CAMLprim value ml_gsl_sf_bessel_jl_steed_array(value x, value x_arr)
{
gsl_sf_bessel_jl_steed_array(Double_array_length(x_arr)-1,
Double_val(x),
Double_array_val(x_arr));
return Val_unit;
}
int test_bessel(void)
{
gsl_sf_result r;
int i;
int s = 0;
int sa;
TEST_SF(s, gsl_sf_bessel_J0_e, (0.1, &r), 0.99750156206604003230, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J0_e, (2.0, &r), 0.22389077914123566805, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J0_e, (100.0, &r), 0.019985850304223122424, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J0_e, (1.0e+10, &r), 2.1755917502468917269e-06, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J1_e, (0.1, &r), 0.04993752603624199756, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J1_e, (2.0, &r), 0.57672480775687338720, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J1_e, (100.0, &r), -0.07714535201411215803, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_J1_e, (1.0e+10, &r), -7.676508175684157103e-06, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (4, 0.1, &r), 2.6028648545684032338e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (5, 2.0, &r), 0.007039629755871685484, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (10, 20.0, &r), 0.18648255802394508321, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (100, 100.0, &r), 0.09636667329586155967, TEST_TOL0, GSL_SUCCESS);
/* exercise the BUG#3 problem */
TEST_SF(s, gsl_sf_bessel_Jn_e, (2, 900.0, &r), -0.019974345269680646400, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (2, 15000.0, &r), -0.0020455820181216382666, TEST_TOL4, GSL_SUCCESS);
#ifdef TEST_LARGE
TEST_SF(s, gsl_sf_bessel_Jn_e, (0, 1.0e+10, &r), 2.1755917502468917269e-06, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (1, 1.0e+10, &r), -7.676508175684157103e-06, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jn_e, (0, 20000, &r), -7.676508175684157103e-06, TEST_TOL4, GSL_SUCCESS);
#endif
TEST_SF(s, gsl_sf_bessel_Y0_e, (0.1, &r), -1.5342386513503668441, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y0_e, (2, &r), 0.5103756726497451196, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y0_e, (256.0, &r), -0.03381290171792454909 , TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y0_e, (4294967296.0, &r), 3.657903190017678681e-06, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y1_e, (0.1, &r), -6.45895109470202698800, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y1_e, (2, &r), -0.10703243154093754689, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y1_e, (100.0, &r), -0.020372312002759793305, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Y1_e, (4294967296.0, &r), 0.000011612249378370766284, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Yn_e, (4, 0.1, &r), -305832.29793353160319, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Yn_e, (5, 2, &r), -9.935989128481974981, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Yn_e, (100, 100.0, &r), -0.16692141141757650654, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Yn_e, (100, 4294967296.0, &r), 3.657889671577715808e-06, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Yn_e, (1000, 4294967296.0, &r), 3.656551321485397501e-06, 2.0e-05, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Yn_e, (2, 15000.0, &r), -0.006185217273358617849, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (1e-10, &r), 0.99999999990000000001, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (0.1, &r), 0.90710092578230109640, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (2, &r), 0.30850832255367103953, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (100.0, &r), 0.03994437929909668265, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_scaled_e, (65536.0, &r), 0.0015583712551952223537, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (0.1, &r), 0.04529844680880932501, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (2, &r), 0.21526928924893765916, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (100.0, &r), 0.03974415302513025267, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_scaled_e, (65536.0, &r), 0.0015583593657207350452, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( -4, 0.1, &r), 2.3575258620054605307e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( 4, 0.1, &r), 2.3575258620054605307e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( 5, 2.0, &r), 0.0013297610941881578142, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( 100, 100.0, &r), 1.7266862628167695785e-22, TEST_TOL0, GSL_SUCCESS);
