What is Matlab? The command line Variables Operators Functions

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2 What is Matlab? The command line Variables Operators Functions

3 Vectors Matrices Control Structures Programming in Matlab Graphics and Plotting

4 A numerical computing environment Simple and effective programming language Matrix and vector-based Includes: conditionals, loops, user-defined recursive functions input and output facilities, tools

5 Can be used for: Implementation of algorithms Mathematics and computation Plotting of information Data manipulation Easy vector and matrix entering and manipulation Interfacing with programs in other languages

6 Matlab as a calculator (=7) (cos(pi) + sin(pi)) (=-1) mean([ ]) (=3) Assignment a = 4 b = 10 d = exp(log(a+b)) (=14) f = tan(a+b)*cos(a+b)/sin(a+b) (=1)

7 General Variables ans: (standard output) pi: (=3.1416) i: (= i) inf: (=Inf) New (Assigned) Variables a1=2; b1=sin(pi/2) c=sqrt(5*a1-b1) (= 3) s= welcome

8 Arithmetical Operators + addition - subtraction * multiplication /, \ division (right, left) ^ exponentiation mod(x,y) modulus (x mod y) x %/% y integer division

9 Logical Operators == equal!= not equal to >,< greater, less than >=,<= greater or equal, less or equal! logical not & logical and logical or

10 Numerical Functions abs(x) absolute value sqrt(x) square root ceil(x) ceiling floor(x) floor round(x, n) round cos(x), sin(x), tan(x), acos(x), cosh(x), acosh(x) log(x) logarithm exp(x) or e^x exponential function

11 Statistical Functions mean(x) sd(x) var(x) quantile(x, p) range(x) sum(x) diff(x) min(x), max(x) mean standard deviation variance p-quantile range sum difference minimum, maximum

12 General Functions who All current variables whos All current variables and their size clear a Clear variable (function) a clear Clear all variables and functions clear all Clear all variables functions and debugging breakpoints close Close Figures

13 General Functions gwd The current directory cd Change the current directory format Set output format clc Clears all input and output from the Command Window

14 Help-Functions help elfun help elmat help( f ) help ops help plot Help for all functions Help for all matrices Help for the function f Help for all Operators Help for Plotting

15 Inline Functions Define a inline function ans: f=inline('sin(x)/cos(x)'); f Inline function: f(x) = sin(x)/cos(x) f(pi/4) (= )

16 Defining by square braces v=[ ] (v = ) v=[1:5] (v = ) v=[1:0.5:2] (v = ) Defining by assignment v=1;v(1)=1;v(2)=22;v(3)=33;v(4)=43;v(5)=555; v (= )

17 Transpose v ans =

18 Accessing Elements v=[1:5] (= ) v(3) (= 3) v(2:4) (= 2 3 4) v(1:2:5) (= 1 3 5) v(3)+v(4)*v(1) (= 7) v(2:4)+v(3:5) (= 5 7 9)

19 Basic operations on vectors = assignment +, - addition, subtraction ^ power function.^ componentwise power function * multiplication.* componentwise multiplication /, \ rigth, left division./,.\ componentwise right, left division

20 Basic operations on vectors (Examples) u=[1:5]; v=[5:-1:1] u+v (= ) u-v (= ) u.^2 (= ) u*v (= 35) u.*v (= ) u./v (= ) u.\v (= )

21 Basic operations on vectors (Examples) u/v (= ) u\v ans =

22 Defining by square braces m = [ 1 2 3; 4 5 6; 7 8 9] m =

23 Defining as a row of column vectors m = [ [1 4 7]' [2 5 8]' [3 6 9]'] m =

24 The transpose matrix of m is defined by m ans =

25 Accessing Elements m = [ 1 2 3; 4 5 6; 7 8 9] m(2,3) (= 6) m(1:2,2:3) ans = m(2,2)+m(1,1) (= 6)

26 Basic operations on matrices = assignment +, - addition, subtraction ^ power function.^ componentwise power function * multiplication.* componentwise multiplication /, \ rigth, left division./,.\ componentwise right, left division

27 Basic operations on matrices (Example) m = [ 1 2 3; 4 5 6; 7 8 9]; n = [ 1 4 7; 2 5 8; 3 6 9]; m+n ans =

28 Basic operations on matrices (Example) m*n ans = n^2 ans =

29 Basic operations on matrices (Example) n.*m ans = m./n ans =

30 if Statement Syntax if expression statement; end if expression statement1; statement2; end

