intro2matlab-basic knowledge about Matlab.pptx

INTRODUCTION TO
MATLAB
Kadin Tseng
Boston University
Scientific Computing and Visualization

 It is developed by The Mathworks, Inc. (http://www.mathworks.com)
 It is an interactive, integrated, environment
• for numerical/symbolic, scientific computations and other apps.
• shorter program development and debugging time than traditional
programming languages such as FORTRAN and C.
• slow (compared with FORTRAN or C) because it is interpreted.
• automatic memory management; no need to declare arrays.
• intuitive, easy to use.
• compact notations.
What is MATrix LABoratory ?
Introduction to MATLAB
2

 Latest version is MATLAB 2012b
 For Windows: double click MATLAB icon
 For Linux Cluster: katana% matlab
 Either case spawns a MATLAB window with >> prompt.
>> % from % to end of line used for code documentation
>> version % this will tell you the running MATLAB version
ans =
7.12.0.635 (R2011a)
>> help % lists available packages/toolboxes on system.
>> help elfun % lists functions in elementary functions package
>> help sin % instructions on the sine function
>> lookfor sine % if you don’t know the function name …
>> doc sin % for full details o ffunction
>> quit % to quit MATLAB
Getting Started With MATLAB
3

 Variable, function, file names
• is case sensitive, e.g., NAME and Name are 2 distinct names.
• variable begins with a letter, e.g., A2z or a2z
• can be a mix of letters, digits, and underscores (e.g., vector_A)
• reserved characters: % = + – ~ ; : ! ' [ ] ( ) , @ # $ & ^
• up to 63 characters
• A function performs a pre-defined task based on input to yield
certain outcome.
 File name
• MATLAB command files should be named with a suffix of ".m", e.g.,
myfile.m. An m-file typically contains a sequence of MATLAB
commands that will be executed in order
• A file may contain a collection of commands, functions
Note: To run, enter m-file, without .m, e.g.,
>> myfile
Rules on Variables and File Names
4

• Some characters are reserved by MATLAB for various purposes. Some
as arithmetic or matrix operators: =, +, - , *, / , and others are used
to perform a multitude of operations. Reserved characters cannot be
used in variable or function names.
• >> % anything after % until the end of line is treated as comments
>>
• >> a = 3 % define a to have the value 3
a =
3
• >> a = 3; % “;” suppresses printing
>>
• >> b = 4; c = 5; % “;” enables multiple commands on same line
>>
• >> d = 6, e = 7; % “,” delimits commands but enables printing
d =
6
Reserved Characters % = ; ,
5

• >> x = 1:2:9 % define vector x with : operator (begin:interval:end)
x =
1 3 5 7 9
• >> y = 3:5 % interval is defaulted to 1; same as y=[3:5]
y =
3 4 5
• >> X = [1, 2, 3; 4, 5, 6] % 2D array. The ; is vertical concatenation.
% [ ] for arrays. Prevents ambiguity
% ; concatenates vertically (new row)
% , concatenates horizontally (new columns)
X =
1 2 3
4 5 6
• >> X(2,3) % ( ) for subscripting; why ans ?
ans =
6
Reserved Characters : [ ] ( )
6

>> x = [1 2 3 … % elipses … means to be continued on the next line
4 5 6]
x =
1 2 3 4 5 6
>> s = 'this is a character string'; % blanks preserved within quotes
>> x = [1 2 3]' % ' performs transpose (e.g., turns row into column)
x =
1
2
3
>> X = [1 2 3; 4 5 6]; size(X) % figure out the size (dimensions) of X
ans =
2 3
>> X = [1 2 3; 4 5 6]; numel(X) % total number of entries in X
ans =
6
Reserved Characters … and '
7

• >> !dir % “!” lets you run a command in MS Windows
Volume in drive C has no label.
Volume Serial Number is 6860-EA46
Directory of C:Program FilesMATLAB704work
01/31/2007 10:56 AM <DIR> .
01/31/2007 10:56 AM <DIR> ..
06/13/2006 12:09 PM 12 foo.exe
06/13/2006 08:57 AM 77 mkcopy.m
• >> !ls -l % “!” lets you run a similar command in Unix/Linux
total 0
-rw-r--r-- 1 kadin scv 0 Jan 19 15:53 file1.m
>> system(‘ls -l’) % more general form; also unix(‘ls -l’)
Reserved Character ! (or system)
8

