6 ** 3*yx5*yx7+6*c_2*c_6 ** 2*y_0 ** 3*y_2+4*c_2*c_6 ** 3*y_0 ** 2*y_2+3*c_2*c_6 ** 2*y_0 ** 2*yx5-12*c_2*c_6 ** 2*y_0 ** 3*yx5-8*c_2*c_6 ** 3*y_0 ** 2*yx5-20*c_1*c_6 ** 2*y_0 ** 3*yx7-20*c_1*c_6 ** 3*y_0 ** 2*yx7-6*c_2*c_6 ** 2*y_2*yx7 ** 2-6*c_2*c_6 ** 2*y_0 ** 2*yx15-6*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7+c_2*c_6*y_0*y_2*yx17+3*c_2*c_6*y_0*yx5*yx7-6*c_2*c_6*y_0*y_2*yx7 ** 2-c_2*c_6*y_0 ** 2*y_2*yx7-2*c_2*c_6 ** 2*y_0*y_2*yx7-2*c_2*c_6*y_0 ** 3*y_2*yx7-6*c_2*c_6 ** 3*y_0*y_2*yx7+2*c_2*c_6*y_0 ** 2*y_2*yx17+4*c_2*c_6 ** 2*y_0*y_2*yx17+6*c_2*c_6*y_0 ** 2*yx5*yx7+12*c_2*c_6 ** 2*y_0*yx5*yx7)/(c_6+y_0) ** 5"],
["c_4*y_1-c_5*y_2+3*c_4*yx3+3*c_5*yx2+3*c_4*yx9-3*c_5*yx8"],
["c_4*yx4-2*c_4*yx3-c_4*y_1+c_5*yx3-c_4*yx9+2*c_4*yx10-2*c_5*yx9+c_3*yx12"],
["c_4*y_1+c_4*yx3+c_3*yx5-2*c_4*yx4-2*c_4*yx10+c_4*yx11-c_5*yx10+2*c_3*yx13"],
["c_3*y_0-c_4*y_1+3*c_4*yx4+3*c_3*yx6-3*c_4*yx11+3*c_3*yx14"],
["-(c_2*y_0 ** 5*yx8-c_4*y_0 ** 5*yx6-c_5*y_0 ** 5*yx5+c_1*y_0 ** 5*yx12-2*c_4*y_0 ** 5*yx13+2*c_5*y_0 ** 5*yx12-c_4*c_6 ** 5*yx6-c_5*c_6 ** 5*yx5+c_1*c_6 ** 5*yx12-2*c_4*c_6 ** 5*yx13+2*c_5*c_6 ** 5*yx12+4*c_2*c_6*y_0 ** 4*yx8+c_2*c_6 ** 4*y_0*yx8-5*c_4*c_6*y_0 ** 4*yx6-5*c_4*c_6 ** 4*y_0*yx6-5*c_5*c_6*y_0 ** 4*yx5-5*c_5*c_6 ** 4*y_0*yx5+5*c_1*c_6*y_0 ** 4*yx12+5*c_1*c_6 ** 4*y_0*yx12+c_2*c_6 ** 4*y_2*yx12-10*c_4*c_6*y_0 ** 4*yx13-10*c_4*c_6 ** 4*y_0*yx13+10*c_5*c_6*y_0 ** 4*yx12+10*c_5*c_6 ** 4*y_0*yx12+2*c_2*c_6 ** 4*yx2*yx5+c_2*c_6 ** 3*yx2*yx15-2*c_2*c_6 ** 3*y_2*yx5 ** 2+6*c_2*c_6 ** 2*y_0 ** 3*yx8+4*c_2*c_6 ** 3*y_0 ** 2*yx8-10*c_4*c_6 ** 2*y_0 ** 3*yx6-10*c_4*c_6 ** 3*y_0 ** 2*yx6-10*c_5*c_6 ** 2*y_0 ** 3*yx5-10*c_5*c_6 ** 3*y_0 ** 2*yx5+10*c_1*c_6 ** 2*y_0 ** 3*yx12+10*c_1*c_6 ** 3*y_0 ** 2*yx12-20*c_4*c_6 ** 2*y_0 ** 3*yx13-20*c_4*c_6 ** 3*y_0 ** 2*yx13+20*c_5*c_6 ** 2*y_0 ** 3*yx12+20*c_5*c_6 ** 3*y_0 ** 2*yx12-2*c_2*c_6*y_0 ** 2*y_2*yx5 ** 2-4*c_2*c_6 ** 2*y_0*y_2*yx5 ** 2+3*c_2*c_6 ** 2*y_0 ** 2*y_2*yx12+6*c_2*c_6 ** 2*y_0 ** 2*yx2*yx5+c_2*c_6*y_0 ** 3*y_2*yx12+3*c_2*c_6 ** 3*y_0*y_2*yx12+2*c_2*c_6*y_0 ** 3*yx2*yx5+6*c_2*c_6 ** 3*y_0*yx2*yx5+3*c_2*c_6*y_2*yx2*yx7 ** 2+c_2*c_6*y_0 ** 2*yx2*yx15+2*c_2*c_6 ** 2*y_0*yx2*yx15-c_2*c_6 ** 2*y_2*yx2*yx17-3*c_2*c_6 ** 2*yx2*yx5*yx7-c_2*c_6*y_0*y_2*yx2*yx17-3*c_2*c_6*y_0*yx2*yx5*yx7)/(c_6+y_0) ** 5"],
["-(c_4*y_0 ** 5*yx6+c_2*y_0 ** 5*yx9+c_1*y_0 ** 5*yx13+c_4*y_0 ** 5*yx13-c_3*y_0 ** 5*yx15-c_4*y_0 ** 5*yx14+c_5*y_0 ** 5*yx13+c_4*c_6 ** 5*yx6+c_1*c_6 ** 5*yx13+c_4*c_6 ** 5*yx13-c_3*c_6 ** 5*yx15-c_4*c_6 ** 5*yx14+c_5*c_6 ** 5*yx13+5*c_4*c_6*y_0 ** 4*yx6+5*c_4*c_6 ** 4*y_0*yx6+4*c_2*c_6*y_0 ** 4*yx9+c_2*c_6 ** 4*y_0*yx9+5*c_1*c_6*y_0 ** 4*yx13+5*c_1*c_6 ** 4*y_0*yx13+c_2*c_6 ** 4*y_2*yx13+5*c_4*c_6*y_0 ** 4*yx13+5*c_4*c_6 ** 4*y_0*yx13-5*c_3*c_6*y_0 ** 4*yx15-5*c_3*c_6 ** 4*y_0*yx15-5*c_4*c_6*y_0 ** 4*yx14-5*c_4*c_6 ** 4*y_0*yx14+5*c_5*c_6*y_0 ** 4*yx13+5*c_5*c_6 ** 4*y_0*yx13+c_2*c_6 ** 4*yx2*yx6+c_2*c_6 ** 4*yx3*yx5+c_2*c_6 ** 3*yx3*yx15+10*c_4*c_6 ** 2*y_0 ** 3*yx6+10*c_4*c_6 ** 3*y_0 ** 2*yx6+6*c_2*c_6 ** 2*y_0 ** 3*yx9+4*c_2*c_6 ** 3*y_0 ** 2*yx9+10*c_1*c_6 ** 2*y_0 ** 3*yx13+10*c_1*c_6 ** 3*y_0 ** 2*yx13+10*c_4*c_6 ** 2*y_0 ** 3*yx13+10*c_4*c_6 ** 3*y_0 ** 2*yx13-10*c_3*c_6 ** 2*y_0 ** 3*yx15-10*c_3*c_6 ** 3*y_0 ** 2*yx15-10*c_4*c_6 ** 2*y_0 ** 3*yx14-10*c_4*c_6 ** 3*y_0 ** 2*yx14+10*c_5*c_6 ** 2*y_0 ** 3*yx13+10*c_5*c_6 ** 3*y_0 ** 2*yx13+3*c_2*c_6 ** 2*y_0 ** 2*y_2*yx13+3*c_2*c_6 ** 2*y_0 ** 2*yx2*yx6+3*c_2*c_6 ** 2*y_0 ** 2*yx3*yx5+c_2*c_6*y_0 ** 3*y_2*yx13+3*c_2*c_6 ** 3*y_0*y_2*yx13+c_2*c_6*y_0 ** 3*yx2*yx6+c_2*c_6*y_0 ** 3*yx3*yx5+3*c_2*c_6 ** 3*y_0*yx2*yx6+3*c_2*c_6 ** 3*y_0*yx3*yx5+3*c_2*c_6*y_2*yx3*yx7 ** 2-2*c_2*c_6 ** 3*y_2*yx5*yx6+c_2*c_6*y_0 ** 2*yx3*yx15+2*c_2*c_6 ** 2*y_0*yx3*yx15-c_2*c_6 ** 2*y_2*yx3*yx17-3*c_2*c_6 ** 2*yx3*yx5*yx7-c_2*c_6*y_0*y_2*yx3*yx17-3*c_2*c_6*y_0*yx3*yx5*yx7-2*c_2*c_6*y_0 ** 2*y_2*yx5*yx6-4*c_2*c_6 ** 2*y_0*y_2*yx5*yx6)/(c_6+y_0) ** 5"],
