[sn,cn,dn] = ellipj(u,m)
[sn,cn,dn] = ellipj(u,m)returns the Jacobian elliptic functions
dnfor the values in
uevaluated at the corresponding parameters in
mcan contain scalars or matrices, but if they are both matrices, they must be the same size.
The Jacobian elliptic functions are defined in terms of the integral:
Sometimes the elliptic functions are defined differently, which can lead to some confusion. The alternate definitions are usually in terms of the modulus
k, which is related to
The Jacobian elliptic functions obey many mathematical identities; for a good sample, see .
The accuracy of the result is
eps; the value of
eps can be changed for a less accurate, but more quickly computed answer.
Compute successive iterates with
Next, calculate the amplitudes in radians using
being careful to unwrap the phases correctly. The Jacobian elliptic functions are then simply
ellipjis limited to the input domain 0 <=
m<= 1. Other values of
mcan be mapped into this range using the transformations described in , equations 16.10 and 16.11.
uis limited to real values.
(c) Copyright 1994 by The MathWorks, Inc.