Introduction to Matlab: Scalars, Vectors, Matrices & Graphics

1. Lecture 2 - Matlab Introduction CVEN 302 August 29, 2001

2. Lecture Goals • Scalar Operations • Vectors Operations • Matrix Operations • Plot & Graphics • Matlab files • Matlab controls

3. Scalar Operations • Addition - a + b • Subtraction - a - b • Multiplication - a * b • Right Division - a / b • Left Division - b \ a • Exponential - a^b

4. Order of Precedence of Arithmetic Operations Precedence ( 1 ) - Parenthesis ( 2 ) - Exponential from left to right ( 3 ) - Multiplication and division from left to right. ( 4 ) - Addition and subtraction from left to right.

5. Vector A vector is defined as a combination of variables values to with components of xj , where j = 1,…n values.

6. Vectors • Matlab is designed for vector and matrix manipulation some of the basic commands are given as

7. Vectors • t’ represents the transpose of the vector “t”. • Individual components can be represented by t = [ 4,5,6,9], where t(3) = 6. • [ ] represent the start and finish of the vector and/or matrix. ( ) represent components of the vector. • A period “.” represent an elemental set of functions, such as multiplication, division,etc.

8. Vector element Operations • Individual addition A + B A + B • Individual subtraction A – B A - B • Individual multiplication A*B A.*B • Individual division (left) A/B A./B • Individual division (right) A\B A.\B • Individual power AB A.^B

9. Hierarchy of the vector operations Precedence ( 1 ) - Parenthesis ( 2 ) - Exponential from left to right ( 3 ) - Multiplication and division from left to right. ( 4 ) - Addition and subtraction from left to right.

10. Vector Operations • Vector product - A is 1 x n vector • The magnitude of the vector is a dot product of the vector.

11. Vector Examples

12. Matrix • A matrix is a two dimensional arrays, where the matrix B is represented by a [ m x n ]

13. Matrix Operations • For addition and subtraction, the matrix sizes must match up. If you are adding to each component of the matrix you can do a simple scalar addition. • Examples: [A] + [B] = [C] [A] + 3 = [D]

14. Matrix Operation • Multiplication of matrices will need to match up the columns to the row values of the following matrix. Scalar multiplication will work. • Division is different. You will either divide member by member, where the matrices are the same size or you will need to find the inverse of the matrix.

15. Matrix Multiplication Examples

16. Graphical Representation • Matlab has a function known as “plot( ), where the values are plotted on an x-y plane. • General format of the graph is given as, plot(x,y,’symbols’) • The symbols represent the color, point shape, and the line type.

17. Plot symbols commands ColorsSymbols Lines y – yellow . – point - – solid line m – mag o – circle : – dots c – cyan x – xmark -. – line dot r – red + – plus - - – dashes g – green * – star b – blue s – square w – white d – diamond k – black v – triangle down ^ – triangle up < – left < – right p – pentagram h – hexagram

18. Plot Commands t = linspace(0, 2*pi); - results in 100 data points y1 = cos(t); - cosine of the points y2 = sin(t); - sine of the points y3 = y1.*y2; - cos(t)*sin(t) plot(t,y1,’-’) ; - plots cosine verse t with a straight line. plot(t,y3,’r:’) - plots cosine*sine verse t with red dots.

19. Plot Commands Example: plot(t,y1,’-’,t,y2,’g*’,t,y3,’r-.’) - plots all 3 axis( [0 2*pi -1.5 1.5]) - adds axes legend(‘cos(t)’,’sin(t)’,’cos(t)*sin(t)’) - legend Note that the [ ] represent an array and ( ) represent a function, and ‘ ‘ represent the symbols.

20. Matlab commands for file management The files can be written as a script, which can be loaded into the memory. From the command line: • “echo” - causes the file to be echoed to the screen. • “what” - shows the type of file in the current directory. • “type” - will present show the file contents

21. Matlab Files There are three types of files: • Data files • Matlab files have their own format for saving data • ascii files are standard text files, which can be printed out or used in excel files. • m-files represent the program files. • function files are functions similar to ‘sin(x)’, cos(x), etc.

22. Data Files Data files can be written in two forms: • Matlab format • ascii format

23. MatLab generates a data file, which will have look like: “filename”.mat File can be loaded into the memory with: load “filename” t = linspace(0, 2*pi) x = cos(t) save data1 t x clear what data1.mat load data1 Matlab data format

24. An ascii file type can be created by adding a flag on the end of the save command save “filename”.dat -ascii t = linspace(0 2*pi) x = sin(t) save data2.dat t x -ascii dir data2.dat clear load data2.dat -ascii ACSII format

25. Matlab Files load “filename” The file will load the file into the same format as it was saved. ASCII Files load “filename.dat” -ascii The file will be loaded as an data array and will require you to modify to obtained the data vectors. Loading Data Files

26. t=linspace(0,2*pi); y1 = sin(x); save data1 t y1; clear (created data1.mat and will show up in home directory.) load data1; (data1 will have created t and y1 vectors.) save data2.dat t y1 -ascii clear (created a ascii file with the data) load data2 -ascii Data file example

27. (loaded an ascii file into memory as data2 array) whos data2 2X100 double array t= data2(1,:); y1= data2(2,:); : assigns the row to the vector Data file example continued

28. Homework • Check the Homework files • create a data file • input a simple program • run the program • plot the results