Add B/A tests

tests/2.B/test_taylor.py

+from sympy import series, atan, nsimplify
+from src.taylor import estimate
+
+
+import pytest
+from sympy.abc import x
+
+def ref_taylor(f, a, N, xval):
+    return nsimplify(series(f, x=x, x0=a, n=N).removeO().subs(x, xval).doit())
+
+
+at_one_tenth = [(0, N, 0.1) for N in range(15)]
+at_two_tenths = [(0, N, 0.2) for N in range(15)]
+at_one = [(0, N, 1) for N in range(15)]
+
+
+@pytest.mark.parametrize('a, N, xval', at_one_tenth + at_two_tenths + at_one)
+def test_arctan_taylor(a, N, xval):
+    result = estimate('arctan', xval, a, atan(a), N)
+    ref = ref_taylor(atan(x), a, N, xval)
+    print(float(result), float(ref))
+    assert abs(float(result) - float(ref)) < 10**(-8)
\ No newline at end of file

tests/3.A/taylor_tests_not_ready.py → tests/3.A/test_estimation.py

-from sympy import series, atan, oo, nsimplify, poly, diff
+from decimal import Decimal
+from sympy import series, atan, nsimplify, diff
 from sympy.calculus.util import Interval, maximum
-from sympy.abc import x
 import math
 
 from src.taylor import arctan
-from decimal import Decimal
 
 import pytest
+from sympy.abc import x
 
 def term(N, xval, a):
     ivl = Interval(xval - 0.001, a + 0.001) + Interval(a - 0.001, xval + 0.001)
-    d = diff(f, x, N + 1)
+    d = diff(atan(x), x, N + 1)
     M = maximum(d, x, ivl)
     return nsimplify(abs(((M * ((x - a)**(N + 1))/math.factorial(N + 1)).subs(x, xval))))
 
-f = atan(x)
+
+def ref_taylor(f, a, N, xval):
+    return nsimplify(series(f, x=x, x0=a, n=N).removeO().subs(x, xval).doit())
 
 def approx_atan(N, xval, a):
-    return nsimplify(series(f, x=x, x0=a, n=N+1).removeO().subs(x, xval).doit()), term(N, xval, a)
+    return ref_taylor(atan(x), a, N, xval), term(N, xval, a)
 
-xval = 0.2
-for q in range(0, 20):
+@pytest.mark.parametrize('q', range(20))
+def test_arctan(q):
     xval = q / 10
-    result, error = approx_atan(11, xval, 0)
-    #print(xval, float(error), abs(math.atan(xval) - result) <= float(error))
+    _, error = approx_atan(10, xval, 0)
     v, e = arctan(Decimal(xval))
-    #print(xval, float(error), abs(math.atan(xval) - float(v)) <= float(error))
-    print(xval, float(e), abs(math.atan(xval) - float(v)), abs(math.atan(xval) - float(v)) <= float(e))
-
+    if xval < 0.9:
+        assert 0 <= float(e) - float(error) < 0.003
+    assert abs(math.atan(xval) - float(v)) <= float(e)