sech

Hyperbolic secant

Syntax

Y = sech(X)

Description

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

Examples

Hyperbolic Secant of Vector

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

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

Y = 1×4

    1.0000    0.0863    0.0037    0.0002

Graph of Hyperbolic Secant Function

Plot the hyperbolic secant over the domain $$-2\pi \le x\le 2\pi$$.

x = -2*pi:0.01:2*pi; 
y = sech(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 Secant

The hyperbolic secant of x is equal to the inverse of the hyperbolic cosine

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

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

$$\text{sech}\left(x\right)=\sec \left(ix\right).$$

Extended Capabilities

Tall Arrays

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

The sech 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 sech 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 sech 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.