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matlabmatrixfindcell-arraysubmatrix

Finding the largest vector inside a matrix

I am trying to find the largest vector inside a matrix compound by vectors with MATLAB, however I am having some difficulties, so I would be very thankful if someone help me. I have this:

The matrix paths (solution of a Dijkstra function), which is a 1000x1000 matrix, whose values are vectors of 1 row and different number of columns (when the columns are bigger than 10, the values appear as "1x11 double, 1x12 double, etc"). The matrix paths have this form:

         1                   2                           3 ....
  1      1                   <1x20 double>              <1x16 double>
  2    <1x20 double>         2                          [2,870,183,492,641,863,611,3]
  3    <1x16 double>     [3,611,863,641,492,183,870,2]   3   
  4    <1x25 double>         <1x12 double>               <1x14 double>
  .
  .
  .

At first I thought in just finding the largest vector in the matrix by 

B = max(length(paths))

However MATLAB returns B = 1000, value which is feasible, but not likely. When trying to find out the position of the vector by using:

[row,column] = find(length(paths) == B)

MATLAB returns row = 1, column = 1, which for sure is wrong... I have thought that maybe is a problem of how MATLAB takes the data. It is like it doesn't consider the entries of the matrix as vectors, because when I enter:

   length(paths(3,2))

It returns me 1, but it should return 8 as I understand, also when introducing:

    paths(3,2)

It returns [1x8 double] but I expect to see the whole vector. I don't know what to do, maybe a "for" loop, I really do not know if MATLAB takes the data of the matrix as vectors or as simple double values.

Solution

  • The cell with the largest vector can be found using cellfun and numel to get the number of elements in each numeric matrix stored in the cells of paths:

    vecLens = cellfun(@numel,paths);
[maxLen,im] = max(vecLens(:));
[rowMax,colMax] = ind2sub(size(vecLens),im)

    This gets a 1000x1000 numeric matrix vecLens containing the sizes, max gets the linear index of the largest element, and ind2sub translates that to row,column indexes.

    A note on length: It gives you the size of the largest dimension. The size of paths is 1000x1000, so length(paths) is 1000. My advice is, Don't ever use length. Use size, specifying the dimension you want.

    If multiple vectors are the same length, you get the first one with the above approach. To get all of them (starting after the max command):

    maxMask = vecLens==maxLen;
if nnz(maxMask)>1,
    [rowMax,colMax] = find(maxMask);
else
    [rowMax,colMax] = ind2sub(size(vecLens),im)
end

    or just

    [rowMax,colMax] = find(vecLens==maxLen);