Study notes-Matlab basic learning

Basics: data type

Infinity: Inf or inf

Pi: pi

String: name='jack'

String array: char('jack','lucy')

>> a=char('lucy','tony')

a =

  2×4 char 数组

    'lucy'
    'tony'

Integer type: uint8, uint16, uint32, uint64, int8, int16, int32, int64

View the most value: intmin('int8'), intmax('int8')

>> intmin('int8')

ans =

  int8

   -128

Floating point number: double (default), single

Floating point precision (minimum resolution of numbers): eps('single'), eps('double')

Floating point precision (the maximum and minimum values of a number): realmax('single'), realmin('double')

>> eps('single')

ans =

  single

  1.1921e-07

 realmax('single')

ans =

  single

  3.4028e+38

Basics: Variables

Operators: +, -, *, /, \, ^

Variable assignment: x=15, x=3*x-12

Variable operation: a=12, b=4, c=a+b-2/b

Variable printing control: use; control

Variable naming: beginning with a letter, up to 63 characters, can contain numbers, letters, and underscores, case-sensitive, no brackets, spaces, and built-in keywords (such as length, sum, end, pi, i, j (imaginary number), eps, sin, cos, size, etc.)

View the built-in variables (keywords): iskeyword

View variables in the workspace: whos

Basics: commonly used built-in functions

Square root: sqrt(x)

Open the nth power: nthroot(x,n)

Exponent: exp(x)

Absolute value: abs(b)

Logarithm: log(x), log10(x) (default is base e)

Trigonometric functions: sin(x), cos(x)...

Myopia function: Take the nearest integer, that is, round (x), round to zero fix(x), round up ceil(x), round down floor(x), and take the remainder rem(x)

Clear memory variables: clear xyz, clear all, clc (clear command window)

View memory variables: who, whos

Vector basis

Row vector: A=[1 2 3 4] or A=[1,2,3,4]

Column vector: A=[1;2;3;4]

Row vector to column vector: B=A(:) or B=A'

View size: size(A), length(A)

>> A=[1 2;3 4;5 6]

A =

     1     2
     3     4
     5     6

>> size(A)

ans =

     3     2

>> length(A)

ans =

     3

size represents the size of the viewing matrix: several rows and several columns

length view the size of the vector: a few lines

Slicing method:

Start from the second element, take it to the end, and number in the order of the column. End can also be replaced by -1, end-1 means to the second to last, end-2 means to the third to last

>> A(2:end)

ans =

     3     5     2     4     6

Starting from the second element, taking 1 as the step size, get to the fourth element

A(2:4)

ans =

     3     5     2

Starting from the second element, using 2 as the step size, take the fifth element

>> A(2:2:5)

ans =

     3     2

Take discrete values:

>> A([1,3,4])

ans =

     1     5     2

Create a linearly distributed vector:

A=1:2:100, starting from 1, take a number every 3 intervals, and get to 100

A=linspace(1,100,99), 99 numbers are selected from 1 to 100, which is also an arithmetic sequence

Newline expression: use...

Scalar and vector operations: just use regular operators

Vector and vector operations: a dot before the operator, such as .+, .*, ./, .^ means one-to-one correspondence operation, if there is no dot, the operation will follow the matrix operation rules

Matrix foundation

Matrix definition:

A=[1,2;2,3] or A=[1 2;2 3]

Multiple expressions: A=[1:2:11;0:5:25;linspace(10,60,6);6 5 4 6 3 2]

>> A=[1:2:11;0:5:25;linspace(10,60,6);6 5 4 6 3 2]

A =

     1     3     5     7     9    11
     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2

Zero matrix: zeros(4,3) four rows and three columns

One matrix: ones(4,3)

Diagonal matrix: eye(5)

>> eye(5)

ans =

     1     0     0     0     0
     0     1     0     0     0
     0     0     1     0     0
     0     0     0     1     0
     0     0     0     0     1

Matrix transpose: A'

The semicolon expression of the matrix:

>> A

A =

     1     3     5     7     9    11
     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2

