Week 12: Matlab/Octave
for Engineering
Applications - Part 1
BJ Furman
06NOV2009
The Plan for Today
„
Matlab/Octavefor engineering applications
Overview of Matlab and Octave
Matlab environment
Octave command line
Basic operations
Script files
Resources for more information
Learning Objectives
„
Explain what Matlab and Octave (M/O)
are
„
Navigate the Matlab user interface and
Octave command line
„
Use M/O as a scratch pad
„
Create script files to execute a sequence
of commands
Matlab and Octave
„
‘High-level’ languages
„
abstracts away the nitty-gritty details
Numerical calculation
oriented toward engineering, mathematical, and
scientific computing
„
„
Powerful graphics and analysis tools
„
„
„
Matlab (Matrix Laboratory)
Controls, signal processing, data analysis, and other
specialized ‘toolboxes’ are available
Widely used in industry
Matlab is commercial software (a student version
is available) http://www.mathworks.com/
Octave is open source and free:
http://www.gnu.org/software/octave/
Matlab (ver. 6.5) Environment (GUI)
Workspace Window
Command
Window
Current Directory
Window
Octave Command Line
Matlab as a ‘scratch pad’
dynamically
typed
Octave as a ‘scratch pad’
dynamically
typed
Matlab/Octave Basics - 1
„
Fundamental element: the array
even scalars --> stored as 1x1 array of double
floating point value
„
How many bytes?
„
See Workspace Window
Useful commands (see documentation for more details!)
who (information about what is in memory)
whos (more detailed information about what is in memory)
clc (clears the command window)
clear (clears all user defined variables)
help name (provides information on command name)
Matlab/Octave Basics - 2
„
Script files
Text files containing Matlab/Octave
statements
„
Type in a text editor (Matlab or Octave) or use
M-file editor in Matlab (File/New/M-File or Ctrl-n)
Comments
Matlab: %
„ Octave: % or #
„
Example: a cool plot
Script File Example
Plot of z ( x, y ) = e
−0.5[ x 2 + 0.5( x − y ) 2 ]
over − 4 ≤ x, y ≤ 4
Octave Script File Example
cool_plot.m needs to be in
the ‘load path’
• Octave: addpath(dir-path)
addpath('C:\Octave\Octave_code')
• Matlab: File/Set Path
Plot of z ( x, y ) = e −0.5[ x
2
+ 0.5( x − y ) 2 ]
over − 4 ≤ x, y ≤ 4
Matlab Script File Example
Ch Example
function exp(-0.5(x*x+0.5(x-y)(x-y)))
z
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
4
3
2
y
1
0
-1
-2
-1
-3
-4 -4
See: chap. 23 of The Ch Language User's Guide
and chap. 2 of The Ch Language Environment Reference
-3
0
1
2
3
4
x
-2
This plot is generated by Ch Student Edition
Excel Example
Matlab/Octave Basics - 3
„
Array creation
A=[1 2 3; 4,5,6; 7 8 9]
„
„
„
size(A)
Indexing elements
Separate elements by spaces or
commas and rows by semicolon
or CR
A(1,2)
Index by enclosing indices in ( )
Contrast how elements are
indexed in C
Adding elements
A(4,2)=13
Contrast with what would happen
in C
Matlab/Octave Basics - 4
„
Vectors (just 1xn or nx1 arrays)
„
Vectors using the colon operator
„
C=1:0.25:2
D=0:5
Linspace
„
B=[sin(pi/4), -2^3, size(A,1)]
E=linspace(0,5,3)
Logspace
F=logspace(1,3,5)
base : increment : limit For an
increment of 1: base : limit
start : end : n For n elements
linearly spaced between start and
end
start : end : n For n elements
logarithmically spaced between
start and end
Matlab/Octave Basics - 5
„
Manipulating arrays
Add a row
„
A=[A; [10 11 12]]
Extract a sub-array
„
„
G=A(1:3,1:2)
Colon operator by itself means, “all the elements”
Can apply to the dimensions of the arrays to access all the elements of
a row or column
Can apply to the entire array to get all the elements as a column vector
ƒ What order will they come out?
Examples
„
„
„
H=[1:4; linspace(10,40,4); 400:-100:100]
I=H([1 2], :) What will this produce?
J=H(:)
Matlab/Octave Basics - 6
„
Special matrices
zeros, ones, eye
„
„
„
K=zeros(3)
L=ones(4)
M=eye(3)
Matlab/Octave Basics - 7
„
Matrix operations
Arithmetic just like with scalars! (But need to
take care that dimensions agree)
„ N=L*7
„ O=N+eye(4)
What will this produce?
„ P=B*E
„ P=B*E’ What will this produce? What does the ‘ do?
„ Q=A+B
„ Q=B+E
„ [1 2]*[3 ; 4] What will this produce?
Matlab/Octave Basics - 8
„
Matrix operations, cont.
Matrix division
„
Recall last week’s circuit analysis
„
R1=10k
R2=R3=5k
V=10V
⎡1
⎢0
⎢
⎢⎣0
Matrix solution
Ri = V ⇒ i = R −1V
use ' left' division to solve for i
i=R\V
‘right’ division ( i = R / V ) solves iR=V --> i = VR-1
−1
− 1⎤ ⎡ i1 ⎤ ⎡ 0 ⎤
0
R1 ⎥ ⎢i2 ⎥ = ⎢V ⎥
⎥⎢ ⎥ ⎢ ⎥
(R2 + R3 ) 0 ⎥⎦ ⎢⎣i3 ⎥⎦ ⎢⎣V ⎥⎦
R
i V
Matlab/Octave Basics - 9
„
Matrix operations, cont.
Element-by-element operations (use . (dot) and
the arithmetic operator)
„
dot product of two vectors
r
r
ˆ
ˆ
ˆ
v1 = 3i + 2 j − 5k
v2 = 2iˆ − 4 ˆj + 10kˆ
r r
what is v1 • v2?
r r
v1 • v2 = (3)( 2) + ( 2)( −4) + ( −5)(10) = 6 − 8 − 50 = −52
in Matlab/Octave :
v1 = [3 2 − 5]
v 2 = [2 − 4 10]
sum( v1 . * v 2)
Matlab/Octave Basics - 10
„
Functions
Like script M-files, but several differences:
„
first line must be of the form:
function [output args] = function_name(input args)
„
variables generated in the function are local to the
function, whereas for script files, variables are global
Make sure you add comments at the start that
describe what the function does
Example: root-mean-square function
Review
References
„
Matlab. (2009, November 6). In Wikipedia, the free
encyclopedia. Retrieved November 6, 2009, from
http://en.wikipedia.org/wiki/Matlab
„
GNU Octave. (2009, October 31). In Wikipedia, the free
encyclopedia. Retrieved November 6, 2009, from
http://en.wikipedia.org/wiki/GNU_Octave
„
Matlab tutorials:
http://www.mathworks.com/academia/student_center/tutorials/la
unchpad.html
Octave tutorial:
http://homepages.nyu.edu/~kpl2/dsts6/octaveTutorial.html
ftp://www.chabotcollege.edu/faculty/bmayer/ChabotEngi
neeringCourses/ENGR-25.htm