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！

  s += sa;

  sa = 0;
  gsl_sf_bessel_jl_array(50, 1.0, J);
  sa += ( test_sf_frac_diff(J[0],  0.84147098480789650670   ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(J[1],  0.30116867893975678925   ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(J[10], 7.116552640047313024e-11 ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(J[50], 3.615274717489787311e-81 ) > TEST_TOL2 );
  gsl_test(sa, "  gsl_sf_bessel_jl_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_jl_steed_array(50, 1.0, J);
  sa += ( test_sf_frac_diff(J[0],  0.84147098480789650670   ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(J[1],  0.30116867893975678925   ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(J[10], 7.116552640047313024e-11 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(J[50], 3.615274717489787311e-81 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_jl_steed_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_yl_array(50, 1.0, Y);
  sa += ( test_sf_frac_diff(Y[0],  -0.5403023058681397174 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[1],  -1.3817732906760362241 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[10], -6.722150082562084436e+08  ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(Y[50], -2.7391922846297571576e+78 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_yl_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_il_scaled_array(50, 1.0, I);
  sa += ( test_sf_frac_diff(I[0],  0.43233235838169365410 ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(I[1],  0.13533528323661269189 ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(I[10], 2.7343719371837065460e-11 ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(I[50], 1.3429606061892023653e-81 ) > TEST_TOL2 );
  gsl_test(sa, "  gsl_sf_bessel_il_scaled_array");
  s += sa;

  sa = 0;
  gsl_sf_bessel_kl_scaled_array(50, 1.0, K);
  sa += ( test_sf_frac_diff(K[0],  1.5707963267948966192     ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[1],  3.1415926535897932385     ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[10], 2.7231075458948147010e+09 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(K[50], 1.1578440432804522544e+79 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_bessel_kl_scaled_array");
  s += sa;

  sa = 0;
  sa += ( gsl_sf_bessel_zero_J0_e(0, &r) != GSL_EINVAL );
  sa += ( r.val != 0.0 );
  s += sa;
  TEST_SF(s, gsl_sf_bessel_zero_J0_e, ( 1,  &r),  2.404825557695771, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J0_e, ( 2,  &r),  5.520078110286304, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J0_e, (20,  &r), 62.048469190227081, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J0_e, (25,  &r), 77.756025630388058, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J0_e, (100, &r), 313.37426607752784, TEST_TOL1, GSL_SUCCESS);

  sa = 0;
  sa += ( gsl_sf_bessel_zero_J1_e(0, &r) != GSL_SUCCESS );
  sa += ( r.val != 0.0 );
  s += sa;
  TEST_SF(s, gsl_sf_bessel_zero_J1_e, ( 1,  &r), 3.831705970207512, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J1_e, ( 2,  &r), 7.015586669815619, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J1_e, (20,  &r), 63.61135669848124, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J1_e, (25,  &r), 79.32048717547630, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_J1_e, (100, &r), 314.9434728377672, TEST_TOL2, GSL_SUCCESS);

  sa = 0;
  sa += ( gsl_sf_bessel_zero_Jnu_e(0.0, 0, &r) != GSL_EINVAL );
  sa += ( r.val != 0.0 );
  s += sa;
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (0.0,  1,  &r),  2.404825557695771, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (0.0,  2,  &r),  5.520078110286304, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (0.0, 20,  &r), 62.048469190227081, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (0.0, 25,  &r), 77.756025630388058, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (0.0, 100, &r), 313.37426607752784, TEST_TOL1, GSL_SUCCESS);

  sa = 0;
  sa += ( gsl_sf_bessel_zero_Jnu_e(1.0, 0, &r) != GSL_SUCCESS );
  sa += (r.val != 0.0);
  s += sa;
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 1, &r),  4.4934094579090641, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 1, &r),  8.7714838159599540, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 2, &r),  7.7252518369377072, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 2, &r),  12.338604197466944, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 3, &r),  10.904121659428900, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 3, &r),  15.700174079711671, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 4, &r),  14.066193912831473, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 4, &r),  18.980133875179921, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 5, &r),  17.220755271930768, TEST_TOL1, GSL_SUCCESS);

