scipy.special.expm1#
- scipy.special.expm1(x, out=None) = <ufunc 'expm1'>#
Compute
exp(x) - 1
.When x is near zero,
exp(x)
is near 1, so the numerical calculation ofexp(x) - 1
can suffer from catastrophic loss of precision.expm1(x)
is implemented to avoid the loss of precision that occurs when x is near zero.- Parameters
- xarray_like
x must contain real numbers.
- outndarray, optional
Optional output array for the function values
- Returns
- scalar or ndarray
exp(x) - 1
computed element-wise.
Examples
>>> from scipy.special import expm1
>>> expm1(1.0) 1.7182818284590451 >>> expm1([-0.2, -0.1, 0, 0.1, 0.2]) array([-0.18126925, -0.09516258, 0. , 0.10517092, 0.22140276])
The exact value of
exp(7.5e-13) - 1
is:7.5000000000028125000000007031250000001318...*10**-13.
Here is what
expm1(7.5e-13)
gives:>>> expm1(7.5e-13) 7.5000000000028135e-13
Compare that to
exp(7.5e-13) - 1
, where the subtraction results in a “catastrophic” loss of precision:>>> np.exp(7.5e-13) - 1 7.5006667543675576e-13