Jacobian Elliptic Function (G Dataflow)

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Determines the Jacobian elliptic function.

x

The input argument.

Default: 0

k

The integrand parameter.

error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

cn

Value of the Jacobi elliptic function cn.

dn

The Jacobi elliptic function dn.

sn

Value of the Jacobi elliptic function sn.

phi

The upper limit of the integral defining the function.

error out

Error information. The node produces this output according to standard error behavior.

Algorithm for Calculating the Jacobian Elliptic Function

The following equations define the Jacobian elliptic function.

$cn\left(x,k\right)=\mathrm{cos}\left(\varphi \right)$
$\mathrm{sn}\left(x,k\right)=\mathrm{sin}\left(\varphi \right)$
$\mathrm{dn}\left(x,k\right)=\sqrt{1-k{\mathrm{sin}}^{2}\varphi }$

where

$x={\int }_{0}^{\varphi }\frac{1}{\sqrt{1-k{\mathrm{sin}}^{2}\theta }}d\theta$

The function is defined according to the following intervals for the input values.

$x\in \Re ,k\in \left[0,1\right]$

For any real value of integrand parameter k in the unit interval, the function is defined for all real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported