So I had to write a program in Matlab to calculate the convolution of two functions, manually. I wrote this simple piece of code that I know is not that optimized probably:

syms recP(x);
recP(x) = rectangularPulse(-1,1,x);
syms triP(x);
triP(x) = triangularPulse(-1,1,x);
t = -10:0.1:10;
s1 = -10:0.1:10;
for i = 1:201
    s1(i) = 0;
    for j = t
        s1(i) = s1(i)   ( recP(j) * triP(t(i)-j) );
    end
end
plot(t,s1);

I have a core i7-7700HQ coupled with 32 GB of RAM. Matlab is stored on my HDD and my Windows is on my SSD. The problem is that this simple code is taking I think at least 20 minutes to run. I have it in a section and I don't run the whole code. Matlab is only taking 18% of my CPU and 3 GB of RAM for this task. Which is I think probably enough, I don't know. But I don't think it should take that long.
Am I doing anything wrong? I've searched for how to increase the RAM limit of Matlab, and I found that it is not limited and it takes how much it needs. I don't know if I can increase the CPU usage of it or not.
Is there any solution to how make things a little bit faster? I have like 6 or 7 of these for loops in my homework and it takes forever if I run the whole live script. Thanks in advance for your help.
(Also, it highlights the piece of code that is currently running. It is the for loop, the outer one is highlighted)

CodePudding user response：

Like Ander said, use the symbolic toolbox in matlab as a last resort. Additionally, when trying to speed up matlab code, focus on taking advantage of matlab's vectorized operations. What I mean by this is matlab is very efficient at performing operations like this:

y = x.*z;

where x and z are some Nx1 vectors each and the operator '.*' is called 'dot multiplication'. This is essentially telling matlab to perform multiplication on x1*z1, x[2]*z[2] .... x[n]*z[n] and assign all the values to the corresponding value in the vector y. Additionally, many of the functions in matlab are able to accept vectors as inputs and perform their operations on each element and return an equal size vector with the output at each element. You can check this for any given function by scrolling down in its documentation to the inputs and outputs section and checking what form of array the inputs and outputs can take. For example, rectangularPulse's documentation says it can accept vectors as inputs. Therefore, you can simplify your inner loop to this:

s1(i) = s1(i)   ( rectangularPulse(-1,1,t) * triP(t(i)-t) );

So to summarize:

1. Avoid the symbolic toolbox in matlab until you have a better handle of what you're doing or you absolutely have to use it.
2. Use matlab's ability to handle vectors and arrays very well.
3. Deconstruct any nested loops you write one at a time from the inside out. Usually this dramatically accelerates matlab code especially when you are new to writing it.

See if you can even further simplify the code and get rid of your outer loop as well.