test_sf.c

开放gsl矩阵运算

  TEST_SF(s,  gsl_sf_clausen_e, (100.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);

  return s;
}


int test_coupling(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s, gsl_sf_coupling_3j_e, (0, 1, 1, 0, 1, -1, &r), sqrt(1.0/2.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1, 0, &r), sqrt(1.0/6.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_3j_e, (2, 4, 6, 0, 2, -2, &r), sqrt(8.0/105.0), TEST_TOL0, GSL_SUCCESS);


  TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 2, &r), 1.0/6.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, 2, &r), - sqrt(1.0/6.0) / 10.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_coupling_9j_e, (8, 4, 10, 7, 3, 8, 1, 1, 2, &r), sqrt(7.0/3.0)/60.0, TEST_TOL2, GSL_SUCCESS);

  return s;
}

int test_dawson(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s, gsl_sf_dawson_e, (1.0e-15, &r), 1.0e-15, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_dawson_e, (0.5, &r), 0.4244363835020222959, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_dawson_e, (2.0, &r), 0.30134038892379196603, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_dawson_e, (1000.0, &r), 0.0005000002500003750009, TEST_TOL0, GSL_SUCCESS);
  
  return s;
}

int test_debye(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s, gsl_sf_debye_1_e, (0.1, &r),  0.975277750004723276, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_1_e, (1.0, &r),  0.777504634112248239, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_1_e, (10.0, &r), 0.164443465679946027, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_2_e, (0.1, &r),  0.967083287045302664,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_2_e, (1.0, &r),  0.70787847562782924,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_2_e, (10.0, &r), 0.0479714980201218708, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_3_e, (0.1, &r),  0.962999940487211048,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_3_e, (1.0, &r),  0.674415564077814667,  TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_3_e, (10.0, &r), 0.0192957656903454886, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_debye_4_e, (0.1, &r),  0.960555486124335944,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_4_e, (1.0, &r),  0.654874068886737049,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_debye_4_e, (10.0, &r), 0.00967367556027115896, TEST_TOL0, GSL_SUCCESS);

  return s;
}


int test_elementary(void)
{
  gsl_sf_result r;
  double x = 0.2*DBL_MAX;
  int s = 0;

  TEST_SF(s,  gsl_sf_multiply_e, (-3.0,2.0, &r), -6.0,          TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_multiply_e, (x, 1.0/x, &r),  1.0,          TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_multiply_e, (x, 0.2, &r),    0.04*DBL_MAX, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_multiply_e, (x, 4.0, &r),    0.8*DBL_MAX,  TEST_TOL1, GSL_SUCCESS);
  s += ( gsl_sf_multiply_e(DBL_MAX, 1.1, &r) != GSL_EOVRFLW);
  s += ( gsl_sf_multiply_e(DBL_MIN,  DBL_MIN, &r) != GSL_EUNDRFLW);
  s += ( gsl_sf_multiply_e(DBL_MIN, -DBL_MIN, &r) != GSL_EUNDRFLW);

  return s;
}


int test_ellint(void)
{
  gsl_sf_result r;
  gsl_mode_t mode = GSL_MODE_DEFAULT;
  int s = 0;
  
  TEST_SF(s,  gsl_sf_ellint_Kcomp_e, ( 0.99, mode, &r), 3.3566005233611923760, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Kcomp_e, ( 0.50, mode, &r), 1.6857503548125960429, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Kcomp_e, (0.010, mode, &r), 1.5708355989121522360, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_Ecomp_e, (0.99, mode, &r), 1.0284758090288040010, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Ecomp_e, (0.50, mode, &r), 1.4674622093394271555, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_Ecomp_e, (0.01, mode, &r), 1.5707570561503852873, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_F_e, (M_PI/3.0, 0.99, mode, &r), 1.3065333392738766762, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_F_e, (M_PI/3.0, 0.50, mode, &r), 1.0895506700518854093, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_F_e, (M_PI/3.0, 0.01, mode, &r), 1.0472129063770918952, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_E_e, (M_PI/3.0, 0.99, mode, &r), 0.8704819220377943536, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_E_e, (M_PI/3.0, 0.50, mode, &r), 1.0075555551444720293, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_E_e, (M_PI/3.0, 0.01, mode, &r), 1.0471821963889481104, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_P_e, (M_PI/3.0, 0.99, 0.5, mode, &r), 1.1288726598764099882, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_P_e, (M_PI/3.0, 0.50, 0.5, mode, &r), 0.9570574331323584890, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_ellint_P_e, (M_PI/3.0, 0.01, 0.5, mode, &r), 0.9228868127118118465, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RF_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 12.36441982979439, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RF_e, (1.0, 2.0, 3.0, mode, &r), 0.7269459354689082, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RD_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 34.0932594919337362, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RD_e, (1.0, 2.0, 3.0, mode, &r), 0.2904602810289906, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RC_e, (1.0, 2.0, mode, &r), 0.7853981633974482, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_ellint_RJ_e, (2.0, 3.0, 4.0, 5.0, mode, &r), 0.1429757966715675, TEST_TOL0, GSL_SUCCESS);


  return s;
}


int test_erf(void)
{
  gsl_sf_result r;
  int s = 0;

