test_hyperg.c

开放gsl矩阵运算

  TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.5, -500, &r), 0.0010010030151059555322, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (1, 1.1, -500, &r), 0.00020036137599690208265, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -1, &r),     0.07227645648935938168, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -10, &r),    0.0003192415409695588126, TEST_TOL1, GSL_SUCCESS);
  /*
  sensitive to the pair_ratio hack in hyperg_1F1.c
  TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -100, &r),  -8.293425316123158950e-16, 50.0*TEST_SNGL, GSL_SUCCESS);
  */
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (10, 1.1, -500, &r),  -3.400379216707701408e-23, TEST_TOL2, GSL_SUCCESS);

  TEST_SF_RLX(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -90, &r),   -7.843129411802921440e-22, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -100, &r),   4.632883869540640460e-24, TEST_SQRT_TOL0, GSL_SUCCESS);

  /* FIXME:
     tolerance is poor, but is consistent within reported error
   */
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (50, 1.1, -110.0, &r), 5.642684651305310023e-26, 0.03, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -1, &r),    0.0811637344096042096, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -10, &r),   0.00025945610092231574387, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -50, &r),   2.4284830988994084452e-13, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -90, &r),   2.4468224638378426461e-22, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -99, &r),   1.0507096272617608461e-23, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -100, &r),  1.8315497474210138602e-24, TEST_TOL2, GSL_SUCCESS);

  /* FIXME:
     Reported error is too small.
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -101, &r), -2.3916306291344452490e-24, 0.04, GSL_SUCCESS);
   */

  /* FIXME:
     Reported error is too small.
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 1.1, -110, &r), -4.517581986037732280e-26, TEST_TOL0, GSL_SUCCESS);
   */

  /* FIXME:
     Result is terrible, but reported error is very large, so consistent.
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, 10.1, -220, &r), -4.296130300021696573e-64, TEST_TOL1, GSL_SUCCESS);
  */

  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 10.0, &r), 10959.603204633058116, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -10.1, 1000.0, &r), 2.0942691895502242831e+23, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -100.1, 10.0, &r),  2.6012036337980078062, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 10.0, &r),  22004.341698908631636, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-1000, -1000.1, 200.0, &r), 7.066514294896245043e+86, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -10.1, -10.0, &r),    0.00018469685276347199258, TEST_TOL0, GSL_SUCCESS);
  /*  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-8.1, -1000.1, -10.0, &r),  0.9218280185080036020, TEST_TOL0, GSL_SUCCESS); */
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 1, &r),  16.936141866089601635, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 10, &r),  771534.0349543820541, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10, -5.1, 100, &r),  2.2733956505084964469e+17, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -1, &r),  0.13854540373629275583, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -10, &r),  -9.142260314353376284e+19, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, -100, &r),  -1.7437371339223929259e+87, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 1, &r),  7.516831748170351173, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 10, &r),  1.0551632286359671976e+11, TEST_SQRT_TOL0, GSL_SUCCESS);
  /*
   These come out way off. On the other hand, the error estimates
   are also very large; so much so that the answers are consistent
   within the reported error. Something will need to be done about
   this eventually
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 50, &r),  -7.564755600940346649e+36, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, -50.1, 100, &r),  4.218776962675977e+55, TEST_TOL3, GSL_SUCCESS);
  */
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -8.1, 0.1, &r),  1.1387201443786421724, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-10.5, -11.1, 1, &r),  2.5682766147138452362, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -80.1, 10, &r),  355145.4517305220603, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -102.1, 10, &r),  18678.558725244365016, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 10, &r),  7.342209011101454, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100.5, -500.1, 100, &r),  1.2077443075367177662e+8, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-500.5, -80.1, 2, &r),  774057.8541325341699, TEST_TOL4, GSL_SUCCESS);
  /*
  UNIMPL
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 1, &r),  -2.1213846338338567395e+12, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 10, &r),  -6.624849346145112398e+39, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, 100, &r),  -1.2413466759089171904e+129, TEST_TOL0, GSL_SUCCESS);
  */
  /*
  UNIMPL
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -1, &r),  34456.29405305551691, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -10, &r),  -7.809224251467710833e+07, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (100, -10.1, -100, &r),   -5.214065452753988395e-07, TEST_TOL0, GSL_SUCCESS);
  */
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 1, &r),  0.21519810496314438414, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 10, &r),  8.196123715597869948, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, 100, &r),  -1.4612966715976530293e+20, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 1, &r),  0.0021267655527278456412, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 10, &r),   2.0908665169032186979e-11, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 20.1, 100, &r),  -0.04159447537001340412, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -1, &r),  2.1214770215694685282e+07, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -10, &r),  1.0258848879387572642e+24, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 1.1, -100, &r),  1.1811367147091759910e+67, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -1, &r),  6.965259317271427390, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -10, &r),  1.0690052487716998389e+07, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-100, 50.1, -100, &r),  6.889644435777096248e+36, TEST_TOL3, GSL_SUCCESS);


