add wegithed least squares approach

cjekel commented 4 years ago

@vkhodygo Can your review this and let me know if it address your desire in https://github.com/cjekel/piecewise_linear_fit_py/pull/60 ?

This approach uses this math:

Example of difference between ordinary pwlf and this weighted least squares fit

What is needed to merge into master

[x] ~~make work with constrained least squares (x_c y_c)~~ abandoned because of ill conditioning
[ ] add tests
[x] add written example to examples.md
[x] ~~ include weights in standard_errors? (not sure about this Feb 11, 2020)~~ Prediction variance with weights doesn't make any sense... but I added weights to standard errors.

cjekel commented 4 years ago

I corrected the weighted sum-of-square of residuals in this equation

vkhodygo commented 4 years ago

Hi, @cjekel

Yes, this is exactly what I wanted. I should probably close my initial PR as redundant. P.S. do you need a hand with this?

cjekel commented 4 years ago

@vkhodygo Not sure when I'll get to finishing this.

The biggest things will be getting constrained least squares to work and getting standard errors to work.

If you want to take a stab at finishing this PR, feel free to go ahead! :) I have no hard deadline for merging this.

cjekel commented 4 years ago

[x] Consider allowing the user to manually specify the weight matrix from Tyler @ UT Austin

Edit: March 2020, going to abandon weight matrix support for now, as this is just extra work for me...

cjekel / piecewise_linear_fit_py