["-(c_2*y_0 ** 5*yx10-c_4*y_0 ** 5*yx6-c_3*y_0 ** 5*yx7+c_1*y_0 ** 5*yx14+2*c_4*y_0 ** 5*yx14-2*c_3*y_0 ** 5*yx16-c_3*c_6 ** 5*yx7-c_4*c_6 ** 5*yx6+c_1*c_6 ** 5*yx14+2*c_4*c_6 ** 5*yx14-2*c_3*c_6 ** 5*yx16-5*c_3*c_6*y_0 ** 4*yx7-5*c_3*c_6 ** 4*y_0*yx7-5*c_4*c_6*y_0 ** 4*yx6-5*c_4*c_6 ** 4*y_0*yx6+4*c_2*c_6*y_0 ** 4*yx10+c_2*c_6 ** 4*y_0*yx10+5*c_1*c_6*y_0 ** 4*yx14+5*c_1*c_6 ** 4*y_0*yx14+c_2*c_6 ** 4*y_2*yx14+10*c_4*c_6*y_0 ** 4*yx14+10*c_4*c_6 ** 4*y_0*yx14-10*c_3*c_6*y_0 ** 4*yx16-10*c_3*c_6 ** 4*y_0*yx16+2*c_2*c_6 ** 4*yx3*yx6+c_2*c_6 ** 3*yx4*yx15-2*c_2*c_6 ** 3*y_2*yx6 ** 2-10*c_3*c_6 ** 2*y_0 ** 3*yx7-10*c_3*c_6 ** 3*y_0 ** 2*yx7-10*c_4*c_6 ** 2*y_0 ** 3*yx6-10*c_4*c_6 ** 3*y_0 ** 2*yx6+6*c_2*c_6 ** 2*y_0 ** 3*yx10+4*c_2*c_6 ** 3*y_0 ** 2*yx10+10*c_1*c_6 ** 2*y_0 ** 3*yx14+10*c_1*c_6 ** 3*y_0 ** 2*yx14+20*c_4*c_6 ** 2*y_0 ** 3*yx14+20*c_4*c_6 ** 3*y_0 ** 2*yx14-20*c_3*c_6 ** 2*y_0 ** 3*yx16-20*c_3*c_6 ** 3*y_0 ** 2*yx16-2*c_2*c_6*y_0 ** 2*y_2*yx6 ** 2-4*c_2*c_6 ** 2*y_0*y_2*yx6 ** 2+3*c_2*c_6 ** 2*y_0 ** 2*y_2*yx14+6*c_2*c_6 ** 2*y_0 ** 2*yx3*yx6+c_2*c_6*y_0 ** 3*y_2*yx14+3*c_2*c_6 ** 3*y_0*y_2*yx14+2*c_2*c_6*y_0 ** 3*yx3*yx6+6*c_2*c_6 ** 3*y_0*yx3*yx6+3*c_2*c_6*y_2*yx4*yx7 ** 2+c_2*c_6*y_0 ** 2*yx4*yx15+2*c_2*c_6 ** 2*y_0*yx4*yx15-c_2*c_6 ** 2*y_2*yx4*yx17-3*c_2*c_6 ** 2*yx4*yx5*yx7-c_2*c_6*y_0*y_2*yx4*yx17-3*c_2*c_6*y_0*yx4*yx5*yx7)/(c_6+y_0) ** 5"],
["-(2*c_2*y_0 ** 5*yx12-c_1*y_0 ** 5*yx5-c_2*y_0 ** 5*yx2+2*c_1*y_0 ** 5*yx15-c_4*y_0 ** 5*yx16+c_5*y_0 ** 5*yx15+2*c_2*c_6 ** 3*yx5 ** 2+2*c_2*c_6 ** 4*yx5 ** 2-c_1*c_6 ** 5*yx5-c_2*c_6 ** 4*yx12+2*c_1*c_6 ** 5*yx15-c_4*c_6 ** 5*yx16+c_5*c_6 ** 5*yx15+6*c_2*c_6 ** 2*y_0 ** 2*yx5 ** 2-4*c_2*c_6*y_0 ** 4*yx2-c_2*c_6 ** 4*y_0*yx2-5*c_1*c_6*y_0 ** 4*yx5-5*c_1*c_6 ** 4*y_0*yx5-c_2*c_6 ** 4*y_2*yx5-c_2*c_6*y_0 ** 3*yx12-3*c_2*c_6 ** 3*y_0*yx12+8*c_2*c_6*y_0 ** 4*yx12+2*c_2*c_6 ** 4*y_0*yx12+10*c_1*c_6*y_0 ** 4*yx15+10*c_1*c_6 ** 4*y_0*yx15+c_2*c_6 ** 3*y_2*yx15+2*c_2*c_6 ** 4*y_2*yx15-5*c_4*c_6*y_0 ** 4*yx16-5*c_4*c_6 ** 4*y_0*yx16+5*c_5*c_6*y_0 ** 4*yx15+5*c_5*c_6 ** 4*y_0*yx15+c_2*c_6 ** 3*yx2*yx7+2*c_2*c_6 ** 4*yx2*yx7+2*c_2*c_6 ** 3*yx5*yx15-6*c_2*c_6 ** 2*y_0 ** 3*yx2-4*c_2*c_6 ** 3*y_0 ** 2*yx2-10*c_1*c_6 ** 2*y_0 ** 3*yx5-10*c_1*c_6 ** 3*y_0 ** 2*yx5+2*c_2*c_6*y_0 ** 2*yx5 ** 2+4*c_2*c_6 ** 2*y_0*yx5 ** 2+2*c_2*c_6*y_0 ** 3*yx5 ** 2+6*c_2*c_6 ** 3*y_0*yx5 ** 2-3*c_2*c_6 ** 2*y_0 ** 2*yx12+12*c_2*c_6 ** 2*y_0 ** 3*yx12+8*c_2*c_6 ** 3*y_0 ** 2*yx12+20*c_1*c_6 ** 2*y_0 ** 3*yx15+20*c_1*c_6 ** 3*y_0 ** 2*yx15-10*c_4*c_6 ** 2*y_0 ** 3*yx16-10*c_4*c_6 ** 3*y_0 ** 2*yx16+10*c_5*c_6 ** 2*y_0 ** 3*yx15+10*c_5*c_6 ** 3*y_0 ** 2*yx15-6*c_2*c_6 ** 2*yx5 ** 2*yx7-3*c_2*c_6 ** 2*y_0 ** 2*y_2*yx5+6*c_2*c_6 ** 2*y_0 ** 2*y_2*yx15+6*c_2*c_6 ** 2*y_0 ** 2*yx2*yx7-c_2*c_6*y_0 ** 3*y_2*yx5-3*c_2*c_6 ** 3*y_0*y_2*yx5+c_2*c_6*y_0 ** 2*y_2*yx15+2*c_2*c_6 ** 2*y_0*y_2*yx15+2*c_2*c_6*y_0 ** 3*y_2*yx15+6*c_2*c_6 ** 3*y_0*y_2*yx15+c_2*c_6*y_0 ** 2*yx2*yx7+2*c_2*c_6 ** 2*y_0*yx2*yx7+2*c_2*c_6*y_0 ** 3*yx2*yx7+6*c_2*c_6 ** 3*y_0*yx2*yx7-6*c_2*c_6*y_0*yx5 ** 2*yx7+6*c_2*c_6*y_2*yx5*yx7 ** 2-3*c_2*c_6 ** 2*y_2*yx5*yx7-4*c_2*c_6 ** 3*y_2*yx5*yx7+2*c_2*c_6*y_0 ** 2*yx5*yx15+4*c_2*c_6 ** 2*y_0*yx5*yx15-2*c_2*c_6 ** 2*y_2*yx5*yx17-3*c_2*c_6*y_0*y_2*yx5*yx7-2*c_2*c_6*y_0*y_2*yx5*yx17-4*c_2*c_6*y_0 ** 2*y_2*yx5*yx7-8*c_2*c_6 ** 2*y_0*y_2*yx5*yx7)/(c_6+y_0) ** 5"],
