All You Really Need to Know about MATLAB (at least for ENCE 201)

Transcription

1 All You Really Need to Know about MATLAB (at least for ENCE 201) Charles W. Schwartz August 2004 The purpose of these notes is to give you a bare bones summary of the subset of MATLAB features that will be most useful for the programming exercises in ENCE 201. MATLAB is a very powerful computational tool that offers a wealth of features beyond those described here. You should consult the MATLAB documentation and Demonstration programs for an overview of these additional advanced features. DOCUMENTATION For details (syntax, usage, etc.) and information on more advanced MATLAB features Help menu from main MATLAB window Online at http// Other useful information Demos from MATLAB Start button Getting Started section online, accessible via link from page http// DATA TYPES By default, all constant and variables in MATLAB are double precision floating point. All computations are also performed in double precision by default. Double precision floating-point numbers in MATLAB have a finite precision of roughly 16 significant decimal digits and a finite range of roughly to VARIABLES Variable names consist of a letter, followed by any number of letters, digits, or underscores. MATLAB uses only the first 31 characters of a variable name. MATLAB is case sensitive; it distinguishes between uppercase and lowercase letters. A and a are not the same variable. To view the value(s) assigned to any variable, simply enter the variable name in the Command window. MATRICES A matrix is entered as a list of its elements following a few basic conventions Separate the elements of a row with blanks or commas. Use a semicolon, ;, to indicate the of each row. Surround the entire list of elements with square brackets, [ ]. 1

2 For example, type in the Command window A = [ ; ; ; ] MATLAB displays the matrix you just entered A = The element in row i and column j of A is denoted by A(i,j). If you try to use the value of an element outside of the matrix, it is an error. On the other hand, if you store a value in an element outside of the matrix, the size increases automatically to accommodate the new element. A scalar is equivalent to a 1x1 matrix. In this case, the square brackets are not required A = 16 OPERATORS Arithmetic Operators Expressions use familiar arithmetic operators and precedence rules. + Addition - Subtraction * Multiplication / Division \ Left division (see "Matrices and Linear Algebra" in MATLAB ^ Power ( ) Specify evaluation order Matrix Operators + Addition - Subtraction * Matrix multiplication Transpose (e.g., A ) inv(a) Matrix inverse det(a) Matrix determinant ( ) Specify evaluation order 2

3 Relational Operators Operator Description < Less than <= Less than or equal to > Greater than >= Greater than or equal to == Equal to ~= Not equal to Logical Operators Operator Description & And Or ~ Not Colon Operator The colon,, is an important operator specific to MATLAB. It occurs in several different forms. The expression 110 is a row vector containing the integers from 1 to To obtain non-unit spacing, specify an increment. For example, is Subscript expressions involving colons refer to portions of a matrix. A(1k,j) is the first k elements of the jth column of A. STATEMENTS AND EXPRESSIONS Arithmetic expressions are written and evaluated in MATLAB much the same as they are in Excel. An example of a MATLAB statement that assigns the result of an arithmetic expression to the variable rho rho = (1+sqrt(5))/2 rho =

4 Matrices and scalars can be combined in expressions. For example, a scalar is subtracted from a matrix by subtracting it from each element B = A B = for the matrix A given earlier under the MATRICES section. If you simply type a statement and press Return or Enter, MATLAB automatically displays the results on screen. However, if you the line with a semicolon, MATLAB performs the computation but does not display any output. If a statement does not fit on one line, use an ellipsis (three periods),..., followed by Return or Enter to indicate that the statement continues on the next line. For example, s = 1-1/2 + 1/3-1/4 + 1/5-1/6 + 1/ /8 + 1/9-1/10 + 1/11-1/12; Blank spaces around the =, +, and - signs are optional, but they improve readability. BUILT-IN FUNCTIONS MATLAB provides a large number of standard elementary mathematical functions. MATLAB also provides many more advanced mathematical functions. For a list of the elementary mathematical functions, type help elfun For a list of more advanced mathematical and matrix functions, type help specfun help elmat Several special functions provide values of useful constants. pi eps Floating-point relative precision, 2-52 realmin Smallest floating-point number, realmax Largest floating-point number, (2-) Inf Infinity NaN../../techd Not-a-number INPUT/OUTPUT Console I/O (i.e., Keyboard and Screen) Keyboard Input The input function displays a prompt and waits for a user response. Its syntax is 4

