Page - 73 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

3.4 Testing 73 Supposewehavewrittena function def add(a, b): return a + b Acorresponding test functioncan thenbe def test_add() expected = 1 + 1 computed = add(1, 1) assert computed == expected, ’1+1=%g’ % computed Test functions canbe in anyprogramfile or in separatefiles, typicallywith names startingwithtest. You can also collect tests in subdirectories: runningpy.test -s -vwill actually run all tests in all test*.pyfiles in all subdirectories, while nosetests -s -v restricts the attention to subdirectorieswhosenames startwith testorendwith_testor_tests. As longasweadd integers, theequality test in thetest_add function is appro- priate,but ifwetry tocalladd(0.1, 0.2) instead,wewill face theroundingerror problemsexplained inSect. 3.4.3,andwemustusea testwith tolerance instead: def test_add() expected = 0.3 computed = add(0.1, 0.2) tol = 1E-14 diff = abs(expected - computed) assert diff < tol, ’diff=%g’ % diff Belowwe shall write test functions for each of the three test procedures we suggested: comparisonwith hand calculations, checking problems that can be ex- actly solved, and checking convergence rates. We stick to testing the trapezoidal integration code and collect all test functions in one common file by the name test_trapezoidal.py. Hand-computednumericalresults Ourprevioushandcalculationsfor twotrape- zoids can be checked against thetrapezoidal function inside a test function (in afiletest_trapezoidal.py): from trapezoidal import trapezoidal def test_trapezoidal_one_exact_result(): """Compare one hand-computed result.""" from math import exp v = lambda t: 3*(t**2)*exp(t**3) n = 2 computed = trapezoidal(v, 0, 1, n) expected = 2.463642041244344 error = abs(expected - computed) tol = 1E-14 success = error < tol msg = ’error=%g > tol=%g’ % (errror, tol) assert success, msg