atanh - Inverse hyperbolic tangent - MATLAB (original) (raw)

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Inverse hyperbolic tangent

Syntax

Description

`Y` = atanh([X](#mw%5Fa2967a89-8550-4a61-a1c9-34be189c2bdc)) returns the inverse hyperbolic tangent of the elements of X. The function accepts both real and complex inputs. All angles are in radians.

example

Examples

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Find the inverse hyperbolic tangent of the elements of vector X. The atanh function acts on X element-wise.

X = [2 -3 1+2i]; Y = atanh(X)

Y = 1×3 complex

0.5493 + 1.5708i -0.3466 - 1.5708i 0.1733 + 1.1781i

Plot the inverse hyperbolic tangent function over the interval -1<x<1.

x = -0.99:0.01:0.99; plot(x,atanh(x)) grid on xlabel('x') ylabel('atanh(x)')

Input Arguments

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Hyperbolic tangent of angle, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. The atanh operation is element-wise whenX is nonscalar.

Data Types: single | double | table | timetable
Complex Number Support: Yes

More About

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For real values x in the domain −1<x<1, the inverse hyperbolic tangent satisfies

For complex numbers z=x+iy as well as real values in the regions − ∞<z<−1 and 1<z<∞, the call atanh(z) returns complex results.

Extended Capabilities

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Theatanh function fully supports tall arrays. For more information, see Tall Arrays.

Usage notes and limitations:

• Generates an error during simulation and returns NaN in generated code when the input value x is real, but the output should be complex. To get the complex result, make the input value complex by passing in complex(x).

The atanh function supports GPU array input with these usage notes and limitations:

• If the output of the function running on the GPU can be complex, then you must explicitly specify its input arguments as complex. For more information, see Work with Complex Numbers on a GPU (Parallel Computing Toolbox).

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a

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The atanh function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.