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ArrayWith Matrix
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Get information about arrays and matrices:
isempty(): is empty, that is []
isscalar(): is a scalar, that is, a single number
isvector(): is a vector, that is, an array or matrix
isrow(): is a row vector
iscolumn(): is a column vector
issparse(): is a sparse matrix
size(): Returns the row and column size of an array or matrix, and returns as [rowline_number, columnline_number]
length(): Returns the largest length in a row or column in an array or matrix
ndims(): Returns the dimensions of an array or matrix
Use the command who to see which variables are
Use the command whos to view the storage status of variables
Create arrays and matrices:
A_matrix = [ 1:3 ; 2:4 ; 3:5 ]
********** Show results **********
a =
1 2 3
2 3 4
3 4 5
*******************************
Where 1:3 is called sharding, the default step size is 1, and the step size is increased from 1 to 3.
Then the result of 1:2:9 is [ 1 3 5 7 9 ], with a step size of 2, and increases to 9. (Of course the step size can be negative)
Matrix operation:
Ordinary operator symbols can also be used directly between a matrix and an array, for example + - * / \
Where / is the left dividing and \ is the right dividing. A_matrix / B_matrix is equivalent to B_matrix \ A_matrix
But there is a difference between the operator symbol ^ and .^:
A_matrix ^ 2 is equivalent to A_matrix * A_matrix
A_matrix .^2 is equivalent to changing each element in the matrix to its own square.
******************************************************
>> a.^2
ans =
1 4 9
4 9 16
9 16 25
*******************************************************
Transpose of the matrix, inverse and point multiplication:
Transpose: Use the symbol ' or .' or usefunction transpose(matrix)
A is a matrix, then the transpose of A is A' A.' transpose(A)
But ' is not a true transpose, because when there are imaginary numbers in the matrix members, the imaginary numbers in the transposed result will become
The conjugated imaginary number of the original imaginary number, for example:
*******************************************************************
>> a = [ 1+1j 2 ; 2+3j 5 ]
a =
1.0000 + 1.0000i 2.0000 + 0.0000i
2.0000 + 3.0000i 5.0000 + 0.0000i
>> a'
ans =
1.0000 - 1.0000i 2.0000 - 3.0000i
2.0000 + 0.0000i 5.0000 + 0.0000i
>> a.'
ans =
1.0000 + 1.0000i 2.0000 + 3.0000i
2.0000 + 0.0000i 5.0000 + 0.0000i
*********************************************************************
Inverse: Use the inv function directly, inv(matrix) to obtain the inverse matrix of the corresponding matrix
Point multiplication: Use the function dot(A_matrix, B_matrix) to complete the point multiplication of matrix A and matrix B
Modify the values of the array and matrix:
**********************************************************************************************
>> A = [ 11 10 9 34 837 ] % Create an array A
A =
11 10 9 34 837
>> C = ( A < 33 ) % Find elements that meet the requirements, return as logical type
C =
1 1 1 0 0
>> whos
Name Size Bytes Class Attributes
A 1x5 40 double
C 1x5 5 logical
>> A(C) = 32 % Modify the value of the corresponding element that meets the < 33 condition through array C
A =
32 32 32 34 837
**********************************************************************************************
Of course, the same operation can be performed through the find function.
A( find( A < 33 ) ) = 32 % Just for the find function, the returned data is the index index number of the element that meets the requirements.
