Engineering H192 – Computer Programming Introduction to MATLAB

Engineering H192 - Computer Programming Introduction to MATLAB Lecture 18 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 1

Engineering H192 - Computer Programming MATLAB MATLAB is a program for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It’s name is derived from MATrix LABoratory. MATLAB has since been expanded and now has builtin functions for solving problems requiring data analysis, signal processing, optimization, and several other types of scientific computations. It also contains functions for 2-D and 3-D graphics and animation. Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 2

Engineering H192 - Computer Programming MATLAB The MATLAB environment is command oriented somewhat like UNIX. A prompt appears on the screen and a MATLAB statement can be entered. When the ENTER key is pressed, the statement is executed, and another prompt appears. If a statement is terminated with a semicolon ( ; ), no results will be displayed. Otherwise results will appear before the next prompt. The following slide is the text from a MATLAB screen. Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 3

Engineering H192 - Computer Programming MATLAB To get started, type one of these commands: helpwin, helpdesk, or demo EDU» a 5; EDU» b a/2 b 2.5000 EDU» Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 4

Engineering H192 - Computer Programming MATLAB Variable Names Variable names ARE case sensitive Variable names can contain up to 63 characters (as of MATLAB 6.5 and newer) Variable names must start with a letter followed by letters, digits, and underscores. Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 5

Engineering H192 - Computer Programming MATLAB Special Variables ans Default variable name for results pi Value of eps Smallest incremental number inf Infinity NaN Not a number e.g. 0/0 i and j i j square root of -1 realmin The smallest usable positive real number realmax The largest usable positive real number Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 6

Engineering H192 - Computer Programming MATLAB Math & Assignment Operators Power Multiplication Division or NOTE: or . a b * or .* a*b / or ./ a/b \ or .\ b\a 56/8 8\56 - (unary) (unary) Addition Subtraction Assignment Winter Quarter or or or or a b a - b a b The Ohio State University Gateway Engineering Education Coalition a. b a.*b a./b b.\a (assign b to a) Lect 18 P. 7

Engineering H192 - Computer Programming Other MATLAB symbols . , % ; : Winter Quarter prompt continue statement on next line separate statements and data start comment which ends at end of line (1) suppress output (2) used as a row separator in a matrix specify range The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 8

Engineering H192 - Computer Programming MATLAB Matrices MATLAB treats all variables as matrices. For our purposes a matrix can be thought of as an array, in fact, that is how it is stored. Vectors are special forms of matrices and contain only one row OR one column. Scalars are matrices with only one row AND one column Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 9

Engineering H192 - Computer Programming MATLAB Matrices A matrix with only one row AND one column is a scalar. A scalar can be created in MATLAB as follows: EDU» a value 23 a value 23 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 10

Engineering H192 - Computer Programming MATLAB Matrices A matrix with only one row is called a row vector. A row vector can be created in MATLAB as follows (note the commas): EDU» rowvec [12 , 14 , 63] rowvec 12 14 Winter Quarter 63 The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 11

Engineering H192 - Computer Programming MATLAB Matrices A matrix with only one column is called a column vector. A column vector can be created in MATLAB as follows (note the semicolons): EDU» colvec [13 ; 45 ; -2] colvec 13 45 -2 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 12

Engineering H192 - Computer Programming MATLAB Matrices A matrix can be created in MATLAB as follows (note the commas AND semicolons): EDU» matrix [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9] matrix 1 4 7 2 5 8 Winter Quarter 3 6 9 The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 13

Engineering H192 - Computer Programming Extracting a Sub-Matrix A portion of a matrix can be extracted and stored in a smaller matrix by specifying the names of both matrices and the rows and columns to extract. The syntax is: sub matrix matrix ( r1 : r2 , c1 : c2 ) ; where r1 and r2 specify the beginning and ending rows and c1 and c2 specify the beginning and ending columns to be extracted to make the new matrix. Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 14

Engineering H192 - Computer Programming MATLAB Matrices A column vector can be extracted from a matrix. As an example we create a matrix below: Here we extract column 2 of the matrix and make a column vector: EDU» matrix [1,2,3;4,5,6;7,8,9] EDU» col two matrix( : , 2) matrix col two 1 4 7 2 5 8 Winter Quarter 3 6 9 2 5 8 The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 15

Engineering H192 - Computer Programming MATLAB Matrices A row vector can be extracted from a matrix. As an example we create a matrix below: EDU» matrix [1,2,3;4,5,6;7,8,9] matrix 1 4 7 2 5 8 Winter Quarter Here we extract row 2 of the matrix and make a row vector. Note that the 2:2 specifies the second row and the 1:3 specifies which columns of the row. EDU» rowvec matrix(2 : 2 , 1 : 3) 3 6 9 rowvec 4 5 6 The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 16

Engineering H192 - Computer Programming Reading Data from files MATLAB supports reading an entire file and creating a matrix of the data with one statement. load mydata.dat; % loads file into matrix. % The matrix may be a scalar, a vector, or a % matrix with multiple rows and columns. The % matrix will be named mydata. size (mydata) % size will return the number % of rows and number of % columns in the matrix length (myvector) % length will return the total % no. of elements in myvector Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 17

