Flexible symbolic function definition

I am using symbolic functions but need it somehow to be flexible in terms of number of variables I use.

For 2 variable I get

syms a b
syms f1(a,b)
z = a + b

For 5 variables I get

syms a b c d e
syms f1(a,b,c,d,e)
z = a + b + c + d + e

I think for the first line of code I can use

syms a [1 N]

where N is number of variables. The results will be

a = (a1 a2)

But how do I create f1(a,b,c...) in a flexible way?

[Paul]

HI Stefan,

Not really sure what you're trying do. How does z play into any of this? Can you give a little more detail on the workflow of how f1 is supposed to be formed, including its right-hand-side definiton?

Are you trying to start with symbolic expression, like z, and conver it into a symfun object with arguments being the variables in z?

[Stefan Engstrom]

Hi Paul,

Thanks for the response.

I want to create a third order polynomial expansion for z based on the symbols.

syms a [1 N_beams]
len_a = length(a);
z=0;
for q1 = 1:len_a
    z = z + a(q1);
    % f1(a,b,c...)
end
z^2*conj(z);
w3 = expand(z^2*conj(z))

The answer is

I would prefer to use a, b, c, etc instead of a with indices as it is easie to read.

f1 is used late in the code where I insert an array for each a,b,c, etc

IM3_exitations(k,:) = double(IM3(k).f3(A,B,C,D));

Answer 1

[Paul]

I'm still not sure what you want. Maybe this?

syms a b c
vars = [a b c];
len_vars = length(vars); % might want to use numel
z=0;
for q1 = 1:len_vars
    z = z + vars(q1);
    % f1(a,b,c...)
end
z^2*conj(z);
w3 = expand(z^2*conj(z))

w3 = 

Create a symfun if desired:

f(symvar(w3)) = w3

f(a, b, c) = 

[Walter Roberson]

You can also do

syms a b c d e f g h i j k l m n o p q r s t u v w x
allvars = [a b c d e f g h i j k l m n o p q r s t u v w x]

allvars = 

vars = allvars(1:3);
len_vars = length(vars); % might want to use numel
z=0;
for q1 = 1:len_vars
    z = z + vars(q1);
    % f1(a,b,c...)
end
z^2*conj(z);
w3 = expand(z^2*conj(z))

w3 = 

f(allvars) = w3

f(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) = 

This is a function that expects all of those positions, but only uses some of them.

Answer 2

[Stefan Engstrom]

Thanks Paul,

It works for the polynomial expansion. Thanks.

Now it is the f3 syms that I don't know what to do.

if I create

syms f3(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x)

Can I then remove, for instance d to x somehow if I only want a,b and c?

[Paul]

I'm going to assume that you want only a, b, and c as arguments because those are the only variables in the function formula

syms f3(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x)
f3(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x) = a*b + b/c

f3(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) = 

formula returns the formula of f3

formula(f3)

ans = 

So using what we have above

args = symvar(formula(f3));
f3(args) = formula(f3)

f3(a, b, c) = 

If my assumption is incorrect, and you really have f3 as symfun without a formula and you just wnat to manipulate its arguments, you can use argnames to get the arguments to f3 and go from there.

Also, I edited my other answer to simplify it.

Answer 3

[Stefan Engstrom]

Thanks again Paul,

How can I remove d and onwards as arguments in f3?

[Paul]

Stefan,

It would be better to follow up with a Comment on the relevant Answer instead of adding a new Answer all the time. Anyway, I don't understand what you're asking here. Are you saying that you have f3 defined without a formula?

syms f3(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x)

Now, what do you want to produce from f3?

[Stefan Engstrom]

It is a long code and a lot of steps in between the "syms" and when I use it.

I started with only one or two arguments, a and b. But now I realize I need to use up to 24, a to x. So I don't want to do 24 "syms f(a.....)". Hence my question.

[Paul]

Still not clear. We don't need to see your full code, just a clear explanation of what you want your code to do. Are you trying to create a symbolic function in some code, but you don't know a priori how many arguments that function will take? Do you have a symbolic function already defined and you want to change the argument signature of that function? Something else? Ideally, you can provide a minimal working example in code that shows what you have working with explanation of how you'd like to make it work better, or a minimal working example that shows what code you have, where your stuck, and the desired end result. Either would help me (or anyone else) help you.

Answer 4

[Walter Roberson]

I suggest that you look at the 'vars' option of matlabFunction