Page - 62 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

62 3 Computing Integrals we just put the statementsweotherwisewouldhaveput in amainprogram, inside a function: def application(): from math import exp v = lambda t: 3*(t**2)*exp(t**3) n = input(’n: ’) numerical = trapezoidal(v, 0, 1, n) # Compare with exact result V = lambda t: exp(t**3) exact = V(1) - V(0) error = exact - numerical print ’n=%d: %.16f, error: %g’ % (n, numerical, error) Nowwecomputeourspecialproblembycallingapplication()as theonlystate- ment in themain program. Both the trapezoidal and application functions reside in thefiletrapezoidal.py,whichcanbe runas Terminal Terminal> python trapezoidal.py n: 4 n=4: 1.9227167504675762, error: -0.204435 3.2.3 MakingaModule Whenwe have the different pieces of our programas a collection of functions, it is very straightforward to create amodule that can be imported in other programs. That is, having our code as amodule,means that thetrapezoidal function can easily be reused by other programs to solve other problems. The requirements of amodule are simple: put everything inside functions and let function calls in the mainprogrambe in theso-called test block: if __name__ == ’__main__’: application() The if test is true if the module file, trapezoidal.py, is run as a program and false if themodule is imported in another program. Consequently, whenwe do from trapezoidal import trapezoidal in some file, the test fails and application() is not called, i.e., our special problem is not solved andwill not print anythingon the screen. On theotherhand, ifwe runtrapezoidal.py in the terminalwindow, the test condition is positive,application() is called, andwe getoutput in thewindow: Terminal Terminal> python trapezoidal.py n: 400 n=400: 1.7183030649495579, error: -2.12365e-05