log1p(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'log1p'>¶
Return the natural logarithm of one plus the input array, element-wise.
log(1 + x).
x : array_like
out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
For other keyword-only arguments, see the ufunc docs.
y : ndarray
Natural logarithm of 1 + x, element-wise.
For real-valued input,
log1pis 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,
log1palways 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,
log1pis a complex analytical function that has a branch cut [-inf, -1] and is continuous from above on it.
log1phandles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.
[R95] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [R96] Wikipedia, “Logarithm”. http://en.wikipedia.org/wiki/Logarithm
>>> np.log1p(1e-99) 1e-99 >>> np.log(1 + 1e-99) 0.0