Hi folks!
Let's say that I have two lists / vectors "t_list" and "y_list" representing the relationship y(t). I also have numerically computed dy/dt and stored it into "dy_dt_list".
The problem is that "dy_dt_list" contains a lot of fluctuations, and that I know that it MONOTONOUSLY DECREASES out of a physical theory.
1) Is there is a simple way in R or Python to carry out a spline regression that reproduces the numerical values of dy/dt(t) in "dy_dt_list" as best it can UNDER THE CONSTRAINT that it keeps decreasing? I thus want to get a monotonously decreasing (dy/dt)_spline as the output.
2) Is there is a simple way in R or Python to carry out a spline regression that reproduces the numerical values of y(t) as best it can UNDER THE CONSTRAINT that (dy/dt)spline keeps decreasing? I thus want to get y_spline as the output, given that the above constraint is fulfilled.
I'd like to avoid having to reinvent the wheel!
P.S: I added an example to clarify things!
This is what you are looking for:
https://arxiv.org/pdf/0811.1705.pdf
The practical solution is given in Supplement 3:
"R code: Supplement 3 (DOI: 10.1214/08-AOAS167SUPPC). Performs a
weighted monotone convex piecewise cubic spline least-squares regression."
There are also packages that provides a function to fit monotonic splines:
https://search.r-project.org/CRAN/refmans/demography/html/cm.spline.html
https://cran.r-project.org/web/packages/splines2/splines2.pdf
Hi!
There is C-library "GNU Scientific Library" - chapter 29 "Numerical Differentiation". It's free software.
There is FORTRAN-C-...-Pyton-library "IMSL". Is it possible documentation will be sufficient supporting? Documentation is free.
Best regards.
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