matlab_tutorial.m

matlab工具箱的应用演示程序,

% Basic MATLAB tutorial for Informatics students
% Predrag Radivojac
% Indiana University School of Informatics
% Bloomington, Indiana
% [e-mail]

% Tutorial is available at
% www.informatics.indiana.edu/predrag

%***********************************************************
% 1. MATLAB Basics
%***********************************************************

% MATLAB is an interpreting programming language that supports all
% basic operations and functions like other programming languages
% (e.g. if-else structure, for loop, while loop, case-switch structure, 
% break, try, catch, return, ...)

% check version of MATLAB
version

% check version of MATLAB and toolboxes
ver

% check working directory
pwd

% delete all variables from the workspace (same as only 'clear')
clear all

% clear screen
clc

% define variable 'a'
% 'a' will be displayed on the screen; semi-colon will stop printouts
a = 10

% use if, for
if (a == 4) % parentheses are not required
   b = a ^ 2 % 'b' equals 'a' squared, b is printed on the screen
elseif (a ~= 10)
   b = a
else
   b = -a
end % note that there is only one 'end' for the whole 'for' structure

% for loop - start with 1, step is 2, end if i <= 10
for i = 1 : 2 : 10
	i   
end

% MATLAB supports help system through its help window, or through help statement from the
% command prompt (e.g. help case)
help case

% There is also a "lookfor" function, when we are not sure what is the exact name of 
% the statement or the function. Lookfor searches for specifiec word through description 
% of all available MATLAB functions e.g. "lookfor write" gives all functions that contains 
% the word write in their description

% In addition, MATLAB has integrated powerful functons for elementary matrix 
% manipulation and numerical linear algebra, elementary and specialized math 
% functions, 2D and 3D graphic, interpolation, polynomials, Fourier transforms,
% sparse matrices, .....

% Unlike other languages it DOES NOT make executable code (a special toolbox is needed for it)
% Instead, it interprets comands of functions written in the script or inside a function.


% Function has a specific syntax and should be called.
% It can have more than one input and output arguments.
% Normally, arguments are transfered by value. It is possible to pass arguments 
% by reference (as common attributes for caller and the function), but you'll 
% never need this...

a = 5; % 'a' is not displayed
b = 4  % 'b' is displayed

% 'operations' is a function that takes two input variables and returns two
% output variables; these two are displayed since no semi-colon is after
% 'operations'
[sum_ab, product_ab] = operations(a, b)
pause(3) % go to sleep for 3 seconds


%***********************************************************
% 2. Matrix Operations
%***********************************************************

A = [1  2  3 
     4  5  6
     7  8  9
     10 11 12]
   
B = [1  3  5
     7  11  13
     17 19  23
     29 31 37]
   
% another way to initialize a matrix   
C = [1 2 3 4; 5 6 7 8; 9 10 11 12]

D = A + B

E = A * C

F = C * B

F1 = inv(sqrt(F))

% notice the use of a dot "." BEFORE a command
A
B
G = B ./ A
G_transpose = G'
G_transpose = transpose(G)

% go to sleep until interrupted (you need to press any key in MATLAB's main window)
pause

% MATLAB is very powerful in matrix computations
% DO NOT USE for loop for matrix calculations
% THERE IS ALWAYS A FASTER WAY TO DO THINGS

% dimensions of the matrix 'A'
[num_rows, num_cols] = size(A)

% or only the number or rows (first dimension)
num_rows = size(A, 1)

% or only the number or columns (second dimension)
num_cols = size(A, 2)
 
A
sum(A)       % sumation performed over columns
sum(A, 1)    % same as above

sum(A, 2)    % sum of rows

sum(sum(A))  % sum all elements in the matrix

% the use of column operator is VERY important in MATLAB
% for instance, let's separate one COLUMN
A
for i = 1 : size(A, 2)
  A_column = A(:, i)
end

% separate one ROW
A
for i = 1 : size(A, 1)
  A_row = A(i, :)
end  

% special matrix functions
diagonal_matrix = diag([1 2 3 4])
all_zeros = zeros(3, 4)
all_ones = ones(4, 2)
identity_matrix = eye(4)


%***********************************************************
% 3. Operations on Strings
%***********************************************************

% define two arbitrary strings
s1 = 'WBuCDefg3'
s2 = 'AAAaAAA'

% concatenate two strings
s = [s1 s2]

% this works with matrices too
A
a1 = [9 8 7 6]'
A1 = [A a1]
a1 = [0 0 0 0]
A1 = [A1; a1]

% back to strings, let's find the beginning of the substring 'AaA' in s
pos = findstr('AAA', s)

% let's form a cell array of strings... (note curly braces for cell arrays)
S{1} = s1
S{2} = s2
S{3} = s
% ... and find all that start with 'AAA'
pos = strmatch('AAA', S)
% ... now find only exact matches (shouldn't be any!)
pos = strmatch('AAA', S, 'exact')

