[mathematical modeling] basic knowledge of MATLAB

MATLAB Basic knowledge of

One 、 Basic knowledge

notes ：matlab Script files are used in , Suffix is .m

1. notes

%% A single line of comments （ There are upper and lower horizontal lines – Can be used to partition ）
% General notes

Multiline comment ： Choose , Shortcut key Ctrl+R
Cancel multiline comment ： Choose , Shortcut key Ctrl+T

2. A semicolon

(1)

a = 3;
a = 5

Add a semicolon after the statement （;）, Indicates that the running results are not displayed , Otherwise, there will be output , As in the above example .

(2) Semicolons can also be used for district branches .

clear;clc

3.clear and clc

clear：
clear keyword —— Delete a variable
clear —— Delete all in the workspace Variable

clc ：
eliminate All text in the command line window , Keep the screen clean .

These two are usually used together , be used for ” initialization “, Prevent previous results from affecting subsequent operations / New script file

4. Input and output （disp and input）

Output ：

a = 100
disp(a)
disp(' This is a string ')
b = [1 2 3]
disp(b);
% notes ：disp Whether there is a semicolon after the function or not ！

Input :

%  Generally, we will input the number 、 vector 、 matrix 、 String, etc. to a variable , Here we give A
A = input(' Please enter A：');% It makes a difference whether you add a semicolon or not , The plus sign will have an output 
B = input(' Please enter B：')%

5. Judgment statement

if The line does not need a colon , At the end of the sentence, be sure to end ending ; The middle sentence should be indented .

a = input(' Please enter the test score :')
if a >= 85  
    disp(' Good grades ')
elseif a >= 60 
    disp(' Pass the grade ')
else
    disp(' Failing in grades ')
end % Indicates that the input is complete , Otherwise, you will be asked to continue to input 

Two 、 data type

1. Numbers

Can perform ordinary operations Add, subtract, multiply, divide, square root, exponential logarithm , Specifically, you can find the corresponding operator in the search box in the upper right corner .
Such as ：
3+3
5-1
6*6
8/8

2. Characters and strings

Use ’ ’ （ Single quotation marks ） or " " （ Double quotes ） Express

str = ' character string ‘

About string functions

(1) Merge two strings

a. function strcat(str1,str2,str3…strn)
eg：strcat(' character string 1',' character string 2')

b.[’ character string 1‘,‘ character string 2’]（ Separate with commas or spaces ）

(2) Convert numbers to strings

function ： num2str()

c = 100
num2str(c)
%  String concatenation 
disp(['c The values for ' num2str(c)])
disp(strcat('c The values for ', num2str(c)))

3. vector （ That's ok / As a 1 Matrix ）

Row vector

a = [1 2 3]
% perhaps  ( Separate the same line with spaces or commas ）
a = [1,2,3]

Column vector

% Semicolons can be used to separate the elements of each line 
a = [1;2;3] 

4. matrix

E = [1,2;3,4;5,6]
% Lines are separated by commas and spaces , Separate different lines with semicolons 

4.1sum Sum up

Vector summation

Whether row vector or column vector , It's all direct summation

E = [1,2,3]% Row vector 
sum(E)
E = [1;2;3]% Column vector 
sum(E)

Matrix sum

Matrix summation needs to be distinguished according to the direction of rows and columns

E = [1 2;3 4;5 6]

% a = sum(x) （ Unspecified , Sum by column , Get a row vector ）
  a = sum(E)

% dim = 1  Indicates sum by column （ Get the line vector ）
% dim = 2  Means sum by line （ Get the column vector ）
  a = sum(E,1)
  a = sum(E,2)

a = sum(x(:) %  Sum the entire matrix 
E(:)  %  Extract matrix by column vector 
a = sum(E(:))

% Another way 
a = sum(sum(E))

a = sum(E( : ) )

4.2 Extract the specified position elements in the matrix

（1） Take an element of the specified row and column （ Output a value ）

A=[1 1 4 1/3 3;1 1 4 1/3 3;1/4 1/4 1 1/3 1/2;3 3 3 1 3;1/3 1/3 2 1/3 1]; 
%  The matrix does not have to be written in one line ！
A
%  The above selection is inconvenient , This makes it easy to output the entire matrix 
A(2,1)
A(3,2)

