How do I get the most linear part of a curve?

Looking for some ideas for solving to get the slope of the most linear part of a non linear curve.

[Birdman]

Do you have numerical array, or just equation?

[Deepika Sundar]

Hello!

Yes I have numerical Array, for stress versus displacement

[Image Analyst]

Over what range? Of course every point of the curve is linear since every point on the curve has a tangent line. So at the very least it can be considered linear at every infinitesimally thin point. And the slope of that line is simply the derivative of your curve/equation. But are you looking for the most linear section over a distance of 2 or 4 or whatever in x?

[Deepika Sundar]

The range that I have arbitarily set is for 10 millimetres of displacement (X axis). Since this range (10mm) shifts left or right according to my experimental Parameters, I would have to Isolate the nearly linear Portion and determine the slope for this Portion. I currently do this in Excel visually.

Answer 1

[Birdman]

One approach might be taking derivative of your numerical array by diff command, then find the minimum value in that vector and using the index, find the corresponding value in your main array. It should go like:

y=diff(x);
[val,idx]=min(y);
minSlope=x(idx+1)

[Deepika Sundar]

So this way I can check for repeating slopes in the range mentioned. Thanks a lot I shall try this.

[Birdman]

Try and let me know the results.

Answer 2

[Russell Marki]

I've done something that kind of works.

n is the length of the window as a fraction of the length of input x and y vectors.

An increase to length_weight will increase the value of a longer window.