find indices of row subsets

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Michal 2018-5-9

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https://ww2.mathworks.cn/matlabcentral/answers/399901-find-indices-of-row-subsets

编辑： Michal 2018-5-11

I am trying to find vectorized matlab function ind = item2ind(item,t) to solve following problem: I have a list of row vectors

item = [2 3 1; 2 1 2; 3 1 1; 1 3 3]

and vector of all possible item elements at each item row vector

t = [1 1 2 2 2 3 3];

I need to find indexes of of separate item rows elements corresponding to the vector t in this way:

ind = [3 6 1; 3 1 4; 6 1 2; 1 6 7]

But

item = [1 1 1]

does not correspond to the vector t, because there are 3 "1" elements, and t contains only 2 "1" elements.

Note: Serial version is inefficient for large item (10000 x 100) and t (1 x 200).

function ind = item2ind(item,t)
[nlp,N] = size(item);
ind = zeros(nlp,N);
for i = 1:nlp
    auxitem = item(i,:);
    auxt = t;
    for j = 1:N
        I = find(auxitem(j) == auxt,1,'first');
        if ~isempty(I)
            auxt(I) = 0;
            ind(i,j) = I;
        else
            error('Incompatible content of item and t.');
        end
    end
end
end

Additional remarks:

Most of the time is spent on the line:

I = find(auxitem(j) == auxt,1,'first');

Is there any clever trick how to speed up this line of code? I tried this, for example, but without any speedup:

I = ipos(auxitem(j) == auxt); I = I(1);

where ipos is preallocated as:

ipos = 1:length(t);

Thanks in advance for any help ...

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Jan 2018-5-9

编辑：Jan 2018-5-9

@Michal: If you provide a relevant set of example data, we could test the speed and the correctness of the suggested code.

What is the maximum value of t?

Do you have a C compiler installed?

Michal 2018-5-9

编辑：Michal 2018-5-9

Please read discussion under Chad's answer.

Typical length of "t" is 30-100, maxmimum value of elements at "t" is equal maximum value of elements at array "item".

Yes I have a C compiler...

Please, keep in mind, that vector "t" is not sorted.

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Answer 1

Michal 2018-5-11

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https://ww2.mathworks.cn/matlabcentral/answers/399901-find-indices-of-row-subsets#answer_319761

编辑：Michal 2018-5-11

在 MATLAB Online 中打开

So far best solution:

function ind = item2ind_new(item,t)
t = t(:);
[m,n] = size(item);
mct = max(accumarray(t,1));
G = accumarray(t,1:length(t),[],@(x) {sort(x)});
G = cellfun(@(x) padarray(x.',[0 mct-length(x)],0,'post'), G, 'UniformOutput', false);
G = vertcat(G{:});
C = cumsum(reshape(item,m,1,n)==item,3);
ia = C(sub2ind(size(C),repelem((1:m).',1,n),repelem(1:n,m,1),repelem(1:n,m,1)));
ind = G(sub2ind(size(G),item,ia));

Any idea how to improve it?

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Answer 2

Jan 2018-5-9

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https://ww2.mathworks.cn/matlabcentral/answers/399901-find-indices-of-row-subsets#answer_319460

编辑：Jan 2018-5-9

在 MATLAB Online 中打开

function ind = item2ind(item, t);
maxRun   = length(t) + 1;
[T , TI] = accumsort(t, maxRun);
ind      = zeros(size(item));
for k = 1:size(item, 1)
   [aItem, aItemI] = accumsort(item(k, :), maxRun);
   % [m, index]    = ismember(aItem, T);
   % Faster with undocumented function:
   [m, index]      = builtin('_ismemberhelper', aItem, T);
   if all(m)
     ind(k, aItemI) = TI(index);
   else
      error('Incompatible item.');
   end
end
end
function [T, TI] = accumsort(t, maxRun)
[sortedT, TI] = sort(t);
T = sortedT * maxRun;
c = -1;
for k = 1:numel(T)
   if T(k) ~= c
      d = 0;
      c = T(k);
   else
      d = d + 1;
   end
   T(k) = T(k) + d;
end
end

For some test data of size [10'000 x 100] I get a runtime of 0.21 sec instead of 1.3 sec of the original version.

