how to build a 3d sparse matrix?

Hi everyone: As we all know these has a sparse function in matlab, for example, there has two vector:

a = [1 2 3 1 5]; b=[1 2 4 1 6];

if I use spase function like this as follow:

sn = sparse(a,b,1);

It will shows the answer like this:

ans =

     (1,1)        2
     (2,2)        1
     (3,4)        1
     (5,6)        1

the third column means the count number of conresponding row and column in a and b. So my qusetion is if it is possible to build a 3d sparse matrix as the extend of the trandtional sparse function as follow: if there has two vector:

aa = [1 2 1 1 2 3]; bb=[1 2 1 1 2 4];cc=[1 2 1 1 2 5];
snn = sparse_3d(aa,bb,cc,1);
snn=
    (1, 1, 1)  3
    (2, 2, 2)  2
    (3, 4, 5)  1

That is very nice of anyone can give me the answer. Thanks ahead! weihua

Answer 1

[Matt J]

You could try my ndSparse class ( Download ),

    >> snn = ndSparse.build([aa',bb',cc'],1)

    snn(:,:,1) =

       (1,1)        3

    snn(:,:,2) =

       (2,2)        2

    snn(:,:,5) =

       (3,4)        1

[Lucademicus]

Hi Matt, I've been trying your ndSparse class, but I'm not sure what the proper way of use is.

In my case I want to use a 3 dimensional sparse, of which two dimensions define a geometric object, the 3rd dimension is for time.

Beforehand I know the size of the 3 dimensions, and an estimate of the number of non-zero elements, so I can use spalloc to pre-allocate the ndSparse object:

AllResults = ndSparse.spalloc([numel(x_vector),numel(y_vector),numel(time)],NNZestimate);

Next, I use normal indexing of the AllResults object as I would do with a 3d-vector, to assign the results of each time step. Before I do that, I place the results in a sparse:

for t = 1:numel(time)
    ....somecalculations...
    AllResults(:,:,t) = sparse(xindices,yindices,aboveresults,numel(x_vector),numel(y_vector));
end

Is this the correct way to work with ndSparse objects?

[Matt J]

You can do that, but the more efficient way is to use ndSparse.build,

  T=numel(time); 
  X=numel(x_vector);
  Y=numel(y_vector);
  
  coordinates=cell(T,1);
  values=cell(T,1);
  
  for t = 1:T
    ....somecalculations...

    coordinates{t}=[xindices(:), yindices(:), xindices(:)*0+t];
    values{t}=aboveresults(:);
    
  end

  coordinates=cell2mat(coordinates);
  values=cell2mat(values);
   
  AllResults = ndSparse.build(coordinates,values,[X,Y,T],NNZestimate);
  

[Lucademicus]

Thank you for the suggestion, it greatly reduced the computational time!

Answer 2

[Steven Lord]

No, sparse matrices are limited to 2 dimensions. If you feel strongly that MATLAB should extend sparse matrices to 3 or more dimensions, please send your use case (how you would use those higher dimensional sparse arrays) to Technical Support and ask them to include that information in the enhancement database.