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: | 2026.1.18 |
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.
This revision was tested with the following requirements and dependencies (other versions may work):
2026.1.18
- Rename chebyshev_invers to chebyshev_inverse (breaking).
- Use multi-phase initialization.
- Improve code quality.
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
- …
Refer to the CHANGES file for older revisions.
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