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constant	Return value
ans	Default variable name , Save recent results . If you do not specify an output variable for the expression ,MATLAB The results will be automatically saved to ans variable
eps	Floating point relative precision . yes MATLAB Tolerance for calculation
realmax	The maximum number of floating-point numbers that a computer can represent
realmin	The smallest floating point number that a computer can represent
pi	PI
i, j	An imaginary unit
inf	Unlimited value . similar n/0 The result of the expression of is inf, among n For the wrong 0 The set of real Numbers
NaN	Indicates an illegal value , Non numerical . similar 0/0 and inf/inf The result of the expression of , And NaN The results of relevant arithmetic operations , as well as n/0,n When it is a complex number, the result is NaN
computer	Computer type
version	MATLAB Version string

2. Variable

MATLAB The first variable must be a letter

MATLAB Case sensitive （a And A It's a different variable ）

3. vector

1. Direct construction method

a=[1 2 3 4 5 6 7]

2. Incremental method to construct vector

The first data of the incremental method is the initial value , The second data is the step size , The third data is the end value .

a=1:2:10
b=10:-2:1

3. Use linspac Construct vectors

linspace The first parameter is zero Initial value , The second value is the end value , The third value is the number of elements in the generated vector, which is a vector constructed in an equal interval way

c=linspace(10,1,20)

4. Use logspace Construct vectors

The first parameter is zero 10^first, The second parameter is 10^last, The third parameter is the number of generated elements

x=logspace(0,1,10)

3、 ... and 、 matrix

1. Simple creation method

We use semicolons to separate when creating a matrix , But we must ensure that the number of elements in each row is the same .

a=[1,2,3;4,5,6;7,8,9]

2. Use meshgrid Construct matrix

this MATLAB function Based on vectors x and y The coordinates contained in the return 2D grid coordinates .X It's a matrix , Each line is x A copy of ;Y It's also a matrix , Each column is y A copy of . coordinate X and Y The grid represented has
length(y) Rows and length(x) Columns .
[X,Y] = meshgrid(x,y)
[X,Y] = meshgrid(x)
[X,Y,Z] = meshgrid(x,y,z)
[X,Y,Z] = meshgrid(x)

3. Construct a special matrix

Letter Count	work can
ones	Create one where all elements are 1 Matrix
zeros	Create one where all elements are 0 Matrix
eye	Create diagonal elements as 1, The other elements are 0 Matrix
diag	Create a diagonal matrix from a vector
magic	Create a square matrix , One line 、 The sum of columns and diagonal elements is equal
rand	Create a matrix or array , The elements are random numbers that obey uniform distribution
randn	Create a matrix or array , The elements are random numbers that obey normal distribution
randperm	Create a vector (1×n Matrix )

4. Aggregation matrix

In the following code , We used C to A On B The top and bottom are spliced together .

When combining different matrices , When a high-precision matrix is combined with a low-precision matrix, the new matrix is of low precision .

5. Describe arrays and matrices

• size – size function
• The length of the maximum dimension - length function
• dimension – ndims function
• Element number – numel function

6. Sort 、 reverse 、 Transposition 、 restore

• Sort - sort/sortrows function
• Flip – flip/fliplr/flipud function
• Transposition – rot90/transpose function
• restore – reshape, squeeze function

7. Get the elements of the matrix

• Use numbered index
• Use linear index
• Use a colon
• Use end keyword

1. Numbering index

2. Linear index

because MATLAB When you save an array, you save it by column , So we need to calculate by column when we do linear indexing .

In the following code, we see that what we are looking for is C(15) The first thing we look for is the first column , There are... In the first column 9 Elements , So our sixth element in the second column is our C(15)

3. Use a colon

Use colon to get all the elements of a row or a column , Or the entire array itself .

4. Use end Keyword to get the elements of the matrix

there end It means our last element , Then we started from 1 Start taking value , To the end , In steps of 3, Get all our data

C(1:3:end)

8. Multidimensional arrays

1. Create a random array with normal distribution

In the following code , What we generate is a 5×3×2 Three dimensional array of

2. Generate an array whose elements are the same constant

3. Use cat Generate multidimensional arrays

Four 、 data type

Data type of variable
     double Type value type
      Not double Type value type
      character string
      Date and time array
      Sort array
      surface
      schedule
      Structure array
      Array of cells
      Function handle

1. character string

• String creation
• String comparison
• String aggregation
• Search and replace strings

1. Create string

When creating a string , It is OK to use single quotation marks or double quotation marks .

Of course, we can also create two-dimensional strings , But the number of elements in each line of string should be the same , And we can use the index of the two-dimensional array to manipulate our two-dimensional string .