5 n = input('prompt_string') The function displays the prompt_string, waits for keyboard input, and then returns the value from the keyboard. If the user inputs an expression, the function evaluates it and returns its value. Pausing Execution Some M-files benefit from pauses between execution steps. The pause command, with no arguments, stops execution until the user presses a key. To pause for n seconds, use pause(n) Screen Output disp(x) displays an array, without printing the array name. If X contains a text string, the string is displayed. Another way to display an array on the screen is to type its name, but this prints a leading "X =," which is not always desirable. For example, use disp in an M-file is to display a matrix with column labels disp(' Corn Oats Hay') disp(rand(5,3)) which results in Corn Oats Hay (See also format and sprintf for screen output with greater format control.) File I/O The load function text files containing numeric data. The text file should be organized as a rectangular table of numbers, separated by blanks, with one row per line, and an equal number of elements in each row. For example, create a text file (e.g., using the Windows Notepad editor) containing these four lines Store the file under the name magik.dat. Then the statement load magik.dat reads the file and creates a variable, magik, containing the example matrix. For more powerful file input/output capabilities (i.e., different file structures, binary files, etc.) see the Programming and Data Types..Input/Output in the online MATLAB documentation at http// 5

6 FLOW CONTROL The most useful flow control constructs in MATLAB are if..elseif..else.. switch..case for while continue break if..elseif..else.. The if statement evaluates a logical expression and executes a group of statements based on the value of the expression. In its simplest form, its syntax is if logical_expression statements If the logical expression is true (1), MATLAB executes all the statements between the if and lines and then continues execution at the line following the statement. If the condition is false (0), MATLAB skips all the statements between the if and lines, and resumes execution at the line following the statement. For example if rem(a,2) == 0 disp('a is even') b = a/2; You can nest any number of if statements. It is a good idea to indent the statement blocks for readability, especially when using nested if statements. The optional elseif and else keywords ext the basic if.. construction and enables execution of alternate groups of statements if logical_expression_1 statements executed if logical_expression_1 = true elseif logical_expression_2 statements executed if logical_expression_2 = true else statement executed if none of the above is true Note that at most only one statement block is executed with this construction (i.e., the first elseif statement block for which the associated logical_expression is true, or the else statement block, if present). 6

7 switch..case The switch construction executes certain statements based on the value of a variable or expression. Its basic form is switch expression case value1 statements % Executes if expression is value1 case value2 statements % Executes if expression is value2... otherwise statements % Executes if expression does not % does not match any case It is a good idea to indent the statement blocks for readability. The example code below shows use of the switch statement to check the variable input_num for certain values. If input_num is -1, 0, or 1, the case statements display the value on screen as text. If input_num is none of these values, execution drops to the otherwise statement and the code displays the text 'other value'. switch input_num case -1 disp('negative one'); case 0 disp('zero'); case 1 disp('positive one'); otherwise disp('other value'); Note Unlike the C language switch statement, MATLAB switch does not fall through. If the first case statement is true, the other case statements do not execute. So, break statements are not required. switch can handle multiple conditions in a single case statement by enclosing the case expression in a cell array. switch var case 1 disp('1') case {2,3,4} disp('2 or 3 or 4') case 5 disp('5') otherwise disp('something else') 7

8 for The for loop executes a statement or group of statements a predetermined number of times. Its syntax is for index = startincrement statements The default increment is 1. You can specify any increment, including a negative one. For positive indices, execution terminates when the value of the index exceeds the value; for negative increments, it terminates when the index is less than the value. For example, this loop executes five times. for i = 26 x(i) = 2*x(i-1); You can nest multiple for loops. for i = 1m for j = 1n A(i,j) = 1/(i + j - 1); It is a good idea to indent the loops for readability, especially when they are nested. while The while loop executes a statement or group of statements repeatedly as long as the controlling expression is true (1). Its syntax is while expression statements For example, this while loop finds the first integer n for which n! (n factorial) is a 100-digit number. n = 1; while prod(1n) < 1e100 n = n + 1; n Exit a while loop at any time using the break statement continue The continue statement passes control to the next iteration of the for or while loop in which it appears, skipping any remaining statements in the body of the loop. In nested loops, continue passes control to the next iteration of the for or while loop enclosing it. 8

