Page - 22 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

22 1 TheFirstFewSteps A Single Curve In Fig.1.1, we saw a nice and smooth curve, showing how the height of a ball developed with time. The reader should realize that, even though the curve is continuousand apparently smooth, it is generated from a collection of pointsonly.That is, for thechosenpoints in time,wehavecomputedtheheight.For times in between, we have computed nothing! So, in principle, we actually do not know what the height is there. However, if only the time step between consecutive height computations is “small enough”, the ball can not experience any significant change in its state of motion. Thus, inserting straight lines between two and two consecutivedata points will be a good approximation.This is exactly what Python does,unlessotherwiseisspecified.With“many”datapoints,as inFig.1.1, thecurve appearssmooth. Wesawpreviously, inball_plot.py, howanarrayy (heights)couldbeplotted againstanothercorrespondingarrayt (points in time)with thestatement plt.plot(t, y) Aplotcommandlike this isvery typicalandoften justwhatweprefer, forexample, inourcase with the ball. It is also possible, however, to plot an array without involving any second array at all. With reference toball_plot.py, this means thaty could have been plotted without any mention oft, and to do that, one could write the plot command rather like plt.plot(y) Thecurvewouldthenhavelookedjust like theoneinFig.1.1,except that thex-axis would span they array indices from 0 to 1000 instead of the correspondingpoints in time(check it andsee foryourself). Quickly testinga (minor)codechange Let us take the opportunity here, to mention how many programmers would go about to check the alternative plot command just mentioned. In ball_plot.py, one would typically just comment out the original lines and insert alternativecodefor these, i.e., as #plt.plot(t, y) #plt.xlabel(’t (s)’) plt.plot(y) plt.xlabel(’Array indices’) One would then run the code and observe the impact of the change,which in thiscase is themodifiedplotdescribedabove. After running the modified code, there are, generally, two alternatives. Shouldtheoriginalversionbekeptorshouldwemakethechangepermanent? With the present ball example, most of us would prefer the original plot, so we would change the code back to its original form (remember to check that itworksasbefore!). When the code change to test is more comprehensive, it is much better to makea separatecopyof thewholeprogram,and thendo the testing there.