  TEST_SF(s, gsl_sf_erfc_e, (-10.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (-5.0000002, &r), 1.9999999999984625433, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (-5.0, &r), 1.9999999999984625402, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (-1.0, &r), 1.8427007929497148693, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (-0.5, &r), 1.5204998778130465377, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (1.0, &r), 0.15729920705028513066, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (3.0, &r), 0.000022090496998585441373, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (7.0, &r), 4.183825607779414399e-23, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erfc_e, (10.0, &r), 2.0884875837625447570e-45, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_log_erfc_e, (-1.0, &r), log(1.842700792949714869), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (-0.1, &r), 0.106576400586522485015, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (-1e-10, &r),  1.1283791670318505967e-10, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (0.0, &r), log(1.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (1e-10, &r), -1.128379167159174551e-10, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (0.001, &r), -0.0011290158896213548027, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (0.1, &r), -0.119304973737395598329, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (1.0, &r), log(0.15729920705028513066), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_log_erfc_e, (10.0, &r), log(2.0884875837625447570e-45), TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_erf_e, (-10.0, &r), -1.0000000000000000000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erf_e, (0.5, &r), 0.5204998778130465377, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erf_e, (1.0, &r), 0.8427007929497148693, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erf_e, (10.0, &r), 1.0000000000000000000, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_erf_Z_e, (1.0, &r),  0.24197072451914334980,   TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_erf_Q_e, (10.0, &r), 7.619853024160526066e-24, TEST_TOL2, GSL_SUCCESS);

  return s;
}


int test_exp(void)
{
  gsl_sf_result r;
  gsl_sf_result_e10 re;
  double x;
  int sa;
  int s = 0;

  TEST_SF(s,  gsl_sf_exp_e, (-10.0, &r), exp(-10.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_exp_e, ( 10.0, &r), exp( 10.0), TEST_TOL0, GSL_SUCCESS);

  sa = 0;
  sa += gsl_sf_exp_e10_e(1.0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
  sa += ( re.err > TEST_TOL1 );
  sa += ( re.e10 != 0 );
  gsl_test(sa, "  gsl_sf_exp_e10_e(1.0, &re)");

  sa = 0;
  sa += gsl_sf_exp_e10_e(2000.0, &re);
  sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 );
  sa += ( re.err > TEST_TOL5 );
  sa += ( re.e10 != 868 );
  gsl_test(sa, "  gsl_sf_exp_e10_e(2000.0, &re)");


  TEST_SF(s, gsl_sf_exp_err_e, (-10.0, TEST_TOL1, &r), exp(-10.0), TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_err_e, ( 10.0, TEST_TOL1, &r), exp( 10.0), TEST_TOL1, GSL_SUCCESS);

  sa = 0;
  sa += gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL1 );
  sa += ( re.err > 32.0 * TEST_SQRT_TOL0 );
  sa += ( re.e10 != 0 );
  gsl_test(sa, "  gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re)");

  sa = 0;
  sa += gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re);
  sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 );
  sa += ( re.err > 1.0e-07 );
  sa += ( re.e10 != 868 );
  gsl_test(sa, "  gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re)");


  x = 0.8*GSL_LOG_DBL_MAX;
  TEST_SF(s, gsl_sf_exp_mult_e, (-10.0,  1.0e-06, &r), 1.0e-06*exp(-10.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (-10.0,  2.0, &r),     2.0*exp(-10.0),     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, -2.0, &r),    -2.0*exp(-10.0),     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0,  1.0e-06, &r), 1.0e-06*exp( 10.0), TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0, -2.0, &r),    -2.0*exp( 10.0),     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.00001, &r),      1.00001*exp(x),     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000001, &r),     1.000001*exp(x),    TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000000001, &r),  1.000000001*exp(x), TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 100.0, &r),        100.0*exp(x),       TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.0e+20, &r),      1.0e+20*exp(x),     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_e, (x, exp(-x)*exp(M_LN2), &r),  2.0, TEST_TOL4, GSL_SUCCESS );

  TEST_SF(s, gsl_sf_exp_mult_err_e, (-10.0, TEST_SQRT_TOL0, 2.0, TEST_SQRT_TOL0, &r), 2.0*exp(-10.0), TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_exp_mult_err_e, (x, TEST_SQRT_TOL0*x, exp(-x)*exp(M_LN2), TEST_SQRT_TOL0*x, &r),  2.0, TEST_SQRT_TOL0, GSL_SUCCESS );

  sa = 0;
  sa += gsl_sf_exp_mult_e10_e(1.0, 1.0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
  sa += ( re.err > TEST_TOL2 );
  sa += ( re.e10 != 0 );
  gsl_test(sa, "gsl_sf_exp_mult_e10_e(1.0, 1.0, &re)");

  sa = 0;
  sa += gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re);
  sa += ( test_sf_frac_diff(re.val, 1.9700711140165661 ) > TEST_TOL3 );
  sa += ( re.err > 1.0e-12 );
  sa += ( re.e10 != 634 );
  gsl_test(sa, "gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re)");

  sa = 0;
  sa += gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re);
  sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
  sa += ( re.err > TEST_TOL2 );