tanh

Hyperbolic tangent

Syntax

Y = tanh(X)

Description

Y = tanh(X) returns the hyperbolic tangent of the elements of X. The tanh function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians.

Examples

Hyperbolic Tangent of Vector

Create a vector and calculate the hyperbolic tangent of each value.

X = [0 pi 2*pi 3*pi];
Y = tanh(X)

Y = 1×4

         0    0.9963    1.0000    1.0000

Graph of Hyperbolic Tangent Function

Plot the hyperbolic tangent function over the domain $$-5\le x\le 5$$.

x = -5:0.01:5; 
y = tanh(x);
plot(x,y) 
grid on

Input Arguments

X — Input angles in radians

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

Input angles in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

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

More About

Hyperbolic Tangent

The hyperbolic tangent of an angle x is the ratio of the hyperbolic sine and hyperbolic cosine

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

In terms of the traditional tangent function with a complex argument, the identity is

$$\tanh \left(x\right)=-i\tan \left(ix\right).$$

Extended Capabilities

Tall Arrays

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

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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

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 tanh function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (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 tanh 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.