31 if Statement Example a = 2; b=3 if (a<b) c = a; end (c = 2) if (a<b) c = a+b; d =c+b; end (d = 8)

32 If-else Statement Syntax if expression statementif; else statementelse; end if expression statementif1; statementif2; else statementelse1; statementelse2; end

33 If-else Statement Example a = 2; b=3 if (a>b) c = a; else c=b end (c = 3) if (a>b) c = a+b; d =c+b; else c = a+b; d =c-b; end (d = 2)

34 switch Statement Syntax switch switch_expr case case_expr statement,..., statement case {case_expr1, case_expr2, case_expr3,...} statement,..., statement otherwise statement,..., statement end

35 switch Statement Example method = 'Bilinear'; switch lower(method) case {'linear','bilinear'} disp('method is linear') otherwise disp('unknown method.') end (Method is linear)

36 while loop Syntax while expression statement; end while expression statement1; statement2; end

37 while loop Example a=1;b=4; while a<b a=a+1 end a = 2 a = 3 a = 4

38 for loop Syntax for i=initval:stepval:endval statement; end for i=initval:stepval:endval statement1; statement2; end

39 for loop Example a=1; for i=1:5:300 a(i)=i+1; end for i=1:300 a(i)=i*2; end

40 Scripts Have no input or output arguments Variable are stored in MATLAB workspace Usually implemented in MATLAB workspace Functions Are program routines Accept input arguments and return output arguments Usually implemented in M-files

41 Scripts (Example) Fibonacci Numbers M-file function to compute the first 10 Fibonacci Numbers % Definiton: f(1)=1, f(2)=1, f(k)=f(k-1)+f(k-2) f=zeros(1,10); f(1)=1; f(2)=1; for i=3:10 f(i)=f(i-1)+f(i-2); end f (f = )

42 Declare M-file function Syntax function [out1, out2,...] = funname(in1,in2,...) % Online Help %Comments, eg, Input, Output, Function code end Defines function funname with inputs in1, in2, etc. and return outputs out1, out2, etc.

43 Declare M-file function ExampleFibonacci Numbers function f = fibonacci(n) % An M-file function to compute the Fibonacci Numbers % Definiton: f(1)=1, f(2)=1, f(k)=f(k-1)+f(k-2) f=zeros(n,1); f(1)=1; f(2)=2; for i=3:n f(i)=f(i-1)+f(i-2); end end f(10) (f = )

44 Basic Plotting plot title x/ylabel grid legend Hold axis plot a a function or a data outputs the title. labels the x/y-axis of the current axes grid lines for 2-D and 3-D plots outputs a legend. retain current graph in figure manipulates used axes properties

45 Basic Plotting (Example) x = -pi:0.1:pi; plot(x,sin(x)); title('sin(x)');xlabel('x'), ylabel('y');

46 Basic Plotting (Example) [X1,X2]=meshgrid([-pi:.05:pi]); Z=((pi^2)/4)*(sin(pi*X1).*sin(pi*X2)); figure; plot3(x1,x2,z); legend('f(x_1,x_2)=\pi^2/4*sin(\pix_1)*sin(\pix_2)') xlabel('x_1','fontsize',12,'fontweight','b'); ylabel('x_2','fontsize',12,'fontweight','b'); zlabel('f(x_1,x_2)','fontsize',12,'fontweight','b');

47 Basic Plotting (Example)

48 Mesh and Surface meshgrid mesh surf colorbar patch hidden generate X and Y arrays for 3-D plots draws a wireframe mesh plot a 3-D shaded surface add a colorbar tool creating patch graphics objects remove hidden lines from mesh plot

49 Mesh and Surface [X1,X2]=meshgrid([-pi:.05:pi]); Z=((pi^2)/4)*(sin(pi*X1).*sin(pi*X2)); figure; surf(x1,x2,z); legend('f(x_1,x_2)=\pi^2/4*sin(\pix_1)*sin(\pix_2)') xlabel('x_1','fontsize',12,'fontweight','b'); ylabel('x_2','fontsize',12,'fontweight','b'); zlabel('f(x_1,x_2)','fontsize',12,'fontweight','b');

50 Mesh and Surface