Page - 79 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

4FunctionsandtheWritingofCode 4.1 Functions:HowtoWriteThem? Untilnow,wehavebenefittedfromusing functions like,e.g.,zerosandlinspace from numpy. These have all been written by others for us to use. Now we will look at how to write such functions ourselves, an absolutely fundamental skill in programming. In its simplest form, a function in a program is much like a mathematical function:someinputnumberx is transformedtosomeoutputnumber.Oneexample is the tanh−1(x) function, calledatan in computer code: it takes one real number as inputand returnsanothernumber.Functions in Pythonare moregeneral andcan take a series of values as input and return one or more results, or simply nothing. Thepurposeof functions is twofold: 1. to group code lines that naturally belong together (making such units of code is a strategywhichmayease theproblemsolvingprocessdramatically),and 2. to parameterize a set of code lines such that they can be written only once and easilybe re-executedwithvariations. Functions that we write ourselves are often referred to as user-defined functions. Throughout this book,we will present many examples, in variouscontexts, of how such functionsmaybewritten. 4.1.1 Example:WritingOurFirstFunction To grasp the first few essentials about function writing, we changeball.py from Sect.1.2, so that the heighty is rathercomputedbyuse of a function that wedefine ourselves.Also, to betterdemonstrate theuse ofour function,we computeyat two pointsintime(notonlyone,asinball.py).Thenewprogramball_function.py thenappearsas def y(v0, t): g = 9.81 # Acceleration of gravity ©The Author(s) 2020 S.Linge, H.P. Langtangen, Programming forComputations -Python, Texts in Computational Science and Engineering 15, https://doi.org/10.1007/978-3-030-16877-3_4 79