1. MEGN 536 – Computational Biomechanics MATLAB: Getting Started Prof. Anthony J. Petrella Computational Biomechanics Group

2. MATLAB Window Command line History Workspace tab (active here) Current directory contents variables in workspace and their values

3. MATLAB Help  To obtain help with any known MATLAB command just type… >> help command_name  To search the help files just select MATLAB Help from the top level menu, hit the F1 key, or type… >> doc

4. Symbol Operation MATLAB form ^ exponentiation: a b a^b * multiplication: ab a*b / right division: a/b a/b \ left division: b/a a\b + addition: a + b a + b - subtraction: a - b a - b Scalar Arithmetic Operations

5. Entering Commands and Expressions  MATLAB retains your previous keystrokes.  Use the up-arrow key to scroll back back through the commands.  Press the key once to see the previous entry, and so on.  Use the down-arrow key to scroll forward. Edit a line using the left- and right-arrow keys the Backspace key, and the Delete key.  Press the Enter key to execute the command.

6. Command Description ans Temporary variable containing the most recent answer. eps Specifies the accuracy of floating point precision. i,j The imaginary unit  1. Inf Infinity. NaN Indicates an undefined numerical result. pi The number . Special Variables and Constants

7. Precedence Operation FirstParentheses, evaluated starting with the innermost pair. SecondExponentiation, evaluated from left to right. ThirdMultiplication and division with equal precedence, evaluated from left to right. FourthAddition and subtraction with equal precedence, evaluated from left to right. Order of Precedence

8. >> 8 + 3*5 ans = 23 >> 8 + (3*5) ans = 23 >>(8 + 3)*5 ans = 55 >>4^2­12­ 8/4*2 ans = 0 >>4^2­12­ 8/(4*2) ans = 3 Examples of Precedence

9. >> 3*4^2 + 5 ans = 53 >>(3*4)^2 + 5 ans = 149 >>27^(1/3) + 32^(0.2) ans = 5 >>27^(1/3) + 32^0.2 ans = 5 >>27^1/3 + 32^0.2 ans = 11 Examples of Precedence (continued)

10. CommandDescription clc Clears the Command window. clear Removes all variables from memory. clear v1 v2 Removes the variables v1 and v2 from memory. exist(‘var’) Determines if a file or variable exists having the name ‘ var ’. quit Stops MATLAB. Commands for managing the work session

11. who Lists the variables currently in memory. whos Lists the current variables and sizes, and indicates if they have imaginary parts. :Colon; generates an array having regularly spaced elements.,Comma; separates elements of an array. ;Semicolon; suppresses screen printing; also denotes a new row in an array....Ellipsis; continues a line. Commands for managing the work session (continued) CommandDescription

12. Practice…  Find the circumference and area of a circle of radius = 2.5 mm  Find the surface area and volume of a sphere of radius 17.2 mm  Use help to learn the difference between the built-in MATLAB functions cos() and cosd()

13. Arrays…

14. How to Create Arrays  You can use the colon ( : ) operator together with the comma and semicolon to create arrays  Colon – create a sequence of numbers in a row  Comma – separate listed elements of a single row, can also use an empty space  Semicolon – separates rows >> p = [1:3;4,5,6;7 8 9] p = 1 2 3 4 5 6 7 8 9 >> r = [5:5:35;35:-5:5] r = 5 10 15 20 25 30 35 35 30 25 20 15 10 5

15. Array Functions  You can find the size of an array with the size() function  You can find the length of a vector with the length() function  Read the help entries for each of these functions >>p = [5:5:35;35:-5:5]; >>size(p) ans = 27 >>r = [4,5 6]; >>length(r) ans = 3

16. Concatenation  You can easily create an array by concatenating two or more existing arrays >> p = ones(3,1) p = 1 >> q = zeros(3,1) q = 0 >> s = [p q q p] s = 1 0 0 1

17. Array Index  You may refer to a single element of an array by using the array index corresponding to the row and column where the number is located in the array >>w = [5:5:35;35:-5:5] ans = 5 10 15 20 25 30 35 35 30 25 20 15 10 5 >>w(2,3) ans = 25  If the array is a vector, you need only specify the column number since there is only a single row and the row number is assumed to be 1 >>u = [6 7 8 9 0]; >>u(2) ans = 7

18. Array Addressing  You can refer to ranges of elements in an array by using the standard index format elements = array(rows,columns)  Example >>w = [2:2:10;10:-2:2]; w = 2 4 6 8 10 10 8 6 4 2 >>w(1:2,3:4) ans = 6 8 6 4 try this >>w(:,5)

19. Array Addressing Other examples of how to address an arbitrary selection of rows & columns from an array >> r = [5:5:35;35:-5:5] r = 5 10 15 20 25 30 35 35 30 25 20 15 10 5 >> r(:,2:5) ans = 10 15 20 25 30 25 20 15 >> r(:,[2,5]) ans = 10 25 30 15