/* BJG: the "exact" values in the following two tests were computed from the
taylor series for I_nu using "long double" and rescaling. The last few digits
are inaccurate due to cumulative roundoff. */
TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( 2, 1e7, &r), 1.261566024466441648e-04, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_scaled_e, ( 2, 1e8, &r), 3.989422729213446112e-05, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_e, (0.1, &r), 1.0025015629340956014, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_e, (2.0, &r), 2.2795853023360672674, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I0_e, (100.0, &r), 1.0737517071310738235e+42, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_e, (0.1, &r), 0.05006252604709269211, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_e, (2.0, &r), 1.59063685463732906340, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_I1_e, (100.0, &r), 1.0683693903381624812e+42, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_e, ( 4, 0.1, &r), 2.6054690212996573677e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_e, ( 5, 2.0, &r), 0.009825679323131702321, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_In_e, ( 100, 100.0, &r), 4.641534941616199114e+21, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (0.1, &r), 2.6823261022628943831, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (2.0, &r), 0.8415682150707714179, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K0_scaled_e, (100.0, &r), 0.1251756216591265789, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (0.1, &r), 10.890182683049696574, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (2.0, &r), 1.0334768470686885732, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K1_scaled_e, (100.0, &r), 0.1257999504795785293, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, ( 4, 0.1, &r), 530040.2483725626207, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, ( 5, 2.0, &r), 69.68655087607675118, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Kn_scaled_e, ( 100, 100.0, &r), 2.0475736731166756813e+19, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K0_e, (0.1, &r), 2.4270690247020166125, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K0_e, (2.0, &r), 0.11389387274953343565, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K0_e, (100.0, &r), 4.656628229175902019e-45, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K1_e, (0.1, &r), 9.853844780870606135, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K1_e, (2.0, &r), 0.13986588181652242728, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_K1_e, (100.0, &r), 4.679853735636909287e-45, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Kn_e, ( 4, 0.1, &r), 479600.2497925682849, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Kn_e, ( 5, 2.0, &r), 9.431049100596467443, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Kn_e, ( 100, 100.0, &r), 7.617129630494085416e-25, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j0_e, (-10.0, &r), -0.05440211108893698134, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j0_e, (0.001, &r), 0.9999998333333416667, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j0_e, ( 1.0, &r), 0.84147098480789650670, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j0_e, ( 10.0, &r), -0.05440211108893698134, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j0_e, (100.0, &r), -0.005063656411097587937, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j0_e, (1048576.0, &r), 3.1518281938718287624e-07, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j1_e, (-10.0, &r), -0.07846694179875154709, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j1_e, (0.01, &r), 0.003333300000119047399, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j1_e, ( 1.0, &r), 0.30116867893975678925, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j1_e, ( 10.0, &r), 