1. Chapter 2
MATLAB Fundamentals

2. MATLAB
Matrix Laboratory

3. Problem-Solving Methodology
H.C. Chen
Problem-Solving Methodology
State the problem clearly
Describe the Input/Output (I/O)
Work the problem by hand
Algorithm - Numerical Method
Develop a MATLAB Solution
Debugging and Testing
Documentation
MATLAB Review

4. Why MATLAB? Industry standard software application
H.C. Chen
Why MATLAB?
Industry standard software application
Wealth of built-in functions and libraries
Toolboxes (add-on software modules) – image and signal processing, control systems design, fuzzy logic, etc.
Has own structured programming language
Ease of application and testing (pre- and post-processing without lots of programming and formatting)
Platform independent
MATLAB Review

5. MATLAB MATLAB is a numerical analysis system
Can write “programs”, but they are not formally compiled
Should still use structured programming
Should still use comments
Comments are indicated by “%” at the beginning of the line

6. Program Documentation
Comments!!!
You must include comments in the computer programs you turn in -- otherwise we will have great difficulty knowing what you are doing

7. For example, here is some cryptic code without comment
for j=0:2
k=(2-j)*(1+3*j)/2
end
What does it do?
Put a comment in
% turns (0,1,2) into (1,2,0)

8. MATLAB Windows Command Window -- enter commands and data
-- print results
Graphics Window
-- display plots and graphs
Edit Window
-- create and modify m-files

9. Managing MATLAB Environment
who or whos -- See the current runtime environment
clear -- remove all variables from memory
clc clear the command window
clf clear the graphics window
save -- save the workspace environment
load -- restore workspace from a disk file
abort -- CTRL-C
help -- help “command”
Really good “help” command

10. MATLAB Syntax No complicated rules
Perhaps the most important thing to remember is semicolons (;) at the end of a line to suppress output
Type “more on” to keep text from leaving screen too fast
diary “filename” saves a text record of session
diary off turns it off

11. MATLAB MATLAB’s basic component is a Vector or Matrix
Even single value variables (Scalars)
All operations are optimized for vector use
Loops run slower in MATLAB than in Fortran (not a vector operation)
“size” command gives size of the matrix

12. Scalars, Vectors, Matrices
MATLAB treat variables as “matrices”
Matrix (m  n) - a set of numbers arranged in rows (m) and columns (n)
Scalar: 1  1 matrix
Row Vector: 1  n matrix
Column Vector: m  1 matrix

13. >> pi
ans =
3.1416
>> size(pi)
>> a=[1 2 3; 4 5 6]
a =
>> size(a)
ans = a=

14. Complex variables MATLAB handles complex arithmetic automatically
No need to compute real and imaginary parts separately
The unit imaginary number i = is preassigned
» x=5+2*i
x = i
» y=5*x+3
y = i

15. MATLAB Example default filename filename “matrix1” » x=3+5-0.2 » who
7.8000
» y=3*x^2+5
y =
» z=x*sqrt(y)
z =
» A=[1 2 3; 4 5 6]
A =
» b=[3;2;5]
b = 3 2 5
» C=A*b
C = 22 52
» who
Your variables are:
A b y
C x z
» whos
Name Size Bytes Class
A x double array
C x double array
b x double array
x x double array
y x double array
z x double array
» save
Saving to: matlab.mat
» save matrix1
default filename
filename “matrix1”

16. Data types All numbers are double precision
Text is stored as arrays of characters
You don’t have to declare the type of data (defined when running)
MATLAB is case-sensitive!!!

17. Variable Names Usually, the name is identified with the problem
Variable names may consist of up to 31 characters
Variable names may be alphabetic, digits, and the underscore character ( _ )
Variable names must start with a letter
ABC, A1, C56, CVEN_302
day, year, iteration, max
time, velocity, distance, area, density, pressure
Time, TIME, time (case sensitive!!)

18. Initializing Variables
Explicitly list the values
reads from a data file
uses the colon (:) operator
reads from the keyboard
A = [1; 3; 5; 10]; B = [1 3 5; ]
C = [ ; 0 1 … (continuation)
1 -2; ]
E = [A; 1; A]; F = [C(2,3); A]

19. Matrix Concatenation

20. Colon Operator Creating new matrices from an existing matrix
F = C(:, 2:3) = [2,5; 0,1; 2,-1; 1,4]

21. Colon Operator Creating new matrices from an existing matrix
E = C(2:3,:) = [-1 0 1; ]

22. Colon Operator Creating new matrices from an existing matrix
G = C(3:4,1:2) = [3,2; 0,1]

23. Colon Operator Variable_name = a:step:b time = 0.0:0.5:2.5
Negative increment
values = 10:-1:2
values = [10, 9, 8, 7, 6, 5, 4, 3, 2]

24. linspace Function
linspace(x1, x2) gives 100 evenly spaced values between x1 and x2
x = linspace(x1,x2)
linspace(a,b,n) generate n equally spaced points between a and b
x = linspace(a,b,n)
» linspace(0,2,11)
ans =
Columns 1 through 7
Columns 8 through 11

25. logspace Function
logspace(a,b,n) generates a logarithmically equally spaced row vector
x = logspace(a,b,n)
logspace(a,b) generates 50 logarithmically equally spaced points
x = logspace(a,b)
» logspace(-4,2,7)
ans =

