chebyfit 2020.1.1

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

Organization:

Laboratory for Fluorescence Dynamics. University of California, Irvine

License:

BSD 3-Clause

Version:

2020.1.1

Requirements

• CPython >= 3.6

• Numpy 1.14

Revisions

2020.1.1

Remove support for Python 2.7 and 3.5. Update copyright.

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