0.07846694179875154709, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j1_e, (100.0, &r), -0.008673825286987815220, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j1_e, (1048576.0, &r), -9.000855242905546158e-07, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j2_e, (-10.0, &r), 0.07794219362856244547, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j2_e, (0.01, &r), 6.666619047751322551e-06, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j2_e, ( 1.0, &r), 0.06203505201137386110, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j2_e, ( 10.0, &r), 0.07794219362856244547, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j2_e, (100.0, &r), 0.004803441652487953480, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_j2_e, (1048576.0, &r), -3.1518539455252413111e-07, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (0, 0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (1, 10.0, &r), 0.07846694179875154709000, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (5, 1.0, &r), 0.00009256115861125816357, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (10, 10.0, &r), 0.06460515449256426427, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (100, 100.0, &r), 0.010880477011438336539, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (2000, 1048576.0, &r), 7.449384239168568534e-07, TEST_SQRT_TOL0, GSL_SUCCESS);
/* related to BUG#3 problem */
TEST_SF(s, gsl_sf_bessel_jl_e, (2, 900.0, &r), -0.0011089115568832940086, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_jl_e, (2, 15000.0, &r), -0.00005955592033075750554, TEST_TOL4, GSL_SUCCESS);
/* Bug report by Mario Santos, value computed from AS 10.1.8 */
TEST_SF(s, gsl_sf_bessel_jl_e, (100, 1000.0, &r), -0.00025326311230945818285, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y0_e, (0.001, &r), -999.99950000004166670, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y0_e, ( 1.0, &r), -0.5403023058681397174, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y0_e, ( 10.0, &r), 0.08390715290764524523, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y0_e, (100.0, &r), -0.008623188722876839341, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y0_e, (65536.0, &r), 0.000011014324202158573930, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y0_e, (4294967296.0, &r), 2.0649445131370357007e-10, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y1_e, ( 0.01, &r), -10000.499987500069444, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y1_e, ( 1.0, &r), -1.3817732906760362241, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y1_e, ( 10.0, &r), 0.06279282637970150586, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y1_e, (100.0, &r), 0.004977424523868819543, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y1_e, (4294967296.0, &r), 1.0756463271573404688e-10, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y2_e, ( 0.01, &r), -3.0000500012499791668e+06, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y2_e, ( 1.0, &r), -3.605017566159968955, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y2_e, ( 10.0, &r), -0.06506930499373479347, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y2_e, (100.0, &r), 0.008772511458592903927, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_y2_e, (4294967296.0, &r), -2.0649445123857054207e-10, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (0, 0.01, &r), -99.995000041666528, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (0, 1.0, &r), -0.54030230586813972, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (1, 10.0, &r), 0.062792826379701506, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (5, 1.0, &r), -999.44034339223641, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (10, 0.01, &r), -6.5473079797378378e+30, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (10, 10.0, &r), -0.172453672088057849, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (100, 1.0, &r), -6.6830794632586775e+186, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (100, 100.0, &r), -0.0229838504915622811, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_yl_e, (2000, 1048576.0, &r), 5.9545201447146155e-07, TEST_SQRT_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (0.1, &r), 0.9063462346100907067, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (2.0, &r), 0.24542109027781645493, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i0_scaled_e, (100.0, &r), 