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https://github.com/cjekel/piecewise_linear_fit_py

fit piecewise linear data for a specified number of line segments
https://github.com/cjekel/piecewise_linear_fit_py

numpy piecewise-linear piecewise-regression python scipy segment segmented tensorflow

Last synced: 5 days ago
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fit piecewise linear data for a specified number of line segments

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README 

        
# About

A library for fitting continuous piecewise linear functions to data. Just specify the number of line segments you desire and provide the data.



![Downloads a month](https://img.shields.io/pypi/dm/pwlf.svg) ![pwlf ci](https://github.com/cjekel/piecewise_linear_fit_py/workflows/pwlf%20ci/badge.svg) [![codecov](https://codecov.io/gh/cjekel/piecewise_linear_fit_py/branch/master/graph/badge.svg?token=AgeDFEQXed)](https://codecov.io/gh/cjekel/piecewise_linear_fit_py) ![PyPI version](https://img.shields.io/pypi/v/pwlf) [![Conda](https://img.shields.io/conda/vn/conda-forge/pwlf)](https://anaconda.org/conda-forge/pwlf)



Check out the [documentation](https://jekel.me/piecewise_linear_fit_py)!



Read the [blog post](http://jekel.me/2017/Fit-a-piecewise-linear-function-to-data/).



![Example of a continuous piecewise linear fit to data.](https://raw.githubusercontent.com/cjekel/piecewise_linear_fit_py/master/examples/examplePiecewiseFit.png)



![Example of a continuous piecewise linear fit to a sine wave.](https://raw.githubusercontent.com/cjekel/piecewise_linear_fit_py/master/examples/sinWaveFit.png)



Now you can perform segmented constant fitting and piecewise polynomials!

![Example of multiple degree fits to a sine wave.](https://raw.githubusercontent.com/cjekel/piecewise_linear_fit_py/master/examples/figs/multi_degree.png)



# Features

For a specified number of line segments, you can determine (and predict from) the optimal continuous piecewise linear function f(x). See [this example](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/examples/fitForSpecifiedNumberOfLineSegments.py).



You can fit and predict a continuous piecewise linear function f(x) if you know the specific x locations where the line segments terminate. See [this example](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/examples/fitWithKnownLineSegmentLocations.py).



If you want to pass different keywords for the SciPy differential evolution algorithm see [this example](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/examples/fitForSpecifiedNumberOfLineSegments_passDiffEvoKeywords.py).



You can use a different optimization algorithm to find the optimal location for line segments by using the objective function that minimizes the sum of square of residuals. See [this example](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/examples/useCustomOptimizationRoutine.py).



Instead of using differential evolution, you can now use a multi-start gradient optimization with fitfast() function. You can specify the number of starting points to use. The default is 2. This means that a latin hyper cube sampling (space filling DOE) of 2 is used to run 2 L-BFGS-B optimizations. See [this example](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/examples/sineWave_time_compare.py) which runs fit() function, then runs the fitfast() to compare the runtime differences!



# Installation



## Python Package Index (PyPI)



You can now install with pip.

```

python -m pip install pwlf

```



## Conda



If you have conda, you can also install from conda-forge.

```

conda install -c conda-forge pwlf

```



## From source



Or clone the repo

```

git clone https://github.com/cjekel/piecewise_linear_fit_py.git

```



then install with pip

```

python -m pip install ./piecewise_linear_fit_py

```



# How it works

This [paper](https://github.com/cjekel/piecewise_linear_fit_py/raw/master/paper/pwlf_Jekel_Venter_v2.pdf) explains how this library works in detail.



This is based on a formulation of a piecewise linear least squares fit, where the user must specify the location of break points. See [this post](http://jekel.me/2018/Continous-piecewise-linear-regression/) which goes through the derivation of a least squares regression problem if the break point locations are known. Alternatively check out [Golovchenko (2004)](http://golovchenko.org/docs/ContinuousPiecewiseLinearFit.pdf).



Global optimization is used to find the best location for the user defined number of line segments. I specifically use the [differential evolution](https://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.differential_evolution.html) algorithm in SciPy. I default the differential evolution algorithm to be aggressive, and it is probably overkill for your problem. So feel free to pass your own differential evolution keywords to the library. See [this example](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/examples/fitForSpecifiedNumberOfLineSegments_passDiffEvoKeywords.py).



# Changelog

All changes now stored in [CHANGELOG.md](https://github.com/cjekel/piecewise_linear_fit_py/blob/master/CHANGELOG.md)



New ```weights=``` keyword allows you to perform weighted pwlf fits! Removed TensorFlow code which can now be found [here](https://github.com/cjekel/piecewise_linear_fit_py_tf). 



# Requirements

Python 2.7+



NumPy >= 1.14.0



SciPy >= 1.2.0



pyDOE >= 0.3.8



# License

MIT License



# Citation



```bibtex

@Manual{pwlf,

author = {Jekel, Charles F. and Venter, Gerhard},

title = {{pwlf:} A Python Library for Fitting 1D Continuous Piecewise Linear Functions},

year = {2019},

url = {https://github.com/cjekel/piecewise_linear_fit_py}

}

```