Seite - 38 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

38 2 BasicConstructions 1 is thenused (combinedwith the startingat 0). Thus, callingrange, for example, as range(6) would return the integers0, 1, 2, 3, 4, 5. Note that decreasing integersmaybeproducedby lettingstart > stop com- bined with a negative step. This makes it easy to, e.g., traverse arrays in either direction. Let usmodifyball_plot.py fromSect. 1.4 to illustrate howusefulfor loops are if you need to traverse arrays. In that examplewe computed the height of the ball at everymilli-second during thefirst secondof its (vertical) flight andplotted theheightversus time. Assumewewant tofind themaximumheight during that time, howcanwedo itwith a computer program? One alternativemay be to compute all the thousand heights, store theminanarray,and then run through thearray topickout themaxi- mum.Theprogram,namedball_max_height.py,may lookas follows. import matplotlib.pyplot as plt v0 = 5 # Initial velocity g = 9.81 # Acceleration of gravity t = linspace(0, 1, 1000) # 1000 points in time interval y = v0*t - 0.5*g*t**2 # Generate all heights # At this point, the array y with all the heights is ready. # Now we need to find the largest value within y. largest_height = y[0] # Starting value for search for i in range(1, 1000): if y[i] > largest_height: largest_height = y[i] print "The largest height achieved was %f m" % (largest_height) # We might also like to plot the path again just to compare plt.plot(t,y) plt.xlabel(’Time (s)’) plt.ylabel(’Height (m)’) plt.show() There is nothingnewhere, except thefor loopconstruction, so let us lookat it inmoredetail. As explainedabove, Pythonunderstands that afor loop is desired when it sees thewordfor. Therange() functionwill produce integers from,and including, 1, up to, and including, 999, i.e. 1000 1. The value in y[0] is used as the preliminary largest height, so that, e.g., the very first check that ismade is testingwhethery[1] is larger than this height. If so,y[1] is stored as the largest height. The for loop thenupdatesi to 2, and continues to checky[2], and so on. Each timewefinda larger number,we store it. Whenfinished,largest_height