scipy.special.boxcox1p#

scipy.special.boxcox1p(x, lmbda, out=None) = <ufunc 'boxcox1p'>#

Compute the Box-Cox transformation of \(1 + x\).

The Box-Cox transformation computed by boxcox1p is

\[\begin{split}y = \begin{cases} ((1+x)^\lambda - 1) / \lambda & \text{if } \lambda \neq 0 \\ \log(1+x) & \text{if } \lambda = 0 \end{cases}\end{split}\]

Returns nan if \(x < -1\). Returns -inf if \(x = -1\) and \(\lambda \leq 0\).

Parameters:

xarray_like: Data to be transformed.
lmbdaarray_like: Power parameter \(\lambda\) of the Box-Cox transform.
outndarray, optional: Optional output array for the function values.

Returns:

yscalar or ndarray: Transformed data.

See also

boxcox: Box-Cox transformation.
inv_boxcox1p: Inverse of the Box-Cox transformation of 1 + x.

Notes

Added in version 0.14.0.

Array API Standard Support

boxcox1p has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	✅	⛔
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. boxcox1p does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

Examples

>>> from scipy.special import boxcox1p
>>> boxcox1p(1e-4, [0, 0.5, 1])
array([  9.99950003e-05,   9.99975001e-05,   1.00000000e-04])
>>> boxcox1p([0.01, 0.1], 0.25)
array([ 0.00996272,  0.09645476])