0.005000000000000000000, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (0.1, &r), 0.030191419289002226846, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (2.0, &r), 0.131868364583275317610, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i1_scaled_e, (100.0, &r), 0.004950000000000000000, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (0.1, &r), 0.0006036559400239012567, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (2.0, &r), 0.0476185434029034785100, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_i2_scaled_e, (100.0, &r), 0.0048515000000000000000, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 0, 0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 1, 0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 4, 0.001, &r), 1.0571434341190365013e-15, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 4, 0.1, &r), 9.579352242057134927e-08, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 5, 2.0, &r), 0.0004851564602127540059, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 5, 100.0, &r), 0.004300446777500000000, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_il_scaled_e, ( 100, 100.0, &r), 1.3898161964299132789e-23, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k0_scaled_e, (0.1, &r), 15.707963267948966192, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k0_scaled_e, (2.0, &r), 0.7853981633974483096, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k0_scaled_e, (100.0, &r), 0.015707963267948966192, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k1_scaled_e, (0.1, &r), 172.78759594743862812, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k1_scaled_e, (2.0, &r), 1.1780972450961724644, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k1_scaled_e, (100.0, &r), 0.015865042900628455854, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k2_scaled_e, (0.1, &r), 5199.335841691107810, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k2_scaled_e, (2.0, &r), 2.5525440310417070063, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_k2_scaled_e, (100.0, &r), 0.016183914554967819868, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_kl_scaled_e, ( 4, 1.0/256.0, &r), 1.8205599816961954439e+14, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_kl_scaled_e, ( 4, 1.0/8.0, &r), 6.1173217814406597530e+06, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_kl_scaled_e, ( 5, 2.0, &r), 138.10735829492005119, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_kl_scaled_e, ( 100, 100.0, &r), 3.985930768060258219e+18, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.0001, 1.0, &r), 0.7652115411876708497, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.0001, 10.0, &r), -0.2459270166445205, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.0009765625, 10.0, &r), -0.2458500798634692, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.75, 1.0, &r), 0.5586524932048917478, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (0.75, 10.0, &r), -0.04968928974751508135, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, ( 1.0, 0.001, &r), 0.0004999999375000026, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, ( 1.0, 1.0, &r), 0.4400505857449335160, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, ( 1.75, 1.0, &r), 0.168593922545763170103, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (30.0, 1.0, &r), 3.482869794251482902e-42, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (30.0, 100.0, &r), 0.08146012958117222297, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (10.0, 1.0, &r), 2.6306151236874532070e-10, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (10.0, 100.0, &r), -0.05473217693547201474, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (10.2, 100.0, &r), -0.03548919161046526864, TEST_TOL2, GSL_SUCCESS);
/* related to BUG#3 problem */