% compare two strings, a standard operation
strcmp(s1, s2)

% check if a variable is a string
isstr(s1) % this IS a string
isstr(S)  % this is NOT a string (it is a cell array of strings)

%***********************************************************
% 4. Basic Statistics and Set Operations
%***********************************************************

A
mean_A_col = mean(A)        % mean over columns
mean_A_row = mean(A, 2)     % mean over rows
std_A_col = std(A)          % standard devaition
std_A_row = std(A, [], 2)   % standard deviation ([] MUST be here - check help for details)
median_A_col = median(A, 1) % median
median_A_row = median(A, 2) % median

% now, switch to set operations
a = [1 2 3 4 5 6 7]
b = [2 4 6 8 10 12]

% find intersection of the two sets (will be a sorted array)
c = intersect(a, b)

% find union of the two (will be a sorted array)
c = union(a, b)

% find difference of the two (note: it is a directional operation)
c = setdiff(a, b)


%***********************************************************
% 5. Find Function, a very useful function
%***********************************************************

c
% find all indices where components of vector c are greater than 3
pos = find(c > 3)

% let's do a more complicated one
c = union(a, b)
pos = find(c > 3 & mod(c, 2) == 0) % greater than 3 and even ('&' is logical AND)

% let's change all elements found before
% note that we are indexing using vector 'pos'
c(pos) = 999

% instrad of logical AND use logal OR
pos = find(c > 3 | mod(c, 2) == 0) % greater than 3 or even
c(pos) = 555


%***********************************************************
% 6. Input/Output
%***********************************************************

% clear screen
clc

% check what variable we have in memory
who

% check what variable we have in memory (more detailed)
whos

% check if matrix A is in the workspace
whos A

% save specified variables into a specified file in ascii format
E
save ascii_matrix.txt E -ascii 

% save specified variables into a specified file in the binary (MATLAB-specific) format
% default extension is *.mat
save bin_matrices A B C

% to save ALL variables, write only a file name. All variables in scope will be saved
save binary_all

clear A
whos       % 'A' is not listed (if it is we should contact MathWorks!!!)

clear all  % delete all variables in scope
clc        % clear screen
whos       % you should see an empty list!

% load variable 'A' from a *.mat file
load binary_all A
whos

% load all variables from a *.mat file
load binary_all 
whos

% load from an ASCII file
E_matrix = load('ascii_matrix.txt')
% or 
load ascii_matrix.txt
E_matrix = ascii_matrix
E

% To read from general binary files, functions fopen, fread etc. have to be used

% ececute an external command (symbol "!" indicates OS command)
!copy ascii_matrix.txt copy_of_ascii_matrix.txt

% delete a file through MATLAB
delete('copy_of_ascii_matrix.txt');

% now, make it again using command 'dos' (for unix systems use 'unix')
dos('copy ascii_matrix.txt copy_of_ascii_matrix.txt');

% eval command, useful in many cases (here just to delete a file, system command again)
file_to_delete = 'copy_of_ascii_matrix.txt';
eval(['! del ' file_to_delete]);

% if you don't want to see operating system displays use 'system' command
% 's' will be the status and 'w' will be OS output
[s, w] = system('dir');
display(w); % see what's in the current directory

%***********************************************************
% 7. Graphics
%***********************************************************

% define vector t (to indicate time)
t = 0 : 0.1 : 5
x = sin(pi * t) + 0.1 * t;
y = cos(pi * t) - 0.2 * t;
plot(t, x);
plot(t, y);

% plot x vs. y
plot(x, y);       % plots 'y' as a function of 'x'
hold on           % enables plotting one figure over another
plot(x, y, 'r*'); % plots blue stars instead of line

% play a bit more with x, y, and z
figure;                 % starts a new (empty) figure
z = 2 * t;
plot3(x, y, z, 'm-d');  % shows magenta diamonds in addition to line

% try a 3-D function (example from MATLAB's Demo)
z = peaks(25);                          
surfl(z);                             
shading interp;                       
colormap(pink);      

% Other nice graphic functions imagesc, meshgrid, ...
% use HELP for these commands

%***********************************************************
% 8. Some Useful Functions, New and Revisited
%***********************************************************

A = [0     7     1     5     0
     1     7     4     6     1
     4     3     9     1     5
     8     9     4     5     0
     9     3     3     5     2
     0     1     4     9     3
     7     7     7     9     9
     8    10     7     5     3
     7     2     9     8     3
     10    4     8     7     4]

A1 = sort(A)       % SORT each column separately
A2 = sort(A, 2)    % SORT each row separately

% FIND all rows (examples) where the values in
% second columen are greater than 5