dpnp.log1p

dpnp.log1p(x, out=None, where=True, order='K', dtype=None, subok=True, **kwargs)

Computes the natural logarithm of (1 + x) for each element \(x_i\) of input array x.

For full documentation refer to numpy.log1p.

Parameters:

x ({dpnp.ndarray, usm_ndarray}) -- Input array, expected to have a floating-point data type.
out ({None, dpnp.ndarray, usm_ndarray}, optional) --
Output array to populate. Array must have the correct shape and the expected data type.

Default: None.
order ({None, "C", "F", "A", "K"}, optional) --
Memory layout of the newly output array, if parameter out is None.

Default: "K".

Returns:

out -- An array containing the element-wise \(\log(1 + x)\) results. The data type of the returned array is determined by the Type Promotion Rules.

Return type:

dpnp.ndarray

Limitations

Parameters where and subok are supported with their default values. Keyword argument kwargs is currently unsupported. Otherwise NotImplementedError exception will be raised.

See also

dpnp.expm1: Calculate \(e^x - 1\), element-wise, the inverse of dpnp.log1p.
dpnp.log: Calculate \(\log(x)\), element-wise.
dpnp.log10: Calculate \(\log_{10}(x)\), element-wise.
dpnp.log2: Calculate \(\log_2(x)\), element-wise.

Notes

For real-valued floating-point input data types, dpnp.log1p provides greater precision than \(\log(1 + x)\) for x so small that \(1 + x == 1\).

dpnp.log1p is a multivalued function: for each x there are infinitely many numbers z such that \(e^z = 1 + x\). The convention is to return the z whose the imaginary part lies in the interval \([-\pi, \pi]\).

For real-valued floating-point input data types, dpnp.log1p always returns real output. For each value that cannot be expressed as a real number or nfinity, it yields NaN.

For complex floating-point input data types, dpnp.log1p is a complex analytic function that has, by convention, the branch cuts \((-\infty, 0)\) and is continuous from above on it.

Examples

>>> import dpnp as np
>>> x = np.arange(3.)
>>> np.log1p(x)
array([0.0, 0.69314718, 1.09861229])

>>> np.log1p(array(1e-99))
array(1e-99)

>>> np.log(array(1 + 1e-99))
array(0.0)