test_hyperg.c

开放gsl矩阵运算

  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 100, &r),  3.284529863685482880e+19, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 10, 1, &r),  1.1043089864100000000e+11, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 1, &r),  1.3991152402448957897e+20, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 10, &r),  5.364469916567136000e+19, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 100, &r),  3.909797568000000000e+12, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 100, 500, &r),  8.082625576697984130e+25, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 0.01, &r),  1.6973422555823855798e+64, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 1, &r),  7.086160198304780325e+63, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 1, 10, &r),  5.332862895528712200e+65, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 1, &r),  -7.106713471565790573e+71, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 1, &r),  2.4661377199407186476e+104, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 10, 10, &r),  5.687538583671241287e+68, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, 100, 10, &r),  1.7880761664553373445e+102, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.01, &r),  4.185245354032917715e+137, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 0.1, &r),  2.4234043408007841358e+137, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1, 10, &r),  -1.8987677149221888807e+139, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 10, 10, &r),  -5.682999988842066677e+143, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 100, 10, &r),  2.3410029853990624280e+189, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-90, 1000, 10, &r),  1.9799451517572225316e+271, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -1, 10, &r),  -9.083195466262584149e+64, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -10, 10, &r),  -1.4418257327071634407e+62, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 0.01, &r),  3.0838993811468983931e+93, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-50, -100, 10, &r),  4.014552630378340665e+95, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -100, 10, &r),  2.0556466922347982030e+162, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 10, &r),  1.1778399522973555582e+219, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-100, -200, 100, &r),  9.861313408898201873e+235, TEST_TOL3, GSL_SUCCESS);


  /* U */

  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 0.0001, &r), 1.0000576350699863577, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 1.0, &r), 0.9999403679233247536, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 0.0001, 100.0, &r), 0.9995385992657260887, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1, 0.0001, &r), 1.0009210608660065989, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1.0, 1.0, &r), 0.9999999925484179084, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 1, &r), 13.567851006281412726, TEST_TOL3, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 10, 5, &r), 1.0006265020064596364, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 10, 10, &r), 0.9999244381454633265, TEST_TOL0, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 1, &r),  2.5890615708804247881e+150, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 10, &r),  2.3127845417739661466e+55, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 100, 50, &r), 6402.818715083582554, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 100, 98, &r), 0.9998517867411840044, TEST_TOL2, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 300, &r),  2.5389557274938010716e+213, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 999, &r), 0.9997195294193261604, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.0001, 1000, 1100, &r),  0.9995342990014584713, TEST_TOL1, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_e, (0.5, 1000, 300, &r), 1.1977955438214207486e+217, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 800, &r), 9.103916020464797207e+08, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 1000, 998, &r), 0.21970269691801966806, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (0.5, 0.5, 1.0, &r), 0.7578721561413121060, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 0.0001, &r), 0.9992361337764090785, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 1, &r), 0.4036664068111504538, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (1, 0.0001, 100, &r), 0.009805780851264329587, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (1, 1.2, 2.0, &r), 0.3835044780075602550, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (1, -0.0001, 1, &r), 0.4036388693605999482, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 1, &r),  27.981926466707438538, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 10, &r),  2.4370135607662056809e-8, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (8, 10.5, 100, &r),  1.1226567526311488330e-16, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (10, -2.5, 10, &r),  6.734690720346560349e-14, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 10, &r),  6.787780794037971638e-13, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (10, 2.5, 50, &r),  2.4098720076596087125e-18, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 1, &r),  -3.990841457734147e+6, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 10, &r),  1.307472052129343e+8, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 50, &r),  3.661978424114088e+16, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 90, &r),  8.09469542130868e+19, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 99, &r),  2.546328328942063e+20, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 100, &r),  2.870463201832814e+20, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 1.1, 200, &r),  8.05143453769373e+23, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 0.1, &r),  -3.043016255306515e+20, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 1, &r),  -3.194745265896115e+12, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 4, &r),  -6.764203430361954e+07, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 10, &r),  -2.067399425480545e+09, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 10.1, 50, &r),  4.661837330822824e+14, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 10, &r),  -6.805460513724838e+66, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 50, &r),  -2.081052558162805e+18, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 80, &r),  2.034113191014443e+14, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 100, &r),  6.85047268436107e+13, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-10.5, 100.4, 200, &r),  1.430815706105649e+20, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-19.5, 82.1, 10, &r),  5.464313196201917432e+60, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 10, &r),  -5.5740216266953e+126, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 40, &r),  5.937463786613894e+91, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 50, &r),  -1.631898534447233e+89, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 70, &r),  3.249026971618851e+84, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_e, (-50.5, 100.1, 100, &r),  1.003401902126641e+85, TEST_TOL1, GSL_SUCCESS);


