Finding the common range between two ranges

I have two matrix such as

X1=[0.316227766016838 0.346410161513775

0.509901951359279 0.529150262212918

1.63401346383682 1.63707055437449

2.28035085019828 2.37276210354093

3.24961536185438 4.78330429724056

4.96689037527506 5.00199960015992

5.06655701635736 6.06959636219741

6.07782855960910 9.43292107461946

9.61145150328503 10 ]

X2=[0.223606797749979 0.223606797749979

0.447213595499958 0.458257569495584

2.11423745118660 2.14242852856286

2.22485954612870 2.27815714997890

3.24653661614959 3.24807635378234

3.28329103187640 4.72652091923859

4.91121166312347 4.94064773081425

5.00299910053960 6.06959636219741

6.07865116617165 9.61093127641645

9.78110423214066 10]

I need to know the common ranges between X1 and X2 if it exist. Dimensions of X1 and X2 are not same

For example (3.28329103187640 4.72652091923859) range is common to both X1 and X2

Similarlyand 5.06655701635736 6.06959636219741 and so-on.

Can anybody help me how to do this in matlab?

[Adam Danz]

The 2 examples you gave are unique pairs of values that are not common between the 2 matrices unless I'm missing something.

[KALYAN ACHARJYA]

For example (3.28329103187640 4.72652091923859) range is common to both X1 and X2

How?

Also note on floating point representation.

[RAJAN PRASAD]

@Adam , Yes they are not common to the matrix. I have given a pictorial of what i need.

@kalyan I am not looking at the common entries but the common range. Thank you

[Adam Danz]

The range is computed by

range(X1,2)
range(X2,2)

and again, there's not a single matching value. Is there supposed to be a matching value?

[addendum]

Based on the answer chosen, I now understand that you want to find the segments in X1 and X2 that overlap.

Answer 1

[Bruno Luong]

You can use this RangeIntersection function on FEX

% Test data
X1=[0.316227766016838	0.346410161513775
0.509901951359279	0.529150262212918
1.63401346383682	1.63707055437449
2.28035085019828	2.37276210354093
3.24961536185438	4.78330429724056
4.96689037527506	5.00199960015992
5.06655701635736	6.06959636219741
6.07782855960910	9.43292107461946
9.61145150328503	10	]

X2=[0.223606797749979	0.223606797749979
0.447213595499958	0.458257569495584
2.11423745118660	2.14242852856286
2.22485954612870	2.27815714997890
3.24653661614959	3.24807635378234
3.28329103187640	4.72652091923859
4.91121166312347	4.94064773081425
5.00299910053960	6.06959636219741
6.07865116617165	9.61093127641645
9.78110423214066	10]

% https://fr.mathworks.com/matlabcentral/fileexchange/24254-interval-merging
[l,r] = RangeIntersection(X1(:,1),X1(:,2),X2(:,1),X2(:,2));
I = [l(:) r(:)]

It returns

I =

    3.2833    4.7265
    5.0666    6.0696
    6.0787    9.4329
    9.7811   10.0000

[RAJAN PRASAD]

Thank you

[Adam Danz]

Yeah, good catch (comment removed); The series of comparisons was difficult to read, anyway. I added a new answer that offers an alternative to the FEX.

Answer 2

[Adam Danz]

This solution matches the outputs produced in Bruno's answer but is simpler and does not rely on external functions.

% Create every combination of [X1, X2] vectors
xCombos = [repelem(sort(X1,2),size(X2,1),1), repmat(sort(X2,2),size(X1,1),1)]; 
% Sort each row to get the sorted index
[~, sortIdx] = sort(xCombos,2); 
% rows of [1 2 3 4] or [3 4 1 2] do not overlap.  All others do.
overlapIdx = ~ismember(sortIdx,[1 2 3 4; 3 4 1 2],'rows');
% pull out the overlaps
I = [max(xCombos(overlapIdx,[1,3]),[],2), min(xCombos(overlapIdx,[2,4]),[],2)];

Method

xCombos is a matrix containing every combination of pairs between X1 and X2.

By sorting the rows of xCombos and looking at the sort index, we can identify which coordinates overlap. Non-overlapping coordinates will have a sorted index of [1 2 3 4] or [3 4 1 2] whereas overlapping combinations will have a different sort index.

After identiying which rows contain overlap, all you need to do is identify the inner values to create the bounds of the internal segment.

[Bruno Luong]

The results won't match all the time. The FEX returns minimal number of intervals.

For example for

X1=[1 3; 4 6; 2 5]; X2=[0 4];

the FEX code

% https://fr.mathworks.com/matlabcentral/fileexchange/24254-interval-merging
[l,r] = RangeIntersection(X1(:,1),X1(:,2),X2(:,1),X2(:,2));
I = [l(:) r(:)];

returns

>> I =

     1     4

Your code

% Create every combination of [X1, X2] vectors
xCombos = [repelem(sort(X1,2),size(X2,1),1), repmat(sort(X2,2),size(X1,1),1)]; 
% Sort each row to get the sorted index
[~, sortIdx] = sort(xCombos,2); 
% rows of [1 2 3 4] or [3 4 1 2] do not overlap.  All others do.
overlapIdx = ~ismember(sortIdx,[1 2 3 4; 3 4 1 2],'rows');
% pull out the overlaps
I = [max(xCombos(overlapIdx,[1,3]),[],2), min(xCombos(overlapIdx,[2,4]),[],2)];

returns

>> I

I =

     1     3
     4     4
     2     4

[Adam Danz]

Ah, I see. Nice function!