1. Matlab Introduction By Grant Keady July 09, and Jan 14

2. Some basics • Matlab is designed to easily manipulate vectors and matrices • You can define a vector by [4;2;6] • You can define a transposed vector by [4,2,6] • You can define a matrix with [4,2,6;3,2,1;5,3,5]

3. More basics • Be careful when multiplying matrices in Matlab • If you have two matrices A and B, A*B will perform the matrix multiplication. If instead you want to multiply element-wise, use A.*B

4. More basics, ctdMore on this later in this class • A\b does the least squares solutionA=[1,0;1,0;0,1]; b=[1;2;1];A\b

5. If you haven’t already,Start Matlab • http://www.cwr.uwa.edu.au/~keady/Matlab/MatlabIntro/indexm.htmlDownload perthMeanTempsData.mIn matlab,cd to whereever you have put it. For me:cd('/Users/keady/Documents/Matlab/MatlabIntro/')

6. perthTemps, ctd • ls % to check the file is theretype perthMeanTempsData.mtype('perthMeanTempsData.m') • YOU DO THE LITTLE PLOT TASK THERE

7. perthTemps, ctd 2 • % PLOT EXAMPLE FOR YOU % Plot months on the horizontal axis and % with temperature in degrees C % on the vertical axis, show for each month, % the meanMaxTemp as a red o % the meanMinTemp as a blue o

8. perthTemps, ctd 3 • SOLUTIONhold onplot(months,meanMaxTemp,'ro');plot(months,meanMinTemp, 'bo');title('perthTemps');

9. perthTemps, ctd 4 • And next I will show you Matlab doing some matrix sums on the data Least squares fit of sinusoidal curvesIs a break for you … I will set other exercises, more in the later lectures than now

10. What I use Matlab for • Numerical computing tasksMost recently, heating of a parked car(the car heating exercise was a little task)1997-2003 integral equation – entry of a wedge into water • Symbolic algebra in Eng. Math teaching • More details in the LaTeX beamer

11. Skills we will need to do things:Writing functions • This is done by creating an M-(function) file • Example (use Matlab’s edit pane, fun.m): function out=fun(x,y) out=x*y-2 • In the command window writing fun(2,5) and pressing return will give 8

12. Things we will do:Simulations • These just consist of generating random numbers to put into one’s functions, and examining the results • There are two types of random number generators; rand and randn • You can generate an n-m array of random numbers by writing rand(n,m)

13. Look at Matlab – Using Help • Students to get help on rand and randnEASY QUESTION: What is the difference between them??? • hist(randn(200,1))

14. Things we will do • I plan to lecture from Chapman’s book.

15. More about Matlab • Matlab is extended by various Toolboxes(Cynical view is that this is to make money, but then again some are free) • Mapping Toolbox, limited licenceGoogle Earth … Mma • Own teaching obsession, Symbolic ToolboxCould re-assemble my ENVE3605 handouts

16. History • I have downloaded another person’s account of the history in a ppt file.(2014, just said the story. SHOW IT HERE only if requested) • There is also an account on wikipedia/MATLAB

17. Symbolic algebra • Not esp. important in this course • You can define symbolic variables in Matlab by writing syms x y • If you then write f=x/y you can use the subs function to substitute in numbers for x and y • subs(f, [x,y], [1,2]) will return 0.5 • subs(f, [x,y], sym([1,2])) will return 1/2

18. Problems with the Sym Toolbox • Symbolic algebra can become tricky in Matlab. E.g. when you want to define a very large number of symbolic variables • You don’t want to write syms x1 x2 x3…x300 by hand • To do this you need something like n = 300; x = sym(zeros(n)); for k = 1:numel(x) x(k) = sym(sprintf('x%d', k)); end

19. What the Sym Toolbox is for? • These are personal opinions • I would use Maple, Mathematica, MuPAD or whatever for larger Symbolics tasks • I like code writing from Symbolics packages, e.g. optimization, and having the Symbolics code the f (function), g (gradient), and h (hessian)

20. Matlab’s inbuilt functions • Matlab has a huge number of functions built in already, including several minimization functions • If possible it is best to use them; they’re fast • If you can’t use these try to avoid for loops as this slows down your function

21. Tips • The Matlab help menu is very useful, it has examples covering all of the basics and many more advanced problems • If that doesn’t work there is a good website http://www.mathworks.com/matlabcentral/ • It is usually enough just to search for your problem on the forum, otherwise you can join yourself and ask

22. A few ‘cool’ things in Matlab • You can create a magic square by just typing magic(n) where n is the size of the square you want • 3D plots look good • To end this PowerPoint (using a demo)(: load handel; player=audioplayer(y,Fs); play(player,[1,(get(player,'SampleRate')*3)])

23. Later lectures – I will be more systematic about programming aspects