Curve Fitting with Known Integrals Python

问题

I have some data that are the integrals of an unknown curve within bins. For your interest, the data is ocean wave energy and the bins are for directions, e.g. 0-15 degrees. If possible, I would like to fit a curve on to the data that conserves the integrals within the bins. I've tried sketching it on a notepad with a pencil and it seems like it could be possible. Does anyone know of any curve-fitting tool in Python to do this, for example in the scipy interpolation sub-package?

Thanks in advance

Edit:

Thanks for the help. If I do it, it looks like I will try the method that is recommended in section 4 of this paper: http://journals.ametsoc.org/doi/abs/10.1175/1520-0485%281996%29026%3C0136%3ATIOFFI%3E2.0.CO%3B2. In theory, it basically uses matrices to make some 'fake' data from the known integrals between each band. When plotted, this data then produces an interpolated line graph that preserves the integrals.

回答1:

It's a little outside my bailiwick, but I can suggest having a look at SciKits to see if there's anything there that might be useful. Other packages to browse would be pandas and StatsModels. Good luck!

回答2:

If you have a curve f(x) which is an approximation to the integral of another curve g(x), i.e. f=int(g,x) then the two are related by the Fundamental theorem of calculus, that is, your original function is the derivative of the first curve g = df/dx. As such you can use numpy.diff or any of the higher order methods to approximate df/dx to obtain an estimate of your original curve.

回答3:

One possibility: calculate the cumulative sum of the bin volumes (np.cumsum), fit an interpolating spline to it, and then take the derivative to get the curve.

scipy splines have methods to calculate the derivatives.

The only limitation, in case it is relevant in your case, the spline through the cumulative sum might not be monotonic, and the derivative might be negative over some intervals.

I guess that the literature on smoothing a histogram looks at similar constraints on the volume of the integral/bin, but I don't have any references ready.

回答4:

1/ fit2histogram

Your question is about fitting an histogram. I just came through documentation for some Python package for Multi-Variate Pattern Analysis, PyMVPA, and some function for histogram fitting is proposed. An example is here: PyMVPA.

However, I guess that set of available distributions is limited to famous distributions.

2/ integral computation

As already mentionned, next solution is to approximate integral value, and to fit a model to the resulting set of data. Either you know explicit expression for the derivative, or you use computational derivation: finite difference, analytical method.

来源：https://stackoverflow.com/questions/11342064/curve-fitting-with-known-integrals-python