>> a = 1:3; % a is a row vector
>> b = 4:6; % b is a row vector
>> c = a + b % c has same shape as a & b
c =
5 7 9
>> A = [a;b] % combines rows to generate 2x3 matrix A; A=a;b ?
A =
1 2 3
4 5 6
>> B = A' % B is transpose of A
B =
1 4
2 5
3 6
Other ways to create B ? (hint: with a and b )
Array operations
9

>> C = A*B % * is overloaded as matrix multiply operator
C =
14 32
32 77
>> D = A.*A % a .* turns matrix multiply to elemental multiply
D =
1 4 9
16 25 36
>> E = A./A % elemental divide
E =
1 1 1
1 1 1
>> who % list existing variables in workspace
Your variables are:
A B C D E a b d
Matrix Operations
10

>> whos % detail listing of workspace variables
Name Size Bytes Class Attributes
A 2x3 48 double
B 3x2 48 double
C 2x2 32 double
D 2x3 48 double
E 2x3 48 double
a 1x3 24 double
b 1x3 24 double
c 1x3 24 double
>> A = single(A); % recast A to single data type to save memory
>> whos
Name Size Bytes Class
A 2x3 24 single
>> clear % delete all workspace variables
Data Precisions
11

for j=1:5 % use for-loops to execute iterations / repetitions
for i=1:3
a(i, j) = i + j ;
end
end
Utilities to initialize or define arrays: ones, rand, eye, . . .
Trigonometric and hyperbolic functions : sin, cos, sqrt, exp, . . .
These utilities can be used on scalar or vector inputs
>> a = sqrt(5); v = [1 2 3]; A = sqrt(v);
For Loops
12

Scalar operation . . .
a = zeros(3); b = zeros(3);
for j=1:3
for i=1:3
a(i,j) = rand; % use rand to generate a random number
if a(i,j) > 0.5
b(i,j) = 1;
end
end
end
Equivalent vector operations . . .
A = rand(3); % A is a 3x3 random number double array
B = zeros(3); % Initialize B as a 3x3 array of zeroes
B(A > 0.5) = 1; % set to 1 all elements of B for which A > 0.5
if Conditional
13

A cell array is a special array of arrays. Each element of the cell
array may point to a scalar, an array, or another cell array.
>> C = cell(2, 3); % create 2x3 empty cell array
>> M = magic(2);
>> a = 1:3; b = [4;5;6]; s = 'This is a string.';
>> C{1,1} = M; C{1,2} = a; C{2,1} = b; C{2,2} = s; C{1,3} = {1};
C =
[2x2 double] [1x3 double] {1x1 cell}
[2x1 double] ‘This is a string.‘ []
>> C{1,1} % prints contents of a specific cell element
ans =
1 3
4 2
>> C(1,:) % prints first row of cell array C; not its content
Related utilities: iscell, cell2mat
Cell Arrays
14

Ideal layout for grouping arrays that are related.
>> name(1).last = ‘Smith’; name(2).last = ‘Hess’;
>> name(1).first = ‘Mary’; name(2).first = ‘Robert’;
>> name(1).sex = ‘female’; name(2).sex = ‘male’;
>> name(1).age = 45; name(2).age = 50;
>> name(2)
ans =
last: 'Hess'
first: 'Robert'
sex: 'male'
age: 50
Alternative style:
>> name = struct(‘last’,{Smith’,’Hess’}, ‘first’,{Mary’,’Robert’},…
(‘sex’,{female’,’male’}, ‘age’,{45,50});
Related utilities: isstruct, fieldnames, getfield, isfield
Structures
15

There are many types of files in MATLAB.
Only script-, function-, and mat-files are covered here:
1.script m-files (.m) -- group of commands; reside in base workspace
2.function m-files (.m) -- memory access controlled; parameters passed
as input, output arguments; reside in own workspace
3.mat files (.mat) -- binary (or text) files handled with save and load
4.mex files (.mex) -- runs C/FORTRAN codes from m-file
5.eng files (.eng) -- runs m-file from C/FORTRAN code
6.C codes (.c) – C codes generated by MATLAB compiler
7.P codes (.p) – converted m-files to hide source for security
File Types
16

If you have a group of commands that are expected to be executed
repeatedly, it is convenient to save them in a file . . .
>> edit mytrig.m % enter commands in editor window
a=sin(x); % compute sine x (radians)
b=cos(x); % compute cosine x (radians)
disp( [‘a = ‘ num2str(a) ] ) % prints a; here, [ . . . ] constitutes a string array
disp( [‘b = ‘ num2str(b) ] ) % prints b
Select File/Save to save it as mytrig.m.
A script shares the same scope with that which it operates. For example,
if it runs from the matlab
Define x, then use it in mytrig.m:
>> x=30*pi/180; % converts 30 degrees to radians
>> mytrig % x is accessible to mytrig.m; share same workspace
a = 0.5000
b = 0.8660
Script m-file
17

