Page - 36 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

36 2 BasicConstructions When run, this program first prints the sum of x and y (i.e., 5), and then it prints theproduct (i.e., 6).Wesee thattreat_xy takes a functionnameas itsfirst parameter. Insidetreat_xy, that function isused to actually call the function that was given as input parameter. Therefore, as shown, wemay call treat_xywith eithersum_xyorprod_xy,dependingonwhetherwewant thesumorproductofx andy tobecalculated. Functionsmayalsobedefinedwithinother functions. It that case, theybecome local functions, or nested functions, knownonly to the function insidewhich they aredefined. Functionsdefined inmainare referred toasglobal functions. Anested functionhasfullaccess toallvariablesintheparentfunction, i.e. thefunctionwithin which it is defined. Short functions can be defined in a compact way, using what is known as a lambdafunction: f = lambda x, y: x + 2*y # Equivalent def f(x, y): return x + 2*y Thesyntaxconsists oflambda followedbya seriesof arguments, colon, andsome Pythonexpression resulting in anobject to be returned fromthe function. Lambda functionsareparticularlyconvenientas functionarguments: print treat_xy(lambda x, y: x*y, x, y) Overheadoffunctioncalls Function calls have the downside of slowing down program execution. Usu- ally, it is a good thing to split a program into functions, but in very computing intensiveparts, e.g., inside longloops,onemustbalancetheconvenienceofcall- ing a function and the computational efficiencyof avoiding function calls. It is a good rule to develop a programusing plenty of functions and then in a later optimization stage, when everything computes correctly, remove function calls that arequantified to slowdownthecode. Here isa littleexampleinIPythonwherewecalculate theCPUtimefordoing arraycomputationswithandwithoutahelper function: In [1]: import numpy as np In [2]: a = np.zeros(1000000) In [3]: def add(a, b): ...: return a + b ...: In [4]: %timeit for i in range(len(a)): a[i] = add(i, i+1) The slowest run took 16.01 times longer than the fastest. This could mean that an intermediate result is being cached 1 loops, best of 3: 178 ms per loop In [5]: %timeit for i in range(len(a)): a[i] = i + (i+1) 10 loops, best of 3: 109 ms per loop