scipy.special.powm1#

scipy.special.powm1(x, y, out=None) = <ufunc 'powm1'>#

Computes x**y - 1.

This function is useful when y is near 0, or when x is near 1.

The function is implemented for real types only (unlike numpy.power, which accepts complex inputs).

Parameters:

xarray_like: The base. Must be a real type (i.e. integer or float, not complex).
yarray_like: The exponent. Must be a real type (i.e. integer or float, not complex).

Returns:

array_like: Result of the calculation

Notes

Added in version 1.10.0.

The underlying code is implemented for single precision and double precision floats only. Unlike numpy.power, integer inputs to powm1 are converted to floating point, and complex inputs are not accepted.

Note the following edge cases:

powm1(x, 0) returns 0 for any x, including 0, inf and nan.
powm1(1, y) returns 0 for any y, including nan and inf.

This function wraps the powm1 routine from the Boost Math C++ library [1].

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

>>> import numpy as np
>>> from scipy.special import powm1

>>> x = np.array([1.2, 10.0, 0.9999999975])
>>> y = np.array([1e-9, 1e-11, 0.1875])
>>> powm1(x, y)
array([ 1.82321557e-10,  2.30258509e-11, -4.68749998e-10])

It can be verified that the relative errors in those results are less than 2.5e-16.

Compare that to the result of x**y - 1, where the relative errors are all larger than 8e-8:

>>> x**y - 1
array([ 1.82321491e-10,  2.30258035e-11, -4.68750039e-10])