（2） Take all the elements of a specified row （ The output is a line vector ）

A
A(2,:)% : Means to take all elements 
A(5,:)

（3） Take all the elements of a specified column （ The output is a column vector ）

A
A(:,1)
A(:,3)

（4） Take all the elements of some specified rows （ The output is a matrix ）

A
A([2,5],:)      %  Take only the second and fifth lines （ altogether 2 That's ok ）
A(2:5,:)        %  Take the second line to the fifth line （ altogether 4 That's ok ）
A(2:2:5,:)     %  Take the second and fourth lines  （ from 2 Start , Each increment 2 A unit of , To 5 end ）

% notes   Generation of arithmetic sequence 
1 : 3 : 10
10:-1:1 %( from 10 Start , Every time -1, To 1 end ）
1:10  % What you didn't say , The difference of equal difference is 1

A(2:end,:)      %  Take the second line to the last line 
A(2:end-1,:)    %  Take the second line to the penultimate line 

Take all the elements ( Spliced by column , The final output is a column vector )

A
A(:)

4.3 size function

size Function usage

size(A) % （1） Used to find the size of matrix , Returns a row vector , The first element is the number of rows of the matrix , The second element is the number of columns 
[r,c] = size(A) % （2） assignment   take A The number of lines assigned to r A The number of columns assigned to c
r = size(A,1)  % （3） Returns the number of rows 
c = size(A,2   %       Returns the number of columns 

4.4 repmat function

B = repmat(A,m,n): The matrix A Copy m×n block , Namely the A As B The elements of ,B from m×n individual A Tiled .

A = [1,2,3;4,5,6]
B = repmat(A,3,2)

4.5 Matrix operations

Matrix addition, subtraction, multiplication and division

A + B 
A - B
A * B
A / B

Find the inverse of a matrix

inv(B)

A = [1,2,3,4]
inv(A)
A/B = A*inv(B)

Multiplication and division between the corresponding elements of two matrices with the same shape

Need to use “ .*" and " ./"

A = [1,2;3,4]
B = [1,0;1,1]
A .* B
A ./ B %MATLAB in  inf Infinity 

Each element is multiplied or divided by a constant at the same time

All four operators can be used

A = [1,2;3,4]
A * 2 %  Same as the following 
A .* 2
A / 2 %  Same as the following 
A ./ 2

Each element multiplies simultaneously

A = [1,2;3,4]
A .^ 2 
A ^ 2 % =A*A
A * A

4.6 Find eigenvalues and eigenvectors

%  stay Matlab in , Calculation of matrix A The function of eigenvalues and eigenvectors of is eig(A), Two of the most commonly used uses ：
A = [1 2 3 ;2 2 1;2 0 3]
% （1）E=eig(A)： O matrix A All eigenvalues of , Make up a vector E.% Each eigenvalue corresponds to a set of eigenvectors 
E=eig(A)
% （2）[V,D]=eig(A)： O matrix A All eigenvalues of , Form a diagonal matrix D, And ask for A The eigenvectors of V The column vector .（V Every column of is D The eigenvector of the eigenvalues of the same column in ）
[V,D]=eig(A)

4.7 find The basic usage of function

Used to return vectors or matrices that are not 0 The location index of the element

X = [1 0 4 -3 0 0 0 8 6]
ind = find(X)
%  It has many uses , For example, before returning 2 It's not for 0 The location of the elements of ：
ind = find(X,2)


%  If X It's a matrix （ A two-dimensional , There are rows and columns ）
X = [1 -3 0;0 0 8;4 0 6] 
% return  1 3 4 8 9, Because it is regarded as a column vector 
ind = find(X)

%  If you need to output in the order of rows and columns 
[r,c] = find(X)
[r,c] = find(X,1)% Just find the first non 0 Elements 

4.8 Matrix and constant size judgment operation

X = [1 -3 0;0 0 8;4 0 6]
X > 0
X == 4