TEST_SF(s, gsl_sf_bessel_Jnu_e, (2.0, 900.0, &r), -0.019974345269680646400, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Jnu_e, (2.0, 15000.0, &r), -0.0020455820181216382666, TEST_TOL4, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (0.0001, 1.0, &r), 0.08813676933044478439, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (0.0001,10.0, &r), 0.05570979797521875261, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 0.75, 1.0, &r), -0.6218694174429746383, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 0.75, 10.0, &r), 0.24757063446760384953, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 1.0, 0.001, &r), -636.6221672311394281, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, ( 1.0, 1.0, &r), -0.7812128213002887165, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (30.0, 1.0, &r), -3.0481287832256432162e+39, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (30.0, 100.0, &r), 0.006138839212010033452, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (10.0, 1.0, &r), -1.2161801427868918929e+08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (10.0, 100.0, &r), 0.05833157423641492875, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Ynu_e, (10.2, 100.0, &r), 0.07169383985546287091, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (0.0001,10.0, &r), 0.12783333709581669672, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, ( 1.0, 0.001, &r), 0.0004995003123542213370, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, ( 1.0, 1.0, &r), 0.20791041534970844887, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (30.0, 1.0, &r), 1.3021094983785914437e-42, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (30.0, 100.0, &r), 0.0004486987756920986146, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (10.0, 1.0, &r), 1.0127529864692066036e-10, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (10.0, 100.0, &r), 0.024176682718258828365, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_scaled_e, (10.2, 100.0, &r), 0.023691628843913810043, TEST_TOL3, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, (0.0001,10.0, &r), 2815.7166269770030352, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, ( 1.0, 0.001, &r), 0.0005000000625000026042, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, ( 1.0, 1.0, &r), 0.5651591039924850272, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, (30.0, 1.0, &r), 3.539500588106447747e-42, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, (30.0, 100.0, &r), 1.2061548704498434006e+40, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, (10.0, 1.0, &r), 2.7529480398368736252e-10, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, (10.0, 100.0, &r), 6.498975524720147799e+41, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Inu_e, (10.2, 100.0, &r), 6.368587361287030443e+41, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (0.0001,10.0, &r), 0.3916319346235421817, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, ( 1.0, 0.001, &r), 1000.9967345590684524, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, ( 1.0, 1.0, &r), 1.6361534862632582465, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (30.0, 1.0, &r), 1.2792629867539753925e+40, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (30.0, 100.0, &r), 10.673443449954850040, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 1.0, &r), 4.912296520990198599e+08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 100.0, &r), 0.20578687173955779807, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 1000.0, &r), 0.04165905142800565788, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.0, 1.0e+8, &r), 0.00012533147624060789938, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_scaled_e, (10.2, 100.0, &r), 0.20995808355244385075, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (0.0001,0.001, &r), 7.023689431812884141, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (0.0001,10.0, &r), 0.000017780062324654874306, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, ( 1.0, 0.001, &r), 999.9962381560855743, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, ( 1.0, 1.0, &r), 0.6019072301972345747, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (10.0, 0.001, &r), 1.8579455483904008064e+38, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (10.0, 1.0, &r), 1.8071328990102945469e+08, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (10.0, 100.0, &r), 7.655427977388100611e-45, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (10.2, 100.0, &r), 7.810600225948217841e-45, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (30.0, 1.0, &r), 4.706145526783626883e+39, TEST_TOL1, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_Knu_e, (30.0, 