def _generate_observed_trajectories(): timepoints = np.arange(0, 20, 0.5) observed_trajectories = [ Trajectory(timepoints, [ 301., 290.1919552, 280.58701279, 272.03059275, 264.39179184, 257.55906225, 251.43680665, 245.94267027, 241.0053685, 236.56293031, 232.56126687, 228.95299703, 225.69647718, 222.75499485, 220.09609439, 217.69101017, 215.51418738, 213.54287512, 211.75677913, 210.13776407, 208.6695974, 207.33772795, 206.12909392, 205.03195581, 204.03575051, 203.13096347, 202.30901645, 201.5621687, 200.88342959, 200.26648137, 199.70561061, 199.19564728, 198.73191049, 198.3101601, 197.92655342, 197.57760651, 197.26015951, 196.97134545, 196.70856234, 196.46944793 ], Moment([1], symbol='y_0')), Trajectory(timepoints, [ 0., 20.10320788, 35.54689328, 47.51901615, 56.88242563, 64.26983231, 70.14921364, 74.86943532, 78.69244584, 81.81623963, 84.39139622, 86.53309942, 88.32994353, 89.85043353, 91.1478162, 92.26369294, 93.23073689, 94.07474712, 94.81620873, 95.47148295, 96.05371852, 96.57355199, 97.03964777, 97.45911583, 97.83783557, 98.18070779, 98.49185119, 98.77475594, 99.03240415, 99.26736458, 99.48186728, 99.67786273, 99.85706877, 100.02100803, 100.17103799, 100.3083751, 100.43411443, 100.54924568, 100.65466632, 100.75119251 ], Moment([2], symbol='yx1')) ] return observed_trajectories
def test_a_three_species_third_order_problem(self): """ Given two vectors of Moments: counter and mcounter (up to third moment) and Given a vector of three species ymat, Then, the answer should match exactlty the expected result :return: """ counter = [Moment([0, 0, 0] , sympy.Integer(1)), Moment([0, 0, 2] , sympy.Symbol("yx1")), Moment([0, 0, 3] , sympy.Symbol("yx2")), Moment([0, 1, 1] , sympy.Symbol("yx3")), Moment([0, 1, 2] , sympy.Symbol("yx4")), Moment([0, 2, 0] , sympy.Symbol("yx5")), Moment([0, 2, 1] , sympy.Symbol("yx6")), Moment([0, 3, 0] , sympy.Symbol("yx7")), Moment([1, 0, 1] , sympy.Symbol("yx8")), Moment([1, 0, 2] , sympy.Symbol("yx9")), Moment([1, 1, 0] , sympy.Symbol("yx10")), Moment([1, 1, 1] , sympy.Symbol("yx11")), Moment([1, 2, 0] , sympy.Symbol("yx12")), Moment([2, 0, 0] , sympy.Symbol("yx13")), Moment([2, 0, 1] , sympy.Symbol("yx14")), Moment([2, 1, 0] , sympy.Symbol("yx15")), Moment([3, 0, 0] , sympy.Symbol("yx16"))] ymat = sympy.Matrix(["y_0","y_1","y_2"]) mcounter = [Moment([0, 0, 0] , sympy.Integer(1)), Moment([0, 0, 1] , sympy.Symbol("y_2")), Moment([0, 0, 2] , sympy.Symbol("x_0_0_2")), Moment([0, 0, 3] , sympy.Symbol("x_0_0_3")), Moment([0, 1, 0] , sympy.Symbol("y_1")), Moment([0, 1, 1] , sympy.Symbol("x_0_1_1")), Moment([0, 1, 2] , sympy.Symbol("x_0_1_2")), Moment([0, 2, 0] , sympy.Symbol("x_0_2_0")), Moment([0, 2, 1] , sympy.Symbol("x_0_2_1")), Moment([0, 3, 0] , sympy.Symbol("x_0_3_0")), Moment([1, 0, 0] , sympy.Symbol("y_0")), Moment([1, 0, 1] , sympy.Symbol("x_1_0_1")), Moment([1, 0, 2] , sympy.Symbol("x_1_0_2")), Moment([1, 1, 0] , sympy.Symbol("x_1_1_0")), Moment([1, 1, 1] , sympy.Symbol("x_1_1_1")), Moment([1, 2, 0] , sympy.Symbol("x_1_2_0")), Moment([2, 