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
License:	BSD 3-Clause
Version:	2025.1.1

Quickstart

Install the chebyfit package and all dependencies from the Python Package Index:

python -m pip install -U chebyfit

See Examples for using the programming interface.

Source code and support are available on GitHub.

Requirements

This revision was tested with the following requirements and dependencies (other versions may work):

• CPython 3.10.11, 3.11.9, 3.12.8, 3.13.1 64-bit
• NumPy 2.1.3

Revisions

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