hello everyone,
i want to fit a list of data points by picewise quadratic function like this,


where 0.6 is the break point that i chose in advance .

the requirements are:
1. the function and its first derivetive at the break point should be continuous,
2. the break point is not known thus is also a parameter to fit.
(but in my data points, i wold like to choose 0.6 as breakpoint in advance )

this picewise quadratic is taken from a empirial expression , so it's not appropriate to take other function forms

The Fit function provided by Maxima plugin seems can not do that:



any suggestion is welcomed, the .sm file is attatched for the datapoints
thanks in advance.
picewise_qudratic_fit.sm (15kb) downloaded 4 time(s).

Edited by user 21 December 2023 03:33:30(UTC)  | Reason: Not specified

I want to fit a list of data points by picewise quadratic function
the requirements are:
1. the function and its first derivative at the break point should be continuous,
2. the break point is not known thus is also a parameter to fit.
................
Quadratic joins at support points automated wrt X vector.
Quadratic derivative can't be smooth at junctions.
Only cubic derivative is smooth at junctions.
Jean

Worksheet30.sm (33kb) downloaded 1 time(s).

Hi. I just take the excelent Stv work and add some basic maths.

picewise_qudratic_fit_b.sm (31kb) downloaded 6 time(s).



Best regards.
Alvaro.

General remark for Fit():

- names for the variables and the parameters must be undefined. Use Clear for repeated fits if assignment was used.
- You can do the fit, evaluate the mean square error and plot the function without actually assigning the variables.
- Sometimes the default precision is not sufficient, then it is advisable to reduce the tolerance (optional argument)

For piecewise functions, use conditionals wrapped in charfun(). In Maxima conditionals evaluate to true or false, charfun() converts that to 1 or 0, so you can do arithmetics and plotting
If you want continuity between the functions, use the conditions to eliminate some parameters symbolically. This enforces these conditions exactly.

For the discontinuous independent functions, the fit can't include x.0 because the target function's dependence on x.0 is piecewise constant between data points. x.0 essentially assigns the data points to the independent fit ranges. So the derivative is zero or undefined, which Fit() can't handle.

For the continuous fit, the inclusion of x.0 as fit variable also fails but with less obvious reason, at least the derivatives of the error wrt x.0 should not be zero between data points.

picewise_qudratic_fit_Kr.sm (83kb) downloaded 7 time(s).

Worksheet66.sm (6kb) downloaded 6 time(s).