diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json
index 27f84d5..378f6b0 100644
--- a/dev/.documenter-siteinfo.json
+++ b/dev/.documenter-siteinfo.json
@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-11T20:47:56","documenter_version":"1.7.0"}}
\ No newline at end of file
+{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-11T22:07:29","documenter_version":"1.7.0"}}
\ No newline at end of file
diff --git a/dev/advanced_usage/index.html b/dev/advanced_usage/index.html
index f5c2d64..54a16d6 100644
--- a/dev/advanced_usage/index.html
+++ b/dev/advanced_usage/index.html
@@ -24,7 +24,7 @@
 fmm.fmm!(target_system, source_system,
     unsort_source_bodies=true, unsort_target_bodies=true) # standard run (defaults)
 fmm.fmm!(target_system, source_system,
-    unsort_source_bodies=false, unsort_target_bodies=false) # sorted bodies (not original indices)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49849075893959255, 0.5011246180164968, 0.50101931980297], 0.8617443734929683, 0.8617443734929683, [-0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063], [0.49752834600881063, 0.49752834600881063, 0.49752834600881063], 0.0, 0.0, fill(0.0), [-49.209733528008485 0.0; 0.0 0.0;;; 3.235503852070556 0.0; 0.0 0.0;;; 0.02681865248285842 0.0; 0.9591193094494834 0.0;;; … ;;; -0.0004469512083583767 0.0; -0.00015932419565861916 0.0;;; -0.00028710529956597804 0.0; -0.00031904516877669385 0.0;;; -7.588266430169126e-6 0.0; -8.400184364295124e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659238828608, 140659238828560, 16))), SingleBranch{Float64}(1:13, 0, 10:9, 1, 1, [0.24972658593518723, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.326393509059363 0.0; 0.0 0.0;;; 0.10174482633884264 0.0; 0.0 0.0;;; -0.07898687772271276 0.0; 0.03841659635534152 0.0;;; … ;;; -9.654710862452212e-7 0.0; -5.591129557725438e-7 0.0;;; 1.175731767951614e-6 0.0; 2.391893864725776e-6 0.0;;; -3.893767927840696e-8 0.0; -4.373076778562484e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21988918332658114 0.0; 0.0 0.0;;; -0.00907173901579822 0.0; -0.08078608463780172 0.0;;; … ;;; 6.639561085749197e-7 0.0; 1.9043445262044332e-6 0.0;;; 3.6078285954161947e-7 0.0; -1.730779168448776e-7 0.0;;; -1.5694464749247868e-8 0.0; -2.5081831237534205e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (12, 15, 19))), SingleBranch{Float64}(14:23, 0, 10:9, 1, 2, [0.7472549319439978, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.505985520323303 0.0; 0.0 0.0;;; -0.0893400706965472 0.0; 0.0 0.0;;; 0.07469760206429724 0.0; -0.23211041531103774 0.0;;; … ;;; -2.392727383648695e-6 0.0; -2.7506172478695797e-7 0.0;;; 1.2869752996385646e-6 0.0; 8.632541193951725e-7 0.0;;; -1.4323853566229846e-7 0.0; 3.40320513459477e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.18613078162840202 0.0; 0.0 0.0;;; -0.03988177380448188 0.0; -0.10881091326674686 0.0;;; … ;;; 3.1493849180079693e-6 0.0; 1.79002742056861e-6 0.0;;; 2.3049009571265728e-7 0.0; -1.3797688581858191e-6 0.0;;; -1.7119818873987816e-7 0.0; 3.217930041360891e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658692815152, 140659353541264, 143825358400))), SingleBranch{Float64}(24:40, 0, 10:9, 1, 3, [0.24972658593518723, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-7.986155913622251 0.0; 0.0 0.0;;; -0.1795979615961002 0.0; 0.0 0.0;;; -0.1708212423759164 0.0; 0.03135320324442914 0.0;;; … ;;; -6.066362373385743e-6 0.0; 2.4234495602853986e-6 0.0;;; 2.327392085993626e-6 0.0; 4.871331224296273e-7 0.0;;; 2.4751088043185402e-8 0.0; -5.827716675663792e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.23122788327035293 0.0; 0.0 0.0;;; -0.04900663119822446 0.0; 0.09175801803089013 0.0;;; … ;;; 4.485772070448108e-6 0.0; -4.4630903906536425e-7 0.0;;; 4.303552019451355e-7 0.0; -1.0428735117063708e-6 0.0;;; -6.452660186998594e-8 0.0; -7.836101483352229e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 141733920768))), SingleBranch{Float64}(41:57, 0, 10:9, 1, 4, [0.7472549319439978, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-9.931355245362722 0.0; 0.0 0.0;;; 0.004639293314162463 0.0; 0.0 0.0;;; 0.10230318193552163 0.0; 0.3431041586399578 0.0;;; … ;;; -5.8057861586053485e-6 0.0; -3.6767179441275553e-6 0.0;;; 1.970849569609788e-6 0.0; -1.1263384149017906e-6 0.0;;; 4.6063384099401923e-7 0.0; -7.362879677517756e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.24833262559729297 0.0; 0.0 0.0;;; -0.04049792411417641 0.0; 0.11830484901746985 0.0;;; … ;;; 7.332767131734295e-6 0.0; -4.818366848970212e-6 0.0;;; 6.296375165101449e-7 0.0; 2.450158453149185e-6 0.0;;; -2.5398566738723024e-7 0.0; -1.9922601565040447e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658692327440, 140658692327472, 143825358400))), SingleBranch{Float64}(58:71, 0, 10:9, 1, 5, [0.24972658593518723, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.0812379817404665 0.0; 0.0 0.0;;; 0.2500525077504865 0.0; 0.0 0.0;;; -0.31821199437047437 0.0; 0.12219381204800842 0.0;;; … ;;; 3.886164164482793e-6 0.0; -7.451230042206713e-6 0.0;;; -1.5655861775267537e-6 0.0; 1.3488384490746591e-6 0.0;;; -2.65136301189794e-7 0.0; -1.0396969077621681e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.23600456619228227 0.0; 0.0 0.0;;; 0.00780054815104303 0.0; 0.01243800251579276 0.0;;; … ;;; -1.457243306148132e-8 0.0; 1.604225902871519e-9 0.0;;; -2.836500215179685e-10 0.0; -3.581821796740947e-10 0.0;;; 1.9003405206797664e-12 0.0; -5.3575717814609175e-12 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 140655883976704, 1))), SingleBranch{Float64}(72:82, 0, 10:9, 1, 6, [0.7472549319439978, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.643660411433685 0.0; 0.0 0.0;;; -0.09740163237448708 0.0; 0.0 0.0;;; 0.30569645349438196 0.0; 0.2359234953909746 0.0;;; … ;;; -9.82916763080865e-7 0.0; -4.2285511081766585e-7 0.0;;; 2.7225441029521644e-6 0.0; -9.866422822602592e-7 0.0;;; -2.884182756506517e-7 0.0; 2.1891312191953625e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.137250125216142 0.0; 0.0 0.0;;; -0.041848288296333136 0.0; 0.07154851443791577 0.0;;; … ;;; 7.308420503707386e-7 0.0; 1.2365335735668517e-8 0.0;;; 1.4021073394047346e-7 0.0; -2.3067492312302074e-7 0.0;;; -1.5499976899256273e-8 0.0; -2.8685176609168157e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658691966256, 140658691966288, 141733920768))), SingleBranch{Float64}(83:89, 0, 10:9, 1, 7, [0.24972658593518723, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-2.3207471469996026 0.0; 0.0 0.0;;; 0.09584922777112714 0.0; 0.0 0.0;;; -0.03459176396777507 0.0; -0.04020642273548641 0.0;;; … ;;; 3.930977957593639e-6 0.0; -1.9071506252246133e-6 0.0;;; 4.262561393862879e-7 0.0; 6.012045573535614e-7 0.0;;; -1.296847519879538e-7 0.0; -1.748757755002258e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.14971540025278463 0.0; 0.0 0.0;;; -0.10199818137039851 0.0; -0.00404107784645201 0.0;;; … ;;; -1.5142366400508734e-6 0.0; -1.807350708728618e-7 0.0;;; 6.688310694761936e-7 0.0; 1.0683350833198992e-7 0.0;;; -9.055558759133121e-8 0.0; -1.8167298693653792e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659292046896, 0, 143825358400))), SingleBranch{Float64}(90:100, 0, 10:9, 1, 8, [0.7472549319439978, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.414197799467094 0.0; 0.0 0.0;;; 0.5897626670629665 0.0; 0.0 0.0;;; -0.1138694027478626 0.0; -0.009802047749392043 0.0;;; … ;;; 1.152740503052551e-5 0.0; -4.517016990218442e-6 0.0;;; -4.140046433990845e-6 0.0; -1.566383749352849e-6 0.0;;; 1.2469713505945974e-7 0.0; 2.024928160458584e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21095730321733874 0.0; 0.0 0.0;;; 0.09347241596581823 0.0; -0.08394581821691316 0.0;;; … ;;; -3.5372171155417328e-6 0.0; -4.908219455216665e-6 0.0;;; -2.1396426594075856e-6 0.0; -4.6629625718216964e-7 0.0;;; -2.2671999108049045e-7 0.0; 1.289627938417499e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659438641160, 140658648808304, 144361781416)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [8, 19, 24, 25, 30, 33, 35, 43, 52, 55  …  37, 41, 42, 49, 64, 71, 78, 79, 87, 88], [90, 83, 24, 72, 58, 59, 25, 1, 60, 73  …  23, 38, 80, 56, 39, 81, 82, 40, 13, 57], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.4660552366407049, 0.13111968284280429, 0.1908671255470663], 0.010673064683743582, 0.8267772979915037), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.3447705767476935, 0.07006788456539503, 0.2923577651940017], 0.004397261752829818, 0.5517592405944612), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.4911645955827536, 0.040324077362882016, 0.317784960572128], 0.004572616745488207, 0.1280946812518453), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.40516617554370093, 0.32616788197738866, 0.056217617276771326], 0.010585392495089252, 0.012104263433355023), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18599865953230243, 0.15030687931482978, 0.12186905472850917], 0.00530068913657312, 0.7976632010743766), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.4346643684051661, 0.13212864017170378, 0.19630837394498046], 0.004567269441401094, 0.39368661127046056), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.0009624129307819196, 0.2950090065083799, 0.07129536266232961], 0.0030690713098188082, 0.49288942845129), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.06701550238862786, 0.25483654814098344, 0.3238706353789649], 0.00505556524793979, 0.4522470321326544), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.1639092692596178, 0.44194134967919385, 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0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6174588851816368, 0.6522104227559661, 0.5847276813173017], 0.00761078545286029, 0.9704213765219395), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5232139755745984, 0.6045990113354003, 0.5429901209014718], 0.0060841769615967035, 0.8911459293930191), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9581632293408542, 0.9135421917156796, 0.7073373243745936], 0.010449665448269006, 0.8357622456841612), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.7658820877217039, 0.9631550531437152, 0.5344687381454426], 0.0068829275392983565, 0.07479369706302341), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.960720320334046, 0.651071293378233, 0.6942906786235435], 0.0097351936375095, 0.44997536837158536), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.7803189670835223, 0.8311591102139488, 0.5707525801936775], 0.008043628052385822, 0.08862350083761417), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5793632955101715, 0.5629439590892656, 0.5388261895900366], 0.008824875260231754, 0.805646285033539), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49850630217496006, 0.5029084590406193, 0.4970227729348794], 0.8572644572282587, 0.8572644572282587, [-0.49494186514743355, 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ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659358428848, 140659358345232, 140659292046128))), SingleBranch{Float64}(43:55, 0, 10:9, 1, 4, [0.7459772347486768, 0.7503793916143361, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.10425315723209527 0.0; -0.0 0.0;;; -0.04040250617839929 0.0; -0.04562408503868281 0.0;;; … ;;; 1.3994426612384809e-7 0.0; 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0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.05941950550840777 0.0; -0.0 0.0;;; -0.06984898585556935 0.0; 0.10325321360106476 0.0;;; … ;;; -6.688472512156468e-7 0.0; -1.4501297809812144e-7 0.0;;; 4.3233604883670166e-7 0.0; -4.1299565937718063e-7 0.0;;; -4.1888246519238254e-8 0.0; -2.4735114753799555e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658609217488, 140658648803120, 140659292046896))), SingleBranch{Float64}(79:86, 0, 10:9, 1, 7, [0.2510353696012433, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.19774130005920343 0.0; -0.0 0.0;;; 0.10337420516639845 0.0; -0.003702501499532632 0.0;;; … ;;; 3.0951077862846165e-6 0.0; -3.337097810420304e-7 0.0;;; -9.336410389602992e-7 0.0; 1.3462336691028458e-7 0.0;;; 9.711269933660484e-8 0.0; -1.7571838450287563e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659438647184, 140659438647632, 140659438648080))), SingleBranch{Float64}(87:100, 0, 10:9, 1, 8, [0.7459772347486768, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281974944, 20753281979104, 140655883977376)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.3108257809580788, 0.018444977603329638, 0.1448495720156966], 0.004532460900544307, 0.6204619994567462), [6.656408075963273, 0.0, 0.0, 0.0, -3.5398731184273053, -9.295941020322173, -5.413464408657029, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.04239416161334009, 0.32064719274449505, 0.48130130480471], 0.009728577099494845, 0.28031926582466293), [7.0836044891461585, 0.0, 0.0, 0.0, -8.857359963224212, -3.7043629243965284, 2.6867154926403254, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.431557182411335, 0.05729104146002573, 0.4039530057283216], 0.007375228802112362, 0.30999664605164), [7.739018612595635, 0.0, 0.0, 0.0, -0.37792795808645685, -9.107993435650643, 1.4755711117578612, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.3760481927883257, 0.30427758942618754, 0.0424352411332668], 0.008737504330345026, 0.3856873023831733), [7.497010356100949, 0.0, 0.0, 0.0, -4.93733078661837, -0.9512848217887391, -9.321732229232445, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.40796257253884594, 0.3169707043296718, 0.17481471770913004], 0.0006599191423210741, 0.6303355439118526), [8.603145628291282, 0.0, 0.0, 0.0, -5.092945448737958, -0.35201620762089525, -5.017596524805857, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.44526311787148065, 0.3123953708377504, 0.0031981489559432807], 0.002234687294853749, 0.2526616143954684), [7.394307495297395, 0.0, 0.0, 0.0, -4.074197603049914, -0.8843005298526739, -12.129516167989486, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.09506281506194814, 0.37886831688663536, 0.2883280135877385], 0.0026513954621956654, 0.34851211014036976), [7.743796789514465, 0.0, 0.0, 0.0, -8.951264053959937, -1.9617883735084023, -4.658746399724488, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.385983388890926, 0.2099869174765614, 0.2103305433014464], 0.002673503120625262, 0.731920338683347), [8.699005360233967, 0.0, 0.0, 0.0, -9.322285862701646, 2.555093162665515, -1.874069896074265, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.4374975251302734, 0.2511138400545102, 0.1042125323068771], 0.0079424961191749, 0.28373707089135336), [8.545986552488209, 0.0, 0.0, 0.0, -10.43682822175596, 6.712123318844789, -6.799535652933345, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.33885320202792324, 0.21079845214701087, 0.07899763839448037], 0.0008797470416774469, 0.6588156699242567), [7.516005325514882, 0.0, 0.0, 0.0, -4.836766418598849, -2.225174045341691, -8.617929217958249, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.761014175927334, 0.5625502355864805, 0.6362450642237143], 0.00477924026951857, 0.08790391023238642), [8.696622821572635, 0.0, 0.0, 0.0, 5.548245493459153, 0.6647207464342835, 6.278537989010481, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.741658189777045, 0.8784627652056287, 0.6026198177064941], 0.0028805176050072864, 0.24086407961581202), [7.541219085822956, 0.0, 0.0, 0.0, 0.3131879052669324, 8.516359052958578, 5.9072937820384634, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6559052253949811, 0.9583482860298168, 0.6198294517560885], 0.008868504569149492, 0.17689335268130646), [6.840663348171893, 0.0, 0.0, 0.0, 0.2944062620800215, 7.712555707441569, 4.705741898589104, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5044880780307363, 0.9392745252820915, 0.8236302658478007], 0.0035072444787534506, 0.5071979794728987), [5.902585114087375, 0.0, 0.0, 0.0, -0.7298300723802948, 5.074581758334187, 4.958470552095021, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.7719706502318479, 0.987371940477909, 0.5992694800324155], 0.000561642365078654, 0.020303598406039902), [6.659400467615292, 0.0, 0.0, 0.0, 0.9370333132030003, 8.321557859554815, 4.446254367712357, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9270141064885, 0.6996533718950176, 0.7573000900883736], 0.005090949172292981, 0.41670321904423535), [7.294560374728856, 0.0, 0.0, 0.0, 0.7797311911756291, 1.8536289165730497, 8.106518301667714, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6705665433906464, 0.8074865918599404, 0.5791268533462717], 0.008580519038422284, 0.2990005802447111), [8.378169492760158, 0.0, 0.0, 0.0, 0.672628905011095, 11.149982109624677, 5.703626251533733, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5199695296735932, 0.5150132871145792, 0.7028351735495706], 0.0037563211861237865, 0.28526666192551975), [8.680614827593462, 0.0, 0.0, 0.0, -3.197166807339375, 0.26787494900673947, 8.549839228303712, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, 0.13080774080166646), [7.060195088980969, 0.0, 0.0, 0.0, -0.8852806157001135, 4.388943223104779, 7.646679439394734, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, 0.6409979037657155), [7.436136404880495, 0.0, 0.0, 0.0, 1.9624183678921265, 3.8680899850301302, 6.034444873485874, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], DerivativesSwitch{true, true, true}())</code></pre><h2 id="Reusing-the-Octree"><a class="docs-heading-anchor" href="#Reusing-the-Octree">Reusing the Octree</a><a id="Reusing-the-Octree-1"></a><a class="docs-heading-anchor-permalink" href="#Reusing-the-Octree" title="Permalink"></a></h2><p>Users are able to define the tree to be used in the FMM by passing in a previously created tree into the <code>fmm!</code> call. For convenience, the <code>upward_pass</code>, <code>horizontal_pass</code>, and <code>downward_pass</code> can be toggled off seperately. These are important to toggle when generating octrees to be reused. Additionally, <code>unsort_target_bodies</code> and <code>unsort_source_bodies</code> should be set to <code>false</code> when generating the reusable trees.</p><ul><li><strong><code>upward_pass</code> creates the multipole expansions for each branch</strong></li><li><strong><code>horizontal_pass</code> evaluates the expansions in the appropriate locations</strong></li><li><strong><code>downward_pass</code> applies parent expansions to children branches</strong></li></ul><pre><code class="language-julia hljs">target_system = generate_gravitational(123, 100)
+    unsort_source_bodies=false, unsort_target_bodies=false) # sorted bodies (not original indices)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49849075893959255, 0.5011246180164968, 0.50101931980297], 0.8617443734929683, 0.8617443734929683, [-0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063], [0.49752834600881063, 0.49752834600881063, 0.49752834600881063], 0.0, 0.0, fill(0.0), [-49.209733528008485 0.0; 0.0 0.0;;; 3.235503852070556 0.0; 0.0 0.0;;; 0.02681865248285842 0.0; 0.9591193094494834 0.0;;; … ;;; -0.0004469512083583767 0.0; -0.00015932419565861916 0.0;;; -0.00028710529956597804 0.0; -0.00031904516877669385 0.0;;; -7.588266430169126e-6 0.0; -8.400184364295124e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835851372880, 139835914313736, 139835767727712))), SingleBranch{Float64}(1:13, 0, 10:9, 1, 1, [0.24972658593518723, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.326393509059363 0.0; 0.0 0.0;;; 0.10174482633884264 0.0; 0.0 0.0;;; -0.07898687772271276 0.0; 0.03841659635534152 0.0;;; … ;;; -9.654710862452212e-7 0.0; -5.591129557725438e-7 0.0;;; 1.175731767951614e-6 0.0; 2.391893864725776e-6 0.0;;; -3.893767927840696e-8 0.0; -4.373076778562484e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21988918332658114 0.0; 0.0 0.0;;; -0.00907173901579822 0.0; -0.08078608463780172 0.0;;; … ;;; 6.639561085749197e-7 0.0; 1.9043445262044332e-6 0.0;;; 3.6078285954161947e-7 0.0; -1.730779168448776e-7 0.0;;; -1.5694464749247868e-8 0.0; -2.5081831237534205e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835851372848, 139835716062976, 414376003006))), SingleBranch{Float64}(14:23, 0, 10:9, 1, 2, [0.7472549319439978, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.505985520323303 0.0; 0.0 0.0;;; -0.0893400706965472 0.0; 0.0 0.0;;; 0.07469760206429724 0.0; -0.23211041531103774 0.0;;; … ;;; -2.392727383648695e-6 0.0; -2.7506172478695797e-7 0.0;;; 1.2869752996385646e-6 0.0; 8.632541193951725e-7 0.0;;; -1.4323853566229846e-7 0.0; 3.40320513459477e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.18613078162840202 0.0; 0.0 0.0;;; -0.03988177380448188 0.0; -0.10881091326674686 0.0;;; … ;;; 3.1493849180079693e-6 0.0; 1.79002742056861e-6 0.0;;; 2.3049009571265728e-7 0.0; -1.3797688581858191e-6 0.0;;; -1.7119818873987816e-7 0.0; 3.217930041360891e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835909861312, 0, 0))), SingleBranch{Float64}(24:40, 0, 10:9, 1, 3, [0.24972658593518723, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-7.986155913622251 0.0; 0.0 0.0;;; -0.1795979615961002 0.0; 0.0 0.0;;; -0.1708212423759164 0.0; 0.03135320324442914 0.0;;; … ;;; -6.066362373385743e-6 0.0; 2.4234495602853986e-6 0.0;;; 2.327392085993626e-6 0.0; 4.871331224296273e-7 0.0;;; 2.4751088043185402e-8 0.0; -5.827716675663792e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.23122788327035293 0.0; 0.0 0.0;;; -0.04900663119822446 0.0; 0.09175801803089013 0.0;;; … ;;; 4.485772070448108e-6 0.0; -4.4630903906536425e-7 0.0;;; 4.303552019451355e-7 0.0; 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0.0;;; -0.31821199437047437 0.0; 0.12219381204800842 0.0;;; … ;;; 3.886164164482793e-6 0.0; -7.451230042206713e-6 0.0;;; -1.5655861775267537e-6 0.0; 1.3488384490746591e-6 0.0;;; -2.65136301189794e-7 0.0; -1.0396969077621681e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.23600456619228227 0.0; 0.0 0.0;;; 0.00780054815104303 0.0; 0.01243800251579276 0.0;;; … ;;; -1.457243306148132e-8 0.0; 1.604225902871519e-9 0.0;;; -2.836500215179685e-10 0.0; -3.581821796740947e-10 0.0;;; 1.9003405206797664e-12 0.0; -5.3575717814609175e-12 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835892839952, 139835892839984, 139835716062976))), SingleBranch{Float64}(72:82, 0, 10:9, 1, 6, [0.7472549319439978, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 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0.004532460900544307, 0.6204619994567462), [6.656408075963273, 0.0, 0.0, 0.0, -3.5398731184273053, -9.295941020322173, -5.413464408657029, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.04239416161334009, 0.32064719274449505, 0.48130130480471], 0.009728577099494845, 0.28031926582466293), [7.0836044891461585, 0.0, 0.0, 0.0, -8.857359963224212, -3.7043629243965284, 2.6867154926403254, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.431557182411335, 0.05729104146002573, 0.4039530057283216], 0.007375228802112362, 0.30999664605164), [7.739018612595635, 0.0, 0.0, 0.0, -0.37792795808645685, -9.107993435650643, 1.4755711117578612, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.3760481927883257, 0.30427758942618754, 0.0424352411332668], 0.008737504330345026, 0.3856873023831733), [7.497010356100949, 0.0, 0.0, 0.0, -4.93733078661837, -0.9512848217887391, -9.321732229232445, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.40796257253884594, 0.3169707043296718, 0.17481471770913004], 0.0006599191423210741, 0.6303355439118526), [8.603145628291282, 0.0, 0.0, 0.0, -5.092945448737958, -0.35201620762089525, -5.017596524805857, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.44526311787148065, 0.3123953708377504, 0.0031981489559432807], 0.002234687294853749, 0.2526616143954684), [7.394307495297395, 0.0, 0.0, 0.0, -4.074197603049914, -0.8843005298526739, -12.129516167989486, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.09506281506194814, 0.37886831688663536, 0.2883280135877385], 0.0026513954621956654, 0.34851211014036976), [7.743796789514465, 0.0, 0.0, 0.0, -8.951264053959937, -1.9617883735084023, -4.658746399724488, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.385983388890926, 0.2099869174765614, 0.2103305433014464], 0.002673503120625262, 0.731920338683347), [8.699005360233967, 0.0, 0.0, 0.0, -9.322285862701646, 2.555093162665515, -1.874069896074265, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.4374975251302734, 0.2511138400545102, 0.1042125323068771], 0.0079424961191749, 0.28373707089135336), [8.545986552488209, 0.0, 0.0, 0.0, -10.43682822175596, 6.712123318844789, -6.799535652933345, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.33885320202792324, 0.21079845214701087, 0.07899763839448037], 0.0008797470416774469, 0.6588156699242567), [7.516005325514882, 0.0, 0.0, 0.0, -4.836766418598849, -2.225174045341691, -8.617929217958249, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.761014175927334, 0.5625502355864805, 0.6362450642237143], 0.00477924026951857, 0.08790391023238642), [8.696622821572635, 0.0, 0.0, 0.0, 5.548245493459153, 0.6647207464342835, 6.278537989010481, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.741658189777045, 0.8784627652056287, 0.6026198177064941], 0.0028805176050072864, 0.24086407961581202), [7.541219085822956, 0.0, 0.0, 0.0, 0.3131879052669324, 8.516359052958578, 5.9072937820384634, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6559052253949811, 0.9583482860298168, 0.6198294517560885], 0.008868504569149492, 0.17689335268130646), [6.840663348171893, 0.0, 0.0, 0.0, 0.2944062620800215, 7.712555707441569, 4.705741898589104, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5044880780307363, 0.9392745252820915, 0.8236302658478007], 0.0035072444787534506, 0.5071979794728987), [5.902585114087375, 0.0, 0.0, 0.0, -0.7298300723802948, 5.074581758334187, 4.958470552095021, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.7719706502318479, 0.987371940477909, 0.5992694800324155], 0.000561642365078654, 0.020303598406039902), [6.659400467615292, 0.0, 0.0, 0.0, 0.9370333132030003, 8.321557859554815, 4.446254367712357, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9270141064885, 0.6996533718950176, 0.7573000900883736], 0.005090949172292981, 0.41670321904423535), [7.294560374728856, 0.0, 0.0, 0.0, 0.7797311911756291, 1.8536289165730497, 8.106518301667714, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6705665433906464, 0.8074865918599404, 0.5791268533462717], 0.008580519038422284, 0.2990005802447111), [8.378169492760158, 0.0, 0.0, 0.0, 0.672628905011095, 11.149982109624677, 5.703626251533733, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5199695296735932, 0.5150132871145792, 0.7028351735495706], 0.0037563211861237865, 0.28526666192551975), [8.680614827593462, 0.0, 0.0, 0.0, -3.197166807339375, 0.26787494900673947, 8.549839228303712, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, 0.13080774080166646), [7.060195088980969, 0.0, 0.0, 0.0, -0.8852806157001135, 4.388943223104779, 7.646679439394734, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, 0.6409979037657155), [7.436136404880495, 0.0, 0.0, 0.0, 1.9624183678921265, 3.8680899850301302, 6.034444873485874, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], DerivativesSwitch{true, true, true}())</code></pre><h2 id="Reusing-the-Octree"><a class="docs-heading-anchor" href="#Reusing-the-Octree">Reusing the Octree</a><a id="Reusing-the-Octree-1"></a><a class="docs-heading-anchor-permalink" href="#Reusing-the-Octree" title="Permalink"></a></h2><p>Users are able to define the tree to be used in the FMM by passing in a previously created tree into the <code>fmm!</code> call. For convenience, the <code>upward_pass</code>, <code>horizontal_pass</code>, and <code>downward_pass</code> can be toggled off seperately. These are important to toggle when generating octrees to be reused. Additionally, <code>unsort_target_bodies</code> and <code>unsort_source_bodies</code> should be set to <code>false</code> when generating the reusable trees.</p><ul><li><strong><code>upward_pass</code> creates the multipole expansions for each branch</strong></li><li><strong><code>horizontal_pass</code> evaluates the expansions in the appropriate locations</strong></li><li><strong><code>downward_pass</code> applies parent expansions to children branches</strong></li></ul><pre><code class="language-julia hljs">target_system = generate_gravitational(123, 100)
