numpy.arcsinh#

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

Inverse hyperbolic sine element-wise.

Parameters:
xarray_like

Input array.

outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must havea shape that the inputs broadcast to. If not provided or None,a freshly-allocated array is returned. A tuple (possible only as akeyword argument) must have length equal to the number of outputs.

wherearray_like, optional

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

**kwargs

For other keyword-only arguments, see theufunc docs.

Returns:
outndarray or scalar

Array of the same shape asx.This is a scalar ifx is a scalar.

Notes

arcsinh is a multivalued function: for eachx there are infinitelymany numbersz such thatsinh(z) = x. The convention is to return thez whose imaginary part lies in[-pi/2, pi/2].

For real-valued input data types,arcsinh always returns real output.For each value that cannot be expressed as a real number or infinity, itreturnsnan and sets theinvalid floating point error flag.

For complex-valued input,arcsinh is a complex analytical function thathas branch cuts[1j, infj] and[-1j, -infj] and is continuous fromthe right on the former and from the left on the latter.

The inverse hyperbolic sine is also known asasinh orsinh^-1.

References

[1]

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”,10th printing, 1964, pp. 86.https://personal.math.ubc.ca/~cbm/aands/page_86.htm

[2]

Wikipedia, “Inverse hyperbolic function”,https://en.wikipedia.org/wiki/Arcsinh

Examples

>>>importnumpyasnp>>>np.arcsinh(np.array([np.e,10.0]))array([ 1.72538256,  2.99822295])
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