Using ismembertol for multiple coincidences

I have two vectors, and I'm trying to find ALL coincidences of one on the other within a certain tolerance.

For example:

A = [5 3 4 2]; B = [2 4 4 4 6 8];

I want to obtain a cell array containing on each cell the numbers of all the coincidences with a tolerance of 1 (or more) units. (A = B +- 1)

I have a solution with zero units (A = B), which would look something like this:

tol = 0;
[tf, ia] = ismembertol(B,A,tol,'DataScale',1); % For tol = 0, this is equivalent to using ismember
idx = 1:numel(B);
ib = accumarray(nonzeros(ia), idx(tf), [], @(x){x}) % This gives the cell array

The output is:

ib = 
[]
[]
[2 3 4]
[1]

Which is as desired.

If I change the tolerance to 1, the code doesn't work as intended. It outputs instead:

tol = 1
[tf, ia] = ismembertol(B,A,tol,'DataScale',1); % For tolerance = 1, this is equivalent to using ismember
idx = 1:numel(B);
ib = accumarray(nonzeros(ia), idx(tf), [], @(x){x}) % This gives the cell array

ib = 
[5]
[2 3 4]
[]
[1]

When I would expect to obtain:

ib = 
[2 3 4 5]
[1 2 3 4]
[2 3 4]
[1]

What am I doing wrong? Is there an alternative solution?

Answer 1

[Bruno Luong]

Using ismembertol is inappropriate

A = [5 3 4 2]; B = [2 4 4 4 6 8];

tol = 1;

[ib,ia]=find(B'<=A+tol & B'>=A-tol);
c = accumarray(ia,ib,[numel(A) 1],@(x){x'})

c = 4×1 cell array
    {[2 3 4 5]}
    {[1 2 3 4]}
    {[  2 3 4]}
    {[      1]}

c{:}

ans = 1×4

2 3 4 5

ans = 1×4

1 2 3 4

ans = 1×3

2 3 4

ans = 1

[Jose Luis Villaescusa Nadal]

Thank you for the quick response! This works great :)

[Jose Luis Villaescusa Nadal]

When A and B are long vectors, matlab quickly runs out of memory, since the find creates an array of size [numel(A), numel(B)]. Ismembertol, seems to be able to deal with this.

Do you think there is a way to overcome this with your solution?

[Bruno Luong]

You could use discretize with edges that are sort(A)-tol and sort(A)+tol instead of find. Details need to be worked out.