find a value between two points

Hey everyone,

I have the following case : (picture linked to the tocpic).

Let's suppose that i have two points with their value on y-axis equals to -20.5 and -19.5. I also know their value on x-axis (let's suppose 10^9 and 2*10^9). I don't have more points between them.

I would like to know : How can I find the value on X-axis of the point that have the value on y-axis equal to -20.

If it's not understandable, I hope the picture linked to it will be helpful !

Thanks you very much !

[Mathieu NOE]

hi

seems you want to have this intermediate point from a curve that passes through the 2 points. have you tried to create this curve or a approximation (fit) of it ? then you can pick anypoint from this curve.

otherwise you could do simple interpolation, but with only two input points this would be limited to a simple linear interpolation , which is not what your picture says.

[dsq dq]

Hi,

This curve is already created I have like ~ 8000 points, so I cannot create it. I looked for the interpolation function but I didn't get how this could help me because I would like to have the exact value for -20 ...

Answer 1

[Star Strider]

Use interp1 or fzero on a monotonically-increasing (or decreasing) curve such as that.

Example —

x = linspace(0, 50);
y = 30*(1-exp(-0.1*x));
f = @(x) 30*(1-exp(-0.1*x));

x_20 = interp1(y, x, 20)                            % From Data

x_20 = 10.9885

f_20 = fzero(@(x) f(x)-20, rand)                    % From Function

f_20 = 10.9861

figure
plot(x, y)
grid
hold on
plot(x_20, 20, '+r')
plot(f_20, 20, 'xg')
hold off

.

[dsq dq]

Yes I see it's working. Just my function is a bit chaotic so it may cross the value (-20) several times. Is there a way to have the value of all the points ? Or need I to split the table ?

[Star Strider]

I am not certain what your function (or data) look like, so I can’t address it precisely. The best way to approach something like that is to subtract 20 from it, and then use interp1 at the zero-crossings:

x = linspace(0, 50, 250);
y = 20*(1-exp(-0.1*x)) + 5*sin(2*pi*x*15);

yfind = 20;
yz = find(diff(sign(y-yfind)));
for k = 1:numel(yz)
    idxrng = max(1,yz(k)-2) : min(numel(x),yz(k)+2);            % Index Range
    xi(k) = interp1(y(idxrng),x(idxrng),yfind);
end
xi

xi = 1×4

18.4762 24.0158 33.6995 41.4991

figure
plot(x, y)
yline(yfind, '--r')
hold on
plot(xi, ones(size(xi))*yfind, 'sg', 'MarkerSize',10)
hold off
grid
legend('Data','Target Value','Interceptions', 'Location','best')

Experiment with my code and your (x,y) data.

.

[dsq dq]

Ok i see. thanks a lot !

[Star Strider]

As always, my pleasure!

.

Answer 2

[KSSV]

Read about interp1. If you have curve data as (x,y), at the point xi you can seek the value using:

yi = interp1(x,y,xi)

[dsq dq]

Hey thanks ! star strider explained it juste below ! thanks for your help