Engineering H192 - Computer Programming Plotting with MATLAB MATLAB will plot one vector vs. another. The first one will be treated as the abscissa (or x) vector and the second as the ordinate (or y) vector. The vectors have to be the same length. MATLAB will also plot a vector vs. its own index. The index will be treated as the abscissa vector. Given a vector “time” and a vector “dist” we could say: plot (time, dist) plot (dist) Winter Quarter % plotting versus time % plotting versus index The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 18

Engineering H192 - Computer Programming Plotting with MATLAB There are commands in MATLAB to "annotate" a plot to put on axis labels, titles, and legends. For example: % To put a label on the axes we would use: xlabel ('X-axis label') ylabel ('Y-axis label') % To put a title on the plot, we would use: title ('Title of my plot') Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 19

Engineering H192 - Computer Programming Plotting with MATLAB Vectors may be extracted from matrices. Normally, we wish to plot one column vs. another. If we have a matrix “mydata” with two columns, we can obtain the columns as a vectors with the assignments as follows: first vector mydata ( : , 1) ; % First column second vector mydata ( : , 2) ; % Second one % and we can plot the data plot ( first vector , second vector ) Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 20

Engineering H192 - Computer Programming Some Useful MATLAB commands who List known variables whos List known variables plus their size help Ex: help sqrt Help on using sqrt lookfor Ex: lookfor sqrt Search for keyword sqrt in m-files what Ex: what a: List MATLAB files in a: clear Clear all variables from work space clear x y Clear variables x and y from work space clc Clear the command window Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 21

Engineering H192 - Computer Programming Some Useful MATLAB commands what dir ls type test delete test cd a: chdir a: pwd which test Winter Quarter List all m-files in current directory List all files in current directory Same as dir Display test.m in command window Delete test.m Change directory to a: Same as cd Show current directory Display current directory path to test.m The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 22

Engineering H192 - Computer Programming A Useless, But Interesting, MATLAB command why Winter Quarter In case you ever needed a reason The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 23

Engineering H192 - Computer Programming MATLAB Relational Operators MATLAB supports six relational operators. Less Than Less Than or Equal Greater Than Greater Than or Equal Equal To Not Equal To Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 24

Engineering H192 - Computer Programming MATLAB Logical Operators MATLAB supports three logical operators. not and or Winter Quarter & % highest precedence % equal precedence with or % equal precedence with and The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 25

Engineering H192 - Computer Programming MATLAB Logical Functions MATLAB also supports some logical functions. xor (exclusive or) Ex: xor (a, b) Where a and b are logical expressions. The xor operator evaluates to true if and only if one expression is true and the other is false. True is returned as 1, false as 0. any (x) returns 1 if any element of x is nonzero all (x) returns 1 if all elements of x are nonzero isnan (x) returns 1 at each NaN in x isinf (x) returns 1 at each infinity in x finite (x) returns 1 at each finite value in x Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 26

Engineering H192 - Computer Programming MATLAB Display formats MATLAB supports 8 formats for outputting numerical results. format long 16 digits format short e 5 digits plus exponent format long e 16 digits plus exponent format hex hexadecimal format bank two decimal digits format positive, negative or zero format rat rational number (215/6) format short default display Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 27

Engineering H192 - Computer Programming Matlab Selection Structures An if - elseif - else structure in MATLAB. Note that elseif is one word. if expression1 % is true % execute these commands elseif expression2 % is true % execute these commands else % the default % execute these commands end Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 28

Engineering H192 - Computer Programming MATLAB Repetition Structures A for loop in MATLAB for x array for x 1: 0.5 : 10 % execute these commands end A while loop in MATLAB while expression while x 10 % execute these commands end Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 29

Engineering H192 - Computer Programming Scalar - Matrix Addition EDU» a 3; EDU» b [1, 2, 3;4, 5, 6] b 1 2 3 4 5 6 EDU» c b a % Add a to each element of b c 4 5 6 7 8 9 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 30

Engineering H192 - Computer Programming Scalar - Matrix Subtraction EDU» a 3; EDU» b [1, 2, 3;4, 5, 6] b 1 2 3 4 5 6 EDU» c b - a %Subtract a from each element of b c -2 -1 0 1 2 3 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 31

Engineering H192 - Computer Programming Scalar - Matrix Multiplication EDU» a 3; EDU» b [1, 2, 3; 4, 5, 6] b 1 2 3 4 5 6 EDU» c a * b % Multiply each element of b by a c 3 6 9 12 15 18 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 32

Engineering H192 - Computer Programming Scalar - Matrix Division EDU» a 3; EDU» b [1, 2, 3; 4, 5, 6] b 1 2 3 4 5 6 EDU» c b / a % Divide each element of b by a c 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 33

Engineering H192 - Computer Programming Transferring Data from Class (R:) to temp When using MATLAB in Windows XP, g16.dat is on Class drive (R:) under ENG H192. Do a file transfer by drag and drop to temp directory cd to \temp in MATLAB load g16.dat to produce a matrix called g16 Create two vectors from the g16 two column matrix Plot vector2 vs vector1 Winter Quarter The Ohio State University Gateway Engineering Education Coalition Lect 18 P. 34