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Fit exponential and harmonic functions using Chebyshev polynomials

Project description

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
Authors:Christoph Gohlke
Organization:Laboratory for Fluorescence Dynamics. University of California, Irvine
License:3-clause BSD
Version:2019.4.22

Revisions

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

Project details


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