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| from itertools import product | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import symbols | |
| from sympy.functions.elementary.exponential import (exp, log) | |
| from sympy.printing.repr import srepr | |
| from sympy.codegen.numpy_nodes import logaddexp, logaddexp2 | |
| x, y, z = symbols('x y z') | |
| def test_logaddexp(): | |
| lae_xy = logaddexp(x, y) | |
| ref_xy = log(exp(x) + exp(y)) | |
| for wrt, deriv_order in product([x, y, z], range(3)): | |
| assert ( | |
| lae_xy.diff(wrt, deriv_order) - | |
| ref_xy.diff(wrt, deriv_order) | |
| ).rewrite(log).simplify() == 0 | |
| one_third_e = 1*exp(1)/3 | |
| two_thirds_e = 2*exp(1)/3 | |
| logThirdE = log(one_third_e) | |
| logTwoThirdsE = log(two_thirds_e) | |
| lae_sum_to_e = logaddexp(logThirdE, logTwoThirdsE) | |
| assert lae_sum_to_e.rewrite(log) == 1 | |
| assert lae_sum_to_e.simplify() == 1 | |
| was = logaddexp(2, 3) | |
| assert srepr(was) == srepr(was.simplify()) # cannot simplify with 2, 3 | |
| def test_logaddexp2(): | |
| lae2_xy = logaddexp2(x, y) | |
| ref2_xy = log(2**x + 2**y)/log(2) | |
| for wrt, deriv_order in product([x, y, z], range(3)): | |
| assert ( | |
| lae2_xy.diff(wrt, deriv_order) - | |
| ref2_xy.diff(wrt, deriv_order) | |
| ).rewrite(log).cancel() == 0 | |
| def lb(x): | |
| return log(x)/log(2) | |
| two_thirds = S.One*2/3 | |
| four_thirds = 2*two_thirds | |
| lbTwoThirds = lb(two_thirds) | |
| lbFourThirds = lb(four_thirds) | |
| lae2_sum_to_2 = logaddexp2(lbTwoThirds, lbFourThirds) | |
| assert lae2_sum_to_2.rewrite(log) == 1 | |
| assert lae2_sum_to_2.simplify() == 1 | |
| was = logaddexp2(x, y) | |
| assert srepr(was) == srepr(was.simplify()) # cannot simplify with x, y | |