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 experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. 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

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])