Transcript AME 150 L - Engineering Class Home Pages

AME 150 L
MATLAB®
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®
MATLAB
vs. Fortran
• MATLAB® Positives
• Fortran Positives
– Interactive mode
– Wealth of 3rd party
“notebooks”
– Matrix Oriented
– Efficient I/O and
Graphics
•
–
–
–
–
• Fortran Negatives
MATLAB® Negatives
– Syntax cumbersome
– Command Line oriented
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First Compiler
Legacy Codes
Efficient Numerically
Portability
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– Debugging Hard
– Cumbersome
– Object Orientation
pasted-on
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®
MATLAB
Usage
• For the next 4 lectures
– Slide will introduce topic
• Useful in reviewing lecture and practicing
• Can pay attention to on-line demonstration
– Demonstration of usage on-line
• Will show details of usage
• Shop proper and improper operation
• First -- Learn to use MATLAB® Help
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Basic Features
• Simple Mathematics
– MATLAB® is like a calculator
• Type in expression and get answer (ans=)
• Suppress answer with trailing semi-colon ;
• Can define variables (like in Fortran)
– MATLAB® operations
• Fortran-like +, -, * and functions
• Exponentiation is ^ (like Basic or Excel)
• 2 Divisions / and \ ( 56/8 same as 8\56 )
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Hierarchy of operations
• Similar to Fortran
–
–
–
–
Expression evaluated left to right
Exponentiation has highest precedence
Multiplication & Division next & equal
Addition & Subtraction next & equal
• Expressions in Parentheses evaluated first
– Start with Innermost & proceed Outward
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Naming Variables
•
•
•
•
Variable names are Case sensitive (!!!)
Names can have up to 31 characters
Names must start with a letter
Names can contain letter, numerical digits,
and underscore (no special characters or
blanks)
• i and j are special (they are 1 )
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Special Variables
flops - number of floating
i or j - imaginary base
ans - unnamed answer
pi - 3.1416…
eps - machine epsilon
point operations
nargin - number of
function input arguments
(1 + eps)>1 (smallest)
nargout - number of
function output arguments
realmin - smallest usable
positive real number
inf - stands for infinity
NaN or nan - not a number realmax - largest usable
positive real number
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Features of calculations
• Complex numbers are natural
EDU» sqrt(-1)
ans =
0+ 1.0000i
• Pi is predefined in a variable
EDU» atan(1)*4-pi
ans =
0
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Cautions
• Special Variables Can Be Redefined!
EDU» pi
ans =
3.1416
EDU» pi=5
pi =
5
EDU» atan(1)*4-pi
ans =
-1.8584
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More Features
• Clear - resets special values and any other
defined variables
• Convenience often misleads
EDU» -1*(1/3)
ans =
-0.3333
EDU» -1^(1/2)
ans =
-1
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EDU» -1^(1/4)
ans =
-1
EDU» sqrt(sqrt(-1))
ans =
0.7071+ 0.7071i
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Comments & Punctuation
• Comments start with %
• Lines are continued by three periods ...
• Comments cannot be continued (but can use
% on next line to make “new” comment)
• Cannot continue in middle of a variable
name
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Complex Numbers
• Complex numbers have a magnitude and
angle (argument in mathematics)
M    M ei = a + b i
where
2
2
1 b
M  a  b   tan
a
a  M cos( ) b  M sin( )
 
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®
MATLAB Complex
Helpers
• Real, imag, abs, and angle
c1 =
1.0000+ 2.0000i
EDU» c2=3*(2-sqrt(-1)*3)
c2 =
6.0000- 9.0000i
EDU» c3=6+sin(-5)*j
c3 =
6.0000+ 0.9589i
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EDU» mag_c1=abs(c1)
mag_c1 =
2.2361
EDU» angle_c1=angle(c1)
angle_c1 =
1.1071
EDU» imag_c1=imag(c1)
imag_c1 =
2
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®
MATLAB Mathematical
Appendix A
(C: Palm Text)
Page 123-124
(Etter & Kuncicky)
Appendiz A
Functions
Page 47,77,116
(E: King Text)
Appendix A
(Hanselman & Littlefield)
(Mathworks Reference)
http://www.mathworks.com/support/books/index.php
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®
MATLAB
Links
• Pointers to other texts
http://www.mathworks.com/support/books/index.php3
• User Contributed Software (“M-Files”)
http://www.mathworks.com/support/ftp/
• On-line Demos
http://www.mathworks.com/products/demos/
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Command Window
• Command Window Workspace
who - lists active variables
whos - more detailed information
clear - clears the workspace (erases all)
clear list of variables- clears variables in list
help - provides general help
help command - provides help on command
more on - pauses on full screen
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Number Display Format
format
format
format
format
format
format
format
format
format
format
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short
long
short e
long e
short g
long g
hex
rat
bank
compact
3.1416
5 digits
3.14159265358979