9 break The break statement terminates the execution of a for loop or while loop. When a break statement is encountered, execution continues with the next statement outside of the loop. In nested loops, break exits from the innermost loop only. GRAPHICS MATLAB has a rich set of built-in functions for creating graphic displays of data and functions. See the Graphics section in the online Getting Started documentation at http// for usage of these graphics features. M-FILES There are two kinds of M-files. Script M-Files Do not accept input arguments or return output arguments Operate on data in the workspace Useful for automating a series of steps you need to perform many times Function M-Files Can accept input arguments and return output arguments Internal variables are local to the function by default Useful for exting the MATLAB language for your application M-files are ordinary text files that you create using a text editor. MATLAB provides a built-in editor, although you can use any text editor you like. Comment lines begin with a percent sign (%). Comment lines can appear anywhere in an M-file, and you can app comments to the of a line of code. For example, % Add up all the vector elements. y = sum(x) % Use the built-in sum function. In addition to comment lines, you can insert blank lines anywhere in an M-file. MATLAB uses a search path to find M-files and other MATLAB-related files. Any file you want to run in MATLAB must reside in the current directory or in a directory that is on the search path. To see which directories are on the search path or to change the search path, select Set Path from the File menu in the desktop, and use the Set Path dialog box. Scripts Scripts are useful for automating series of MATLAB commands, such as computations that you have to perform repeatedly from the command line. They are the simplest kind of M-file because they have no input or output arguments. Scripts operate on existing data in the workspace, or they 9

10 can create new data on which to operate. Any variables that scripts create remain in the workspace after the script finishes so you can use them for further computations. For example, these statements calculate rho for several trigonometric functions of theta, then create a series of polar plots. % An M-file script to produce % Comment lines % "flower petal" plots theta = -pi0.01pi; % Computations rho(1,) = 2*sin(5*theta).^2; rho(2,) = cos(10*theta).^3; rho(3,) = sin(theta).^2; rho(4,) = 5*cos(3.5*theta).^3; for k = 14 polar(theta,rho(k,)) % Graphics output pause These lines can be saved as a script in an M-file called petals.m. Typing petals at the MATLAB command line executes the statements in the script. After the script displays a plot, press Return to move to the next plot. When execution completes, the variables (i, theta, and rho) remain in the workspace. To see a listing of them, enter whos at the command prompt. Functions Functions are M-files that accept input arguments and return output arguments. They operate on variables within their own workspace. This is separate from the workspace you access at the MATLAB command prompt. For example, the following function calculates the average of the elements in a vector. function y = average(x) % AVERAGE Mean of vector elements. % AVERAGE(X), where X is a vector, is the mean of vector elements. % Nonvector input results in an error. [m,n] = size(x); if (m==1 & n>1) (m>1 & n==1) y = sum(x)/length(x); %actual computation else %error--input not a vector error('input must be a vector') These commands are stored in an M-file called average.m. The average function accepts a single input argument and returns a single output argument. To call the average function, enter z = 199; average(z) ans = 50 10

11 The function definition line informs MATLAB that the M-file contains a function, and specifies the argument calling sequence of the function. The function definition line for the average function is Note While the function name specified on the function definition line does not have to be the same as the filename, it is strongly recommed that you use the same name for both. If the function has multiple output values, enclose the output argument list in square brackets. Input arguments, if present, are enclosed in parentheses. Use commas to separate multiple input or output arguments. Here's a more complicated example. function [x, y, z] = sphere(theta, phi, rho) If there is no output, leave the output blank function printresults(x) or use empty square brackets function [] = printresults(x) The variables that you pass to the function do not need to have the same name as those in the function definition line. The function body contains all the MATLAB code that performs computations and assigns values to output arguments. The statements in the function body can consist of function calls, programming constructs like flow control and interactive input/output, calculations, assignments, comments, and blank lines. The values of all local variables within a function are cleared from memory after the function has been exited unless they are explicitly declared persistent. You can call function M-files from either the MATLAB command line or from within other M- files. Be sure to include all necessary arguments, enclosing input arguments in parentheses and output arguments in square brackets. Subfunctions Function M-files can contain code for more than one function. The first function in the file is the primary function, the function invoked with the M-file name. Additional functions within the file are subfunctions that are only visible to the primary function or other subfunctions in the same file. Each subfunction begins with its own function definition line. The functions immediately follow each other. The various subfunctions can occur in any order, as long as the primary function appears first. 11

12 function [avg,med] = newstats(u) % Primary function % NEWSTATS Find mean and median with internal functions. n = length(u); avg = mean(u,n); med = median(u,n); function a = mean(v,n) % Calculate average. a = sum(v)/n; % Subfunction function m = median(v,n) % Calculate median. w = sort(v); if rem(n,2) == 1 m = w((n+1)/2); else m = (w(n/2)+w(n/2+1))/2; % Subfunction Functions within the same M-file cannot access the same variables unless you declare them as global within the pertinent functions (global declaration) or pass them as arguments. return The return statement terminates the current sequence of commands and returns control to the invoking function. A called function normally transfers control to the function that invoked it when it reaches the of the function. return may be inserted within the called function to force an early termination and to transfer control to the invoking function. 12