 source_system = generate_gravitational(321, 100)
 
 target_tree, source_tree = fmm.fmm!(target_system, source_system;
@@ -36,10 +36,10 @@
 fmm.fmm!(system,
     nearfield=true, farfield=true, self_induced=true) # standard run (defaults)
 fmm.fmm!(system,
-    nearfield=false, farfield=true, self_induced=true) # nearfield not evaluated</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49850630217496006, 0.5029084590406193, 0.4970227729348794], 0.8572644572282587, 0.8572644572282587, [-0.49494186514743355, 0.49494186514743355, -0.49494186514743355, 0.49494186514743355, -0.49494186514743355, 0.49494186514743355], [0.49494186514743355, 0.49494186514743355, 0.49494186514743355], 0.0, 0.0, fill(0.0), [-48.34870113041748 0.0; 0.0 0.0;;; 2.598422019775752 0.0; 0.0 0.0;;; -1.2227362282002523 0.0; 0.8450131042390987 0.0;;; … ;;; -8.791709687591729e-5 0.0; -0.0004287156900488262 0.0;;; 8.822613231853985e-5 0.0; -0.00020008302331153626 0.0;;; -1.2615951275491288e-5 0.0; -3.065550426595302e-6 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (8, 140659384061824, 5))), SingleBranch{Float64}(1:14, 0, 10:9, 1, 1, [0.2510353696012433, 0.25543752646690254, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-6.487390818499682 0.0; 0.0 0.0;;; 0.1316240843801879 0.0; 0.0 0.0;;; 0.025249123866722074 0.0; 0.110233400590797 0.0;;; … ;;; -3.455130567368021e-6 0.0; 5.924004312810844e-7 0.0;;; 1.5153888935850128e-6 0.0; -1.7047891151365984e-6 0.0;;; 1.5070525582333026e-7 0.0; 1.8849553081710956e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.2148612382952998 0.0; -0.0 0.0;;; -0.04833896697010254 0.0; -0.08941268169127015 0.0;;; … ;;; 3.5751904359505736e-6 0.0; 3.0080507578758053e-7 0.0;;; 3.8236458599367976e-7 0.0; 8.757176386082573e-7 0.0;;; -5.567979953388733e-8 0.0; 7.122692732518039e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658657092592, 140658657092624, 140659260278144))), SingleBranch{Float64}(15:32, 0, 10:9, 1, 2, [0.7459772347486768, 0.25543752646690254, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-11.124170053937009 0.0; 0.0 0.0;;; 0.41138770543633796 0.0; 0.0 0.0;;; 0.016803023250878363 0.0; -0.14477677533550787 0.0;;; … ;;; -8.963509625362107e-6 0.0; 4.693012478346667e-6 0.0;;; 4.410168138692953e-6 0.0; -2.126045985106235e-7 0.0;;; -1.8361776114546595e-8 0.0; -2.1883614233265213e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.11109187197856953 0.0; -0.0 0.0;;; -0.09395587638099494 0.0; -0.03393406206661734 0.0;;; … ;;; -3.0928893153242635e-7 0.0; -5.266357454009592e-7 0.0;;; -8.453485198034652e-8 0.0; -4.5314409979717737e-7 0.0;;; 1.3384370562270982e-8 0.0; -8.18136577012236e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (1, 140659259732144, 0))), SingleBranch{Float64}(33:42, 0, 10:9, 1, 3, [0.2510353696012433, 0.7503793916143361, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-5.116346939838825 0.0; 0.0 0.0;;; -0.08994400460681298 0.0; 0.0 0.0;;; -0.13497721301696344 0.0; 0.06706823073367696 0.0;;; … ;;; -1.0362892970772102e-6 0.0; 1.2247154898001747e-6 0.0;;; -1.868656271304562e-7 0.0; 1.6661679454393324e-6 0.0;;; 6.543631075683181e-7 0.0; -6.940763763815243e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.1902545870569238 0.0; -0.0 0.0;;; -0.08523619914991601 0.0; 0.10063606184199078 0.0;;; … ;;; 4.515701992660869e-6 0.0; 2.690965808809799e-6 0.0;;; 2.2681808274429954e-6 0.0; -7.785616815693268e-7 0.0;;; 1.2086933929990936e-7 0.0; -3.097138724670615e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (51539607561, 42949672975, 8))), SingleBranch{Float64}(43:55, 0, 10:9, 1, 4, [0.7459772347486768, 0.7503793916143361, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-6.531648389278439 0.0; 0.0 0.0;;; 0.27836630809952023 0.0; 0.0 0.0;;; 0.0024199382270112084 0.0; 0.3732722019731095 0.0;;; … ;;; 3.376714829662012e-6 0.0; -2.67253441421499e-6 0.0;;; -1.3437328271781197e-6 0.0; 8.280933433509673e-7 0.0;;; -2.6353089381680604e-7 0.0; -4.924657915182052e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.10425315723209527 0.0; -0.0 0.0;;; -0.04040250617839929 0.0; -0.04562408503868281 0.0;;; … ;;; 1.3994426612384809e-7 0.0; -9.646789543011186e-8 0.0;;; 5.8163042620289284e-8 0.0; 1.4387157402797034e-8 0.0;;; 3.2488834697645844e-9 0.0; 6.2058798109508465e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (3161095930592, 3161095930592, 0))), SingleBranch{Float64}(56:68, 0, 10:9, 1, 5, [0.2510353696012433, 0.25543752646690254, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-6.660580658394574 0.0; 0.0 0.0;;; -0.395153340334315 0.0; 0.0 0.0;;; 0.05979789873527955 0.0; 0.07530541218541535 0.0;;; … ;;; 2.090523898062051e-6 0.0; -2.515462436886501e-6 0.0;;; 1.3306773654521538e-6 0.0; 8.501110961871042e-7 0.0;;; -4.5790897504950176e-7 0.0; 1.3805850178672174e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.1406114031795701 0.0; 0.0 0.0;;; 0.04115679478744828 0.0; -0.03533755162400021 0.0;;; … ;;; -1.2881546024813352e-7 0.0; -2.0655710448954946e-7 0.0;;; -4.840981119340681e-8 0.0; -1.5172010562775518e-8 0.0;;; -3.596485511575488e-9 0.0; 1.545042368324494e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), SingleBranch{Float64}(69:78, 0, 10:9, 1, 6, [0.7459772347486768, 0.25543752646690254, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-5.009402189699274 0.0; 0.0 0.0;;; -0.19304510892164647 0.0; 0.0 0.0;;; 0.12963654004199454 0.0; 0.10016855294092004 0.0;;; … ;;; -2.032871463751076e-6 0.0; 1.1604382246619326e-6 0.0;;; 1.6073455016687304e-6 0.0; 7.525148568942718e-7 0.0;;; -2.1131812349704138e-7 0.0; -2.403269261044048e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.05941950550840777 0.0; -0.0 0.0;;; -0.06984898585556935 0.0; 0.10325321360106476 0.0;;; … ;;; -6.688472512156468e-7 0.0; -1.4501297809812144e-7 0.0;;; 4.3233604883670166e-7 0.0; -4.1299565937718063e-7 0.0;;; -4.1888246519238254e-8 0.0; -2.4735114753799555e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658690541584, 140659385139056, 8))), SingleBranch{Float64}(79:86, 0, 10:9, 1, 7, [0.2510353696012433, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-3.769527893701526 0.0; 0.0 0.0;;; -0.01938418608836119 0.0; 0.0 0.0;;; -0.0011822923413632442 0.0; -0.1457672462486248 0.0;;; … ;;; -1.035853369522652e-5 0.0; 1.2914125498780046e-6 0.0;;; -2.4874690174267746e-7 0.0; -3.1553943207752724e-6 0.0;;; 4.921174899074237e-7 0.0; 2.978833721286661e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.19774130005920343 0.0; -0.0 0.0;;; 0.10337420516639845 0.0; -0.003702501499532632 0.0;;; … ;;; 3.0951077862846165e-6 0.0; -3.337097810420304e-7 0.0;;; -9.336410389602992e-7 0.0; 1.3462336691028458e-7 0.0;;; 9.711269933660484e-8 0.0; -1.7571838450287563e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), SingleBranch{Float64}(87:100, 0, 10:9, 1, 8, [0.7459772347486768, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-3.6496341870681537 0.0; 0.0 0.0;;; -0.04231060050009968 0.0; 0.0 0.0;;; -0.05660139398222258 0.0; -0.12020325670765074 0.0;;; … ;;; 1.2674714042901395e-7 0.0; 9.742117200541327e-7 0.0;;; 6.169136545969979e-7 0.0; -3.979999499773143e-7 0.0;;; 1.6497981578864858e-7 0.0; 5.910575433895744e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659273171824, 140659292055136, 0)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.00551624732815934, 0.2538490889415096), [7.0834787492030005, 0.0, 0.0, 0.0, 5.568735643477791, 2.9213884843016737, 0.7633475677477748, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8192008435733007, 0.9541592624784624, 0.8458950823510601], 0.0014709561750558223, 0.03209667335274724), [5.114232575764009, 0.0, 0.0, 0.0, 2.446182605378621, 4.41119482090726, 3.440180697344876, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.586748700554989, 0.12181263792534469, 0.7894931647499924], 0.0016174951280755708, 0.8935369466209786), [6.585365931828452, 0.0, 0.0, 0.0, 2.5334789856996256, -5.935281910533853, 5.877738846695876, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6192588014774537, 0.47764531343080796, 0.8041934288169849], 0.003639098305331564, 0.8236563299357046), [7.314225348781349, 0.0, 0.0, 0.0, 2.0263196413417575, -0.5909579553411834, 6.438131407639304, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.12353811904859124, 0.7400202596259494, 0.7057473220960516], 0.004975260027225807, 0.9340155879013086), [5.994006655657172, 0.0, 0.0, 0.0, -3.6150300092368397, 3.588312709800555, 2.445983480158574, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9919607797239652, 0.8036971367794874, 0.29827230692896456], 0.006659427674753824, 0.4842893268146866), [6.3093512714054905, 0.0, 0.0, 0.0, 6.811100230860857, 3.229004706340305, 0.7635631719803121, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.49265789199054244, 0.17985285886739166, 0.6397154045236242], 0.004022070032387327, 0.6922349538863742), [7.856042192681273, 0.0, 0.0, 0.0, 0.5375760890909462, -5.141800886434623, 1.9448732399847593, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.22768758746068596, 0.26780944724527167, 0.8309795986773825], 0.006802835099514221, 0.6911617055492341), [8.668207473779663, 0.0, 0.0, 0.0, -3.782240224623742, 18.504359731864223, 92.23746117912798, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0010425988209884726, 0.09206661519876747), [7.388934820369321, 0.0, 0.0, 0.0, -0.5191138373209423, 4.756088137496654, -3.410201822139256, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.00633005068065063, 0.37737321139310276), [7.64606632116185, 0.0, 0.0, 0.0, 0.09461688248299382, 7.241804506257593, 4.346937745416622, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.3562026836409853, 0.3635243844573359, 0.309727986680287], 0.0038713948967191466, 0.43490959394031214), [8.717797558762465, 0.0, 0.0, 0.0, -5.329362059354715, 1.927215437532789, 2.1413599561398255, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6547290646713112, 0.8311844039711347, 0.3538049975932579], 0.004154302641783906, 0.5842214092626906), [6.95468678089278, 0.0, 0.0, 0.0, -0.26889425383548615, 5.455632900159945, 0.18581332796087613, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5388794936906567, 0.04350921485134718, 0.23629199234128806], 0.006559279199653211, 0.9196974029361853), [7.405157852909614, 0.0, 0.0, 0.0, -0.6529358028805777, -11.2963043390672, -2.91169792948822, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, 0.13080774080166646), [6.808606792136021, 0.0, 0.0, 0.0, -0.9111986992873469, 5.362862739910923, 4.495324132308462, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6177567582580967, 0.38039525218264447, 0.37934078500465196], 0.010186078857427224, 0.2366140514268097), [11.921598844654353, 0.0, 0.0, 0.0, 7.200411754134824, 89.02612612758858, 98.32074510763668, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6781091106154422, 0.44334927922889245, 0.36064371233973214], 0.01036251002724151, 0.2743759198193091), [9.314269146067007, 0.0, 0.0, 0.0, 8.622634737411559, 10.442703018323094, 2.8516623050362013, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.20158107237490663, 0.3238946945648584, 0.24399963650509682], 0.009664372151238956, 0.47733204119516204), [7.6745848038899, 0.0, 0.0, 0.0, -6.292867218536123, -1.9303407565718314, -4.440111319869195, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, 0.4401491209134364), [7.332967741437809, 0.0, 0.0, 0.0, -9.697414526287979, -8.79693777899164, -1.907340053628442, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, 0.17728847529212788), [7.947029043250998, 0.0, 0.0, 0.0, -1.1234362906646078, 4.290370818176258, 6.7821312097650095, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, 0.6409979037657155), [6.637146429694789, 0.0, 0.0, 0.0, 3.5215079301835996, 3.242536913859295, 4.5734372311785485, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[], DerivativesSwitch{true, true, true}())</code></pre><h2 id="Resize-and-Recenter-Branches"><a class="docs-heading-anchor" href="#Resize-and-Recenter-Branches">Resize and Recenter Branches</a><a id="Resize-and-Recenter-Branches-1"></a><a class="docs-heading-anchor-permalink" href="#Resize-and-Recenter-Branches" title="Permalink"></a></h2><p>The initial creation of the octree will create uniformly sized and spaced branches in each level. These branches are not centered or optimally sized with relation to the bodies they contain. As a default, the <code>fmm!</code> call resizes and recenters these branches to utilize the smallest possible radius that contains all the bodies in each branch[<a href="../theory/#DENG2021265">3</a>]. This feature can be toggled with the <code>source_shrink_recenter</code> and <code>target_shrink_recenter</code> parameters.</p><pre><code class="language-julia hljs">target_system = generate_gravitational(123, 100)
+    nearfield=false, farfield=true, self_induced=true) # nearfield not evaluated</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49850630217496006, 0.5029084590406193, 0.4970227729348794], 0.8572644572282587, 0.8572644572282587, [-0.49494186514743355, 0.49494186514743355, -0.49494186514743355, 0.49494186514743355, -0.49494186514743355, 0.49494186514743355], [0.49494186514743355, 0.49494186514743355, 0.49494186514743355], 0.0, 0.0, fill(0.0), [-48.34870113041748 0.0; 0.0 0.0;;; 2.598422019775752 0.0; 0.0 0.0;;; -1.2227362282002523 0.0; 0.8450131042390987 0.0;;; … ;;; -8.791709687591729e-5 0.0; -0.0004287156900488262 0.0;;; 8.822613231853985e-5 0.0; -0.00020008302331153626 0.0;;; -1.2615951275491288e-5 0.0; -3.065550426595302e-6 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835852832368, 139835852832400, 416568829732))), SingleBranch{Float64}(1:14, 0, 10:9, 1, 1, [0.2510353696012433, 0.25543752646690254, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-6.487390818499682 0.0; 0.0 0.0;;; 0.1316240843801879 0.0; 0.0 0.0;;; 0.025249123866722074 0.0; 0.110233400590797 0.0;;; … ;;; -3.455130567368021e-6 0.0; 5.924004312810844e-7 0.0;;; 1.5153888935850128e-6 0.0; -1.7047891151365984e-6 0.0;;; 1.5070525582333026e-7 0.0; 1.8849553081710956e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.2148612382952998 0.0; -0.0 0.0;;; -0.04833896697010254 0.0; -0.08941268169127015 0.0;;; … ;;; 3.5751904359505736e-6 0.0; 3.0080507578758053e-7 0.0;;; 3.8236458599367976e-7 0.0; 8.757176386082573e-7 0.0;;; -5.567979953388733e-8 0.0; 7.122692732518039e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 415509289671))), SingleBranch{Float64}(15:32, 0, 10:9, 1, 2, [0.7459772347486768, 0.25543752646690254, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-11.124170053937009 0.0; 0.0 0.0;;; 0.41138770543633796 0.0; 0.0 0.0;;; 0.016803023250878363 0.0; -0.14477677533550787 0.0;;; … ;;; -8.963509625362107e-6 0.0; 4.693012478346667e-6 0.0;;; 4.410168138692953e-6 0.0; -2.126045985106235e-7 0.0;;; -1.8361776114546595e-8 0.0; -2.1883614233265213e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.11109187197856953 0.0; -0.0 0.0;;; -0.09395587638099494 0.0; -0.03393406206661734 0.0;;; … ;;; -3.0928893153242635e-7 0.0; -5.266357454009592e-7 0.0;;; -8.453485198034652e-8 0.0; -4.5314409979717737e-7 0.0;;; 1.3384370562270982e-8 0.0; -8.18136577012236e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281974944, 20753281979104, 141733921440))), SingleBranch{Float64}(33:42, 0, 10:9, 1, 3, [0.2510353696012433, 0.7503793916143361, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-5.116346939838825 0.0; 0.0 0.0;;; -0.08994400460681298 0.0; 0.0 0.0;;; -0.13497721301696344 0.0; 0.06706823073367696 0.0;;; … ;;; -1.0362892970772102e-6 0.0; 1.2247154898001747e-6 0.0;;; -1.868656271304562e-7 0.0; 1.6661679454393324e-6 0.0;;; 6.543631075683181e-7 0.0; -6.940763763815243e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.1902545870569238 0.0; -0.0 0.0;;; -0.08523619914991601 0.0; 0.10063606184199078 0.0;;; … ;;; 4.515701992660869e-6 0.0; 2.690965808809799e-6 0.0;;; 2.2681808274429954e-6 0.0; -7.785616815693268e-7 0.0;;; 1.2086933929990936e-7 0.0; -3.097138724670615e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (51539607552, 4294967311, 1241245548544))), SingleBranch{Float64}(43:55, 0, 10:9, 1, 4, [0.7459772347486768, 0.7503793916143361, 0.24955184036116262], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-6.531648389278439 0.0; 0.0 0.0;;; 0.27836630809952023 0.0; 0.0 0.0;;; 0.0024199382270112084 0.0; 0.3732722019731095 0.0;;; … ;;; 3.376714829662012e-6 0.0; -2.67253441421499e-6 0.0;;; -1.3437328271781197e-6 0.0; 8.280933433509673e-7 0.0;;; -2.6353089381680604e-7 0.0; -4.924657915182052e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.10425315723209527 0.0; -0.0 0.0;;; -0.04040250617839929 0.0; -0.04562408503868281 0.0;;; … ;;; 1.3994426612384809e-7 0.0; -9.646789543011186e-8 0.0;;; 5.8163042620289284e-8 0.0; 1.4387157402797034e-8 0.0;;; 3.2488834697645844e-9 0.0; 6.2058798109508465e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 143288556673))), SingleBranch{Float64}(56:68, 0, 10:9, 1, 5, [0.2510353696012433, 0.25543752646690254, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-6.660580658394574 0.0; 0.0 0.0;;; -0.395153340334315 0.0; 0.0 0.0;;; 0.05979789873527955 0.0; 0.07530541218541535 0.0;;; … ;;; 2.090523898062051e-6 0.0; -2.515462436886501e-6 0.0;;; 1.3306773654521538e-6 0.0; 8.501110961871042e-7 0.0;;; -4.5790897504950176e-7 0.0; 1.3805850178672174e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.1406114031795701 0.0; 0.0 0.0;;; 0.04115679478744828 0.0; -0.03533755162400021 0.0;;; … ;;; -1.2881546024813352e-7 0.0; -2.0655710448954946e-7 0.0;;; -4.840981119340681e-8 0.0; -1.5172010562775518e-8 0.0;;; -3.596485511575488e-9 0.0; 1.545042368324494e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835895374544, 139835895374576, 1242779380730))), SingleBranch{Float64}(69:78, 0, 10:9, 1, 6, [0.7459772347486768, 0.25543752646690254, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-5.009402189699274 0.0; 0.0 0.0;;; -0.19304510892164647 0.0; 0.0 0.0;;; 0.12963654004199454 0.0; 0.10016855294092004 0.0;;; … ;;; -2.032871463751076e-6 0.0; 1.1604382246619326e-6 0.0;;; 1.6073455016687304e-6 0.0; 7.525148568942718e-7 0.0;;; -2.1131812349704138e-7 0.0; -2.403269261044048e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.05941950550840777 0.0; -0.0 0.0;;; -0.06984898585556935 0.0; 0.10325321360106476 0.0;;; … ;;; -6.688472512156468e-7 0.0; -1.4501297809812144e-7 0.0;;; 4.3233604883670166e-7 0.0; -4.1299565937718063e-7 0.0;;; -4.1888246519238254e-8 0.0; -2.4735114753799555e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (4294967297, 1, 413856241763))), SingleBranch{Float64}(79:86, 0, 10:9, 1, 7, [0.2510353696012433, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-3.769527893701526 0.0; 0.0 0.0;;; -0.01938418608836119 0.0; 0.0 0.0;;; -0.0011822923413632442 0.0; -0.1457672462486248 0.0;;; … ;;; -1.035853369522652e-5 0.0; 1.2914125498780046e-6 0.0;;; -2.4874690174267746e-7 0.0; -3.1553943207752724e-6 0.0;;; 4.921174899074237e-7 0.0; 2.978833721286661e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.19774130005920343 0.0; -0.0 0.0;;; 0.10337420516639845 0.0; -0.003702501499532632 0.0;;; … ;;; 3.0951077862846165e-6 0.0; -3.337097810420304e-7 0.0;;; -9.336410389602992e-7 0.0; 1.3462336691028458e-7 0.0;;; 9.711269933660484e-8 0.0; -1.7571838450287563e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281981120, 0, 413008291478))), SingleBranch{Float64}(87:100, 0, 10:9, 1, 8, [0.7459772347486768, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [-3.6496341870681537 0.0; 0.0 0.0;;; -0.04231060050009968 0.0; 0.0 0.0;;; -0.05660139398222258 0.0; -0.12020325670765074 0.0;;; … ;;; 1.2674714042901395e-7 0.0; 9.742117200541327e-7 0.0;;; 6.169136545969979e-7 0.0; -3.979999499773143e-7 0.0;;; 1.6497981578864858e-7 0.0; 5.910575433895744e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (1, 0, 415114290605)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.00551624732815934, 0.2538490889415096), [7.0834787492030005, 0.0, 0.0, 0.0, 5.568735643477791, 2.9213884843016737, 0.7633475677477748, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8192008435733007, 0.9541592624784624, 0.8458950823510601], 0.0014709561750558223, 0.03209667335274724), [5.114232575764009, 0.0, 0.0, 0.0, 2.446182605378621, 4.41119482090726, 3.440180697344876, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.586748700554989, 0.12181263792534469, 0.7894931647499924], 0.0016174951280755708, 0.8935369466209786), [6.585365931828452, 0.0, 0.0, 0.0, 2.5334789856996256, -5.935281910533853, 5.877738846695876, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6192588014774537, 0.47764531343080796, 0.8041934288169849], 0.003639098305331564, 0.8236563299357046), [7.314225348781349, 0.0, 0.0, 0.0, 2.0263196413417575, -0.5909579553411834, 6.438131407639304, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.12353811904859124, 0.7400202596259494, 0.7057473220960516], 0.004975260027225807, 0.9340155879013086), [5.994006655657172, 0.0, 0.0, 0.0, -3.6150300092368397, 3.588312709800555, 2.445983480158574, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9919607797239652, 0.8036971367794874, 0.29827230692896456], 0.006659427674753824, 0.4842893268146866), [6.3093512714054905, 0.0, 0.0, 0.0, 6.811100230860857, 3.229004706340305, 0.7635631719803121, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.49265789199054244, 0.17985285886739166, 0.6397154045236242], 0.004022070032387327, 0.6922349538863742), [7.856042192681273, 0.0, 0.0, 0.0, 0.5375760890909462, -5.141800886434623, 1.9448732399847593, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.22768758746068596, 0.26780944724527167, 0.8309795986773825], 0.006802835099514221, 0.6911617055492341), [8.668207473779663, 0.0, 0.0, 0.0, -3.782240224623742, 18.504359731864223, 92.23746117912798, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0010425988209884726, 0.09206661519876747), [7.388934820369321, 0.0, 0.0, 0.0, -0.5191138373209423, 4.756088137496654, -3.410201822139256, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.00633005068065063, 0.37737321139310276), [7.64606632116185, 0.0, 0.0, 0.0, 0.09461688248299382, 7.241804506257593, 4.346937745416622, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.3562026836409853, 0.3635243844573359, 0.309727986680287], 0.0038713948967191466, 0.43490959394031214), [8.717797558762465, 0.0, 0.0, 0.0, -5.329362059354715, 1.927215437532789, 2.1413599561398255, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6547290646713112, 0.8311844039711347, 0.3538049975932579], 0.004154302641783906, 0.5842214092626906), [6.95468678089278, 0.0, 0.0, 0.0, -0.26889425383548615, 5.455632900159945, 0.18581332796087613, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5388794936906567, 0.04350921485134718, 0.23629199234128806], 0.006559279199653211, 0.9196974029361853), [7.405157852909614, 0.0, 0.0, 0.0, -0.6529358028805777, -11.2963043390672, -2.91169792948822, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, 0.13080774080166646), [6.808606792136021, 0.0, 0.0, 0.0, -0.9111986992873469, 5.362862739910923, 4.495324132308462, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6177567582580967, 0.38039525218264447, 0.37934078500465196], 0.010186078857427224, 0.2366140514268097), [11.921598844654353, 0.0, 0.0, 0.0, 7.200411754134824, 89.02612612758858, 98.32074510763668, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6781091106154422, 0.44334927922889245, 0.36064371233973214], 0.01036251002724151, 0.2743759198193091), [9.314269146067007, 0.0, 0.0, 0.0, 8.622634737411559, 10.442703018323094, 2.8516623050362013, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.20158107237490663, 0.3238946945648584, 0.24399963650509682], 0.009664372151238956, 0.47733204119516204), [7.6745848038899, 0.0, 0.0, 0.0, -6.292867218536123, -1.9303407565718314, -4.440111319869195, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, 0.4401491209134364), [7.332967741437809, 0.0, 0.0, 0.0, -9.697414526287979, -8.79693777899164, -1.907340053628442, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, 0.17728847529212788), [7.947029043250998, 0.0, 0.0, 0.0, -1.1234362906646078, 4.290370818176258, 6.7821312097650095, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, 0.6409979037657155), [6.637146429694789, 0.0, 0.0, 0.0, 3.5215079301835996, 3.242536913859295, 4.5734372311785485, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[], DerivativesSwitch{true, true, true}())</code></pre><h2 id="Resize-and-Recenter-Branches"><a class="docs-heading-anchor" href="#Resize-and-Recenter-Branches">Resize and Recenter Branches</a><a id="Resize-and-Recenter-Branches-1"></a><a class="docs-heading-anchor-permalink" href="#Resize-and-Recenter-Branches" title="Permalink"></a></h2><p>The initial creation of the octree will create uniformly sized and spaced branches in each level. These branches are not centered or optimally sized with relation to the bodies they contain. As a default, the <code>fmm!</code> call resizes and recenters these branches to utilize the smallest possible radius that contains all the bodies in each branch[<a href="../theory/#DENG2021265">3</a>]. This feature can be toggled with the <code>source_shrink_recenter</code> and <code>target_shrink_recenter</code> parameters.</p><pre><code class="language-julia hljs">target_system = generate_gravitational(123, 100)
