Matlab Matrixaddress

user_11772800 0
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During my course I came across that expression:

A(:,end:-1:1)

I have trouble to understand and read the morphemic structure of the 2nd Operand "end;-1;1"

Lets take the example:

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

I am aware of:

A(:).. Outputs [1 2 3; 4 5 6; 7 8 9] as rows. Operator is :.
A(1,:).. Outputs [1 2 3; 4 5 6; 7 8 9] as columns Operator is , then , .
A(:,1).. Outputs [1 2 3; 4 5 6; 7 8 9] as rows. Operator is , beforehand : .

A(:,end:-1:1)

Output in Matlab show me: 3x3 Matrix.

How am I supposed to read the structure?

  1. Graphem: : ..show me the rows,
  2. Graphem: end:-1 .. ??
  3. Graphem: :1 ..

Somehow ":" was for me the operator for show all of the elements.

It makes sense to me that the "Operand1 , Operand2" shows me the 2 Dimensional Matrix.

  • First Idea:
    The end:-1:1 expression seemed to me like a loop. So -1, 0, 1 => **3x Elements** ?
    But when I type

    A(1,end:3)
    it only shows me the 3rd row.

  • Second Idea:

    A(end:-1:1,1)
    It shows me the inverted Matrix..

My background:
I am a undergraduate student from the field of language.
I build in my freetime the 8-Bit Sap1 according Ben Eater.
So I am familiar with program memory or instruction memory.
I understand only the result, but not how it is achieved by the MATLAB compiler.
Someone said to me that the "Matrixaddressing is somehow optimized". Looking forward to a helpful answer in each step. :)

Thanks in advance!

matrix-indexing matrix matlab programming-languages syntax
3 Answers

The end keyword in matrix indexing indicates index of last element in the corresponding dimension. So, A(:,end:-1:1) simply means A(:, size(A, 2):-1:1), which in you example (A=[1 2 3; 4 5 6; 7 8 9]), is equivalent to A(:, 3:-1:1).

But to understand what it does, you need to know what 3:-1:1 does. It creates a subrange. You already know 1:3 creates [1, 2, 3]. 1:3 is simplified form of 1:1:3: rangeStrart:increment:rangeEnd. Now, 3:1 or 3:1:1 creates an empty vector, because rangeStart is greater than rangeEnd. To create [3, 2, 1] you need to use a negative step: 3:-1:1.

So, A(:,end:-1:1) means A(:, [3, 2, 1]), which inverts order of rows of A. Also, A(:,end:3) means A(:, 3:3) and eventually A(:, 3), which returns 3rd row of A.

Edit: about your misunderstandings, addressed by @CrisLuengo

I am aware of:
A(:).. Outputs [1 2 3; 4 5 6; 7 8 9] as rows. Operator is :.
A(1,:).. Outputs [1 2 3; 4 5 6; 7 8 9] as columns Operator is , then , .
A(:,1).. Outputs [1 2 3; 4 5 6; 7 8 9] as rows. Operator is ,beforehand : .

  • A(3, 2) is the element in the 3,2 position (third row, second column) of A
  • A(1, :) is equivalent to A(1, 1:size(A, 2)) and A(1, 1:end) and is the first row of A
  • A(:, 1) is equivalent to A(1:size(A, 1), 1) and A(1:end, 1) and is the first column of A
  • A(:) is equivalent to A(1:numel(A)) and is a single column containing all elements of A
user_20930770

In MATLAB, when accessing an array, it is accessed as A(row#,col#). row# and col# can either be integers or a vector of integers. If they are integers then one spot in the matrix is accessed. If they are vectors then MATLAB will loop through the vector and choose spots in A which correspond to the integers in the vector.

end:-1:1 creates a vector which contains the integers ranging from the number of columns (in this case because you put this vector in the col section: A(row#,col#)) to 1. Ex: 4x5 matrix, end:-1:1 would be [5 4 3 2 1].

When you put : in the row part of the matrix, that means you access all rows of the matrix.

Here's an example of A(:,end:-1:1)

The col# vector (:) is [1 2 3] and the row# vector (end:-1:1) is [3 2 1]

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

A(:,end:-1:1)

[3, 5, 7]
user_118107150

I think you're overthinking this slightly. If we have a vector

A = [1 2 3]

and we call A(end:-1:1), then we get a vector [3 2 1]. The indexing has returned the same vector, with the values reversed. If we now have a matrix

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

and call A(:, end:-1:1), we get the matrix with the same values in each row, but now the columns have been reversed to give

A(:, end:-1:1) = [3 2 1; 6 5 4; 9 8 7].

Recall what the colon means in this context.

If we define a vector, v = (1:10), we get a vector with the first element being 1, the last element being 10 and each value in between being integers in steps of 1. If we instead define v = (1:2:10), we get the same, but the elements are separated by 2, not 1.

end:-1:1 is a vector made in just the same way. The first number is the final element in the row of A, and the final number is the first element in the row. Each number is separated by a value of -1. If we try

v = 10:-1:1

we get [10 9 8 7 6 5 4 3 2 1]. If we call v(2:4) we get the second, third and fourth elements of v. If we call v(1:end), we simply get v. If we call v(end:-1:1), we return v, with the elements in the reversed order.

Edit A typo.

user_146917510
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