How to improve this function execution?

Hi, I have a code that includes a complex function which returns a column vector.

The function can be explained in this simplified form:

V = @(S1, S2, S3, S4, X1, X2, X3, X4) [...

a * S1/(S1 + S2) * X1;

b * X2;

c * S2/(S3 + S4) * X3;

d * S1/(S1 + S4) * X4;

....

];

where S and X are variables; a,b,c,d constants.

Since the code provides many calls of this function, and the profiler graph has clearly shown the large time necessary for its execution, how can I do to improve the performances?

I'm not interested to modify the overall code, but only the management of this function. Maybe, could I enter the function in different format (binary, csv,...) or as a file? Currently, the function is inside one of the code-related scripts (.m file).

Thanks

[Matt J]

where S and X are variables; a,b,c,d constants.

Are they all scalars?

[Elia Paini]

No, S and X are vectors

[Matt J]

If they are vectors of the same size, the code you have posted will not evaluate the expressions element-wise (and will do something slower instead). If they are meant to be element-wise, then see my answer below.

Answer 1

[Matt J]

Since the code provides many calls of this function

Instead of calling the function multiple times, call it just one time or just a few times but with vector inputs. To enable vectorized input, use .* and ./

[a,b,c,d]=deal(1);


V  =   @(S1, S2, S3, S4, X1, X2, X3, X4)   [...      
            a .* S1./(S1 + S2) .* X1;
            b .* X2;
            c .*  S2./(S3 + S4) .* X3;
            d .* S1./(S1 + S4) .* X4
];

X1=rand(1,5);
X2=rand(1,5);
X3=rand(1,5);
X4=rand(1,5);
S1=rand(1,5);
S2=rand(1,5);
S3=rand(1,5);
S4=rand(1,5);

V(S1, S2, S3, S4, X1, X2, X3, X4)

ans = 4×5

0.0999 0.0116 0.1395 0.2693 0.1265 0.1044 0.8347 0.1419 0.0073 0.2531 0.0101 0.1552 0.1668 0.1691 0.1464 0.2829 0.2579 0.4367 0.7545 0.0059

[Elia Paini]

Actually, S and X are elements (which form a vector).

But I need to consider them as elements, not vector, because of other aspects of the code

[Matt J]

But I need to consider them as elements, not vector, because of other aspects of the code

That sounds doubtful. The better line of inquiry might be, do you really have to do that.

But anyway, the answer to your question is, no, you cannot speed up the execution if you must process the inputs as scalars, other than perhaps to use parallel computing toolbox functions like parfor.