 source_system = generate_gravitational(321, 100)
 
 fmm.fmm!(target_system, source_system,
     source_shrink_recenter=true, target_shrink_recenter=true) # standard run (defaults)
 fmm.fmm!(target_system, source_system,
-    source_shrink_recenter=false, target_shrink_recenter=false) # no branch recentering</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49849075893959255, 0.5011246180164968, 0.50101931980297], 0.8617443734929683, 0.8617443734929683, [-0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063], [0.49752834600881063, 0.49752834600881063, 0.49752834600881063], 0.0, 0.0, fill(0.0), [-49.209733528008485 0.0; 0.0 0.0;;; 3.235503852070556 0.0; 0.0 0.0;;; 0.02681865248285842 0.0; 0.9591193094494834 0.0;;; … ;;; -0.0004469512083583767 0.0; -0.00015932419565861916 0.0;;; -0.00028710529956597804 0.0; -0.00031904516877669385 0.0;;; -7.588266430169126e-6 0.0; -8.400184364295124e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 432022829898))), SingleBranch{Float64}(1:13, 0, 10:9, 1, 1, [0.24972658593518723, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.326393509059363 0.0; 0.0 0.0;;; 0.10174482633884264 0.0; 0.0 0.0;;; -0.07898687772271276 0.0; 0.03841659635534152 0.0;;; … ;;; -9.654710862452212e-7 0.0; -5.591129557725438e-7 0.0;;; 1.175731767951614e-6 0.0; 2.391893864725776e-6 0.0;;; -3.893767927840696e-8 0.0; -4.373076778562484e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21988918332658114 0.0; 0.0 0.0;;; -0.00907173901579822 0.0; -0.08078608463780172 0.0;;; … ;;; 6.639561085749197e-7 0.0; 1.9043445262044332e-6 0.0;;; 3.6078285954161947e-7 0.0; -1.730779168448776e-7 0.0;;; -1.5694464749247868e-8 0.0; -2.5081831237534205e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 430488950719))), SingleBranch{Float64}(14:23, 0, 10:9, 1, 2, [0.7472549319439978, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.505985520323303 0.0; 0.0 0.0;;; -0.0893400706965472 0.0; 0.0 0.0;;; 0.07469760206429724 0.0; -0.23211041531103774 0.0;;; … ;;; -2.392727383648695e-6 0.0; -2.7506172478695797e-7 0.0;;; 1.2869752996385646e-6 0.0; 8.632541193951725e-7 0.0;;; -1.4323853566229846e-7 0.0; 3.40320513459477e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.18613078162840202 0.0; 0.0 0.0;;; -0.03988177380448188 0.0; -0.10881091326674686 0.0;;; … ;;; 3.1493849180079693e-6 0.0; 1.79002742056861e-6 0.0;;; 2.3049009571265728e-7 0.0; -1.3797688581858191e-6 0.0;;; -1.7119818873987816e-7 0.0; 3.217930041360891e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 432022829898))), SingleBranch{Float64}(24:40, 0, 10:9, 1, 3, [0.24972658593518723, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-7.986155913622251 0.0; 0.0 0.0;;; -0.1795979615961002 0.0; 0.0 0.0;;; -0.1708212423759164 0.0; 0.03135320324442914 0.0;;; … ;;; -6.066362373385743e-6 0.0; 2.4234495602853986e-6 0.0;;; 2.327392085993626e-6 0.0; 4.871331224296273e-7 0.0;;; 2.4751088043185402e-8 0.0; -5.827716675663792e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.23122788327035293 0.0; 0.0 0.0;;; -0.04900663119822446 0.0; 0.09175801803089013 0.0;;; … ;;; 4.485772070448108e-6 0.0; -4.4630903906536425e-7 0.0;;; 4.303552019451355e-7 0.0; -1.0428735117063708e-6 0.0;;; -6.452660186998594e-8 0.0; -7.836101483352229e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 431406102875))), SingleBranch{Float64}(41:57, 0, 10:9, 1, 4, [0.7472549319439978, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-9.931355245362722 0.0; 0.0 0.0;;; 0.004639293314162463 0.0; 0.0 0.0;;; 0.10230318193552163 0.0; 0.3431041586399578 0.0;;; … ;;; -5.8057861586053485e-6 0.0; -3.6767179441275553e-6 0.0;;; 1.970849569609788e-6 0.0; -1.1263384149017906e-6 0.0;;; 4.6063384099401923e-7 0.0; -7.362879677517756e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.24833262559729297 0.0; 0.0 0.0;;; -0.04049792411417641 0.0; 0.11830484901746985 0.0;;; … ;;; 7.332767131734295e-6 0.0; -4.818366848970212e-6 0.0;;; 6.296375165101449e-7 0.0; 2.450158453149185e-6 0.0;;; -2.5398566738723024e-7 0.0; -1.9922601565040447e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 432022829898))), SingleBranch{Float64}(58:71, 0, 10:9, 1, 5, [0.24972658593518723, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.0812379817404665 0.0; 0.0 0.0;;; 0.2500525077504865 0.0; 0.0 0.0;;; -0.31821199437047437 0.0; 0.12219381204800842 0.0;;; … ;;; 3.886164164482793e-6 0.0; -7.451230042206713e-6 0.0;;; -1.5655861775267537e-6 0.0; 1.3488384490746591e-6 0.0;;; -2.65136301189794e-7 0.0; -1.0396969077621681e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.23600456619228227 0.0; 0.0 0.0;;; 0.00780054815104303 0.0; 0.01243800251579276 0.0;;; … ;;; -1.457243306148132e-8 0.0; 1.604225902871519e-9 0.0;;; -2.836500215179685e-10 0.0; -3.581821796740947e-10 0.0;;; 1.9003405206797664e-12 0.0; -5.3575717814609175e-12 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 429750419385))), SingleBranch{Float64}(72:82, 0, 10:9, 1, 6, [0.7472549319439978, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.643660411433685 0.0; 0.0 0.0;;; -0.09740163237448708 0.0; 0.0 0.0;;; 0.30569645349438196 0.0; 0.2359234953909746 0.0;;; … ;;; -9.82916763080865e-7 0.0; -4.2285511081766585e-7 0.0;;; 2.7225441029521644e-6 0.0; -9.866422822602592e-7 0.0;;; -2.884182756506517e-7 0.0; 2.1891312191953625e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.137250125216142 0.0; 0.0 0.0;;; -0.041848288296333136 0.0; 0.07154851443791577 0.0;;; … ;;; 7.308420503707386e-7 0.0; 1.2365335735668517e-8 0.0;;; 1.4021073394047346e-7 0.0; -2.3067492312302074e-7 0.0;;; -1.5499976899256273e-8 0.0; -2.8685176609168157e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 432022829898))), 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-4.1299565937718063e-7 0.0;;; -4.1888246519238254e-8 0.0; -2.4735114753799555e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 431322503448))), SingleBranch{Float64}(79:86, 0, 10:9, 1, 7, [0.2510353696012433, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.19774130005920343 0.0; -0.0 0.0;;; 0.10337420516639845 0.0; -0.003702501499532632 0.0;;; … ;;; 3.0951077862846165e-6 0.0; -3.337097810420304e-7 0.0;;; -9.336410389602992e-7 0.0; 1.3462336691028458e-7 0.0;;; 9.711269933660484e-8 0.0; -1.7571838450287563e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659421046512, 140658694308880, -1))), SingleBranch{Float64}(87:100, 0, 10:9, 1, 8, [0.7459772347486768, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659421046512, 140658694308880, 3)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.00551624732815934, 0.2538490889415096), [17.271409969161304, 0.0, 0.0, 0.0, 41.685412355141416, 34.12426438870282, -51.63876083740611, 0.0, 0.0, 0.0  … 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0.8284024454950295, 11.665202214285912, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0010425988209884726, 0.09206661519876747), [17.722712907499606, 0.0, 0.0, 0.0, -9.940219848256183, 17.727356485985396, -29.098711105724526, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.00633005068065063, 0.37737321139310276), [16.05489877164097, 0.0, 0.0, 0.0, -1.3860752481739533, 7.346902899243912, 19.030178738198078, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.3562026836409853, 0.3635243844573359, 0.309727986680287], 0.0038713948967191466, 0.43490959394031214), [17.98003272398291, 0.0, 0.0, 0.0, -6.176928042529583, -6.83720001434035, -5.104865976947373, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6547290646713112, 0.8311844039711347, 0.3538049975932579], 0.004154302641783906, 0.5842214092626906), [19.759661981521948, 0.0, 0.0, 0.0, 2.1460904804827003, 22.402074129288803, 38.03301983987145, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5388794936906567, 0.04350921485134718, 0.23629199234128806], 0.006559279199653211, 0.9196974029361853), [15.25309168181086, 0.0, 0.0, 0.0, 10.352682001138295, -27.645326895875023, -2.5692266359007827, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, 0.13080774080166646), [14.120390177961934, 0.0, 0.0, 0.0, -1.770561231400227, 8.777886446209552, 15.293358878789466, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6177567582580967, 0.38039525218264447, 0.37934078500465196], 0.010186078857427224, 0.2366140514268097), [19.989481091602663, 0.0, 0.0, 0.0, 8.002207700492232, -27.907771334220058, -16.494951316871173, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6781091106154422, 0.44334927922889245, 0.36064371233973214], 0.01036251002724151, 0.2743759198193091), [19.81705582450624, 0.0, 0.0, 0.0, 12.06418885791642, -5.798482118132713, -4.308943660676608, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.20158107237490663, 0.3238946945648584, 0.24399963650509682], 0.009664372151238956, 0.47733204119516204), [16.09145579771531, 0.0, 0.0, 0.0, -9.056889348091818, -6.4324259288317, -9.833126873177216, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, 0.4401491209134364), [14.946809903378847, 0.0, 0.0, 0.0, -14.889338356696868, 0.1483895783560294, 4.026318082371973, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, 0.17728847529212788), [15.085750970541683, 0.0, 0.0, 0.0, -19.61109590484976, -9.907966126632697, 6.262829492967415, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, 0.6409979037657155), [14.872272809760988, 0.0, 0.0, 0.0, 3.9248367357842517, 7.73617997006026, 12.068889746971752, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], DerivativesSwitch{true, true, true}())</code></pre></article><nav class="docs-footer"><a 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+    source_shrink_recenter=false, target_shrink_recenter=false) # no branch recentering</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49849075893959255, 0.5011246180164968, 0.50101931980297], 0.8617443734929683, 0.8617443734929683, [-0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063], [0.49752834600881063, 0.49752834600881063, 0.49752834600881063], 0.0, 0.0, fill(0.0), [-49.209733528008485 0.0; 0.0 0.0;;; 3.235503852070556 0.0; 0.0 0.0;;; 0.02681865248285842 0.0; 0.9591193094494834 0.0;;; … ;;; -0.0004469512083583767 0.0; -0.00015932419565861916 0.0;;; -0.00028710529956597804 0.0; -0.00031904516877669385 0.0;;; -7.588266430169126e-6 0.0; -8.400184364295124e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835868900016, 139835868900048, 139835767718704))), SingleBranch{Float64}(1:13, 0, 10:9, 1, 1, [0.24972658593518723, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.326393509059363 0.0; 0.0 0.0;;; 0.10174482633884264 0.0; 0.0 0.0;;; -0.07898687772271276 0.0; 0.03841659635534152 0.0;;; … ;;; -9.654710862452212e-7 0.0; -5.591129557725438e-7 0.0;;; 1.175731767951614e-6 0.0; 2.391893864725776e-6 0.0;;; -3.893767927840696e-8 0.0; -4.373076778562484e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21988918332658114 0.0; 0.0 0.0;;; -0.00907173901579822 0.0; -0.08078608463780172 0.0;;; … ;;; 6.639561085749197e-7 0.0; 1.9043445262044332e-6 0.0;;; 3.6078285954161947e-7 0.0; -1.730779168448776e-7 0.0;;; -1.5694464749247868e-8 0.0; -2.5081831237534205e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835716062976, 139835716062976, 139835767718704))), SingleBranch{Float64}(14:23, 0, 10:9, 1, 2, [0.7472549319439978, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.505985520323303 0.0; 0.0 0.0;;; -0.0893400706965472 0.0; 0.0 0.0;;; 0.07469760206429724 0.0; -0.23211041531103774 0.0;;; … ;;; -2.392727383648695e-6 0.0; -2.7506172478695797e-7 0.0;;; 1.2869752996385646e-6 0.0; 8.632541193951725e-7 0.0;;; -1.4323853566229846e-7 0.0; 3.40320513459477e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.18613078162840202 0.0; 0.0 0.0;;; -0.03988177380448188 0.0; -0.10881091326674686 0.0;;; … ;;; 3.1493849180079693e-6 0.0; 1.79002742056861e-6 0.0;;; 2.3049009571265728e-7 0.0; -1.3797688581858191e-6 0.0;;; -1.7119818873987816e-7 0.0; 3.217930041360891e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (1, 0, 20))), SingleBranch{Float64}(24:40, 0, 10:9, 1, 3, [0.24972658593518723, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-7.986155913622251 0.0; 0.0 0.0;;; -0.1795979615961002 0.0; 0.0 0.0;;; -0.1708212423759164 0.0; 0.03135320324442914 0.0;;; … ;;; -6.066362373385743e-6 0.0; 2.4234495602853986e-6 0.0;;; 2.327392085993626e-6 0.0; 4.871331224296273e-7 0.0;;; 2.4751088043185402e-8 0.0; -5.827716675663792e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.23122788327035293 0.0; 0.0 0.0;;; -0.04900663119822446 0.0; 0.09175801803089013 0.0;;; … ;;; 4.485772070448108e-6 0.0; -4.4630903906536425e-7 0.0;;; 4.303552019451355e-7 0.0; -1.0428735117063708e-6 0.0;;; -6.452660186998594e-8 0.0; -7.836101483352229e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835090528128, 139835090528144, 0))), SingleBranch{Float64}(41:57, 0, 10:9, 1, 4, [0.7472549319439978, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-9.931355245362722 0.0; 0.0 0.0;;; 0.004639293314162463 0.0; 0.0 0.0;;; 0.10230318193552163 0.0; 0.3431041586399578 0.0;;; … ;;; -5.8057861586053485e-6 0.0; -3.6767179441275553e-6 0.0;;; 1.970849569609788e-6 0.0; -1.1263384149017906e-6 0.0;;; 4.6063384099401923e-7 0.0; -7.362879677517756e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.24833262559729297 0.0; 0.0 0.0;;; -0.04049792411417641 0.0; 0.11830484901746985 0.0;;; … ;;; 7.332767131734295e-6 0.0; -4.818366848970212e-6 0.0;;; 6.296375165101449e-7 0.0; 2.450158453149185e-6 0.0;;; -2.5398566738723024e-7 0.0; -1.9922601565040447e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835090528224, 139835829213856, 139835914346112))), SingleBranch{Float64}(58:71, 0, 10:9, 1, 5, [0.24972658593518723, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.0812379817404665 0.0; 0.0 0.0;;; 0.2500525077504865 0.0; 0.0 0.0;;; -0.31821199437047437 0.0; 0.12219381204800842 0.0;;; … ;;; 3.886164164482793e-6 0.0; -7.451230042206713e-6 0.0;;; -1.5655861775267537e-6 0.0; 1.3488384490746591e-6 0.0;;; -2.65136301189794e-7 0.0; -1.0396969077621681e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.23600456619228227 0.0; 0.0 0.0;;; 0.00780054815104303 0.0; 0.01243800251579276 0.0;;; … ;;; -1.457243306148132e-8 0.0; 1.604225902871519e-9 0.0;;; -2.836500215179685e-10 0.0; -3.581821796740947e-10 0.0;;; 1.9003405206797664e-12 0.0; -5.3575717814609175e-12 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835090528257, 139835735744976, 0))), SingleBranch{Float64}(72:82, 0, 10:9, 1, 6, [0.7472549319439978, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.643660411433685 0.0; 0.0 0.0;;; -0.09740163237448708 0.0; 0.0 0.0;;; 0.30569645349438196 0.0; 0.2359234953909746 0.0;;; … ;;; -9.82916763080865e-7 0.0; -4.2285511081766585e-7 0.0;;; 2.7225441029521644e-6 0.0; -9.866422822602592e-7 0.0;;; -2.884182756506517e-7 0.0; 2.1891312191953625e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.137250125216142 0.0; 0.0 0.0;;; -0.041848288296333136 0.0; 0.07154851443791577 0.0;;; … ;;; 7.308420503707386e-7 0.0; 1.2365335735668517e-8 0.0;;; 1.4021073394047346e-7 0.0; -2.3067492312302074e-7 0.0;;; -1.5499976899256273e-8 0.0; -2.8685176609168157e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835851580576, 139835851580448, 2886218027744))), SingleBranch{Float64}(83:89, 0, 10:9, 1, 7, [0.24972658593518723, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-2.3207471469996026 0.0; 0.0 0.0;;; 0.09584922777112714 0.0; 0.0 0.0;;; -0.03459176396777507 0.0; -0.04020642273548641 0.0;;; … ;;; 3.930977957593639e-6 0.0; -1.9071506252246133e-6 0.0;;; 4.262561393862879e-7 0.0; 6.012045573535614e-7 0.0;;; -1.296847519879538e-7 0.0; -1.748757755002258e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.14971540025278463 0.0; 0.0 0.0;;; -0.10199818137039851 0.0; -0.00404107784645201 0.0;;; … ;;; -1.5142366400508734e-6 0.0; -1.807350708728618e-7 0.0;;; 6.688310694761936e-7 0.0; 1.0683350833198992e-7 0.0;;; -9.055558759133121e-8 0.0; -1.8167298693653792e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835767718704, 139835767718704, 1))), SingleBranch{Float64}(90:100, 0, 10:9, 1, 8, [0.7472549319439978, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.414197799467094 0.0; 0.0 0.0;;; 0.5897626670629665 0.0; 0.0 0.0;;; -0.1138694027478626 0.0; -0.009802047749392043 0.0;;; … ;;; 1.152740503052551e-5 0.0; -4.517016990218442e-6 0.0;;; -4.140046433990845e-6 0.0; -1.566383749352849e-6 0.0;;; 1.2469713505945974e-7 0.0; 2.024928160458584e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21095730321733874 0.0; 0.0 0.0;;; 0.09347241596581823 0.0; -0.08394581821691316 0.0;;; … ;;; -3.5372171155417328e-6 0.0; -4.908219455216665e-6 0.0;;; -2.1396426594075856e-6 0.0; -4.6629625718216964e-7 0.0;;; -2.2671999108049045e-7 0.0; 1.289627938417499e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 139835914320128)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [8, 19, 24, 25, 30, 33, 35, 43, 52, 55  …  37, 41, 42, 49, 64, 71, 78, 79, 87, 88], [90, 83, 24, 72, 58, 59, 25, 1, 60, 73  …  23, 38, 80, 56, 39, 81, 82, 40, 13, 57], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.7287348331279035, 0.8645178072081, 0.9863586950447876], 0.002824412632887574, 0.3155425281087243), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.04871498957839171, 0.5228239956008278, 0.9981161184046683], 0.0010354523583936332, 0.10074227409525549), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.26339547338830394, 0.8205923530535013, 0.013801744155504059], 0.000561123611422205, 0.48127815547923203), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9156175145346829, 0.2751207698440503, 0.5246024619099758], 0.0098534859774698, 0.26935622770690937), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.23794338253051606, 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… ;;; -1.2881546024813352e-7 0.0; -2.0655710448954946e-7 0.0;;; -4.840981119340681e-8 0.0; -1.5172010562775518e-8 0.0;;; -3.596485511575488e-9 0.0; 1.545042368324494e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835868904816, 139835851580688, 4800))), SingleBranch{Float64}(69:78, 0, 10:9, 1, 6, [0.7459772347486768, 0.25543752646690254, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.05941950550840777 0.0; -0.0 0.0;;; -0.06984898585556935 0.0; 0.10325321360106476 0.0;;; … ;;; -6.688472512156468e-7 0.0; -1.4501297809812144e-7 0.0;;; 4.3233604883670166e-7 0.0; -4.1299565937718063e-7 0.0;;; -4.1888246519238254e-8 0.0; -2.4735114753799555e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835914852936, 0, 413776301541))), SingleBranch{Float64}(79:86, 0, 10:9, 1, 7, [0.2510353696012433, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.19774130005920343 0.0; -0.0 0.0;;; 0.10337420516639845 0.0; -0.003702501499532632 0.0;;; … ;;; 3.0951077862846165e-6 0.0; -3.337097810420304e-7 0.0;;; -9.336410389602992e-7 0.0; 1.3462336691028458e-7 0.0;;; 9.711269933660484e-8 0.0; -1.7571838450287563e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835914940048, 139835914907744, 8589934594))), SingleBranch{Float64}(87:100, 0, 10:9, 1, 8, [0.7459772347486768, 0.7503793916143361, 0.7444937055085962], 0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835851580816, 139835767727712, 139835767718704)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.00551624732815934, 0.2538490889415096), [17.271409969161304, 0.0, 0.0, 0.0, 41.685412355141416, 34.12426438870282, -51.63876083740611, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8192008435733007, 0.9541592624784624, 0.8458950823510601], 0.0014709561750558223, 0.03209667335274724), [11.529739095286155, 0.0, 0.0, 0.0, 1.024496302655218, 10.679868569840236, 10.166694863850497, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.586748700554989, 0.12181263792534469, 0.7894931647499924], 0.0016174951280755708, 0.8935369466209786), [13.46622737210304, 0.0, 0.0, 0.0, 4.201427260478692, -11.777746989315899, 8.494900903588235, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6192588014774537, 0.47764531343080796, 0.8041934288169849], 0.003639098305331564, 0.8236563299357046), [16.810905005346296, 0.0, 0.0, 0.0, 20.653133771733803, 22.29084743955388, 12.956920331242188, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.12353811904859124, 0.7400202596259494, 0.7057473220960516], 0.004975260027225807, 0.9340155879013086), [13.212106090876661, 0.0, 0.0, 0.0, -6.564084687557748, 10.714720577279024, 7.1489651530156975, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9919607797239652, 0.8036971367794874, 0.29827230692896456], 0.006659427674753824, 0.4842893268146866), [15.293301715719982, 0.0, 0.0, 0.0, 20.840068737911185, 6.203972731398467, 2.3564006118821963, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.49265789199054244, 0.17985285886739166, 0.6397154045236242], 0.004022070032387327, 0.6922349538863742), [16.030214365478127, 0.0, 0.0, 0.0, 4.854825245033792, -12.82436694878877, 9.932648614159953, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.22768758746068596, 0.26780944724527167, 0.8309795986773825], 0.006802835099514221, 0.6911617055492341), [13.477674670011098, 0.0, 0.0, 0.0, -7.615430967959103, 0.8284024454950295, 11.665202214285912, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0010425988209884726, 0.09206661519876747), [17.722712907499606, 0.0, 0.0, 0.0, -9.940219848256183, 17.727356485985396, -29.098711105724526, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.00633005068065063, 0.37737321139310276), [16.05489877164097, 0.0, 0.0, 0.0, -1.3860752481739533, 7.346902899243912, 19.030178738198078, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.3562026836409853, 0.3635243844573359, 0.309727986680287], 0.0038713948967191466, 0.43490959394031214), [17.98003272398291, 0.0, 0.0, 0.0, -6.176928042529583, -6.83720001434035, -5.104865976947373, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6547290646713112, 0.8311844039711347, 0.3538049975932579], 0.004154302641783906, 0.5842214092626906), [19.759661981521948, 0.0, 0.0, 0.0, 2.1460904804827003, 22.402074129288803, 38.03301983987145, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5388794936906567, 0.04350921485134718, 0.23629199234128806], 0.006559279199653211, 0.9196974029361853), [15.25309168181086, 0.0, 0.0, 0.0, 10.352682001138295, -27.645326895875023, -2.5692266359007827, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, 0.13080774080166646), [14.120390177961934, 0.0, 0.0, 0.0, -1.770561231400227, 8.777886446209552, 15.293358878789466, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6177567582580967, 0.38039525218264447, 0.37934078500465196], 0.010186078857427224, 0.2366140514268097), [19.989481091602663, 0.0, 0.0, 0.0, 8.002207700492232, -27.907771334220058, -16.494951316871173, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6781091106154422, 0.44334927922889245, 0.36064371233973214], 0.01036251002724151, 0.2743759198193091), [19.81705582450624, 0.0, 0.0, 0.0, 12.06418885791642, -5.798482118132713, -4.308943660676608, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.20158107237490663, 0.3238946945648584, 0.24399963650509682], 0.009664372151238956, 0.47733204119516204), [16.09145579771531, 0.0, 0.0, 0.0, -9.056889348091818, -6.4324259288317, -9.833126873177216, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, 0.4401491209134364), [14.946809903378847, 0.0, 0.0, 0.0, -14.889338356696868, 0.1483895783560294, 4.026318082371973, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, 0.17728847529212788), [15.085750970541683, 0.0, 0.0, 0.0, -19.61109590484976, -9.907966126632697, 6.262829492967415, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, 0.6409979037657155), [14.872272809760988, 0.0, 0.0, 0.0, 3.9248367357842517, 7.73617997006026, 12.068889746971752, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], DerivativesSwitch{true, true, true}())</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../guided_examples/">« Guided Examples</a><a class="docs-footer-nextpage" href="../reference/">Reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/guided_examples/index.html b/dev/guided_examples/index.html
