MATLAB

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MATLAB
Matrix Laboratory
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Internet Resources Dr. H-C Chens CVEN 302 Web
Page http//ceprofs.tamu.edu/hchen/cven302.html F
or MATLAB, select chap01b.ppt, or
click http//ceprofs.tamu.edu/hchen/cven302/chap01
b.ppt
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Programming The ideal style of programming is
structured

• Break down a larger goal into tasks
• Develop a module for each task
• A module has a single entrance and exit
• Modules are reusable

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Use MATLAB to solve a problem

• State the problem clearly
• Describe the Input/Output (I/O)
• Algorithm - Numerical Method
• Develop a MATLAB program
• Debugging and Testing
• Documentation
• If needed, work the problem by hand

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Compiler and Program Execution
input
Machine language program
Computer Program
Link/ Load
Compiler
Execute
output
MATLAB Execution Interactive environment - does
not require formal compilation, linking/loading,
and execution Scripts - develop and execute
m-files that contain MATLAB commands
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Important!You must include comments in your
programs you turn in - otherwise we will have
great difficulty knowing what you are thinking
and doing. You will have difficulty knowing what
you were doing if you need to reuse the programs.
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MATLABs 3 Windows
Command Window - enter commands and data
- print results Graphics Window - display
plots and graphs Edit Window - create and
modify m-files
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Two simple MATLAB programs (also called
scripts) Filename lec2a.m
Find sum of 1 to b Comments begin with
cd y\cven302\ clear all sum 0 b input('what
is the value of b? ') for i 1 b sum
sum i end
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Filename lec2b.m
plot 1/x v.s. tanh x clc a linspace(0,5) f
1./a g tanh(a) plot(a,f,'-', a,
g,'--') axis(0 3 0 2) xlabel ('x') ylabel
('y') title ('Plot 1/x and tanh x') text(0.7,
1.6, '1/x') text(2, 1.1, 'tanh x')
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Now we have seen Command Window, Graphics Window,
and Edit Window There is another window which is
very usefulthe Help Window You can also type
help in Commend Window e.g., help input
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help input INPUT Prompt for user input.
R INPUT('How many apples') gives the user the
prompt in the text string and then waits for
input from the keyboard. The input can be any
MATLAB expression, which is evaluated, using
the variables in the current workspace, and the
result returned in R. If the user presses
the return key without entering anything,
INPUT returns an empty matrix. R
INPUT('What is your name','s') gives the prompt
in the text string and waits for character
string input. The typed input is not
evaluated the characters are simply returned as
a MATLAB string. See also KEYBOARD.
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MATLABs basic component is a matrixi.e., all
variables are treated as matrices All operations
are vectorized (optimized for vector use) Loops
run much slower in MATLAB than in Fortran (not a
vector operation)
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Scalar, vector, and matrix
Matrix
m ? n matrix m rows (m 3)n columns (n 4)
Scalar k 5 1?1 matrix
Vector
1?4 matrix, or a row vector
3?1 matrix, or a column vector
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• Variable
• may consist up to 31 characters
• starting with a letter and followed by any
  combination of letters, digits, and underscores
  (Variable names must start with a letter)
• punctuation marks and spaces should not be
  included

e.g., CVEN_302, TIME, Time, time, velocity,
force_x, force_y
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Data Type

• All numbers are double precision
• Text is stored as arrays of characters
• You dont have to declare the type of data
  (defined when running)
• Variables are case sensitive

e.g., CVEN_302, TIME, Time, time, velocity,
force_x, force_y
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Arithmetic operation of scalars
Addition ab subtraction a-bmultiplication
ab division a/bexponentiation ab ab
Elementary math functions
abs(x) absolute value sqrt(x) square root
x(1/2)sin(x) sine asin(x) inverse
sinesinh(x) hyperbolic sine asinh(x) inverse
hyperbolic sinelog(x) natural
logarithm log10(x) common logarithmexp(x)
exponental ex (e 2.7183.)
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a 5 b 3 ab ans 15 d ans
3 d 45 e ans 3 e e 45
a2 ans 25
a/b ans 1.6667 format long a/b ans
1.66666666666667 format short a/b ans
1.6667
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exp(2) ans 7.3891 102 ans 100
log(100) ans 4.6052 log10(100) ans
2 pi ans 3.1416
- result not displayedformat long - 15
digitsformat short - 5 digitsans - result from
previous calculationpi - ?
Ctrl-c terminate a running program
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Array Operations

• An array operation is performed
  element-by-element - Need . in front of the
  operator

