Matlab learning notes (3) matrix and cube

Iii. Subscript:

Column J of row I of matrix A is represented as a (I, j ). That is, a (2, 4) indicates the elements in the 2nd columns of 4th rows.

Therefore, the sum of the elements in column 4 can be calculated as follows:

A () + a (2, 4) + a (3, 4) + a (4, 4)

This will generate:

Ans =

34

However, this is not the best way to solve the sum of elements in a column.

Of course, you can use a subscript to describe data members, such as a (k). This is mainly used to indicate the k elements of a row vector or column vector. But it can also be applied to two-dimensional arrays. On the one hand, a matrix can be described as a long column vector composed of the columns of the original matrix, so a (8) can represent

A (4, 2 ).

If you try to read the elements of a (), an error will occur because the subscript cannot cross-border.

In other words, if you access an element outside the original matrix, the size is automatically adjusted to a new order.

For example:

X =;

X (4, 5) = 17

Will generate:

X =

16 3 2 13 0
5 10 11 8 0
9 6 7 12 0
4 15 14 1 17

 

4. colon (:) Operator

The colon operator is a particularly important operator in MATLAB. It appears in MATLAB in different forms.

Expression:

1: 10

Represents a group of row vectors composed of integers from 1 to 10.

1 2 3 4 5 6 7 8 9 10

To get a non-unit space and create a growth volume, you can:

100:-7:50

Indicates:

100 93 86 79 72 65 58 51

At the same time

0: PI/4: pi

Indicates:

0 0.7854 1.5708 2.3562 3.1416

The subscript expression introduces the colon operator to determine the position of the matrix:

A (1: K, j): 1 to k elements in column J of matrix

Sum (A (, 4): calculates the sum of the elements in the fourth column.

But this is not the best. The colon itself represents all elements of a certain row vector or a certain column vector in the matrix. At the same time, the keyword end indicates the last column or the last row.

Therefore:

Sum (A (:, end): calculates the last column of matrix.

Ans =

34

Why is the magic and value of the 4*4 cube 34?

Because the integers from 1 to 16 are evenly divided into four groups with the following values:

Sum (1:16)/4

Result:

Ans =

34

 

5. Magic function:

MATLAB has a built-in function to build a cube of any size. This function is magic.

B = magic (4)

Will generate:

B =

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

This matrix is roughly the same as matrix A. The only difference is the sequence of the second and third columns.

To change matrix B to A, that is, to swap the two columns in the middle

A = B (:, [1, 3, 2, 4])

That is to say, each row of B is rearranged in the order of 1, 3, and 2, and the result is:

A =
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1

 

This section describes the following topics:

1. Underlying applications

2. Add new elements to the existing matrix

3. Colon Operator

4. End keyword

5. How to rearrange the matrix order