[matlab] matrix operation

Matrix operation

Generate matrix

How to generate row matrix ：

1. Colon expressions

   x = 1:1:5 
   % 1 2 3 4 5
   

   In steps 1, from 1 To 5 Generate value , Form row matrix .

   If the step size is not set , The default step size is 1.

2. linspace(a, b, n)

   linspace(1, 5, 5)
   % 1 2 3 4 5
   

   from 1 To 5 Generate 5 A numerical , Form row matrix .

   from a To b Generate n A numerical , Form row matrix .

   If we do not set up n, The default is 100.

A matrix is generated from a matrix

repmat function

B = repmat(A, m, n)： The matrix A As a whole , Horizontal replication m Time , Copy vertically n Time , obtain $m\times n$ individual A A matrix formed by a matrix , Return to the new matrix .

B = repmat(A, [m, n])： Same as above , The general usage of this call form is ：C = repmat(A, size(B));.

A = randi(10, 2, 3) %  produce [1, 10] Of 2×3 Matrix 
B = repmat(A, 3, 2)

give the result as follows ：

A =

     9     4     1
     7    10     5

B =

     9     4     1     9     4     1
     7    10     5     7    10     5
     9     4     1     9     4     1
     7    10     5     7    10     5
     9     4     1     9     4     1
     7    10     5     7    10     5

How matrix elements are referenced

1. Reference matrix elements by subscript

   A(3, 4) Get matrix A The elements in the third row and the fourth column .

   A(5, 7) = 2 The matrix A The elements in the fifth row and seventh column are set to 2, If the matrix A The previous size was less than five rows and seven columns , Then the matrix is extended , Unassigned elements are set to 0.

2. Reference matrix elements by ordinal numbers

   Column priority , from 1 Start .

   The sequence number and subscript correspond to each other , With $m\times n$ matrix A For example , Matrix elements A(i, j) The serial number of is $(j-1)\times m+i$.

The sequence numbers and subscripts of matrix elements can be used sub2ind and ind2sub Functions convert to each other .

1. sub2ind function : The row of the specified element in the matrix 、 Convert the column subscript to the stored sequence number . The invocation format is ：D = sub2ind(S, I, J)

   among ,S Is a matrix composed of rows and columns ,I A matrix formed for the row coordinates of the matrix elements to be transformed , That is, the coordinates of multiple matrix elements can be converted at one time , alike ,J A matrix consisting of the column coordinates of the matrix elements to be transformed ,D Is the corresponding sequence number matrix . obviously ,I and J Must be a homomorphic matrix .

   A = [1:3;4:6]
   D = sub2ind(size(A), [1 2;2 2], [1 1;3 2])
   

   give the result as follows ：

   A =
        1     2     3
        4     5     6
   D =
        1     2
        6     4
   

   size(A) Returns a matrix A The row matrix is composed of the number of rows and the number of columns .

2. ind2sub function ： The sequence number of the matrix element will be converted into the corresponding subscript , Its calling format is ：[I, J] = ind2sub(S, D)

   The letters have the same meaning as above .D It can also be a matrix , Got I and J It's also a matrix .

   [I J] = ind2sub([3 3], [1 3 5])
   

   give the result as follows ：

   I =
        1     3     2
   J =
        1     1     2
   

Get submatrix

A (i, : )	The first i All elements of the line
A ( : , j)	The first j All elements of the column
A( i : i+m , k : k+m )	The first i～i+m Within the line and on page k～k+m All elements in the column
A( i : i+m , : )	The first i～i+m All elements of the line

end Operator ： Indicates the subscript of the end element of a dimension .

