atanh — hyperbolic tangent inverse
t=atanh(x)
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).
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.