phasorpy.experimental#

Experimental functions.

The phasorpy.experimental module provides functions related to phasor analysis for evaluation. The functions may be removed or moved to other modules in future releases.

phasorpy.experimental.anscombe_transform(data, /, **kwargs)[source]#

Return Anscombe variance-stabilizing transformation.

The Anscombe transformation normalizes the standard deviation of noisy, Poisson-distributed data. It can be used to transform un-normalized phasor coordinates to approximate standard Gaussian distributions.

Parameters:

data (array_like) – Noisy Poisson-distributed data to be transformed.
**kwargs – Optional arguments passed to numpy universal functions.

Returns:

Anscombe-transformed data with variance of approximately 1.

Return type:

ndarray

Notes

The Anscombe transformation according to [1]:

\[z = 2 \cdot \sqrt{x + 3 / 8}\]

References

Examples

>>> z = anscombe_transform(numpy.random.poisson(10, 10000))
>>> numpy.allclose(numpy.std(z), 1.0, atol=0.1)
True

phasorpy.experimental.anscombe_transform_inverse(data, /, *, approx=False, **kwargs)[source]#

Return inverse Anscombe transformation.

Parameters:

data (array_like) – Anscombe-transformed data.
approx (bool, default: False) – If true, return approximation of exact unbiased inverse.
**kwargs –
Optional arguments passed to numpy universal functions.

Returns:

Inverse Anscombe-transformed data.

Return type:

ndarray

Notes

The inverse Anscombe transformation according to [1]:

\[x = (z / 2.0)^2 - 3 / 8\]

The approximate inverse Anscombe transformation according to [2] and [3]:

\[x = 1/4 \cdot z^2 + 1/4 \cdot \sqrt{3/2} \cdot z^{-1} - 11/8 \cdot z^{-2} + 5/8 \cdot \sqrt{3/2} \cdot z^{-3} - 1/8\]

References

Examples

>>> x = numpy.random.poisson(10, 100)
>>> x2 = anscombe_transform_inverse(anscombe_transform(x))
>>> numpy.allclose(x, x2, atol=1e-3)
True