test_bessel.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* specfunc/test_bessel.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/* Author:  G. Jungman */

#include <config.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_sf.h>
#include "test_sf.h"

static double J[100];
static double Y[100];
static double I[100];
static double K[100];

int test_bessel(void)
{
  gsl_sf_result r;
  int i;
  int s = 0;
  int sa;

  TEST_SF(s, gsl_sf_bessel_J0_e, (0.1, &r),     0.99750156206604003230,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_J0_e, (2.0, &r),     0.22389077914123566805,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_J0_e, (100.0, &r),   0.019985850304223122424,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_J0_e, (1.0e+10, &r), 2.1755917502468917269e-06, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_J1_e, (0.1, &r),      0.04993752603624199756,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_J1_e, (2.0, &r),      0.57672480775687338720,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_J1_e, (100.0, &r),   -0.07714535201411215803,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_J1_e, (1.0e+10, &r), -7.676508175684157103e-06, TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Jn_e, (4, 0.1, &r),     2.6028648545684032338e-07, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jn_e, (5, 2.0, &r),     0.007039629755871685484,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jn_e, (10, 20.0, &r),   0.18648255802394508321,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jn_e, (100, 100.0, &r), 0.09636667329586155967,    TEST_TOL0, GSL_SUCCESS);

  /* exercise the BUG#3 problem */
  TEST_SF(s, gsl_sf_bessel_Jn_e, (2, 900.0, &r), -0.019974345269680646400, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jn_e, (2, 15000.0, &r), -0.0020455820181216382666, TEST_TOL4, GSL_SUCCESS);

#ifdef TEST_LARGE
  TEST_SF(s, gsl_sf_bessel_Jn_e, (0, 1.0e+10, &r), 2.1755917502468917269e-06, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jn_e, (1, 1.0e+10, &r), -7.676508175684157103e-06, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jn_e, (0, 20000, &r), -7.676508175684157103e-06, TEST_TOL4, GSL_SUCCESS);
#endif

  TEST_SF(s, gsl_sf_bessel_Y0_e, (0.1, &r),         -1.5342386513503668441,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Y0_e, (2, &r),            0.5103756726497451196,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Y0_e, (256.0, &r),       -0.03381290171792454909 ,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Y0_e, (4294967296.0, &r), 3.657903190017678681e-06, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Y1_e, (0.1, &r),         -6.45895109470202698800,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Y1_e, (2, &r),           -0.10703243154093754689,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Y1_e, (100.0, &r),       -0.020372312002759793305,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Y1_e, (4294967296.0, &r), 0.000011612249378370766284, TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Yn_e, (4, 0.1, &r),            -305832.29793353160319,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Yn_e, (5, 2, &r),              -9.935989128481974981,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Yn_e, (100, 100.0, &r),        -0.16692141141757650654,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Yn_e, (100, 4294967296.0, &r),  3.657889671577715808e-06, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Yn_e, (1000, 4294967296.0, &r), 3.656551321485397501e-06, 2.0e-05, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Yn_e, (2, 15000.0, &r), -0.006185217273358617849, TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (1e-10, &r),   0.99999999990000000001,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (0.1, &r),     0.90710092578230109640,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (2, &r),       0.30850832255367103953,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (100.0, &r),   0.03994437929909668265,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (65536.0, &r), 0.0015583712551952223537, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (0.1, &r),     0.04529844680880932501,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (2, &r),       0.21526928924893765916,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (100.0, &r),   0.03974415302513025267,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (65536.0, &r), 0.0015583593657207350452, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_In_scaled_e, (  -4,    0.1, &r), 2.3575258620054605307e-07, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_In_scaled_e, (   4,    0.1, &r), 2.3575258620054605307e-07, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_In_scaled_e, (   5,    2.0, &r), 0.0013297610941881578142, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( 100,  100.0, &r), 1.7266862628167695785e-22, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_I0_e, (0.1, &r), 1.0025015629340956014, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I0_e, (2.0, &r), 2.2795853023360672674, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I0_e, (100.0, &r), 1.0737517071310738235e+42, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_I1_e, (0.1, &r), 0.05006252604709269211,      TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I1_e, (2.0, &r), 1.59063685463732906340,      TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_I1_e, (100.0, &r), 1.0683693903381624812e+42, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_In_e, (   4,    0.1, &r), 2.6054690212996573677e-07, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_In_e, (   5,    2.0, &r), 0.009825679323131702321,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_In_e, ( 100,  100.0, &r), 4.641534941616199114e+21,  TEST_TOL2, GSL_SUCCESS);


  TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (0.1, &r), 2.6823261022628943831, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (2.0, &r), 0.8415682150707714179, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (100.0, &r), 0.1251756216591265789, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (0.1, &r), 10.890182683049696574, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (2.0, &r), 1.0334768470686885732, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (100.0, &r), 0.1257999504795785293, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, (   4,    0.1, &r), 530040.2483725626207, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, (   5,    2.0, &r), 69.68655087607675118, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, ( 100,  100.0, &r), 2.0475736731166756813e+19, TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_K0_e, (0.1, &r), 2.4270690247020166125, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K0_e, (2.0, &r), 0.11389387274953343565, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K0_e, (100.0, &r), 4.656628229175902019e-45, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_K1_e, (0.1, &r), 9.853844780870606135,       TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K1_e, (2.0, &r), 0.13986588181652242728,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_K1_e, (100.0, &r), 4.679853735636909287e-45, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Kn_e, (   4,    0.1, &r), 479600.2497925682849,     TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Kn_e, (   5,    2.0, &r), 9.431049100596467443,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Kn_e, ( 100,  100.0, &r), 7.617129630494085416e-25, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_j0_e, (-10.0, &r), -0.05440211108893698134, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j0_e, (0.001, &r), 0.9999998333333416667, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j0_e, (  1.0, &r), 0.84147098480789650670, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j0_e, ( 10.0, &r), -0.05440211108893698134, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j0_e, (100.0, &r), -0.005063656411097587937, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j0_e, (1048576.0, &r), 3.1518281938718287624e-07, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_j1_e, (-10.0, &r), -0.07846694179875154709, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j1_e, (0.01, &r), 0.003333300000119047399, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j1_e, (  1.0, &r), 0.30116867893975678925, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j1_e, ( 10.0, &r), 0.07846694179875154709, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j1_e, (100.0, &r), -0.008673825286987815220, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j1_e, (1048576.0, &r), -9.000855242905546158e-07, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_j2_e, (-10.0, &r), 0.07794219362856244547, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j2_e, (0.01, &r), 6.666619047751322551e-06, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j2_e, (  1.0, &r), 0.06203505201137386110, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j2_e, ( 10.0, &r), 0.07794219362856244547, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j2_e, (100.0, &r), 0.004803441652487953480, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_j2_e, (1048576.0, &r), -3.1518539455252413111e-07, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_jl_e, (0, 0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_jl_e, (1,       10.0, &r),   0.07846694179875154709000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_jl_e, (5,        1.0, &r),   0.00009256115861125816357, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_jl_e, (10,      10.0, &r),   0.06460515449256426427,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_jl_e, (100,    100.0, &r),   0.010880477011438336539,   TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_jl_e, (2000, 1048576.0, &r), 7.449384239168568534e-07,  TEST_SQRT_TOL0, GSL_SUCCESS);

  /* related to BUG#3 problem */
  TEST_SF(s, gsl_sf_bessel_jl_e, (2, 900.0, &r),   -0.0011089115568832940086,  TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_jl_e, (2, 15000.0, &r), -0.00005955592033075750554, TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_y0_e, (0.001, &r), -999.99950000004166670, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y0_e, (  1.0, &r), -0.5403023058681397174, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y0_e, ( 10.0, &r), 0.08390715290764524523, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y0_e, (100.0, &r), -0.008623188722876839341, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y0_e, (65536.0, &r), 0.000011014324202158573930, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y0_e, (4294967296.0, &r), 2.0649445131370357007e-10, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_y1_e, ( 0.01, &r), -10000.499987500069444, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y1_e, (  1.0, &r), -1.3817732906760362241, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y1_e, ( 10.0, &r), 0.06279282637970150586, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y1_e, (100.0, &r), 0.004977424523868819543, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y1_e, (4294967296.0, &r), 1.0756463271573404688e-10, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_bessel_y2_e, ( 0.01, &r), -3.0000500012499791668e+06, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y2_e, (  1.0, &r), -3.605017566159968955, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y2_e, ( 10.0, &r), -0.06506930499373479347, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y2_e, (100.0, &r), 0.008772511458592903927, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_y2_e, (4294967296.0, &r), -2.0649445123857054207e-10, TEST_SQRT_TOL0, GSL_SUCCESS);