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| from mpmath import * | |
| def test_diff(): | |
| mp.dps = 15 | |
| assert diff(log, 2.0, n=0).ae(log(2)) | |
| assert diff(cos, 1.0).ae(-sin(1)) | |
| assert diff(abs, 0.0) == 0 | |
| assert diff(abs, 0.0, direction=1) == 1 | |
| assert diff(abs, 0.0, direction=-1) == -1 | |
| assert diff(exp, 1.0).ae(e) | |
| assert diff(exp, 1.0, n=5).ae(e) | |
| assert diff(exp, 2.0, n=5, direction=3*j).ae(e**2) | |
| assert diff(lambda x: x**2, 3.0, method='quad').ae(6) | |
| assert diff(lambda x: 3+x**5, 3.0, n=2, method='quad').ae(540) | |
| assert diff(lambda x: 3+x**5, 3.0, n=2, method='step').ae(540) | |
| assert diffun(sin)(2).ae(cos(2)) | |
| assert diffun(sin, n=2)(2).ae(-sin(2)) | |
| def test_diffs(): | |
| mp.dps = 15 | |
| assert [chop(d) for d in diffs(sin, 0, 1)] == [0, 1] | |
| assert [chop(d) for d in diffs(sin, 0, 1, method='quad')] == [0, 1] | |
| assert [chop(d) for d in diffs(sin, 0, 2)] == [0, 1, 0] | |
| assert [chop(d) for d in diffs(sin, 0, 2, method='quad')] == [0, 1, 0] | |
| def test_taylor(): | |
| mp.dps = 15 | |
| # Easy to test since the coefficients are exact in floating-point | |
| assert taylor(sqrt, 1, 4) == [1, 0.5, -0.125, 0.0625, -0.0390625] | |
| def test_diff_partial(): | |
| mp.dps = 15 | |
| x,y,z = xyz = 2,3,7 | |
| f = lambda x,y,z: 3*x**2 * (y+2)**3 * z**5 | |
| assert diff(f, xyz, (0,0,0)).ae(25210500) | |
| assert diff(f, xyz, (0,0,1)).ae(18007500) | |
| assert diff(f, xyz, (0,0,2)).ae(10290000) | |
| assert diff(f, xyz, (0,1,0)).ae(15126300) | |
| assert diff(f, xyz, (0,1,1)).ae(10804500) | |
| assert diff(f, xyz, (0,1,2)).ae(6174000) | |
| assert diff(f, xyz, (0,2,0)).ae(6050520) | |
| assert diff(f, xyz, (0,2,1)).ae(4321800) | |
| assert diff(f, xyz, (0,2,2)).ae(2469600) | |
| assert diff(f, xyz, (1,0,0)).ae(25210500) | |
| assert diff(f, xyz, (1,0,1)).ae(18007500) | |
| assert diff(f, xyz, (1,0,2)).ae(10290000) | |
| assert diff(f, xyz, (1,1,0)).ae(15126300) | |
| assert diff(f, xyz, (1,1,1)).ae(10804500) | |
| assert diff(f, xyz, (1,1,2)).ae(6174000) | |
| assert diff(f, xyz, (1,2,0)).ae(6050520) | |
| assert diff(f, xyz, (1,2,1)).ae(4321800) | |
| assert diff(f, xyz, (1,2,2)).ae(2469600) | |
| assert diff(f, xyz, (2,0,0)).ae(12605250) | |
| assert diff(f, xyz, (2,0,1)).ae(9003750) | |
| assert diff(f, xyz, (2,0,2)).ae(5145000) | |
| assert diff(f, xyz, (2,1,0)).ae(7563150) | |
| assert diff(f, xyz, (2,1,1)).ae(5402250) | |
| assert diff(f, xyz, (2,1,2)).ae(3087000) | |
| assert diff(f, xyz, (2,2,0)).ae(3025260) | |
| assert diff(f, xyz, (2,2,1)).ae(2160900) | |
| assert diff(f, xyz, (2,2,2)).ae(1234800) | |