• It is declared with the key word function, with optional input
parameters on the right and optional output on the left of =. All
other parameters within function reside in function’s own workspace.
Use MATLAB editor to create file: >> edit average.m
function avg=average(x)
% function avg=average(x)
% Computes the average of x
% x (input) matrix for which an average is sought
% avg (output) the average of x
avg = sum(x)/numel(x); % the average
end
Save the above with File/Save
• Recommendation: saves file with name same as function name
• It may be called from a script, another function, or on command line:
• >> a = average(1:3) % a = (1 + 2 + 3) / 3
a =
2
>> help average % prints contiguous lines with % in average
Function m-files
18

Scripts
• Pros:
- convenient; script’s variables are in same workspace as caller’s
• Cons:
- slow; script comands loaded and interpreted each time it is used
- risks of variable name conflict inside & outside of script
Functions
• Pros:
• Scope of function’s variables is confined to within function. No
worry for name conflict with those outside of function.
• What comes in and goes out are tightly controlled which helps when
debugging becomes necessary.
• Compiled the first time it is used; runs faster subsequent times.
• Easily be deployed in another project.
• Auto cleaning of temporary variables.
• Cons:
• I/O are highly regulated, if the function requires many pre-defined
variables, it is cumbersome to pass in and out of the function – a
script m-file is more convenient.
Script or Function m-file ?
19

>> magic(n) % creates a special n x n matrix; handy for testing
>> zeros(n,m) % creates n x m matrix of zeroes (0)
>> ones(n,m) % creates n x m matrix of ones (1)
>> rand(n,m) % creates n x m matrix of random numbers
>> repmat(a,n,m) % replicates a by n rows and m columns
>> diag(M) % extracts the diagonals of a matrix M
>> help elmat % list all elementary matrix operations ( or elfun)
>> abs(x); % absolute value of x
>> exp(x); % e to the x-th power
>> fix(x); % rounds x to integer towards 0
>> log10(x); % common logarithm of x to the base 10
>> rem(x,y); % remainder of x/y
>> mod(x, y); % modulus after division – unsigned rem
>> sqrt(x); % square root of x
>> sin(x); % sine of x; x in radians
>> acoth(x) % inversion hyperbolic cotangent of x
Some Frequently Used Functions
20

 Line plot
 Bar graph
 Surface plot
 Contour plot
 MATLAB tutorial on 2D, 3D visualization tools as well as other graphics
packages available in our tutorial series.
MATLAB Graphics
21

>> t = 0:pi/100:2*pi;
>> y = sin(t);
>> plot(t,y)
Line Plot
22

>> xlabel(‘t’);
>> ylabel(‘sin(t)’);
>> title(‘The plot of t vs sin(t)’);
Line Plot
23

>> y2 = sin(t-0.25);
>> y3 = sin(t+0.25);
>> plot(t,y,t,y2,t,y3) % make 2D line plot of 3 curves
>> legend('sin(t)','sin(t-0.25)','sin(t+0.25',1)
Line Plot
24

Generally, MATLAB’s default graphical settings are adequate which make
plotting fairly effortless. For more customized effects, use the get and set
commands to change the behavior of specific rendering properties.
>> hp1 = plot(1:5) % returns the handle of this line plot
>> get(hp1) % to view line plot’s properties and their values
>> set(hp1, ‘lineWidth’) % show possible values for lineWidth
>> set(hp1, ‘lineWidth’, 2) % change line width of plot to 2
>> gcf % returns current figure handle
>> gca % returns current axes handle
>> get(gcf) % gets current figure’s property settings
>> set(gcf, ‘Name’, ‘My First Plot’) % Figure 1 => Figure 1: My First Plot
>> get(gca) % gets the current axes’ property settings
>> figure(1) % create/switch to Figure 1 or pop Figure 1 to the front
>> clf % clears current figure
>> close % close current figure; “close 3” closes Figure 3
>> close all % close all figures
Customizing Graphical Effects
25

