https://github.com/cgohlke/chebyfit

Fit exponential and harmonic functions using Chebyshev polynomials.

https://github.com/cgohlke/chebyfit

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Fit exponential and harmonic functions using Chebyshev polynomials.

README.rst

..
  This file is generated by setup.py

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: 2025.8.1

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 `_ 3.11.9, 3.12.10, 3.13.5, 3.14.0rc 64-bit
- `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:

.. code-block:: python

    >>> 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:

.. code-block:: python

    >>> 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:

.. code-block:: python

    >>> 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

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