acsch

Inverse hyperbolic cosecant

Syntax

Y = acsch(X)

Description

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

Examples

Inverse Hyperbolic Cosecant of Vector

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

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

Y = 1×3 complex

   0.4812 + 0.0000i  -0.3275 + 0.0000i   0.2156 - 0.4016i

Plot the Inverse Hyperbolic Cosecant Function

Plot the inverse hyperbolic cosecant function over the intervals $$-20\le x\le -1$$ and $$1\le x\le 20$$.

x1 = -20:0.01:-1; 
x2 = 1:0.01:20; 
plot(x1,acsch(x1),x2,acsch(x2))
grid on
xlabel('x')
ylabel('acsch(x)')

Input Arguments

X — Hyperbolic cosecant of angle

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

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

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

More About

Inverse Hyperbolic Cosecant

For real values $$x$$ in the domain $$x<0$$ and $$x>0$$, the inverse hyperbolic cosecant satisfies

$${\text{csch}}^{-1}\left(z\right)={\sinh }^{-1}\left(\frac{1}{z}\right)=\log \left(\frac{1}{x}+\sqrt{\frac{1}{x^2}+1}\right).$$

For complex numbers $$z=x+iy$$, the call acsch(z) returns complex results.

Extended Capabilities

Tall Arrays

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

The acsch 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.

The acsch 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 acsch 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™.

The acsch 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 acsch 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.