/*************************************************************************
* Complete elliptic integral of the second kind
*
* Approximates the integral
*
*
* pi/2
* -
| | 2
| E(m) = | sqrt( 1 - m sin t ) dt
| |
| -
| 0
|
| using the approximation
|
| P(x) - x log x Q(x).
|
| ACCURACY:
|
| Relative error:
| arithmetic domain # trials peak rms
| IEEE 0, 1 10000 2.1e-16 7.3e-17
|
| Cephes Math Library, Release 2.8: June, 2000
| Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
*************************************************************************/
public static double EllipticIntegralE(double m)
{
var result = Elliptic.EllipticIntegralE(m);
return(result);
}
/*************************************************************************
* Incomplete elliptic integral of the second kind
*
* Approximates the integral
*
*
* phi
* -
| |
| 2
| E(phi_\m) = | sqrt( 1 - m sin t ) dt
|
| |
| -
| 0
|
| of amplitude phi and modulus m, using the arithmetic -
| geometric mean algorithm.
|
| ACCURACY:
|
| Tested at random arguments with phi in [-10, 10] and m in
| [0, 1].
| Relative error:
| arithmetic domain # trials peak rms
| IEEE -10,10 150000 3.3e-15 1.4e-16
|
| Cephes Math Library Release 2.8: June, 2000
| Copyright 1984, 1987, 1993, 2000 by Stephen L. Moshier
*************************************************************************/
public static double IncompleteEllipticIntegralE(double phi, double m)
{
var result = Elliptic.IncompleteEllipticIntegralE(phi, m);
return(result);
}
/*************************************************************************
* Complete elliptic integral of the first kind
*
* Approximates the integral
*
*
*
* pi/2
* -
| |
| dt
| K(m) = | ------------------
| 2
| | sqrt( 1 - m sin t )
| -
| 0
|
| where m = 1 - m1, using the approximation
|
| P(x) - log x Q(x).
|
| The argument m1 is used rather than m so that the logarithmic
| singularity at m = 1 will be shifted to the origin; this
| preserves maximum accuracy.
|
| K(0) = pi/2.
|
| ACCURACY:
|
| Relative error:
| arithmetic domain # trials peak rms
| IEEE 0,1 30000 2.5e-16 6.8e-17
|
| Àëãîðèòì âçÿò èç áèáëèîòåêè Cephes
*************************************************************************/
public static double EllipticIntegralKHighPrecision(double m1)
{
var result = Elliptic.EllipticIntegralKHighPrecision(m1);
return(result);
}
