solving equations initially written as strings using fsolve

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S H 2019-4-29

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评论： Matt J 2019-4-29

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Is it possible to solve the following equations that are initially written as string expressions?

eqns={...
    'x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)-1';...
    'x(1)-a*x(2)';...
    'x(2)-a*x(3)';...
    'x(3)-a*x(4)';...
    'x(4)-a*x(5)';...
    'x(5)-a*x(6)';...
    'x(6)-a*x(7)'};
for kk=1:7
    myF{kk}=str2func(eqns{kk});
end
funeqns=@(x) myF{:};
a=2;
x0=0.5*ones(1,7);
opts=optimoptions('fsolve','Algorithm','trust-region','TolFun',1e-12,...
    'TolX',1e-12,'Display','off');
fs=fsolve(funeqns,x0,opts)';

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John D'Errico 2019-4-29

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Is it possible? Probably. But you need to do significantly more than just call str2func, as for example, this is not a valid function:

str2func(eqns{1})
Warning: The input to STR2FUNC "x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)-1" is not a valid function name. This will generate an error in a future release. 
ans =
  function_handle with value:
    @x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)-1

Also, MATLAB will not be able to automatically know that x is a vector of unknowns, but a is apparently something known. You would need to do some of the thinking for MATLAB there. For example, suppose that both a and x are variables in the base workspace.

S H 2019-4-29

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Thank you John. What should be done if there are many equations written in different files as expressions. Is there any way to solve them besides rewriting those equations in Matlab command window?