1. Programming in MATLAB ME 303

2. Outline of Lecture What is Matlab? Windows? Data Types –arrays: char, numeric, struct, cell Operators –arithmetic, relational, logical Flow Control –conditionals, case, while, etc. M-functions –syntax –examples of simple functions –writing and debugging a simple MATLAB function

3. What is Matlab ? MATLAB® is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar noninteractive language such as C or Fortran. So where other programming languages work with numbers one at a time, MATLAB allows you to work with entire matrices quickly and easily.FORTRAN: real*8 A(10,10), B(10,10), C(10,10) do i=1,10 do j=1,10 C(i,j) = A(i,j) + B(i,j) 10 continue 20 continue MATLAB: C = A + B The name MATLAB stands for matrix laboratory.

4. A software environment for interactive (No need to declare variables) numerical computations >> 2+3*4/2 >> a=5e-3; b=1; a+b Examples: –Matrix computations and linear algebra –Solving nonlinear equations –Numerical solution of differential equations –Mathematical optimization –Statistics and data analysis –Signal processing –Modelling of dynamical systems –Solving partial differential equations –Simulation of engineering systems What is Matlab ?

6. M-file editor/debugger window

7. Getting Help To get help: MATLAB main menu -> Help -> MATLAB Help

8. Type one of the following commands in the command window: –help – lists all the help topics –help topic – provides help for the specified topic –help command – provides help for the specified command –helpwin – opens a separate help window for navigation –Lookfor keyword – search all M-files for keyword Online resource( http://www.mathworks.com ) http://www.mathworks.com >> demo in matlab Getting Help

9. Variables Variable names: –Must start with a letter. –May contain only letters, digits, and the underscore “_”. –MATLAB is case sensitive, for example one & ONE are different variables. –MATLAB only recognizes the first 31 characters in a variable name. Assignment statement: –Variable = number; –Variable = expression; Example: >> t = 1234; –>> t = 1234 –t = – 1234

10. Variables Special variables: –ans: default variable name for the result. –pi: π = 3.1415926 …… –eps: ε= 2.2204e-016, smallest value by which two numbers can differ –inf: ∞, infinity –NAN or nan: not-a-number Commands involving variables: –who: lists the names of the defined variables –whos: lists the names and sizes of defined variables –clear: clears all variables –clear name: clears the variable name –clc: clears the command window –clf: clears the current figure and the graph window

11. Arrays A row vector in MATLAB can be created by an explicit list, starting with a left bracket, entering the values separated by spaces (or commas) and closing the vector with a right bracket. A column vector can be created the same way, and the rows are separated by semicolons. Example: –>> x = [ 0 0.25*pi 0.5*pi 0.75*pi pi] –x = x is a row vector. – 0 0.7854 1.5708 2.3562 3.1416 –y=[0; 0.25*pi; 0.5*pi; 0.75*pi; pi] –y = y is a column vector. – 0 – 0.7854 – 1.5708 – 2.3562 – 3.1416

12. Vector Addressing- A vector element is addressed in MATLAB with an integer index enclosed in parentheses. Example: –>> x(3) –ans = – 1.5708 <- 3rd element of vector X The colon notation may be used to address a block of elements (start:increment:end) Example: –>> x(1:2:5) –ans = – 0 1.5708 3.1416 Arrays

13. Some useful commands: x = start:end Create row vector x starting with start, counting by 1, ending at end x = start:increment:end Create row vector x starting with start, counting by increment, ending at or before end x = linspace(start,end,number) Create linearly spaced row vector x starting with start, ending at end, having number elements x = logspace(start,end,number) Create logarithmically spaced row vector x starting with start, ending with end, having number elements length(x)Returns the length of vector x y = x’Transpose of vector x dot(x,y),cross(x,y) Returns the scalar dot and vector cross product of the vector x and y Arrays

14. Matrices A matrix –rectangular array of numbers –1-by-1 matrices, which are scalars, and –to matrices with only one row or column, which are vectors. –It begins with [, and end with ] –Spaces or commas are used to separate elements in a row –Semicolon or enter is used to separate rows A = [1,2,3;4,-5,6;5,-6,7] MATLAB has other ways of storing both numeric and nonnumeric data, but in the beginning, it is usually best to think of everything as a matrix.

