/* modified version of bessel_k that accepts a work array instead of
allocating one. */
double bessel_k_ex(double x, double alpha, double expo, double *bk)
{
long nb, ncalc, ize;
#ifdef IEEE_754
/* NaNs propagated correctly */
if (ISNAN(x) || ISNAN(alpha)) return x + alpha;
#endif
if (x < 0) {
ML_ERROR(ME_RANGE, "bessel_k");
return ML_NAN;
}
ize = (long)expo;
if(alpha < 0)
alpha = -alpha;
nb = 1+ (long)floor(alpha);/* nb-1 <= |alpha| < nb */
alpha -= (double)(nb-1);
K_bessel(&x, &alpha, &nb, &ize, bk, &ncalc);
if(ncalc != nb) {/* error input */
if(ncalc < 0)
MATHLIB_WARNING4(_("bessel_k(%g): ncalc (=%ld) != nb (=%ld); alpha=%g. Arg. out of range?\n"),
x, ncalc, nb, alpha);
else
MATHLIB_WARNING2(_("bessel_k(%g,nu=%g): precision lost in result\n"),
x, alpha+(double)nb-1);
}
x = bk[nb-1];
return x;
}
attribute_hidden
double pbeta_raw(double x, double a, double b, int lower_tail, int log_p)
{
// treat limit cases correctly here:
if(a == 0 || b == 0 || !R_FINITE(a) || !R_FINITE(b)) {
// NB: 0 < x < 1 :
if(a == 0 && b == 0) // point mass 1/2 at each of {0,1} :
return (log_p ? -M_LN2 : 0.5);
if (a == 0 || a/b == 0) // point mass 1 at 0 ==> P(X <= x) = 1, all x > 0
return R_DT_1;
if (b == 0 || b/a == 0) // point mass 1 at 1 ==> P(X <= x) = 0, all x < 1
return R_DT_0;
// else, remaining case: a = b = Inf : point mass 1 at 1/2
if (x < 0.5) return R_DT_0; else return R_DT_1;
}
// Now: 0 < a < Inf; 0 < b < Inf
double x1 = 0.5 - x + 0.5, w, wc;
int ierr;
//====
bratio(a, b, x, x1, &w, &wc, &ierr, log_p); /* -> ./toms708.c */
//====
// ierr in {10,14} <==> bgrat() error code ierr-10 in 1:4; for 1 and 4, warned *there*
if(ierr && ierr != 11 && ierr != 14)
MATHLIB_WARNING4(_("pbeta_raw(%g, a=%g, b=%g, ..) -> bratio() gave error code %d"),
x, a,b, ierr);
return lower_tail ? w : wc;
} /* pbeta_raw() */
/* modified version of bessel_j that accepts a work array instead of
allocating one. */
double bessel_j_ex(double x, double alpha, double *bj)
{
long nb, ncalc;
double na;
#ifdef IEEE_754
/* NaNs propagated correctly */
if (ISNAN(x) || ISNAN(alpha)) return x + alpha;
#endif
if (x < 0) {
ML_ERROR(ME_RANGE, "bessel_j");
return ML_NAN;
}
na = floor(alpha);
if (alpha < 0) {
/* Using Abramowitz & Stegun 9.1.2
* this may not be quite optimal (CPU and accuracy wise) */
return(bessel_j_ex(x, -alpha, bj) * cos(M_PI * alpha) +
((alpha == na) ? 0 :
bessel_y_ex(x, -alpha, bj) * sin(M_PI * alpha)));
}
nb = 1 + (long)na; /* nb-1 <= alpha < nb */
alpha -= (nb-1);
J_bessel(&x, &alpha, &nb, bj, &ncalc);
if(ncalc != nb) {/* error input */
if(ncalc < 0)
MATHLIB_WARNING4(_("bessel_j(%g): ncalc (=%ld) != nb (=%ld); alpha=%g. Arg. out of range?\n"),
x, ncalc, nb, alpha);
else
MATHLIB_WARNING2(_("bessel_j(%g,nu=%g): precision lost in result\n"),
x, alpha+nb-1);
}
x = bj[nb-1];
return x;
}
// unused now from R
double bessel_j(double x, double alpha)
{
int nb, ncalc;
double na, *bj;
#ifndef MATHLIB_STANDALONE
const void *vmax;
#endif
#ifdef IEEE_754
/* NaNs propagated correctly */
if (ISNAN(x) || ISNAN(alpha)) return x + alpha;
#endif
if (x < 0) {
ML_ERROR(ME_RANGE, "bessel_j");
return ML_NAN;
}
na = floor(alpha);
if (alpha < 0) {
/* Using Abramowitz & Stegun 9.1.2
* this may not be quite optimal (CPU and accuracy wise) */
return(((alpha - na == 0.5) ? 0 : bessel_j(x, -alpha) * cospi(alpha)) +
((alpha == na ) ? 0 : bessel_y(x, -alpha) * sinpi(alpha)));
}
else if (alpha > 1e7) {
MATHLIB_WARNING("besselJ(x, nu): nu=%g too large for bessel_j() algorithm", alpha);
return ML_NAN;
}
nb = 1 + (int)na; /* nb-1 <= alpha < nb */
alpha -= (double)(nb-1);
#ifdef MATHLIB_STANDALONE
bj = (double *) calloc(nb, sizeof(double));
#ifndef _RENJIN
if (!bj) MATHLIB_ERROR("%s", _("bessel_j allocation error"));
#endif
#else
vmax = vmaxget();
bj = (double *) R_alloc((size_t) nb, sizeof(double));
#endif
J_bessel(&x, &alpha, &nb, bj, &ncalc);