index 84e4709..9c54cca 100644
--- a/dev/guided_examples/index.html
+++ b/dev/guided_examples/index.html
@@ -129,7 +129,7 @@
 0.06721954776336198</code></pre><h2 id="Evaluate-Source-on-Target"><a class="docs-heading-anchor" href="#Evaluate-Source-on-Target">Evaluate Source on Target</a><a id="Evaluate-Source-on-Target-1"></a><a class="docs-heading-anchor-permalink" href="#Evaluate-Source-on-Target" title="Permalink"></a></h2><p><code>FastMutipole</code> allows for the evaluation of source systems on target systems while leaving the source systems unaltered.</p><pre><code class="language-julia hljs">target_system = generate_gravitational(123, 100)
 source_system = generate_gravitational(321, 100)
 
-fmm.fmm!(target_system, source_system)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49849075893959255, 0.5011246180164968, 0.50101931980297], 0.8617443734929683, 0.8617443734929683, [-0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063], [0.49752834600881063, 0.49752834600881063, 0.49752834600881063], 0.0, 0.0, fill(0.0), [-49.209733528008485 0.0; 0.0 0.0;;; 3.235503852070556 0.0; 0.0 0.0;;; 0.02681865248285842 0.0; 0.9591193094494834 0.0;;; … ;;; -0.0004469512083583767 0.0; -0.00015932419565861916 0.0;;; -0.00028710529956597804 0.0; -0.00031904516877669385 0.0;;; -7.588266430169126e-6 0.0; -8.400184364295124e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658686973712, 140658686973744, 1))), SingleBranch{Float64}(1:13, 0, 10:9, 1, 1, [0.24972658593518723, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.326393509059363 0.0; 0.0 0.0;;; 0.10174482633884264 0.0; 0.0 0.0;;; -0.07898687772271276 0.0; 0.03841659635534152 0.0;;; … ;;; -9.654710862452212e-7 0.0; -5.591129557725438e-7 0.0;;; 1.175731767951614e-6 0.0; 2.391893864725776e-6 0.0;;; -3.893767927840696e-8 0.0; -4.373076778562484e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21988918332658114 0.0; 0.0 0.0;;; -0.00907173901579822 0.0; -0.08078608463780172 0.0;;; … ;;; 6.639561085749197e-7 0.0; 1.9043445262044332e-6 0.0;;; 3.6078285954161947e-7 0.0; -1.730779168448776e-7 0.0;;; -1.5694464749247868e-8 0.0; -2.5081831237534205e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (3, 3, 0))), SingleBranch{Float64}(14:23, 0, 10:9, 1, 2, [0.7472549319439978, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.505985520323303 0.0; 0.0 0.0;;; -0.0893400706965472 0.0; 0.0 0.0;;; 0.07469760206429724 0.0; -0.23211041531103774 0.0;;; … ;;; -2.392727383648695e-6 0.0; -2.7506172478695797e-7 0.0;;; 1.2869752996385646e-6 0.0; 8.632541193951725e-7 0.0;;; -1.4323853566229846e-7 0.0; 3.40320513459477e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.18613078162840202 0.0; 0.0 0.0;;; -0.03988177380448188 0.0; -0.10881091326674686 0.0;;; … ;;; 3.1493849180079693e-6 0.0; 1.79002742056861e-6 0.0;;; 2.3049009571265728e-7 0.0; -1.3797688581858191e-6 0.0;;; -1.7119818873987816e-7 0.0; 3.217930041360891e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659240390400, 140659240390400, 0))), SingleBranch{Float64}(24:40, 0, 10:9, 1, 3, [0.24972658593518723, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-7.986155913622251 0.0; 0.0 0.0;;; -0.1795979615961002 0.0; 0.0 0.0;;; -0.1708212423759164 0.0; 0.03135320324442914 0.0;;; … ;;; -6.066362373385743e-6 0.0; 2.4234495602853986e-6 0.0;;; 2.327392085993626e-6 0.0; 4.871331224296273e-7 0.0;;; 2.4751088043185402e-8 0.0; -5.827716675663792e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.23122788327035293 0.0; 0.0 0.0;;; -0.04900663119822446 0.0; 0.09175801803089013 0.0;;; … ;;; 4.485772070448108e-6 0.0; -4.4630903906536425e-7 0.0;;; 4.303552019451355e-7 0.0; -1.0428735117063708e-6 0.0;;; -6.452660186998594e-8 0.0; -7.836101483352229e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (14, 19, 24))), SingleBranch{Float64}(41:57, 0, 10:9, 1, 4, [0.7472549319439978, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-9.931355245362722 0.0; 0.0 0.0;;; 0.004639293314162463 0.0; 0.0 0.0;;; 0.10230318193552163 0.0; 0.3431041586399578 0.0;;; … ;;; -5.8057861586053485e-6 0.0; -3.6767179441275553e-6 0.0;;; 1.970849569609788e-6 0.0; -1.1263384149017906e-6 0.0;;; 4.6063384099401923e-7 0.0; -7.362879677517756e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.24833262559729297 0.0; 0.0 0.0;;; -0.04049792411417641 0.0; 0.11830484901746985 0.0;;; … ;;; 7.332767131734295e-6 0.0; -4.818366848970212e-6 0.0;;; 6.296375165101449e-7 0.0; 2.450158453149185e-6 0.0;;; -2.5398566738723024e-7 0.0; -1.9922601565040447e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (8, 10, 12))), SingleBranch{Float64}(58:71, 0, 10:9, 1, 5, [0.24972658593518723, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.0812379817404665 0.0; 0.0 0.0;;; 0.2500525077504865 0.0; 0.0 0.0;;; -0.31821199437047437 0.0; 0.12219381204800842 0.0;;; … ;;; 3.886164164482793e-6 0.0; -7.451230042206713e-6 0.0;;; -1.5655861775267537e-6 0.0; 1.3488384490746591e-6 0.0;;; -2.65136301189794e-7 0.0; -1.0396969077621681e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.23600456619228227 0.0; 0.0 0.0;;; 0.00780054815104303 0.0; 0.01243800251579276 0.0;;; … ;;; -1.457243306148132e-8 0.0; 1.604225902871519e-9 0.0;;; -2.836500215179685e-10 0.0; -3.581821796740947e-10 0.0;;; 1.9003405206797664e-12 0.0; -5.3575717814609175e-12 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (8, 10, 12))), SingleBranch{Float64}(72:82, 0, 10:9, 1, 6, [0.7472549319439978, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.643660411433685 0.0; 0.0 0.0;;; -0.09740163237448708 0.0; 0.0 0.0;;; 0.30569645349438196 0.0; 0.2359234953909746 0.0;;; … ;;; -9.82916763080865e-7 0.0; -4.2285511081766585e-7 0.0;;; 2.7225441029521644e-6 0.0; -9.866422822602592e-7 0.0;;; -2.884182756506517e-7 0.0; 2.1891312191953625e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.137250125216142 0.0; 0.0 0.0;;; -0.041848288296333136 0.0; 0.07154851443791577 0.0;;; … ;;; 7.308420503707386e-7 0.0; 1.2365335735668517e-8 0.0;;; 1.4021073394047346e-7 0.0; -2.3067492312302074e-7 0.0;;; -1.5499976899256273e-8 0.0; -2.8685176609168157e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 140658660330000))), SingleBranch{Float64}(83:89, 0, 10:9, 1, 7, [0.24972658593518723, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-2.3207471469996026 0.0; 0.0 0.0;;; 0.09584922777112714 0.0; 0.0 0.0;;; -0.03459176396777507 0.0; -0.04020642273548641 0.0;;; … ;;; 3.930977957593639e-6 0.0; -1.9071506252246133e-6 0.0;;; 4.262561393862879e-7 0.0; 6.012045573535614e-7 0.0;;; -1.296847519879538e-7 0.0; -1.748757755002258e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.14971540025278463 0.0; 0.0 0.0;;; -0.10199818137039851 0.0; -0.00404107784645201 0.0;;; … ;;; -1.5142366400508734e-6 0.0; -1.807350708728618e-7 0.0;;; 6.688310694761936e-7 0.0; 1.0683350833198992e-7 0.0;;; -9.055558759133121e-8 0.0; -1.8167298693653792e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (1, 0, 140658593845616))), SingleBranch{Float64}(90:100, 0, 10:9, 1, 8, [0.7472549319439978, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.414197799467094 0.0; 0.0 0.0;;; 0.5897626670629665 0.0; 0.0 0.0;;; -0.1138694027478626 0.0; -0.009802047749392043 0.0;;; … ;;; 1.152740503052551e-5 0.0; -4.517016990218442e-6 0.0;;; -4.140046433990845e-6 0.0; -1.566383749352849e-6 0.0;;; 1.2469713505945974e-7 0.0; 2.024928160458584e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … 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0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659292046128, 140659292046128, 0)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.00551624732815934, [0.2538490889415096, 0.33415153638191886, 0.4273278808735992, 0.867547200255958]), [108.51946935250929, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8192008435733007, 0.9541592624784624, 0.8458950823510601], 0.0014709561750558223, [0.03209667335274724, 0.3505458214588266, 0.9303323763821093, 0.9594335994071538]), [72.44348727911604, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.586748700554989, 0.12181263792534469, 0.7894931647499924], 0.0016174951280755708, [0.8935369466209786, 0.3548676566528912, 0.13179829123412257, 0.9411330896079791]), [84.61080196753738, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6192588014774537, 0.47764531343080796, 0.8041934288169849], 0.003639098305331564, [0.8236563299357046, 0.45048364263035023, 0.8913769757127503, 0.7110385498005108]), [105.6260313299836, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.12353811904859124, 0.7400202596259494, 0.7057473220960516], 0.004975260027225807, [0.9340155879013086, 0.753277849991045, 0.7295997282994879, 0.16238042514897943]), [83.01411086709412, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9919607797239652, 0.8036971367794874, 0.29827230692896456], 0.006659427674753824, [0.4842893268146866, 0.5997019277391098, 0.4536933650141408, 0.3249034202416199]), [96.09064863847617, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.49265789199054244, 0.17985285886739166, 0.6397154045236242], 0.004022070032387327, [0.6922349538863742, 0.7468540519107453, 0.09667869010406493, 0.45910253524716227]), [100.7208073721113, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.22768758746068596, 0.26780944724527167, 0.8309795986773825], 0.006802835099514221, [0.6911617055492341, 0.821283430881433, 0.5644095995557176, 0.030378874865931382]), [84.68272746156016, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0010425988209884726, [0.09206661519876747, 0.4379647602849879, 0.23146826213384353, 0.6471427793654219]), [111.35508934376354, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.00633005068065063, [0.37737321139310276, 0.2404468114408953, 0.2221494346545283, 0.5096964769051421]), [100.87590407023012, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.3562026836409853, 0.3635243844573359, 0.309727986680287], 0.0038713948967191466, [0.43490959394031214, 0.0758000769135273, 0.3487409265919944, 0.30331684418426996]), [112.97187743393756, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6547290646713112, 0.8311844039711347, 0.3538049975932579], 0.004154302641783906, [0.5842214092626906, 0.881611313975086, 0.009146364153274189, 0.9806631480861379]), [124.15361783713384, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5388794936906567, 0.04350921485134718, 0.23629199234128806], 0.006559279199653211, [0.9196974029361853, 0.17022568799250704, 0.2638800824351736, 0.6514229873225715]), [95.83800154421716, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, [0.13080774080166646, 0.22271994897768166, 0.6048365813194562, 0.052884966374337816]), [88.72102809781342, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6177567582580967, 0.38039525218264447, 0.37934078500465196], 0.010186078857427224, [0.2366140514268097, 0.31694750597495125, 0.29912838760350746, 0.623451826337517]), [125.5976138929021, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6781091106154422, 0.44334927922889245, 0.36064371233973214], 0.01036251002724151, [0.2743759198193091, 0.7285911206511895, 0.03773808039378912, 0.04331783284230861]), [124.51423398809521, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.20158107237490663, 0.3238946945648584, 0.24399963650509682], 0.009664372151238956, [0.47733204119516204, 0.4603052801344075, 0.9298297825042643, 0.358424742237733]), [101.10559863933453, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, [0.4401491209134364, 0.8609926737185056, 0.1638092551671958, 0.22646456871949416]), [93.91357637411625, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, [0.17728847529212788, 0.12630836876865192, 0.9645167219705122, 0.8221674765296613]), [94.78656884587767, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, [0.6409979037657155, 0.15911501872567757, 0.5356210909593669, 0.6799181470255188]), [93.44524600265673, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], DerivativesSwitch{true, true, true}())</code></pre><h2 id="Evaluate-Multiple-Sources-on-Multiple-Targets"><a class="docs-heading-anchor" href="#Evaluate-Multiple-Sources-on-Multiple-Targets">Evaluate Multiple Sources on Multiple Targets</a><a id="Evaluate-Multiple-Sources-on-Multiple-Targets-1"></a><a class="docs-heading-anchor-permalink" href="#Evaluate-Multiple-Sources-on-Multiple-Targets" title="Permalink"></a></h2><p>The FMM also supports the evaluation of multiple source systems on multiple target systems. The user is also able to evaluate a single source on multiple targets or multiple sources on a single target with any combination of supported system types.</p><pre><code class="language-julia hljs">vortex_path = normpath(joinpath(splitdir(pathof(fmm))[1], &quot;..&quot;, &quot;test&quot;, &quot;vortex.jl&quot;))
+fmm.fmm!(target_system, source_system)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.49849075893959255, 0.5011246180164968, 0.50101931980297], 0.8617443734929683, 0.8617443734929683, [-0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063, -0.49752834600881063, 0.49752834600881063], [0.49752834600881063, 0.49752834600881063, 0.49752834600881063], 0.0, 0.0, fill(0.0), [-49.209733528008485 0.0; 0.0 0.0;;; 3.235503852070556 0.0; 0.0 0.0;;; 0.02681865248285842 0.0; 0.9591193094494834 0.0;;; … ;;; -0.0004469512083583767 0.0; -0.00015932419565861916 0.0;;; -0.00028710529956597804 0.0; -0.00031904516877669385 0.0;;; -7.588266430169126e-6 0.0; -8.400184364295124e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835914329536, 139835914330432, 0))), SingleBranch{Float64}(1:13, 0, 10:9, 1, 1, [0.24972658593518723, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-6.326393509059363 0.0; 0.0 0.0;;; 0.10174482633884264 0.0; 0.0 0.0;;; -0.07898687772271276 0.0; 0.03841659635534152 0.0;;; … ;;; -9.654710862452212e-7 0.0; -5.591129557725438e-7 0.0;;; 1.175731767951614e-6 0.0; 2.391893864725776e-6 0.0;;; -3.893767927840696e-8 0.0; -4.373076778562484e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21988918332658114 0.0; 0.0 0.0;;; -0.00907173901579822 0.0; -0.08078608463780172 0.0;;; … ;;; 6.639561085749197e-7 0.0; 1.9043445262044332e-6 0.0;;; 3.6078285954161947e-7 0.0; -1.730779168448776e-7 0.0;;; -1.5694464749247868e-8 0.0; -2.5081831237534205e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835071738016, 139835914319760, 139835712794656))), SingleBranch{Float64}(14:23, 0, 10:9, 1, 2, [0.7472549319439978, 0.25236044501209143, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.505985520323303 0.0; 0.0 0.0;;; -0.0893400706965472 0.0; 0.0 0.0;;; 0.07469760206429724 0.0; -0.23211041531103774 0.0;;; … ;;; -2.392727383648695e-6 0.0; -2.7506172478695797e-7 0.0;;; 1.2869752996385646e-6 0.0; 8.632541193951725e-7 0.0;;; -1.4323853566229846e-7 0.0; 3.40320513459477e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.18613078162840202 0.0; 0.0 0.0;;; -0.03988177380448188 0.0; -0.10881091326674686 0.0;;; … ;;; 3.1493849180079693e-6 0.0; 1.79002742056861e-6 0.0;;; 2.3049009571265728e-7 0.0; -1.3797688581858191e-6 0.0;;; -1.7119818873987816e-7 0.0; 3.217930041360891e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835914346497, 139835722962256, 432920450458))), SingleBranch{Float64}(24:40, 0, 10:9, 1, 3, [0.24972658593518723, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-7.986155913622251 0.0; 0.0 0.0;;; -0.1795979615961002 0.0; 0.0 0.0;;; -0.1708212423759164 0.0; 0.03135320324442914 0.0;;; … ;;; -6.066362373385743e-6 0.0; 2.4234495602853986e-6 0.0;;; 2.327392085993626e-6 0.0; 4.871331224296273e-7 0.0;;; 2.4751088043185402e-8 0.0; -5.827716675663792e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.23122788327035293 0.0; 0.0 0.0;;; -0.04900663119822446 0.0; 0.09175801803089013 0.0;;; … ;;; 4.485772070448108e-6 0.0; -4.4630903906536425e-7 0.0;;; 4.303552019451355e-7 0.0; -1.0428735117063708e-6 0.0;;; -6.452660186998594e-8 0.0; -7.836101483352229e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835767718704, 139835076568576, 139835071738208))), SingleBranch{Float64}(41:57, 0, 10:9, 1, 4, [0.7472549319439978, 0.7498887910209021, 0.25225514679856464], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-9.931355245362722 0.0; 0.0 0.0;;; 0.004639293314162463 0.0; 0.0 0.0;;; 0.10230318193552163 0.0; 0.3431041586399578 0.0;;; … ;;; -5.8057861586053485e-6 0.0; -3.6767179441275553e-6 0.0;;; 1.970849569609788e-6 0.0; -1.1263384149017906e-6 0.0;;; 4.6063384099401923e-7 0.0; -7.362879677517756e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … 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0.0;;; -0.31821199437047437 0.0; 0.12219381204800842 0.0;;; … ;;; 3.886164164482793e-6 0.0; -7.451230042206713e-6 0.0;;; -1.5655861775267537e-6 0.0; 1.3488384490746591e-6 0.0;;; -2.65136301189794e-7 0.0; -1.0396969077621681e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.23600456619228227 0.0; 0.0 0.0;;; 0.00780054815104303 0.0; 0.01243800251579276 0.0;;; … ;;; -1.457243306148132e-8 0.0; 1.604225902871519e-9 0.0;;; -2.836500215179685e-10 0.0; -3.581821796740947e-10 0.0;;; 1.9003405206797664e-12 0.0; -5.3575717814609175e-12 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835829215489, 139835735020000, 139835767718704))), SingleBranch{Float64}(72:82, 0, 10:9, 1, 6, [0.7472549319439978, 0.25236044501209143, 0.7497834928073753], 0.43087218674648414, 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0.14971540025278463 0.0; 0.0 0.0;;; -0.10199818137039851 0.0; -0.00404107784645201 0.0;;; … ;;; -1.5142366400508734e-6 0.0; -1.807350708728618e-7 0.0;;; 6.688310694761936e-7 0.0; 1.0683350833198992e-7 0.0;;; -9.055558759133121e-8 0.0; -1.8167298693653792e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281979104, 672, 431793782032))), SingleBranch{Float64}(90:100, 0, 10:9, 1, 8, [0.7472549319439978, 0.7498887910209021, 0.7497834928073753], 0.43087218674648414, 0.43087218674648414, [-0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531, -0.24876417300440531, 0.24876417300440531], [0.24876417300440531, 0.24876417300440531, 0.24876417300440531], 0.0, 0.0, fill(0.0), [-5.414197799467094 0.0; 0.0 0.0;;; 0.5897626670629665 0.0; 0.0 0.0;;; -0.1138694027478626 0.0; -0.009802047749392043 0.0;;; … ;;; 1.152740503052551e-5 0.0; -4.517016990218442e-6 0.0;;; -4.140046433990845e-6 0.0; -1.566383749352849e-6 0.0;;; 1.2469713505945974e-7 0.0; 2.024928160458584e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.21095730321733874 0.0; 0.0 0.0;;; 0.09347241596581823 0.0; -0.08394581821691316 0.0;;; … ;;; -3.5372171155417328e-6 0.0; -4.908219455216665e-6 0.0;;; -2.1396426594075856e-6 0.0; -4.6629625718216964e-7 0.0;;; -2.2671999108049045e-7 0.0; 1.289627938417499e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835914940048, 139835914828240, 0)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [8, 19, 24, 25, 30, 33, 35, 43, 52, 55  …  37, 41, 42, 49, 64, 71, 78, 79, 87, 88], [90, 83, 24, 72, 58, 59, 25, 1, 60, 73  …  23, 38, 80, 56, 39, 81, 82, 40, 13, 57], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.7287348331279035, 0.8645178072081, 0.9863586950447876], 0.002824412632887574, [0.3155425281087243, 0.5242721608260215, 0.3037915019715359, 0.5092362809736347]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.04871498957839171, 0.5228239956008278, 0.9981161184046683], 0.0010354523583936332, [0.10074227409525549, 0.4506225909463669, 0.17491391238059328, 0.06082060195439776]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.26339547338830394, 0.8205923530535013, 0.013801744155504059], 0.000561123611422205, [0.48127815547923203, 0.597575664859812, 0.25621397411396096, 0.24376337038602525]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9156175145346829, 0.2751207698440503, 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0.42863222861412936, 0.42863222861412936, [-0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677, -0.24747093257371677, 0.24747093257371677], [0.24747093257371677, 0.24747093257371677, 0.24747093257371677], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.0593731535051507 0.0; -0.0 0.0;;; 0.08539386253795012 0.0; 0.039405099639804875 0.0;;; … ;;; -1.6817191281206375e-8 0.0; -5.988143577896676e-8 0.0;;; 3.0556184471062655e-8 0.0; -1.9110878655930648e-7 0.0;;; -3.415675534882339e-8 0.0; 5.09167765671537e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835767718704, 139835767718704, 1518020287460)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [11, 19, 33, 43, 59, 63, 67, 68, 69, 72  …  20, 24, 31, 37, 42, 48, 60, 74, 94, 100], [69, 87, 70, 71, 79, 43, 56, 57, 44, 88  …  12, 55, 30, 99, 31, 32, 13, 68, 14, 100], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.00551624732815934, [0.2538490889415096, 0.33415153638191886, 0.4273278808735992, 0.867547200255958]), [108.51946935250929, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8192008435733007, 0.9541592624784624, 0.8458950823510601], 0.0014709561750558223, [0.03209667335274724, 0.3505458214588266, 0.9303323763821093, 0.9594335994071538]), [72.44348727911604, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.586748700554989, 0.12181263792534469, 0.7894931647499924], 0.0016174951280755708, [0.8935369466209786, 0.3548676566528912, 0.13179829123412257, 0.9411330896079791]), [84.61080196753738, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6192588014774537, 0.47764531343080796, 0.8041934288169849], 0.003639098305331564, [0.8236563299357046, 0.45048364263035023, 0.8913769757127503, 0.7110385498005108]), [105.6260313299836, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.12353811904859124, 0.7400202596259494, 0.7057473220960516], 0.004975260027225807, [0.9340155879013086, 0.753277849991045, 0.7295997282994879, 0.16238042514897943]), [83.01411086709412, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.9919607797239652, 0.8036971367794874, 0.29827230692896456], 0.006659427674753824, [0.4842893268146866, 0.5997019277391098, 0.4536933650141408, 0.3249034202416199]), [96.09064863847617, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.49265789199054244, 0.17985285886739166, 0.6397154045236242], 0.004022070032387327, [0.6922349538863742, 0.7468540519107453, 0.09667869010406493, 0.45910253524716227]), [100.7208073721113, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.22768758746068596, 0.26780944724527167, 0.8309795986773825], 0.006802835099514221, [0.6911617055492341, 0.821283430881433, 0.5644095995557176, 0.030378874865931382]), [84.68272746156016, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0010425988209884726, [0.09206661519876747, 0.4379647602849879, 0.23146826213384353, 0.6471427793654219]), [111.35508934376354, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.00633005068065063, [0.37737321139310276, 0.2404468114408953, 0.2221494346545283, 0.5096964769051421]), [100.87590407023012, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Body{Float64}([0.3562026836409853, 0.3635243844573359, 0.309727986680287], 0.0038713948967191466, [0.43490959394031214, 0.0758000769135273, 0.3487409265919944, 0.30331684418426996]), [112.97187743393756, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6547290646713112, 0.8311844039711347, 0.3538049975932579], 0.004154302641783906, [0.5842214092626906, 0.881611313975086, 0.009146364153274189, 0.9806631480861379]), [124.15361783713384, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5388794936906567, 0.04350921485134718, 0.23629199234128806], 0.006559279199653211, [0.9196974029361853, 0.17022568799250704, 0.2638800824351736, 0.6514229873225715]), [95.83800154421716, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5109351365074641, 0.7269107204213763, 0.8057341233600875], 0.002916397428800248, [0.13080774080166646, 0.22271994897768166, 0.6048365813194562, 0.052884966374337816]), [88.72102809781342, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6177567582580967, 0.38039525218264447, 0.37934078500465196], 0.010186078857427224, [0.2366140514268097, 0.31694750597495125, 0.29912838760350746, 0.623451826337517]), [125.5976138929021, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6781091106154422, 0.44334927922889245, 0.36064371233973214], 0.01036251002724151, [0.2743759198193091, 0.7285911206511895, 0.03773808039378912, 0.04331783284230861]), [124.51423398809521, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.20158107237490663, 0.3238946945648584, 0.24399963650509682], 0.009664372151238956, [0.47733204119516204, 0.4603052801344075, 0.9298297825042643, 0.358424742237733]), [101.10559863933453, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, [0.4401491209134364, 0.8609926737185056, 0.1638092551671958, 0.22646456871949416]), [93.91357637411625, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, [0.17728847529212788, 0.12630836876865192, 0.9645167219705122, 0.8221674765296613]), [94.78656884587767, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, [0.6409979037657155, 0.15911501872567757, 0.5356210909593669, 0.6799181470255188]), [93.44524600265673, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], DerivativesSwitch{true, true, true}())</code></pre><h2 id="Evaluate-Multiple-Sources-on-Multiple-Targets"><a class="docs-heading-anchor" href="#Evaluate-Multiple-Sources-on-Multiple-Targets">Evaluate Multiple Sources on Multiple Targets</a><a id="Evaluate-Multiple-Sources-on-Multiple-Targets-1"></a><a class="docs-heading-anchor-permalink" href="#Evaluate-Multiple-Sources-on-Multiple-Targets" title="Permalink"></a></h2><p>The FMM also supports the evaluation of multiple source systems on multiple target systems. The user is also able to evaluate a single source on multiple targets or multiple sources on a single target with any combination of supported system types.</p><pre><code class="language-julia hljs">vortex_path = normpath(joinpath(splitdir(pathof(fmm))[1], &quot;..&quot;, &quot;test&quot;, &quot;vortex.jl&quot;))
