Symbolic Substitution and conversion to double is too time consuming

Hi,

I am doing a symbolic substitution and then converting the resultant into double.

for i=1:size(X_scaled,1) % for each row in X_scaled
    Psi_new=Psi;
    for j=1:size(Psi_new,1) % for each row in Psi
        Psi_new{j}=subs(Psi_new{j},x,X_scaled(i,:)); % for each variable
        Num_Psi(i,j)=double(Psi_new{j});
    end
end

X_scaled: 5000 by 7 matrix with numerical values; each column cell contains a value of one out of 7 variables.

Psi: 36 by 1 cell matrix; each cell having a symbolic expression of 7 symbols (an expression made of 7 variables).

x: 1 by 7 cell array containing the names of the 7 symbols (variables)

So, the final output in Num_Psi would be 5000 *36 values.

I need to substitute the 7 values from X_scaled into each cell of Psi. However, apparently the substitution process is quite slow. This code take hours.

Is there any way to speed up the substition process?

Many thanks for looking into the problem.

Aksh

[Dyuman Joshi]

It would be better if you share your code and specify what exactly you are trying to do.

Answer 1

[Ayush]

Hi Aksh,

I understand that you want to optimise your code that is performing symbolic substitution interactively.

Some possible workarounds for optimisation are:

1. Pre-allocate memory: Pre-allocating memory for the “Psi_new” and “Num_Psi” matrix before the loop to improve performance. Since dynamic allocation leads to more memory usage.

2. Vectorisation: To avoid using nested loops, you can vectorise the substitution process. You can use the “arrayfun” function to apply the function to each element of the “Psi” array. To covert the elements of “Psi” (symbolic expression matrix) into a set of functions you can use the “matlabFunction”. You can refer to the below documentation to know more about the “arrayfun” and “matlabFunction” function:

- Apply function to each element of array - MATLAB arrayfun - MathWorks India

- Convert symbolic expression to function handle or file - MATLAB matlabFunction - MathWorks India

3. Parallel Computation: If you have access to the Parallel Computing Toolbox, you can use the “parfor” loop to enable parallel computation to utilise multiple cores or processors. You can refer to the below documentation to know more about the “parfor” function:

- Parallel for-loop - MATLAB parfor - MathWorks India

Hope it helps,

Regards,

Ayush Misra