Solve nonlinear equation with positive solution (fsolve)
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Hello, I would like to solve 3 non linear equation:
F(1) = 0.44*x(1) + 0.23*x(2) + 0.33*x(3) - 5140;
F(2) = 0.23*x(1) + 0.44*x(2) + 0.33*x(3) - 4970;
F(3) = 4*(0.44 + 0.23)*(x(1)*x(2)/(3*x(2)+x(1))) + 0.33*x(3) - 4380;
Here, x is 3 different young modulus and my problem is, using fsolve give me negative values... Do you know if it's possible to find positive values or should I try another way ?
Thank for yours answers
답변 (2개)
sloppydisk
2018년 6월 7일
You can set an assumption on the equations using assume, in this case there seem to be no solutions for this problem.
x = sym('x', [3 1]);
F(1) = 0.44*x(1) + 0.23*x(2) + 0.33*x(3) - 5140==0;
F(2) = 0.23*x(1) + 0.44*x(2) + 0.33*x(3) - 4970==0;
F(3) = 4*(0.44 + 0.23)*(x(1)*x(2)/(3*x(2)+x(1))) + 0.33*x(3) - 4380==0;
assume(x>=0)
sol1 = solve(F, x)
Star Strider
2018년 6월 7일
I am not certain what the values of ‘x’ should be.
Try these:
fcn = @(x) [0.44*x(1) + 0.23*x(2) + 0.33*x(3) - 5140; 0.23*x(1) + 0.44*x(2) + 0.33*x(3) - 4970; 4*(0.44 + 0.23)*(x(1)*x(2)/(3*x(2)+x(1))) + 0.33*x(3) - 4380];
[xs,fv] = fsolve(@(x) norm(fcn(x)), [1; 1; 1])
[xs,fv] = fmincon(@(x) sum(fcn(x)), [1; 1; 1], [], [], [], [], [0; 0; 0],[1; 1; 1]*Inf)
The first one provides a sort of ‘pseudo-constraint’ using the norm of the output. The second uses fmincon to constrain the parameters, however since it requires that the argument function return a scalar, leaves that as a problem for you to solve. (I arbitrarily chose to sum them here.)
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