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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:

2026.11.15

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 3.12.10, 3.13.17, 3.14.10, 3.15.2 64-bit

  • Numpy 2.5.4

Revisions

2026.11.15

  • Fix buffer overflows in fit_harmonic_decay and for numcoef=1.

  • Fix singular matrix detection and improve polynomial root finding.

  • Fix out-of-bounds axis, byte-swapped, and non-contiguous input handling.

  • Use common array converters and helper functions in C extensions.

  • Improve error messages.

2026.8.8

  • Fix code review issues.

  • Improve docstrings.

  • Make C extension ABI3 and free-threading compatible.

  • Drop support for Python 3.11 and numpy 2.0 (SPEC0).

  • Support Python 3.15.

2026.1.18

  • …

Refer to the CHANGES file for older revisions.

Examples

Import fit functions:

>>> from chebyfit import fit_exponentials, fit_harmonic_decay

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

Metadata

Release files for chebyfit 2026.11.15

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

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Source distribution for chebyfit 2026.11.15
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Built distributions (wheels)

Table of built distributions (wheels) for chebyfit 2026.11.15
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chebyfit-2026.11.15-cp315-cp315t-win_arm64.whl CPython 3.15 CPython 3.15 free-threading Windows ARM64 Details for chebyfit-2026.11.15-cp315-cp315t-win_arm64.whl
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chebyfit-2026.11.15-cp315-cp315t-win32.whl CPython 3.15 CPython 3.15 free-threading Windows x86-32 Details for chebyfit-2026.11.15-cp315-cp315t-win32.whl
chebyfit-2026.11.15-cp315-cp315t-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl CPython 3.15 CPython 3.15 free-threading Linux glibc 2.17+ x86-64, Linux glibc 2.28+ x86-64 Details for chebyfit-2026.11.15-cp315-cp315t-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl
chebyfit-2026.11.15-cp315-cp315t-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.15 CPython 3.15 free-threading Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details for chebyfit-2026.11.15-cp315-cp315t-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl
chebyfit-2026.11.15-cp315-cp315t-macosx_11_0_arm64.whl CPython 3.15 CPython 3.15 free-threading macOS 11.0+ ARM64 Details for chebyfit-2026.11.15-cp315-cp315t-macosx_11_0_arm64.whl
chebyfit-2026.11.15-cp315-cp315t-macosx_10_15_x86_64.whl CPython 3.15 CPython 3.15 free-threading macOS 10.15+ x86-64 Details for chebyfit-2026.11.15-cp315-cp315t-macosx_10_15_x86_64.whl
chebyfit-2026.11.15-cp314-cp314t-win_arm64.whl CPython 3.14 CPython 3.14 free-threading Windows ARM64 Details for chebyfit-2026.11.15-cp314-cp314t-win_arm64.whl
chebyfit-2026.11.15-cp314-cp314t-win_amd64.whl CPython 3.14 CPython 3.14 free-threading Windows x86-64 Details for chebyfit-2026.11.15-cp314-cp314t-win_amd64.whl
chebyfit-2026.11.15-cp314-cp314t-win32.whl CPython 3.14 CPython 3.14 free-threading Windows x86-32 Details for chebyfit-2026.11.15-cp314-cp314t-win32.whl
chebyfit-2026.11.15-cp314-cp314t-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ x86-64, Linux glibc 2.28+ x86-64 Details for chebyfit-2026.11.15-cp314-cp314t-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl
chebyfit-2026.11.15-cp314-cp314t-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details for chebyfit-2026.11.15-cp314-cp314t-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl
chebyfit-2026.11.15-cp314-cp314t-macosx_11_0_arm64.whl CPython 3.14 CPython 3.14 free-threading macOS 11.0+ ARM64 Details for chebyfit-2026.11.15-cp314-cp314t-macosx_11_0_arm64.whl
chebyfit-2026.11.15-cp314-cp314t-macosx_10_15_x86_64.whl CPython 3.14 CPython 3.14 free-threading macOS 10.15+ x86-64 Details for chebyfit-2026.11.15-cp314-cp314t-macosx_10_15_x86_64.whl
chebyfit-2026.11.15-cp312-abi3-win_arm64.whl CPython 3.12 abi3 Windows ARM64 Details for chebyfit-2026.11.15-cp312-abi3-win_arm64.whl
chebyfit-2026.11.15-cp312-abi3-win_amd64.whl CPython 3.12 abi3 Windows x86-64 Details for chebyfit-2026.11.15-cp312-abi3-win_amd64.whl
chebyfit-2026.11.15-cp312-abi3-win32.whl CPython 3.12 abi3 Windows x86-32 Details for chebyfit-2026.11.15-cp312-abi3-win32.whl
chebyfit-2026.11.15-cp312-abi3-pyemscripten_2026_5_wasm32.whl CPython 3.12 abi3 PyEmscripten 2026.5+ WebAssembly Details for chebyfit-2026.11.15-cp312-abi3-pyemscripten_2026_5_wasm32.whl
chebyfit-2026.11.15-cp312-abi3-pyemscripten_2026_0_wasm32.whl CPython 3.12 abi3 PyEmscripten 2026.0+ WebAssembly Details for chebyfit-2026.11.15-cp312-abi3-pyemscripten_2026_0_wasm32.whl
chebyfit-2026.11.15-cp312-abi3-pyemscripten_2025_0_wasm32.whl CPython 3.12 abi3 PyEmscripten 2025.0+ WebAssembly Details for chebyfit-2026.11.15-cp312-abi3-pyemscripten_2025_0_wasm32.whl
chebyfit-2026.11.15-cp312-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl CPython 3.12 abi3 Linux glibc 2.17+ x86-64, Linux glibc 2.28+ x86-64 Details for chebyfit-2026.11.15-cp312-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl
chebyfit-2026.11.15-cp312-abi3-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl CPython 3.12 abi3 Linux glibc 2.17+ ARM64, Linux glibc 2.28+ ARM64 Details for chebyfit-2026.11.15-cp312-abi3-manylinux2014_aarch64.manylinux_2_17_aarch64.manylinux_2_28_aarch64.whl
chebyfit-2026.11.15-cp312-abi3-macosx_11_0_arm64.whl CPython 3.12 abi3 macOS 11.0+ ARM64 Details for chebyfit-2026.11.15-cp312-abi3-macosx_11_0_arm64.whl
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Release files / chebyfit-2026.11.15-cp312-abi3-pyemscripten_2026_5_wasm32.whl

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Release files / chebyfit-2026.11.15-cp312-abi3-manylinux2014_x86_64.manylinux_2_17_x86_64.manylinux_2_28_x86_64.whl

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