A = reshape(1:20, [5, 4])'
A1 = A([1 4], 3:end)
A2 = A(end:-1:1, : )

give the result as follows ：

A =

     1     2     3     4     5
     6     7     8     9    10
    11    12    13    14    15
    16    17    18    19    20

A1 =

     3     4     5
    18    19    20

A2 =

    16    17    18    19    20
    11    12    13    14    15
     6     7     8     9    10
     1     2     3     4     5

reshape Function explanation

reshape Function is a Column first function , Whether it's taking numbers from a matrix or adding numbers to a new matrix , All are carried out according to the principle of column priority .

reshape Standard usage of functions ：reshape(A, [ROW, COL]) or reshape(A, ROW, COL), On the premise that the total number of elements of the matrix remains unchanged , The matrix A Transform into $ROW\times COL$ Matrix , Return to the new matrix .

How to understand "shape Function is a column first function "？

A = 1:6
A1 = reshape(A, [2, 3])

give the result as follows ：

A =

     1     2     3     4     5     6

A1 =

     1     3     5
     2     4     6

take A The number in is 1 The element as A1 The number in is 1 The elements of , take A The number in is 2 The element as A1 The number in is 2 The elements of ,……, take A The number in is 6 The element as A1 The number in is 6 The elements of . This fills the new matrix A1, Because this function assigns values to the new matrix according to the sequence number of the elements , The order of element numbering is column first , So this function is a column first function .

The essence of this function is to change the number of rows and columns of the original matrix , But it does not change the number of elements of the original matrix and its storage order .

another ： May refer to

---

For the above structure $4\times 5$ A matrix that is incremented by rows , Must first construct $5\times 4$ Matrix , Then perform the transpose operation . among ,' Is to perform transpose operation .

A1 The matrix is obtained A The first row of the matrix goes from the third column to the fifth column （ That's the last column ） And the fourth row from the third column to the fifth column （ That's the last column ） All the elements of , The corresponding positions of these elements remain unchanged , But the absolute position changes , That is, fill a new matrix with these numbers .

A2 A matrix can be understood as a matrix A Flip the matrix up and down . Take the fourth line first （ The last line ） All the elements of , It is equivalent to putting all the elements of the fourth line in A2 The first line of the matrix , Take all the elements in the third row , It is equivalent to putting all the elements of the third line in A2 The second line of the matrix ,……, Thus, the operation of turning up and down is realized . Note that the step size is set to -1, Otherwise default to 1, The default is 1 It is impossible to realize from end Reduced to 1 Of , So there will be mistakes . This is a special usage or technique .

Delete submatrix

Delete the submatrix by assigning an empty matrix to the submatrix .

A = reshape(1:20, 5, 4)';
A([2 4], :) = []

give the result as follows ：

A =

     1     2     3     4     5
    11    12    13    14    15

Our assignment results in A The matrix has lost all the elements of the second and fourth rows , new A A matrix is a $2\times 5$ Matrix .

If we want to delete the submatrix of A The middle doesn't go with A The first line of 、 The last line 、 Will a submatrix that intersects the first and last columns succeed , If successful, what will the new matrix look like ？

A = reshape(1:20, 5, 4)';
A(2:3, 2:4) = []

give the result as follows ：

 An empty assignment can only have one non colon index . % ERROR!

We got a false warning ,“ An empty assignment can only have one non colon index ”, This means that if we want to set the submatrix to an empty matrix , It must be a submatrix composed of several complete columns or rows , That is, at most one non colon index .（ You can also understand it as , This is the only requirement , To ensure that the output is a legitimate matrix , If you don't ask , Can you imagine what the output is ？）

Special usage of colon index

B(:) You get the matrix B The column vector formed by the elements of , It is still column priority .

B = [1 2 3; 4 5 6; 7 8 9]
B(:)

give the result as follows ：

B =

     1     2     3
     4     5     6
     7     8     9

ans =

     1
     4
     7
     2
     5
     8
     3
     6
     9

It can be seen that B(:) Equivalent to reshape(B, 6, 1) The matrix B Convert to six rows and one column .

therefore , For any matrix A,A(:) Equivalent to reshape(A, ROW×COL, 1).