mars.tensor.arccosh#

mars.tensor.arccosh(x, out=None, where=None, **kwargs)[source]#

Inverse hyperbolic cosine, element-wise.

Parameters

  • x (array_like) – Input tensor.

  • out (Tensor, None, or tuple of Tensor 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 tensor is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

  • 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 –

Returns

arccosh – Array of the same shape as x.

Return type

Tensor

See also

cosh, arcsinh, sinh, arctanh, tanh

Notes

arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [-pi, pi] and the real part in [0, inf].

For real-valued input data types, arccosh 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, arccosh is a complex analytical function that has a branch cut [-inf, 1] and is continuous from above on it.

References

1

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

2

Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arccosh

Examples

>>> import mars.tensor as mt

>>> mt.arccosh([mt.e, 10.0]).execute()
array([ 1.65745445,  2.99322285])
>>> mt.arccosh(1).execute()
0.0