["-(2*c_2*y_0 ** 5*yx13-c_1*y_0 ** 5*yx6-c_2*y_0 ** 5*yx3+2*c_1*y_0 ** 5*yx16-c_3*y_0 ** 5*yx17+c_4*y_0 ** 5*yx16-c_1*c_6 ** 5*yx6-c_2*c_6 ** 4*yx13+2*c_1*c_6 ** 5*yx16-c_3*c_6 ** 5*yx17+c_4*c_6 ** 5*yx16-4*c_2*c_6*y_0 ** 4*yx3-c_2*c_6 ** 4*y_0*yx3-5*c_1*c_6*y_0 ** 4*yx6-5*c_1*c_6 ** 4*y_0*yx6-c_2*c_6 ** 4*y_2*yx6-c_2*c_6*y_0 ** 3*yx13-3*c_2*c_6 ** 3*y_0*yx13+8*c_2*c_6*y_0 ** 4*yx13+2*c_2*c_6 ** 4*y_0*yx13+10*c_1*c_6*y_0 ** 4*yx16+10*c_1*c_6 ** 4*y_0*yx16+c_2*c_6 ** 3*y_2*yx16+2*c_2*c_6 ** 4*y_2*yx16-5*c_3*c_6*y_0 ** 4*yx17-5*c_3*c_6 ** 4*y_0*yx17+5*c_4*c_6*y_0 ** 4*yx16+5*c_4*c_6 ** 4*y_0*yx16+c_2*c_6 ** 3*yx3*yx7+2*c_2*c_6 ** 3*yx5*yx6+2*c_2*c_6 ** 4*yx3*yx7+2*c_2*c_6 ** 4*yx5*yx6+2*c_2*c_6 ** 3*yx6*yx15-6*c_2*c_6 ** 2*y_0 ** 3*yx3-4*c_2*c_6 ** 3*y_0 ** 2*yx3-10*c_1*c_6 ** 2*y_0 ** 3*yx6-10*c_1*c_6 ** 3*y_0 ** 2*yx6-3*c_2*c_6 ** 2*y_0 ** 2*yx13+12*c_2*c_6 ** 2*y_0 ** 3*yx13+8*c_2*c_6 ** 3*y_0 ** 2*yx13+20*c_1*c_6 ** 2*y_0 ** 3*yx16+20*c_1*c_6 ** 3*y_0 ** 2*yx16-10*c_3*c_6 ** 2*y_0 ** 3*yx17-10*c_3*c_6 ** 3*y_0 ** 2*yx17+10*c_4*c_6 ** 2*y_0 ** 3*yx16+10*c_4*c_6 ** 3*y_0 ** 2*yx16-3*c_2*c_6 ** 2*y_0 ** 2*y_2*yx6+6*c_2*c_6 ** 2*y_0 ** 2*y_2*yx16+6*c_2*c_6 ** 2*y_0 ** 2*yx3*yx7+6*c_2*c_6 ** 2*y_0 ** 2*yx5*yx6-c_2*c_6*y_0 ** 3*y_2*yx6-3*c_2*c_6 ** 3*y_0*y_2*yx6+c_2*c_6*y_0 ** 2*y_2*yx16+2*c_2*c_6 ** 2*y_0*y_2*yx16+2*c_2*c_6*y_0 ** 3*y_2*yx16+6*c_2*c_6 ** 3*y_0*y_2*yx16+c_2*c_6*y_0 ** 2*yx3*yx7+2*c_2*c_6 ** 2*y_0*yx3*yx7+2*c_2*c_6*y_0 ** 2*yx5*yx6+2*c_2*c_6*y_0 ** 3*yx3*yx7+4*c_2*c_6 ** 2*y_0*yx5*yx6+6*c_2*c_6 ** 3*y_0*yx3*yx7+2*c_2*c_6*y_0 ** 3*yx5*yx6+6*c_2*c_6 ** 3*y_0*yx5*yx6+6*c_2*c_6*y_2*yx6*yx7 ** 2-3*c_2*c_6 ** 2*y_2*yx6*yx7-4*c_2*c_6 ** 3*y_2*yx6*yx7+2*c_2*c_6*y_0 ** 2*yx6*yx15+4*c_2*c_6 ** 2*y_0*yx6*yx15-2*c_2*c_6 ** 2*y_2*yx6*yx17-6*c_2*c_6 ** 2*yx5*yx6*yx7-3*c_2*c_6*y_0*y_2*yx6*yx7-2*c_2*c_6*y_0*y_2*yx6*yx17-6*c_2*c_6*y_0*yx5*yx6*yx7-4*c_2*c_6*y_0 ** 2*y_2*yx6*yx7-8*c_2*c_6 ** 2*y_0*y_2*yx6*yx7)/(c_6+y_0) ** 5"],