15. Matrices Indexing Matrices Indexing using parentheses >> A(2,3) Index submatrices using vectors of row and column indices >> A([2 3],[1 2]) Ordering of indices is important! >> B=A([3 2],[2 1]) >> B=[A(3,2),A(3,1);A(2,2);A(2,1)]

16. Indexing Matrices Index complete row or column using the colon operator >> A(1,:) Can also add limit index range >> A(1:2,:) >> A([1 2],:) General notation for colon operator >> v=1:5 >> w=1:2:5 Matrices

17. Element-by-Element Array-Array Mathematics Example: >> x = [1 2 3]; >> y = [4 5 6]; >> z = x.* y z = 4 10 18 operationAlgebraic FormMATLAB Additiona + b Subtractiona – b Multiplicationa x ba.* b Divisiona / ba./ b Exponentiationabab a.^ b Matrices

18. zeros(n)Returns a n X n matrix of zeros zeros(m,n)Returns a m X n matrix of zeros ones(n)Returns a n X n matrix of ones ones(m,n)Returns a m X n matrix of ones size(A) For a m X n matrix A, returns the row vector [m,n] containing the number of rows and columns in matrix length(A)Returns the larger of the number of rows or columns in A TransposeB=A’ Identity Matrix eye(n) -> returns an n X n identity matrix eye(m,n) -> returns an m X n matrix with ones on the main diagonal and zeros elsewhere Addition and SubtractionC =A +B C =A - B Scalar MultiplicationB = α A, where α is a scalar Matrix MultiplicationC = A * B Matrix InverseB = inv(A), A must be a square matrix in this case Matrix powersB = A * A, A must be a square matrix Determinantdet(A), A must be a square matrix

19. Expressions Numbers 3 -99 0.0001 9.6397238 1.60210e-20 6.02252e23 1i -3.14159j 3e5i All numbers are stored internally using the long format. 16 significant decimal digits and a finite range of roughly 10-308 to 10+308. Variables S=5, Ali=6, a=4 A=3 a=? Functions Help elfun Help specfun Help elmat Variables are stored in the workspace who – list current variables whos – detailed list of variables clear – removes all variables from the workspace

20. Data Types in MATLAB

22. Uint8 and Doubles(Numeric) Double –almost all MATLAB functions expect doubles as arguments return doubles e.g., need to convert uint8 to double before performing any math operations » a = 1:10 a = 1 2 3 4 5 6 7 8 9 10 » b = uint8(a) b = 1 2 3 4 5 6 7 8 9 10 » whos Name Size Bytes Class a 1x10 80 double array b 1x10 10 uint8 array » b*2 ??? Error using ==> * Function '*' not defined for variables of class 'uint8'. » (double(b))*2 ans = 2 4 6 8 10 12 14 16 18 20

23. Char Data Type » c = ['hello']; » whos Name Size Bytes Class c 1x5 10 char array Grand total is 5 elements using 10 bytes » c(1) ans = h » d = [c,' again']; » d d = hello again » » b = ['hello';'again']; » size(b) ans = 2 5 » b b = hello again » name = 'Thomas R. Lee'; The class and ischar functions show name's identity as a character array: class(name) ans = char ischar(name) ans = 1

24. Structure Data Type image.name = 'Tom'; » image.height = 3; » image.width = 3; » image.data = [8 10 2; 22 7 22; 2 4 7]; » whos Name Size Bytes Class image 1x1 590 struct array Grand total is 18 elements using 590 bytes >> image.name = 'Tom' image = name: 'Tom' >> image.height = 3; >> image.height = 3 image = name: 'Tom' height: 3 >> image.data = [8 10 2; 22 7 22; 2 4 7] image = name: 'Tom' height: 3 data: [3x3 double] >> image.width = 3 image = name: 'Tom' height: 3 data: [3x3 double] width: 3 >> image image = name: 'Tom' height: 3 data: [3x3 double] width: 3

25. A cell array provides a storage mechanism for dissimilar kinds of data. You can store arrays of different types and/or sizes within the cells of a cell array. For example, you can store a 1-by-50 char array, a 7-by-13 double array, and a 1-by-1 uint32 in cells of the same cell array. To access data in a cell array, you use the same matrix indexing as with other MATLAB matrices and arrays. However, with cell array indexing, you use curly braces, {}, instead of square brackets an parentheses around the array indices. For example, A{2,5} accesses the cell in row 2 and column 5 of cell array A. Cell Arrays Data Type

26. Operators Arithmetic –numeric computations, e.g., 2^10 Relational –quantitative comparison of operands –e.g., a < b Logical –AND, OR, NOT –return Boolean variable, 1 (TRUE) or 0 (FALSE)

27. Arithmetic Operators Transpose, a’ Power, a^2 Addition, multiplication, division – a(1)*b(2) –a*b works if a and b are matrices with appropriate dimensions (columns(a) = rows(b)) –a.*b (element by element) except for matrix operations, most operands must be of the same size, unless one is a scalar

