Solve non-linear system of equations with variable number of unknowns

Hi everyone, I need some help. I have written a script to form system of nonlinear equations using the symbolic toolbox (because the equation forms are not fixed and dependant on certain parameters) and I need to solve them. I know how to solve a system of nonlinear equations with multiple unknowns, by parameterising the function as follows:

matfun=matlabFunction( symbolic_eqn ); 

funMiddleMan = @(f) matfun(f(1),f(2),f(3),f(4),f(5),f(6),f(7),f(8),f(9),f(10),...
                                f(11),f(12)); % the function has 12 unknowns                            
x0=zeros(1,12);

[soln_fs,fval_fs]=fsolve(funMiddleMan,x0); 

However, for the case where I wish to vary the number of unknowns in "symbolic_eqn", what should I do do make this work? For now, the only idea I can think of is by writing an inelegant list of conditional statements of the form:

switch num_unknowns
    case N
        funMiddleMan = @(f) matfun(f(1),f(2),...,f(N)); %for N number of variables
    [...]
end

Would you please guide me on how I can solve this problem?

Thank you for your help and time.

[Ash Ash]

If it's not possible to do so and I need to use a list of conditional statements please do let me know. Thank you

Answer 1

[Walter Roberson]

%{
matfun = matlabFunction( symbolic_eqn, 'vars', [list variables here]); 
%}

for example

N = 5;
syms F [1 N]
expr = sum(randn(1,N) .* F);
f1 = matlabFunction( expr, 'vars', F)

f1 = function_handle with value:
    @(F1,F2,F3,F4,F5)F1.*3.599379160893824e-1-F2.*1.002299459586992-F3.*1.613867501380812e-1-F4.*1.083541721318095+F5.*2.742004284674245e-1

But most of the time it is easier to instead

f2 = matlabFunction( expr, 'vars', {F} )

f2 = function_handle with value:
    @(in1)in1(:,1).*3.599379160893824e-1-in1(:,2).*1.002299459586992-in1(:,3).*1.613867501380812e-1-in1(:,4).*1.083541721318095+in1(:,5).*2.742004284674245e-1

That second use of matlabFunction expects to be passed a row vector of N values, rather than N individual values.

[Ash Ash]

ahhhh that should solve my problem. I will give it a try soon. Thank you!

[Ash Ash]

This line was what I needed to solve the problem. Thank you!

f2 = matlabFunction( expr, 'vars', {F} )

However, I tried to run your code (and some alternatives that I cound think of) but I couldn't get it to work exactly because of this error:

>> N = 5;
syms [1 N]
Error using syms (line 228)
Invalid variable name.

For the sake of learning, I'm interested to know how to make this line work. would you please help me with this? I'm using R2018b. Maybe this is the issue?

[Walter Roberson]

I used

syms F [1 N]

You omitted the F.

[Ash Ash]

Oops sorry for not clarifying. I tried both

N = 5;
syms F [1 N]

and

syms [1 N]

but they both produced errors.

Error using syms (line 228)
Invalid variable name.

[Walter Roberson]

F = sym('F', [1 N]);

would still have been needed in your release.

[Ash Ash]

aha! I get it now, I'm familiar with the usage of "sym". Thank you for responding . Merry Christmas to you!