Counting and removing rows with the same numbers in a particular order

I have a data set with purmutation differences. I want to find all the rows that have the same numbers in the same order but potentially not in the same column. For example:

A = [1234;4123;3412]

would be considered the same and I would want to count these three rows and then delete two of them.

If this does not make sense please let me know, but I appreciate any help I can get. Thank you

[the cyclist]

Just want to confirm, because the solution would be different: Is the first row a 4-digit number, or four 1-digit numbers?

If it's a single 4-digit number, are you guaranteed that all rows will have the same number of digits?

[Rik]

Do you have these values stored as numeric values like you showed above, or as char?

[Spencer Giglio]

It is all one digit numbers and they are stored as numeric values within a matrix.

[Spencer Giglio]

The row is anywhere from 3 to 17 columns long depending on what size I need to analyze.

Answer 1

[Rik]

Assuming this is indeed the input data you have:

A = [1234;4123;3412];

B=arrayfun(@(x) sort(sprintf('%d',round(x))),A,'UniformOutput',0);
C=unique(B);
D=cellfun(@str2double,C);

Either C or D should be what you want.

Edit:

If you have an array of one digit numbers you can skip the conversion to char and back:

A = [1 2 3 4;4 1 2 3;3 4 1 2];
D = unique(sort(A,2),'rows');

[Spencer Giglio]

Thank you, I believe that worked. Is there a way to count how many were simplified. For example, in this case we had 3 rows with 2 of them getting eliminated, is there a way to count that for a much larger set?

To explain further, I am trying to create unique equivlence classes represented by one row per class and want to count how many rows are included in each equivlence class.

could you also explain why it is 2 in sort(A,2). What is the 2 refrencing? I apologize if this is basic but I am still learning matlab.

I am seeing that the issue with the unique(sort(A,2),'rows') is that it groups the rows independantly of the order of the numbers. For example I would not want 1,2,3,4 in the same class as 1,3,2,4 but I would want it in the same class as 4,1,2,3. Does that make sense? Order matters

[Rik]

If you look at the documentation for the unique function you will see that there is a way to convert back with the indices. These indices can be used with histcounts.

The 2 in the call to sort is refering to which dimension sort should operate on, as you could have read in its documentation.

My code was predicated on the assumption that order didn't matter. I need to have a longer look at this to find a solution. You can probably use circshift on each row until some metric is true (e.g. the lowest value is at the front). Such a metric would allow you to still use unique.

[the cyclist]

Spenser, there is a lesson here for you. It's better to think a bit more carefully about your question, and provide all the detail upfront. You would have saved everyone, including yourself, a lot of time.

Answer 2

[the cyclist]

Pending answers to the questions in the comments, something like this will work on your input as written:

A = [1234;4123;3412];
[~,indexToUniqueA] = unique(sort(num2str(A),2),'row');
uniqueSortedA = A(indexToUniqueA);