Page - 10 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

10 1 TheFirstFewSteps This programproduces a plot of the vertical positionwith time, as seen inFig- ure 1.1. As you notice, the code lines from theball.pyprogram inChapter 1.2 havenotchangedmuch,but theheight is nowcomputedandplotted fora thousand points in time! Let us takea lookat thedifferencesbetween thenewprogramandourprevious program.Fromthe top, thefirstdifferencewenoticeare the lines from numpy import * from matplotlib.pyplot import * Yousee thewordimporthere, soyouunderstand thatnumpymustbea library, or moduleinPythonterminology.This librarycontainsa lotofveryuseful functional- ity formathematical computing,while thematplotlib.pyplotmodule contains functionality for plotting curves. The above import statement constitutes a quick wayof populatingyourprogramwith all necessary functionality formathematical computing and plotting. However, we actuallymake use of only a few functions in the present program: linspace,plot, xlabel, and ylabel. Many computer scientists will therefore argue that we should explicitly import whatwe need and noteverything(the star*): from numpy import linspace from matplotlib.pyplot import plot, xlabel, ylabel Otherswill claim that we should do a slightly different import and prefix library functionsby the libraryname: import numpy as np import matplotlib.pyplot as plt ... t = np.linspace(0, 1, 1001) ... plt.plot(t, y) plt.xlabel(’t (s)’) plt.ylabel(’y (m)’) Wewilluseall three techniques,andsinceallof themare insowidespreaduse,you shouldbe familiarwith them too. However, for themost part in this bookweshall do from numpy import * from matplotlib.pyplot import * for convenience and for making Python programs that look very similar to their Matlabcounterparts. The functionlinspace takes3parameters, and isgenerallycalledas linspace(start, stop, n) This is our first example of a Python function that takesmultiple arguments. The linspace function generates n equally spaced coordinates, starting with start