if(ncalc != nb) {/* error input */
if(ncalc < 0)
MATHLIB_WARNING4(_("bessel_j(%g): ncalc (=%d) != nb (=%d); alpha=%g. Arg. out of range?\n"),
x, ncalc, nb, alpha);
else
MATHLIB_WARNING2(_("bessel_j(%g,nu=%g): precision lost in result\n"),
x, alpha+(double)nb-1);
}
x = bj[nb-1];
#ifdef MATHLIB_STANDALONE
free(bj);
#else
vmaxset(vmax);
#endif
return x;
}
double bessel_y(double x, double alpha)
{
long nb, ncalc;
double na, *by;
#ifndef MATHLIB_STANDALONE
const void *vmax;
#endif
#ifdef IEEE_754
/* NaNs propagated correctly */
if (ISNAN(x) || ISNAN(alpha)) return x + alpha;
#endif
if (x < 0) {
ML_ERROR(ME_RANGE, "bessel_y");
return ML_NAN;
}
na = floor(alpha);
if (alpha < 0) {
/* Using Abramowitz & Stegun 9.1.2
* this may not be quite optimal (CPU and accuracy wise) */
return(bessel_y(x, -alpha) * cos(M_PI * alpha) -
((alpha == na) ? 0 :
bessel_j(x, -alpha) * sin(M_PI * alpha)));
}
nb = 1+ (long)na;/* nb-1 <= alpha < nb */
alpha -= (nb-1);
#ifdef MATHLIB_STANDALONE
by = (double *) calloc(nb, sizeof(double));
if (!by) MATHLIB_ERROR("%s", _("bessel_y allocation error"));
#else
vmax = vmaxget();
by = (double *) R_alloc((size_t) nb, sizeof(double));
#endif
Y_bessel(&x, &alpha, &nb, by, &ncalc);
if(ncalc != nb) {/* error input */
if(ncalc == -1)
return ML_POSINF;
else if(ncalc < -1)
MATHLIB_WARNING4(_("bessel_y(%g): ncalc (=%ld) != nb (=%ld); alpha=%g. Arg. out of range?\n"),
x, ncalc, nb, alpha);
else /* ncalc >= 0 */
MATHLIB_WARNING2(_("bessel_y(%g,nu=%g): precision lost in result\n"),
x, alpha+nb-1);
}
x = by[nb-1];
#ifdef MATHLIB_STANDALONE
free(by);
#else
vmaxset(vmax);
#endif
return x;
}
double bessel_k(double x, double alpha, double expo)
{
long nb, ncalc, ize;
double *bk;
#ifndef MATHLIB_STANDALONE
const void *vmax;
#endif
#ifdef IEEE_754
/* NaNs propagated correctly */
if (ISNAN(x) || ISNAN(alpha)) return x + alpha;
#endif
if (x < 0) {
ML_ERROR(ME_RANGE, "bessel_k");
return ML_NAN;
}
ize = (long)expo;
if(alpha < 0)
alpha = -alpha;
nb = 1+ (long)floor(alpha);/* nb-1 <= |alpha| < nb */
alpha -= (double)(nb-1);
#ifdef MATHLIB_STANDALONE
bk = (double *) calloc(nb, sizeof(double));
if (!bk) MATHLIB_ERROR("%s", _("bessel_k allocation error"));
#else
vmax = vmaxget();
bk = (double *) R_alloc((size_t) nb, sizeof(double));
#endif
K_bessel(&x, &alpha, &nb, &ize, bk, &ncalc);
if(ncalc != nb) {/* error input */
if(ncalc < 0)
MATHLIB_WARNING4(_("bessel_k(%g): ncalc (=%ld) != nb (=%ld); alpha=%g. Arg. out of range?\n"),
x, ncalc, nb, alpha);
else
MATHLIB_WARNING2(_("bessel_k(%g,nu=%g): precision lost in result\n"),
x, alpha+(double)nb-1);
}
x = bk[nb-1];
#ifdef MATHLIB_STANDALONE
free(bk);
#else
vmaxset(vmax);
#endif
return x;
}
/* Called from R: modified version of bessel_j(), accepting a work array
* instead of allocating one. */
double bessel_j_ex(double x, double alpha, double *bj)
{
int nb, ncalc;
double na;
#ifdef IEEE_754
/* NaNs propagated correctly */
if (ISNAN(x) || ISNAN(alpha)) return x + alpha;
#endif
if (x < 0) {
ML_ERROR(ME_RANGE, "bessel_j");
return ML_NAN;
}
na = floor(alpha);
if (alpha < 0) {
/* Using Abramowitz & Stegun 9.1.2
* this may not be quite optimal (CPU and accuracy wise) */
return(((alpha - na == 0.5) ? 0 : bessel_j_ex(x, -alpha, bj) * cospi(alpha)) +
((alpha == na ) ? 0 : bessel_y_ex(x, -alpha, bj) * sinpi(alpha)));
}
else if (alpha > 1e7) {
MATHLIB_WARNING("besselJ(x, nu): nu=%g too large for bessel_j() algorithm", alpha);
return ML_NAN;
}
nb = 1 + (int)na; /* nb-1 <= alpha < nb */
alpha -= (double)(nb-1); // ==> alpha' in [0, 1)
J_bessel(&x, &alpha, &nb, bj, &ncalc);
if(ncalc != nb) {/* error input */
if(ncalc < 0)
MATHLIB_WARNING4(_("bessel_j(%g): ncalc (=%d) != nb (=%d); alpha=%g. Arg. out of range?\n"),
x, ncalc, nb, alpha);
else
MATHLIB_WARNING2(_("bessel_j(%g,nu=%g): precision lost in result\n"),
x, alpha+(double)nb-1);
}
x = bj[nb-1];
return x;
}