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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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