Page - 33 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

2.2 Functions 33 one single return statement. Be prepared for critical comments if you return whereveryouwant... Anexpressionyouwilloftenencounterwhendealingwithprogramming,ismain program,or thatsomecodeis inmain. This isnothingparticular toPython,andsim- ply refers to thatpartof theprogramwhich isoutside functions.However,note that thedef line of functions is counted intomain. So, inball_function.pyabove, all statementsoutside the functionyare inmain, andalso the linedef y(t):. A functionmay take no arguments, ormany, inwhich case they are just listed within the parentheses (following the function name) and separated by a comma. Let us illustrate. Take a slight variation of the ball example and assume that the ball isnot thrownstraightup,butat anangle, so that twocoordinatesareneeded to specify itspositionatany time.According toNewton’s laws (whenair resistance is negligible), theverticalposition isgivenbyy.t/Dv0yt 0:5gt2andthehorizontal positionbyx.t/Dv0xt.Wecan includeboth theseexpressions inanewversionof ourprogram that prints thepositionof theball for chosen times. Assumewewant to evaluate these expressions at two points in time, t D 0:6s and t D 0:9s. We canpick somenumbers for the initial velocity componentsv0yandv0x, name the programball_position_xy.py,andwrite it forexampleas def y(v0y, t): g = 9.81 # Acceleration of gravity return v0y*t - 0.5*g*t**2 def x(v0x, t): return v0x*t initial_velocity_x = 2.0 initial_velocity_y = 5.0 time = 0.6 # Just pick one point in time print x(initial_velocity_x, time), y(initial_velocity_y, time) time = 0.9 # ... Pick another point in time print x(initial_velocity_x, time), y(initial_velocity_y, time) Nowwecomputeandprint the twocomponents for theposition, for eachof the two chosen points in time. Notice how each of the two functions now takes two arguments. Running theprogramgives theoutput 1.2 1.2342 1.8 0.52695 Afunctionmayalsohaveno returnvalue, inwhichcasewesimplydrop the re- turnstatement,oritmayreturnmorethanonevalue. Forexample, thetwofunctions we just definedcouldalternativelyhavebeenwrittenasone: def xy(v0x, v0y, t): g = 9.81 # acceleration of gravity return v0x*t, v0y*t - 0.5*g*t**2