Math function to find saturation point of a curve

Does anybody know an algorithm in c to find the saturation point in a curve of saturation?

The curve could change its increasing speed in a sharp or in a smooth way, and have noise included, so it's not as simple as I thought.

I tried calculating the derivative of atan(delta_y/delta_x), but it doesn't work fine开发者_开发知识库 for all the curves.

It appears you're trying to ascertain, numerically, when the gradient of a function, fitted to some data points from a chemistry experiment, is less than one. It also seems like your data is noisy and you want to determine when the gradient would be less than one if the noise wasn't there.

Firstly, let's forget about the noise. You do not want to do this:

atan(((y(i)-y(i-1))/(x(i)-x(i-1)))*180/PI

There is no need to compute the angle of the gradient when you have the gradient is right there. Just compare (y(i)-y(i-1))/(x(i)-x(i-1)) to 1.

Secondly, if there is noise you can't trust derivatives computed like that. But to do better we really need to know more about your problem. There are infinitely many ways to interpret your data. Is there noise in the x values, or just in the y values? Do we expect this curve to have a characteristic shape or can it do anything.

I'll make a guess: This is some kind of chemistry thing where the y values rapidly increase but then the rate of increase slows down, so that in the absence of noise we have y = A(1-exp(-B*x)) for some A and B. If that's the case then you can use a non-linear regression algorithm to fit such a curve to your points and then test when the gradient of the fitted curve is less than 1.

But without more data, your question will be hard to answer. If you really are unwilling to give more information I'd suggest a quick and dirty filtering of your data. Eg. at any time estimate the true value of y by using a weighted average of the previous y values using weights that drop off exponentially the further back in time you go. Eg. instead of using y[i] use z[i] where

z[i] = sum over j = 0 to i of w[i,j]*y[j] / sum over j = 0 to i of w[i,j]

where

w[i,j] = exp(A*(x[j]-x[i]))

and A is some number that you tune by hand until you get the results you want. Try this, and plotting the z[i] as you tweak A. See if it does what you want.

We can get the maxima or minima of a curve quite easily from the function parameters of the curve.Can't see whats the reason why you getting inconsistent results.

I think the problem might be while trying to include the noise curve with the original .So make sure that you mixes these curves in a proper way.There is nothing wrong with the atan or any other math function you used. The problem is with your implementation which you haven't specified here.