 include(vortex_path)
 
 function generate_vortex(seed, n_bodies; radius_factor=0.1, strength_factor=1.0)
@@ -152,15 +152,15 @@
 source_one = generate_gravitational(125, 100)
 source_two = generate_vortex(126, 100)
 
-fmm.fmm!((target_one, target_two), (source_one, source_two))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(MultiTree{Float64, 2, Tuple{Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, Vector{Tuple{Main.Vorton{Float64}, Vector{Float64}, Vector{Float64}}}}, 5}(MultiBranch{Float64, 2}[MultiBranch{Float64, 2}(UnitRange{Int64}[1:100, 1:100], 8, 2:9, 0, -1, [0.5026259736883681, 0.5006093989915064, 0.506575304253488], 0.8619975055877627, 0.8619975055877627, [-0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073], [0.49767449189188073, 0.49767449189188073, 0.49767449189188073], 0.0, 0.0, fill(0.0), [-47.330269153011905 0.0; 0.0 0.0;;; -1.4300081297763314 0.0; 0.0 0.0;;; -0.0020279707713188877 0.0; -0.0810447498230098 0.0;;; … ;;; -0.001102965892865963 0.0; -4.646297296899838e-5 0.0;;; 0.0001693966781257666 0.0; -9.944313846444004e-5 0.0;;; -2.862980365746775e-5 0.0; -1.3838857277821314e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658588182176, 140659292046064, 413693021126))), MultiBranch{Float64, 2}(UnitRange{Int64}[1:14, 1:12], 0, 10:9, 1, 1, [0.2537887277424278, 0.251772153045566, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-7.499871222570643 0.0; 0.0 0.0;;; 0.14134763322386673 5.876318899706723; 0.0 0.0;;; -0.27781448587580504 -3.399262014326455; -0.21357159879163193 -3.034004529419432;;; … ;;; 2.528007054727247e-6 -5.198140515345906e-6; -3.5865531122720975e-7 -2.2816070849536322e-6;;; -5.825983403314016e-6 1.668839102392757e-7; 7.346808214947709e-7 -5.3432822173448825e-6;;; 4.452343181626718e-7 2.8737566545769717e-6; -5.919437972505053e-7 1.5152180081065892e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.07563716034391843 0.0; 0.0 0.0;;; -0.09383556353568245 0.0; 0.04427676342595527 0.0;;; … ;;; -7.732499867406854e-9 0.0; 3.051715598564347e-8 0.0;;; 6.995691193611116e-8 0.0; 3.5849287145216293e-7 0.0;;; 5.9328907145372435e-8 0.0; 8.075902066539915e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281974944, 20753281979104, 672))), MultiBranch{Float64, 2}(UnitRange{Int64}[15:25, 13:23], 0, 10:9, 1, 2, [0.7514632196343085, 0.251772153045566, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.786962147547788 0.0; 0.0 0.0;;; -0.08046626758682532 4.410294461276509; 0.0 0.0;;; 0.07917686087068565 -3.2482101027014534; 0.013486487172595357 -2.7368772194723507;;; … ;;; 2.9550574604507674e-6 -2.7285638004285373e-6; -1.3518437065648355e-6 3.5595636693251586e-6;;; -5.234086734876242e-7 3.555165107606909e-6; -9.92570608622439e-7 -1.2783154363676133e-6;;; 1.9554981220314482e-7 7.438288253934825e-7; 4.1692108973748044e-7 1.062118867108326e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.051280316864532494 0.0; 0.0 0.0;;; 0.026829953422987274 0.0; -0.0748119800766262 0.0;;; … ;;; 1.899571107442584e-8 0.0; -1.1328956225594303e-8 0.0;;; 1.6387380676626464e-8 0.0; 8.366465479549419e-8 0.0;;; 2.6126169093897e-8 0.0; 3.9732453187322435e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281974944, 20753281979104, 20753281974944))), MultiBranch{Float64, 2}(UnitRange{Int64}[26:39, 24:38], 0, 10:9, 1, 3, [0.2537887277424278, 0.7494466449374467, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.461237959815938 0.0; 0.0 0.0;;; -0.06455233958895452 10.059074305326293; 0.0 0.0;;; 0.01453666265401074 -4.529151153045262; 0.035733159549641055 -3.1853673726340865;;; … ;;; 2.185651803566736e-6 2.939983733331748e-6; -2.1020197866396055e-6 2.2769594810854188e-5;;; 6.413575350526986e-7 8.118082850156805e-6; -2.6281938845417287e-6 -5.2015670950708256e-6;;; 3.216724613459501e-7 -7.86771014197628e-7; 6.657658982750058e-7 1.327187878612661e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.19697053746278903 0.0; 0.0 0.0;;; -0.06982836891659083 0.0; 0.0559260760892909 0.0;;; … ;;; 9.125962831737276e-7 0.0; 1.864939988205681e-6 0.0;;; -4.7557482138149605e-7 0.0; -2.2413312341668466e-7 0.0;;; 4.644704815088655e-8 0.0; -1.1114538610052121e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), MultiBranch{Float64, 2}(UnitRange{Int64}[40:49, 39:53], 0, 10:9, 1, 4, [0.7514632196343085, 0.7494466449374467, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.3477273311870865 0.0; 0.0 0.0;;; -0.16435855694757204 9.721186791516416; 0.0 0.0;;; 0.12294219903268079 -4.248526417696294; -0.0332377231093299 -4.252662383598009;;; … ;;; -8.13710641459531e-6 2.8580911633519164e-6; -6.231810556349974e-7 6.864144066599249e-6;;; 2.2119897970051911e-7 -2.346400167145746e-6; -3.7089074074201864e-6 -1.3558413583447434e-5;;; -5.605149079948702e-7 1.52790392922525e-6; -7.910253772220518e-7 1.307628828750524e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.1203246909098602 0.0; 0.0 0.0;;; 0.10905156210654654 0.0; -0.06508193456155464 0.0;;; … ;;; -4.7489710223826224e-8 0.0; -1.0937320874843271e-6 0.0;;; -7.162458392092633e-7 0.0; -1.0897602359520343e-6 0.0;;; -2.4771546198069067e-7 0.0; -1.200508235984114e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658686425584, 140658686425616, 140659438709824))), MultiBranch{Float64, 2}(UnitRange{Int64}[50:59, 54:61], 0, 10:9, 1, 5, [0.2537887277424278, 0.251772153045566, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.768609585113875 0.0; 0.0 0.0;;; -0.0008241017990052862 5.180157724215509; 0.0 0.0;;; -0.13506173196838803 -2.648291420360042; 0.3386931330435938 -1.2864699484118736;;; … ;;; -9.014507135353242e-7 -7.018939476416647e-6; -3.5641213887785376e-6 5.502324767485222e-6;;; -1.5099245250969104e-7 -5.154080100681363e-6; -4.196134456734228e-6 6.012899693515811e-6;;; -1.3480597057727598e-7 3.5575244532127094e-6; -1.0043910673550508e-6 -5.975371881267255e-7], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.11256203287810052 0.0; 0.0 0.0;;; -0.020966539634629522 0.0; -0.029270807438235014 0.0;;; … ;;; 4.475633321570958e-8 0.0; -1.3548142320263519e-8 0.0;;; -6.2495612685646185e-9 0.0; -4.803194607824211e-9 0.0;;; -1.6989228380302114e-11 0.0; 5.039640229144699e-10 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659438875344, 140659438647552, 140659372903920))), MultiBranch{Float64, 2}(UnitRange{Int64}[60:70, 62:69], 0, 10:9, 1, 6, [0.7514632196343085, 0.251772153045566, 0.7554125501994283], 0.43099875279388133, 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-2.80138885224981e-6 0.0; 1.2383970011340801e-6 0.0;;; 1.524189158643975e-7 0.0; -5.614092520865809e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658687641040, 140658687641072, 140659292051408))), MultiBranch{Float64, 2}(UnitRange{Int64}[71:84, 70:84], 0, 10:9, 1, 7, [0.2537887277424278, 0.7494466449374467, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.357829793323234 0.0; 0.0 0.0;;; -0.4061642214854503 9.5704574266076; 0.0 0.0;;; 0.03137691545227036 -3.3376101500858075; -0.23075631586093312 -3.916290355677398;;; … ;;; 3.3014050982660475e-6 -7.670618662800918e-6; -5.208062214551448e-6 -3.057767276954066e-5;;; 2.870869148786357e-6 -6.334327079983546e-6; 1.7481832131259466e-6 1.8943763991561415e-5;;; -4.1528628356866803e-7 3.2824458852436157e-7; 7.872102020772641e-7 4.794973342512074e-7], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.035440982172832425 0.0; 0.0 0.0;;; -0.04873145295472853 0.0; -0.03622519786432454 0.0;;; … ;;; -3.726393398184811e-9 0.0; 1.0306788187000984e-8 0.0;;; -1.6740465940925586e-8 0.0; 1.1078967570105604e-8 0.0;;; 6.868461008583211e-9 0.0; 3.754551936342892e-10 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659373705232, 140659373705264, 140659372785664))), MultiBranch{Float64, 2}(UnitRange{Int64}[85:100, 85:100], 0, 10:9, 1, 8, [0.7514632196343085, 0.7494466449374467, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, 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5.740532260866596e-10 0.0;;; 9.277122132969723e-11 0.0; 6.446550403600691e-11 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 415720293899)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], ([5, 19, 24, 38, 39, 43, 51, 53, 60, 62  …  20, 29, 45, 52, 54, 58, 76, 82, 83, 99], [16, 18, 46, 56, 57, 58, 62, 64, 66, 73  …  35, 38, 47, 48, 49, 52, 63, 71, 82, 83]), ([40, 26, 85, 50, 1, 86, 27, 60, 61, 87  …  69, 48, 58, 49, 13, 84, 70, 59, 100, 14], [39, 54, 85, 24, 70, 40, 13, 86, 62, 71  …  60, 23, 83, 52, 53, 12, 68, 69, 61, 84]), (Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.557859214605901, 0.9505794906131003, 0.3404453566099245], 0.009400118805868503, [0.4279926935042637, 0.5792958612811091, 0.7737051496094961, 0.755089351578363]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 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(Main.Vorton{Float64}([0.9077908593045806, 0.3939808726568609, 0.1924335604037214], [0.5681911381173306, 0.06084849139338322, 0.9611920275200003], 0.00920463305134842), [0.0, 0.0, 0.0, 0.0, -320.3332114842369, -34.58377130895539, 368.0839198461781, 230.13536494966473, 324.9842959812287, -428.13261855501696, 107.45354565095035, -237.813327378721, -4.6510844969917695], [5.002262904567566, 20.106483412927478, -27.95795361610942, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.680305220184172, 0.45142673639459907, 0.6565158730370251], [0.9871517007068787, 0.536191701519787, 0.8044608001295422], 0.01032776912661538), [0.0, 0.0, 0.0, 0.0, 3.5290366718469843, -165.41852935577367, 215.10016845722762, -68.86842304729687, 23.303633729181946, 247.64379943807933, 100.32617617358432, -249.17334079623583, -26.832670401028913], [9.74821219150256, 3.092276196613873, -11.616523984606683, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.5772900725131546, 0.19456471074413395, 0.9691695971486246], [0.029308796906382772, 0.237901194890202, 0.8225322140924277], 0.005855920250376647), [0.0, 0.0, 0.0, 0.0, -12.590937064305567, -5.8931029583027374, -6.052580045726423, -9.567705795412877, 6.983084969341174, -3.8613455886210613, 7.032438744361059, -4.783126247213283, 5.607852094964389], [11.241725102135732, -6.223353028275995, -4.338609044329697, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07881482026287556, 0.16694384061777157, 0.7453082600322598], [0.36751517071734363, 0.08464781300384328, 0.7877792123673903], 0.006719633426946119), [0.0, 0.0, 0.0, 0.0, 26.415864678954573, -20.050867256931426, -0.8178529266405452, -4.549102666819707, -34.45901507382465, 11.628461542970213, 18.752918414945103, -27.01043418561137, 8.043150394870079], [9.920823853550871, -10.194323634205208, 1.9599671382805932, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.34386745978232425, 0.15114271162865245, 0.8692858825227187], [0.34380421639038017, 0.49221567013213885, 0.7577396026981709], 0.007165314050997217), [0.0, 0.0, 0.0, 0.0, -59.79113188139079, -1.9709498200711613, -26.762698675340847, 54.10917654100488, 45.492034964801626, -261.8421332968958, 164.44096188607392, -25.562476104392736, 14.299096916589178], [14.394628290815083, -3.672764630088914, -9.378589297611173, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7924111084524182, 0.7258577993874293, 0.4074759819413786], [0.004779849956308646, 0.10815467687383273, 0.6365113178025307], 0.004211825485699923), [0.0, 0.0, 0.0, 0.0, 10.465389536407542, 94.68236585742876, -78.85761169691806, 70.89533439823704, -134.6061639041499, 47.9278980522469, -155.00862689153615, 43.986774759861845, 124.14077436774228], [-17.950340377015056, 21.149992040957308, 1.7437458219519797, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.15007164548253604, 0.13891454905930323, 0.8854146060893755], [0.2322606392244514, 0.24943996074378283, 0.6529923359002099], 0.004730386058191863), [0.0, 0.0, 0.0, 0.0, 59.442434719016205, 26.31264290953867, -7.788753592832606, 63.14513611059529, -47.72166333663818, 20.19110915521419, -57.46819208991416, 29.471415735207678, -11.720771382378052], [14.768178748060738, -8.861646545075095, 1.2188993808980852, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.178892411148747, 0.8198348637351619, 0.746693545507861], [0.05374276809352163, 0.28259697683790064, 0.9963633829133356], 0.004082068996145551), [0.0, 0.0, 0.0, 0.0, 57.050592206607114, -90.21090922096973, 48.878961267701186, -82.68306936940297, 14.29503143257214, 31.74239957362232, 12.320723650538946, 83.85090301869836, -71.34562363917927], [-0.03144901666306661, -15.583012096242426, 13.750015093195545, 0.0, 0.0, 0.0])  …  (Main.Vorton{Float64}([0.4598055261641393, 0.09042082143339258, 0.5640409504623178], [0.6396964311422774, 0.5845421243866575, 0.5349929592419193], 0.001124964196695102), [0.0, 0.0, 0.0, 0.0, 382.09609513254355, 228.00822947658645, -354.08488347129423, -954.163507769204, 241.5556796267648, -189.6437242626885, -169.1205368140404, 434.7509477257039, -623.6517747593078], [20.887342734108213, -2.735476925891841, -5.502211836582691, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9572197333627137, 0.6426548339644926, 0.6552399747905221], [0.747485027142634, 0.23562083902231445, 0.23561754824795678], 0.0027436327111542455), [0.0, 0.0, 0.0, 0.0, 15.061487372616561, -26.10806509511263, 22.112106061527545, -41.88706206809685, 42.58929055731519, -11.079768202200608, -8.832598907394338, 0.18603518576434164, -57.65077792993176], [0.6561052462927573, 10.15339318367006, -12.7859063446062, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.8050706937073655, 0.005451816228509987, 0.6194543923497148], [0.2893241621284488, 0.15343050371415934, 0.45483197600289493], 0.0033418266341768534), [0.0, 0.0, 0.0, 0.0, -6.235476091786627, 2.7558002187956046, 2.9497273741924195, 10.232663073288112, 3.190253764733486, -17.021401404515075, 0.5779868577948659, -5.568330421328691, 3.0452223270531427], [8.099441084807626, 1.7447616146476344, -9.964573343111939, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.8372242495059112, 0.1880062901030637, 0.329865236819033], [0.6964852800076098, 0.41732935474694366, 0.12800112947157438], 0.008074470339380045), [0.0, 0.0, 0.0, 0.0, 47.94685325237328, -51.324186953826846, 4.847239236476755, -34.28059339724347, 40.769072683232345, 6.830704526226973, 33.07160266107869, 73.1016517686344, -88.71592593560563], [8.754889219586548, -1.8218252892777913, -7.180948488310969, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.049017597531493595, 0.18258465318130024, 0.04079265592099135], [0.6643772290446401, 0.25419876795775076, 0.0111761955710723], 0.006867801058606931), [0.0, 0.0, 0.0, 0.0, -27.31628247323072, 24.233190449744797, -0.3379485823927118, -11.924411796320792, 11.796570800683952, 4.254545828100499, -0.052136141612230326, 2.7632399691705896, 15.519711672546764], [-3.3270429646506385, 1.727457486302319, 2.4540759698751926, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9446211092215213, 0.5773644194640194, 0.41562195208459896], [0.06814741604330621, 0.16749916233272766, 0.7091985108360725], 0.0031542415121338305), [0.0, 0.0, 0.0, 0.0, 1.8215164214546353, -43.0534679191244, 21.758774568979174, -1.455109738812573, 32.13601155444825, 15.440864606507798, 40.155527530783026, -3.0240868014144886, -33.9575279759029], [-1.4567847361429935, 15.2886865778917, -13.296049302008182, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.02765456454632287, 0.1228176034412326, 0.7897475889795191], [0.5848018551658597, 0.4374509112686895, 0.6003922163899991], 0.0010159571328096377), [0.0, 0.0, 0.0, 0.0, 26.979366295589013, -14.345761341507757, -2.1051658180464075, 8.158019109103137, -26.582227133027917, 11.360653361273496, 4.9604405244283765, -1.6498848360812965, -0.39713916256110293], [8.800785520582927, -8.37524017976289, 1.6105446403166235, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.09100727263849917, 0.5794817445557756, 0.6291868753365321], [0.04589763740992747, 0.2683934891175124, 0.9312357743393328], 0.004951543147051906), [0.0, 0.0, 0.0, 0.0, 7.2826254124701535, 200.02901760661942, -231.96691984886604, -180.55079830561596, 172.343725105568, 48.94235243035011, 203.53488904458027, 29.0355615056544, -179.62635051803812], [-0.04772504081689664, -20.681704217331202, 12.630047100731876, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7215125397666922, 0.3101399108971986, 0.9120708158457793], [0.036429367243270616, 0.6439997561017691, 0.35149929330560925], 0.0006879838266934451), [0.0, 0.0, 0.0, 0.0, -10.842172139751918, 15.190887004020365, -17.834678493148925, 41.594173476581865, -5.397510782923477, -20.116652682634676, -1.618663520420014, -10.434703724772072, 16.239682922675396], [9.914485943053739, -4.739369747570147, -7.025390474122207, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07014988405111922, 0.5286443270294893, 0.24380912629526263], [0.620780571763883, 0.8699240224718836, 0.5642401605234335], 0.0003071608128254314), [0.0, 0.0, 0.0, 0.0, 101.93059974405706, 17.590681314952022, -320.9252338856423, 442.5488472353321, -219.0466532545508, -19.474434088571872, -146.04873079853883, 40.3055813981039, 117.11605351049374], [-12.779350368008263, -1.3595250276884299, 13.026821975903577, 0.0, 0.0, 0.0])]), Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], (DerivativesSwitch{true, true, true}(), DerivativesSwitch{true, true, true}()))</code></pre><h2 id="Non-Potential-Flow-Applications"><a class="docs-heading-anchor" href="#Non-Potential-Flow-Applications">Non-Potential Flow Applications</a><a id="Non-Potential-Flow-Applications-1"></a><a class="docs-heading-anchor-permalink" href="#Non-Potential-Flow-Applications" title="Permalink"></a></h2><p>As a default, target systems will be evaluated and returned with <code>scalar_potential</code>, <code>velocity</code>, and <code>velocity_gradient</code> fields populated. (Note that the vector potential is not explicitly tracked, though its induced velocity and velocity gradient are.) In some situations, only some of these values may be required. By inputting a boolean vector of the same length as target systems, the user is able to speed up the calculation by not storing unecessary values.</p><p class="math-container">\[\overline{V} = -\nabla \phi + \nabla \times \overline{\psi}\]</p><table><tr><th style="text-align: right"></th><th style="text-align: right"><span>$\phi$</span></th><th style="text-align: right"><span>$\overline{\psi}$</span></th><th style="text-align: right"><span>$\overline{V}$</span></th><th style="text-align: right"><span>$\nabla \overline{V}$</span></th></tr><tr><td style="text-align: right"><code>fmm!</code> Keyword Arguments</td><td style="text-align: right"><code>scalar_potential</code></td><td style="text-align: right"><code>vector_potential</code></td><td style="text-align: right"><code>velocity</code></td><td style="text-align: right"><code>velocity_gradient</code></td></tr><tr><td style="text-align: right">Fluid Dynamics</td><td style="text-align: right">Scalar Potential</td><td style="text-align: right">Stream Function</td><td style="text-align: right">Fluid Velocity</td><td style="text-align: right">Velocity Gradient</td></tr><tr><td style="text-align: right">Electrostatics</td><td style="text-align: right">Electric Potential</td><td style="text-align: right">-</td><td style="text-align: right">Electric Field</td><td style="text-align: right">Field Gradient Tensor</td></tr><tr><td style="text-align: right">Magnetostatics</td><td style="text-align: right">-</td><td style="text-align: right">Magnetic Vector Potential</td><td style="text-align: right">Magnetic Field</td><td style="text-align: right">Field Gradient Tensor</td></tr><tr><td style="text-align: right">Gravity</td><td style="text-align: right">Gravitational Potential</td><td style="text-align: right">-</td><td style="text-align: right">Gravitational Acceleration</td><td style="text-align: right">Acceleration Gradient Tensor</td></tr></table><pre><code class="language-julia hljs">target_one = generate_gravitational(123, 100)
+fmm.fmm!((target_one, target_two), (source_one, source_two))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(MultiTree{Float64, 2, Tuple{Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, Vector{Tuple{Main.Vorton{Float64}, Vector{Float64}, Vector{Float64}}}}, 5}(MultiBranch{Float64, 2}[MultiBranch{Float64, 2}(UnitRange{Int64}[1:100, 1:100], 8, 2:9, 0, -1, [0.5026259736883681, 0.5006093989915064, 0.506575304253488], 0.8619975055877627, 0.8619975055877627, [-0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073], [0.49767449189188073, 0.49767449189188073, 0.49767449189188073], 0.0, 0.0, fill(0.0), [-47.330269153011905 0.0; 0.0 0.0;;; -1.4300081297763314 0.0; 0.0 0.0;;; -0.0020279707713188877 0.0; -0.0810447498230098 0.0;;; … ;;; -0.001102965892865963 0.0; -4.646297296899838e-5 0.0;;; 0.0001693966781257666 0.0; -9.944313846444004e-5 0.0;;; -2.862980365746775e-5 0.0; -1.3838857277821314e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), MultiBranch{Float64, 2}(UnitRange{Int64}[1:14, 1:12], 0, 10:9, 1, 1, [0.2537887277424278, 0.251772153045566, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-7.499871222570643 0.0; 0.0 0.0;;; 0.14134763322386673 5.876318899706723; 0.0 0.0;;; -0.27781448587580504 -3.399262014326455; -0.21357159879163193 -3.034004529419432;;; … ;;; 2.528007054727247e-6 -5.198140515345906e-6; -3.5865531122720975e-7 -2.2816070849536322e-6;;; -5.825983403314016e-6 1.668839102392757e-7; 7.346808214947709e-7 -5.3432822173448825e-6;;; 4.452343181626718e-7 2.8737566545769717e-6; -5.919437972505053e-7 1.5152180081065892e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.07563716034391843 0.0; 0.0 0.0;;; -0.09383556353568245 0.0; 0.04427676342595527 0.0;;; … ;;; -7.732499867406854e-9 0.0; 3.051715598564347e-8 0.0;;; 6.995691193611116e-8 0.0; 3.5849287145216293e-7 0.0;;; 5.9328907145372435e-8 0.0; 8.075902066539915e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 413681739000))), MultiBranch{Float64, 2}(UnitRange{Int64}[15:25, 13:23], 0, 10:9, 1, 2, [0.7514632196343085, 0.251772153045566, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.786962147547788 0.0; 0.0 0.0;;; -0.08046626758682532 4.410294461276509; 0.0 0.0;;; 0.07917686087068565 -3.2482101027014534; 0.013486487172595357 -2.7368772194723507;;; … ;;; 2.9550574604507674e-6 -2.7285638004285373e-6; -1.3518437065648355e-6 3.5595636693251586e-6;;; -5.234086734876242e-7 3.555165107606909e-6; -9.92570608622439e-7 -1.2783154363676133e-6;;; 1.9554981220314482e-7 7.438288253934825e-7; 4.1692108973748044e-7 1.062118867108326e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.051280316864532494 0.0; 0.0 0.0;;; 0.026829953422987274 0.0; -0.0748119800766262 0.0;;; … ;;; 1.899571107442584e-8 0.0; -1.1328956225594303e-8 0.0;;; 1.6387380676626464e-8 0.0; 8.366465479549419e-8 0.0;;; 2.6126169093897e-8 0.0; 3.9732453187322435e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 413681739000))), MultiBranch{Float64, 2}(UnitRange{Int64}[26:39, 24:38], 0, 10:9, 1, 3, [0.2537887277424278, 0.7494466449374467, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.461237959815938 0.0; 0.0 0.0;;; -0.06455233958895452 10.059074305326293; 0.0 0.0;;; 0.01453666265401074 -4.529151153045262; 0.035733159549641055 -3.1853673726340865;;; … ;;; 2.185651803566736e-6 2.939983733331748e-6; -2.1020197866396055e-6 2.2769594810854188e-5;;; 6.413575350526986e-7 8.118082850156805e-6; -2.6281938845417287e-6 -5.2015670950708256e-6;;; 3.216724613459501e-7 -7.86771014197628e-7; 6.657658982750058e-7 1.327187878612661e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.19697053746278903 0.0; 0.0 0.0;;; -0.06982836891659083 0.0; 0.0559260760892909 0.0;;; … ;;; 9.125962831737276e-7 0.0; 1.864939988205681e-6 0.0;;; -4.7557482138149605e-7 0.0; -2.2413312341668466e-7 0.0;;; 4.644704815088655e-8 0.0; -1.1114538610052121e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 414550893515))), MultiBranch{Float64, 2}(UnitRange{Int64}[40:49, 39:53], 0, 10:9, 1, 4, [0.7514632196343085, 0.7494466449374467, 0.2577380583075476], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.3477273311870865 0.0; 0.0 0.0;;; -0.16435855694757204 9.721186791516416; 0.0 0.0;;; 0.12294219903268079 -4.248526417696294; -0.0332377231093299 -4.252662383598009;;; … ;;; -8.13710641459531e-6 2.8580911633519164e-6; -6.231810556349974e-7 6.864144066599249e-6;;; 2.2119897970051911e-7 -2.346400167145746e-6; -3.7089074074201864e-6 -1.3558413583447434e-5;;; -5.605149079948702e-7 1.52790392922525e-6; -7.910253772220518e-7 1.307628828750524e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.1203246909098602 0.0; 0.0 0.0;;; 0.10905156210654654 0.0; -0.06508193456155464 0.0;;; … ;;; -4.7489710223826224e-8 0.0; -1.0937320874843271e-6 0.0;;; -7.162458392092633e-7 0.0; -1.0897602359520343e-6 0.0;;; -2.4771546198069067e-7 0.0; -1.200508235984114e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (3161095930528, 2886218027744, 141733921440))), MultiBranch{Float64, 2}(UnitRange{Int64}[50:59, 54:61], 0, 10:9, 1, 5, [0.2537887277424278, 0.251772153045566, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.768609585113875 0.0; 0.0 0.0;;; -0.0008241017990052862 5.180157724215509; 0.0 0.0;;; -0.13506173196838803 -2.648291420360042; 0.3386931330435938 -1.2864699484118736;;; … ;;; -9.014507135353242e-7 -7.018939476416647e-6; -3.5641213887785376e-6 5.502324767485222e-6;;; -1.5099245250969104e-7 -5.154080100681363e-6; -4.196134456734228e-6 6.012899693515811e-6;;; -1.3480597057727598e-7 