1. Outline What is MATLAB MATLAB desktop Variables, Vectors and Matrices Matrix operations Array operations Built-in functions: Scalar, Vector, Matrix Data visualization− 2D Plots Flow control: ‘if’, ‘for’ User-defined functions 1

2. High level language for technical computing Stands for Matrix Laboratory Easy to do linear algebra, calculus, signals and systems and the most complex calculations a human brain can think of. What is MATLAB MATLAB High level languages, C, C++, Basic, Fortran, Pascal, etc. Assembly Language 2

3. MATLAB desktop 3

4. MATLAB desktop (cont.) 1.Menu and toolbar 2.Command window 4

5. MATLAB desktop (cont.) 3.Command history4.Workspace 5

6. MATLAB desktop (cont.) 5.Variable editor 6

7. MATLAB desktop (cont.) 6.Editor 7

8. MATLAB basics What is difference? VariableVector/ArrayMatrix 1×1 Single value 1×N or M×1 Row or column vector M×N 8

9. Variables No need for types. i.e. All variables are created with double precision unless specified. After these statements, the variables are 1×1 matrices with double precision. Enter ‘who’ command in command window to view all active variables Enter ‘whos’ command to view all active variables with their size, allocated memory size and type of variable. int a; double b; float c; Example: >> a = 5; >> b = 2; 9

10. Vectors or Row vectorColumn vector >> r = [1 2 3 4 5]; or r = [1,2,3,4,5]; >> c = [6;7;8;9;10]; 10

11. Matrices Almost all entities in MATLAB are matrices. Order of Matrix − m × n m = number of rows n = number of rows Vectors are special case of Matrices − m = 1row vector − n = 1column vector Define A vector is always a matrix but a matrix is not necessarily a vector Use ‘size (variable/vector/matrix name)’ to find its size. >> A = [1 2; 3 4] >> B = [16 3 5; 7 5 10] 11

12. Creating Vectors Creating vector with equally spaced intervals >> x = 0:0.5:2 x = 0 0.5000 1.0000 1.5000 2.0000 Creating vector with n equally spaced intervals >> x = linspace(0,2,5) x = 0 0.5000 1.0000 1.5000 2.0000 12

13. Creating Matrices from functions zeros(m, n): matrix with all zeros ones(m, n): matrix with all ones. eye(m, n): the identity matrix rand(m, n): uniformly distributed random randn(m, n): normally distributed random magic(m): square matrix whose elements have the same sum, along the row, column and diagonal. 13

14. Matrix operations ^ : exponentiation * : multiplication / : division \ : left division. The operation A\B is effectively the same as INV(A)*B, although left division is calculated differently and is much quicker. + : addition - : subtraction 14

15. Array operations Evaluated element by element.’ : array transpose.^ : array power.* : array multiplication./ : array division Very different from Matrix operations 15

16. Example Perform the following task. Define matrices ‘A’ and ‘B’ >> A=[1 2;3 4]; >> B=[5 6;7 8]; Find product of ‘A’ and ‘B’ using Matrix and Array operator. Which one is correct?? Hint: Solve on paper before using MATLAB 16

17. Matrix Indexing Given the matrix: Then: A(1,2) = 0.6068 A(3) = 0.6068 A(:,1) = [0.9501 0.2311 ] A(1,2:3)=[ 0.6068 0.4231 ] 17

18. Adding Elements to a Vector or a Matrix >> C=[1 2; 3 4] C= 1 2 3 4 >> C(3,:)=[5 6]; C= 1 2 3 4 5 6 >> D=linspace(4,12,3); >> E=[C D’] E= 1 2 4 3 4 8 5 6 12 >> A=1:3 A= 1 2 3 >> A(4:6)=5:2:9 A= 1 2 3 5 7 9 >> B=1:2 B= 1 2 >> B(5)=7; B= 1 2 0 0 7 18

19. Built-in Functions: Scalar Functions sin: trigonometric sine cos: trigonometric cosine tan: trigonometric tangent asin: trigonometric inverse sine (arcsine) acos: trigonometric inverse cosine (arccosine) atan: trigonometric inverse tangent (arctangent) exp: exponential log: natural logarithm log10: base 10 logarithm abs: absolute value angle: phase value sqrt: square root rem: remainder 19

20. Built-in Functions: Vector Functions max: largest component min: smallest component length: length of a vector sort: sort in ascending order sum: sum of elements prod: product of elements mean: mean value std: standard deviation 20

21. Built-in Functions: Matrix Functions size: size of a matrix det: determinant of a square matrix inv: inverse of a matrix rank: rank of a matrix rref: reduced row echelon form eig: eigenvalues and eigenvectors poly: characteristic polynomial lu: LU factorization qr: QR factorization chol: cholesky decomposition svd: singular value decomposition 21

22. Data visualization − 2D plots If ‘x’ and ‘y’ are two vectors of the same length then ‘ plot(x,y) ’ plots x versus y. Example: Plot y=cos(x) from −π to π with increment of 0.01 » x=-pi:0.01:pi; » y=cos(x); » plot(x,y) 22

23. 2D plots − Overlay plots To change curve style, specify marker style plot(xdata, ydata, ‘marker_style’); Example >> x=-5:0.1:5; >> y=x.^2; >> p1=plot(x, y, 'r:s'); Use hold on for overlaying graphs >> hold on; >> z=x.^3; >> p2=plot(x, z,‘b-o'); 23

24. 2D plots − Annotation Use title, xlabel, ylabel and legend for annotation Example >> title('Demo plot'); >> xlabel('X Axis'); >> ylabel('Y Axis'); >> legend([pl, p2], 'x^2', 'x^3'); 24

25. 2D plots − Line types y: yellow m: magenta c: cyan r: red g: green b: blue w: white k: black.: point o: circle x: x-mark +: plus -: solid *: star :: dotted -.: dashdot --: dashed 25

26. 2D plots − Other commands figure: opens new window for plot close all: closes all opened figures subplot: creates an array of plots in the same window loglog: plot using log-log scale semilogx: plot using log scale on the x-axis semilogy: plot using log scale on the y-axis 26

27. Flow control: ‘for’ loop A loop is a statement which is executed repeatedly. If you want to repeat some commands, you can use ‘for’ loop. Must tell MATLAB where to start and where to end. for index = start : end program statements : end Example for i=1:4 i end 27

28. Flow control: ‘if’ statement Execute statements if condition is true if (condition_1) program statements elseif (condition_2) program statements else program statements end 28 Dummy examples if (x<5) : end if (a<3) : elseif (b~=5) : end

29. Flow control: Operators 29 Logical operators <: less than >: greater than <=: less than or equal to >=: greater than or equal to ==: equal to ~=: not equal to Logical operators &: and |: or ~: not

30. User-defined functions 30 Functions are m-files which can be executed by specifying some inputs and supply some desired outputs. function output = functionname(inputs) function [out1,out2,…] = functionname(in1,in2…) Write this command at the beginning of the m-file and save the m-file with a file name same as the function name.

31. User-defined functions (cont.) 31 Examples Write a function which takes a number and returns its square. Write a function which takes the square of the input matrix if the input indicator is equal to 1. And takes the element by element square of the input matrix if the input indicator is equal to 2