MATLAB is an interactive language which can be used for numerical analysis and data visualization, and it is widely used in the analysis and design of vibration control engineering. A variety of toolboxes allow MATLAB to be extended to different areas.
1.1 Matrix Generation
A matrix is a collection of values organized by rows and columns (column).
A=[1 2 3 4;5 6 7 8;9 10 11 12]
The matrix can be transpose (transpose) with an apostrophe (apostrophe)
B=a '
Use a colon (colon) between two integers to generate all integers between two integers
A=1:8 generates line vectors (row vector) a=[1 2 3 4 5 6 7 8]
Use a colon between three numbers to generate all numbers in the middle number of steps between two numbers
b=0.0:. 2:1 generates a row vector (row vector) b=[0.0 0.2 0.4 0.6 0.8 1.0]
Other ways to build it are as follows:
C=linspace (0,10,21)//Generate linear space line vector (21 generated between 0~10)
D=logspace ( -1,1,10)//Generate logarithmic space row vectors (10 generated between -1~1)
Eye (3)//Generate 3*3 unit matrix (identity matrix)
Zeros (3,2)//Generate 3*2 full 0 matrix
1.2 Matrix Processing
Number of matrix cells
Suppose there is a matrix A (2,3)
Size (A) returns the number of rows and columns
D=size (A)//d=[2 3]
Length (A) returns the maximum value in all dimensions
E=length (rand (2,3,5))//e=5
Transpose (Transpose)
A
Get a column or a row in a matrix
A (:, 3)//Get the 3rd column of data in a
A (2,:)//Get the 2nd row of data in a
Matrix point multiplication, two matrix dimensions must be exactly the same
A (2,3); B (2,3); C=a.*b;
If it is a square matrix, similar to E, multiple multiplication can be abbreviated as
E.^4
Matrix multiplication
A (2,3); B (3,2); C=a*b//c should be C (2,2)
If it is a square matrix, similar to E, multiple multiplication can be abbreviated as
E^4
1.3 Functions
MATLAB contains many standard functions, such as sin and cos
i=0+1.0i;
j=0+1.0i;
cos (pi) =-1;
EXP (1) = 2.7183;
LOG (exp (1)) = 1;
LOG10 (10) = 1;
INV () returns the inverse matrix of the matrix (inverse matrix)
b=Inv (A);
Det () Returns the value of the determinant of the matrix (determinant of a matrix)
Det (A);
Trace () returns the sum of the main diagonal values of the matrix
Trace (A);
You can use the Help function name to get a description of the function
1.4 Drawing
MATLAB can be convenient for drawing rich numerical graphics.
e.g in [pi/100, 10pi] The figure of sin (x) x/
X=pi/100:pi/100:10*pi;
Y=sin (x)/x;
Plot (x, y);
grid;
Common drawing functions:
Plot (x, y)//Paint function
Subplot ()//a sheet of paper to draw multiple graphs, to determine the position of the diagram
Figure
Subplot (2,1,1);
Plot (x,y1);
Subplot (2,1,2);
Plot (x,y2);
Title ()
Xlabel ();
Ylabel ();
Grid
1.5 Programming
1.5.1 M-File
Files that contain many MATLAB statements are called M files.
1.5.2 Cycle
For loop
For N=0:10
X (n+1) =sin (PI*N/10);
End
Loops can be nested
H=zeors (5)
For K=1:5
For L=1:5
H (k,l) =1/(K+L-1)
End
End
1.5.3 If statement
If condition
Statement
End
If condition
Statement
else condition
Statement
End
1.5.4 Sub-function
functions [return value] = function name (parameter)
function [mean] = stat (x)
n = length (x);
mean = SUM (x)/n;
"Vibration simulation using MATLAB" chapter I "Fundamentals of Matlab"