Page - 20 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

20 1 TheFirstFewSteps t = np.linspace(0, 1, 1001) y = v0*t - 0.5*g*t**2 plt.plot(t, y) # plots all y coordinates vs. all t coordinates plt.xlabel(’t (s)’) # places the text t (s) on x-axis plt.ylabel(’y (m)’) # places the text y (m) on y-axis plt.show() # displays the figure This program produces a plot of the vertical position with time, as seen in Fig.1.1. As you notice, the code lines fromtheball.pyprogramin Sect.1.2 have notchangedmuch,but theheight isnowcomputedandplottedfora thousandpoints in time! Let us take a closer look at this program. At the top, we recognize the import statements import numpy as np import matplotlib.pyplot as plt As we know by now, these statements imply that items from numpy and matplotlib.pyplotmustbe prefixedwithnpandplt, respectively. The linspaceFunction Next, there is a call to the functionlinspace from the numpy library. When n evenly spaced floating point numbers are sought on an interval [a,b],linspacemaygenerallybecalled like this: np.linspace(a, b, n) Thismeans that thecall t = np.linspace(0, 1, 1001) creates 1001 coordinates between 0 and 1, inclusive at both ends. The mathemati- cally inclined reader might agree that 1001 coordinates correspond to 1000 equal- Fig. 1.1 Plot generated by the script ball_plot.py showing the vertical position of the ball (computed for a thousand points in time)