Return the natural logarithm of one plus the input array, element-wise.
LAX-backend implementation of
log1p(). Original docstring below.
log1p(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])
log(1 + x).
x (array_like) – Input values.
y – Natural logarithm of 1 + x, element-wise. This is a scalar if x is a scalar.
- Return type
exp(x) - 1, the inverse of log1p.
For real-valued input, log1p is accurate also for x so small that 1 + x == 1 in floating-point accuracy.
Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = 1 + x. The convention is to return the z whose imaginary part lies in [-pi, pi].
For real-valued input data types, log1p always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nanand sets the invalid floating point error flag.
For complex-valued input, log1p is a complex analytical function that has a branch cut [-inf, -1] and is continuous from above on it. log1p handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/
Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm
>>> np.log1p(1e-99) 1e-99 >>> np.log(1 + 1e-99) 0.0