Phy lab

A Python package for basic data analysis and curve fitting for Physics laboratory students.

Table of contents

• Phy lab
  • Table of contents
  • Philosophy behind this
    • How this library came about
  • Contents
    • model functions
    • testing and printing of fit results
    • curve-fitting routines
    • Fourier transform utilities
    • data plotting
    • importing data from files
  • Setting up
    • Prerequisites
    • Installation
  • Using Phy lab
  • Development
  • License

Philosophy behind this

Because this was written by someone starting to learn about experimental Physics and Python (for students in a similar situation) all the functions in this module try to use only the basic data structures and functionalities found in Python that are briefly discussed with students (functions, arrays & not much else). This is why you won't find classes, methods or even dicts in this package and why the code inside may be very, very inefficient/ugly. On the upside though, all the definitions inside should be easily comprehensible and modifiable by anyone just starting out with programming.

How this library came about

While writing the python scripts for individual experiments (at UniPi's Physics Lab) I noticed that a significant amount of code was common to almost all of them. I started writing down these common functions in a python module everytime this happened, so that I could import them later to save a lot of time and hassle. That's basically the story behind it: a collection of useful ideas I had while learning how to analyze experimental data with Python's SciPy. Now that it's grown into a powerful enough collection of tools, I decided to release it for any and all students that may find it helpful for dealing with similar problems.

Contents

• The main module containing all the functions. lab
• A simple showcase of a couple of things this library allows you to do. circfit
  • Finding the best-fitting circle and ellipse for simulated or real sampled data points.
  • A quick comparison between using curve_fit, an algebraic circle fit (weighted Coope method) and an algebraic ellipse fit.
  • Plotting the $\chi^2(a, b)$ surface for a pair of parameters $a, b$ of the circle or the ellipse.
• Folder containing further examples and data that can be used in the demos. examples

For another example of where this package can come in handy feel free to check out FFT repository and Lock-in detector. A small paper (in italiano) on fitting, computing Fourier transforms and/or simulating the effect of a Lock-in detector on real sampled signals or internally generated ones.

model functions

A few definitions of the model functions more commonly encountered in the first years of Physics lab (e.g. dampened oscillator, square wave) along with a few digital filters (e.g. Butterworth). Right at the beginning of the module so you can immediately start adding the models you need.

testing and printing of fit results

Goodness of fit tests, evaluation of parameter uncertainties and correlations (chi-square test, errcor). Simple print formatters that allow you to quickly display the results of a fit and associated uncertainties with the desired number of significant digits. (print correlations, print parameters)

curve-fitting routines

Weighted least-square fitting accounting for uncertainties on x and y axes with linear error propagation (propagated fit), relying on scipy.optimize.curve_fit. Weighted orthogonal distance regression thanks to ODRPACK. Weighted algebraic fits (like ellipse fit and others).

Fourier transform utilities

Functions for computing FFTs of real and complex signals and other associated quantities (sampling, FFT, FWHM), applying window functions and displaying their output through Matplotlib (plotfft).

data plotting

Instead of having to write multiple calls to function in order to: activate axis minor ticks, setting their size, orientation and spacing, placing grids, setting errorbar sizes, etc.. (stuff that's present in almost all experimental graphs) You can set some sensible defaults for plots of fitted data, so you can do all of the above in a faster and less error-prone way. (grid, plot fit & residuals)

importing data from files

Load a selected range of data from (.txt, .csv, .py, etc.) files as NumPy arrays, loop over files in a directory with a few calls to function (measured range, file loop).

Setting up

This library was written entirely in Python 3.x, but because of its entry level design should be effortless to readapt to Python 2.x. Should be completely OS independent.

Prerequisites

Phy lab requires three core packages from the SciPy ecosystem to work: Numpy, SciPy and Matplotlib. You should be able to obtain all 3 via pip

python -m pip install --user --upgrade numpy scipy matplotlib

Check SciPy's installation page for more details.

Installation

The cleanest way to install and manage phylab is using pip:

python -m pip install --user phylab

Then simply import the main module with

import phylab as lab

Alternatively, you can clone the repository or download the latest release manually and import the main module directly inside your script just as before.

Using Phy lab

For a quick guide on how to use this library and to show just how much of a difference using these few functions can have, compare beat and beat_naive. These two scripts do the same thing, but the first one is three times shorter at 50 lines, runs ~ 0.2 seconds (30%) faster using less memory and can be easily extended to work with more than 2 datasets, remove outliers, compute FFT and so on... As you can see for example in beat_ext.

Development

Any and all suggestions are always appreciated, If you want to contribute in any way don't hesitate to contact me. I'm always happy to learn something new, so if you know how to improve any part of the code, find something that needs fixing or even if you'd like to see something added going forwards, feel free to let me know (here or at bernardo.tomelleri@gmail.com).

License

Phy lab is licensed under the GNU General Public License v3.0 or later.