Optimizing program to get faster results

Hello;

I am trying to solve equation using (syms) then evaluating the result. The program is working. However, each loop taking almost 27 second. Is there anyway that I can optimize program so it will work faster?

I used the below code

clear;
clc;
syms A B C D E ; 
R=((4*B*A)/((D-C)^2+(B+A)^2));
R1=((4*B*A)/((D+C)^2+(B+A)^2));
F1 = ellipticK(R);
I1 = ellipticE(R);
F2 = ellipticK(R1);
I2 = ellipticE(R1);
P= ((((A*B)^(1/2))/(2*E*(R^(1/2))))*(((2 - R)*F1) -...
    (2*I1)))-(((((A*B)^(1/2))/(2*E*(R1^(1/2)))))* ...
    (((2 - R1)*F2) - (2*I2)));
P1=feval(symengine,'simplify',P,'IgnoreAnalyticConstraints');

X=(1/B)*(diff(P1,D));
X1=feval(symengine,'simplify',X,'IgnoreAnalyticConstraints');
[B,D]= meshgrid(linspace(0.1,10),linspace(0.1,10));
E=3;
N1 = 10*rand(100000,1);
N2 = 5*rand(100000,1);
M(:)=0;
for i=1:100000
    tic
    A=N1(i);C=N2(i);
    F = matlabFunction(X1);
    B = F(A, B, C, D, E);
    In(:,:,i)=B(:,:); 
    fprintf('%d\n ', i); 
    toc
end

[Adam]

doc profile

is the first place to start. Find out which lines are actually taking the time before you try to optimise anything.

The Matlab profiler is very easy and intuitive to use, unlike some I have used for other languages.

[Math Tec]

@ Adam. Than you.

B = F(A, B, C, D, E); This line and each Loop are taking around 27 sec

[Adam]

Well, if you click on that in the profiler you should be able to drill down further into that. I don;t use the symbolic toolbox so I don't really know what a lot of this code is doing or what

matlabFunction

is supposed to be - it sounds a ridiculously generic name. Is it a builtin function and is it returning a function handle?

[Stephen23]

@Adam: matlabFunction converts a symbolic expression into a MATLAB function handle.

[Karan Gill]

• Why do you define B D E as symbolic and then redefine them as numbers/arrays?
• Why use "feval" instead of directly using the "simplify" function?
• Instead of calling a matlab function 100,000 times, can you instead try using "subs" to substitute the arrays in?

[Math Tec]

Thank you.

- I define it as as symbols because this is part of the program. I use it in the next line to find the derivative (X=(1/B)*(diff(P1,D));).

- For the second and third part, I do not know how to do it. I hope if you can help me to do it

Answer 1

[Karan Gill]

Following up on my comment above:

1. Do not overwrite symbolic variables with numeric values. So don't do

syms B D

and then

[B,D]= meshgrid(linspace(0.1,10),linspace(0.1,10));

Call B and D something else when you initialize the numeric values.

2. Use "simplify" directly. See the documentation for it.

3. Instead of using a loop, use "subs" to substitute an array for the symbolic variable. Again, see the doc for "subs".