0, 0] , sympy.Symbol("x_2_0_0")), Moment([2, 0, 1] , sympy.Symbol("x_2_0_1")), Moment([2, 1, 0] , sympy.Symbol("x_2_1_0")), Moment([3, 0, 0] , sympy.Symbol("x_3_0_0"))] answer = sympy.Matrix(raw_to_central(counter, ymat, mcounter)) expected = sympy.Matrix( [[" 1*y_2**2 + x_0_0_2 - 2*y_2**2"], [" -1*y_2**3 - 3*x_0_0_2*y_2 + x_0_0_3 + 3*y_2**3"], [" 1*y_1*y_2 + x_0_1_1 - 2*y_1*y_2"], [" -1*y_1*y_2**2 - x_0_0_2*y_1 - 2*x_0_1_1*y_2 + x_0_1_2 + 3*y_1*y_2**2"], [" 1*y_1**2 + x_0_2_0 - 2*y_1**2"], [" -1*y_1**2*y_2 - 2*x_0_1_1*y_1 - x_0_2_0*y_2 + x_0_2_1 + 3*y_1**2*y_2"], [" -1*y_1**3 - 3*x_0_2_0*y_1 + x_0_3_0 + 3*y_1**3"], [" 1*y_0*y_2 + x_1_0_1 - 2*y_0*y_2"], [" -1*y_0*y_2**2 - x_0_0_2*y_0 - 2*x_1_0_1*y_2 + x_1_0_2 + 3*y_0*y_2**2"], [" 1*y_0*y_1 + x_1_1_0 - 2*y_0*y_1"], ["-1*y_0*y_1*y_2 - x_0_1_1*y_0 - x_1_0_1*y_1 - x_1_1_0*y_2 + x_1_1_1 + 3*y_0*y_1*y_2"], [" -1*y_0*y_1**2 - x_0_2_0*y_0 - 2*x_1_1_0*y_1 + x_1_2_0 + 3*y_0*y_1**2"], [" 1*y_0**2 + x_2_0_0 - 2*y_0**2"], [" -1*y_0**2*y_2 - 2*x_1_0_1*y_0 - x_2_0_0*y_2 + x_2_0_1 + 3*y_0**2*y_2"], [" -1*y_0**2*y_1 - 2*x_1_1_0*y_0 - x_2_0_0*y_1 + x_2_1_0 + 3*y_0**2*y_1"], [" -1*y_0**3 - 3*x_2_0_0*y_0 + x_3_0_0 + 3*y_0**3"]]) self.assertEqual(answer, expected)
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 _generate_ode_problem(): # Create an ODEProblem from dimer instance c_0 = Symbol('c_0') c_1 = Symbol('c_1') c_2 = Symbol('c_2') constants = [c_0, c_1, c_2] y_0 = Symbol('y_0') yx1 = Symbol('yx1') right_hand_side = MutableDenseMatrix( [[ -2 * c_0 * y_0 * (y_0 - 1) - 2 * c_0 * yx1 + 2 * c_1 * (Float('0.5', prec=15) * c_2 - Float('0.5', prec=15) * y_0) ], [ Float('4.0', prec=15) * c_0 * y_0**2 - Float('4.0', prec=15) * c_0 * y_0 + Float('2.0', prec=15) * c_1 * c_2 - Float('2.0', prec=15) * c_1 * y_0 - yx1 * (Float('8.0', prec=15) * c_0 * y_0 - Float('8.0', prec=15) * c_0 + Float('2.0', prec=15) * c_1) ]]) ode_lhs_terms = [ Moment(np.array([1]), symbol=y_0), Moment(np.array([2]), symbol=yx1) ] dimer_problem = ODEProblem('MEA', ode_lhs_terms, right_hand_side, constants) return dimer_problem
def test_different_descriptions_make_trajectories_different(self): """ Given two Trajectories that differ only by values, they should be treated as different """ t1 = Trajectory([1, 2, 3], [3, 2, 1], Moment([1], symbol='description')) t2 = Trajectory([1, 2, 3], [3, 2, 1], Moment([1], symbol='description')) self.assertNotEqual(t1, t2)
def test_equality_treats_equal_things_as_equal(self): """ Given two Trajectories that were equal, they should be comparable with ==. """ t1 = Trajectory([1, 2, 3], [3, 2, 1], Moment([1], symbol='description')) t2 = Trajectory([1, 2, 3], [3, 2, 1], Moment([1], symbol='description')) self.assertEqual(t1, t2)
