Page - 9 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

1.4 APythonProgramwithVectorizationandPlotting 9 We will often use this import statement and then get access to all common mathematical functions. This latter statement is inserted in a program named ball_angle.py: from math import * x = 10 # Horizontal position y = 10 # Vertical position angle = atan(y/x) print (angle/pi)*180 Thisprogramrunsperfectly andproduces45.0asoutput, as it should. At first, it may seem cumbersome to have code in libraries, since you have to knowwhich library to import to get the desired functionality. Having everything available anytime would be convenient, but this also means that you fill up the memory of your programwith a lot of information that you ratherwould use for computationsonbigdata. Pythonhassomany librarieswith somuchfunctionality thatonesimplyneeds to importwhat is needed ina specificprogram. 1.4 APythonProgramwithVectorizationandPlotting Wereturn to theproblemwhereaball is thrownupin theairandwehaveaformula for the vertical position y of the ball. Saywe are interested in y at everymilli- second for the first secondof the flight. This requires repeating the calculation of yDv0t 0:5gt2one thousand times. Wewill also drawagraphofy versus t for t 2 Œ0;1 . Drawing suchgraphson a computer essentiallymeans drawing straight lines between points on the curve, soweneedmanypoints tomake thevisual impressionofasmoothcurve.Withone thousandpoints, asweaimtocomputehere, thecurve looks indeedverysmooth. InPython, the calculations and thevisualizationof the curvemaybedonewith theprogramball_plot.py, reading from numpy import linspace import matplotlib.pyplot as plt v0 = 5 g = 9.81 t = linspace(0, 1, 1001) y = v0*t - 0.5*g*t**2 plt.plot(t, y) plt.xlabel(’t (s)’) plt.ylabel(’y (m)’) plt.show()