28. Arithmetic Operators Transpose, a’ Power, a^2 Addition, multiplication, division – a(1)*b(2) –a*b works if a and b are matrices with appropriate dimensions (columns(a) = rows(b)) –a.*b (element by element) except for matrix operations, operands must be of the same size, unless one is a scalar » a = [2 3]; » b = [4 5]; » a(1)*b(2) ans = 10 » a*b ??? Error using ==> * Inner matrix dimensions must agree. » a*b' ans = 23 » a.*b ans = 8 15 » b/2 ans = 2.0000 2.5000

29. Relational Operators, >=, ==, ~= compare corresponding elements of arrays with same dimensions if one is scalar, one is not, the scalar is compared with each element result is element by element, 1 or 0

30. Relational Operators, >=, ==, ~= compare corresponding elements of arrays with same dimensions if one is scalar, one is not, the scalar is compared with each element result is element by element 1 or 0 » a a = 2 3 » b b = 4 5 » a > b ans = 0 0 » b > a ans = 1 1 » a > 2 ans = 0 1

31. Logical Operators Logical operators (combinations of relational operators) &(and) |(or) ~(not) Logical functions xor isempty any all

32. Flow Control If –if logical_expression – statements –End if (beta(1)==0)&(alpha(1)~=0) K(1,1)=K(1,1)-(ko*beta(1)/alpha(1)); F(1)=F(1)-(ko*gama(1)/alpha(1)); end Else and elseif The else statement has no logical condition. The statements associated with it execute if the preceding if (and possibly elseif condition) is false (0). The elseif statement has a logical condition that it evaluates if the preceding if (and possibly elseif condition) is false (0). The statements associated with it execute if its logical condition is true (1). You can have multiple elseif statements within an if block. if n < 0 % If n negative, display error message. disp('Input must be positive'); elseif rem(n,2) == 0 % If n positive and even, divide by 2. A = n/2; else A = (n+1)/2; % If n positive and odd, increment and divide. end

33. Flow Control switch, case, and otherwise switch expression (scalar or string) case value1 statements % Executes if expression is value1 case value2 statements % Executes if expression is value2. otherwise statements % Executes if expression does not % match any case end switch input_num case -1 disp('negative one'); case 0 disp('zero'); case 1 disp('positive one'); otherwise disp('other value'); end

34. Flow Control Use the for statement to loop a specific number of times. The while statement is more suitable for basing the loop execution on how long a condition continues to be true or false. For for index = start:increment:end statements end for m = 1:5 for n = 1:100 A(m, n) = 1/(m + n - 1); end While while expression statements end while prod(1:n) < 1e100 n = n + 1; end

35. 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. Flow Control fid = fopen('magic.m', 'r'); count = 0; while ~feof(fid) line = fgetl(fid); if isempty(line) | strncmp(line, '%', 1) continue end count = count + 1; end disp(sprintf('%d lines', count));

36. Flow Control 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 fid = fopen('fft.m', 'r'); s = ''; while ~feof(fid) line = fgetl(fid); if isempty(line) break end s = strvcat(s, line); end disp(s)

37. a=input('a='); b=input('b='); c=input(‘please neter the value…’); input-output user_entry = input('prompt') displays prompt as a prompt on the screen, waits for input from the keyboard, and returns the value entered in user_entry. user_entry = input('prompt','s') returns the entered string as a text variable rather than as a variable name or numerical value reply = input('Do you want more? Y/N [Y]: ','s'); if isempty(reply) reply = 'Y'; end count = fprintf(fid,format,A,...) formats the data in the real part of matrix A (and in any additional matrix arguments) under control of the specified format string, and writes it to the file associated with file identifier fid. Fid is 1 for standard output (the screen) or 2 for standard error. The format argument is a string containing C language conversion specifications

38. input-output fprintf('A unit circle has circumference %g radians.\n',2*pi) A unit circle has circumference 6.283186 radians. B = [8.8 7.7; 8800 7700] fprintf(1,'X is %6.2f meters or %8.3f mm\n',9.9,9900,B) display the lines: X is 9.90 meters or 9900.000 mm X is 8.80 meters or 8800.000 mm X is 7.70 meters or 7700.000 mm

39. A,B,C Δ <0 ? Yes No A=0 ? No solution Yes No X1=….. X2=….. clear disp('This program is written... ') fprintf('\n') a=input('enter a='); while a==0 disp('a ya sifirdan farkli bir deger veriniz') a=input('Please re-enter the value of a='); end Delta=b^2-4*a*c; if Delta<0 ‘No solution’ else x1=(-b+sqrt(Delta))/(2*a); x2=(-b-sqrt(Delta))/(2*a); fprintf('First root=%5.5f \nSecond root=%5.5f',x1,x2) end