def test_equality_treats_equal_things_as_equal(self): """ Given two Trajectories that were equal, they should be comparable with ==. """ t_sensitivity_1 = Trajectory([1,2,3], [3, 2, 1], Moment([1], symbol='description')) t_sensitivity_2 = Trajectory([1,2, 3], [-5, -9, -1], Moment([1], symbol='description')) t1 = TrajectoryWithSensitivityData([1, 2, 3], [3, 2, 1], Moment([1], symbol='description'), [t_sensitivity_1, t_sensitivity_2]) t2 = TrajectoryWithSensitivityData([1, 2, 3], [3, 2, 1], Moment([1], symbol='description'), [t_sensitivity_1, t_sensitivity_2]) self.assertEqual(t1, t2)
def test_traj_collection_to_file(self): tr2 = Trajectory([1, 2, 3, 4, 5, 6], [3, 2, 1, 5, 2, 4], Moment([1], symbol='y_1')) tr1 = Trajectory([1, 2, 3, 4, 5, 6], [3, 2, 1, 5, 2, 4], Moment([1], symbol='y_2')) tc = TrajectoryCollection([tr1,tr2]) file = tempfile.mktemp(suffix=".csv") try: with open(file,"w") as out: tc.to_csv(out) finally: os.unlink(file)
def test_different_timepoints_make_trajectories_different(self): """ Given two TrajectoriesWithSensitivityData that differ only by sensitivity data they should be reported as different """ t_sensitivity_1 = Trajectory([1,2,3], [3, 2, 1], Moment([1], symbol='sensitivity1')) t_sensitivity_2 = Trajectory([1,2, 3], [-5, -9, -1], Moment([1], symbol='sensitivity2')) t_sensitivity_3 = Trajectory([1,2,3], [-5, -9, -100], Moment([1], symbol='sensitivity2')) t1 = TrajectoryWithSensitivityData([1, 2, 3], [3, 2, 1], Moment([1], symbol='description'), [t_sensitivity_1, t_sensitivity_2]) t2 = TrajectoryWithSensitivityData([1, 2, 3], [3, 2, 1], Moment([1], symbol='description'), [t_sensitivity_1, t_sensitivity_3]) self.assertNotEqual(t1, t2)
def generate_single_simulation(self, x): """ Generate a single SSA simulation :param x: an integer to reset the random seed. If None, the initial random number generator is used :return: a list of :class:`~means.simulation.Trajectory` one per species in the problem :rtype: list[:class:`~means.simulation.Trajectory`] """ #reset random seed if x: self.__rng = np.random.RandomState(x) # perform one stochastic simulation time_points, species_over_time = self._gssa(self.__initial_conditions, self.__t_max) # build descriptors for first order raw moments aka expectations (e.g. [1, 0, 0], [0, 1, 0] and [0, 0, 1]) descriptors = [] for i, s in enumerate(self.__species): row = [0] * len(self.__species) row[i] = 1 descriptors.append(Moment(row, s)) # build trajectories trajectories = [Trajectory(time_points, spot, desc) for spot, desc in zip(species_over_time, descriptors)] return trajectories
def test_trajectory_with_sensitivities_serialisation(self): term = Moment([1, 0, 0], 'x') x = Trajectory([1, 2, 3], [3, 2, 1], SensitivityTerm(term, 'x')) y = Trajectory([1, 2, 3], [7, 8, 9], SensitivityTerm(term, 'y')) t = TrajectoryWithSensitivityData([1, 2, 3], [-1, -2, -3], term, sensitivity_data=[x, y]) self._roundtrip(t)
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_single_traj_to_file(self): trajectory = Trajectory([1, 2, 3, 4, 5, 6], [3, 2, 1,5, 2, 4], Moment([1], symbol='description')) file = tempfile.mktemp(suffix=".csv") try: with open(file,"w") as out: trajectory.to_csv(out) finally: os.unlink(file)
