Page - 11 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

1.4 APythonProgramwithVectorizationandPlotting 11 Fig. 1.1 Plot generated by the scriptball_plot.py showing the vertical position of the ball at a thousandpoints in time andendingwithstop. Theexpressionlinspace(0, 1, 1001)creates 1001co- ordinates between 0 and 1 (including both 0 and 1). Themathematically inclined readerwillnotice that1001coordinatescorrespondto1000equal-sized intervals in Œ0;1 and that thecoordinatesare thengivenby ti D i=1000 (i D0;1;:: :;1000). Thevalue returned fromlinspace (beingstored int) is anarray, i.e., acollec- tion of numbers. Whenwe start computingwith this collection of numbers in the arithmetic expressionv0*t - 0.5*g*t**2, the expression is calculated for every number int (i.e., every ti for i D 0;1;:: :;1000), yielding a similar collection of 1001numbers in the resulty. That is,y is alsoanarray. This technique of computing all numbers “in one chunk” is referred to as vec- torization.Whenit canbeused, it isveryhandy,sinceboth theamountofcodeand computation time is reduced compared towriting a corresponding for or while loop (Chapter2) fordoing thesame thing. Theplottingcommandsaresimple: 1. plot(t, y)meansplottingall theycoordinatesversusall thetcoordinates 2. xlabel(’t (s)’)places the textt (s)on thex axis 3. ylabel(’y (m)’)places the texty (m)on they axis At this stage, you are strongly encouraged to do Exercise 1.4. It builds on the example above, but ismuch simpler bothwith respect to themathematics and the amountofnumbers involved.