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MEGN 536 – Computational Biomechanics MATLAB: Getting Started

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MEGN 536 – Computational BiomechanicsMATLAB: Getting Started

Prof. Anthony J. Petrella

Computational Biomechanics Group

variables in workspace

and their values

Current directory contents

Workspace tab

(active here)

Command line

History

- 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

Symbol Operation MATLAB form

^exponentiation:aba^b

*multiplication:aba*b

/right division:a/b a/b

\left division:b/a a\b

+addition:a + ba + b

-subtraction:a - ba - b

- 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.

Command Description

ansTemporary variable containing the most recent answer.

epsSpecifies the accuracy of floating point precision.

i,jThe imaginary unit Ö-1.

InfInfinity.

NaNIndicates an undefined numerical result.

piThe number p.

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.

>> 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

>> 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

CommandDescription

clcClears the Command window.

clearRemoves all variables from memory.

clear v1 v2Removes the variables v1 and v2 from memory.

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

quitStops MATLAB.

CommandDescription

whoLists the variables currently in memory.

whosLists 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.

- Find the circumference and area of a circleof radius = 2.5 mm
- Find the surface area and volume of a sphereof radius 17.2 mm
- Use help to learn the difference between the built-in MATLAB functions cos()and cosd()

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

- 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

- 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

- 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

- 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)

- 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

- 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

- 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 causesscreen output to be suppressed!

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

- In the interactive mode, in which all commands are entered directly in the Command Window, or…
- 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.

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

save & execute

comments

MATLAB

commands

- 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

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

>> 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)')

>> 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)')

if x < 3

color = ‘r’;

elseif x < 7

color = ‘b’;

elseif x < 11

color = ‘c’;

else

color = ‘m’;

end

if x < 3

color = ‘r’;

else

if x < 7

color = ‘b’;

else

if x < 11

color = ‘c’;

else

color = ‘m’;

end

end

end

- 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

- 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

- 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

[num,txt] = xlsread(‘excel_filename.xls’)

- numeric data put into num variable
- text data put into txt variable

- Using the save command…
>> save filenamevar1 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

- Using the save command…
>> save filenamevar1 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