20. Example – Linear Indexing What happens when a single index is used to address elements of a matrix? >> r r = 5 10 15 20 25 30 35 35 30 25 20 15 10 5 >> r(2) ans = 35 >> r(5) ans = 15 >> r([2 7 13]) ans = 35 20 35

21. Assignment You can store the results of a calculation in a specified location in an array for i = 1:10, s(i,1) = sqrt(5*i); end >> s = 2.2361 3.1623 3.8730 4.4721 5.0000 5.4772 5.9161 6.3246 6.7082 7.0711 Note: the semicolon causes screen output to be suppressed! Only after the loop completes is the output specifically requested by typing the variable name

22. More Advanced Topics: Scripts, User-Defined Functions, Conditionals, Loops, Files

23. 1.In the interactive mode, in which all commands are entered directly in the Command Window, or… 2.By running a MATLAB commands stored in a script file. This type of file contains MATLAB commands, so running it is equivalent to typing all the commands— one at a time—at the Command Window prompt. You can run the file by typing its name at the command line. You can execute commands in MATLAB in two ways:

24. What happens when you type func_name() 1.MATLAB first checks to see if func_name() is a variable and if so, displays its value. 2.If not, MATLAB then checks to see if func_name() is one of its own commands, and executes it if it is. 3.If not, MATLAB then looks in the current directory for a file named func_name.m and executes func_name() if it finds it. 4.If not, MATLAB then searches the directories in its search path, in order, for func_name.m and then executes it if found.

25. The MATLAB Script Editor / Debugger comments MATLAB commands save & execute

26. Keep in mind when using script files:  The name of a script file must begin with a letter, and may include digits and the underscore character, up to 31 characters  Do not give a script file the same name as a variable  Do not give a script file the same name as a MATLAB command or function; you can check to see if a command, function or file name already exists by using the exist() command

27. MATLAB User-Defined Functions function [output variables] = function_name (input variables)  Note: [output variables] is NOT an array  You may use multiple output variables separated by commas, but each will be output individually  Example: Working Session >> [s,t] = two_out(3,5) s = 30.6000 t = 2.6471 Function Definition function [p,q]=two_out(x,y) p = 17*x^2/y; q = y*x/17*x;

28. MATLAB Plotting >> x = [0:pi/10:2*pi]; >> y = sin(x); >> plot(x,y,'g.-','MarkerSize',15,'LineWidth',2) >> title('Example Plot of y = sin(x)'); >> xlabel('x (units)'); >> ylabel('y = sin(x)')

29. Plot Layout with subplot() >> x = [0:pi/10:2*pi]; >> y1 = sin(x); y2 = cos(x); >> subplot(2,1,1) >> plot(x,y1,'g.-','MarkerSize',15,'LineWidth',2) >> xlabel('x (units)'); >> ylabel('y_1 = sin(x)') >> subplot(2,1,2) >> plot(x,y2,'g.-','MarkerSize',15,'LineWidth',2) >> xlabel('x (units)'); >> ylabel('y_2 = cos(x)')

30. Conditional Statements if x < 3 color = ‘r’; else if x < 7 color = ‘b’; else if x < 11 color = ‘c’; else color = ‘m’; end if x < 3 color = ‘r’; elseif x < 7 color = ‘b’; elseif x < 11 color = ‘c’; else color = ‘m’; end

31. for Loops  Standard structure… for loop variable = min:inc:max statements end  Basic example… for k = 5:10:35 x = k^2 end k = 5, 15, 25, 35 x = 25, 225, 625, 1225 Note: if inc is not specified, it defaults to unity

32. Importing Data from a Text File  Using the load command… >> load subject_data.dat; >> s = load(‘subject_data.dat’); Reads ASCII data in columns Creates array named subject_data.dat Reads ASCII data in columns Creates array named s

33. Importing Data from a Text File (cont.)  Using the dlmread command… >> RESULT = DLMREAD(FILENAME,DELIMITER,R,C); Reads delimited ASCII data starting at row R and column C Creates array named RESULT

34. Importing Data from an Excel File [num,txt] = xlsread(‘excel_filename.xls’)  numeric data put into num variable  text data put into txt variable

35. Saving Data to ASCII File  Using the save command… >> save filename var1 var2… –ASCII –tabs; For example… >> B = [2 6; 5 7; 8 4]; >> save array_B.dat B –ASCII –tabs; Saves array B in the ASCII file array_B.dat Columns of B become tab-delimited columns of array_B.dat

36. Saving Data to Binary File  Using the save command… >> save filename var1 var2… For example… >> B = [2 6; 5 7; 8 4]; >> save array_B B Saves array B in the binary file array_B.mat Advantage: binary files load faster than ascii