Flip and sort operations of matrix:
For sorting, you can use the sort function to sort(X, DIM, MODE)
X: For array or matrix DIM: dimension dimension mode: 'ascend' positive order 'descend' inverse order
The column sorting default is 1, and the mode is 'ascend' positive order
***********************************************************
>> a = [ 3:5 ; 1:3 ; 4:6 ]
a =
3 4 5
1 2 3
4 5 6
>> sort(a)
ans =
1 2 3
3 4 5
4 5 6
***********************************************************
Functions that can be used for flipping arrays and matrices are
rot90( matrix , k ) matrix counterclockwise rotation k*90 degrees [ rotate 90 degree ]
flipr(A) matrix rotates left and right [ flip left , flip right ]
flipud(A) matrix rotates up and down [ flip up , flip down ]
**************************************************************
>> a = [ 1:9 ; 2:10 ]
a =
1 2 3 4 5 6 7 8 9
2 3 4 5 6 7 8 9 10
>> flipud(a)
ans =
2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9
>> a % The call to the function does not change the matrix a
a =
1 2 3 4 5 6 7 8 9
2 3 4 5 6 7 8 9 10
>> fliplr(a)
ans =
9 8 7 6 5 4 3 2 1
10 9 8 7 6 5 4 3 2
a =
1 2 3 4 5 6 7 8 9
2 3 4 5 6 7 8 9 10
>> rot90(a,1)
ans =
9 10
8 9
7 8
6 7
5 6
4 5
3 4
2 3
1 2
**************************************************************
Summarize the matrix:
(1) Use the function sum function to sum the matrix
sum( A_matrix , Dim ) Dim: The default dimension is 1, that is, the default is column sum
Use sum twice for a matrix to get the sum of each element of the matrix
****************************************************
>> a
a =
1.0000 + 1.0000i 2.0000 + 0.0000i
2.0000 + 3.0000i 5.0000 + 0.0000i
>> sum(a)
ans =
3.0000 + 4.0000i 7.0000 + 0.0000i
>> sum(a,2)
ans =
3.0000 + 1.0000i
7.0000 + 3.0000i
>> sum(sum(a))
ans =
10.0000 + 4.0000i
*****************************************************
(2) Use the accumulation function cumsum to accumulate the matrix
cumsum(A,DIM) DIM defaults to 1, operate on columns
If matrix A is [
a1 a2 a3 ;
b1 b2 b3 ;
c1 c2 c3
]
Then after using cumsum function for A, the result is
[
a1 a2 a3 ;
a1+b1 a2+b2 a3+b3 ;
a1+b1+c1 a2+b2+c2 a3+b3+c3
]
*****************************************************
>> a
a =
1.0000 + 1.0000i 2.0000 + 0.0000i
2.0000 + 3.0000i 5.0000 + 0.0000i
0.0000 + 5.0000i 6.0000 + 8.0000i
>> cumsum(a)
ans =
1.0000 + 1.0000i 2.0000 + 0.0000i
3.0000 + 4.0000i 7.0000 + 0.0000i
3.0000 + 9.0000i 13.0000 + 8.0000i
*****************************************************
Construct a new matrix through the original matrix:
(1) Construct a new matrix using the existing matrix as the basic element, and use the repmat function:
**************************************************************
>> a = [ 1:3 ; 2:4 ]
a =
1 2 3
2 3 4
>> repmat(a,2,3)
% Construct a matrix with matrix a as the basic element
% [ a a a ; a a a ]
ans =
1 2 3 1 2 3 1 2 3
2 3 4 2 3 4 2 3 4
1 2 3 1 2 3 1 2 3
2 3 4 2 3 4 2 3 4
**************************************************************
(2) Create a new matrix using the existing matrix as diagonal blocks and use the blkdiag function:
**************************************************************
>> blkdiag(a,a)
ans =
1 2 3 0 0 0
2 3 4 0 0 0
0 0 0 1 2 3
0 0 0 2 3 4
>> blkdiag(a,a,a)
ans =
1 2 3 0 0 0 0 0 0
2 3 4 0 0 0 0 0 0
0 0 0 1 2 3 0 0 0
0 0 0 2 3 4 0 0 0
0 0 0 0 0 0 1 2 3
0 0 0 0 0 0 2 3 4
**************************************************************
(3) Modify the matrix shape and use the function reshape, but the number of elements in the original matrix remains unchanged:
**************************************************************
>> size(a)
ans =
2 3
>> a
a =
1 2 3
2 3 4
>> reshape(a,3,2)
ans =
1 3
2 3
2 4
**************************************************************