>> A(:,1:3),A(2:4,1:end),A(2:4,1:end-1)

ans =

     1     3     5
     0     5    10
    10    20    30
     6     5     4


ans =

     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2


ans =

     0     5    10    15    20
    10    20    30    40    50
     6     5     4     6     3

Discrete value:

A =

     1     3     5     7     9    11
     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2

>> A(1:3,[1 3])

ans =

     1     5
     0    10
    10    30

Condition value:

Deletion of matrix elements: A(:,2:4)=[]

The splicing of the matrix: C=[AB]

Commonly used matrix built-in functions

Create a diagonal matrix:

v=[2 4 7],v=diag(v)

v =

     2     4     7


v =

     2     0     0
     0     4     0
     0     0     7

Reverse access to focus elements:


>> v=rand(10,5),v=diag(v)

v =

    0.2760    0.7513    0.8407    0.3517    0.0759
    0.6797    0.2551    0.2543    0.8308    0.0540
    0.6551    0.5060    0.8143    0.5853    0.5308
    0.1626    0.6991    0.2435    0.5497    0.7792
    0.1190    0.8909    0.9293    0.9172    0.9340
    0.4984    0.9593    0.3500    0.2858    0.1299
    0.9597    0.5472    0.1966    0.7572    0.5688
    0.3404    0.1386    0.2511    0.7537    0.4694
    0.5853    0.1493    0.6160    0.3804    0.0119
    0.2238    0.2575    0.4733    0.5678    0.3371


v =

    0.2760
    0.2551
    0.8143
    0.5497
    0.9340

Change the matrix shape: reshape(A)

A =

     1     3     5     7     9    11
     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2

>> reshape(A,3,8)

ans =

     1     6    20    10     7     6    50    25
     0     3     5    30    15     9     3    60
    10     5     5     4    40    20    11     2

Get matrix size: size(A)

Get the maximum value of the matrix:

%%按列取最小值，n代表该最小值在该列中第几个元素
>> [d,n]=min(A)

d =

     0     3     4     6     3     2


n =

     2     1     4     4     4     4

>> A

A =

     1     3     5     7     9    11
     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2

>> max(A)

ans =

    10    20    30    40    50    60

>> max(max(A))

ans =

    60

Summation: sum(A)

Sort: sort(A)

Median: medium(A)

Average: mean(A)

Standard deviation: std(A)

>> A

A =

     1     3     5     7     9    11
     0     5    10    15    20    25
    10    20    30    40    50    60
     6     5     4     6     3     2

>> sum(A)

ans =

    17    33    49    68    82    98

>> sort(A)

ans =

     0     3     4     6     3     2
     1     5     5     7     9    11
     6     5    10    15    20    25
    10    20    30    40    50    60

>> mean(A)

ans =

    4.2500    8.2500   12.2500   17.0000   20.5000   24.5000

>> std(A)

ans =

    4.6458    7.8899   12.1209   15.8535   20.8886   25.4886

>> median(A)

ans =

    3.5000    5.0000    7.5000   11.0000   14.5000   18.0000

Dot product: dot(A,B)

random number:

rand generates a random number of type double between 0 and 1

rand(1,5) produces a matrix of one row and five columns with arbitrary elements between 0 and 1

rand(10): Generate a matrix of 10 rows and 10 columns

randperm(10), a positive integer in the specified range

>> randperm(10)

ans =

     1     5     7     3     4     6     8     9    10     2

Random numbers from standard normal distribution: randn(4,3)

Eigenvalues and eigenvectors: [v,d]=eig(A), if A is a square matrix

Matrix operations

Addition, subtraction, multiplication and division: +, -, .*, ./dot multiplication *, /cross multiplication

Matrix inversion: inv(A)

Script editor

Script definition: .m file

Script code writing:% comment

Script function writing: the use of function

Script function run: name

f is the output value, the script name must be consistent with the function name

Anonymous function:

>> f2=@(x,y)2*x^2-4*x*y+y^2;
>> f2(2,3)

ans =

    -7