numpy.log

numpy.log(x[, out]) = <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:

x : array_like

Input value.

Returns:

y : ndarray

The natural logarithm of x, element-wise.

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.

References

[R44]

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/

[R45]

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

Examples

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