Matlab creates random sequential

Question

I would like to create a 4-dimensional array with a random number of consecutive in each row. They should always begin in the first column and end with a random column. Example:

array(:,:,1,1) = [ 1 1 1 0 0 0;
                   1 1 0 0 0 0;
                   1 1 1 1 1 0;
                   ...         ]

One could do this with 3 for loops, but this is inefficient:

array = zeros(n,n,n,n);
for i= 1:n
   for j = 1:n
      for k =1:n
         rows = ceil(n*rand());
         array(k,1:rows,j,i) = 1;
      end
   end
end

Can anyone find a better solution? Thank!!

Answer 1

A simple and direct approach (may not be truly random)

rows = 8; %%// Number of rows
cols = 7; %%// Number of columns
ch3 = 3; %%// Number of elements in the 3rd dimension
ch4 = 2; %%// Number of elements in the 4th dimension

array = sort(round(rand(rows,cols,ch3,ch4)),2,'descend')

Bsxfun's approach (much faster than below, and really random)

%%// Sizes
rows = 8; %%// Number of rows
cols = 7; %%// Number of columns
ch3 = 3; %%// Number of elements in the 3rd dimension
ch4 = 2; %%// Number of elements in the 4th dimension

%%// Get a 2D array with every row starting with a one
rows2 = rows*ch3*ch4;
a1 = reshape(1:rows2*cols,rows2,[]);
col = randi(cols,[1 rows2]);
b1 = bsxfun(@plus,(col-1)*rows2,1:rows2)';%//'
out = bsxfun(@le,a1,b1);

%%// Rearrange those to 4D
a2 = reshape(out',[rows*cols ch3 ch4]);%//'
a3 = reshape(a2,cols,rows,ch3,ch4);
array = permute(a3,[2 1 3 4]);

Test results

We compare the above two approaches with the Rodi approach.

Datasize I:
rows = 80;  %// Number of rows
cols = 70;  %// Number of columns
ch3  = 30;  %// Number of elements in the 3rd dimension
ch4  = 2; %// Number of elements in the 4th dimension

Results:
Elapsed time with SORT approach is:   0.0083445sec
Elapsed time with BSXFUN approach is: 0.0021sec
Elapsed time with RODY approach is:   0.0063026sec

Datasize II:
rows = 80;  %// Number of rows
cols = 70;  %// Number of columns
ch3  = 30;  %// Number of elements in the 3rd dimension
ch4  = 20; %// Number of elements in the 4th dimension

Results:
Elapsed time with SORT approach is:   0.07875sec
Elapsed time with BSXFUN approach is: 0.012329sec
Elapsed time with RODY approach is:   0.055937sec


Datasize III:
rows = 800;  %// Number of rows
cols = 70;  %// Number of columns
ch3  = 30;  %// Number of elements in the 3rd dimension
ch4  = 20; %// Number of elements in the 4th dimension

Results:
Elapsed time with SORT approach is:   0.87257sec
Elapsed time with BSXFUN approach is: 0.17624sec
Elapsed time with RODY approach is:   0.57786sec


Datasize IV:
rows = 800;  %// Number of rows
cols = 140;  %// Number of columns
ch3  = 30;  %// Number of elements in the 3rd dimension
ch4  = 20; %// Number of elements in the 4th dimension

Results:
Elapsed time with SORT approach is:   1.8508sec
Elapsed time with BSXFUN approach is: 0.35349sec
Elapsed time with RODY approach is:   0.71918sec

bsxfun , , , Rody, .

Answer 2

" ":

rows = 80;  %// Number of rows
cols = 70;  %// Number of columns
ch3  = 30;  %// Number of elements in the 3rd dimension
ch4  = 200; %// Number of elements in the 4th dimension

%// number of 1 in each row. Select the appropriate class to make 
%// sure peak memory remains acceptably small
intClasses = {'uint8' 'uint16' 'uint32' 'uint64'}; 
maxSizes   = cellfun(@(x) double(intmax(x)), intClasses);
numOnes    = randi(cols, rows*ch3*ch4,1, ...
                   intClasses{find(cols <= maxSizes, 1,'first')});

clear intClasses maxSizes   

%// Loop through all rows and flip the appropriate number of bits
array = false(rows*ch3*ch4, cols);
for ii  = 1:numel(numOnes)
    array(ii,1:numOnes(ii)) = true; end

clear ii numOnes    

%// Reshape into desired dimensions
array = reshape(array.', cols,rows,ch3,ch4);
array = permute(array, [2 1 3 4]);

clear rows cols ch3 ch4

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`(cols-1)·rows²·ch3²·ch4² + (cols+1)·rows·ch3·ch4

( ) 8- double , cols·rows·ch3·ch4 1- ^ _ ^

: , Divakar , profile -memory:

Divakar:

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