Merge pull request #56 from JHay0112/integration-tests

Integration tests

Author: JHay0112

tests/test_approximate_definite_integral.py

@@ -0,0 +1,56 @@
+'''
+    Tests the approximate definite integral functions provided in jmath.approximation
+'''
+
+# - Imports
+
+from .tools import random_integer, repeat
+from ..jmath.approximation import trapezium_rule, right_hand_rule, left_hand_rule
+
+# - Tests
+
+@repeat
+def test_on_increasing_func():
+    """Tests that on an increasing linear function the left hand rule underestimates, the right hand rule over estimates, and trapezium rule is exact"""
+    coeffecient = random_integer(1, 100)
+    linear_function = lambda x : coeffecient*x
+    lower_bound = random_integer(0, 98)
+    upper_bound = random_integer(lower_bound + 1, 100)
+    samples = upper_bound - lower_bound
+    
+    # Find exact area since it is linear
+    exact_area = 0.5*upper_bound*linear_function(upper_bound) - 0.5*lower_bound*linear_function(lower_bound)
+
+    # Use approximations
+    trapezium_area = trapezium_rule(linear_function, lower_bound, upper_bound, samples)
+    left_area = left_hand_rule(linear_function, lower_bound, upper_bound, samples)
+    right_area = right_hand_rule(linear_function, lower_bound, upper_bound, samples)
+
+    # Assert trapezium and exact match to 5 dp
+    assert round(trapezium_area, 5) == round(exact_area, 5)
+
+    # Assert left less than trapezium less than right
+    assert left_area < trapezium_area < right_area
+
+@repeat
+def test_on_decreasing_func():
+    """Tests that on a decreasing linear function the left hand rule overestimates, the right hand rule underestimates, and trapezium rule is exact"""
+    coeffecient = random_integer(-100, -1)
+    linear_function = lambda x : coeffecient*x
+    lower_bound = random_integer(0, 98)
+    upper_bound = random_integer(lower_bound + 1, 100)
+    samples = upper_bound - lower_bound
+    
+    # Find exact area since it is linear
+    exact_area = 0.5*upper_bound*linear_function(upper_bound) - 0.5*lower_bound*linear_function(lower_bound)
+
+    # Use approximations
+    trapezium_area = trapezium_rule(linear_function, lower_bound, upper_bound, samples)
+    left_area = left_hand_rule(linear_function, lower_bound, upper_bound, samples)
+    right_area = right_hand_rule(linear_function, lower_bound, upper_bound, samples)
+
+    # Assert trapezium and exact match to 5 dp
+    assert round(trapezium_area, 5) == round(exact_area, 5)
+
+    # Assert left moe than trapezium more than right
+    assert left_area > trapezium_area > right_area

tests/tools.py

@@ -12,11 +12,11 @@
 
 def repeat(func):
     """
-        Wrapper that repeats a function 10 times.
+        Wrapper that repeats a function 100 times.
     """
     @wraps(func)
     def inner():
-        for i in range(10):
+        for i in range(100):
             return func()
 
     return inner