2. Type conversion

Use mat2str Function to convert an array to a string

Use int2str Function to convert integer data to string data

2. Function handle

Function handles are used to hold MATLAB All information related to the operation of functions in

Here we define a function （. Point multiplication , That is, to process every element in our matrix .）

So the function represented by the following code is f=(3-2x)^2*x

function f=myfun(x)
f=(3-2.*x).^2.*x;

x=fminbnd(@myfun,0,1.5)

In the code above , We have achieved the goal of 0 and 1.5 Pass it into our above method , Then the process of finding the minimum , Then we can get our x The value is 1.4999

5、 ... and 、M Document design

     Variable
     expression
     Process control
     function
    M file
     Program debugging and error handling

1. Variable

local variable ： The scope of local variables is limited to this function
Global variables ： For global variables global Keyword to declare , Its scope of action is the whole M file

2. expression

• The value represents
• Operator
• Handle string expressions

3. The value represents

MATLAB Using traditional numerical representation . For longer numbers , Use scientific counting , Use letters e Specified in 10 Is the power of the base . For imaginary numbers i or j As a suffix .

4. Operator

• Arithmetic operator
• Relational operator
• Logical operators
• Operator precedence

1. Arithmetic operator

Operator	say bright	Operator	say bright
+	Add	.*	Dot by dot
-	reduce	./	Divide right by element
*	Matrix multiplication	.\	Divide left by element
/ (a/b)	Right division of a matrix ,a ride b The inverse of	.^	Exponentiation per element
\ (a\b)	Matrix left Division ,a Inverse multiplication of b	'	Complex conjugate transpose
^	The power of a matrix	()	Specify the calculation order

2. Relational operator

Operator	Sketch Statement	Operator	Sketch Statement
<	Less than	>=	Greater than or equal to
<=	Less than or equal to	==	be equal to
>	Greater than	~=	It's not equal to

3. Logical operators

Operator	Letter Count	Sketch Statement	in example
&	and	The values at the same position in both arrays are not 0 When to return to 1, Otherwise return to 0	A & B=01001 or and(A,B)
\|	or	A value at the same position in two arrays has a non 0 When to return to 1, Otherwise return to 0	A \| B=11101 or or(A,B)
~	not	Invert the elements in the array , It's not 0 Value to 0,0 Turn into 1	~A=10010 or not(A)
	xor	There is only one non - element in the same position in two arrays 0 When to return to 1, Otherwise return to 0	xor(A,B)=10100
	any(C)	If any of the elements in the vector is not 0, return 1; Otherwise return to 0	any(C) ans= 0 1 1
	all(C)	If all the elements in the vector are not 0, return 1, Otherwise return to 0	all(C) ans= 0 1 0
&&		If the expressions at both ends of the symbol are true , return true(1); Otherwise return to 0	a=8; a>5 && a<10 ans= 1
\|\|		If one of the expressions at both ends of the symbol is true , return true(1); Otherwise return to 0	a=11; a>5 \|\| a<10 ans= 1

xor Function demonstration

4. Operator precedence

• parentheses ()
• Transposition (.')、 power (.^)、 Complex conjugate transpose (')、 The power of a matrix (^)
• One dollar plus (+)、 One dollar minus (-)、 Logical not (~)
• ride (.*)、 Divide right (./)、 be demoted (.\)、 Matrix multiplication (*)、 Right division of a matrix (/)、 Matrix left Division (\)
• Add (+)、 reduce (-)
• The colon operator (:)
• Less than (<)、 Less than or equal to (<=)、 Greater than (>)、 Greater than or equal to (>=)、 be equal to (==)、 It's not equal to (~=)
• By element AND(&)
• By element OR(|)
•&&
•||

5. Process control

• Under controlled conditions
• Cycle control
• Program termination control

1. Under controlled conditions

Here we define a process control function .

This is the result of our test

Of course, I can also pass Switch-case Statement to implement process control

2. Cycle control

for loop
while loop

for loop

while loop

function f=testif(x)
sum=1;
while(x>=1)
    sum=sum*x;
    x=x-1;
f=sum;
end

3. Program termination control

command	Where to use it	Sketch Statement
break	for or while loop	When it appears , Exit loop , In nested loops , Enter the adjacent outer loop
continue	for or while loop	Skip the remaining statements in this loop , Enter the next iteration of this loop
return	Anywhere	When it appears , Exit the function immediately , Enter the calling function of the function

6、 ... and . function

1. Anonymous functions

Anonymous functions can be implemented quickly when implementing some simple functions

[email protected](arglist) expr

2. Check the number of input parameters

Use nargin You can determine the number of input parameters of the function ,nargout Function can determine the number of output parameters

function c = w(a, b)
  if (nargin == 1)
      c = 1;
  elseif (nargin == 2)
      c = 2;
  end

3. Function handle

Handle function allows our function to use a simple variable

function c = w(x)
 c=sin(x);
end

In the following code , We will w Method is passed to our x

Then when we can pass feval function , The first parameter is passed into our method , The second parameter is passed into our specific argument .

Of course, we can also pass in a string of data for batch calculation

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