["-(c_1*y_0 ** 6-c_0*y_0 ** 5-c_0*c_6 ** 5+c_2*y_0 ** 5*y_2-3*c_2*y_0 ** 5*yx5-3*c_1*y_0 ** 5*yx7+3*c_2*y_0 ** 5*yx15+3*c_1*y_0 ** 5*yx17-10*c_0*c_6 ** 2*y_0 ** 3-10*c_0*c_6 ** 3*y_0 ** 2+10*c_1*c_6 ** 2*y_0 ** 4+10*c_1*c_6 ** 3*y_0 ** 3+5*c_1*c_6 ** 4*y_0 ** 2-5*c_0*c_6*y_0 ** 4-5*c_0*c_6 ** 4*y_0+5*c_1*c_6*y_0 ** 5+c_1*c_6 ** 5*y_0+c_2*c_6 ** 4*yx5-3*c_1*c_6 ** 5*yx7-c_2*c_6 ** 3*yx15-3*c_2*c_6 ** 4*yx15+3*c_1*c_6 ** 5*yx17+4*c_2*c_6*y_0 ** 4*y_2+c_2*c_6 ** 4*y_0*y_2+c_2*c_6*y_0 ** 3*yx5+3*c_2*c_6 ** 3*y_0*yx5-12*c_2*c_6*y_0 ** 4*yx5-3*c_2*c_6 ** 4*y_0*yx5-15*c_1*c_6*y_0 ** 4*yx7-15*c_1*c_6 ** 4*y_0*yx7-3*c_2*c_6*y_2*yx7 ** 2+9*c_2*c_6*y_2*yx7 ** 3-c_2*c_6 ** 3*y_2*yx7-3*c_2*c_6 ** 4*y_2*yx7-c_2*c_6*y_0 ** 2*yx15-2*c_2*c_6 ** 2*y_0*yx15-3*c_2*c_6*y_0 ** 3*yx15-9*c_2*c_6 ** 3*y_0*yx15+12*c_2*c_6*y_0 ** 4*yx15+3*c_2*c_6 ** 4*y_0*yx15+15*c_1*c_6*y_0 ** 4*yx17+15*c_1*c_6 ** 4*y_0*yx17+c_2*c_6 ** 2*y_2*yx17+3*c_2*c_6 ** 3*y_2*yx17+3*c_2*c_6 ** 4*y_2*yx17+3*c_2*c_6 ** 2*yx5*yx7+9*c_2*c_6 ** 3*yx5*yx7+6*c_2*c_6 ** 4*yx5*yx7+3*c_2*c_6 ** 3*yx7*yx15+6*c_2*c_6 ** 2*y_0 ** 3*y_2+4*c_2*c_6 ** 3*y_0 ** 2*y_2+3*c_2*c_6 ** 2*y_0 ** 2*yx5-18*c_2*c_6 ** 2*y_0 ** 3*yx5-12*c_2*c_6 ** 3*y_0 ** 2*yx5-30*c_1*c_6 ** 2*y_0 ** 3*yx7-30*c_1*c_6 ** 3*y_0 ** 2*yx7-9*c_2*c_6 ** 2*y_2*yx7 ** 2-6*c_2*c_6 ** 3*y_2*yx7 ** 2-9*c_2*c_6 ** 2*y_0 ** 2*yx15+18*c_2*c_6 ** 2*y_0 ** 3*yx15+12*c_2*c_6 ** 3*y_0 ** 2*yx15+30*c_1*c_6 ** 2*y_0 ** 3*yx17+30*c_1*c_6 ** 3*y_0 ** 2*yx17-9*c_2*c_6 ** 2*yx5*yx7 ** 2-6*c_2*c_6*y_0 ** 2*y_2*yx7 ** 2-12*c_2*c_6 ** 2*y_0*y_2*yx7 ** 2-9*c_2*c_6 ** 2*y_0 ** 2*y_2*yx7+9*c_2*c_6 ** 2*y_0 ** 2*y_2*yx17+18*c_2*c_6 ** 2*y_0 ** 2*yx5*yx7+c_2*c_6*y_0*y_2*yx17+3*c_2*c_6*y_0*yx5*yx7-9*c_2*c_6*y_0*y_2*yx7 ** 2-c_2*c_6*y_0 ** 2*y_2*yx7-2*c_2*c_6 ** 2*y_0*y_2*yx7-3*c_2*c_6*y_0 ** 3*y_2*yx7-9*c_2*c_6 ** 3*y_0*y_2*yx7+3*c_2*c_6*y_0 ** 2*y_2*yx17+6*c_2*c_6 ** 2*y_0*y_2*yx17+3*c_2*c_6*y_0 ** 3*y_2*yx17+9*c_2*c_6 ** 3*y_0*y_2*yx17-9*c_2*c_6*y_0*yx5*yx7 ** 2+9*c_2*c_6*y_0 ** 2*yx5*yx7+18*c_2*c_6 ** 2*y_0*yx5*yx7+6*c_2*c_6*y_0 ** 3*yx5*yx7+18*c_2*c_6 ** 3*y_0*yx5*yx7+3*c_2*c_6*y_0 ** 2*yx7*yx15+6*c_2*c_6 ** 2*y_0*yx7*yx15-3*c_2*c_6 ** 2*y_2*yx7*yx17-3*c_2*c_6*y_0*y_2*yx7*yx17)/(c_6+y_0) ** 5"]
