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