100.0, &r), 3.970602055959398739e-43, TEST_TOL2, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (0.0001,1.0e-100, &r), 5.439794449319847, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (0.0001,0.0001, &r), 2.232835507214331, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (0.0001,10.0, &r), -10.93743282256098, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 1.0e-100, &r), 230.2585092994045, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 1.0e-10, &r), 23.025850929940456840, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 0.001, &r), 6.907751517131146, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, ( 1.0, 1.0, &r), -0.5076519482107523309, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (30.0, 1.0e-100, &r), 6999.113586185543475, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (30.0, 1.0, &r), 91.34968784026325464, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (30.0, 100.0, &r), -97.63224126416760932, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (100.0, 1.0e-100, &r), 23453.606706185466825, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (100.0, 1.0, &r), 427.7532510250188083, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (100.0, 100.0, &r), -55.53422771502921431, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (1000.0, 1.0e-100, &r), 236856.183755993135, TEST_TOL0, GSL_SUCCESS);
TEST_SF(s, gsl_sf_bessel_lnKnu_e, (10000.0, 1.0e-100, &r), 2.39161558914890695e+06, TEST_TOL0, GSL_SUCCESS);
sa = 0;
gsl_sf_bessel_Jn_array(3, 38, 1.0, J);
sa += ( test_sf_frac_diff(J[0], 0.0195633539826684059190 ) > TEST_TOL1);
sa += ( test_sf_frac_diff(J[1], 0.0024766389641099550438 ) > TEST_TOL1);
sa += ( test_sf_frac_diff(J[10], 1.9256167644801728904e-14 ) > TEST_TOL1);
sa += ( test_sf_frac_diff(J[35], 6.911232970971626272e-57 ) > TEST_TOL1);
gsl_test(sa, " gsl_sf_bessel_Jn_array");
s += sa;
sa = 0;
gsl_sf_bessel_Yn_array(3, 38, 1.0, Y);
sa += ( test_sf_frac_diff(Y[0], -5.821517605964728848 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(Y[1], -33.27842302897211870 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(Y[10], -1.2753618701519837595e+12 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(Y[35], -1.2124435663593357154e+54 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_Yn_array");
s += sa;
sa = 0;
gsl_sf_bessel_In_scaled_array(3, 38, 1.0, I);
sa += ( test_sf_frac_diff(I[0], 0.0081553077728142938170 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(I[1], 0.0010069302573377758637 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(I[10], 7.341518665628926244e-15 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(I[35], 2.5753065298357542893e-57 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_In_scaled_array");
s += sa;
sa = 0;
gsl_sf_bessel_In_array(3, 38, 1.0, Y);
sa += ( test_sf_frac_diff(Y[0], 0.0221684249243319024760 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(Y[1], 0.0027371202210468663251 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(Y[10], 1.9956316782072007564e-14 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(Y[35], 7.000408942764452901e-57 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_In_array");
s += sa;
sa = 0;
gsl_sf_bessel_Kn_array(3, 38, 1.0, K);
sa += ( test_sf_frac_diff(K[0], 7.101262824737944506 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(K[1], 44.23241584706284452 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(K[10], 1.9215763927929940846e+12 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(K[35], 1.8789385023806051223e+54 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_Kn_array");
s += sa;
sa = 0;
gsl_sf_bessel_Kn_scaled_array(3, 38, 1.0, K);
sa += ( test_sf_frac_diff(K[0], 19.303233695596904277 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(K[1], 120.23617222591483717 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(K[10], 5.223386190525076473e+12 ) > TEST_TOL0 );
sa += ( test_sf_frac_diff(K[35], 5.107484387813251411e+54 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_Kn_scaled_array");
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(99, 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 );
sa += ( test_sf_frac_diff(J[80], 1.136352423414503264e-144 ) > TEST_TOL1 );
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;