26. Special Matrices

27. Scalar Arithmetic Operations
In order of priority
(Matrix inverse)
Example: x = (a + b*c)/d^2
count = count + 1

28. Order of Precedence of Arithmetic Operations
Parentheses, starting with the innermost pair
Exponentiation, from left to right
Multiplication and division with equal precedence, from left to right
Addition and subtraction with equal precedence, from left to right
Examples: factor = 1 + b/v + c/v^2
slope = (y2 - y1)/(x2 - x1)
loss = f * length/dia * (1/2 * rho * v^2)
func = *(3*x^4 + (x + 2/x)^2)

29. Order of Precedence of Arithmetic Operations
The priority order can be overridden with parentheses
» a=3; b=5; c=2;
» s1 = a-b*c
s1 = -7
» s2=(a-b)*c
s2 = -4
» y = -7.3^2
y =
» y=(-7.3)^2
Multiplication has higher priority than subtraction
Exponentiation has higher priority than negation

30. Array Operations An array operation is performed element-by-element
MATLAB: C = A.*B;

31. Element-by-Element Operations

32. Vector and Matrix operations
But a*b gives an error (undefined) because dimensions are incorrect. Need to use .*

33. Vectorized Matrix Operations

34. Array Operations for m  n Matrices

35. Matrix Transpose

36. Built-in Functions All the standard operators +, , *, /, ^
Sqrt( ), abs( ), sin( ), cos( ), exp( ), tanh( ), acos( ), log( ), log10( ), etc.
These operators are vectorized

37. Built-in Functions
Certain functions, such as exponential and square root, have matrix definition also
Use “help expm” and “help sqrtm” for details
>> A = [1 3 5; 2 4 6; ]
A =
>> B = sqrt(A)
B =
i i
>> C = sqrtm(A)
C =
i i i
i i i
i i i
(element by element)
(C*C = A)

38. MATLAB Graphics
One of the best things about MATLAB is interactive graphics
“plot” is the one you will be using most often
Many other 3D plotting functions -- plot3, mesh, surfc, etc.
Use “help plot” for plotting options
To get a new figure, use “figure”
logarithmic plots available using semilogx, semilogy and loglog

39. Plotting Commands plot(x,y) defaults to a blue line
plot(x,y,’ro’) uses red circles
plot(x,y,’m*’) uses magenta asterisks
If you want to put two plots on the same graph, use “hold on”
plot(a,b,’r:’) (red dotted line)
hold on
plot(a,c,’ko’) (black circles)

40. Free-Falling Bungee Jumper
Use built-in functions sqrt & tanh
>> g = 9.81; m = 75.2; cd = 0.24;
>> t = 0:1:20
t =
Columns 1 through 15
Columns 16 through 21
>> v=sqrt(g*m/cd)*tanh(sqrt(g*cd/m)*t)
v =
Columns 1 through 9
Columns 10 through 18
Columns 19 through 21

41. Plot the velocity versus time curve
>> plot(t,v); grid on
>> title('Free Falling Bungee Jumper')
>> xlabel('time t (second)'); ylabel('velocity v (m/s)')
>> print –djpeg bungee.jpg
How to change line thickness, line color, font size, symbols, marker size, etc.?

42. Color, Symbols, and Line Types
Use “help plot” to find available Specifiers
b blue point solid
g green o circle : dotted
r red x x-mark dashdot
c cyan plus dashed
m magenta * star
y yellow s square
k black d diamond
v triangle (down)
^ triangle (up)
< triangle (left)
> triangle (right)
p pentagram
h hexagram
Colors Symbols Line Types

43. Adjust line thickness, font size, marker size, etc.
» x=0:0.1:5;
» y=2*x.^3-12*x.^2+8*x-6;
» H=plot(x,y,'b',x,y,'r*');
» set(H,'LineWidth',3,'MarkerSize',12)
» xlabel('x'); ylabel('y');
» title('f(x)=2x^3-12x^2+8x-6');
» print -djpeg075 poly.jpg
Adjust line thickness, font size, marker size, etc.
element-by-element operations x.^n

44. » x=0:0.1:10;
» y=sin(2.*pi*x)+cos(pi*x);
» H1=plot(x,y,'m'); set(H1,'LineWidth',3); hold on;
» H2=plot(x,y,'bO'); set(H2,'LineWidth',3,'MarkerSize',10); hold off;
» xlabel('x'); ylabel('y');
» title('y = sin(2\pix)+cos(\pix)');
» print -djpeg075 function.jpg

45. » x=0:0.1:3; y1=exp(-x); y2=sqrt(x);
» H=plot(x,y1,'b-',x,y2,'r--');
» set(H,'LineWidth',3)
» xlabel('x'); ylabel('y'); title('MATLAB Plots');
» H1=text(1.8,0.2,'exp(-x)'); set(H1,'FontSize',18);
» H2=text(1.8,1.3,'sqrt(x)'); set(H2,'FontSize',18);

46. figure or figure (#) : open a figure
Plotting Commands
plot (x, y) plot(x1, y1, x2, y2)
plot (x, y, ‘color symbol line style’)
» x = linspace(0, 2*pi);
» y = sin (2.*x);
» z = cos (0.5*x);
» plot (x, y)
» plot (x, y, x, z)
» figure (2)
» plot (x, y, 'r o -'); grid on
» hold on
» plot (x, z, 'b * :')
figure or figure (#) : open a figure
(red, circle, solid line)
(blue, star, dotted line)

47. Graphics Commands Axis, Labels, and Title
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 (Time)
» ylabel (Temperature)
» title (Temperature Record : )
» text (17, 120, Record High )
» text (85, -40, Record Low )
» axis ([ ]) » hold off
  - text string

48. CVEN 302-501 Homework No. 1 Chapter 2
Problems 2.2 (15), 2.4 (15), 2.7 (20), 2.10 (20), 2.11 (20).
Due Friday. 09/05/2008 at the beginning of the period