3.5575244532127094e-6; -1.0043910673550508e-6 -5.975371881267255e-7], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.11256203287810052 0.0; 0.0 0.0;;; -0.020966539634629522 0.0; -0.029270807438235014 0.0;;; … ;;; 4.475633321570958e-8 0.0; -1.3548142320263519e-8 0.0;;; -6.2495612685646185e-9 0.0; -4.803194607824211e-9 0.0;;; -1.6989228380302114e-11 0.0; 5.039640229144699e-10 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (3161095930528, 2886218027744, 672))), MultiBranch{Float64, 2}(UnitRange{Int64}[60:70, 62:69], 0, 10:9, 1, 6, [0.7514632196343085, 0.251772153045566, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.6995373983658775 0.0; 0.0 0.0;;; -0.226188905136008 3.677475516378436; 0.0 0.0;;; -0.038937156550284735 -2.5171015089578783; -0.29803097221656427 -2.2333489901345933;;; … ;;; -4.152573541563101e-6 2.0044427363543273e-6; -3.6936070425416564e-6 -2.1325029628985765e-6;;; 2.173487342197061e-6 2.868425050078561e-6; -8.071153365030427e-7 -1.950602288335767e-6;;; -5.683976842176204e-7 1.2853220827340282e-6; 6.412124498508532e-7 3.478490587942194e-6], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.1553180709409666 0.0; 0.0 0.0;;; -0.09289808291753082 0.0; 0.11456471052155748 0.0;;; … ;;; 3.1527654798849906e-6 0.0; 1.6142945545284847e-6 0.0;;; -2.80138885224981e-6 0.0; 1.2383970011340801e-6 0.0;;; 1.524189158643975e-7 0.0; -5.614092520865809e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (1, 139835905755152, 275038569243))), MultiBranch{Float64, 2}(UnitRange{Int64}[71:84, 70:84], 0, 10:9, 1, 7, [0.2537887277424278, 0.7494466449374467, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.357829793323234 0.0; 0.0 0.0;;; -0.4061642214854503 9.5704574266076; 0.0 0.0;;; 0.03137691545227036 -3.3376101500858075; -0.23075631586093312 -3.916290355677398;;; … ;;; 3.3014050982660475e-6 -7.670618662800918e-6; -5.208062214551448e-6 -3.057767276954066e-5;;; 2.870869148786357e-6 -6.334327079983546e-6; 1.7481832131259466e-6 1.8943763991561415e-5;;; -4.1528628356866803e-7 3.2824458852436157e-7; 7.872102020772641e-7 4.794973342512074e-7], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.035440982172832425 0.0; 0.0 0.0;;; -0.04873145295472853 0.0; -0.03622519786432454 0.0;;; … ;;; -3.726393398184811e-9 0.0; 1.0306788187000984e-8 0.0;;; -1.6740465940925586e-8 0.0; 1.1078967570105604e-8 0.0;;; 6.868461008583211e-9 0.0; 3.754551936342892e-10 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 415355812824))), MultiBranch{Float64, 2}(UnitRange{Int64}[85:100, 85:100], 0, 10:9, 1, 8, [0.7514632196343085, 0.7494466449374467, 0.7554125501994283], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 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Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (4832, 0, 0)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], ([5, 19, 24, 38, 39, 43, 51, 53, 60, 62  …  20, 29, 45, 52, 54, 58, 76, 82, 83, 99], [16, 18, 46, 56, 57, 58, 62, 64, 66, 73  …  35, 38, 47, 48, 49, 52, 63, 71, 82, 83]), ([40, 26, 85, 50, 1, 86, 27, 60, 61, 87  …  69, 48, 58, 49, 13, 84, 70, 59, 100, 14], [39, 54, 85, 24, 70, 40, 13, 86, 62, 71  …  60, 23, 83, 52, 53, 12, 68, 69, 61, 84]), (Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.557859214605901, 0.9505794906131003, 0.3404453566099245], 0.009400118805868503, [0.4279926935042637, 0.5792958612811091, 0.7737051496094961, 0.755089351578363]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.4665724969813344, 0.7527119243585907, 0.37990008755992277], 0.008009455207989609, [0.03215302412332721, 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-51.324186953826846, 4.847239236476755, -34.28059339724347, 40.769072683232345, 6.830704526226973, 33.07160266107869, 73.1016517686344, -88.71592593560563], [8.754889219586548, -1.8218252892777913, -7.180948488310969, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.049017597531493595, 0.18258465318130024, 0.04079265592099135], [0.6643772290446401, 0.25419876795775076, 0.0111761955710723], 0.006867801058606931), [0.0, 0.0, 0.0, 0.0, -27.31628247323072, 24.233190449744797, -0.3379485823927118, -11.924411796320792, 11.796570800683952, 4.254545828100499, -0.052136141612230326, 2.7632399691705896, 15.519711672546764], [-3.3270429646506385, 1.727457486302319, 2.4540759698751926, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9446211092215213, 0.5773644194640194, 0.41562195208459896], [0.06814741604330621, 0.16749916233272766, 0.7091985108360725], 0.0031542415121338305), [0.0, 0.0, 0.0, 0.0, 1.8215164214546353, -43.0534679191244, 21.758774568979174, -1.455109738812573, 32.13601155444825, 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[-0.04772504081689664, -20.681704217331202, 12.630047100731876, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7215125397666922, 0.3101399108971986, 0.9120708158457793], [0.036429367243270616, 0.6439997561017691, 0.35149929330560925], 0.0006879838266934451), [0.0, 0.0, 0.0, 0.0, -10.842172139751918, 15.190887004020365, -17.834678493148925, 41.594173476581865, -5.397510782923477, -20.116652682634676, -1.618663520420014, -10.434703724772072, 16.239682922675396], [9.914485943053739, -4.739369747570147, -7.025390474122207, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07014988405111922, 0.5286443270294893, 0.24380912629526263], [0.620780571763883, 0.8699240224718836, 0.5642401605234335], 0.0003071608128254314), [0.0, 0.0, 0.0, 0.0, 101.93059974405706, 17.590681314952022, -320.9252338856423, 442.5488472353321, -219.0466532545508, -19.474434088571872, -146.04873079853883, 40.3055813981039, 117.11605351049374], [-12.779350368008263, -1.3595250276884299, 13.026821975903577, 0.0, 0.0, 0.0])]), Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], (DerivativesSwitch{true, true, true}(), DerivativesSwitch{true, true, true}()))</code></pre><h2 id="Non-Potential-Flow-Applications"><a class="docs-heading-anchor" href="#Non-Potential-Flow-Applications">Non-Potential Flow Applications</a><a id="Non-Potential-Flow-Applications-1"></a><a class="docs-heading-anchor-permalink" href="#Non-Potential-Flow-Applications" title="Permalink"></a></h2><p>As a default, target systems will be evaluated and returned with <code>scalar_potential</code>, <code>velocity</code>, and <code>velocity_gradient</code> fields populated. (Note that the vector potential is not explicitly tracked, though its induced velocity and velocity gradient are.) In some situations, only some of these values may be required. By inputting a boolean vector of the same length as target systems, the user is able to speed up the calculation by not storing unecessary values.</p><p class="math-container">\[\overline{V} = -\nabla \phi + \nabla \times \overline{\psi}\]</p><table><tr><th style="text-align: right"></th><th style="text-align: right"><span>$\phi$</span></th><th style="text-align: right"><span>$\overline{\psi}$</span></th><th style="text-align: right"><span>$\overline{V}$</span></th><th style="text-align: right"><span>$\nabla \overline{V}$</span></th></tr><tr><td style="text-align: right"><code>fmm!</code> Keyword Arguments</td><td style="text-align: right"><code>scalar_potential</code></td><td style="text-align: right"><code>vector_potential</code></td><td style="text-align: right"><code>velocity</code></td><td style="text-align: right"><code>velocity_gradient</code></td></tr><tr><td style="text-align: right">Fluid Dynamics</td><td style="text-align: right">Scalar Potential</td><td style="text-align: right">Stream Function</td><td style="text-align: right">Fluid Velocity</td><td style="text-align: right">Velocity Gradient</td></tr><tr><td style="text-align: right">Electrostatics</td><td style="text-align: right">Electric Potential</td><td style="text-align: right">-</td><td style="text-align: right">Electric Field</td><td style="text-align: right">Field Gradient Tensor</td></tr><tr><td style="text-align: right">Magnetostatics</td><td style="text-align: right">-</td><td style="text-align: right">Magnetic Vector Potential</td><td style="text-align: right">Magnetic Field</td><td style="text-align: right">Field Gradient Tensor</td></tr><tr><td style="text-align: right">Gravity</td><td style="text-align: right">Gravitational Potential</td><td style="text-align: right">-</td><td style="text-align: right">Gravitational Acceleration</td><td style="text-align: right">Acceleration Gradient Tensor</td></tr></table><pre><code class="language-julia hljs">target_one = generate_gravitational(123, 100)
 target_two = generate_vortex(124, 100)
 
 source_one = generate_gravitational(125, 100)
 
 fmm.fmm!((target_one, target_two), source_one, scalar_potential=[true, false],
-    velocity=[true, true], velocity_gradient=[false, false])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.48179464439418035, 0.5006093989915064, 0.5135846646682118], 0.8619975055877627, 0.8619975055877627, [-0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073], [0.49767449189188073, 0.49767449189188073, 0.49767449189188073], 0.0, 0.0, fill(0.0), [-47.330269153011905 0.0; 0.0 0.0;;; -1.0538836054878957 0.0; 0.0 0.0;;; 0.2581437255104959 0.0; 0.32417697579794513 0.0;;; … ;;; -0.0008324020930813901 0.0; 9.584516978454677e-5 0.0;;; 0.00022605569837265332 0.0; 0.0002001737355761634 0.0;;; -4.788589382345488e-5 0.0; -1.5737437600225223e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659273224193, 140658654464144, 140658674668176))), SingleBranch{Float64}(1:14, 0, 10:9, 1, 1, [0.23295739844823998, 0.251772153045566, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-7.499871222570643 0.0; 0.0 0.0;;; 0.1511775172236864 0.0; 0.0 0.0;;; -0.17159862481145716 0.0; -0.07777421111649871 0.0;;; … ;;; 6.654374417721039e-6 0.0; -1.8320398726639646e-6 0.0;;; -2.831979898952648e-7 0.0; 2.7274227268680686e-6 0.0;;; 2.980421231232696e-7 0.0; -1.6644915713327277e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.0475716488261706 0.0; 0.0 0.0;;; 0.1195015413964381 0.0; -0.0717249489633772 0.0;;; … ;;; 8.551990292441558e-8 0.0; 1.6785191448426871e-6 0.0;;; -4.1703590062913545e-7 0.0; -6.208746591492499e-7 0.0;;; -3.967431800726344e-7 0.0; -1.8617643569857076e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (20753281981152, 6208, 4))), SingleBranch{Float64}(15:26, 0, 10:9, 1, 2, [0.7306318903401208, 0.251772153045566, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.832802684288696 0.0; 0.0 0.0;;; -0.005174662477621744 0.0; 0.0 0.0;;; 0.15820729244290432 0.0; 0.12484604144375797 0.0;;; … ;;; 1.0332065930653744e-6 0.0; 2.1649761195969315e-6 0.0;;; 1.9104310530934324e-7 0.0; -6.94223215499619e-7 0.0;;; -5.3899273439794484e-8 0.0; 1.718878795742581e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.2486704739166461 0.0; 0.0 0.0;;; -0.04736999921415913 0.0; -0.07388436286704142 0.0;;; … ;;; 3.2349671327322305e-6 0.0; -4.544322257288448e-7 0.0;;; 4.005786149725973e-7 0.0; 4.6634514669915355e-7 0.0;;; -1.2450376693078546e-8 0.0; 4.157089031438735e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (4294967297, 140659247289680, 140659280801088))), SingleBranch{Float64}(27:41, 0, 10:9, 1, 3, [0.23295739844823998, 0.7494466449374467, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.731488675573531 0.0; 0.0 0.0;;; 0.011400475589984096 0.0; 0.0 0.0;;; 0.1188574386355909 0.0; 0.02054364764978861 0.0;;; … ;;; 1.8724041357624202e-6 0.0; -6.740573259352781e-8 0.0;;; -9.062764401980581e-7 0.0; -1.5028718156848473e-7 0.0;;; -2.656402793225009e-7 0.0; 8.050058723093146e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.0776597288395956 0.0; 0.0 0.0;;; 0.05043299396916734 0.0; 0.12172661720283631 0.0;;; … ;;; 4.666416807814993e-7 0.0; 1.931492763086916e-7 0.0;;; -3.331198811096547e-10 0.0; -9.752745318068186e-7 0.0;;; 3.0569272167597004e-7 0.0; -1.267750090624772e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658568634368, 140658568634400, 140659292045312))), SingleBranch{Float64}(42:51, 0, 10:9, 1, 4, [0.7306318903401208, 0.7494466449374467, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.3477273311870865 0.0; 0.0 0.0;;; -0.05661650963523443 0.0; 0.0 0.0;;; 0.049045688737453436 0.0; -0.029735712471123377 0.0;;; … ;;; 7.249010232689599e-7 0.0; 5.074419050401502e-7 0.0;;; 8.467912089590641e-7 0.0; -1.2457046357912389e-7 0.0;;; -3.3486020944921064e-8 0.0; -9.682938343398542e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.13073333033410794 0.0; 0.0 0.0;;; 0.11180913231923639 0.0; -0.10452524002081365 0.0;;; … ;;; -1.015939496560566e-6 0.0; -1.245007835412755e-6 0.0;;; 2.9624679866733807e-6 0.0; 4.0125695067632e-7 0.0;;; -5.708910699960474e-7 0.0; 4.050818336718332e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659292045328, 140659292046128, 0))), SingleBranch{Float64}(52:61, 0, 10:9, 1, 5, [0.23295739844823998, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.768609585113875 0.0; 0.0 0.0;;; -0.035764396889667704 0.0; 0.0 0.0;;; -0.16228372078844444 0.0; 0.23742079553987183 0.0;;; … ;;; 5.056014420212356e-7 0.0; 2.136901791719658e-7 0.0;;; 1.7169448653861497e-6 0.0; -1.3242169437551442e-6 0.0;;; 7.066422746939443e-8 0.0; -6.418001947143367e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.08253975941558067 0.0; 0.0 0.0;;; 0.09963720788809316 0.0; 0.12010366689568278 0.0;;; … ;;; 1.4850469385811878e-6 0.0; -8.244164692731008e-7 0.0;;; 1.9004462221190685e-6 0.0; 7.403606419704646e-7 0.0;;; -2.4336181277641484e-7 0.0; -7.318122304914546e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659400465168, 140659400465200, 30064771075))), SingleBranch{Float64}(62:71, 0, 10:9, 1, 6, [0.7306318903401208, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 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MultiTree{Float64, 2, Tuple{Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, Vector{Tuple{Main.Vorton{Float64}, Vector{Float64}, Vector{Float64}}}}, 5}(MultiBranch{Float64, 2}[MultiBranch{Float64, 2}(UnitRange{Int64}[1:100, 1:100], 8, 2:9, 0, -1, [0.49801566262999436, 0.49520356617852135, 0.4970227729348794], 0.8574652475891061, 0.8574652475891061, [-0.4950577915163195, 0.4950577915163195, -0.4950577915163195, 0.4950577915163195, -0.4950577915163195, 0.4950577915163195], [0.4950577915163195, 0.4950577915163195, 0.4950577915163195], 0.0, 0.0, fill(0.0), [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, 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0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.18036026635324287, 0.173123936892006, 0.6038823023290261], 0.010016593230124706, [0.4401491209134364, 0.8609926737185056, 0.1638092551671958, 0.22646456871949416]), [85.06258300857247, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.072210006218703, 0.3521154604071077, 0.4644130786564624], 0.0037743609975635275, [0.17728847529212788, 0.12630836876865192, 0.9645167219705122, 0.8221674765296613]), [87.35657697788763, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.8247874340282866, 0.5795916665384359, 0.8038668590137469], 0.0035401668870093193, [0.6409979037657155, 0.15911501872567757, 0.5356210909593669, 0.6799181470255188]), [92.93042970237086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])], Tuple{Main.Vorton{Float64}, Vector{Float64}, Vector{Float64}}[(Main.Vorton{Float64}([0.6956808381416713, 0.4853785553982539, 0.4648049213765313], [0.7054270031323241, 0.70014541220553, 0.49839208412207514], 0.008389531007170116), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.6528326495428173, 0.8783095326823105, 0.6955937752833566], [0.992073216064829, 0.03702391218002421, 0.052040147154059024], 0.008559673062325765), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9077908593045806, 0.3939808726568609, 0.1924335604037214], [0.5681911381173306, 0.06084849139338322, 0.9611920275200003], 0.00920463305134842), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.680305220184172, 0.45142673639459907, 0.6565158730370251], [0.9871517007068787, 0.536191701519787, 0.8044608001295422], 0.01032776912661538), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.5772900725131546, 0.19456471074413395, 0.9691695971486246], [0.029308796906382772, 0.237901194890202, 0.8225322140924277], 0.005855920250376647), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07881482026287556, 0.16694384061777157, 0.7453082600322598], [0.36751517071734363, 0.08464781300384328, 0.7877792123673903], 0.006719633426946119), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.34386745978232425, 0.15114271162865245, 0.8692858825227187], [0.34380421639038017, 0.49221567013213885, 0.7577396026981709], 0.007165314050997217), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7924111084524182, 0.7258577993874293, 0.4074759819413786], [0.004779849956308646, 0.10815467687383273, 0.6365113178025307], 0.004211825485699923), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.15007164548253604, 0.13891454905930323, 0.8854146060893755], [0.2322606392244514, 0.24943996074378283, 0.6529923359002099], 0.004730386058191863), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.178892411148747, 0.8198348637351619, 0.746693545507861], [0.05374276809352163, 0.28259697683790064, 0.9963633829133356], 0.004082068996145551), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Vorton{Float64}([0.4598055261641393, 0.09042082143339258, 0.5640409504623178], [0.6396964311422774, 0.5845421243866575, 0.5349929592419193], 0.001124964196695102), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9572197333627137, 0.6426548339644926, 0.6552399747905221], [0.747485027142634, 0.23562083902231445, 0.23561754824795678], 0.0027436327111542455), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.8050706937073655, 0.005451816228509987, 0.6194543923497148], [0.2893241621284488, 0.15343050371415934, 0.45483197600289493], 0.0033418266341768534), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.8372242495059112, 0.1880062901030637, 0.329865236819033], [0.6964852800076098, 0.41732935474694366, 0.12800112947157438], 0.008074470339380045), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.049017597531493595, 0.18258465318130024, 0.04079265592099135], [0.6643772290446401, 0.25419876795775076, 0.0111761955710723], 0.006867801058606931), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9446211092215213, 0.5773644194640194, 0.41562195208459896], [0.06814741604330621, 0.16749916233272766, 0.7091985108360725], 0.0031542415121338305), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.02765456454632287, 0.1228176034412326, 0.7897475889795191], [0.5848018551658597, 0.4374509112686895, 0.6003922163899991], 0.0010159571328096377), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.09100727263849917, 0.5794817445557756, 0.6291868753365321], [0.04589763740992747, 0.2683934891175124, 0.9312357743393328], 0.004951543147051906), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7215125397666922, 0.3101399108971986, 0.9120708158457793], [0.036429367243270616, 0.6439997561017691, 0.35149929330560925], 0.0006879838266934451), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07014988405111922, 0.5286443270294893, 0.24380912629526263], [0.620780571763883, 0.8699240224718836, 0.5642401605234335], 0.0003071608128254314), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])]), Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], (DerivativesSwitch{true, true, false}(), DerivativesSwitch{false, true, false}()))</code></pre><h2 id="Saving-Generated-Trees"><a class="docs-heading-anchor" href="#Saving-Generated-Trees">Saving Generated Trees</a><a id="Saving-Generated-Trees-1"></a><a class="docs-heading-anchor-permalink" href="#Saving-Generated-Trees" title="Permalink"></a></h2><p>A given <code>fmm!</code> call will typically return a single tree (if performed on the entire system) or two seperate source/target trees (if called on a source and a target). The function call can also be modified to save these trees.</p><pre><code class="language-julia hljs">target_filepath = &quot;target_tree&quot;
+    velocity=[true, true], velocity_gradient=[false, false])</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.48179464439418035, 0.5006093989915064, 0.5135846646682118], 0.8619975055877627, 0.8619975055877627, [-0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073], [0.49767449189188073, 0.49767449189188073, 0.49767449189188073], 0.0, 0.0, fill(0.0), [-47.330269153011905 0.0; 0.0 0.0;;; -1.0538836054878957 0.0; 0.0 0.0;;; 0.2581437255104959 0.0; 0.32417697579794513 0.0;;; … ;;; -0.0008324020930813901 0.0; 9.584516978454677e-5 0.0;;; 0.00022605569837265332 0.0; 0.0002001737355761634 0.0;;; -4.788589382345488e-5 0.0; -1.5737437600225223e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), SingleBranch{Float64}(1:14, 0, 10:9, 1, 1, [0.23295739844823998, 0.251772153045566, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-7.499871222570643 0.0; 0.0 0.0;;; 0.1511775172236864 0.0; 0.0 0.0;;; -0.17159862481145716 0.0; -0.07777421111649871 0.0;;; … ;;; 6.654374417721039e-6 0.0; -1.8320398726639646e-6 0.0;;; -2.831979898952648e-7 0.0; 2.7274227268680686e-6 0.0;;; 2.980421231232696e-7 0.0; -1.6644915713327277e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.0475716488261706 0.0; 0.0 0.0;;; 0.1195015413964381 0.0; -0.0717249489633772 0.0;;; … ;;; 8.551990292441558e-8 0.0; 1.6785191448426871e-6 0.0;;; -4.1703590062913545e-7 0.0; -6.208746591492499e-7 0.0;;; -3.967431800726344e-7 0.0; -1.8617643569857076e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835889330096, 139835889330160, 139835170368720))), SingleBranch{Float64}(15:26, 0, 10:9, 1, 2, [0.7306318903401208, 0.251772153045566, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.832802684288696 0.0; 0.0 0.0;;; -0.005174662477621744 0.0; 0.0 0.0;;; 0.15820729244290432 0.0; 0.12484604144375797 0.0;;; … ;;; 1.0332065930653744e-6 0.0; 2.1649761195969315e-6 0.0;;; 1.9104310530934324e-7 0.0; -6.94223215499619e-7 0.0;;; -5.3899273439794484e-8 0.0; 1.718878795742581e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.2486704739166461 0.0; 0.0 0.0;;; -0.04736999921415913 0.0; -0.07388436286704142 0.0;;; … ;;; 3.2349671327322305e-6 0.0; -4.544322257288448e-7 0.0;;; 4.005786149725973e-7 0.0; 4.6634514669915355e-7 0.0;;; -1.2450376693078546e-8 0.0; 4.157089031438735e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), SingleBranch{Float64}(27:41, 0, 10:9, 1, 3, [0.23295739844823998, 0.7494466449374467, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.731488675573531 0.0; 0.0 0.0;;; 0.011400475589984096 0.0; 0.0 0.0;;; 0.1188574386355909 0.0; 0.02054364764978861 0.0;;; … ;;; 1.8724041357624202e-6 0.0; -6.740573259352781e-8 0.0;;; -9.062764401980581e-7 0.0; -1.5028718156848473e-7 0.0;;; -2.656402793225009e-7 0.0; 8.050058723093146e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.0776597288395956 0.0; 0.0 0.0;;; 0.05043299396916734 0.0; 0.12172661720283631 0.0;;; … ;;; 4.666416807814993e-7 0.0; 1.931492763086916e-7 0.0;;; -3.331198811096547e-10 0.0; -9.752745318068186e-7 0.0;;; 3.0569272167597004e-7 0.0; -1.267750090624772e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835767718704, 139835767718704, 139835767727712))), SingleBranch{Float64}(42:51, 0, 10:9, 1, 4, [0.7306318903401208, 0.7494466449374467, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.3477273311870865 0.0; 0.0 0.0;;; -0.05661650963523443 0.0; 0.0 0.0;;; 0.049045688737453436 0.0; -0.029735712471123377 0.0;;; … ;;; 7.249010232689599e-7 0.0; 5.074419050401502e-7 0.0;;; 8.467912089590641e-7 0.0; -1.2457046357912389e-7 0.0;;; -3.3486020944921064e-8 0.0; -9.682938343398542e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.13073333033410794 0.0; 0.0 0.0;;; 0.11180913231923639 0.0; -0.10452524002081365 0.0;;; … ;;; -1.015939496560566e-6 0.0; -1.245007835412755e-6 0.0;;; 2.9624679866733807e-6 0.0; 4.0125695067632e-7 0.0;;; -5.708910699960474e-7 0.0; 4.050818336718332e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 0))), SingleBranch{Float64}(52:61, 0, 10:9, 1, 5, [0.23295739844823998, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.768609585113875 0.0; 0.0 0.0;;; -0.035764396889667704 0.0; 0.0 0.0;;; -0.16228372078844444 0.0; 0.23742079553987183 0.0;;; … ;;; 5.056014420212356e-7 0.0; 2.136901791719658e-7 0.0;;; 1.7169448653861497e-6 0.0; -1.3242169437551442e-6 0.0;;; 7.066422746939443e-8 0.0; -6.418001947143367e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.08253975941558067 0.0; 0.0 0.0;;; 0.09963720788809316 0.0; 0.12010366689568278 0.0;;; … ;;; 1.4850469385811878e-6 0.0; -8.244164692731008e-7 0.0;;; 1.9004462221190685e-6 0.0; 7.403606419704646e-7 0.0;;; -2.4336181277641484e-7 0.0; -7.318122304914546e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835175755568, 139835175755616, 139835175755664))), SingleBranch{Float64}(62:71, 0, 10:9, 1, 6, [0.7306318903401208, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 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[0.029308796906382772, 0.237901194890202, 0.8225322140924277], 0.005855920250376647), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07881482026287556, 0.16694384061777157, 0.7453082600322598], [0.36751517071734363, 0.08464781300384328, 0.7877792123673903], 0.006719633426946119), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.34386745978232425, 0.15114271162865245, 0.8692858825227187], [0.34380421639038017, 0.49221567013213885, 0.7577396026981709], 0.007165314050997217), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7924111084524182, 0.7258577993874293, 0.4074759819413786], [0.004779849956308646, 0.10815467687383273, 0.6365113178025307], 0.004211825485699923), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.15007164548253604, 0.13891454905930323, 0.8854146060893755], [0.2322606392244514, 0.24943996074378283, 0.6529923359002099], 0.004730386058191863), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.178892411148747, 0.8198348637351619, 0.746693545507861], [0.05374276809352163, 0.28259697683790064, 0.9963633829133356], 0.004082068996145551), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Vorton{Float64}([0.4598055261641393, 0.09042082143339258, 0.5640409504623178], [0.6396964311422774, 0.5845421243866575, 0.5349929592419193], 0.001124964196695102), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9572197333627137, 0.6426548339644926, 0.6552399747905221], [0.747485027142634, 0.23562083902231445, 0.23561754824795678], 0.0027436327111542455), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.8050706937073655, 0.005451816228509987, 0.6194543923497148], [0.2893241621284488, 0.15343050371415934, 0.45483197600289493], 0.0033418266341768534), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.8372242495059112, 0.1880062901030637, 0.329865236819033], [0.6964852800076098, 0.41732935474694366, 0.12800112947157438], 0.008074470339380045), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.049017597531493595, 0.18258465318130024, 0.04079265592099135], [0.6643772290446401, 0.25419876795775076, 0.0111761955710723], 0.006867801058606931), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9446211092215213, 0.5773644194640194, 0.41562195208459896], [0.06814741604330621, 0.16749916233272766, 0.7091985108360725], 0.0031542415121338305), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.02765456454632287, 0.1228176034412326, 0.7897475889795191], [0.5848018551658597, 0.4374509112686895, 0.6003922163899991], 0.0010159571328096377), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.09100727263849917, 0.5794817445557756, 0.6291868753365321], [0.04589763740992747, 0.2683934891175124, 0.9312357743393328], 0.004951543147051906), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7215125397666922, 0.3101399108971986, 0.9120708158457793], [0.036429367243270616, 0.6439997561017691, 0.35149929330560925], 0.0006879838266934451), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07014988405111922, 0.5286443270294893, 0.24380912629526263], [0.620780571763883, 0.8699240224718836, 0.5642401605234335], 0.0003071608128254314), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])]), Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], (DerivativesSwitch{true, true, false}(), DerivativesSwitch{false, true, false}()))</code></pre><h2 id="Saving-Generated-Trees"><a class="docs-heading-anchor" href="#Saving-Generated-Trees">Saving Generated Trees</a><a id="Saving-Generated-Trees-1"></a><a class="docs-heading-anchor-permalink" href="#Saving-Generated-Trees" title="Permalink"></a></h2><p>A given <code>fmm!</code> call will typically return a single tree (if performed on the entire system) or two seperate source/target trees (if called on a source and a target). The function call can also be modified to save these trees.</p><pre><code class="language-julia hljs">target_filepath = &quot;target_tree&quot;