{
double Y0[1];
sa = 0;
gsl_sf_bessel_yl_array(0, 1.0, Y0);
sa += ( test_sf_frac_diff(Y0[0], -0.5403023058681397174 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_yl_array (lmax=0)");
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_il_scaled_array(50, 0.0, I);
sa += ( test_sf_frac_diff(I[0], 1.0 ) > TEST_TOL2 );
sa += ( test_sf_frac_diff(I[1], 0.0 ) > TEST_TOL2 );
sa += ( test_sf_frac_diff(I[10], 0.0 ) > TEST_TOL2 );
sa += ( test_sf_frac_diff(I[50], 0.0 ) > TEST_TOL2 );
gsl_test(sa, " gsl_sf_bessel_il_scaled_array (L=0)");
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;
{
double K0[1];
sa = 0;
gsl_sf_bessel_kl_scaled_array(0, 1.0, K0);
sa += ( test_sf_frac_diff(K[0], 1.5707963267948966192 ) > TEST_TOL0 );
gsl_test(sa, " gsl_sf_bessel_kl_scaled_array (lmax=0)");
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;
}
//------------------------------------------------------------------------------
//void CKonst(int lmax, double *cma, double *cpa, double *cza,
// double *KmLm, double *KoLo, double *KpLM,
// double *KmlM, double *Kolo, double *Kplm){
// int i=0;
// int l, m;
// for(l=0;l<=lmax;l++){
// for(m=-l;m<=l;m++){
// cma[i]=cm(l,m);
// cza[i]=m;
// cpa[i]=cp(l,m);
// KmLm[i]=Km(l+1,m,m-1);
// KoLo[i]=Ko(l+1,m,m );
// KpLM[i]=Kp(l+1,m,m+1);
// KmlM[i]=Km(l ,m,m+1);
// Kolo[i]=Ko(l ,m,m );
// Kplm[i]=Kp(l ,m,m-1);
// i++;
// }
// }
//}
////------------------------------------------------------------------------------
//// CALCULATION OF CONSTANTS - ONE MORE LOOP - POSITION INDEPENDENT
////------------------------------------------------------------------------------
//// L DEPENDENT
//double CL[LMAX];
//double LL[LMAX];
//// CONSTANTS FOR X
//double CM[LMAX];
//double CZ[LMAX];
//double CP[LMAX];
//// CONSTANTS FOR Y AND V
//KmLm[LMAX];
//KoLo[LMAX];
//KpLM[LMAX];
//KmlM[LMAX];
//Kolo[LMAX];
//Kplm[LMAX];
//// SINGLE LOOP
//for(int l=1;l<=lmax;l++){
// for(int m=-l; m<=l; m++){
// CL[jlm(l,m)]=l;
// LL[jlm(l,m)]=2*l+1;
// CM[jlm(l,m)]=cm(l,m);
// CZ[jlm(l,m)]=m;
// CP[jlm(l,m)]=cp(l,m);
// KmLm[jlm(l,m)]=Km(l+1,m,m-1);
// KoLo[jlm(l,m)]=Ko(l+1,m,m );
// KpLM[jlm(l,m)]=Kp(l+1,m,m+1);
// KmlM[jlm(l,m)]=Km(l ,m,m+1);
// Kolo[jlm(l,m)]=Ko(l ,m,m );
// Kplm[jlm(l,m)]=Kp(l ,m,m-1);
// }
//}
//------------------------------------------------------------------------------
// POSITION DEPENDENT CALCULATIONS - MULTIPLES LOOPS - COMPLETE CALCULATIONS
//------------------------------------------------------------------------------
void VectorSphericalWaveFunctions(double *k,double *x, double *y, double *z,int *lmax,
double complex *GTE, double complex *GTM,
double complex *Em, double complex *Ez, double complex *Ep,
double complex *Hm, double complex *Hz, double complex *Hp
){
// printf("%d\t%E\t%E\t%E\t%E\n",*lmax+1,*k,*x,*y,*z);
int l,m;
int LMAX=*lmax*(*lmax+2);
int LMAXE=(*lmax+1)*(*lmax+3);
double cph;
double sph;
double rho=sqrt(*x*(*x)+*y*(*y));
double r=sqrt(rho*rho+*z*(*z));
double sth=rho/r;
double cth=*z/r;
if((*x==0)&&(*y==0)){
cph=1;
sph=0;
}else{
cph=*x/rho;
sph=*y/rho;
}
// Spherical Bessel Funtions
double JLM[*lmax+2];
// double *JLM=&JLM0[0];
gsl_sf_bessel_jl_steed_array(*lmax+1,*k*r,JLM);
/* CALCULATIONS OK
for(l=0;l<(*lmax+2);l++){
printf("%d\t%f\t%E\n",l,*k*r,JLM[l]);
}
*/
// Qlm - primeiros 4 termos
double Qlm[LMAXE];
Qlm[jlm(0, 0)]=1/sqrt(4*M_PI);
Qlm[jlm(1, 1)]=-gammaQ(1)*sth*Qlm[jlm(0,0)]; // Q11
Qlm[jlm(1, 0)]=sqrt(3.0)*cth*Qlm[jlm(0,0)]; // Q10
Qlm[jlm(1,-1)]=-Qlm[jlm(1,1)]; // Q11*(-1)
// Complex Exponencial for m=-1,0,1
double complex Eim[2*(*lmax)+3];
Eim[*lmax-1]=(cph-I*sph);
Eim[*lmax ]=1+I*0;
Eim[*lmax+1]=(cph+I*sph);
// Ylm - primeiros 4 termos
double complex Ylm[LMAXE];
Ylm[jlm(0, 0)]=Qlm[jlm(0, 0)];
Ylm[jlm(1,-1)]=Qlm[jlm(1,-1)]*Eim[*lmax-1];
Ylm[jlm(1, 0)]=Qlm[jlm(1, 0)];
Ylm[jlm(1, 1)]=Qlm[jlm(1, 1)]*Eim[*lmax+1];
/* OK jl, Qlm, Ylm
for(l=0;l<2;l++){
for(m=-l;m<=l;m++){
printf("%d\t%d\t%d\t%f\t%f\t%f+%fi\n",l,m,jlm(l,m),JLM[jlm(l,m)],Qlm[jlm(l,m)],creal(Ylm[jlm(l,m)]),cimag(Ylm[jlm(l,m)]));
}
}
printf("======================================================================\n");
*/
// VECTOR SPHERICAL HARMONICS
double complex XM; //[LMAX];
double complex XZ; //[LMAX];
double complex XP; //[LMAX];
double complex YM; //[LMAX];
