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

Question

Ash Ash 2020-12-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/687323-solve-non-linear-system-of-equations-with-variable-number-of-unknowns

评论： Ash Ash 2020-12-25

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.

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Ash Ash 2020-12-10

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

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Answer 1

Walter Roberson 2020-12-10

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/687323-solve-non-linear-system-of-equations-with-variable-number-of-unknowns#answer_571014

在 MATLAB Online 中打开

%{
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.