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！

  TEST_SF(s,  gsl_sf_bessel_yl_e, (0,        0.01, &r), -99.995000041666528,    TEST_TOL0, GSL_SUCCESS); 
  TEST_SF(s,  gsl_sf_bessel_yl_e, (0,        1.0, &r),  -0.54030230586813972,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_yl_e, (1,       10.0, &r),   0.062792826379701506,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_yl_e, (5,        1.0, &r),  -999.44034339223641,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_yl_e, (10,       0.01, &r), -6.5473079797378378e+30, TEST_TOL0, GSL_SUCCESS); 
  TEST_SF(s,  gsl_sf_bessel_yl_e, (10,      10.0, &r),  -0.172453672088057849,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_yl_e, (100,      1.0, &r),  -6.6830794632586775e+186, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_yl_e, (100,    100.0, &r),  -0.0229838504915622811,   TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_bessel_yl_e, (2000, 1048576.0, &r), 5.9545201447146155e-07,  TEST_SQRT_TOL0, GSL_SUCCESS);


  TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (0.1, &r), 0.9063462346100907067, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (2.0, &r), 0.24542109027781645493, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (100.0, &r), 0.005000000000000000000, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (0.1, &r), 0.030191419289002226846, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (2.0, &r), 0.131868364583275317610, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (100.0, &r), 0.004950000000000000000, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (0.1, &r), 0.0006036559400239012567, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (2.0, &r), 0.0476185434029034785100, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (100.0, &r), 0.0048515000000000000000, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_il_scaled_e, (   4, 0.001, &r), 1.0571434341190365013e-15, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_il_scaled_e, (   4,   0.1, &r), 9.579352242057134927e-08,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_il_scaled_e, (   5,   2.0, &r), 0.0004851564602127540059,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_il_scaled_e, (   5, 100.0, &r), 0.004300446777500000000,   TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 100, 100.0, &r), 1.3898161964299132789e-23, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_k0_scaled_e, (0.1, &r), 15.707963267948966192, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_k0_scaled_e, (2.0, &r), 0.7853981633974483096, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_k0_scaled_e, (100.0, &r), 0.015707963267948966192, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_k1_scaled_e, (0.1, &r), 172.78759594743862812, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_k1_scaled_e, (2.0, &r), 1.1780972450961724644, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_k1_scaled_e, (100.0, &r), 0.015865042900628455854, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_k2_scaled_e, (0.1, &r), 5199.335841691107810, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_k2_scaled_e, (2.0, &r), 2.5525440310417070063, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_k2_scaled_e, (100.0, &r), 0.016183914554967819868, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_kl_scaled_e, (   4, 1.0/256.0, &r), 1.8205599816961954439e+14, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_kl_scaled_e, (   4, 1.0/8.0, &r),   6.1173217814406597530e+06, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_kl_scaled_e, (   5,   2.0, &r),     138.10735829492005119,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_kl_scaled_e, ( 100, 100.0, &r),     3.985930768060258219e+18,  TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.0001, 1.0, &r),         0.7652115411876708497,  TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.0001, 10.0, &r),       -0.2459270166445205,     TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.0009765625, 10.0, &r), -0.2458500798634692,     TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.75, 1.0, &r),           0.5586524932048917478,  TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.75, 10.0, &r),         -0.04968928974751508135, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, ( 1.0, 0.001, &r), 0.0004999999375000026,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, ( 1.0,   1.0, &r), 0.4400505857449335160,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, ( 1.75,  1.0, &r), 0.168593922545763170103,     TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (30.0,   1.0, &r), 3.482869794251482902e-42,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (30.0, 100.0, &r), 0.08146012958117222297,    TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (10.0,   1.0, &r), 2.6306151236874532070e-10, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (10.0, 100.0, &r), -0.05473217693547201474,   TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (10.2, 100.0, &r), -0.03548919161046526864,   TEST_TOL2, GSL_SUCCESS);

