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

New in version 0.17.0.

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