test_gamma.c

开放gsl矩阵运算

  TEST_SF(s,   gsl_sf_doublefact_e, (7, &r), 105.0 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_doublefact_e, (33, &r), 6.332659870762850625e+18 , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_lnfact_e, (0, &r), 0.0 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnfact_e, (1, &r), 0.0 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnfact_e, (7, &r), 8.525161361065414300 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnfact_e, (33, &r), 85.05446701758151741 , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_lndoublefact_e, (0, &r), 0.0  , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lndoublefact_e, (7, &r), 4.653960350157523371  , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lndoublefact_e, (33, &r), 43.292252022541719660 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lndoublefact_e, (34, &r), 45.288575519655959140 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lndoublefact_e, (1034, &r), 3075.6383796271197707 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lndoublefact_e, (1035, &r), 3078.8839081731809169 , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_lnchoose_e, (7,3, &r), 3.555348061489413680 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnchoose_e, (5,2, &r), 2.302585092994045684 , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_choose_e, (7,3, &r), 35.0 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_choose_e, (5,2, &r), 10.0 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_choose_e, (500,200, &r), 5.054949849935532221e+144 , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_lnpoch_e, (5, 1.0/65536.0, &r), 0.000022981557571259389129, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnpoch_e, (5, 1.0/256.0, &r),   0.005884960217985189004,    TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnpoch_e, (7,3, &r), 6.222576268071368616, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_lnpoch_e, (5,2, &r), 3.401197381662155375, TEST_TOL0, GSL_SUCCESS);

  TEST_SF_SGN(s, gsl_sf_lnpoch_sgn_e, (-4.5, 0.25, &r, &sgn), 0.7430116475119920117, TEST_TOL1, 1.0, GSL_SUCCESS);
  TEST_SF_SGN(s, gsl_sf_lnpoch_sgn_e, (-4.5, 1.25, &r, &sgn), 2.1899306304483174731, TEST_TOL1, -1.0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_poch_e, (7,3, &r), 504.0 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_poch_e, (5,2, &r), 30.0  , TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_poch_e, (5,1.0/256.0, &r), 1.0059023106151364982 , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_pochrel_e, (7,3, &r), 503.0/3.0, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pochrel_e, (5,2, &r), 29.0/2.0, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pochrel_e, (5,0.01, &r), 1.5186393661368275330, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pochrel_e, (-5.5,0.01, &r), 1.8584945633829063516, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pochrel_e, (-5.5,-1.0/8.0, &r), 1.0883319303552135488, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pochrel_e, (-5.5,-1.0/256.0, &r), 1.7678268037726177453, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_pochrel_e, (-5.5,-11.0, &r), 0.09090909090939652475, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_gamma_inc_P_e, (0.001, 0.001, &r), 0.9936876467088602902, TEST_TOL0, GSL_SUCCESS) ;
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (0.001, 1.0, &r), 0.9997803916424144436, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (0.001, 10.0, &r), 0.9999999958306921828, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (1.0, 0.001, &r), 0.0009995001666250083319, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (1.0, 1.01, &r), 0.6357810204284766802, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (1.0, 10.0, &r), 0.9999546000702375151, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (10.0, 10.01, &r), 0.5433207586693410570, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (10.0, 20.0, &r), 0.9950045876916924128, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (1000.0, 1000.1, &r), 0.5054666401440661753, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (1000.0, 2000.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
  
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (0.001, 0.001, &r), 0.006312353291139709793, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (0.001, 1.0, &r), 0.00021960835758555639171, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (0.001, 2.0, &r), 0.00004897691783098147880, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (0.001, 5.0, &r), 1.1509813397308608541e-06, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (1.0, 0.001, &r), 0.9990004998333749917, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (1.0, 1.01, &r), 0.3642189795715233198, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (1.0, 10.0, &r), 0.00004539992976248485154, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (10.0, 10.01, &r), 0.4566792413306589430, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (10.0, 100.0, &r), 1.1253473960842733885e-31, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (1000.0, 1000.1, &r), 0.4945333598559338247, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (1000.0, 2000.0, &r), 6.847349459614753180e-136, TEST_TOL2, GSL_SUCCESS);

  /* designed to trap the a-x=1 problem */
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (100,  99.0, &r), 0.5266956696005394, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_Q_e, (200, 199.0, &r), 0.5188414119121281, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (100,  99.0, &r), 0.4733043303994607, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_gamma_inc_P_e, (200, 199.0, &r), 0.4811585880878718, TEST_TOL2, GSL_SUCCESS);


  TEST_SF(s, gsl_sf_lnbeta_e, (1.0e-8, 1.0e-8, &r),  19.113827924512310617 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0e-8, 0.01, &r),  18.420681743788563403 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0e-8, 1.0, &r),  18.420680743952365472 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0e-8, 10.0, &r),  18.420680715662683009 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0e-8, 1000.0, &r),  18.420680669107656949 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (0.1, 0.1, &r), 2.9813614810376273949 , TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (0.1, 1.0, &r),  2.3025850929940456840 , TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (0.1, 100.0, &r),  1.7926462324527931217 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (0.1, 1000, &r),  1.5619821298353164928 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0, 1.00025, &r),  -0.0002499687552073570, TEST_TOL4, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0, 1.01, &r),  -0.009950330853168082848 , TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (1.0, 1000.0, &r),  -6.907755278982137052 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (100.0, 100.0, &r),  -139.66525908670663927 , TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (100.0, 1000.0, &r),  -336.4348576477366051 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_lnbeta_e, (100.0, 1.0e+8, &r),  -1482.9339185256447309 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_e, (1.0,   1.0, &r), 1.0                   , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_e, (1.0, 1.001, &r), 0.9990009990009990010 , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_e, (1.0,   5.0, &r), 0.2                   , TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_e, (1.0,  100.0, &r), 0.01                  , TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_e, (10.0, 100.0, &r), 2.3455339739604649879e-15 , TEST_TOL2, GSL_SUCCESS);


  TEST_SF(s,  gsl_sf_beta_inc_e, (1.0, 1.0, 0.0, &r), 0.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (1.0, 1.0, 1.0, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (0.1, 0.1, 1.0, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0,  1.0, 0.5, &r), 0.5, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 0.1,  1.0, 0.5, &r), 0.9330329915368074160, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (10.0,  1.0, 0.5, &r), 0.0009765625000000000000, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (50.0,  1.0, 0.5, &r), 8.881784197001252323e-16, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0,  0.1, 0.5, &r), 0.06696700846319258402, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0, 10.0, 0.5, &r), 0.99902343750000000000, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0, 50.0, 0.5, &r), 0.99999999999999911180, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0,  1.0, 0.1, &r), 0.10, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0,  2.0, 0.1, &r), 0.19, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 1.0,  2.0, 0.9, &r), 0.99, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (50.0, 60.0, 0.5, &r), 0.8309072939016694143, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (90.0, 90.0, 0.5, &r), 0.5, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, ( 500.0,  500.0, 0.6, &r), 0.9999999999157549630, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (5000.0, 5000.0, 0.4, &r), 4.518543727260666383e-91, TEST_TOL5, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (5000.0, 5000.0, 0.6, &r), 1.0, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_beta_inc_e, (5000.0, 2000.0, 0.6, &r), 8.445388773903332659e-89, TEST_TOL5, GSL_SUCCESS);


  return s;
}