Fit exponential and harmonic functions using Chebyshev polynomials
==================================================================
Chebyfit is a Python library that implements the algorithms described in:
Analytic solutions to modelling exponential and harmonic functions using
Chebyshev polynomials: fitting frequency-domain lifetime images with
photobleaching. G C Malachowski, R M Clegg, and G I Redford.
J Microsc. 2007; 228(3): 282-295. doi: 10.1111/j.1365-2818.2007.01846.x
:Author: `Christoph Gohlke <https://www.cgohlke.com>`_
:License: BSD 3-Clause
:Version: 2025.8.1
Quickstart
----------
Install the chebyfit package and all dependencies from the
`Python Package Index <https://pypi.org/project/chebyfit/>`_::
python -m pip install -U chebyfit
See `Examples`_ for using the programming interface.
Source code and support are available on
`GitHub <https://github.com/cgohlke/chebyfit>`_.
Requirements
------------
This revision was tested with the following requirements and dependencies
(other versions may work):
- `CPython <https://www.python.org>`_ 3.11.9, 3.12.10, 3.13.5, 3.14.0rc 64-bit
- `NumPy <https://pypi.org/project/numpy/>`_ 2.3.2
Revisions
---------
2025.8.1
- Drop support for Python 3.10, support Python 3.14.
2025.1.1
- Improve type hints.
- Drop support for Python 3.9, support Python 3.13.
2024.5.24
- Fix docstring examples not correctly rendered on GitHub.
2024.4.24
- Support NumPy 2.
2024.1.6
- Support Python 3.12.
2023.4.22
- Drop support for Python 3.8 and numpy < 1.21 (NEP29).
2022.9.29
- Add type hints.
- Convert to Google style docstrings.
2022.8.26
- Update metadata.
- Drop support for Python 3.7 (NEP 29).
2021.6.6
- Fix compile error on Python 3.10.
- Drop support for Python 3.6 (NEP 29).
2020.1.1
- Drop support for Python 2.7 and 3.5.
2019.10.14
- Support Python 3.8.
- Fix numpy 1type FutureWarning.
2019.4.22
- Fix setup requirements.
2019.1.28
- Move modules into chebyfit package.
- Add Python wrapper for _chebyfit C extension module.
- Fix static analysis issues in _chebyfit.c.
Examples
--------
Fit two-exponential decay function:
>>> deltat = 0.5
>>> t = numpy.arange(0, 128, deltat)
>>> data = 1.1 + 2.2 * numpy.exp(-t / 33.3) + 4.4 * numpy.exp(-t / 55.5)
>>> params, fitted = fit_exponentials(data, numexps=2, deltat=deltat)
>>> numpy.allclose(data, fitted)
True
>>> params['offset']
array([1.1])
>>> params['amplitude']
array([[4.4, 2.2]])
>>> params['rate']
array([[55.5, 33.3]])
Fit harmonic function with exponential decay:
>>> tt = t * (2 * math.pi / (t[-1] + deltat))
>>> data = 1.1 + numpy.exp(-t / 22.2) * (
... 3.3 - 4.4 * numpy.sin(tt) + 5.5 * numpy.cos(tt)
... )
>>> params, fitted = fit_harmonic_decay(data, deltat=0.5)
>>> numpy.allclose(data, fitted)
True
>>> params['offset']
array([1.1])
>>> params['rate']
array([22.2])
>>> params['amplitude']
array([[3.3, 4.4, 5.5]])
Fit experimental time-domain image:
>>> data = numpy.fromfile('test.b&h', dtype='float32').reshape((256, 256, 256))
>>> data = data[64 : 64 + 64]
>>> params, fitted = fit_exponentials(data, numexps=1, numcoef=16, axis=0)
>>> numpy.allclose(data.sum(axis=0), fitted.sum(axis=0))
True
Raw data
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