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/* k1.c
*
* Modified Bessel function, third kind, order one
*
*
*
* SYNOPSIS:
*
* double x, y, k1();
*
* y = k1( x );
*
*
*
* DESCRIPTION:
*
* Computes the modified Bessel function of the third kind
* of order one of the argument.
*
* The range is partitioned into the two intervals [0,2] and
* (2, infinity). Chebyshev polynomial expansions are employed
* in each interval.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0, 30 30000 1.2e-15 1.6e-16
*
* ERROR MESSAGES:
*
* message condition value returned
* k1 domain x <= 0 NPY_INFINITY
*
*/
/* k1e.c
*
* Modified Bessel function, third kind, order one,
* exponentially scaled
*
*
*
* SYNOPSIS:
*
* double x, y, k1e();
*
* y = k1e( x );
*
*
*
* DESCRIPTION:
*
* Returns exponentially scaled modified Bessel function
* of the third kind of order one of the argument:
*
* k1e(x) = exp(x) * k1(x).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0, 30 30000 7.8e-16 1.2e-16
* See k1().
*
*/
/*
* Cephes Math Library Release 2.8: June, 2000
* Copyright 1984, 1987, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
* in the interval [0,2].
*
* lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
*/
static double A[] = {
-7.02386347938628759343E-18,
-2.42744985051936593393E-15,
-6.66690169419932900609E-13,
-1.41148839263352776110E-10,
-2.21338763073472585583E-8,
-2.43340614156596823496E-6,
-1.73028895751305206302E-4,
-6.97572385963986435018E-3,
-1.22611180822657148235E-1,
-3.53155960776544875667E-1,
1.52530022733894777053E0
};
/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
* in the interval [2,infinity].
*
* lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
*/
static double B[] = {
-5.75674448366501715755E-18,
1.79405087314755922667E-17,
-5.68946255844285935196E-17,
1.83809354436663880070E-16,
-6.05704724837331885336E-16,
2.03870316562433424052E-15,
-7.01983709041831346144E-15,
2.47715442448130437068E-14,
-8.97670518232499435011E-14,
3.34841966607842919884E-13,
-1.28917396095102890680E-12,
5.13963967348173025100E-12,
-2.12996783842756842877E-11,
9.21831518760500529508E-11,
-4.19035475934189648750E-10,
2.01504975519703286596E-9,
-1.03457624656780970260E-8,
5.74108412545004946722E-8,
-3.50196060308781257119E-7,
2.40648494783721712015E-6,
-1.93619797416608296024E-5,
1.95215518471351631108E-4,
-2.85781685962277938680E-3,
1.03923736576817238437E-1,
2.72062619048444266945E0
};
extern double MINLOG;
double k1(x)
double x;
{
double y, z;
if (x == 0.0) {
mtherr("k1", SING);
return NPY_INFINITY;
}
else if (x < 0.0) {
mtherr("k1", DOMAIN);
return NPY_NAN;
}
z = 0.5 * x;
if (x <= 2.0) {
y = x * x - 2.0;
y = log(z) * i1(x) + chbevl(y, A, 11) / x;
return (y);
}
return (exp(-x) * chbevl(8.0 / x - 2.0, B, 25) / sqrt(x));
}
double k1e(x)
double x;
{
double y;
if (x == 0.0) {
mtherr("k1e", SING);
return NPY_INFINITY;
}
else if (x < 0.0) {
mtherr("k1e", DOMAIN);
return NPY_NAN;
}
if (x <= 2.0) {
y = x * x - 2.0;
y = log(0.5 * x) * i1(x) + chbevl(y, A, 11) / x;
return (y * exp(x));
}
return (chbevl(8.0 / x - 2.0, B, 25) / sqrt(x));
}
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