How do I iterate through each element in an n-dimensional matrix in MATLAB

Question

I have a problem  I need to iterate through every element in an n-dimensional matrix in MATLAB  The problem is  I don t know how to do this for an arbitrary number of dimensions  I know I can say  for i   1 size m 1      for j   1 size m 2          for k   1 size m 3    and so on  but is there a way to do it for an arbitrary number of dimensions

User · Answer

The idea of a linear index for arrays in matlab is an important one. An array in MATLAB is really just a vector of elements, strung out in memory. MATLAB allows you to use either a row and column index, or a single linear index. For example,

A = magic(3)
A =
     8     1     6
     3     5     7
     4     9     2

A(2,3)
ans =
     7

A(8)
ans =
     7

We can see the order the elements are stored in memory by unrolling the array into a vector.

As you can see, the 8th element is the number 7. In fact, the function find returns its results as a linear index.

find(A>6)
ans =
     1
     6
     8

The result is, we can access each element in turn of a general n-d array using a single loop. For example, if we wanted to square the elements of A (yes, I know there are better ways to do this), one might do this:

B = zeros(size(A));
for i = 1:numel(A)
  B(i) = A(i).^2;
end

B
B =
    64     1    36
     9    25    49
    16    81     4

There are many circumstances where the linear index is more useful. Conversion between the linear index and two (or higher) dimensional subscripts is accomplished with the sub2ind and ind2sub functions.

The linear index applies in general to any array in matlab. So you can use it on structures, cell arrays, etc. The only problem with the linear index is when they get too large. MATLAB uses a 32 bit integer to store these indexes. So if your array has more then a total of 2^32 elements in it, the linear index will fail. It is really only an issue if you use sparse matrices often, when occasionally this will cause a problem. (Though I don't use a 64 bit MATLAB release, I believe that problem has been resolved for those lucky individuals who do.)

User · Answer

You could make a recursive function do the work   Let L   size M  Let idx   zeros L 1  Take length L  as the maximum depth Loop for idx depth    1 L depth  If your depth is length L   do the element operation  else call the function again with depth 1   Not as fast as vectorized methods if you want to check all the points  but if you don t need to evaluate most of them it can be quite a time saver

User · Answer

these solutions are more faster  about 11   than using numel    for idx   reshape array 1           element   element   idx  end   or   for idx   array          element   element   idx  end   UPD  tnx  rayryeng for detected error in last answer    Disclaimer  The timing information that this post has referenced is incorrect and inaccurate due to a fundamental typo that was made  see comments stream below as well as the edit history - specifically look at the first version of this answer    Caveat Emptor

User · Answer

If you look deeper into the other uses of size you can see that you can actually get a vector of the size of each dimension  This link shows you the documentation   www mathworks com access helpdesk help techdoc ref size html  After getting the size vector  iterate over that vector  Something like this  pardon my syntax since I have not used Matlab since college    d   size m   dims   ndims m   for dimNumber   1 dims    for i   1 d dimNumber              Make this into actual Matlab-legal syntax  and I think it would do what you want   Also  you should be able to do Linear Indexing as described here

User · Answer

One other trick is to use ind2sub and sub2ind  In conjunction with numel and size  this can let you do stuff like the following  which creates an N-dimensional array  and then sets all the elements on the  diagonal  to be 1   d   zeros  3  4  5  6      Let s pretend this is a user input nel   numel  d    sz   size  d    szargs   cell  1  ndims  d        We ll use this with ind2sub in the loop for ii 1 nel       szargs        ind2sub  sz  ii      Convert linear index back to subscripts     if all   szargs 2 end      szargs 1      On the diagonal          d  ii     1      end end

User · Answer

You want to simulate n-nested for loops    Iterating through n-dimmensional array can be seen as increasing the n-digit number   At each dimmension we have as many digits as the lenght of the dimmension   Example   Suppose we had array matrix   int       T new int 3  4  5     in  for notation  we have   for int x 0 x lt 3 x       for int y 0 y lt 4 y           for int z 0 z lt 5 z              T x  y  z        to simulate this you would have to use the  n-digit number notation   We have 3 digit number  with 3 digits for first  4 for second and five for third digit  We have to increase the number  so we would get the sequence  0 0 0 0 0 1 0 0 2     0 0 3 0 0 4 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 2 0 0 2 1 0 2 2 0 2 3 0 2 4 0 3 0 0 3 1 0 3 2 0 3 3 0 3 4 and so on   So you can write the code for increasing such n-digit number  You can do it in such way that you can start with any value of the number and increase decrease the digits by any numbers  That way you can simulate nested for loops that begin somewhere in the table and finish not at the end   This is not an easy task though  I can t help with the matlab notation unfortunaly

User · Answer

You can use linear indexing to access each element   for idx   1 numel array      element   array idx           end   This is useful if you don t need to know what i j k  you are at   However  if you don t need to know what index you are at  you are probably better off using arrayfun

User · Answer

As pointed out in a few other answers  you can iterate over all elements in a matrix A  of any dimension  using a linear index from 1 to numel A  in a single for loop  There are also a couple of functions you can use  arrayfun and cellfun   Let s first assume you have a function that you want to apply to each element of A  called my func   You first create a function handle to this function   fcn    my func    If A is a matrix  of type double  single  etc   of arbitrary dimension  you can use arrayfun to apply my func to each element   outArgs   arrayfun fcn  A     If A is a cell array of arbitrary dimension  you can use cellfun to apply my func to each cell   outArgs   cellfun fcn  A     The function my func has to accept A as an input  If there are any outputs from my func  these are placed in outArgs  which will be the same size dimension as A   One caveat on outputs    if my func returns outputs of different sizes and types when it operates on different elements of A  then outArgs will have to be made into a cell array  This is done by calling either arrayfun or cellfun with an additional parameter value pair   outArgs   arrayfun fcn  A   UniformOutput   false   outArgs   cellfun fcn  A   UniformOutput   false

[arrays] How do I iterate through each element in an n-dimensional matrix in MATLAB?

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