Interpolation of matrices with data points having changing derivative

Dear all,

I am trying to define a spline for a set of data whose derivative goes to zero after a certain set of time. Then I have to use this spline for interpolation in a for loop using ppval. But the problem is that in reality the derivative of the spline approaches to zero but the defined spline goes on increasing. At the start both values are matching, the actual and the spline but at larger values the deviation is greater.

In actual scenario, at approximately 20 value at the x axis, the y axis value keeps on increasing, but after that the y value remain approximately constant, even if x-axis value goes to infinity.

Thank you for your response in advance.

Regards

[Torsten]

A spline is not suited to extrapolate your y-values as x approaches infinity. If I understand correctly what you write, I think this is what you try to do.

[Mathieu NOE]

I think It would be nice to have some data and a graph to understand what you are trying to do

[Mathieu NOE]

hello @Muhammad Hassaan Bin Tariq

problem solved ?

[Muhammad Hassaan Bin Tariq]

Thank you for your responses. Yes this was what I was trying to do.

Sorry I am not able to share the data due to confidentiality in research. However, the general trend of the graph is as follows:

I have tried to interpolate with pchip in curve fitting toolbox and then extrapolate using nearest neighbour. But nearest neighbour just keeps the last value constant which is not the case. pchip changes the trend totally in extrapolation. Linear takes it to negative which formula does not permit. Plus the saving and calling the interpolation as variables of workspace made the time much longer which increases computational cost as compared to making a spline and calling as ppvalue in the for loop.

[Mathieu NOE]

so you could use the last samples ,take the average slope and do some extrapolation ?

[Muhammad Hassaan Bin Tariq]

Slope is approximately constant but it keeps on decreasing by a minute amount.

[Mathieu NOE]

I am unsure if we are on the same page

I supposed you are still looking for a way to make to your extrapolation - but maybe you have reached your goal

otherwise, if the end of the curve has almost contant slope , why not extrapolate with that info (with a linear curve ?)

[Muhammad Hassaan Bin Tariq]

The extrapolation with linear seems to be close. It goes below zero after a large value which is not the case in the equation. But the equation is a bit complex with square roots included inside double integral.

Furthermore, I am not able to reach correct answer for the overall question. Maybe there is some problem other than interpolation with the question.

[Mathieu NOE]

I don't know if it makes sense , but we could do the linear extrapolation with the linear model until it reaches y = 0 and then stay at y= 0 if that's what you want

[Star Strider]

If youu have a mathematical description of the process that produces your data, use it as a model and fit the model function to your data to estimate the parameters. I never suggest extrapolating, since you never actually know what the function does outside of the region-of-fit, however that might work to estimate the asymptotes or the derivative asymptotes, if that is what you want to do.

[Muhammad Hassaan Bin Tariq]

@Mathieu NOE Yes I tried this to push the model to stay at zero but it was still not giving results as required.

[Muhammad Hassaan Bin Tariq]

@Star Strider Can you please explain how can I proceed for this estimation?

[Star Strider]

@Muhammad Hassaan Bin Tariq — If you have a mathematical description of the process that created your data, convert that to a function that can be used as the objective function in one of the appropriate optimisation functions, for example lsqcurvefit (although there are several to choose from, depending on what you want). Once you get good estimates for the parameters, you can evaluate the function for other values of the independent variable.

You can also use the Symbolic Math Toolbox to calculate the derivative of the function, and convert that to an anonymous function that can then evaluate the derivative with the estimated parameters at given values of the independent variable.