double complex YZ; //[LMAX];
double complex YP; //[LMAX];
double complex VM; //[LMAX];
double complex VZ; //[LMAX];
double complex VP; //[LMAX];
// HANSEN MULTIPOLES
double complex MM; //[LMAX];
double complex MZ; //[LMAX];
double complex MP; //[LMAX];
double complex NM; //[LMAX];
double complex NZ; //[LMAX];
double complex NP; //[LMAX];
// OTHERS
double kl;
// MAIN LOOP
for(l=1;l<=(*lmax);l++){
//------------------------------------------------------------------------------
//Qlm extremos positivos um passo a frente
Qlm[jlm(l+1, l+1)]=-gammaQ(l+1)*sth*Qlm[jlm(l,l)];
Qlm[jlm(l+1, l )]= deltaQ(l+1)*cth*Qlm[jlm(l,l)];
//Qlm extremos negativos um passo a frente
Qlm[jlm(l+1,-l-1)]=pow(-1,l+1)*Qlm[jlm(l+1, l+1)];
Qlm[jlm(l+1,-l )]=pow(-1,l )*Qlm[jlm(l+1, l )];
// Exponenciais um passo a frente
Eim[*lmax+l+1]=Eim[*lmax+l]*(cph+I*sph);
Eim[*lmax-l-1]=Eim[*lmax-l]*(cph-I*sph);
// Harmonicos esfericos extremos um passo a frente
Ylm[jlm(l+1, l+1)]=Qlm[jlm(l+1, l+1)]*Eim[*lmax+l+1];
Ylm[jlm(l+1, l )]=Qlm[jlm(l+1, l )]*Eim[*lmax+l ];
Ylm[jlm(l+1,-l-1)]=Qlm[jlm(l+1,-l-1)]*Eim[*lmax-l-1];
Ylm[jlm(l+1,-l )]=Qlm[jlm(l+1,-l )]*Eim[*lmax-l ];
// others
kl=1/(sqrt(l*(l+1)));
for(m=0; m<l; m++){
// Demais valores de Qlm e Ylm
Qlm[jlm(l+1, m)]=alfaQ(l+1,m)*cth*Qlm[jlm(l,m)]-betaQ(l+1,m)*Qlm[jlm(l-1,m)];
Qlm[jlm(l+1,-m)]=pow(-1,m)*Qlm[jlm(l+1, m)];
Ylm[jlm(l+1, m)]=Qlm[jlm(l+1, m)]*Eim[*lmax+m];
Ylm[jlm(l+1,-m)]=Qlm[jlm(l+1,-m)]*Eim[*lmax-m];
}
//------------------------------------------------------------------------------
// for(m=-(l+1); m<=(l+1); m++){
// Ylm[jlm(l+1,m)]=Qlm[jlm(l+1,m)]*Eim[*lmax+m];
// }
// for(m=-l; m<=l; m++){
// printf("%d\t%d\t%d\t%f\t%f+%fi\t%f+%fi\n",l,m,jlm(l,m)+1,Qlm[jlm(l,m)],creal(Eim[*lmax+m]),cimag(Eim[*lmax+m]),creal(Ylm[jlm(l,m)]),cimag(Ylm[jlm(l,m)]));
// }
//------------------------------------------------------------------------------
for(int m=-l; m<=l; m++){
XM=kl*cm(l,m)*Ylm[jlm(l,m-1)]/sqrt(2);
XZ=kl*m*Ylm[jlm(l,m )];
XP=kl*cp(l,m)*Ylm[jlm(l,m+1)]/sqrt(2);
// printf("--------X--------------------------------\n");
printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(XM),cimag(XM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(XZ),cimag(XZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(XP),cimag(XP));
YM=(-Kp(l,m,m-1)*Ylm[jlm(l,m-1)]+Km(l+1,m,m-1)*Ylm[jlm(l+1,m-1)])/sqrt(2);
YZ= Ko(l,m,m )*Ylm[jlm(l,m )]+Ko(l+1,m,m )*Ylm[jlm(l+1,m )];
YP=( Km(l,m,m+1)*Ylm[jlm(l,m+1)]-Kp(l+1,m,m+1)*Ylm[jlm(l+1,m+1)])/sqrt(2);
// printf("--------Y--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(YM),cimag(YM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(YZ),cimag(YZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(YP),cimag(YP));
VM=kl*(-(l+1)*Kp(l,m,m-1)*Ylm[jlm(l,m-1)]-l*Km(l+1,m,m-1)*Ylm[jlm(l+1,m-1)])/sqrt(2);
VZ=kl*( (l+1)*Ko(l,m,m )*Ylm[jlm(l,m )]-l*Ko(l+1,m,m )*Ylm[jlm(l+1,m )]);
VP=kl*( (l+1)*Km(l,m,m+1)*Ylm[jlm(l,m+1)]+l*Kp(l+1,m,m+1)*Ylm[jlm(l+1,m+1)])/sqrt(2);
// printf("--------V--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(VM),cimag(VM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(VZ),cimag(VZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(VP),cimag(VP));
// CALCULATION OF HANSEM MULTIPOLES
MM=JLM[l]*XM;
MZ=JLM[l]*XZ;
MP=JLM[l]*XP;
// printf("--------M--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(MM),cimag(MM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(MZ),cimag(MZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(MP),cimag(MP));
NM=((l+1)*JLM[l-1]-l*JLM[l+1])*VM/(2*l+1)+sqrt(l*(l+1))*JLM[l]*YM;
NZ=((l+1)*JLM[l-1]-l*JLM[l+1])*VZ/(2*l+1)+sqrt(l*(l+1))*JLM[l]*YZ;
NP=((l+1)*JLM[l-1]-l*JLM[l+1])*VP/(2*l+1)+sqrt(l*(l+1))*JLM[l]*YP;
// printf("--------N--------------------------------\n");
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(NM),cimag(NM));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(NZ),cimag(NZ));
// printf("%d\t%d\t%d\t%f+%fi\n",l,m,jlm(l,m),creal(NP),cimag(NP));
// CALCULATION OF THE ELECTROMAGNETIC FIELDS
*Em=*Em+MM*GTE[jlm(l,m)]-NM*GTM[jlm(l,m)];
*Ez=*Ez+MZ*GTE[jlm(l,m)]-NZ*GTM[jlm(l,m)];
*Ep=*Ep+MP*GTE[jlm(l,m)]-NP*GTM[jlm(l,m)];
*Hm=*Hm+MM*GTM[jlm(l,m)]+NM*GTE[jlm(l,m)];
*Hz=*Hz+MZ*GTM[jlm(l,m)]+NZ*GTE[jlm(l,m)];
*Hp=*Hp+MP*GTM[jlm(l,m)]+NP*GTE[jlm(l,m)];
}
}
}
