Matrix of unknown length in MATLAB?

Question

I'm trying to set up a zero matrix of variable length with two columns into which I can output the results of a while loop (with the intention of using it to store the step data from Euler's method with adjusted time-steps). The length will be determined by the number of iterations of the loop.

I'm wondering if there's a way I can do this while I'm running the loop or whether I need to set it up to begin with, and how to go about doing that.

Answer 1

MATLAB uses dynamic typing with automatic memory management. This means, you don't need to declare a matrix of a fixed size before using it - you can change it as you go along and MATLAB will dynamically allocate memory for you.

BUT it is way more efficient to allocate memory for the matrix first and then use it. But if your programs needs this kind of flexibility, go for it.

I'm guessing you need to keep appending rows to your matrix. The following code should work.

Matrix = [];

while size(Matrix,1) <= 10
    Matrix = [Matrix;rand(1,2)];
end

disp(Matrix);

Here, we're dynamically reallocating the space required for Matrix every time you add a new row. If you know beforehand, say, an upper bound on the number of rows you're going to have, you can declare Matrix = zeros(20,2) and then insert each row into the matrix incrementally.

% Allocate space using the upper bound of rows (20)
Matrix = zeros(20,2);
k = 1;
for k = 1:10
   Matrix(k,:) = rand(1,2);
end
% Remove the rest of the dummy rows
Matrix(k+1:end,:) = [];

Answer 2

if the number of columns is fixed you can always add rows to your matrix (inside the loop)

e.g.

while (....)
   .....
   new_row =[x y] ; % new row with values x & y
   mat = [mat ; new_row];

of course if you know the number of iterations before the while loop it's more efficient to pre-allocate the matrix

Answer 3

Another flavor of the same thing that Jacob posted.

for counter = 1:10
    Matrix(counter,:) = rand(1,2);
end
disp(Matrix);

One "nice" thing about this is you can guess a minimum size to help the performance along.

Answer 4

Another approach that has performance in mind while still trying to be space-efficient, is to preallocate memory in large batches, adding more batches as needed. This is well suited if you have to add a large number of items without knowing how many beforehand.

BLOCK_SIZE = 2000;                          % initial capacity (& increment size)
listSize = BLOCK_SIZE;                      % current list capacity
list = zeros(listSize, 2);                  % actual list
listPtr = 1;                                % pointer to last free position

while rand<1-1e-5                           % (around 1e5 iterations on avrg)
  % push items on list
  list(listPtr,:) = [rand rand];            % store new item
  listPtr = listPtr + 1;                    % increment position pointer

  % add new block of memory if needed
  if( listPtr+(BLOCK_SIZE/10) > listSize )  % less than 10%*BLOCK_SIZE free slots
    listSize = listSize + BLOCK_SIZE;       % add new BLOCK_SIZE slots
    list(listPtr+1:listSize,:) = 0;
  end
end
list(listPtr:end,:) = [];                   % remove unused slots

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EDIT: As a time comparison, consider the following cases:

1. The same code as above done for 50000 iterations.
2. Preallocating the entire matrix beforehand: list = zeros(50000,2); list(k,:) = [x y];
3. Dynamically adding vectors to matrix: list = []; list(k,:) = [x y];

On my machine, the results were:

1) Elapsed time is 0.080214 seconds.
2) Elapsed time is 0.065513 seconds.
3) Elapsed time is 24.433315 seconds.