])
closer = NormalClosure(max_order, multivariate=True)
answer = closer.close(self.__mfk, central_from_raw_exprs,self.__n_counter, k_counter)
self.assertTrue(sympy_expressions_equal(answer, expected))
def test_centralmoments_using_p53model(self):
"""
Given the p53 model hard codded bellow,the result of central moment should match exactly the expected one
:return:
"""
counter_nvecs = [[0, 0, 0], [0, 0, 2], [0, 1, 1], [0, 2, 0], [1, 0, 1], [1, 1, 0], [2, 0, 0]]
mcounter_nvecs = [[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 2], [0, 1, 1], [0, 2, 0],
[1, 0, 1], [1, 1, 0], [2, 0, 0]]
counter = [Moment(c,sympy.Symbol("YU{0}".format(i))) for i,c in enumerate(counter_nvecs)]
mcounter = [Moment(c,sympy.Symbol("y_{0}".format(i))) for i,c in enumerate(mcounter_nvecs)]
m = to_sympy_matrix([
['c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)',
0,
0,
0,
'c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0)',
0,
'-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2'],
[
'c_3*y_0 - c_4*y_1',
0,
0,
0,
0,
0,
0],
[
'c_4*y_1 - c_5*y_2',
0,
0,
0,
0,
0,
0
]])
species = to_sympy_matrix(['y_0', 'y_1', 'y_2'])
propensities = to_sympy_matrix(['c_0',
'c_1 * y_0',
'c_2*y_0*y_2/(c_6 + y_0)',
'c_3*y_0',
'c_4*y_1',
'c_5*y_2'])
stoichiometry_matrix = to_sympy_matrix([[1, -1, -1, 0, 0, 0],
[0, 0, 0, 1, -1, 0],
[0, 0, 0, 0, 1, -1]])
answer = eq_central_moments(counter, mcounter, m, species, propensities, stoichiometry_matrix, 2)
expected = to_sympy_matrix([
[" 2*c_4*y_1*y_2 + c_4*y_1 - 2*c_5*y_2**2 + c_5*y_2 - 2*y_1*(c_4*y_1 - c_5*y_2)"," -2*c_5"," 2*c_4"," 0"," 0"," 0"," 0"],