  /* 2F1 */

  TEST_SF(s, gsl_sf_hyperg_2F1_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8.1, 1, 0.5, &r), 0.14147385378899930422, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, 1, -0.5, &r), 4945.136718750000000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, 0.5, &r),  -906.6363636363636364, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, -8, -5.5, -0.5, &r), 24565.363636363636364, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 1, -0.5, &r), -0.006476312098196747669, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, 0.5, &r), 4205.714285714285714, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (8, 8, 5, -0.5, &r), 0.0028489656290296436616, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, 1, 0.99, &r), 1.2363536673577259280e+38 , TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, 0.99, &r), 3.796186436458346579e+46, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -1.5, -0.99, &r), 0.14733409946001025146, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, 0.99, &r), -1.1301780432998743440e+65, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -8.5, -0.99, &r), -8.856462606575344483, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, 0.99, &r), 2.0712920991876073253e+95, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -21.5, -0.99, &r), -74.30517015382249216, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, 0.99, &r),  -3.186778061428268980e+262, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (9, 9, -100.5, -0.99, &r),  2.4454358338375677520, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_e, (25, 25, 1, -0.5, &r), -2.9995530823639545027e-06, TEST_SQRT_TOL0, GSL_SUCCESS);


  /* 2F1 conj */

  TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (1, 1, 1, 0.5, &r), 3.352857095662929028, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, 0.5, &r), 1.7078067538891293983e+09, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, 0.5, &r), 285767.15696901140627, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 1, -0.5, &r), 0.007248196261471276276, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (8, 8, 5, -0.5, &r), 0.00023301916814505902809, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_e, (25, 25, 1, -0.5, &r), 5.1696944096e-06, TEST_SQRT_TOL0, GSL_SUCCESS);

  /* FIXME: the "true" values here may not be so good */
  /*
  TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.01, 1.0, -0.02, &r), 0.999803886708565   , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F0_e, (0.1,  0.5, -0.02, &r), 0.999015947934831   , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F0_e, (1,   1, -0.02, &r), 0.980755496569062    , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F0_e, (8,   8, -0.02, &r), 0.3299059284994299   , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F0_e, (50, 50, -0.02, &r), 2.688995263773233e-13, TEST_TOL0, GSL_SUCCESS);
  */


  /* 2F1 renorm */

  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (1, 1, 1, 0.5, &r), 2.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 1, 0.5, &r), 12451584.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, 0.5, &r), 0.13671875, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, 1, -0.5, &r), 4945.13671875, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, 0.5, &r), -83081.19167659493609, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, -8, -5.5, -0.5, &r), 2.2510895952730178518e+06, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (8, 8, 5, 0.5, &r), 175.2380952380952381, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, 0.99, &r), 1.6063266334913066551e+46, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (9, 9, -1.5, -0.99, &r), 0.06234327316254516616, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -1, 0.5, &r), 4949760.0, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -10, 0.5, &r), 139408493229637632000.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_renorm_e, (5, 5, -100, 0.5, &r), 3.0200107544594411315e+206, TEST_TOL3, GSL_SUCCESS);
  
  /* 2F1 conj renorm */

  TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, 0.99, &r), 5.912269095984229412e+49, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (9, 9, -1.5, -0.99, &r), 0.10834020229476124874, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -1, 0.5, &r), 1.4885106335357933625e+08, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -10, 0.5, &r), 7.968479361426355095e+21, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_2F1_conj_renorm_e, (5, 5, -100, 0.5, &r), 3.1113180227052313057e+208, TEST_TOL3, GSL_SUCCESS);


  return s;
}