arrays - Split vector in MATLAB

Question

I'm trying to elegantly split a vector. For example,

vec = [1 2 3 4 5 6 7 8 9 10]

According to another vector of 0's and 1's of the same length where the 1's indicate where the vector should be split - or rather cut:

cut = [0 0 0 1 0 0 0 0 1 0]

Giving us a cell output similar to the following:

[1 2 3] [5 6 7 8] [10]

Answer 1

Solution code

You can use cumsum & accumarray for an efficient solution -

%// Create ID/labels for use with accumarray later on
id = cumsum(cut)+1   

%// Mask to get valid values from cut and vec corresponding to ones in cut
mask = cut==0        

%// Finally get the output with accumarray using masked IDs and vec values 
out = accumarray(id(mask).',vec(mask).',[],@(x) {x})

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Benchmarking

Here are some performance numbers when using a large input on the three most popular approaches listed to solve this problem -

N = 100000;  %// Input Datasize

vec = randi(100,1,N); %// Random inputs
cut = randi(2,1,N)-1;

disp('-------------------- With CUMSUM + ACCUMARRAY')
tic
id = cumsum(cut)+1;
mask = cut==0;
out = accumarray(id(mask).',vec(mask).',[],@(x) {x});
toc

disp('-------------------- With FIND + ARRAYFUN')
tic
N = numel(vec);
ind = find(cut);
ind_before = [ind-1 N]; ind_before(ind_before < 1) = 1;
ind_after = [1 ind+1]; ind_after(ind_after > N) = N;
out = arrayfun(@(x,y) vec(x:y), ind_after, ind_before, 'uni', 0);
toc

disp('-------------------- With CUMSUM + ARRAYFUN')
tic
cutsum = cumsum(cut);
cutsum(cut == 1) = NaN;  %Don't include the cut indices themselves
sumvals = unique(cutsum);      % Find the values to use in indexing vec for the output
sumvals(isnan(sumvals)) = [];  %Remove NaN values from sumvals
output = arrayfun(@(val) vec(cutsum == val), sumvals, 'UniformOutput', 0);
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Runtimes

-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.068102 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.117953 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 12.560973 seconds.

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Special case scenario: In cases where you might have runs of 1's, you need to modify few things as listed next -

%// Mask to get valid values from cut and vec corresponding to ones in cut
mask = cut==0  

%// Setup IDs differently this time. The idea is to have successive IDs.
id = cumsum(cut)+1
[~,~,id] = unique(id(mask))
      
%// Finally get the output with accumarray using masked IDs and vec values 
out = accumarray(id(:),vec(mask).',[],@(x) {x})

Sample run with such a case -

>> vec
vec =
     1     2     3     4     5     6     7     8     9    10
>> cut
cut =
     1     0     0     1     1     0     0     0     1     0
>> celldisp(out)
out{1} =
     2
     3
out{2} =
     6
     7
     8
out{3} =
    10