How to solve an equation contains norminv?
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Susan
el 28 de Feb. de 2023
Comentada: Susan
el 1 de Mzo. de 2023
Hi all,
I'd like to solve the following equation.
sol = [];
for L = -20:10:120
syms x
eqn = 10*log10(10.^(0.1*(norminv(x)*7.6 + 9.88)) + 10.^(0.1*(norminv(x)*6.5 + 12.1)) + 10.^(-0.3)) == L
S = solve(eqn);
sol = [sol S];
end
I modified the equation by replacing the norminv (x) with -sqrt(2)*erfcinv(2*x), i.e.,
sol = [];
for L = -20:10:120
syms x
eqn = 10*log10(10.^(0.1*(-sqrt(2)*erfcinv(2*x)*7.6 + 9.88)) + 10.^(0.1*(-sqrt(2)*erfcinv(2*x)*6.5 + 12.1)) + 10.^(-0.3)) == L
S = solve(eqn);
sol = [sol S];
end
However, I got a warning saying, "Warning: Unable to find explicit solution. For options, see help.". So, I add the following lines, hoping to solve the equation, but still unsuccessful.
S = solve(eqn);
string(lhs(eqn)-rhs(eqn))
sol = [sol vpasolve(eqn, [-143, -109.5937])]
Could someone please help me out?
Thanks in advance
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Respuesta aceptada
Walter Roberson
el 28 de Feb. de 2023
syms x
eqn = 10*log10(10.^(0.1*(-sqrt(2)*erfcinv(2*x)*7.6 + 9.88)) + 10.^(0.1*(-sqrt(2)*erfcinv(2*x)*6.5 + 12.1)) + 10.^(-0.3))
double(limit(eqn, x, 1e-200))
double(limit(eqn, x, 1-sym(1e-50)))
The left hand side is the same for all of them, and you cannot get it down below -3 and cannot get it much above 120-ish. So there is no real-valued solution for L = -20 or L = -10
For the other values... use vpasolve() with around 0.01 as an initial guess, and after that use the previous solution as the initial guess for the next round.
9 comentarios
Walter Roberson
el 1 de Mzo. de 2023
That is why I coded test for empty result in https://www.mathworks.com/matlabcentral/answers/1920765-how-to-solve-an-equation-contains-norminv#comment_2640465
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