40. Plotting type help graph2d... Plotting a point: –>>plot (variablename, ‘symbol’) Example: Complex variable >>z = 1 + 0.5j; >>plot(z,‘*') Commands for axes: CommandDescription axis([xmin xmax ymin ymax])Define minimum and maximum values of the axes axis squareProduce a square plot axis equalEqual scaling factors for both axes axis normalTurn off axis square, equal axis (auto)Return the axis to defaults

41. Plotting Plotting curves: –plot(x,y) – generate a linear plot of the values of x (horizontal axis) and y (vertical axis) –semilogx(x,y) - generate a plot of the values of x (logarithmic scale) and y (linear scale) –semilogy(x,y) - –loglog(x,y) - generate a plot of the values of x and y (both logarithmic scale) Multiple curves –plot(x,y,w,z) – multiple curves can be plotted on the same graph: y vs. x and z vs. w –legend(‘string1’,’string2’, …) – used to distinguish between plots on the same graph Multiple figures –figure(n) – use in creation of multiple plot windows before the command plot() –close – closes the figure n window –close all – closes all the plot windows Subplots: –subplot(m,n,p) – m by n grid of windows, with p specifying the current plot as the pth window

42. Plotting Example: (polynomial function) –Plot the polynomial using linear/linear, log/linear, linear/log, log/log scale >>% generate te polynomial: >>x=linspace(0,10,100); >>y=2*x.^2+7*x+9; >>% plotting the polynomial: >>figure(1); >>subplot(2,2,1),plot(x,y); >>title('polynomial, linear/linear scale'); >>ylabel('y'),grid; >>subplot(2,2,2),semilogx(x,y); >>title('polynomial, log/linear scale'); >>ylabel('y'),grid; >>subplot(2,2,3),semilogy(x,y); >>title('polynomial, linear/log scale'); >>ylabel('y'),grid; >>subplot(2,2,4),loglog(x,y); >>title('polynomial, log/log scale'); >>ylabel('y'),grid;

43. Plotting Adding new curves to the exsiting graph Use the hold command to add lines/points to an existing plot –hold on – retain existing axes, add new curves to current axes. –hold off – release the current figure windows for new plots Grids and labels: CommandDescription grid onAdd dashed grids lines at the tick marks grid offRemoves grid lines (default) GridToggles grid status (off to on or on to off) title(‘text’)Labels top of plot with text xlabel(‘text’)Labels horizontal (x) axis with text ylabel(‘text’)Labels vertical (y) axis with text text(x,y,’text’)Adds text to location (x,y) on the current axes, where (x,y) is in units from the current plot

44. M-Files Before, we have executed the commands in the command window. The more general way is to create a M-file. The M-file is a text file that consists a group of MATLAB commands. MATLAB can open and execute the commands exactly as if they were entered at the MATLAB command window. To run the M-files, just type the file name in the command window. (make sure the current working directory is set correctly)

45. User Defined Function Add the following command in the beginning of your m-file: function [output variables] = function_name (input variables); –Note: the function_name should be the same as your file name to avoid confusion. Calling your function: –A user-defined function is called by the name of the m-file, not the name given in the function definition. –Type in the m-file name like other pre-defined commands. Comments: –The first few lines should be comments, as they will be displayed if help is requested for the function name. the first comment line is reference by the lookfor command.

46. Example ( circle1.m) function y = circle1(center,radius,nop,style) % circle1 draws a circle with center defined as a vector 'center' % radius as a scalar 'radius'. 'nop' is the number of points on the circle % 'style' is the style of the point. % Example to use: circle1([1 3],4,500, ':'); [m,n] = size(center); if (~((m == 1) | (n == 1)) | (m == 1 & n == 1)) error('Input must be a vector') end close all x0=center(1); y0=center(2); t0=2*pi/nop; axis equal axis([x0-radius-1 x0+radius+1 y0-radius-1 y0+radius+1]) hold on for i=1:nop+1 pos1=radius*cos(t0*(i-1))+x0; pos2=radius*sin(t0*(i-1))+y0; plot(pos1,pos2,style); end User Defined Function

47. In command window: –>> help circle1 –circle1 draws a circle with center defined as a vector 'center' radius as a scalar 'radius'. 'nop' is the number of points on the circle 'style' is the style of the point – Example to use: circle1([1 3],4,500,':'); Example: plot a circle with center (3,1), radius 5 using 500 points and style '--': –>> circle1([3 1],5,500,'--'); Result in the Figure window

48. References Matlab help www.mathworks.com 58:111 Numerical Calculations (Univ. Of Iowa) 2E1215 course of Mikael Johanson Dr. Ali A. JalaliMatlab Workshop of Dr. Ali A. Jalali Hakan Çopur’s Introductory Matlab PresentationHakan Çopur’s Introductory Matlab Presentation