How to find x values from y value in "fit" function?

Hi, I have some data and with this data I create a fit function:

f = fit(x,y,'smoothingspline');

plot(f,x,y);

I need to find X values in two points like in the picture.

I tried to use :

z = x(y==y_i);

But what I get is:

0×1 empty double column vector

How can I solve this problem?

Thanks in advance

Answer 1

[David Hill]

yval=-62;
eqn=@(x)feval(f,x)-yval
X1=fzero(eqn,4.8);
X2=fzero(eqn,5.3);

[Kanan Yagublu]

Thank you for your answer, but how did you get 4.8 and 5.3? Are they approximation from the graph?

Because when I change the data set the code doesn't work

[Kanan Yagublu]

@David Hill and how can I modify it so it will not depend on 4.8 and 5.3 ?

Answer 2

[Steven Lord]

Set up a sample polynomial fit.

x = randn(10, 1);
y = (x-1).*(x+1); % polynomial is y = x^2-1 = (x-1)*(x+1)
p = fit(x, y, 'poly2')

p = 
     Linear model Poly2:
     p(x) = p1*x^2 + p2*x + p3
     Coefficients (with 95% confidence bounds):
       p1 =           1  (1, 1)
       p2 =   6.259e-17  (-2.697e-16, 3.949e-16)
       p3 =          -1  (-1, -1)

Find the points where p takes on the value y = 3.

plusOneSolution = fzero(@(x) p(x)-3, 1)

plusOneSolution = 2

minusOneSolution = fzero(@(x) p(x)-3, -1)

minusOneSolution = -2

Check that evaluating the fit at those two points gives us the value y = 3.

check = p([plusOneSolution, minusOneSolution])

check = 2×1

3.0000 3.0000