Elljac {gsl} | R Documentation |
Elliptic functions
Description
Elljac functions as per the Gnu Scientific Library, reference manual
section 7.14 and AMS-55, chapter 16. These functions are
declared in header file gsl_sf_elljac.h
Usage
elljac(u, m, give=FALSE, strict=TRUE)
gsl_sn(z,m)
gsl_cn(z,m)
gsl_dn(z,m)
gsl_ns(z,m)
gsl_nc(z,m)
gsl_nd(z,m)
gsl_sc(z,m)
gsl_sd(z,m)
gsl_cs(z,m)
gsl_cd(z,m)
gsl_ds(z,m)
gsl_dc(z,m)
Arguments
u , m |
input: real values |
z |
input: complex values |
give |
Boolean with |
strict |
Boolean, with |
Details
A straightforward wrapper for the gsl_sf_elljac_e
function of the GSL library, except for gsl_sn()
, gsl_cn()
, and
gsl_dn()
, which implement 16.21.1 to 16.21.4 (thus taking complex
arguments); and gsl_ns()
et
seq which are the minor elliptic functions.
Function sn_cn_dn()
is not really intended for the end-user.
Author(s)
Robin K. S. Hankin
References
https://www.gnu.org/software/gsl/
Examples
K <- ellint_F(phi=pi/2,k=sqrt(1/2)) #note the sqrt: m=k^2
u <- seq(from=0,to=4*K,by=K/24)
jj <- elljac(u,1/2)
plot(u,jj$sn,type="l",xaxt="n",yaxt="n",bty="n",ylab="",xlab="",main="Fig 16.1, p570")
lines(u,jj$cn,lty=2)
lines(u,jj$dn,lty=3)
axis(1,pos=0,at=c(K,2*K,3*K,4*K),labels=c("K","2K","3K","4K"))
abline(0,0)
axis(2,pos=0,at=c(-1,1))
text(1.8*K,0.6,"sn u")
text(1.6*K,-0.5,"cn u")
text(2.6*K,0.9,"dn u")
a <- seq(from=-5,to=5,len=100)
jj <- outer(a,a,function(a,b){a})
z <- jj+1i*t(jj)
e <- Re(gsl_cd(z,m=0.2))
e[abs(e)>10] <- NA
contour(a,a,e,nlev=55)
[Package gsl version 2.1-8 Index]