log1p(x[, out]) = <ufunc 'log1p'>¶
Return the natural logarithm of one plus the input array, element-wise.
log(1 + x).
x : array_like
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.
[R48] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [R49] Wikipedia, “Logarithm”. http://en.wikipedia.org/wiki/Logarithm
>>> np.log1p(1e-99) 1e-99 >>> np.log(1 + 1e-99) 0.0