Math::Fitting

Raku package for line, curve, and hyper-plane fitting over sets of points.

Installation

From Zef ecosystem:

zef install Math::Fitting

From GitHub:

zef install https://github.com/antononcube/Raku-Math-Fitting.git

Usage examples

Here is data that is an array of pairs logarithms of GDP and electricity production of different countries:

my @data =
        (11.773906839650255e0, 11.253864992156679e0), (12.171286902172696e0, 12.009204578014298e0),
        (12.107713405070312e0, 11.437962903093876e0), (12.696829332236298e0, 12.00401094268482e0),
        (11.28266350477445e0, 11.499283586840601e0), (12.585056018658895e0, 11.775388329493465e0),
        (10.723949075934968e0, 10.54745313463026e0), (11.389785159542825e0, 10.928944887584644e0),
        (13.167988368224217e0, 12.856756553879103e0), (11.019424327650983e0, 10.472888033769635e0),
        (10.198154686798192e0, 9.331143140569578e0), (11.395702941127277e0, 10.772811339725912e0),
        (12.031878183906066e0, 11.516569745919236e0), (11.430963567030055e0, 10.855585778720567e0),
        (10.21302480711734e0, 10.138888016785716e0), (11.857393542118762e0, 11.520472966745002e0),
        (11.223299730942632e0, 10.933368427760566e0), (12.15978767072575e0, 11.78868016913858e0),
        (11.190367918582032e0, 10.557867961568022e0), (11.733248321280731e0, 11.226857570288722e0),
        (10.839510106614012e0, 10.677157910153495e0), (11.191959374358786e0, 11.17621400228234e0),
        (12.215911663039382e0, 11.808235068507617e0), (12.420008212627797e0, 11.723537761532056e0),
        (11.551553518127756e0, 10.519077512018512e0), (11.845171164859963e0, 11.528956530193586e0),
        (12.212327463463307e0, 11.782617762483701e0), (11.479897117669006e0, 11.355095745306354e0),
        (13.320906155798967e0, 12.6405552706939e0);

@data.elems;

# 29

Remark: The data was taken from "Data::Geographics", [AAp1].

Here is a corresponding plot (using "Text::Plot", [AAp2]):

use Text::Plot;

text-list-plot(@data, title => 'lg(GDP) vs lg(Electricity Production)', x-label => 'GDP', y-label => 'EP');

# lg(GDP) vs lg(Electricity Production)
# +--------+-------+-------+-------+--------+-------+-------++
# +                                                          +  13.00
# |                                                    * *   |
# |                                                          |
# +                                   *        *             +  12.00
# |                                   **  *  *               |
# |                     *  *     *  **                       |        E
# +                   *        **                            +  11.00 P
# |             *      * **                                  |
# |           *    *  *     *                                |
# +   *                                                      +  10.00
# |                                                          |
# |   *                                                      |
# +                                                          +   9.00
# +--------+-------+-------+-------+--------+-------+-------++
#          10.50   11.00   11.50   12.00    12.50   13.00   13.50
#                             GDP

Here is corresponding linear model fit, a functor (i.e. objects that does Callable):

use Math::Fitting;
my &f = linear-model-fit(@data);

# Math::Fitting::FittedModel(type => linear, data => (29, 2), response-index => 1)

Here are the best fit parameters (fit coefficients):

&f('BestFitParameters');

# [0.6719587872748085 0.9049080671822028]

Here we call the functor over a range of values:

(10...13)».&f

# (9.721039459096838 10.62594752627904 11.530855593461244 12.435763660643445)

Here are the corresponding residuals:

text-list-plot(&f('residuals'))

# +---+--------+--------+--------+---------+--------+--------+
# |                                                          |
# +                     *                         *          + 0.60
# +                                                          + 0.40
# |            *                                             |
# +      *            *   *            *        *            + 0.20
# |   *    *                  *          *               *   |
# +                *        *                         *      + 0.00
# |              *               * * *        *     *        |
# +                 *          *           *                 +-0.20
# |    *                                    *          *     |
# +                                                          +-0.40
# +          *                                               +-0.60
# |                                                          |
# +---+--------+--------+--------+---------+--------+--------+
#     0.00     5.00     10.00    15.00     20.00    25.00

TODO

• TODO Implementation

  • TODO Multi-dimensional Linear Model Fit (LMF)

  • TODO Using user specified function basis

  • TODO More LMF diagnostics

References

[AAp1] Anton Antonov, Data::Geographics Raku package, (2024), GitHub/antononcube.

[AAp2] Anton Antonov, Text::Plot Raku package, (2022-2023), GitHub/antononcube.

[PSp1] Paweł Szulc, Statistics::LinearRegression Raku package, (2017), GitHub/hipek8.