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 _sample_inference(): r = Inference(problem=_sample_problem(), starting_parameters=[1, 2, 3, 4, 5, 6, 7], starting_conditions=[1, 2, 3], variable_parameters=['c_0', 'c_1'], observed_trajectories=[ Trajectory([1, 2], [2, 3], Moment([1, 0, 0], 'x')) ], distance_function_type='gamma', maxh=0.01) # Some simulation kwargs return r
def test_a_two_species_problem(self): """ Given two vectors of Moments: counter and mcounter (up to second moment) and Given a vector of two species ymat, Then, the answer should match exactlty the expected result :return: """ ymat = sympy.Matrix(["y_0","y_1"]) 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)] answer = raw_to_central(counter, ymat, mcounter) expected = sympy.Matrix([ ["y_0*y_1**2 - 2*y_1**2 + y_3"], ["y_0**2*y_1 - y_0*y_1 - y_1*y_2 + y_4"], ["y_0**3 - 2*y_0*y_2 + y_5"]]) self.assertEqual(answer, expected)
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 check_initialisation(variable_parameters, expected_parameters_with_variability, expected_initial_conditions_with_variability, expected_constraints): p = Inference( self.dimer_problem, parameters, initial_conditions, variable_parameters, [Trajectory([1, 2, 3], [1, 2, 3], Moment([1], symbol='x'))]) self.assertEquals(p.starting_parameters_with_variability, expected_parameters_with_variability) self.assertEqual(p.starting_conditions_with_variability, expected_initial_conditions_with_variability) self.assertEqual(p.constraints, expected_constraints)
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_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)
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_trajectory_collection_serialisation(self): t1 = Trajectory([1, 2, 3], [3, 2, 1], Moment([1, 2, 3], 'x')) t2 = Trajectory([1, 2, 3], [3, 2, 1], Moment([1, 0, 0], 'y')) tc = TrajectoryCollection([t1, t2]) self._roundtrip(tc)
def test_trajectory_serialisation(self): t = Trajectory([1, 2, 3], [3, 2, 1], Moment([1, 2, 3], 'x')) self._roundtrip(t)
def test_ode_problem_lna_serialisation_works(self): c_0 = Symbol('c_0') c_1 = Symbol('c_1') y_0 = Symbol('y_0') c_2 = Symbol('c_2') y_2 = Symbol('y_2') c_6 = Symbol('c_6') c_3 = Symbol('c_3') c_4 = Symbol('c_4') y_1 = Symbol('y_1') c_5 = Symbol('c_5') V_00 = Symbol('V_00') V_02 = Symbol('V_02') V_20 = Symbol('V_20') V_01 = Symbol('V_01') V_21 = Symbol('V_21') V_22 = Symbol('V_22') V_10 = Symbol('V_10') V_12 = Symbol('V_12') V_11 = Symbol('V_11') right_hand_side = MutableDenseMatrix( [[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_4 * y_1 - c_5 * y_2], [ 2 * V_00 * (-c_1 + c_2 * y_0 * y_2 / (c_6 + y_0)**2 - c_2 * y_2 / (c_6 + y_0)) - V_02 * c_2 * y_0 / (c_6 + y_0) - V_20 * c_2 * y_0 / (c_6 + y_0) + c_0**Float('1.0', prec=15) + (c_1 * y_0)**Float('1.0', prec=15) + (c_2 * y_0 * y_2 / (c_6 + y_0))**Float('1.0', prec=15) ], [ V_00 * c_3 - V_01 * c_4 + V_01 * (-c_1 + c_2 * y_0 * y_2 / (c_6 + y_0)**2 - c_2 * y_2 / (c_6 + y_0)) - V_21 * c_2 * y_0 / (c_6 + y_0) ], [ V_01 * c_4 - V_02 * c_5 + V_02 * (-c_1 + c_2 * y_0 * y_2 / (c_6 + y_0)**2 - c_2 * y_2 / (c_6 + y_0)) - V_22 * c_2 * y_0 / (c_6 + y_0) ], [ V_00 * c_3 - V_10 * c_4 + V_10 * (-c_1 + c_2 * y_0 * y_2 / (c_6 + y_0)**2 - c_2 * y_2 / (c_6 + y_0)) - V_12 * c_2 * y_0 / (c_6 + y_0) ], [ V_01 * c_3 + V_10 * c_3 - 2 * V_11 * c_4 + (c_3 * y_0)**Float('1.0', prec=15) + (c_4 * y_1)**Float('1.0', prec=15) ], [ V_02 * c_3 + V_11 * c_4 - V_12 * c_4 - V_12 * c_5 - (c_4 * y_1)**Float('1.0', prec=15) ], [ V_10 * c_4 - V_20 * c_5 + V_20 * (-c_1 + c_2 * y_0 * y_2 / (c_6 + y_0)**2 - c_2 * y_2 / (c_6 + y_0)) - V_22 * c_2 * y_0 / (c_6 + y_0) ], [ V_11 * c_4 + V_20 * c_3 - V_21 * c_4 - V_21 * c_5 - (c_4 * y_1)**Float('1.0', prec=15) ], [ V_12 * c_4 + V_21 * c_4 - 2 * V_22 * c_5 + (c_4 * y_1)**Float('1.0', prec=15) + (c_5 * y_2)**Float('1.0', prec=15) ]]) ode_lhs_terms = [ Moment(np.array([1, 0, 0]), symbol=y_0), Moment(np.array([0, 1, 0]), symbol=y_1), Moment(np.array([0, 0, 1]), symbol=y_2), VarianceTerm((0, 0), V_00), VarianceTerm((0, 1), V_01), VarianceTerm((0, 2), V_02), VarianceTerm((1, 0), V_10), VarianceTerm((1, 1), V_11), VarianceTerm((1, 2), V_12), VarianceTerm((2, 0), V_20), VarianceTerm((2, 1), V_21), VarianceTerm((2, 2), V_22) ] constants = ['c_0', 'c_1', 'c_2', 'c_3', 'c_4', 'c_5', 'c_6'] problem = ODEProblem('LNA', ode_lhs_terms, right_hand_side, constants) self._roundtrip(problem) # Now make sure to access problem.right_hand_side_as_function as this sometimes breaks pickle f = problem.right_hand_side_as_function # Do roundtrip again self._roundtrip(problem)
def generate_n_and_k_counters(max_order, species, central_symbols_prefix="M_", raw_symbols_prefix="x_"): r""" Makes a counter for central moments (n_counter) and a counter for raw moment (k_counter). Each is a list of :class:`~means.approximation.ode_problem.Moment`s. Therefore, each :class:`~means.approximation.ode_problem.Moments` is represented by both a vector of integer and a symbol. :param max_order: the maximal order of moment to be computer (will generate a list of moments up to `max_order + 1`) :param species: the name of the species :return: a pair of lists of :class:`~means.core.descriptors.Moment`s corresponding to central, and raw moments, respectively. :rtype: (list[:class:`~mea ns.core.descriptors.Moment`],list[:class:`~mea ns.core.descriptors.Moment`]) """ n_moments = max_order + 1 # first order moments are always 1 k_counter = [Moment([0] * len(species), sp.Integer(1))] n_counter = [Moment([0] * len(species), sp.Integer(1))] # build descriptors for first order raw moments aka expectations (e.g. [1, 0, 0], [0, 1, 0] and [0, 0, 1]) descriptors = [] for i in range(len(species)): row = [0] * len(species) row[i] = 1 descriptors.append(row) # We use species name as symbols for first order raw moment k_counter += [Moment(d, s) for d, s in zip(descriptors, species)] # Higher order raw moment descriptors k_counter_descriptors = [ i for i in itertools.product(range(n_moments + 1), repeat=len(species)) if 1 < sum(i) <= n_moments ] #this mimics the order in the original code k_counter_descriptors = sorted(k_counter_descriptors, lambda x, y: sum(x) - sum(y)) #k_counter_descriptors = [[r for r in reversed(k)] for k in k_counter_descriptors] k_counter_symbols = [ sp.Symbol(raw_symbols_prefix + "_".join([str(s) for s in count])) for count in k_counter_descriptors ] k_counter += [ Moment(d, s) for d, s in zip(k_counter_descriptors, k_counter_symbols) ] # central moments n_counter_descriptors = [m for m in k_counter_descriptors if sum(m) > 1] # arbitrary symbols n_counter_symbols = [ sp.Symbol(central_symbols_prefix + "_".join([str(s) for s in count])) for count in n_counter_descriptors ] n_counter += [ Moment(c, s) for c, s in zip(n_counter_descriptors, n_counter_symbols) ] return n_counter, k_counter
def _sample_problem(): lhs_terms = [ Moment(np.array([1, 0, 0]), symbol='y_0'), Moment(np.array([0, 1, 0]), symbol='y_1'), Moment(np.array([0, 0, 1]), symbol='y_2'), Moment(np.array([0, 0, 2]), symbol='yx1'), Moment(np.array([0, 1, 1]), symbol='yx2'), Moment(np.array([0, 2, 0]), symbol='yx3'), Moment(np.array([1, 0, 1]), symbol='yx4'), Moment(np.array([1, 1, 0]), symbol='yx5'), Moment(np.array([2, 0, 0]), symbol='yx6') ] constants = ['c_0', 'c_1', 'c_2', 'c_3', 'c_4', 'c_5', 'c_6'] c_0 = Symbol('c_0') c_1 = Symbol('c_1') y_0 = Symbol('y_0') c_2 = Symbol('c_2') y_2 = Symbol('y_2') c_6 = Symbol('c_6') yx4 = Symbol('yx4') yx6 = Symbol('yx6') c_3 = Symbol('c_3') c_4 = Symbol('c_4') y_1 = Symbol('y_1') c_5 = Symbol('c_5') yx2 = Symbol('yx2') yx1 = Symbol('yx1') yx3 = Symbol('yx3') yx5 = Symbol('yx5') rhs = MutableDenseMatrix([ [ c_0 - c_1 * y_0 - c_2 * y_0 * y_2 / (c_6 + y_0) + yx4 * (c_2 * y_0 / (c_6 + y_0)**2 - c_2 / (c_6 + y_0)) + yx6 * (-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], [c_4 * y_1 - c_5 * y_2], [ 2 * c_4 * y_1 * y_2 + c_4 * y_1 + 2 * c_4 * yx2 - 2 * c_5 * y_2**2 + c_5 * y_2 - 2 * c_5 * yx1 - 2 * y_2 * (c_4 * y_1 - c_5 * y_2) ], [ c_3 * y_0 * y_2 + c_3 * yx4 + c_4 * y_1**2 - c_4 * y_1 * y_2 - c_4 * y_1 + c_4 * yx3 - 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) + yx2 * (-c_4 - c_5) ], [ 2 * c_3 * y_0 * y_1 + c_3 * y_0 + 2 * c_3 * yx5 - 2 * c_4 * y_1**2 + c_4 * y_1 - 2 * c_4 * yx3 - 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 * yx1 / (c_6 + y_0) + c_4 * y_0 * y_1 + c_4 * yx5 - 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)) + yx4 * (-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_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_1 - c_1 * y_0 * y_1 - c_2 * y_0 * y_1 * y_2 / (c_6 + y_0) - c_2 * y_0 * yx2 / (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)) + yx4 * (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))) + yx5 * (-c_1 + c_2 * y_0 * y_2 / (c_6 + y_0)**2 - c_2 * y_2 / (c_6 + y_0) - c_4) + yx6 * (-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)) ], [ 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)) + yx4 * (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))) + yx6 * (-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)) ] ]) problem = ODEProblem(method='MEA', left_hand_side_descriptors=lhs_terms, right_hand_side=rhs, parameters=constants) return problem