 source_filepath = &quot;source_tree&quot;
 
 target_tree, source_tree = fmm.fmm!((target_one, target_two), source_one;
     save_tree_target=true, save_name_target=target_filepath,
-    save_tree_source=true, save_name_source=source_filepath)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.48179464439418035, 0.5006093989915064, 0.5135846646682118], 0.8619975055877627, 0.8619975055877627, [-0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073], [0.49767449189188073, 0.49767449189188073, 0.49767449189188073], 0.0, 0.0, fill(0.0), [-47.330269153011905 0.0; 0.0 0.0;;; -1.0538836054878957 0.0; 0.0 0.0;;; 0.2581437255104959 0.0; 0.32417697579794513 0.0;;; … ;;; -0.0008324020930813901 0.0; 9.584516978454677e-5 0.0;;; 0.00022605569837265332 0.0; 0.0002001737355761634 0.0;;; -4.788589382345488e-5 0.0; -1.5737437600225223e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658923270976, 140659292046128, 140655883976704))), SingleBranch{Float64}(1:14, 0, 10:9, 1, 1, [0.23295739844823998, 0.251772153045566, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-7.499871222570643 0.0; 0.0 0.0;;; 0.1511775172236864 0.0; 0.0 0.0;;; -0.17159862481145716 0.0; -0.07777421111649871 0.0;;; … ;;; 6.654374417721039e-6 0.0; -1.8320398726639646e-6 0.0;;; -2.831979898952648e-7 0.0; 2.7274227268680686e-6 0.0;;; 2.980421231232696e-7 0.0; -1.6644915713327277e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.0475716488261706 0.0; 0.0 0.0;;; 0.1195015413964381 0.0; -0.0717249489633772 0.0;;; … ;;; 8.551990292441558e-8 0.0; 1.6785191448426871e-6 0.0;;; -4.1703590062913545e-7 0.0; -6.208746591492499e-7 0.0;;; -3.967431800726344e-7 0.0; -1.8617643569857076e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658679665520, 140658679665552, 140659292055136))), SingleBranch{Float64}(15:26, 0, 10:9, 1, 2, [0.7306318903401208, 0.251772153045566, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-5.832802684288696 0.0; 0.0 0.0;;; -0.005174662477621744 0.0; 0.0 0.0;;; 0.15820729244290432 0.0; 0.12484604144375797 0.0;;; … ;;; 1.0332065930653744e-6 0.0; 2.1649761195969315e-6 0.0;;; 1.9104310530934324e-7 0.0; -6.94223215499619e-7 0.0;;; -5.3899273439794484e-8 0.0; 1.718878795742581e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.2486704739166461 0.0; 0.0 0.0;;; -0.04736999921415913 0.0; -0.07388436286704142 0.0;;; … ;;; 3.2349671327322305e-6 0.0; -4.544322257288448e-7 0.0;;; 4.005786149725973e-7 0.0; 4.6634514669915355e-7 0.0;;; -1.2450376693078546e-8 0.0; 4.157089031438735e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (0, 0, 414864795464))), SingleBranch{Float64}(27:41, 0, 10:9, 1, 3, [0.23295739844823998, 0.7494466449374467, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.731488675573531 0.0; 0.0 0.0;;; 0.011400475589984096 0.0; 0.0 0.0;;; 0.1188574386355909 0.0; 0.02054364764978861 0.0;;; … ;;; 1.8724041357624202e-6 0.0; -6.740573259352781e-8 0.0;;; -9.062764401980581e-7 0.0; -1.5028718156848473e-7 0.0;;; -2.656402793225009e-7 0.0; 8.050058723093146e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.0776597288395956 0.0; 0.0 0.0;;; 0.05043299396916734 0.0; 0.12172661720283631 0.0;;; … ;;; 4.666416807814993e-7 0.0; 1.931492763086916e-7 0.0;;; -3.331198811096547e-10 0.0; -9.752745318068186e-7 0.0;;; 3.0569272167597004e-7 0.0; -1.267750090624772e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (3, 4, 0))), SingleBranch{Float64}(42:51, 0, 10:9, 1, 4, [0.7306318903401208, 0.7494466449374467, 0.2647474187222715], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.3477273311870865 0.0; 0.0 0.0;;; -0.05661650963523443 0.0; 0.0 0.0;;; 0.049045688737453436 0.0; -0.029735712471123377 0.0;;; … ;;; 7.249010232689599e-7 0.0; 5.074419050401502e-7 0.0;;; 8.467912089590641e-7 0.0; -1.2457046357912389e-7 0.0;;; -3.3486020944921064e-8 0.0; -9.682938343398542e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.13073333033410794 0.0; 0.0 0.0;;; 0.11180913231923639 0.0; -0.10452524002081365 0.0;;; … ;;; -1.015939496560566e-6 0.0; -1.245007835412755e-6 0.0;;; 2.9624679866733807e-6 0.0; 4.0125695067632e-7 0.0;;; -5.708910699960474e-7 0.0; 4.050818336718332e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659438875649, 140659279441296, 433462360018))), SingleBranch{Float64}(52:61, 0, 10:9, 1, 5, [0.23295739844823998, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-3.768609585113875 0.0; 0.0 0.0;;; -0.035764396889667704 0.0; 0.0 0.0;;; -0.16228372078844444 0.0; 0.23742079553987183 0.0;;; … ;;; 5.056014420212356e-7 0.0; 2.136901791719658e-7 0.0;;; 1.7169448653861497e-6 0.0; -1.3242169437551442e-6 0.0;;; 7.066422746939443e-8 0.0; -6.418001947143367e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.08253975941558067 0.0; 0.0 0.0;;; 0.09963720788809316 0.0; 0.12010366689568278 0.0;;; … ;;; 1.4850469385811878e-6 0.0; -8.244164692731008e-7 0.0;;; 1.9004462221190685e-6 0.0; 7.403606419704646e-7 0.0;;; -2.4336181277641484e-7 0.0; -7.318122304914546e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658602017024, 140658676917328, 140659237130816))), SingleBranch{Float64}(62:71, 0, 10:9, 1, 6, [0.7306318903401208, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-6.65369686162497 0.0; 0.0 0.0;;; -0.33832705107850786 0.0; 0.0 0.0;;; 0.03648439580080508 0.0; -0.2893007691915242 0.0;;; … ;;; -9.56553625327193e-7 0.0; -2.2026067778364347e-6 0.0;;; 1.9474701214310728e-6 0.0; 5.648080340882214e-8 0.0;;; -4.831687600971158e-7 0.0; 4.5322428445436293e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.1120955954162618 0.0; 0.0 0.0;;; 0.018512552533617777 0.0; 0.0663651054717656 0.0;;; … ;;; -2.0236147622849254e-7 0.0; -1.903004423018463e-7 0.0;;; 4.885027079146498e-8 0.0; -9.322703900889062e-8 0.0;;; 1.2652353474943286e-8 0.0; 2.7049821370130747e-9 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140658647627952, 140658647628000, 140658647628048))), SingleBranch{Float64}(72:83, 0, 10:9, 1, 7, [0.23295739844823998, 0.7494466449374467, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-4.426804767086749 0.0; 0.0 0.0;;; -0.33604471722409424 0.0; 0.0 0.0;;; 0.13234132530752615 0.0; -0.1606673862693206 0.0;;; … ;;; 1.1458834355307562e-6 0.0; -1.4643331074881864e-6 0.0;;; 8.012013073683108e-8 0.0; 7.658765166251638e-7 0.0;;; -2.960351828451514e-7 0.0; -7.415640875943139e-8 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.08779121028896275 0.0; 0.0 0.0;;; 0.0024206596390341506 0.0; -0.08622261451422439 0.0;;; … ;;; -1.793369218013121e-8 0.0; 2.1248188421746336e-7 0.0;;; 2.0121767805487402e-7 0.0; 2.2685828324326742e-8 0.0;;; 5.565730178295652e-9 0.0; -3.93993876207998e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659438647552, 140659344849808, 140659438648448))), SingleBranch{Float64}(84:100, 0, 10:9, 1, 8, [0.7306318903401208, 0.7494466449374467, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037, -0.24883724594594037, 0.24883724594594037], [0.24883724594594037, 0.24883724594594037, 0.24883724594594037], 0.0, 0.0, fill(0.0), [-9.069268025566352 0.0; 0.0 0.0;;; -0.31850085207032125 0.0; 0.0 0.0;;; 0.11944690591762133 0.0; 0.1906943971623366 0.0;;; … ;;; -6.760562163890454e-6 0.0; 3.950077335221274e-6 0.0;;; 6.1795388617324575e-6 0.0; 5.467181615162473e-8 0.0;;; -8.913747733183657e-7 0.0; -4.836258226795493e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; 0.027307294502641133 0.0; 0.0 0.0;;; 0.11562444322657306 0.0; 0.007173497524932848 0.0;;; … ;;; -7.594532495054794e-7 0.0; -1.4282037498218524e-7 0.0;;; 1.9866669481961943e-7 0.0; 5.027272869736831e-8 0.0;;; 1.6559747198033837e-7 0.0; 5.301068040987261e-8 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (140659267134224, 140658602017088, 140659438655616)))], UnitRange{Int64}[1:1, 2:9], [2, 3, 4, 5, 6, 7, 8, 9], [5, 19, 24, 38, 39, 43, 51, 53, 60, 62  …  20, 29, 45, 52, 54, 58, 76, 82, 83, 99], [42, 27, 84, 52, 1, 85, 28, 62, 63, 86  …  26, 50, 60, 51, 13, 83, 71, 61, 100, 14], Tuple{Main.Body{Float64}, Vector{Float64}}[(Main.Body{Float64}([0.557859214605901, 0.9505794906131003, 0.3404453566099245], 0.009400118805868503, [0.4279926935042637, 0.5792958612811091, 0.7737051496094961, 0.755089351578363]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.4665724969813344, 0.7527119243585907, 0.37990008755992277], 0.008009455207989609, [0.03215302412332721, 0.30401585392069863, 0.39844830923765007, 0.05175624298006909]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.655364218417507, 0.5420094641040476, 0.5949064366117462], 0.00966985017093868, [0.45318687939721236, 0.714833285253085, 0.8014821280258599, 0.0423294989420161]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.46020494037027904, 0.1183049591166877, 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0.377504748209773]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.503364457080568, 0.4739102794439455, 0.8882313721777293], 0.007003767860720454, [0.647938265577496, 0.5462740370511083, 0.4481538479575009, 0.42773190354588286]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.6419909113170134, 0.3653123773611996, 0.9713497759206838], 0.0043579616572875434, [0.8917110271026161, 0.6439207339714714, 0.5036025955048534, 0.4437995597691393]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Body{Float64}([0.5660529652176645, 0.9595746577303932, 0.8477086241617172], 0.0035640681857256975, [0.5419453685002806, 0.3427439265408987, 0.032196858193411226, 0.18518731541358224]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 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(Main.Vorton{Float64}([0.7924111084524182, 0.7258577993874293, 0.4074759819413786], [0.004779849956308646, 0.10815467687383273, 0.6365113178025307], 0.004211825485699923), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.15007164548253604, 0.13891454905930323, 0.8854146060893755], [0.2322606392244514, 0.24943996074378283, 0.6529923359002099], 0.004730386058191863), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.178892411148747, 0.8198348637351619, 0.746693545507861], [0.05374276809352163, 0.28259697683790064, 0.9963633829133356], 0.004082068996145551), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  …  (Main.Vorton{Float64}([0.4598055261641393, 0.09042082143339258, 0.5640409504623178], [0.6396964311422774, 0.5845421243866575, 0.5349929592419193], 0.001124964196695102), [0.0, 0.0, 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[0.6643772290446401, 0.25419876795775076, 0.0111761955710723], 0.006867801058606931), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.9446211092215213, 0.5773644194640194, 0.41562195208459896], [0.06814741604330621, 0.16749916233272766, 0.7091985108360725], 0.0031542415121338305), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.02765456454632287, 0.1228176034412326, 0.7897475889795191], [0.5848018551658597, 0.4374509112686895, 0.6003922163899991], 0.0010159571328096377), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.09100727263849917, 0.5794817445557756, 0.6291868753365321], [0.04589763740992747, 0.2683934891175124, 0.9312357743393328], 0.004951543147051906), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.7215125397666922, 0.3101399108971986, 0.9120708158457793], [0.036429367243270616, 0.6439997561017691, 0.35149929330560925], 0.0006879838266934451), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07014988405111922, 0.5286443270294893, 0.24380912629526263], [0.620780571763883, 0.8699240224718836, 0.5642401605234335], 0.0003071608128254314), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])]), Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], (DerivativesSwitch{true, true, true}(), DerivativesSwitch{true, true, true}()))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../quickstart/">« Quick Start</a><a 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+    save_tree_source=true, save_name_source=source_filepath)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">(SingleTree{Float64, Vector{Tuple{Main.Body{Float64}, Vector{Float64}}}, 5}(SingleBranch{Float64}[SingleBranch{Float64}(1:100, 8, 2:9, 0, -1, [0.48179464439418035, 0.5006093989915064, 0.5135846646682118], 0.8619975055877627, 0.8619975055877627, [-0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073, -0.49767449189188073, 0.49767449189188073], [0.49767449189188073, 0.49767449189188073, 0.49767449189188073], 0.0, 0.0, fill(0.0), [-47.330269153011905 0.0; 0.0 0.0;;; -1.0538836054878957 0.0; 0.0 0.0;;; 0.2581437255104959 0.0; 0.32417697579794513 0.0;;; … ;;; -0.0008324020930813901 0.0; 9.584516978454677e-5 0.0;;; 0.00022605569837265332 0.0; 0.0002001737355761634 0.0;;; -4.788589382345488e-5 0.0; -1.5737437600225223e-5 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 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0.23742079553987183 0.0;;; … ;;; 5.056014420212356e-7 0.0; 2.136901791719658e-7 0.0;;; 1.7169448653861497e-6 0.0; -1.3242169437551442e-6 0.0;;; 7.066422746939443e-8 0.0; -6.418001947143367e-7 0.0], [0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; … ;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0;;; 0.0 0.0; 0.0 0.0], [1.0 0.0; 0.0 0.0;;; -0.08253975941558067 0.0; 0.0 0.0;;; 0.09963720788809316 0.0; 0.12010366689568278 0.0;;; … ;;; 1.4850469385811878e-6 0.0; -8.244164692731008e-7 0.0;;; 1.9004462221190685e-6 0.0; 7.403606419704646e-7 0.0;;; -2.4336181277641484e-7 0.0; -7.318122304914546e-7 0.0], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (139835914548368, 139835914547920, 139835914447808))), SingleBranch{Float64}(62:71, 0, 10:9, 1, 6, [0.7306318903401208, 0.251772153045566, 0.7624219106141522], 0.43099875279388133, 0.43099875279388133, [-0.24883724594594037, 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(Main.Vorton{Float64}([0.7215125397666922, 0.3101399108971986, 0.9120708158457793], [0.036429367243270616, 0.6439997561017691, 0.35149929330560925], 0.0006879838266934451), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), (Main.Vorton{Float64}([0.07014988405111922, 0.5286443270294893, 0.24380912629526263], [0.620780571763883, 0.8699240224718836, 0.5642401605234335], 0.0003071608128254314), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0])]), Val{5}(), 50), Tuple{Int32, Int32, Int64}[], StaticArraysCore.SVector{2, Int32}[[2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [2, 3], [3, 3]  …  [8, 8], [9, 8], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9]], (DerivativesSwitch{true, true, true}(), DerivativesSwitch{true, true, true}()))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../quickstart/">« Quick Start</a><a 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docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Introduction</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Introduction</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/byuflowlab/FastMultipole" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/byuflowlab/FastMultipole/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="FastMultipole"><a class="docs-heading-anchor" href="#FastMultipole">FastMultipole</a><a id="FastMultipole-1"></a><a class="docs-heading-anchor-permalink" href="#FastMultipole" title="Permalink"></a></h1><p><em>A fast, multi-system, multi-kernel, differentiable implementation of the fast multipole method for use with scalar-plus-vector potential N-body problems in pure Julia.</em></p><p><strong>Author</strong>: Ryan Anderson</p><p><strong>Features</strong>:</p><ul><li>solves <span>$N$</span>-body problems governed by the Laplace (<span>$1/r$</span>) kernel, with work planned to support the Helmholtz kernel in the future</li><li>incorporates seamlessly into existing Julia code without modifications (just the addition of a few interface functions)</li><li>offers convenience functions for determining the expansion coefficients for source points, vortex points, source panels, and dipole panels (this list is growing!)</li><li>provides velocity and velocity gradient (or their equivalent for non-fluids problems) obtained using analytic expressions (no finite difference)</li><li>uses <span>$O(p^4)$</span> multipole-to-local translation operator (where <span>$p$</span> is the expansion order), though this may improve in the near future</li><li>automated CPU-parallelization of expansions and direct interactions</li><li>supports GPU-parallelization of direct interactions using <a href="https://github.com/JuliaGPU/CUDA.jl">CUDA</a></li><li><a href="https://github.com/JuliaDiff/ForwardDiff.jl">ForwardDiff</a> and <a href="https://github.com/JuliaDiff/ReverseDiff.jl">ReverseDiff</a> compatible</li></ul><p><strong>Installation</strong>:</p><pre><code class="language-julia hljs">pkg&gt; add https://github.com/byuflowlab/FastMultipole.git</code></pre><p><strong>Documentation</strong>:</p><ul><li>learn basic useage in the <a href="quickstart/">Quick Start</a> tutorial</li><li>discover more features in the <a href="guided_examples/">Guided Examples</a></li><li>fine-tune performance in the <a href="advanced_usage/">Advanced Usage</a> section (for FMM experts)</li><li>see the full <a href="reference/">API</a></li><li>brush up on the <a href="theory/">Theory</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="quickstart/">Quick Start »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option 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Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Introduction · FastMultipole.jl</title><meta name="title" content="Introduction · FastMultipole.jl"/><meta property="og:title" content="Introduction · FastMultipole.jl"/><meta property="twitter:title" content="Introduction · FastMultipole.jl"/><meta name="description" content="Documentation for FastMultipole.jl."/><meta property="og:description" content="Documentation for FastMultipole.jl."/><meta property="twitter:description" content="Documentation for FastMultipole.jl."/><meta property="og:url" content="https://flow.byu.edu/FastMultipole/"/><meta property="twitter:url" content="https://flow.byu.edu/FastMultipole/"/><link rel="canonical" href="https://flow.byu.edu/FastMultipole/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" 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href="assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>FastMultipole.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Introduction</a></li><li><a class="tocitem" href="quickstart/">Quick Start</a></li><li><a class="tocitem" href="guided_examples/">Guided Examples</a></li><li><a class="tocitem" href="advanced_usage/">Advanced Usage</a></li><li><a class="tocitem" href="reference/">Reference</a></li><li><a class="tocitem" href="theory/">Theory</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Introduction</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Introduction</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/byuflowlab/FastMultipole" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/byuflowlab/FastMultipole/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="FastMultipole"><a class="docs-heading-anchor" href="#FastMultipole">FastMultipole</a><a id="FastMultipole-1"></a><a class="docs-heading-anchor-permalink" href="#FastMultipole" title="Permalink"></a></h1><p><em>A fast, multi-system, multi-kernel, differentiable implementation of the fast multipole method for use with scalar-plus-vector potential N-body problems in pure Julia.</em></p><p><strong>Author</strong>: Ryan Anderson</p><p><strong>Features</strong>:</p><ul><li>solves <span>$N$</span>-body problems governed by the Laplace (<span>$1/r$</span>) kernel, with work planned to support the Helmholtz kernel in the future</li><li>incorporates seamlessly into existing Julia code without modifications (just the addition of a few interface functions)</li><li>offers convenience functions for determining the expansion coefficients for source points, vortex points, source panels, and dipole panels (this list is growing!)</li><li>provides velocity and velocity gradient (or their equivalent for non-fluids problems) obtained using analytic expressions (no finite difference)</li><li>uses <span>$O(p^4)$</span> multipole-to-local translation operator (where <span>$p$</span> is the expansion order), though this may improve in the near future</li><li>automated CPU-parallelization of expansions and direct interactions</li><li>supports GPU-parallelization of direct interactions using <a href="https://github.com/JuliaGPU/CUDA.jl">CUDA</a></li><li><a href="https://github.com/JuliaDiff/ForwardDiff.jl">ForwardDiff</a> and <a href="https://github.com/JuliaDiff/ReverseDiff.jl">ReverseDiff</a> compatible</li></ul><p><strong>Installation</strong>:</p><pre><code class="language-julia hljs">pkg&gt; add https://github.com/byuflowlab/FastMultipole.git</code></pre><p><strong>Documentation</strong>:</p><ul><li>learn basic useage in the <a href="quickstart/">Quick Start</a> tutorial</li><li>discover more features in the <a href="guided_examples/">Guided Examples</a></li><li>fine-tune performance in the <a href="advanced_usage/">Advanced Usage</a> section (for FMM experts)</li><li>see the full <a href="reference/">API</a></li><li>brush up on the <a href="theory/">Theory</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="quickstart/">Quick Start »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 11 November 2024 22:07">Monday 11 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/quickstart/index.html b/dev/quickstart/index.html
index 78042fc..1b2cbcf 100644
--- a/dev/quickstart/index.html
+++ b/dev/quickstart/index.html
@@ -45,4 +45,4 @@
 
 percent_error = abs.((system.potential[1,:] .- direct_system.potential[1,:]) ./ direct_system.potential[1,:])
 
-@show maximum(percent_error)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4.748757699729193e-7</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Introduction</a><a class="docs-footer-nextpage" href="../guided_examples/">Guided Examples »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 11 November 2024 20:47">Monday 11 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+@show maximum(percent_error)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4.748757699729193e-7</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Introduction</a><a class="docs-footer-nextpage" href="../guided_examples/">Guided Examples »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 11 November 2024 22:07">Monday 11 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/reference/index.html b/dev/reference/index.html
index a5264b0..7056b1d 100644
--- a/dev/reference/index.html
+++ b/dev/reference/index.html
@@ -1,2 +1,2 @@
 <!DOCTYPE html>