>> x = magic(3); % generate data for bar graph
>> bar(x) % create bar chart
>> grid % add grid
• To add a legend, either use the legend command or via insert in the Menu
Bar on the figure. Many other actions are available in Tools.
• It is convenient to use the Menu Bar to change a figure’s properties
interactively. However, the set command is handy for non-interactive
changes, as in an m-file.
• Similarly, save a graph via the Menu Bar’s File / Save as or
>> print –djpeg 'mybar' % file mybar.jpg saved in current dir
Save A Plot With print
26

>> x = magic(3); % generate data for bar graph
>> bar(x) % create bar chart
>> grid % add grid for clarity
2D Bar Graph
27

• Many MATLAB utilities are available in both command and function forms.
• For this example, both forms produce the same effect:
• >> print –djpeg 'mybar' % print as a command
• >> print('-djpeg', 'mybar') % print as a function
• For this example, the command form yields an unintentional outcome:
• >> myfile = 'mybar'; % myfile is defined as a string
• >> print –djpeg myfile % as a command, myfile is treated as text
• >> print('-djpeg', myfile) % as a function, myfile is treated as a variable
• Other frequently used utilities that are available in both forms are:
• save, load
Use MATLAB Command or Function ?
28

>> Z = peaks; % generate data for plot; peaks returns function values
>> surf(Z) % surface plot of Z
Try these commands also:
>> shading flat
>> shading interp
>> shading faceted
>> grid off
>> axis off
>> colorbar
>> colormap(‘winter’)
>> colormap(‘jet’)
Surface Plot
29

>> Z = peaks;
>> contour(Z, 20) % contour plot of Z with 20 contours
>> contourf(Z, 20); % with color fill
>> colormap('hot') % map option
>> colorbar % make color bar
Contour Plots
30

• Integration of cosine from 0 to π/2.
• Use mid-point rule for simplicity.
Integration Example
31
h
h
i
a
dx
x
dx
x
m
i
m
i
ih
a
h
i
a
b
a
)
)
(
cos(
)
cos(
)
cos( 2
1
1
1
)
1
(



 

 




mid-point of increment
cos(x)
h
a = 0; b = pi/2; % range
m = 8; % # of increments
h = (b-a)/m; % increment

% integration with for-loop
tic
m = 100;
a = 0; % lower limit of integration
b = pi/2; % upper limit of integration
h = (b – a)/m; % increment length
integral = 0; % initialize integral
for i=1:m
x = a+(i-0.5)*h; % mid-point of increment i
integral = integral + cos(x)*h;
end
toc
Integration Example — using for-loop
32
X(1) = a + h/2 X(m) = b - h/2
a
h
b

% integration with vector form
tic
m = 100;
a = 0; % lower limit of integration
b = pi/2; % upper limit of integration
h = (b – a)/m; % increment length
x = a+h/2:h:b-h/2; % mid-point of m increments
integral = sum(cos(x))*h;
toc
Integration Example — using vector form
33
X(1) = a + h/2 X(m) = b - h/2
a
h
b

1. Use the editor to write a program to generate the figure that describe the
integration scheme we discussed. (Hint: use plot to plot the cosine curve.
Use bar to draw the rectangles that depict the integrated value for each
interval. Save as plotIntegral.m
2. Compute the integrals using 10 different increment sizes (h), for m=10, 20,
30, . . . , 100. Plot these 10 values to see how the solution converges to the
analytical value of 1.
Hands On Exercise
34

a = 0; b=pi/2; % lower and upper limits of integration
m = 8; % number of increments
h = (b-a)/m; % increment size
x= a+h/2:h:b-h/2; % m mid-points
bh = bar(x,cos(x),1,'c'); % make bar chart with the bars in cyan
hold % all plots will be superposed on same figure
x = a:h/10:b; % use more points at which to evaluate cosine
f = cos(x); % compute cosine at x
ph = plot(x,f,'r'); % plots x vs f, in red
% Compute integral with different values of m to study convergence
for i=1:10
n(i) = 10+(i-1)*10;
h = (b-a)/n(i);
x = a+h/2:h:b-h/2;
integral(i) = sum(cos(x)*h);
end
figure % create a new figure
plot(n, integral)
Hands On Exercise Solution
35

 SCV home page (www.bu.edu/tech/research)
 Resource Applications
www.bu.edu/tech/accounts/special/research/accounts
 Help
• System
• help@katana.bu.edu, bu.service-now.com
• Web-based tutorials (
www.bu.edu/tech/research/training/tutorials)
(MPI, OpenMP, MATLAB, IDL, Graphics tools)
• HPC consultations by appointment
• Kadin Tseng (kadin@bu.edu)
• Yann Tambouret (yannpaul@bu.edu)
Useful SCV Info
36

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