error in computing atanh
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Francisco Peñuñuri
on 13 Feb 2021
Edited: Francisco Peñuñuri
on 13 Feb 2021
When computing atanh(3.1) in R2018.a and R2020.a the complex part has positive sign.
When computing in fortran (and Mathematica) the result is negative.
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David Goodmanson
on 13 Feb 2021
Edited: David Goodmanson
on 13 Feb 2021
Hello Francisco,
The imaginary part is i*pi/2, so the two answers are a+i*pi/2 and a-i*pi/2, where a is real. Both answers are equally valid, so unless an answer is violating some prearranged standard set by the particular software invoked, there is not an error. Note that
tanh(a+i*b) = tanh(a+i*b+i*n*pi)
so there is an ambiguity modulo i*pi in the atahh function..
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John D'Errico
on 13 Feb 2021
But there is no international standards commission that decides which is the principal branch to take on some multi-valued result. And while it seems pretty standard to take the POSITIVE branch for a sqrt, so it may have seemed just as logical to take the positive branch here.
The result is valid and non-unique. You cannot say more than that.
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