Page - 71 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

3.3 Branching(if,elifandelse) 71 The solution illustrates a simple, and very common, search procedure, looping through an array by use of a for loop to find the maximum value. Our program ball_max_height.pyreads import numpy as np import matplotlib.pyplot as plt v0 = 5 # Initial velocity g = 9.81 # Acceleration of gravity t = np.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, # and we need to find the largest value within y. largest_height = y[0] # Starting value for search for i in range(1, len(y), 1): if y[i] > largest_height: largest_height = y[i] print(’The largest height achieved was {:g} m’.format(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() We focus our attention on the new thing here, the search performed by thefor loop.The value iny[0] is used as a starting value forlargest_height. The very first check then, tests whethery[1] is larger than this height. If so,y[1] is stored as the largest height. The for loop then updates i to 2, and continues to check y[2], and so on. Each time we find a larger number, we store it. When finished, largest_heightwill contain the largestnumber fromthearrayy. Whenyourun theprogram,youget The largest height achieved was 1.27421 m whichcompares favorably to theplot that popsup (seeFig.1.1). The observant reader has already seen the similarity of finding the maximum height and finding the time of flight, as we addressed previously in Sect.3.2.1. In fact, we could alternatively have solved the maximum height problem here by utilizing that y[i+1] > y[i] as the ball moves towards the top. Doing this, our search loopcouldhavebeenwritten i = 0 while y[i+1] > y[i]: i = i + 1 When the conditiony[i+1] > y[i]becomesFalse, we could reporty[i+1] as ourapproximationof themaximumheight, forexample.