Get a set of 10000 unique random 2-D coordinates

I have an array that is 512 rows by 256 columns (i.e Nrows=512, Ncols=256) and I want the 2-d coordinates of a random sample of size 10000 without replacement from this array. I managed to do this with the code below but is seems rather clunky. Seems like there is a cleaner way to do this. Any help appreciated.

Nrows=512; Ncols=256;
row_mat = zeros(Nrows,Ncols);
col_mat = zeros(Nrows,Ncols);
for i=1:Nrows
   row_mat(i,:) = i; 
end
for i=1:Ncols
   col_mat(:,i) = i; 
end
ind = [row_mat(:) col_mat(:)];
[temp,idx] = datasample(ind(:,1),10000,'Replace',false);
I = [ind(idx,1) ind(idx,2)]; % This is my list of 10000 unique random coordinates

Answer 1

[Star Strider]

See if this does what you want:

Array = rand(256,512);                              % Original Array (Created)
idx = randperm(numel(Array), 1E+4);                 % Generate Vector OF Random Indices
[row_sub,col_sub] = ind2sub(size(Array), idx);      % Convert To Subscripts (If Necessary)
sub_mtx = [row_sub(:), col_sub(:)];                 % Matrix Of Subscripts (Rows Of Matrix)

Answer 2

[John D'Errico]

Easy enough. Two lines of code, if you don't count that I defined N and Asize to make this somewhat general.

N = 10000;
Asize = [512,256];
[Ir,Ic] = ind2sub(Asize,randperm(prod(Asize),N));
I = [Ir',Ic'];

By the way, as you wrote it I'd STRONGLY suggest learning what the functions meshgrid and/or ndgrid do. Or, you might think about how you might create that matrix using a generalized outer product. bsxfun, for example. Even better, if you have the current release of MATLAB (R2016b or later), try this:

zeros(Nrows,1) + (1:Ncols)

The point is, start learning how to use vector and array operations in MATLAB, rather than loops.