numpy.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.
Calculates log(1 + x)
.
Parameters: |
x : array_like Input values. 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 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. **kwargs For other keyword-only arguments, see the ufunc docs. |
---|---|
Returns: |
y : ndarray Natural logarithm of |
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 nan
and 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.
[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
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https://docs.scipy.org/doc/numpy-1.14.2/reference/generated/numpy.log1p.html