NAG Library Function Document
nag_real_jacobian_elliptic (s21cac) evaluates the Jacobian elliptic functions sn, cn and dn.
||nag_real_jacobian_elliptic (double u,
nag_real_jacobian_elliptic (s21cac) evaluates the Jacobian elliptic functions of argument
, called the amplitude
, is defined by the integral
The elliptic functions are sometimes written simply as
, avoiding explicit reference to the argument
Another nine elliptic functions may be computed via the formulae
(see Abramowitz and Stegun (1972)
nag_real_jacobian_elliptic (s21cac) is based on a procedure given by Bulirsch (1960)
, and uses the process of the arithmetic-geometric mean (16.9 in Abramowitz and Stegun (1972)
). Constraints are placed on the values of
in order to avoid the possibility of machine overflow.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Bulirsch R (1960) Numerical calculation of elliptic integrals and elliptic functions Numer. Math. 7 76–90
u – doubleInput
m – doubleInput
On entry: the argument and the argument of the functions, respectively.
- , where ;
- if , .
sn – double *Output
cn – double *Output
dn – double *Output
On exit: the values of the functions , and , respectively.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument had an illegal value.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG
is too large when used in conjunction with the supplied argument u
it must be less than
On entry, is too large: it must be less than .
In principle the function is capable of achieving full relative precision in the computed values. However, the accuracy obtainable in practice depends on the accuracy of the standard elementary functions such as SIN and COS.
8 Parallelism and Performance
This example reads values of the argument and argument from a file, evaluates the function and prints the results.
10.1 Program Text
Program Text (s21cace.c)
10.2 Program Data
Program Data (s21cace.d)
10.3 Program Results
Program Results (s21cace.r)