With calling ismember the runtime is 0.41 sec. Internally ismember calls the helper function builtin('_ismemberhelper') for sorted data of type double. If it is known already, that the input is sorted, calling the internal function avoids the overhead.

If you have a C compiler, converting accumsort to a C-mex would be useful.

maxRun must a any number greater than the highest number of repetitions in t. length(t)+1 is guaranteed to be larger.

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Michal 2018-5-9

编辑：Michal 2018-5-9

在 MATLAB Online 中打开

I tried to convert accumsort to C-mex (MATLAB Coder), but the mex file shows very poor performance (2x slower than MATLAB version). Actually, I am not familiar with manual C-mex file writing...

But the main problem is trade of between number of unique elements at vector "t" and overall performance. Chad's algorithm is significantly faster than yours in a case of low number unique elements of "t".

This is Chad's final code, for your info:

function ind = item2ind(item,t)
unique_t = unique(t);
ind = zeros(size(item));
% a single 'for' loop as long as the unique elements of t
for jj = 1:length(unique_t)
    O = zeros(size(item));
    O(item == unique_t(jj)) = 1;
    positions_of_t = [0 find(t == unique_t(jj))];
    % adding zero so sub_index call below will always reference a non-zero element   
    if max(sum(O,2)) > numel(positions_of_t)
        error('Incompatible content of item and t.');
    else
        sub_index = cumsum(O,2) .* O + 1;
        ind = ind + positions_of_t(sub_index);
        % this is why we needed the 0 in positions_of_t above
    end
end

Case1:

t = 1:30;
tt = repmat(t,1,1);
[~,p] = sort(rand(100000,30),2);
item = tt(p);
tic;ind1 = item2ind_Chad(item,tt);toc
tic;ind2 = item2ind_Jan(item,tt);toc
Elapsed time is 2.363570 seconds.
Elapsed time is 1.420776 seconds.

Case2:

t = 1:10;
tt = repmat(t,1,3);
[~,p] = sort(rand(100000,30),2);
item = tt(p);
tic;ind1 = item2ind_Chad(item,tt);toc
tic;ind2 = item2ind_Jan(item,tt);toc
Elapsed time is 0.804354 seconds.
Elapsed time is 1.414612 seconds.

Jan 2018-5-9

在 MATLAB Online 中打开

As far as I can see, my code can be parallelized also directly:

parfor k = 1:size(item, 1)

I've made a very interesting experiment with a C-Mex function:

// file: accumsortX.c
// mex -O accumsortX.c
#include "mex.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
  double *t, *T, maxT, c, d;
  size_t n;
    t    = mxGetPr(prhs[0]);
    maxT = mxGetScalar(prhs[1]);
    n    = mxGetNumberOfElements(prhs[0]);
    plhs[0] = mxCreateUninitNumericMatrix(1, n, mxDOUBLE_CLASS, mxREAL);
    T       = mxGetPr(plhs[0]);
    c = *t - 1;
    while (n-- != 0) {
       if (c != *t) {
          d = 0.0;
          c = *t;
       } else {
          d += 1.0;
       }
       *T++ = maxT * *t++ + d;
    }
    return;
  }

It has exactly the same speed as the Matlab version of accumsort - but I've moved the sorting to the main function:

function ind = item2ind_jan2(item,t)
maxT    = max(t) + 1;
[T, TI] = sort(t);
T       = accumsort(T, maxT);
ind     = zeros(size(item));
for k = 1:size(item, 1)
   [aItem, aItemI] = sort(item(k, :));
   aItem           = accumsort(aItem, maxT);
   [m, index]      = builtin('_ismemberhelper', aItem, T);
   if all(m)
      ind(k, aItemI) = TI(index);
   else
      error('item not compatible to t.');
   end
end
end
function [T] = accumsort(t, maxT)
T = t * maxT;
c = -1;
for k = 1:numel(T)
   if T(k) ~= c
      d = 0;
      c = T(k);
   else
      d = d + 1;
   end
   T(k) = T(k) + d;
end
end

Replacing accumsort() by accumsortX() does not change the run-time, even if I do not create a new vector in the Mex but write to the original array.

