scipy.special.exprel#

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

Relative error exponential, (exp(x) - 1)/x.

When x is near zero, exp(x) is near 1, so the numerical calculation of exp(x) - 1 can suffer from catastrophic loss of precision. exprel(x) is implemented to avoid the loss of precision that occurs when x is near zero.

Parameters:

xndarray: Input array. x must contain real numbers.
outndarray, optional: Optional output array for the function values

Returns:

scalar or ndarray: (exp(x) - 1)/x, computed element-wise.

See also

expm1

Notes

Added in version 0.17.0.

exprel 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	⚠️ no JIT	⛔
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

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

>>> exprel(0.01)
1.0050167084168056
>>> exprel([-0.25, -0.1, 0, 0.1, 0.25])
array([ 0.88479687,  0.95162582,  1.        ,  1.05170918,  1.13610167])

Compare exprel(5e-9) to the naive calculation. The exact value is 1.00000000250000000416....

>>> exprel(5e-9)
1.0000000025

>>> (np.exp(5e-9) - 1)/5e-9
0.99999999392252903