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# atanh()

Usage:
 ```atanh(x), x REAL or a structure with REAL components ```

Keywords: transformations
```atanh(x) returns the inverse hyperbolic tangent of the elements of x,
when x is a REAL scalar, vector, matrix or array.  The result has the
same shape as x.  In terms of other functions, atanh(x) =
.5*log((1+x)/(1-x)).

This transform is sometimes called the Fisher z-transform.  When r is a
sample Pearson correlation from a bivariate normal sample of size N and
population correlation rho, atanh(r) is approximately normal with mean
rho and variance 1/(N-2).

When any element of x is MISSING, so is the corresponding element of
atanh(x).  When any element of x >= 1 or <= -1, the corresponding
element of atanh(x) is MISSING.  In both cases a warning message is
printed.

When x is a structure, all of whose non-structure components are REAL,
atanh(x) is a structure of the same shape and with the same component
names as x, with each non-structure component transformed by atanh().