Symbolic array pre-allocation

Symbolic array pre-allocation only allocates pointers as I understood it from reading the forum. This is causing a major slowdown in code we are looking at

a=sym(zeros(50000,1));

Filling the area with relatively simple expression e.g. '3+sqrt(5)/sqrt(7)' a serious slowdown is noted around the 9000th index.

Would it be possible to allocate memory by defining the sym array (in the definition) with large expressions '3+sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4)+sqrt(5)+sqrt(6)+sqrt(7)' for all elements 1:50000, so that effectively a memory allocation is forced at the definition step. Is this possible in the definition of sym? I tried repmat, but didn't get it too work.

[Siddharth Sundar]

- Can you check the output of the memory command before and after the 9000th iteration of the for loop you are to define these expressions? - What is the expression you are using in the 9000th iteration?

[lvn]

Here is a minimal examples that reproduces the behavior (and answers your questions). Thanks for trying to help!

list1=sym(zeros(50000,1));
for a=1:50000
    tic
    list1(a)=sym('pi+1+1');
    z=toc;
    [uV, sV] = memory; 
    fprintf('Iteration: %d, Time: %f, Memory available: %f\n', a, z,  sV.PhysicalMemory.Available);
end

% ...
% Iteration: 8255, Time: 0.002197, Memory available: 5797949440.000000
% Iteration: 8256, Time: 0.001595, Memory available: 5797949440.000000
% Iteration: 8257, Time: 0.001827, Memory available: 5797949440.000000
% Iteration: 8258, Time: 0.002016, Memory available: 5797949440.000000
% Iteration: 8259, Time: 0.001667, Memory available: 5797949440.000000
% Iteration: 8260, Time: 0.001540, Memory available: 5797949440.000000
% Iteration: 8261, Time: 0.001582, Memory available: 5797949440.000000
% Iteration: 8262, Time: 0.001593, Memory available: 5797949440.000000
% Iteration: 8263, Time: 0.001547, Memory available: 5797949440.000000
% Iteration: 8264, Time: 0.001544, Memory available: 5797949440.000000
% Iteration: 8265, Time: 0.034461, Memory available: 5797949440.000000 <--- Factor 30 slower!!
% Iteration: 8266, Time: 0.030669, Memory available: 5797949440.000000
% Iteration: 8267, Time: 0.030971, Memory available: 5797949440.000000
% Iteration: 8268, Time: 0.031167, Memory available: 5797949440.000000
% Iteration: 8269, Time: 0.030904, Memory available: 5797949440.000000
% Iteration: 8270, Time: 0.031072, Memory available: 5797949440.000000

Answer 1

[Stefan Wehmeier]

My question is in which form do you have the 50000 entries you want to fill in. As strings in a cell array A? Then

B = cellfun(@sym, A, 'UniformOutput', false);
list1 = [B{:}];

is better. Or really 50000 times the same string? Then avoid calling sym(..) on it in a loop.

All sym vectors are internally vectors of pointers. You cannot pre-allocate the memory these pointers point to ...