MATLAB C A.?B
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Arithmetic operation of Arrays
Addition ab subtraction a-bmultiplication
a.b division a./bexponentiation a.b ab
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MATLAB variables and matrix operation
b 4 5 6 b 4 5 6 c 1
3 2 c 1 3 2
c 1 3 2 c 1 3 2 d
c' d 1 3 2
- a new line
? - transpose
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b c ans 31 b.d ans 4 15
12 b./d ans 4.0000 1.6667 3.0000
f b d 3 6 8 f 4 5 6
1 3 2 3 6 8
b.d 41 53 62b./d 4/1 5/3 6/2
f(2,3) ans 2 size(f)
b
d
3 6 8
size - size of a matrix
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Matrix Operation (conti.)
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Colon Operator

• Creating new matrices from an existing matrix

C 1,2,5 -1,0,1 3,2,-1 0,1,4 F C(, 23)
2,5 0,1 2,-1 1,4 E C(23,) -1 0 1 3
2 -1 G C(34,12) 3,2 0,1
all columns
rows 2 to 3
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a step b gives number from a to b with the
specified step between elements step 1 if not
specified
x 110 x 1 2 3 4 5
6 7 8 9 10 t 1 2 10 t
1 3 5 7 9 k 5-1-3 k
5 4 3 2 1 0 -1 -2 -3
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What if the step is not easy to calculate, or is
an odd number?
y linspace (a, b, n_pts)
y linspace (0, 1, 4) y 0 0.3333
0.6667 1.0000
y linspace (0,1)a number of 100 for n_pts is
assigned.
2 end points are included in n_pts.
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Some useful special matrices
eye (3) ans 1 0 0 0 1
0 0 0 1 ones (3) ans 1
1 1 1 1 1 1 1 1
ones (1,4) ans 1 1 1 1
eye (m,n) eye (n)ones (m,n) ones (n) zeros
(m,n) zeros (n)
zeros (2,3) ans 0 0 0 0
0 0
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Plotting
plot (x, y) plot(x1, y1, x2, y2) plot (x, y,
color symbol line style)
x linspace(0, 2pi) y sin (x) z cos
(x) plot (x, y) plot (x, y, x, z) figure
(2) plot (x, y, 'r o -') grid on hold on
plot (x, z, 'b x ')
figure or figure () open a figure
add grids
try help plot
red, circle, solid
blue, x-mark, dotted
try grid off
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Plotting (continue)
xlabel ( label ) ylabel ( label )title (
title of the plot )text ( x_location,
y_location, text )axis ( x_min x_max y_min
y_max )
xlabel ('x') ylabel ('y') title ('sine and
cosine') text (2, 1, 'This is a sine
fuction') axis (0 2pi -2 2) hold off
? ? - text string
hold on hold the plots to avoid overwriting
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Plotting (continue)
subplot ( m, n, figure number ) - break the
figure window into m by n small figures, and plot
the specified figure
figure subplot (3, 2, 1) plot (x, y)
subplot (3, 2, 2) plot (x, z) subplot (3, 2,
4) plot (x, y-z)
1
2
3
4
5
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semilogx (x, y) logarithmic scales for the x
axis. semilogy (x, y) logarithmic scales for the
y axis. loglog (x, y) logarithmic scales for the
x and y axes
x 10.-10.12 y exp(x) figure(1) semilogy
(x,y,'') figure(2) loglog(x,y,'-s') grid on
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More control on plotting
get(H) get object properties set(H,'PropertyName',
PropertyValue,...) set object properties
figure(2) h loglog(x,y,'-sr') grid
on get(h) set(h, 'LineWidth',2) set(h,
'MarkerFaceColor', 0 0 1)
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Some useful commands
who list of current variablesclc
clear the command windowclf clear the
graphical windows clear x clear the
variable xclear all clear all
variablesclose close the current
figureclose all close all figurescd
y\cven302\ change directorydir list
all fileswhat list all m-filesCTRL-C
Abort
semicolons () at the end of line Calculation
results will not be displaced on the command
window
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Initializing Variables

• Explicitly list the values
• reads from a data file
• uses the colon operator
• reads from the keyboard

?
?
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Input and output (I/O)
a input ( enter a value or string ) - wait
for input from the keyboard load file_name -
input an existing data file (ASCII format)
diary file_name - save anything in the Command
Windowdiary off save file_name variable(s)
-ascii - save the data of the variable(s) to a
file in ASCII format
You may need to go to certain directory before
loading and/or saving files
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diary tmp.dat a 1 2 3 4 5 6 a 1
2 3 4 5 6 save a_file.dat a
-ascii load a_file.dat b a_file b 1
2 3 4 5 6 d input ('give
a value to d ') give a value to d 5 d
5 diary off
Save in the tmp.dat file
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M-Files Scripts and Functions

