update bessli0 rat coefs

Author: heltonmc

src/besseli.jl

@@ -175,7 +175,7 @@ function besseli0(z::ComplexF64)
         # use power series for I0
         r = evalpoly(z*z, (1.0, 0.25, 0.015625, 0.00043402777777777775, 6.781684027777777e-6, 6.781684027777778e-8, 4.709502797067901e-10, 2.4028075495244395e-12, 9.385966990329842e-15, 2.896903392077112e-17, 7.242258480192779e-20, 1.4963343967340453e-22, 2.5978027721077174e-25, 3.842903509035085e-28, 4.9016626390753635e-31, 5.4462918211948485e-34, 5.318644356635594e-37))
     else
-        if angle(z) <= π / 4.4
+        if angle(z) <= π / 5.0
             # use power series but evaluated using second order horner scheme
             zz = z*z
             z4 = zz*zz
@@ -184,9 +184,9 @@ function besseli0(z::ComplexF64)
 
         else
             # use rational approximation based on AAA algorithm
-            zz = (-1.3144540816651462 + 20.054693865816724im, -1.2152720220184496 + 18.54146805523844im, -1.0758582968968085 + 16.41442564500392im, -0.9186088936209557 + 14.015263371275323im, -0.7533475204960969 + 11.49386205943562im, -0.5838248556039682 + 8.907445998843897im, -0.41092161465730614 + 6.269452314652046im, -0.32055227293065935 + 4.890682596894067im, 16.906716750808087 + 10.865287107782516im, 0.26715371754140166 + 20.098224520867603im, 4.121994532242284 + 2.6493699394695174im, 4.053028754723365 + 19.68712670537236im, -0.5018982035099 + 7.657486833198153im, 9.416081350634247 + 17.758023876497013im, 1.9674895590143007 + 4.487648029332259im, -1.275759132467892 + 19.46432302583941im, 7.709313889965882 + 4.954475197822861im, 13.72022229845232 + 14.68895844098729im, -0.3541218766747901 + 5.402855776372861im, -0.9973883749616251 + 15.217205990064667im, 5.067285183070908 + 3.256546447342955im, 2.1309472708925585 + 19.986722185708082im, -0.8162780120038937 + 12.453995821138065im, -0.6642234573493526 + 10.134091621337502im)
-            w  = (0.023435912479136792 + 0.0im, -0.07518141047674767 + 0.0475948197731169im, 0.02099862365431344 + 0.10227799317706024im, -0.044790606134137025 - 0.0019900581421525287im, 0.05092855107420865 - 0.030284027691088355im, 0.11876822116350058 + 0.3545737241031229im, -0.2800428715703842 + 0.1385502878368521im, 0.07056156978707125 - 0.015640049217372977im, -0.06946091028316168 + 0.016066454632345423im, 0.08524646892263366 + 0.0953622756709394im, -0.02790219158045262 + 0.07064926802304639im, 0.1422314233425249 - 0.2536760604980481im, -0.20586363442913913 + 0.3014383126557577im, 0.20547145538054265 - 0.17388658146749558im, -0.13839690210608482 - 0.07997812132261209im, -0.005116954351018287 + 0.07859682420061695im, 0.0409490985507271 - 0.2642881024594653im, -0.04174610452138103 - 0.23810783641445965im, -0.14078210159561536 - 0.17647153499232213im, -0.07672294420555978 + 0.08789101702567167im, -0.15544491331665283 - 0.17872134246439533im, 0.2746212867658749 + 0.0633913060138901im, 0.003561860807958012 + 0.005781000943183686im, 0.22467614820711904 + 0.050873741433048215im)
-            f = (4.11757504005866 - 4.095512734321109im, -2.247112620034342 + 3.680759784557969im, 3.7834318298173315 + 0.562243565983836im, 1.025044899237516 - 2.4295763517152302im, -1.1024728966418114 - 0.9985456859791928im, -0.7134052191604513 + 0.634168698676205im, 0.35489432819051814 + 0.8984965319188546im, 0.15105140195420463 - 0.7254114647779558im, 0.401057852147248 - 0.0014084695668244449im, 0.5404571564588408 - 0.1885021348797114im, 0.407770977742567 - 0.00680290179701475im, 0.3994965367795384 - 0.0024661141779376626im, 0.8312271064319111 - 1.0050503936637845im, 0.40006191058465196 - 0.002248719754950748im, 0.4055260568863696 - 0.01689191195791546im, 5.210832430161148 + 1.7413278357835171im, 0.40364747476765517 - 0.003288380266379im, 0.40062798907705705 - 0.0018845654535970921im, -0.39383201186515915 - 0.17987628384333437im, -2.053184226968296 + 1.6069066509951657im, 0.40617427977861376 - 0.005320233415147144im, 0.4034434765080089 - 0.006086635360116373im, -0.07645988937623527 + 1.981923553555365im, 1.8844134122620073 + 0.24179792442042025im)
+            zz = (4.45 + 3.2052728679295117im, 4.455420677104106 + 17.0im, 4.45 + 15.382484426852667im, 4.45 + 5.591125152996643im, 4.45 + 8.721074610794474im, 4.45 + 12.593761762936332im, 13.99545555483758 + 3.2im, 4.45 + 10.449153300661845im, 13.99448098692729 + 17.0im, 4.45 + 4.364295914717135im, 5.74410737590207 + 17.0im, 7.015857771516533 + 3.2im, 8.431271890243135 + 17.0im, 4.45 + 14.193575953103643im, 10.028155979725057 + 3.2im, 14.0 + 12.056471942775644im, 5.0784076766983475 + 3.2im)
+            w = (-0.08402970424774468 + 0.0im, -0.025416959445504525 + 0.008064492555082617im, -0.12436237574219852 + 0.09773493772114668im, -0.10773790109082547 + 0.09931091918808033im, -0.04136192882523951 - 0.10845822138428568im, -0.12376621749712938 - 0.1560380316634484im, 0.1440093676081139 + 0.07630216514159634im, -0.11981155913520558 - 0.10502286007991138im, -0.09732103082699156 + 0.12394089091215946im, -0.2024491672690207 - 0.008074664453662488im, -0.032009598780432726 + 0.1399683216091626im, 0.1635093206102166 - 0.2625104018116356im, -0.0069195515849893256 + 0.23685845201445335im, -0.22780106527284 - 0.08591498944175457im, 0.31071127502007534 - 0.15037952246380232im, 0.5169717201599435 + 0.3199985816199036im, 0.057776769164925704 - 0.2256791564859297im)
+            f = (0.40650720354357883 - 0.006334133391405162im, 0.3996077953677851 - 0.0028305511728273568im, 0.39967704085612976 - 0.0030016547219227385im, 0.4030249334706483 - 0.006007622393381157im, 0.40100073574830397 - 0.004755573523837742im, 0.40005639633772716 - 0.003557024462101866im, 0.4024594080667488 - 0.0008405204317908334im, 0.40054207447089496 - 0.004211100015366804im, 0.40036795014598564 - 0.0018064878102966003im, 0.4045859012569077 - 0.00644263857738687im, 0.3997607686595453 - 0.00268586039668089im, 0.4051483029145814 - 0.0031164474364945016im, 0.4000585212223849 - 0.0024151743246614353im, 0.39982888182793785 - 0.003319036953780421im, 0.40367802519983587 - 0.0016111929572418197im, 0.4009968019331028 - 0.0018465588128410255im, 0.4062550837386149 - 0.005276094572860034im)
             f = f.*w
             s1 = 0.0 + 0.0im
             s2 = 0.0 + 0.0im