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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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