How to do a cycle through a N-dimensional grid, if n is not fixed?

I know there is ngrid, but you have to know n. What if I want to do n for cycles, but I don't know n at the moment, it is a variable.

[Mr M.]

And one additional thing. Since number of gridpoints can be very large. It would be nice to have a solution where you don't want to store the gridponts, just go through them!

[Stephen23]

Mr M.'s "Answer" moved here:

I would like to go through the grid points of an N-dimensional grid, but N is an input parameter. For example in each dimension I would like K gridponts, so I have KxKxKx...xK = K^N points. If i know that N=2, I can use meshgrid, or in case of N=5, I can use [X1,X2,X3,X4,X5] = ngrid(1:K,1:K,1:K,1:K,1:K); But N is a variable! How to go through the gridpoints?

Answer 1

[Guillaume]

Please don't use answer boxes when commenting. Use the Comment on this Question or comment on this Answer box.

If I understood you want to generate N Nd arrays with ndgrid with N being unknown in advance. No problem, use the expansion of cell arrays into comma-separated lists to do that:

N = 5;  %value can change
K = 4;  %value can change
Ndarrays = cell(1, N);  %create cell array to receive outputs of ndgrid
[Ndarrays{:}] = ndgrid(1:K);  %fills all N Nd arrays

And in case, your K is different for each dimension, then:

N = randi([3 6]);  %randomly chose N between 3 and 6. For demo
K = randi([2 7], 1, N);  %randomly chose N K  between 2 and 7. For demo

sizeinputs = arrayfun(@(k) 1:k, K, 'UniformOutput', false);  %generate the inputs of ndgrid as a cell array
ndarrays = cell(1, N);
[ndarrays{:}] = ndgrid(sizeinputs{:});

[Mr M.]

Thank you very much! And what if I dont want to store the gridpoints, because both K and N are large numbers? It would be nice to have a solution where you just go through the gridpoints without storing them!

[Guillaume]

"It would be nice to have a solution where you just go through the gridpoints without storing them".

Well, then this has nothing to do with ndgrid, you just need a loop. However, note that if storing the grid points is a problem because there are two many, then iterating over the grid points is most likely to also be a problem because it would take too long. Nonetheless:

N = randi([3 6]);  %randomly chose N between 3 and 6. For demo
K = randi([2 7], 1, N);  %randomly chose N K  between 2 and 7. For demo

numpoints = prod(K);
gridcoordinates = cell(1, N);
for ptidx = 1:numpoints
   [gridcoordinates{:}] = ind2sub(K, ptidx);
   fprintf('Gridpoints: %s\n', sprintf('%d ', gridcoordinates{:}));  %for demo
end

[Mr M.]

Thank you, this works for me! But may I ask what is this syntax: [gridcoordinates{:}] ? And why we need cells?

[Guillaume]

Using cell arrays is the only way you can assign the variable number of outputs (N outputs) of ind2sub. As per the link in my initial answer, [gridcoordinates{:}] is equivalent to

[gridcoordinates{1}, gridcoordinates{2}, ..., gridcoordinates{N}] = ind2sub(...);

[Mr M.]

Thanks, and how to convert gridcoordinates to a vector?

[Guillaume]

cell2mat(gridcoordinates)

or

 [gridcoordinates{:}]

[Ali Taheri]

Dear Guillaume

What about this program?

The size of the x{:} is not the same. How can ndgrid command be written when n changes?

step=2.5;
n=4;
for j=1:n
        x{j}=(x_min(j):step:x_max(j)); % x_min(:) and x_max(:) are known
end
[x{1},x{2},x{3},x{4}] = ndgrid(x{1},x{2},x{3},x{4});

[Stephen23]

@Ali Taheri: you use the syntax that is explained and shown in detail in Guillaume's Answer:

[x{:}] = ndgrid(x{:});

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/13480-optimization-of-a-multivariable-function#comment_1976500