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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 | |