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_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_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_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_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_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(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_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_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_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_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)
