CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/struve.c

/*							struve.c
 *
 *      Struve function
 *
 *
 *
 * SYNOPSIS:
 *
 * double v, x, y, struve();
 *
 * y = struve( v, x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Computes the Struve function Hv(x) of order v, argument x.
 * Negative x is rejected unless v is an integer.
 *
 * This module also contains the hypergeometric functions 1F2
 * and 3F0 and a routine for the Bessel function Yv(x) with
 * noninteger v.
 *
 *
 *
 * ACCURACY:
 *
 * Not accurately characterized, but spot checked against tables.
 *
 */

/*
Cephes Math Library Release 2.81:  June, 2000
Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#define DEBUG 0
#ifdef ANSIPROT
extern double gamma(double);
extern double pow(double, double);
extern double sqrt(double);
extern double yn(int, double);
extern double jv(double, double);
extern double fabs(double);
extern double floor(double);
extern double sin(double);
extern double cos(double);
double yv(double, double);
double onef2(double, double, double, double, double *);
double threef0(double, double, double, double, double *);
#else
double gamma(), pow(), sqrt(), yn(), yv(), jv(), fabs(), floor();
double sin(), cos();
double onef2(), threef0();
#endif
static double stop = 1.37e-17;
extern double MACHEP;

double onef2(a, b, c, x, err) double a, b, c, x;
double *err;
{
  double n, a0, sum, t;
  double an, bn, cn, max, z;

  an = a;
  bn = b;
  cn = c;
  a0 = 1.0;
  sum = 1.0;
  n = 1.0;
  t = 1.0;
  max = 0.0;

  do {
    if (an == 0)
      goto done;
    if (bn == 0)
      goto error;
    if (cn == 0)
      goto error;
    if ((a0 > 1.0e34) || (n > 200))
      goto error;
    a0 *= (an * x) / (bn * cn * n);
    sum += a0;
    an += 1.0;
    bn += 1.0;
    cn += 1.0;
    n += 1.0;
    z = fabs(a0);
    if (z > max)
      max = z;
    if (sum != 0)
      t = fabs(a0 / sum);
    else
      t = z;
  } while (t > stop);

done:

  *err = fabs(MACHEP * max / sum);

#if DEBUG
  printf(" onef2 cancellation error %.5E\n", *err);
#endif

  goto xit;

error:
#if DEBUG
  printf("onef2 does not converge\n");
#endif
  *err = 1.0e38;

xit:

#if DEBUG
  printf("onef2( %.2E %.2E %.2E %.5E ) =  %.3E  %.6E\n", a, b, c, x, n, sum);
#endif
  return (sum);
}

double threef0(a, b, c, x, err) double a, b, c, x;
double *err;
{
  double n, a0, sum, t, conv, conv1;
  double an, bn, cn, max, z;

  an = a;
  bn = b;
  cn = c;
  a0 = 1.0;
  sum = 1.0;
  n = 1.0;
  t = 1.0;
  max = 0.0;
  conv = 1.0e38;
  conv1 = conv;

  do {
    if (an == 0.0)
      goto done;
    if (bn == 0.0)
      goto done;
    if (cn == 0.0)
      goto done;
    if ((a0 > 1.0e34) || (n > 200))
      goto error;
    a0 *= (an * bn * cn * x) / n;
    an += 1.0;
    bn += 1.0;
    cn += 1.0;
    n += 1.0;
    z = fabs(a0);
    if (z > max)
      max = z;
    if (z >= conv) {
      if ((z < max) && (z > conv1))
        goto done;
    }
    conv1 = conv;
    conv = z;
    sum += a0;
    if (sum != 0)
      t = fabs(a0 / sum);
    else
      t = z;
  } while (t > stop);

done:

  t = fabs(MACHEP * max / sum);
#if DEBUG
  printf(" threef0 cancellation error %.5E\n", t);
#endif

  max = fabs(conv / sum);
  if (max > t)
    t = max;
#if DEBUG
  printf(" threef0 convergence %.5E\n", max);
#endif

  goto xit;

error:
#if DEBUG
  printf("threef0 does not converge\n");
#endif
  t = 1.0e38;

xit:

#if DEBUG
  printf("threef0( %.2E %.2E %.2E %.5E ) =  %.3E  %.6E\n", a, b, c, x, n, sum);
#endif

  *err = t;
  return (sum);
}

extern double PI;

double struve(v, x) double v, x;
{
  double y, ya, f, g, h, t;
  double onef2err, threef0err;

  f = floor(v);
  if ((v < 0) && (v - f == 0.5)) {
    y = jv(-v, x);
    f = 1.0 - f;
    g = 2.0 * floor(f / 2.0);
    if (g != f)
      y = -y;
    return (y);
  }
  t = 0.25 * x * x;
  f = fabs(x);
  g = 1.5 * fabs(v);
  if ((f > 30.0) && (f > g)) {
    onef2err = 1.0e38;
    y = 0.0;
  } else {
    y = onef2(1.0, 1.5, 1.5 + v, -t, &onef2err);
  }

  if ((f < 18.0) || (x < 0.0)) {
    threef0err = 1.0e38;
    ya = 0.0;
  } else {
    ya = threef0(1.0, 0.5, 0.5 - v, -1.0 / t, &threef0err);
  }

  f = sqrt(PI);
  h = pow(0.5 * x, v - 1.0);

  if (onef2err <= threef0err) {
    g = gamma(v + 1.5);
    y = y * h * t / (0.5 * f * g);
    return (y);
  } else {
    g = gamma(v + 0.5);
    ya = ya * h / (f * g);
    ya = ya + yv(v, x);
    return (ya);
  }
}

/* Bessel function of noninteger order
 */

double yv(v, x) double v, x;
{
  double y, t;
  int n;

  y = floor(v);
  if (y == v) {
    n = v;
    y = yn(n, x);
    return (y);
  }
  t = PI * v;
  y = (cos(t) * jv(v, x) - jv(-v, x)) / sin(t);
  return (y);
}

/* Crossover points between ascending series and asymptotic series
 * for Struve function
 *
 *	 v	 x
 *
 *	 0	19.2
 *	 1	18.95
 *	 2	19.15
 *	 3	19.3
 *	 5	19.7
 *	10	21.35
 *	20	26.35
 *	30	32.31
 *	40	40.0
 */