  /* Bug report from Fernando Pilotto */

  TEST_SF(s, gsl_sf_hyperg_1F1_e, (-2.05, 1.0, 5.05, &r), 3.79393389516785e+00, TEST_TOL3, GSL_SUCCESS);

  /* U for integer parameters */

  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.0001, &r),  8.634088070212725330, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.01, &r),  4.078511443456425847, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 0.5, &r),  0.9229106324837304688, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 2.0, &r),  0.3613286168882225847, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 100, &r),  0.009901942286733018406, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1, 1000, &r),  0.0009990019940238807150, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 0.01, &r),  7.272361203006010000e+16, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1, &r),  1957.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 5, &r),  1.042496, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 8, &r),  0.3207168579101562500, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 50, &r),  0.022660399001600000000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 100, &r),  0.010631236727200000000, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 8, 1000, &r),  0.0010060301203607207200, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 1, &r),  1.7403456103284421000e+16, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 20, 20, &r),  0.22597813610531052969, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 1, &r),  3.374452117521520758e+61, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 50, 50, &r),  0.15394136814987651785, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 0.1, &r),  1.0418325171990852858e+253, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1, &r),  2.5624945006073464385e+154, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 50, &r),  3.0978624160896431391e+07, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 100, &r),  0.11323192555773717475, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 200, &r),  0.009715680951406713589, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 100, 1000, &r),  0.0011085142546061528661, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, 1000, 2000, &r),  0.0009970168547036318206, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 1, &r),  0.29817368116159703717, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1, 10, &r),  0.07816669698940409380, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 1, &r),  0.08271753756946041959, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 5, &r),  0.06127757419425055261, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 10, &r),  0.04656199948873187212, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -10, 20, &r),  0.031606421847946077709, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 0.01, &r),  0.009900000099999796950, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 1, &r),  0.009802970197050404429, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 10, &r),  0.009001648897173103447, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 20, &r),  0.008253126487166557546, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 50, &r),  0.006607993916432051008, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 90, &r),  0.005222713769726871937, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -100, 110, &r),  0.004727658137692606210, TEST_TOL2, GSL_SUCCESS);
  TEST_SF_RLX(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1, &r),   0.0009980029970019970050, TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (1, -1000, 1010, &r),  0.0004971408839859245170, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.001, &r),  0.0007505359326875706975, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 0.5, &r),  6.449509938973479986e-06, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 8, &r),  6.190694573035761284e-10, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 1, 20, &r),  3.647213845460374016e-12, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 1, &r),  0.12289755012652317578, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 10, &r),  5.687710359507564272e-09, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (8, 8, 20, &r),  2.8175404594901039724e-11, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.01, &r),  1.0099979491941914867e+196, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 0.1, &r),  1.0090713562719862833e+97, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 1, &r),  0.009998990209084729106, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (100, 100, 20, &r),  1.3239363905866130603e-131, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 0.01, &r),  3.274012540759009536e+06, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 1, &r),  1.5202710000000000000e+06, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_hyperg_U_int_e, (-10, 1, 10, &r),  1.0154880000000000000e+08, TEST_TOL0, GSL_SUCCESS);