[sn,cn,dn] = ellipj(u,m)
[sn,cn,dn] = ellipj(u,m)
returns the Jacobian elliptic functions sn
, cn
, and dn
for the values in u
evaluated at the corresponding parameters in m
. Inputs u
and m
can 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:
Then
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
m
by:
The Jacobian elliptic functions obey many mathematical identities; for a good sample, see [1].
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
ellipj
is limited to the input domain 0 <= m
<= 1. Other values of m
can be mapped into this range using the transformations described in [1], equations 16.10 and 16.11. u
is limited to real values.
ellipke
(c) Copyright 1994 by The MathWorks, Inc.