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))
def run(self): """ Overrides the default _run() private method. Performs the complete analysis :return: A fully computed set of Ordinary Differential Equations that can be used for further simulation :rtype: :class:`~means.core.problems.ODEProblem` """ S = self.model.stoichiometry_matrix amat = self.model.propensities ymat = self.model.species n_species = len(ymat) # dPdt is matrix of each species differentiated w.r.t. time # The code below literally multiplies the stoichiometry matrix to a column vector of propensities # from the right (::math::`\frac{dP}{dt} = \mathbf{Sa}`) dPdt = S * amat # A Is a matrix of each species (rows) and the derivatives of their stoichiometry matrix rows # against each other species # Code below computes the matrix A, that is of size `len(ymat) x len(ymat)`, for which each entry # ::math::`A_{ik} = \sum_j S_{ij} \frac{\partial a_j}{\partial y_k} = \mathfb{S_i} \frac{\partial \mathbf{a}}{\partial y_k}` A = sp.Matrix(len(ymat), len(ymat), lambda i, j: 0) for i in range(A.rows): for k in range(A.cols): A[i, k] = reduce(operator.add, [ S[i, j] * sp.diff(amat[j], ymat[k]) for j in range(len(amat)) ]) # `diagA` is a matrix that has values sqrt(a[i]) on the diagonal (0 elsewhere) diagA = sp.Matrix( len(amat), len(amat), lambda i, j: amat[i]**sp.Rational(1, 2) if i == j else 0) # E is stoichiometry matrix times diagA E = S * diagA variance_terms = [] cov_matrix = [] for i in range(len(ymat)): row = [] for j in range(len(ymat)): if i <= j: symbol = 'V_{0}_{1}'.format(i, j) variance_terms.append( VarianceTerm(position=(i, j), symbol=symbol)) else: # Since Vi,j = Vj,i, i.e. covariance are equal, we only record Vi,j but not Vj,i symbol = 'V_{0}_{1}'.format(j, i) variance_terms.append( VarianceTerm(position=(j, i), symbol=symbol)) row.append(symbol) cov_matrix.append(row) V = sp.Matrix(cov_matrix) # Matrix of variances (diagonal) and covariances of species i and j differentiated wrt time. # I.e. if i=j, V_ij is the variance, and if i!=j, V_ij is the covariance between species i and species j dVdt = A * V + V * (A.T) + E * (E.T) # build ODEProblem object rhs_redundant = sp.Matrix([i for i in dPdt] + [i for i in dVdt]) #generate ODE terms n_vectors = [ tuple([1 if i == j else 0 for i in range(n_species)]) for j in range(n_species) ] moment_terms = [ Moment(nvec, lhs) for (lhs, nvec) in zip(ymat, n_vectors) ] ode_description = moment_terms + variance_terms non_redundant_idx = [] ode_terms = [] # remove repetitive covariances, as Vij = Vji for i, cov in enumerate(ode_description): if cov in ode_terms: continue else: ode_terms.append(cov) non_redundant_idx.append(i) rhs = [] for i in non_redundant_idx: rhs.append(rhs_redundant[i]) out_problem = ODEProblem("LNA", ode_terms, rhs, sp.Matrix(self.model.parameters)) return out_problem
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)