MATLAB Ch 3 – Functions & Files

1. MATLAB Ch 3 – Functions & Files EGR1302

2. Outline • Introduction • Elementary mathematical operations • User-defined functions • Working with data files

3. Introduction • Review from Ch 1 • MATLAB mathematical functions • Pair of parentheses after function name encloses function’s argument • Can be part of mathematical expression • Users can define functions • MATLAB has commands and functions for managing the work session

4. Introduction • MATLAB has many built-in functions • Users may define functions • Convenient use • Advanced function capability • Function handles • Anonymous functions • Subfunctions • Nested functions • MATLAB allows input/output of data files

5. Section 3.1 Elementary mathematical functions

6. Finding relevant functions • Command – lookfor • Seeks the word in the help descriptions of the MATLAB help system • If user does not know the name of function >> lookforimaginary i - Imaginary unit. j - Imaginary unit. complex - Construct complex result from real and imaginary parts. imag - Complex imaginary part.

7. Finding relevant functions

8. Finding relevant functions • Command – disp • If user knows correct spelling of a MATLAB function • Same output as selecting complex hyperlink after using lookfor command >> dispcomplex

9. Tables 3.1-1, 3.1-2, 3.1-3 • List of some common mathematical functions (pp. 142, 146, 148) • Exponential & logarithmic • Complex number • Numeric • Trigonometric • Hyperbolic

10. Example – complex functions >> x=-3+4i; >> y=6-8i; >> mag_x = abs(x) mag_x = 5 >> mag_y = abs(y) mag_y = 10 >> mag_product = abs(x*y) mag_product = 50

11. Example – complex functions >> angle_x = angle(x) angle_x = 2.2143 >> angle_y = angle(y) angle_y = -0.9273 >> sum_angles = angle_x + angle_y sum_angles = 1.2870 >> angle_product = angle(x*y) angle_product = 1.2870

12. Section 3.2 User-defined functions

13. Functions files • Differences between script & functions M-files • All functions variables are local • Values available only within function • Useful when repeating a set of commands multiple times • Building blocks of larger programs • First line in function  function definition line • List of inputs and outputs

14. Function definition line • Distinguishes function from script • function – must be lower case • Output variables must be enclosed in square brackets • Input variables must be enclosed in parentheses • func_namemust be same as name of M-file • Use exist function before naming a function function[output vars]=func_name(input vars)

15. Simple function example function z = fun(x,y) u = 3*x; z = u + 6*y.^2; >> z = fun(3,7) z = 303 >> y = [3 4 5]; >> z = fun(y,7) z = 303 306 309 >> fun(3,7) ans = 303 >> z ??? Undefined function or variable 'z'. >> u ??? Undefined function or variable 'u'.

16. Functions • Suppress output of function by putting semicolon after the function call • Only order of arguments is important, not names of arguments • Arrays can be used as input arguments • May have more than one output

17. Variations in function line • One input, one output: • Brackets are optional • Two inputs, one output • One input, two outputs • No named output: function sqplot(side) function [area_square] = square(side) OR function area_square = square(side) function [volume_box] = box(height,width,length) function [area_circle,circumf] = circle(radius) function sqplot(side)

18. 2nd simple function example function [A, C] = circle(r) A = pi*r.^2; C = 2*pi*r; >> [A, C] = circle(4) A = 50.2655 C = 25.1327 >> r = [3 4 5]; >> [A, C] = circle(r) A = 28.2743 50.2655 78.5398 C = 18.8496 25.1327 31.4159

19. Comments in functions • Comment lines, starting with %, may be placed anywhere in function file • If user types help to obtain information about function • All comment lines immediately following function definition line up to first blank or executable line is displayed • If user types lookfor command • First comment line is displayed

20. Local variables • Names of input variables given in function are local to the function • Other variable names can be used when calling the function • All variables inside a function are erased after the function finishes executing • Except when the same variable names appear in the output variable list used in the function call

21. Global variables • global command declares certain variables global • Their values are available to the basic workspace and to other functions that declare these variables global. • Any assignment to those variables, in any function or in the base workspace, is available to all the other functions declaring them global. global a x q

22. Finding the zeros of a function • function is a string containing the name of the function • x0 is a user-supplied guess for the zero • Returns a value of x that is near x0 • Identifies only points where the function crosses the x-axis • Not points where the function just touches the axis. fzero(‘function’, x0) >> fzero('cos',2) ans = 1.5708

23. Using fzero with user-defined functions • To find the zeros of more complicated functions, it is more convenient to define the function in a function file function y = f1(x) y = x + 2*exp(-x) - 3; >> x = fzero('f1',-1) x = -0.5831 >> x = fzero('f1',2) x = 2.8887

24. Finding the minimum of a function • function is a string containing the name of the function • Returns a value of x that minimizes the function in the interval x1 ≤ x ≤ x2 fminbnd(‘function’, x1,x2) >> fminbnd('cos', 0,4) ans = 3.1416

25. Finding the minimum of a function • For functions of more than one variable • function is a string containing the name of the function • Vector x0 is a guess that must be supplied by the user. fminsearch(‘function’, x0) function f = f4(x) f = x(1).*exp(-x(1).^2-x(2).^2); >> fminsearch('f4',[0,0]) ans = -0.7071 0.0000

26. Design optimization example • Example 3.2-2, p. 161

27. Section 3.4 Working with data files

28. Importing data files • Typical ASCII file • Header lines • One or more lines of text • Contain comments, creation date, column headings • Data • Arranged in rows & columns • Each number in a row may be separated • Spaces • Commas • Tab

29. Importing data files • Importing an externally generated file in ASCII format • Matlab can not import data that is separated (i.e., delimited) by commas • To import a comma-delimited ASCII file, some pre-processing is required • First, open data file in a text editor (e.g., Notepad) • Second, delete the text header lines • Third, replace each comma with at least one space (i.e., use Replace function)

30. Importing data files • Importing an externally generated file in ASCII format • Matrix is generated • Name of matrix is filename with extension stipped off • This command creates a matrix named “tensile_test” load filename load tensile_test.txt

31. Importing data files • Excel spreadsheets may be imported into Matlab • Save Excel file in 2003 format (i.e., .xlsextension) • Imports file into array A • Imports all numeric data into array A and all text data into array B A = xlsread(‘filename’) [A, B] = xlsread(‘filename’)

32. Import Wizard • Allows for importing a variety of ASCII file formats • Space-delimited files • Mixed text and numeric files • Files with text headers • Files with non-space delimiters • Commas • Semi-colons • Tabs

33. Import Wizard • What you must know before you may import the data file • How many data items are in each row? • Are the data items numeric, text strings, or a mixture of both types? • Does each row or column have a descriptive text header? • What character is used as the delimiter that separates items in each row into columns?

34. Import Wizard • Caution • Import Wizard overwrites any existing variable in the workspace with no warning message! • Dialog boxes ask you to: • Specify the name of the file you want to import • Specify the delimiter used in the file • Select the variables that you want to import

35. Import Wizard

36. End of Chapter 3

37. Slides that I do not plan to use

38. Outline • Introduction • Elementary mathematical operations • User-defined functions • Advanced function programming • Working with data files

39. Section 3.3 Advanced function programming

40. Function handles • Create a function handle to any function by using the at sign, @, before the function name. • Name the handle • Use the handle to reference the function • sine_handle is a user-selected name for the handle >>sine_handle = @sin;

41. Function handles • A common use • Pass the function as an argument to another function • Example - plot sin x over 0 £x £ 6 as follows: • Cumbersome way to plot the sine function • However, the concept can be extended to create a general purpose plotting function that accepts a function as an input >>plot([0:0.01:6],sine_handle,[0:0.01:6])

42. Function handles • function x = gen_plot(fun_handle, interval) • plot(interval, fun_handle, interval) • You may call this function to plot the sin x over 0 £x £ 6 as follows: • >>gen_plot(sine_handle,[0:0.01:6]) • or • >>gen_plot(@sin,[0:0.01:6])