atanh
=====

hyperbolic tangent inverse



Calling Sequence
~~~~~~~~~~~~~~~~


::

    t=atanh(x)




Arguments
~~~~~~~~~

:x real or complex vector/matrix
: :t real or complex vector/matrix
:



Description
~~~~~~~~~~~

The components of vector `t` are the hyperbolic tangent inverse of the
corresponding entries of vector `x`. Definition domain is `[-1,1]` for
the real function (see Remark).



Remark
~~~~~~

In Scilab (as in some others numerical software) when you try to
evaluate an elementary mathematical function outside its definition
domain in the real case, then the complex extension is used (with a
complex result). The more famous example being the sqrt function (try
`sqrt(-1)` !). This approach have some drawbacks when you evaluate the
function at a singular point which may led to different results when
the point is considered as real or complex. For the `atanh` this
occurs for `-1` and `1` because the at these points the imaginary part
do not converge and so `atanh(1) = +Inf + i NaN` while `atanh(1) =
+Inf` for the real case (as lim x->1- of atanh(x)). So when you
evaluate this function on the vector `[1 2]` then like `2` is outside
the definition domain, the complex extension is used for all the
vector and you get `atanh(1) = +Inf + i NaN` while you get `atanh(1) =
+Inf` with `[1 0.5]` for instance.



Examples
~~~~~~~~


::

    // example 1
    x=[0,%i,-%i]
    `tanh`_(atanh(x))
    
    // example 2
    x = [-%inf -3 -2 -1 0 1 2 3 %inf]
    `ieee`_(2)
    atanh(`tanh`_(x))
    
    // example 3 (see Remark)
    `ieee`_(2)
    atanh([1 2])
    atanh([1 0.5])




See Also
~~~~~~~~


+ `tanh`_ hyperbolic tangent
+ `ieee`_ set floating point exception mode


.. _ieee: ieee.html
.. _tanh: tanh.html