• You can create and save code in text files using
  MATLAB Editor/Debugger or other text editors
  (called m-files since the ending must be .m)
• M-file is an ASCII text file similar to FORTRAN
  or C source codes ( computer programs)
• A script can be executed by typing the file name,
  or using the run command

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Functions distinguished from the script that the
first line is of the form function x
function_name (input arguments) function x, y
function_name (input arguments)
A function has to be stored as a stand-along file
ended with .m. The name of the function is
usually (but not necessary) the same as the name
of the file.
Difference between scripts and functions Scripts
share variables with the main workspaceFunctions
do not
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Approximate integral f(x) 1/x3 using basic
trapezoid rule
File name trap_ex.m
function t trap_ex(a, b) t (b - a) (a(-3)
b(-3)) / 2
y trap_ex (1, 3) y 1.0370
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Approximate integral f(x) 1/x3 using basic
trapezoid rule with n steps used
File name trap_ex2.m
function t trap_ex2(a, b, step) dx (b -
a)/step x1 a t 0 for i 1 step x1
a (i-1)dx x2 a idx t t (x2 -
x1) (x1(-3) x2(-3)) / 2 end
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y trap_ex2 (1,3,1) y 1.0370 y
trap_ex2 (1,3,2) y 0.6435 y trap_ex2
(1,3,100) y 0.4445 y trap_ex2
(1,3,1000) y 0.4444 format long y
trap_ex2 (1,3,1000) y 0.44444543209743
x1 ??? Undefined function or variable 'x1'.
Why?
Exact solution 0.444444444444 .
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feval - evaluate function specified by string
my_func.m
function y my_func(x) function 1/x3 y
x.(-3)
basic_trap.m
function q basic_trap(f, a, b) trapezoid rule
with input function f ya feval(f, a) yb
feval(f, b) q (b - a) (ya yb)/2
feval('my_func', 1) ans 1
y basic_trap ('my_func', 1,3) y 1.0370
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Decision Making Control Flow (a) For
Loops (b) While Loops (c) If-Else Structures
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For Loops
for x array commandsend
Without this line you will getWarning
Reference to uninitialized variable z.
z 0 for i 110 y(11-i) i z
zi end
y y 10 9 8 7 6 5
4 3 2 1 disp(z) 55
disp (x) - display the value of x
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Filename lec2a.m
Find sum of 1 to b Comments begin with
cd y\cven302\ clear all sum 0 b input('what
is the value of b? ') for i 1 b sum
sum i end
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While Loops
while expression commandsend
(is true)
eps 1 count 0 while (1eps) gt 1 eps
eps/2 count count 1 end eps
eps2 display(count-1)
Determining machine epsilon
eps 2.2204e-016 ans 52
Floating point relative accuracy
52 digits in double precision (64 bit)
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Floating point
exponent
a number
digit
base
d1? 0 normalized floating-point system
Single precision 32 bits (23 for digit, 8 for
exponent, 1for sign Double precision 64 bits
(52, 11, 1)
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eps 1 count 0 while (1eps) gt 1 eps
eps/2 count count 1 end eps
eps2 display(count-1)
What if we omit this operation?
The loop becomes an infinite loop because the
statement is always true.
Use break to terminate while and for loops
prematurely (or set a limit in while loops)
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If-Else Structures
if expression (is true) commandsend
if expression 1 commands 1elseif expression
2 commands 2elseif expression 3 commands
3 else commands nend
if expression commands 1else commands 2end
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Relational Operators lt less thanlt less than or
equal togt greater thangt greater than or equal
to equal to not equal to
Logical Operators and or not
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(No Transcript)
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a input('what is the value of input data?
') if a gt 0 sign 1 elseif a lt 0 sign
-1 else sign 0 end disp(sign)
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Print figures to image files
print - print out current figure print -djpeg
filename - save current figure in jpeg
formatprint -djpeg filename - save current
figure in jpeg format with (resolution level)
between 0 and 100 (default 75) print -dtiff
filename - save current figure in tiff
format print -dpsc filename - save current
figure in color PostScript format
See help print for more
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Filename lec2b.m
plot 1/x v.s. tanh x clc a linspace(0,5) f
1./a g tanh(a) plot(a,f,'-', a,
g,'--') axis(0 3 0 2) xlabel ('x') ylabel
('y') title ('Plot 1/x and tanh x') text(0.7,
1.6, '1/x') text(2, 1.1, 'tanh x')
cd y\cven302 print -djpeg myfigure1 print
-djpeg100 myfigure2