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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
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