chebyfit 2026.1.18

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:

2026.1.18

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 3.11.9, 3.12.10, 3.13.11, 3.14.2 64-bit

• NumPy 2.4.1

Revisions

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.

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