How can I find indices of a vector where the difference between the preceding and current element is x?

I have a large 1*X vector, indices, of integers. The elements of the vector almost always are 1 greater than the previous elements but sometimes there's a "jump" where the current element might be 100 bigger than the preceding.

Ex:

indices = [5,6,7,8,9,134,135,136,137,138,403,404,405]

I would like to find the index before this change occurs

changes = [5,10]

This is so that I can split indices like so:

a1 = indices(1:changes(1))
a2 = indices(changes(1)+1:changes(2))

and so on.

Any help would be greatly appreciated.

EDIT: I know I could do this using a for loop but I would like to use "the MATLAB way" i.e. using the function find.

[Stephen23]

Regarding variables a1, a2, "and so on":

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

[Shan Langlais]

Thanks, it was a bad example. It was just to illustrate which chunks I could slice out. What I actually had in mind putting the chunks in a cell array.

Answer 1

[Stephen23]

>> X = [5,6,7,8,9,134,135,136,137,138,403,404,405];
>> D = diff(find([true,diff(X)>100,true]));
>> C = mat2cell(X,1,D);
>> C{:}
ans =
   5   6   7   8   9
ans =
   134   135   136   137   138
ans =
   403   404   405

EDIT: to allow for decreasing values/jumps as well, include abs like this:

D = diff(find([true,abs(diff(X))>100,true]));

[Shan Langlais]

Thank you very much, this works and is better than what I had in mind. Would you mind explaining what find([true,diff(X)>100,true]) actually does? It looks very cryptic to me.

[Stephen23]

D = diff(find([true,diff(X)>100,true]));
                    diff(X)>100          % true where difference > 100, i.e. block boundaries.
              [true,           ,true]    % ensure vector ends are marked as block boundaries.
         find(                       )   % get positions of block boundaries.
D = diff(                             )  % difference of block boundary positions gets length of each block.

If you want to understand how it works I would suggest that you simply try each part with your data vector: first diff(X), then diff(X)>100, etc.

Answer 2

[Damo Nair]

Hi Stephen,

Sorry to nitpick, but when I tried ...

X = [5,6,7,8,9,134,135,136,70 80 20 10 137,138,403,404,405 199 230 276]; it gives

5 6 7 8 9

134 135 136 70 80 20 10

137 138

403 404 405 199 230 276

the difference between the 1st & last for the 2nd & 4th sequences are more than 100. Is this a shortcoming or wasn't the OP not interested in large breaks in the sequence?

Thanks Damo.

[Stephen23]

"the difference between the 1st & last for the 2nd & 4th sequences are more than 100"

As far as I can tell the original question does not place any limitation on the differences within a sequence, only on between sequences, in fact the title states this explicitly: "How can I find indices of a vector where the difference between the preceding and current element is x?", which is exactly what my code does. If you are interested in the maximum difference within a sequence then you can ask a new question.

Note the my answers assumes that the values strictly increase: if you want to include decreasing values and jumps (i.e difference between adjacent values is less than -100), then simply add abs:

>> X = [5,6,7,8,9,134,135,136,70,80,20,10,137,138,403,404,405,199,230,276];
>> D = diff(find([true,abs(diff(X))>100,true]));
>> C = mat2cell(X,1,D);
>> C{:}
ans =
   5   6   7   8   9
ans =
   134   135   136    70    80    20    10
ans =
   137   138
ans =
   403   404   405
ans =
   199   230   276

"...or wasn't the OP not interested in large breaks in the sequence?"

You would have to ask Shan Langlais about what they were interested in, I can only go by what was written in the question.