But let me repeat: I still have no idea how you measure the timings, because for your given input data:

t = 1:10;
tt = repmat(t,1,3);
[~,p] = sort(rand(100000,30),2);
item = tt(p);

I get the error message for incompatible items. Please clarify this detail, because I'm eager to reproduce your timings in any way.

Wick 2018-5-10

Interesting. Jan's code is always faster on my computer than the numbers you gave. My code is faster on my machine for the short runs but for the long runs your machine is faster. It appears your memory subsystem is a bit more efficient.

Michal 2018-5-10

@Jan any progress or new ideas on your site?

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Answer 3

Wick 2018-5-9

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https://ww2.mathworks.cn/matlabcentral/answers/399901-find-indices-of-row-subsets#answer_319411

编辑：Wick 2018-5-9

在 MATLAB Online 中打开

Here you go. At the sizes you suggested, this shouldn't take too long. It has a single 'for' loop that cycles through the unique values of 't'.

I'm using logical indexing to identify all the elements in 'item' that match the given unique 't' and summing across the row. If the sum exceeds the number of times that value showed up in 't' you get your error. Otherwise I'm using 'cumsum' in a creative fashion (in my ever so humble opinion) to provide the indexes back to the location of the unique value in the original vector 't'.

Good Luck!

    function ind = item2ind(item,t)
    unique_t = unique(t); 
    ind = zeros(size(item));
    try
        % a single 'for' loop as long as the unique elements of t
        for jj = 1:length(unique_t)
            O = zeros(size(item));
            O(item == unique_t(jj)) = 1;
            positions_of_t = [0 find(t == unique_t(jj))];
            % adding zero so sub_index call below will always reference a non-zero element
            sub_index = cumsum(O,2) .* O + 1;
            ind = ind + positions_of_t(sub_index);
            % this is why we needed the 0 in positions_of_t above
        end
    catch
        error('Incompatible content of item and t.');
    end

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Wick 2018-5-9

编辑：Wick 2018-5-9

在 MATLAB Online 中打开

I don't have the parallel toolbox and you have a fast computer. :) That took me 28 seconds.

It surprises me it's that slow. Let me play.

Edit: The trouble is the memory time spent assigning the values of positions_of_t. The following code is slower on my system but the loop should now be parallelizable. Therefore, you can try this with the parallel toolbox loop and see if it speeds things up.

    function ind = item2ind(item,t)
    unique_t = unique(t); 
    ind = zeros([size(item) numel(unique_t)]);
    try
        % a single 'for' loop as long as the unique elements of t
        for jj = 1:length(unique_t)
            O = zeros(size(item));
            O(item == unique_t(jj)) = 1;
            positions_of_t = [0 find(t == unique_t(jj))];
            % adding zero so sub_index call below will always reference a non-zero element
            sub_index = cumsum(O,2) .* O + 1;
            ind(:,:,jj) = positions_of_t(sub_index);
            % this is why we needed the 0 in positions_of_t above
        end
    catch
        error('Incompatible content of item and t.');
    end
    ind = sum(ind,3);

Michal 2018-5-9

This is strange, my code perfectly works with both data case examples you mentioned above … ??!!

Wick 2018-5-9

Jan,

My code is faster for small length 't' and much, much slower for large 't'. You vectorized in a completely different way than I did (and used an undocumented function but we won't use that against you). My question is, is there some rule of thumb my snippet of code didn't follow that I should change how I code things? I've always felt I was pretty good at vectorizing my MATLAB code but I've been coming here to learn how to be better. Obviously, you know some tricks I don't.

Thanks.

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