Solving a Matrix of Independent Equations At the Same Time

Could you help me fix the syntax of the solve function in the following codes? There should be at least as many answers as the size of the data grid.

syms a b x
[a,b] = ndgrid(-2:2:2,-3:3:3);
equ = x == a.*x - 9.*b.*x.^2 + 128;
answers=solve(equ,x)

It is better to avoid "for loops" to increase the speed. The actual grid data and equations are much more complicated than what I am showing here that cannot be symbilically solved.

It is okay to keep the solutions in a 3 by 3 cell matrix where each cell contains the solutions.

[Stephen23]

"It is better to avoid "for loops" to increase the speed. "

Why? What is the problem with using a for loop?

[S H]

If the speed of two codes with the same functionality are measured using tic and toc, the code with "for loop" is always slower that the code with vector calculation.

[Stephen23]

"If the speed of two codes with the same functionality are measured using tic and toc, the code with "for loop" is always slower that the code with vector calculation."

That is incorrect. If vectorized code requires creating large intermediate arrays it can very easily be much slower that looped code, if it is possible at all. Most probably this also depends on the available memory and the MATLAB version too.

Answer 1

[madhan ravi]

syms a b x
equ = x == a.*x - 9.*b.*x.^2 + 128;
answers=solve(equ,x);
[a,b] = ndgrid(-2:2:2,-3:3:3);
Answers=matlabFunction(answers);
Answers(a,b) % final

[S H]

Your code is very nice. Thank you. But as I said in the question, the actual equation in my script is much more complicated than what I am showing here and trying to solve it symbolically is not possible even after adding assume constraints. When solving the equation, Matlab generates the following message:

Warning: Solutions are valid under the following conditions...

and the symbolic results showed by Matlab do not make sense. That is why I am trying to solve the equation numerically rather than symbolically and because of that, the order of presented code is better not to be changed. First define the data and then evaluate equation at those data points and finally solve.

[madhan ravi]

Anytime :) , Then I believe loop is inevitable. Why not upload your script or the equation that you try to solve??

[S H]

That is a very helpful comment. Maybe you can help me solve the symbolic equation correctly. The equation is:

equ = IDS == (151115727451828646838272.*(IDS./GS - (3.*G1)./(G1 + G2) + 2./5).^2.*((6293851573638341.*(3.*GD - IDS))./(483570327845851669882470400.*GD) - (18881554720915023.*G1)./(483570327845851669882470400.*(G1 + G2)) + 1579756744983223591./1208925819614629174706176000))./6800207735332289

IDS is parameter I want to solve over the data grid defines by G1, G2, GD and GS which are are all positive real numbers.

[madhan ravi]

solve(equ,IDS,'maxDegree',3) % and then follow the same method I showed in my answer

[S H]

Amazing. Thank you.

[madhan ravi]

Anytime :)