CMPS 1371 Introduction to Computing for Engineers

1. CMPS 1371Introduction to Computing for Engineers FUNCTIONS

2. Functions • MATLAB uses function names consistent with most major programming languages For example • sqrt • sin • cos • log

3. Function Input can be either scalars or matrices

4. Using Predefined Functions • Functions consist of • Name • Input argument(s) • Output sqrt (x) = result • In MATLAB sqrt(4) ans = 2

5. Some functions require multiple inputs • Remainder function returns the remainder in a division problem • For example the remainder of 10/3, is 1

6. Some functions return multiple results • size function determines the number of rows and columns

7. You can assign names to the output

8. Nesting Functions

9. Functions • There are functions for almost anything you want to do • Use the help feature to find out what they are and how to use them • From the command window • From the help selection on the menu bar

10. Elementary Math Functions • abs(x) absolute value • sign(x) plus or minus • exp(x) ex • log(x) natural log • log10(x) log base 10

11. Rounding Functions • round(x) • fix(x) • floor(x) • ceil(x)

12. Discrete Mathematics • factor(x) • gcd(x,y) greatest common denominator • lcm(x) lowest common multiple • rats(x) represent x as a fraction • factorial(x) • primes(x) • isprime(x)

13. Trigonometric Functions • sin(x) sine • cos(x) cosine • tan(x) tangent • asin(x) inverse sine • sinh(x) hyperbolic sine • asinh(x) inverse hyperbolic sine • sind(x) sine with degree input • asind(x) inverse sin with degree output

14. Data Analysis • max(x) • min(x) • mean(x) • median(x) • sum(x) • prod(x) • sort(x)

15. Variance and Standard Deviation • std(x) • var(x)

16. Random Numbers • rand(x) • Returns an x by x matrix of random numbers between 0 and 1 • rand(n,m) • Returns an n by m matrix of random numbers

17. Computational Limits • MATLAB’s computational range on most computers is: • 10-308 • 10308 • When you divide by 0, the computer returns Inf

18. Function specification function <results> = <name> ( <parameter-list> ) % <Help comments – used with help, lookfor > % <usage, theory, alg> <code> • The names of variables in functions are only visible in the function. • Scripts are used for the top level call to the functions. • Functions must be saved in an M-file of the same name as the function. (For now in the working directory.) (Actually filename is the name of the function!)

19. r h r h vol cyl A simple example • Suppose I have a cylinder, and I want the volume: • Going to write a function, called cyl, which will input the radius and the height of the cylinder and produce the desired volume

20. Function cylinder • Write function function volume = cyl(radius, height) % CYLINDER computes volume of circular cylinder % given radius and height % Use: % vol=cylinder(radius, height) % volume=pi.*radius^2.*height; % why the dots? • Save as m-file with function name (cyl.m) • Type help cyl

21. Results of Cylinder

22. M-function Workspace • Each time an m-function is executed, a new workspace is created just for that instance • All variables except arguments and returned variable are defined only in the function workspace • Function variables are not defined in Base workspace, nor are Base variables defined in function workspace • Function workspace is destroyed when function completes • Function variables are “hidden” from world (and from accidental misuse or alteration)

23. Restrictions, style • Functions do not use INPUT or DISP or any real input output unless specified in the assignment or for debugging • Semi colons – use semi colons unless you need to see step by step results when debugging • Can’t save and run a function. Why not? • Because doesn’t know the calling environment or context.

24. Test Cylinder Function • Create a script: test_cyl Rad = Input(‘Radius:’) Disp(rad) % note different names Ht = Input(‘Height:’) Disp(ht) Cyl(rad,ht) • Try with vectors.

25. How are M-Functions Located? • Sometimes it is important to know how Matlab will look for an m-function, especially if two have the same name… • First checks current workspace • is it a built-in Matlab function? • is it a sub-function in the current function? • is it a private function? • is it in the current directory? • is it in the Matlab path, searching from the current directory down? • The first instance is used and any others are ignored • This can cause problems if you don’t understand… • It can also let you replace functions with different versions

26. Multiple Values Functions • M-functions Can Return Multiple Values • The returned variable from an M-function can be a scalar or an array (even a cell array) • M-functions can use the [ ] constructor to return an array formed from multiple scalar values

27. Multiple Value Return • Lets update our cylinder function to return the area and the volume: function [area volume] = cylAV(radius, height) % CYLINDER computes volume of circular cylinder % given radius and height % Use: % [ar, vol] =cylinder(radius, height) % volume=pi.*radius^2.*height; area = 2 .* pi .* height + 2.* pi .*r .*r;