chore: import upstream snapshot with attribution

mpmath/tests/test_diff.py

@@ -0,0 +1,59 @@
+from mpmath import (chop, cos, diff, diffs, diffun, e, exp, j, log, sin, sqrt,
+                    taylor)
+
+
+def test_diff():
+    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():
+    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():
+    # 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():
+    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)