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import math
from sympy.core.symbol import symbols
from sympy.functions.elementary.exponential import exp
from sympy.codegen.rewriting import optimize
from sympy.codegen.approximations import SumApprox, SeriesApprox
def test_SumApprox_trivial():
x = symbols('x')
expr1 = 1 + x
sum_approx = SumApprox(bounds={x: (-1e-20, 1e-20)}, reltol=1e-16)
apx1 = optimize(expr1, [sum_approx])
assert apx1 - 1 == 0
def test_SumApprox_monotone_terms():
x, y, z = symbols('x y z')
expr1 = exp(z)*(x**2 + y**2 + 1)
bnds1 = {x: (0, 1e-3), y: (100, 1000)}
sum_approx_m2 = SumApprox(bounds=bnds1, reltol=1e-2)
sum_approx_m5 = SumApprox(bounds=bnds1, reltol=1e-5)
sum_approx_m11 = SumApprox(bounds=bnds1, reltol=1e-11)
assert (optimize(expr1, [sum_approx_m2])/exp(z) - (y**2)).simplify() == 0
assert (optimize(expr1, [sum_approx_m5])/exp(z) - (y**2 + 1)).simplify() == 0
assert (optimize(expr1, [sum_approx_m11])/exp(z) - (y**2 + 1 + x**2)).simplify() == 0
def test_SeriesApprox_trivial():
x, z = symbols('x z')
for factor in [1, exp(z)]:
x = symbols('x')
expr1 = exp(x)*factor
bnds1 = {x: (-1, 1)}
series_approx_50 = SeriesApprox(bounds=bnds1, reltol=0.50)
series_approx_10 = SeriesApprox(bounds=bnds1, reltol=0.10)
series_approx_05 = SeriesApprox(bounds=bnds1, reltol=0.05)
c = (bnds1[x][1] + bnds1[x][0])/2 # 0.0
f0 = math.exp(c) # 1.0
ref_50 = f0 + x + x**2/2
ref_10 = f0 + x + x**2/2 + x**3/6
ref_05 = f0 + x + x**2/2 + x**3/6 + x**4/24
res_50 = optimize(expr1, [series_approx_50])
res_10 = optimize(expr1, [series_approx_10])
res_05 = optimize(expr1, [series_approx_05])
assert (res_50/factor - ref_50).simplify() == 0
assert (res_10/factor - ref_10).simplify() == 0
assert (res_05/factor - ref_05).simplify() == 0
max_ord3 = SeriesApprox(bounds=bnds1, reltol=0.05, max_order=3)
assert optimize(expr1, [max_ord3]) == expr1
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