  /* Something wrong with the tolerances on these */
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 5, &r),  22.217799896561268, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 8.0, 5, &r),  26.266814641176644, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (20.0, 5, &r),  41.413065513892636, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 6, &r),  20.371302959287563, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 6, &r),  25.430341154222704, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 8.0, 6, &r),  29.545659670998550, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 7, &r),  23.519452498689007, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 7, &r),  28.626618307291138, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 8.0, 7, &r),  32.795800037341462, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 8, &r),  26.666054258812674, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 8, &r),  31.811716724047763, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (10.0, 8, &r),  38.761807017881651, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 9, &r),  29.811598790892959, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 9, &r),  34.988781294559295, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (10.0, 9, &r),  42.004190236671805, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 1.5, 10, &r),  32.956389039822477, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 10, &r),  38.159868561967132, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 10, &r),  52.017241278881633, TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 11,  &r), 41.326383254047406, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 11,  &r), 55.289204146560061, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 12,  &r), 44.4893191232197314, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 12,  &r), 58.5458289043850856, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 13,  &r), 47.6493998066970948, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 13,  &r), 61.7897598959450550, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 14,  &r), 50.8071652030063595, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 14,  &r), 65.0230502510422545, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 15,  &r), 53.9630265583781707, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 15,  &r), 68.2473219964207837, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 16,  &r), 57.1173027815042647, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 16,  &r), 71.4638758850226630, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 17,  &r), 60.2702450729428077, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 17,  &r), 74.6737687121404241, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 18,  &r), 63.4220540458757799, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 18,  &r), 77.8778689734863729, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 19,  &r), 66.5728918871182703, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 19,  &r), 81.0768977206328326, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 5.0, 20,  &r), 69.722891161716742,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (15.0, 20,  &r), 84.271459069716442,  TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 23.0, 11,  &r), 65.843393469524653, TEST_TOL6, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 30.0, 11,  &r), 74.797306585175426, TEST_TOL6, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 32.0, 15,  &r), 90.913637691861741, TEST_TOL6, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 50.0, 15,  &r), 113.69747988073942, TEST_TOL6, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (  5.0, 22,  &r), 76.020793430591605, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 10.0, 22,  &r), 83.439189796105756, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, ( 12.0, 22,  &r), 86.345496520534055, TEST_TOL6, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (100.0, 22,  &r), 199.82150220122519, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_bessel_zero_Jnu_e, (500.0, 22,  &r), 649.34132440891735, TEST_TOL2, GSL_SUCCESS);

  sa = 0;
  for(i=0; i<100; i++) {
    J[i] = i/10.0;
  }
  gsl_sf_bessel_sequence_Jnu_e(2.0, GSL_MODE_DEFAULT, 100, J);
  sa += ( test_sf_frac_diff(J[1],  0.0012489586587999188454 ) > TEST_TOL1 );
  sa += ( test_sf_frac_diff(J[20], 0.3528340286156377192 ) > TEST_TOL4 );
  sa += ( test_sf_frac_diff(J[50], 0.0465651162777522155 ) > TEST_TOL4 );
  gsl_test(sa, "  gsl_sf_sequence_Jnu_e(2)");
  s += sa;

  sa = 0;
  for(i=0; i<100; i++) {
    J[i] = i;
  }
  gsl_sf_bessel_sequence_Jnu_e(12.0, GSL_MODE_DEFAULT, 100, J);
  sa += ( test_sf_frac_diff(J[1],   4.999718179448405289e-13 ) > TEST_TOL1 );
  sa += ( test_sf_frac_diff(J[5],   7.627813166084551355e-05 ) > TEST_TOL1 );
  sa += ( test_sf_frac_diff(J[7],   2.655620035894568062e-03 ) > TEST_TOL3 );
  sa += ( test_sf_frac_diff(J[10],  6.337025497015601509e-02 ) > TEST_TOL3 );
  sa += ( test_sf_frac_diff(J[15],  0.23666584405476805591 ) > TEST_TOL3 );
  sa += ( test_sf_frac_diff(J[30],  0.14825335109966010021 ) > TEST_TOL3 );
  sa += ( test_sf_frac_diff(J[70],  0.04109913716555364262 ) > TEST_TOL4 );
  sa += ( test_sf_frac_diff(J[99], -0.0015052760501176728  ) > TEST_TOL5 );
  gsl_test(sa, "  gsl_sf_sequence_Jnu_e(12)");
  s += sa;

  sa = 0;
  for(i=0; i<100; i++) {
    J[i] = i * 20;
  }
  gsl_sf_bessel_sequence_Jnu_e(1000.0, GSL_MODE_DEFAULT, 100, J);
  sa += ( test_sf_frac_diff(J[50],  0.04473067294796404088 ) > TEST_TOL5 );
  sa += ( test_sf_frac_diff(J[99],  0.01400619760349853902 ) > TEST_TOL6 );
  gsl_test(sa, "  gsl_sf_sequence_Jnu_e(1000)");
  s += sa;


  return s;
}