Spline interpolation in matlab in order to predict value

Question

I have the situation like on this image below:

This plot is the result of two vectors:

fi = [41.309180589278, 41.8087915220215, 42.8081880760916         


        

Answer 1

One way to find a zero crossing is to "turn the graph sideways", having fi be a function of m, and interpolate to find m=0. But interp1 requires the m input to be monotonic, which this is not. In fact, this function has two different values for each m.

MATLAB knows the fzeros function, which finds a zero crossing of a function numerically. It requires a function as input. We can define an anonymous function using interp1, which returns m-1 for any value of x. Here, x is defined by fi and f(x) by m:

fi = [41.309180589278, 41.8087915220215, 42.8081880760916, ...
      43.8078181874395, 44.8076823745539, 45.8077808710707, 46.3079179803177];
m = [1.00047608139868, 1.00013712198767, 0.999680989440986, ...
     0.999524195487826, 0.999671686649694, 1.00012913666266, 1.00047608139868];
fun = @(x)interp1(fi,m,x)-1;
x1 = fzero(fun,42)
x2 = fzero(fun,46)

This gives me:

x1 =  42.109
x2 =  45.525

Note that we needed to know the approximate locations for these two zeros. There is no easy way around this that I know of. If one knows that there are two zero crossings, and the general shape of the function, one can find the local minimum:

[~,fimin] = min(m);
fimin = fi(fimin);

and then find the zero crossings between each of the end points and the local minimum:

x1 = fzero(fun,[fi(1),fimin])
x2 = fzero(fun,[fimin,fi(end)])

Answer 2

You need to use an anonymous function so that you can pass additional arguments to interp1.

Try this

fi = [41.309180589278, 41.8087915220215, 42.8081880760916, ...
      43.8078181874395, 44.8076823745539, 45.8077808710707, 46.3079179803177];
m = [1.00047608139868, 1.00013712198767, 0.999680989440986, ...
     0.999524195487826, 0.999671686649694, 1.00012913666266, 1.00047608139868];

fzero(@(x) 1-interp1(fi,m,x), 43)
fzero(@(x) 1-interp1(fi,m,x), 45)

The 43 and 45 are the initialization for x for fzero. You need to run the fzero twice to find the two solutions.