Placing values(numbers) in a multilayers cell matrix in MATLAB

Question

Assume Q is a matrix which has 3 cells and in each cell it has 2 other cells, means:

Q={ { [] [] } ; { [] [] }; { [] [] } }

Moreover, if we have "a" and "b" which they have 3 member each, and we would like to place

"a(1,1)" into "Q{1}{1}",

"b(1,1)" into "Q{1}{2}",

"a(2,1)" into "Q{2}{1}",

"b(2,1)" into "Q{2}{2}",

"a(3,1)" into "Q{3}{1}",

"b(3,1)" into "Q{3}{2}",

For example, if

a = [2; 3; 4];
b = [1; 5; 8] 

Then Q should be like

Q={{2 1}; 
   {3 5}; 
   {4 8}}

Please note that we need a vectorized code and not a for-loop code as I already have the latter one, as shown next -

for i=1:size(Q,2)

     Q{i}{1}=a(i,:)
     Q{i}{2}=b(i,:)

end

Thanks.

Answer 1

Code

Q = mat2cell(num2cell([a b]),ones(1,numel(a)),2)

---

Example

Code with input and output display

a = [2; 3; 4]; %// Inputs
b = [1; 5; 8];

Q = mat2cell(num2cell([a b]),ones(1,numel(a)),2); %// Output

celldisp(Q) %// Display results

Output on code run

Q{1}{1} =
     2
Q{1}{2} =
     1
Q{2}{1} =
     3
Q{2}{2} =
     5
Q{3}{1} =
     4
Q{3}{2} =
     8

---

Benchmarking

Function for loop method

function out = loop1(a,b)

out = cell(size(a,1),1); 
for i=1:size(out,1) 
    out{i}{1}=a(i,:); 
    out{i}{2}=b(i,:);
end

return;

Function for vectorized method

function out = vec1(a,b)

out = mat2cell(num2cell([a b]),ones(1,numel(a)),2);

return;

Benchmarking Code

N_arr = [50 100 200 500 1000 2000 5000 10000 50000]; %// array elements for N

timeall = zeros(2,numel(N_arr));
for k1 = 1:numel(N_arr)
    
    N = N_arr(k1);
    a = randi(9,N,1);
    b = randi(9,N,1);
    
    f = @() loop1(a,b);
    timeall(1,k1) = timeit(f);
    clear f
    
    f = @() vec1(a,b);
    timeall(2,k1) = timeit(f);
    clear f
end

%// Graphical display of benchmark results
figure,
hold on
plot(N_arr,timeall(1,:),'-ro')
plot(N_arr,timeall(2,:),'-kx')
legend('Loop Method','Vectorized Method')
xlabel('Datasize (N) ->'),ylabel('Time(sec) ->')

Results

Conclusions

Looks like vectorized method is the way to go, as it's showing almost double the performance (in terms of runtime) as compared to the loop approach across a wide range of datasizes.