15 digits
3.146e+00
+ exponent
3.14159265358979e+00
3.1416
better of shorts
3.14159265358979
400921fb5442d18
hexadecimal
355/113
rational approximation
3.14
2 decimal digits
suppresses extra line feeds
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Command Window Control
clc
Clear command window
home
cursor to upper left corner
more on Pages the command window
computer
version
ver
quit
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tells what computer you are running on
Short version information
long version information
Stop using Matlab
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Script M-files
• Can create scripts of commands
• Called “m-files” because extension is .m
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Special M-File Commands
disp(variable) display results - no variable names
echo
control echoing of script commands
input
prompt user for input
keyboard
Give temporary control to keyboard
pause
pause until any key pressed
pause n
pause n seconds, then continue
waitforbuttonpress
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MATLAB Session
Control
• A file called startup.m (in your search
path) will execute every time you start
MATLAB®
• Suggestions for a startup file
– Keep a diary (copy) of day’s session (you can
edit it to remove irrelevant material)
– set more on
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Sample Startup file
% This is the startup.m initialization file
more on
%pause on a full screen
dfile=strcat(date,'.txt'); %make date string
diary(dfile);
%Create a diary file
%named with today's date
disp(strcat(‘Diary created:',datestr(now,0)))
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File & Directory Management
• Save, load & deleting variables
save
save list
load
load list
stores all variables in matlab.mat
stores variables in list
loads all variables from matlab.mat
loads just variables in list
These commands are for initializing workspace
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File Management Details
save(fname , ['var1','var2',…])
saves variables var1 and var2 into file
stored in string fname
delete('data.mat')
deletes named file
Lots of low-level file I/O - we will not use in
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Exist Command Details
EXIST('A') returns:
0 if A does not exist
1 if A is a variable in the workspace
2 if A is a file [usually M-file] on MATLAB's search path
3 if A is a MEX-file on MATLAB's search path
4 if A is a MDL-file on MATLAB's search path
5 if A is a built-in MATLAB function
6 if A is a P-file on MATLAB's search path
7 if A is a directory
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Embedded OS Commands
cd or pwd
Show or change present working directory
p=cd
Return present working directory
dir or ls Display files in current directory
d=dir
return current working directory
p=matlabroot
return dir path to Matlab
type cow Type cow.m in Command window
what
Type organized listing of Matlab files
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®
MATLAB
•
•
•
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•
•
Special Features
Vectors and Arrays (and array operations)
Plotting
Linear Algebra
Polynomials (and their roots)
Solutions of Systems of Equations
Problem Solving
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®
MATLAB Arrays
• MATLAB® has many features to work with
arrays of numbers (vectors & matrices)
• Definition:
x=[ list of elements separated by , or blanks ]
each element may be an arbitrary expression
x = [0 0.1*pi,.2*pi … 0.9*pi pi]
y=sin(x) produces an array result
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®
MATLAB Arrays
(2)
• Arrays have the following properties
– 1-D Arrays can be rows or columns
(use ; to signal end of row)
– 2-D Arrays have rows and columns
– MATLAB® can handle higher numbers of
dimensions - extra dimensions are “pages”
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®
MATLAB Arrays
(3)
• An Array is referred to by its name (same as
naming variables)
• An element of an array is indicated by an
index (enclosed in parentheses)
V = [1 2 3 4 5]
V(3) is 3
V(:3) is [1 2 3]
V(2:) is [2 3 4 5]
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The Colon “:” operator
• The Colon is used to create equi-spaced lists
x=[1:4] is [1 2 3 4]
N1:N2 starts at N1 and increments by 1 to N2
x=[1:2:9] is [1 3 5 7 9]
N1:N2:N3 starts at N1, increments by N2 until reach N3
Angle=[180:-1:0] generates a list of 181 angles
from 180 to 0 (in reverse order)
Radians=pi/180*Angle (same but in radians)
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Scalars and Vectors
• Scalars can be added, subtracted, multiplied
or divided into vectors (element by element)
» x=[1 3 5 7 9];y=3*x
y =
3
9
15
21
» z=x+7
z =
8
10 12 14 16
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The Dot “. “ Operator
• Some operators don’t make sense
» x^2
??? Error using ==> ^
Matrix must be square.
» x.^2
ans =
1
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The Dot “. “ Operator (continued)
• The Dot before an operator signals that you
want top perform the same operation on
every element in an array
x =
1
y =
3
» x.*y
ans =
3
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