39 views (last 30 days)

I have a set of data points in 2D that I want to use fit(x,y,'modeltype') function to test the curve fit of different types of functions. I have tried Fourier series, polynomial, two-term exponential and two-term power functions (one on the increasing and one on the decresing interval). I have two constraints that I want to implement but I dont know how. It is the value and the first derivative in one point. I want the following to hold (the data points are somewhat like an U upside down):

f(1)=1, df/dx(1)=0

How do I implement these connstraints? For these to hold (or be as close to 1 and 0 as possible) is more important than the curve to match all the other data points.

Thank you in advance!

Cyrus Tirband
on 31 Oct 2019

If you absolutely have to make sure your constraints are met, you have to change your fitting equation so that all possible solutions satisfy your constraints. Consider the 2nd degree polynomial:

if the constraints are y'(1) = 0, and y(1) = 1; we get

Your fitting equation then becomes

Which will give shitty results since it only has one degree of freedom. But this is just an example, if you start with a 4th degree polynomial, your fitting equation will have three degrees of freedom. The fit function will then take care of the rest and minimize the least squares cost.

Opportunities for recent engineering grads.

Apply Today
## 2 Comments

## Direct link to this comment

https://ww2.mathworks.cn/matlabcentral/answers/488545-derivative-constraint-in-curve-fitting#comment_762267

⋮## Direct link to this comment

https://ww2.mathworks.cn/matlabcentral/answers/488545-derivative-constraint-in-curve-fitting#comment_762267

## Direct link to this comment

https://ww2.mathworks.cn/matlabcentral/answers/488545-derivative-constraint-in-curve-fitting#comment_762272

⋮## Direct link to this comment

https://ww2.mathworks.cn/matlabcentral/answers/488545-derivative-constraint-in-curve-fitting#comment_762272

Sign in to comment.