  /* related to BUG#3 problem */
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (2.0, 900.0, &r),   -0.019974345269680646400,  TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Jnu_e, (2.0, 15000.0, &r), -0.0020455820181216382666, TEST_TOL4, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Ynu_e, (0.0001, 1.0, &r),  0.08813676933044478439,    TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, (0.0001,10.0, &r),  0.05570979797521875261,    TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 0.75,  1.0, &r), -0.6218694174429746383,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 0.75, 10.0, &r),  0.24757063446760384953,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 1.0, 0.001, &r), -636.6221672311394281,      TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 1.0,   1.0, &r), -0.7812128213002887165,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, (30.0,   1.0, &r), -3.0481287832256432162e+39, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, (30.0, 100.0, &r),  0.006138839212010033452,   TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, (10.0,   1.0, &r), -1.2161801427868918929e+08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, (10.0, 100.0, &r),  0.05833157423641492875,    TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Ynu_e, (10.2, 100.0, &r),  0.07169383985546287091,    TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (0.0001,10.0, &r), 0.12783333709581669672,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, ( 1.0, 0.001, &r), 0.0004995003123542213370,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, ( 1.0,   1.0, &r), 0.20791041534970844887,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (30.0,   1.0, &r), 1.3021094983785914437e-42, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (30.0, 100.0, &r), 0.0004486987756920986146,  TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (10.0,   1.0, &r), 1.0127529864692066036e-10, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (10.0, 100.0, &r), 0.024176682718258828365,   TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (10.2, 100.0, &r), 0.023691628843913810043,   TEST_TOL3, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Inu_e, (0.0001,10.0, &r), 2815.7166269770030352,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, ( 1.0, 0.001, &r), 0.0005000000625000026042,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, ( 1.0,   1.0, &r), 0.5651591039924850272,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, (30.0,   1.0, &r), 3.539500588106447747e-42,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, (30.0, 100.0, &r), 1.2061548704498434006e+40, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, (10.0,   1.0, &r), 2.7529480398368736252e-10, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, (10.0, 100.0, &r), 6.498975524720147799e+41,  TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Inu_e, (10.2, 100.0, &r), 6.368587361287030443e+41,  TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (0.0001,10.0, &r), 0.3916319346235421817, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, ( 1.0, 0.001, &r), 1000.9967345590684524, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, ( 1.0,   1.0, &r), 1.6361534862632582465, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (30.0,   1.0, &r), 1.2792629867539753925e+40, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (30.0, 100.0, &r), 10.673443449954850040, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0,   1.0, &r), 4.912296520990198599e+08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 100.0, &r), 0.20578687173955779807, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 1000.0, &r), 0.04165905142800565788, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 1.0e+8, &r), 0.00012533147624060789938, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.2, 100.0, &r), 0.20995808355244385075, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_Knu_e, (0.0001,0.001, &r), 7.023689431812884141,      TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (0.0001,10.0, &r), 0.000017780062324654874306, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, ( 1.0, 0.001, &r), 999.9962381560855743,      TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, ( 1.0,   1.0, &r), 0.6019072301972345747,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (10.0, 0.001, &r), 1.8579455483904008064e+38, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (10.0,   1.0, &r), 1.8071328990102945469e+08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (10.0, 100.0, &r), 7.655427977388100611e-45,  TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (10.2, 100.0, &r), 7.810600225948217841e-45,  TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (30.0,   1.0, &r), 4.706145526783626883e+39,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_Knu_e, (30.0, 100.0, &r), 3.970602055959398739e-43,  TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (0.0001,1.0e-100, &r), 5.439794449319847, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (0.0001,0.0001, &r), 2.232835507214331, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (0.0001,10.0, &r), -10.93743282256098, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 1.0e-100, &r), 230.2585092994045, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 1.0e-10, &r), 23.025850929940456840, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 0.001, &r), 6.907751517131146, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0,   1.0, &r), -0.5076519482107523309, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (30.0, 1.0e-100, &r), 6999.113586185543475, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (30.0,   1.0, &r), 91.34968784026325464, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (30.0, 100.0, &r), -97.63224126416760932, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (100.0, 1.0e-100, &r), 23453.606706185466825, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (100.0, 1.0, &r), 427.7532510250188083, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (100.0, 100.0, &r), -55.53422771502921431, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (1000.0, 1.0e-100, &r), 236856.183755993135, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_lnKnu_e, (10000.0, 1.0e-100, &r), 2.39161558914890695e+06, TEST_TOL0, GSL_SUCCESS);

  sa = 0;
  gsl_sf_bessel_Jn_array(3, 38, 1.0, J);
  sa += ( test_sf_frac_diff(J[0],  0.0195633539826684059190  ) > TEST_TOL1);
  sa += ( test_sf_frac_diff(J[1],  0.0024766389641099550438  ) > TEST_TOL1);
  sa += ( test_sf_frac_diff(J[10], 1.9256167644801728904e-14 ) > TEST_TOL1);
  sa += ( test_sf_frac_diff(J[35], 6.911232970971626272e-57  ) > TEST_TOL1);
  gsl_test(sa, "  gsl_sf_bessel_Jn_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_Yn_array(3, 38, 1.0, Y);
  sa += ( test_sf_frac_diff(Y[0],  -5.821517605964728848      ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[1],  -33.27842302897211870      ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[10], -1.2753618701519837595e+12 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[35], -1.2124435663593357154e+54 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_Yn_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_In_scaled_array(3, 38, 1.0, I);
  sa += ( test_sf_frac_diff(I[0],  0.0081553077728142938170  ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(I[1],  0.0010069302573377758637  ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(I[10], 7.341518665628926244e-15  ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(I[35], 2.5753065298357542893e-57 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_In_scaled_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_In_array(3, 38, 1.0, Y);
  sa += ( test_sf_frac_diff(Y[0],   0.0221684249243319024760  ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[1],   0.0027371202210468663251  ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[10],  1.9956316782072007564e-14 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[35],  7.000408942764452901e-57  ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_In_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_Kn_array(3, 38, 1.0, K);
  sa += ( test_sf_frac_diff(K[0],  7.101262824737944506 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[1],  44.23241584706284452 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[10], 1.9215763927929940846e+12 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[35], 1.8789385023806051223e+54 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_Kn_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_Kn_scaled_array(3, 38, 1.0, K);
  sa += ( test_sf_frac_diff(K[0],  19.303233695596904277 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[1],  120.23617222591483717 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[10], 5.223386190525076473e+12 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[35], 5.107484387813251411e+54 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_Kn_scaled_array");