["c_3*y_0*y_2 + c_4*y_1**2 - c_4*y_1*y_2 - c_4*y_1 - c_5*y_1*y_2 - y_1*(c_3*y_0 - c_4*y_1) - y_2*(c_4*y_1 - c_5*y_2)"," 0"," -c_4 - c_5"," c_4"," c_3"," 0"," 0"],
["2*c_3*y_0*y_1 + c_3*y_0 - 2*c_4*y_1**2 + c_4*y_1 - 2*y_2*(c_3*y_0 - c_4*y_1)"," 0"," 0"," -2*c_4"," 0"," 2*c_3","0"],
["c_0*y_2 - c_1*y_0*y_2 - c_2*y_0*y_2**2/(c_6 + y_0) + c_4*y_0*y_1 - c_5*y_0*y_2 - y_1*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) - y_3*(c_4*y_1 - c_5*y_2)"," -c_2*y_0/(c_6 + y_0)"," 0"," 0"," -c_1 + 2*c_2*y_0*y_2/(c_6 + y_0)**2 - 2*c_2*y_2/(c_6 + y_0) - c_5 - y_1*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))","c_4"," -c_2*y_0*y_2**2/(c_6 + y_0)**3 + c_2*y_2**2/(c_6 + y_0)**2 - y_1*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)"],
["c_0*y_1 - c_1*y_0*y_1 - c_2*y_0*y_1*y_2/(c_6 + y_0) + c_3*y_0**2 - c_4*y_0*y_1 - y_2*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) - y_3*(c_3*y_0 - c_4*y_1)"," 0"," -c_2*y_0/(c_6 + y_0)"," 0"," c_2*y_0*y_1/(c_6 + y_0)**2 - c_2*y_1/(c_6 + y_0) - y_2*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))"," -c_1 + c_2*y_0*y_2/(c_6 + y_0)**2 - c_2*y_2/(c_6 + y_0) - c_4"," -c_2*y_0*y_1*y_2/(c_6 + y_0)**3 + c_2*y_1*y_2/(c_6 + y_0)**2 + c_3 - y_2*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)"],
["2*c_0*y_0 + c_0 - 2*c_1*y_0**2 + c_1*y_0 - 2*c_2*y_0**2*y_2/(c_6 + y_0) + c_2*y_0*y_2/(c_6 + y_0) - 2*y_3*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0))"," 0"," 0"," 0"," 2*c_2*y_0**2/(c_6 + y_0)**2 - 4*c_2*y_0/(c_6 + y_0) - c_2*y_0/(c_6 + y_0)**2 + c_2/(c_6 + y_0) - 2*y_3*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))"," 0"," -2*c_1 - 2*c_2*y_0**2*y_2/(c_6 + y_0)**3 + 4*c_2*y_0*y_2/(c_6 + y_0)**2 + c_2*y_0*y_2/(c_6 + y_0)**3 - 2*c_2*y_2/(c_6 + y_0) - c_2*y_2/(c_6 + y_0)**2 - 2*y_3*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)"]
])
assert_sympy_expressions_equal(answer, expected)
