atanh

Inverse hyperbolic tangent

Syntax

Y = atanh(X)

Description

Y = atanh(X) returns the inverse hyperbolic tangent of the elements of X. The function accepts both real and complex inputs. All angles are in radians.

Examples

Inverse Hyperbolic Tangent of Vector

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

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

X — Hyperbolic tangent of angle

scalar | vector | matrix | multidimensional array | table | timetable

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

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

More About

Inverse Hyperbolic Tangent

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

$${\tanh }^{-1}\left(x\right)=\frac{1}{2}\log \left(\frac{1+x}{1-x}\right).$$

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

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

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

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

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).

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

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).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023a: Perform calculations directly on tables and timetables

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.