MATLAB Programming

1. MATLAB Programming COMM2M Harry R. Erwin, PhD University of Sunderland

2. Sources • James E. Gentle, 2002, Elements of Computational Statistics, Springer.

3. Topics • Operators and Flow Control • M-Files • Functions • Input and Output • M-File Style • Optimization • Tutorial • Individual Project

4. Operators and Flow Control • Relational and Logical Operators • Flow Control

5. Relational Operators • The six relational operators are: • == (equal) • ^= (not equal) • < • > • <= • >= • True is 1 and false is 0 • Comparisons involving matrices produce matrices.

6. ischar isempty isequal isfinite isieee isinf islogical isnan isnumeric isreal issparse Logical Functions

7. Logical Operators • & (logical and) • | (logical or) • ~ (logical not) • xor (logical exclusive or) • all (true if all elements of vector are nonzero) • any (true if any element of vector is nonzero)

8. Find • The find() command returns the indices corresponding to the non-zero elements of a vector. Applied to a matrix M, it works with M(:). • This can be used with any of these functions and operators. • If f was generated by f = find(X), then X(f) are the non-zero elements of X.

9. If Then Else if expression (handled like C/C++/Java) statements (comma separated on one line) elseif expression2 (optional) elseif statements else (optional) final set of statements end

10. For Loop • Convenient (but avoid if performance-critical; use vectors instead) for variable = expression for statements (, sep if 1 line) end • Expression is usually i:s:j. It can be a matrix, in which case the columns from first to last are used.

11. While Loop while expression statements end • As long as expression remains true (^==0) • for and while loops can be terminated with a break. • continue jumps back to the loop start. • Infinite loop: while 1, …, end

12. Switch Statement switch expression case value1 statements case value2 statements case value3 statements otherwise statements (optional) end • The case value can be a value list within {…} forming a cell array. • This is different from C!!!!!

13. M-Files • Scripts—no input or output arguments and operate on variables in the workspace • Functions—contain a function definition line and can work with input and output arguments. Internal variables are local unless declared global.

14. Scripts • Format for a script called spin.m: %SPIN % describes what it does executable statements

15. Functions function retval = name(arguments) %NAME one line description. (H1 line) % more details including arguments code statements, eventually setting retval • The name of the m-file should be the name of the function. • The H1 line should omit ‘the’ and ‘a’. It should start with a capital letter and end with ‘.’. • There is usually a blank line after the header. • The return command can be used to exit.

16. Editing M-Files • M-files are ASCII files, so you can use any text editor. • MATLAB has a built-in editor/debugger. • Type edit • Or use the menu in Windows systems. • MATLAB maintains a search path to find M-files. Use the path and addpath commands. There is also a path browser that can be called by pathtool. • Relevant commands available include what, lookfor, help, type, exist, and more.

17. Function Details • Functions can be passed as argument to other functions. Such an argument is preceded by @, e.g., @fun. Handle it using feval. • Functions can also be passed as name strings. This is not preferred. • The vectorize() function can be used to convert multiplication, division, and exponentiation to array operations

18. Subfunctions • Any M-file can contain local functions after the first one that can be called by the first one or other subfunctions. • Usually you head a subfunction with % Subfunction • Subfunctions can be arguments. • Functions and subfunctions can call themselves recursively.

19. Input and Output • User input • Screen display • Reading and writing text files

20. User Input • The input function will display a prompt and wait for user input. Input is interpreted as a string if input is called with a second argument ‘s’. • The function ginput collects data via mouse click coordinates. • The function pause() suspends execution until a key is clicked. pause(n) waits n seconds.

21. Screen Display • If you don’t append a ‘;’ there will be output to the screen. • The disp(var) function displays var. • The fprintf function gives more sophisticated control. • The sprintf function returns a string that fprintf would have printed.

22. Text Files • Type help iofun for the list of functions that support text and binary file io. • These are generally similar to C functions.

23. M-File Style • Be careful to fully document your files. In particular, provide an example of how the function can be used that can be cut and pasted. • Space around logical operators and = • One statement per line • Indentation to emphasize structure. • Matrix names should be capitalized.

24. Optimization • You may compile M-files. • Vectorize, don’t shade your eyes: n = 5e5; x = randn(n,1); tic, s = 0; for i=1:n, s = s+x(i)^2; end, toc Elapsed time = 8.35 tic, s = sum(x.^2); toc Elapsed time = 0.06

25. More Optimization • Preallocate large arrays. Otherwise they may be expanded one row/column at a time. • The repmat function is much faster than anything that involves manipulating individual matrix entries. • Empty arrays/matrices are handled by extrapolating operations on non-empty ones. This may be very convenient.

26. Grand Tour Tutorial • When a cluster of data points is rotated, patterns in the data may become apparent. • Rotations are orthogonal transformations that preserve the norms of the data vectors and the angles between. • Simple rotation matrices start with the identity matrix and change the four elements aii, aij, aji, and ajj. aiiand ajjare replaced with cos(),aijbecomes sin(), and ajibecomes -sin().

27. Generalized Rotation Matrices • A generalized rotation matrix, Q, is the product of (d2-d)/2 such simple rotation matrices. Q = Q12Q13…Q1dQ23Q24…Q2d…Qd-1,d

28. Constructing the Plot • Rotating a plot in all directions, and projecting into the first two or three dimensions is called a “Grand Tour” (Asimov 1985). • You can take for the values of ij, tij modulo 2 where the ijare linearly independent over the integers. Suitable constants are the square roots of the first (d2-d)/2 primes. • Plot the first two (or three) dimensions. • Suitable data can be found here: <http://lib.stat.cmu.edu/> • Step time and observe the changes.

29. Suitable Data Can Be Found At: • <http://lib.stat.cmu.edu/>