numpy.log

numpy.log(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'log'>

Natural logarithm, element-wise.

The natural logarithm log is the inverse of the exponential function, so that log(exp(x)) = x. The natural logarithm is logarithm in base e.

Parameters:

xarray_like

Input value.

outndarray, 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.

wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.

**kwargs

For other keyword-only arguments, see the ufunc docs.

Returns:

yndarray

The natural logarithm of x, element-wise. This is a scalar if x is a scalar.

See also

log10, log2, log1p, emath.log

Notes

Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = x. The convention is to return the z whose imaginary part lies in (-pi, pi].

For real-valued input data types, log 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, log is a complex analytical function that has a branch cut [-inf, 0] and is continuous from above on it. log handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.

In the cases where the input has a negative real part and a very small negative complex part (approaching 0), the result is so close to -pi that it evaluates to exactly -pi.

References

[1]

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. https://personal.math.ubc.ca/~cbm/aands/page_67.htm

[2]

Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm

Examples

>>> np.log([1, np.e, np.e**2, 0])
array([  0.,   1.,   2., -Inf])