MEGN 536 – Computational Biomechanics MATLAB: Getting Started

Prof. Anthony J. Petrella Computational Biomechanics Group

MATLAB Window

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

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

Scalar Arithmetic Operations

Symbol Operation

^ * / \ + exponentiation: multiplication: right division: left division: addition: subtraction:

b/a a

+

b a b ab a/b a

-

b

MATLAB form

a^b a*b a/b a\b a + b a - b

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.

Special Variables and Constants

Command

ans eps

Description

Temporary variable containing the most recent answer.

Specifies the accuracy of floating point precision.

i,j The imaginary unit  1.

Inf Infinity.

NaN pi Indicates an undefined numerical result.

The number p .

Order of Precedence

Precedence

First innermost pair.

Operation

Parentheses, evaluated starting with the Second Exponentiation, evaluated from left to right.

Third Fourth Multiplication and division with equal precedence, evaluated from left to right.

Addition and subtraction with equal precedence, evaluated from left to right.

Examples of Precedence

>> 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 (continued)

>> 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

Commands for managing the work session

Command

clc clear clear v1 v2 exist(‘var’) quit

Description

Clears the Command window.

Removes all variables from memory.

Removes the variables v1 and v2 from memory.

Determines if a file or variable exists having the name ‘ var ’ .

Stops MATLAB.

Commands for managing the work session (continued)

Command

who whos ; : , ...

Description

Lists the variables currently in memory.

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.

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()

Arrays…

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

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 = 2 7 >>r = [4,5 6]; >>length(r) ans = 3

Concatenation

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



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

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)

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

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

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 Note: the semicolon causes screen output to be suppressed!

>> s = 2.2361

3.1623

3.8730

4.4721

5.0000

5.4772

5.9161

6.3246

6.7082

7.0711

Only after the loop completes is the output specifically requested by typing the variable name

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

You can execute commands in MATLAB in two ways: 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.

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.

The MATLAB Script Editor / Debugger

save & execute comments MATLAB commands

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

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:

Function Definition

function [p,q]=two_out(x,y) p = 17*x^2/y; q = y*x/17*x;

Working Session

>> [s,t] = two_out(3,5) s = 30.6000

t = 2.6471

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)') Example Plot of y = sin(x) 1 0.8

0.6

0.4

0.2

0 -0.2

-0.4

-0.6

-0.8

-1 0 1 2 3 x (units) 4 5 6 7

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)'); 1 >> ylabel('y_2 = cos(x)') 0.5

0 -0.5

-1 0 1 2 3 x (units) 4 5 1 0.5

0 -0.5

-1 0 1 2 3 x (units) 4 5 6 7 6 7

Conditional Statements

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

for

Loops

  Standard structure… for

loop variable = min:

inc

:max statements

end Basic example… for k = 5:10:35 x = k^2 end Note: if

inc

is not specified, it defaults to unity

k = 5, 15, 25, 35 x = 25, 225, 625, 1225

Importing Data from a Text File

 Using the load command… >> load subject_data.dat; Reads ASCII data in columns Creates array named subject_data.dat

>> s = load(‘subject_data.dat’); Reads ASCII data in columns Creates array named s

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

Importing Data from an Excel File

[num,txt] = xlsread(‘excel_filename.xls’)   numeric data put into num variable text data put into txt variable

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

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