-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Reference · FastMultipole.jl</title><meta name="title" content="Reference · FastMultipole.jl"/><meta property="og:title" content="Reference · FastMultipole.jl"/><meta property="twitter:title" content="Reference · FastMultipole.jl"/><meta name="description" content="Documentation for FastMultipole.jl."/><meta property="og:description" content="Documentation for FastMultipole.jl."/><meta property="twitter:description" content="Documentation for FastMultipole.jl."/><meta property="og:url" content="https://flow.byu.edu/FastMultipole/reference/"/><meta property="twitter:url" content="https://flow.byu.edu/FastMultipole/reference/"/><link rel="canonical" href="https://flow.byu.edu/FastMultipole/reference/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" 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href="../assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">FastMultipole.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Introduction</a></li><li><a class="tocitem" href="../quickstart/">Quick Start</a></li><li><a class="tocitem" href="../guided_examples/">Guided Examples</a></li><li><a class="tocitem" href="../advanced_usage/">Advanced Usage</a></li><li class="is-active"><a class="tocitem" href>Reference</a></li><li><a class="tocitem" href="../theory/">Theory</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a 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title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Reference"><a class="docs-heading-anchor" href="#Reference">Reference</a><a id="Reference-1"></a><a class="docs-heading-anchor-permalink" href="#Reference" title="Permalink"></a></h1><ul><li><a href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool, Tuple}"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.DerivativesSwitch-Tuple{Any, Any, Any}"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.DerivativesSwitch"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool}"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.ExpansionSwitch"><code>FastMultipole.ExpansionSwitch</code></a></li><li><a href="#FastMultipole.MultiBranch"><code>FastMultipole.MultiBranch</code></a></li><li><a href="#FastMultipole.MultiTree"><code>FastMultipole.MultiTree</code></a></li><li><a href="#FastMultipole.ProbeSystem-Union{Tuple{Array{StaticArraysCore.SVector{3, TF}, 1}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a></li><li><a href="#FastMultipole.ProbeSystem"><code>FastMultipole.ProbeSystem</code></a></li><li><a href="#FastMultipole.ProbeSystem-Union{Tuple{Matrix{TF}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a></li><li><a href="#FastMultipole.SingleBranch"><code>FastMultipole.SingleBranch</code></a></li><li><a href="#FastMultipole.SortWrapper-Tuple{Any}"><code>FastMultipole.SortWrapper</code></a></li><li><a href="#FastMultipole.Tree"><code>FastMultipole.Tree</code></a></li><li><a href="#FastMultipole.EmptyTree-Tuple{Any}"><code>FastMultipole.EmptyTree</code></a></li><li><a href="#FastMultipole.accumulate_charge!-Union{Tuple{TF}, Tuple{AbstractVector{&lt;:Branch{TF}}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge!</code></a></li><li><a href="#FastMultipole.accumulate_charge_bodies!-Union{Tuple{TF}, Tuple{Array{SingleBranch{TF}, 1}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge_bodies!</code></a></li><li><a href="#FastMultipole.add_line!-Tuple{ProbeSystem, Vararg{Any, 4}}"><code>FastMultipole.add_line!</code></a></li><li><a href="#FastMultipole.back_rotate_local_y!-NTuple{7, Any}"><code>FastMultipole.back_rotate_local_y!</code></a></li><li><a href="#FastMultipole.back_rotate_multipole_y!-NTuple{6, Any}"><code>FastMultipole.back_rotate_multipole_y!</code></a></li><li><a href="#FastMultipole.back_rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.back_rotate_z!</code></a></li><li><a href="#FastMultipole.calculate_ib!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_ib!</code></a></li><li><a href="#FastMultipole.calculate_pj!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_pj!</code></a></li><li><a href="#FastMultipole.d2rdx2-Tuple{Any, Any, Any}"><code>FastMultipole.d2rdx2</code></a></li><li><a href="#FastMultipole.direct!-Tuple{Tuple}"><code>FastMultipole.direct!</code></a></li><li><a href="#FastMultipole.direct!-Tuple{Any, Any}"><code>FastMultipole.direct!</code></a></li><li><a href="#FastMultipole.drdx-Tuple{Any, Any, Any}"><code>FastMultipole.drdx</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{Any}, Tuple{PE}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Any, Any}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.get_P-Tuple{Any, Any, Any, Any, Any, Any, Any, Union{EqualSpheres, UnequalBoxes, UnequalSpheres}}"><code>FastMultipole.get_P</code></a></li><li><a href="#FastMultipole.local_to_local!-Union{Tuple{LH}, Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Val{P}, Val{LH}}} where {P, LH}"><code>FastMultipole.local_to_local!</code></a></li><li><a href="#FastMultipole.mirrored_source_to_vortex!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.mirrored_source_to_vortex!</code></a></li><li><a href="#FastMultipole.multipole_to_local!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.multipole_to_local!</code></a></li><li><a href="#FastMultipole.reset!-Tuple{ProbeSystem}"><code>FastMultipole.reset!</code></a></li><li><a href="#FastMultipole.resort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.resort!</code></a></li><li><a href="#FastMultipole.rotate_multipole_y!-NTuple{8, Any}"><code>FastMultipole.rotate_multipole_y!</code></a></li><li><a href="#FastMultipole.rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.rotate_z!</code></a></li><li><a href="#FastMultipole.shrink_branch!-Tuple{Any, Any, Any}"><code>FastMultipole.shrink_branch!</code></a></li><li><a href="#FastMultipole.source_to_dipole!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_dipole!</code></a></li><li><a href="#FastMultipole.source_to_vortex_point!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_vortex_point!</code></a></li><li><a href="#FastMultipole.translate_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_local_z!</code></a></li><li><a href="#FastMultipole.translate_multipole_to_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_to_local_z!</code></a></li><li><a href="#FastMultipole.translate_multipole_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_z!</code></a></li><li><a href="#FastMultipole.unsort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.unsort!</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch" href="#FastMultipole.DerivativesSwitch"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch</code></pre><p>Switch indicating whether the scalar potential, vector potential, velocity, and/or velocity gradient should be computed for a target system. Information is stored as type parameters, allowing the compiler to compile away if statements.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L54-L58">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch-Tuple{Any, Any, Any}" href="#FastMultipole.DerivativesSwitch-Tuple{Any, Any, Any}"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch(scalar_potential, velocity, velocity_gradient)</code></pre><p>Constructs a tuple of <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> objects.</p><p><strong>Arguments</strong></p><ul><li><code>scalar_potential::Vector{Bool}</code>: a vector of <code>::Bool</code> indicating whether the scalar potential should be computed for each target system</li><li><code>velocity::Vector{Bool}</code>: a vector of <code>::Bool</code> indicating whether the velocity should be computed for each target system</li><li><code>velocity_gradient::Vector{Bool}</code>: a vector of <code>::Bool</code> indicating whether the velocity gradient should be computed for each target system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/derivativesswitch.jl#L1-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool, Tuple}" href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool, Tuple}"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch(scalar_potential, velocity, velocity_gradient, target_systems)</code></pre><p>Constructs a <code>::Tuple</code> of indentical <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> objects of the same length as <code>target_systems</code> (if it is a <code>::Tuple</code>), or a single <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> (if <code>target_system</code> is not a <code>::Tuple</code>)</p><p><strong>Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: a <code>::Bool</code> indicating whether the scalar potential should be computed for each target system</li><li><code>velocity::Bool</code>: a <code>::Bool</code> indicating whether the velocity should be computed for each target system</li><li><code>velocity_gradient::Bool</code>: a <code>::Bool</code> indicating whether the velocity gradient should be computed for each target system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/derivativesswitch.jl#L33-L44">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool}" href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool}"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch(scalar_potential, velocity, velocity_gradient)</code></pre><p>Constructs a single <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> object.</p><p><strong>Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: a <code>::Bool</code> indicating whether the scalar potential should be computed for the target system</li><li><code>velocity::Bool</code>: a <code>::Bool</code> indicating whether the velocity should be computed for the target system</li><li><code>velocity_gradient::Bool</code>: a <code>::Bool</code> indicating whether the velocity gradient should be computed for the target system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/derivativesswitch.jl#L17-L28">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ExpansionSwitch" href="#FastMultipole.ExpansionSwitch"><code>FastMultipole.ExpansionSwitch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ExpansionSwitch</code></pre><p>Switch indicating which expansions should be used:</p><ol><li>scalar potential (<code>SP</code>)</li><li>vector potential via Lamb-Helmholtz decomposition (<code>VP</code>)</li></ol></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L61-L68">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.MultiBranch" href="#FastMultipole.MultiBranch"><code>FastMultipole.MultiBranch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">MultiBranch{TF,N} &lt;: Branch{TF}</code></pre><p>Branch object used to sort more than one system into an octree. Type parameters represent:</p><ul><li><code>TF</code>: the floating point type (would be a dual number if using algorithmic differentiation)</li><li><code>N</code>: the number of systems represented</li></ul><p><strong>Fields</strong></p><ul><li><code>bodies_index::Vector{UnitRange}</code>: vector of unit ranges indicating the index of bodies in each represented system, respectively</li><li><code>n_branches::Int</code>: number of child branches corresponding to this branch</li><li><code>branch_index::UnitRange</code>: indices of this branch&#39;s child branches</li><li><code>i_parent::Int</code>: index of this branch&#39;s parent</li><li><code>i_leaf::Int</code>: if this branch is a leaf, what is its index in its parent <code>&lt;:Tree</code>&#39;s <code>leaf_index</code> field</li><li><code>center::Vector{TF}</code>: center of this branch at which its multipole and local expansions are centered</li><li><code>source_radius::TF</code>: if this branch is a leaf, distance from <code>center</code> to the outer edge of farthest body contained in this branch; otherwise, this is the distance from <code>center</code> to the corner of its <code>source_box</code></li><li><code>target_radius::TF</code>: distance from <code>center</code> to the farthest body center contained in this branch</li><li><code>source_box::Vector{TF}</code>: vector of length 6 containing the distances from the center to faces of a rectangular prism completely enclosing all bodies with their finite radius in the negative x, positive x, negative y, positive y, negative z, and positive z directions, respectively</li><li><code>target_box::Vector{TF}</code>: vector of length 3 containing the distances from the center to faces of a rectangular prism completely enclosing all body centers in the x, y, and z direction, respectively</li><li>multipole_expansion::Array{TF,3}<code>: array of size (2,2,) containing the multipole expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li>local_expansion::Array{TF,3}<code>: array of size</code>(2,2,(p+1)(p+2)/2)<code>containing the local expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li><code>harmonics::Array{TF,3}</code>: array of size <code>(2,2,(p+1)(p+2)/2)</code> used as storage for regular harmonics, irregular harmonics, or whatever is needed, and is indexed as multipole and local expansions</li><li><code>lock::ReentrantLock</code>: lock used to avoid data race conditions when modifying this branch or its corresponding bodies</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L154-L179">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.MultiTree" href="#FastMultipole.MultiTree"><code>FastMultipole.MultiTree</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>bodies[index<em>list] is the same sort operation as performed by the tree sorted</em>bodies[inverse<em>index</em>list] undoes the sort operation performed by the tree</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L268-L271">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ProbeSystem" href="#FastMultipole.ProbeSystem"><code>FastMultipole.ProbeSystem</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ProbeSystem</code></pre><p>Convenience system for defining locations at which the potential, velocity, or velocity gradient may be desired.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L319-L323">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ProbeSystem-Union{Tuple{Array{StaticArraysCore.SVector{3, TF}, 1}}, Tuple{TF}} where TF" href="#FastMultipole.ProbeSystem-Union{Tuple{Array{StaticArraysCore.SVector{3, TF}, 1}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ProbeSystem(positions; kwargs...)</code></pre><p>A convenience system constructor for calculating the influence of source systems at locations not already described by a system object. It behaves like a system whose elements induce a null potential field.</p><p><strong>Arguments</strong></p><ul><li><code>positions::Vector{SVector{3,Float64}}</code>: a vector of position vectors of each probe</li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: whether or not to compute the scalar potential at each probe location</li><li><code>vector_potential::Bool</code>: whether or not to compute the vector potential at each probe location</li><li><code>velocity::Bool</code>: whether or not to compute the velocity at each probe location</li><li><code>velocity_gradient::Bool</code>: whether or not to compute the velocity gradient at each probe location</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/probe.jl#L9-L25">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ProbeSystem-Union{Tuple{Matrix{TF}}, Tuple{TF}} where TF" href="#FastMultipole.ProbeSystem-Union{Tuple{Matrix{TF}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ProbeSystem(positions; kwargs...)</code></pre><p>Dispatch of <a href="#FastMultipole.ProbeSystem"><code>ProbeSystem</code></a> accepting a matrix of horizontally concatenated column vectors describing the position of each probe. Optional arguments are identical.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/probe.jl#L35-L39">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.SingleBranch" href="#FastMultipole.SingleBranch"><code>FastMultipole.SingleBranch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SingleBranch{TF} &lt;: Branch{TF}</code></pre><p>Branch object used to sort a single system into an octree. Type parameters represent:</p><ul><li><code>TF</code>: the floating point type (would be a dual number if using algorithmic differentiation)</li></ul><p><strong>Fields</strong></p><ul><li><code>bodies_index::UnitRange</code>: unit range indicating the index of bodies in the represented system</li><li><code>n_branches::Int</code>: number of child branches corresponding to this branch</li><li><code>branch_index::UnitRange</code>: indices of this branch&#39;s child branches</li><li><code>i_parent::Int</code>: index of this branch&#39;s parent</li><li><code>i_leaf::Int</code>: if this branch is a leaf, what is its index in its parent <code>&lt;:Tree</code>&#39;s <code>leaf_index</code> field</li><li><code>center::Vector{TF}</code>: center of this branch at which its multipole and local expansions are centered</li><li><code>source_radius::TF</code>: if this branch is a leaf, distance from <code>center</code> to the outer edge of farthest body contained in this branch; otherwise, this is the distance from <code>center</code> to the corner of its <code>source_box</code></li><li><code>target_radius::TF</code>: distance from <code>center</code> to the farthest body center contained in this branch</li><li><code>source_box::Vector{TF}</code>: vector of length 6 containing the distances from the center to faces of a rectangular prism completely enclosing all bodies with their finite radius in the negative x, positive x, negative y, positive y, negative z, and positive z directions, respectively</li><li><code>target_box::Vector{TF}</code>: vector of length 3 containing the distances from the center to faces of a rectangular prism completely enclosing all body centers in the x, y, and z direction, respectively</li><li>multipole_expansion::Array{TF,3}<code>: array of size (2,2,) containing the multipole expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li>local_expansion::Array{TF,3}<code>: array of size</code>(2,2,(p+1)(p+2)/2)<code>containing the local expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li><code>harmonics::Array{TF,3}</code>: array of size <code>(2,2,(p+1)(p+2)/2)</code> used as storage for regular harmonics, irregular harmonics, or whatever is needed, and is indexed as multipole and local expansions</li><li><code>lock::ReentrantLock</code>: lock used to avoid data race conditions when modifying this branch or its corresponding bodies</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L208-L232">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.SortWrapper-Tuple{Any}" href="#FastMultipole.SortWrapper-Tuple{Any}"><code>FastMultipole.SortWrapper</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SortWrapper(system)</code></pre><p>Convenience wrapper for systems whose elements cannot be sorted in-place (e.g. structured grids). The resulting object is treated like any other <code>system</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/sortwrapper.jl#L1-L5">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.Tree" href="#FastMultipole.Tree"><code>FastMultipole.Tree</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">abstract type Tree{TF,P} end</code></pre><p>Supertype of all octree structures with <code>TF</code> the floating point type and <code>P</code> the expansion order.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/containers.jl#L261-L265">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.EmptyTree-Tuple{Any}" href="#FastMultipole.EmptyTree-Tuple{Any}"><code>FastMultipole.EmptyTree</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">EmptyTree(system)</code></pre><p>Returns an empty tree. Used if <code>system</code> is empty.</p><p><strong>Arguments</strong></p><ul><li><code>system</code>: the system from which a tree is to be created</li></ul><p><strong>Returns</strong></p><ul><li><code>tree</code>: if <code>typeof(system)&lt;:Tuple</code>, a <code>::MultiTree</code> is returned; otherwise, a <code>::SingleTree</code> is returned</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/tree.jl#L105-L118">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.accumulate_charge!-Union{Tuple{TF}, Tuple{AbstractVector{&lt;:Branch{TF}}, Any, Any}} where TF" href="#FastMultipole.accumulate_charge!-Union{Tuple{TF}, Tuple{AbstractVector{&lt;:Branch{TF}}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">accumulate_charge!(branches, systems, branch_index)</code></pre><p>Computes the sum of the absolute value of body source strengths, as well as the sum of the L2 norm of the dipole strengths, and store them in each branch, inheriting values from child branches if available.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/tree.jl#L792-L797">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.accumulate_charge_bodies!-Union{Tuple{TF}, Tuple{Array{SingleBranch{TF}, 1}, Any, Any}} where TF" href="#FastMultipole.accumulate_charge_bodies!-Union{Tuple{TF}, Tuple{Array{SingleBranch{TF}, 1}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge_bodies!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">accumulate_charge!(branch, systems)</code></pre><p>Computes the sum of the absolute value of body source strengths, as well as the sum of the L2 norm of the dipole strengths, based on source bodies directly, and store them in each branch.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/tree.jl#L824-L829">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.add_line!-Tuple{ProbeSystem, Vararg{Any, 4}}" href="#FastMultipole.add_line!-Tuple{ProbeSystem, Vararg{Any, 4}}"><code>FastMultipole.add_line!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_line!(probes::ProbeSystem, x1, x2, n_probes, i_last)</code></pre><p>Adds <code>n_probes</code> probes in a line between <code>x1</code> and <code>x2</code>. Specifically, they are added at the midpoint of equally partiti    oned segments of the line.</p><p><strong>Arguments</strong></p><ul><li><code>probes::ProbeSystem</code>: the probe system whose <code>.position</code> field is to be updated</li><li><code>x1::Vector{Float64}</code>: the first point defining the line along which probes are to be added</li><li><code>x2::Vector{Float64}</code>: the second point defining the line along which probes are to be added</li><li><code>n_probes::Int</code>: number of probes to be added</li><li><code>i_last::Int</code>: index of the last probe in <code>probes</code></li></ul><p><strong>Output</strong></p><ul><li><code>i_last::Int</code>: updated index of the last probe in <code>probes</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/probe.jl#L113-L130">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.back_rotate_local_y!-NTuple{7, Any}" href="#FastMultipole.back_rotate_local_y!-NTuple{7, Any}"><code>FastMultipole.back_rotate_local_y!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assumes Ts, Hs<em>π2, and ηs</em>mag have all been precomputed. Resets target_weights.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/rotate.jl#L784-L786">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.back_rotate_multipole_y!-NTuple{6, Any}" href="#FastMultipole.back_rotate_multipole_y!-NTuple{6, Any}"><code>FastMultipole.back_rotate_multipole_y!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assumes Ts, Hs<em>π2, and ζs</em>mag have all been precomputed. Resets target_weights.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/rotate.jl#L584-L586">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.back_rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.back_rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.back_rotate_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assumes eimϕs have already been computed. DOES NOT overwrite rotated weights (unlike other rotate functions); rather, accumulates on top of it.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/rotate.jl#L345-L347">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.calculate_ib!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.calculate_ib!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_ib!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>assumes j has already been calculated</p><p>Note: if X0<em>real is replaced with X0</em>real + Xw_real, etc., this becomes bnm (as used for volumes) instead of inm (as used for panels)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/bodytomultipole.jl#L169-L173">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.calculate_pj!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.calculate_pj!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_pj!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>assumes q has already been calculated</p><p>If X0<em>real is replaced with X0</em>real + Xv_real, etc., the result becomes jnm instead of pnm, as used for panels.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/bodytomultipole.jl#L132-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.d2rdx2-Tuple{Any, Any, Any}" href="#FastMultipole.d2rdx2-Tuple{Any, Any, Any}"><code>FastMultipole.d2rdx2</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>dr<em>k/dx</em>idx_j</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/derivatives.jl#L1-L3">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.direct!-Tuple{Any, Any}" href="#FastMultipole.direct!-Tuple{Any, Any}"><code>FastMultipole.direct!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">direct!(target_system, source_system; derivatives_switches)</code></pre><p>Applies all interactions of <code>source_system</code> acting on <code>target_system</code> without multipole acceleration.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_system</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_system</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/direct.jl#L33-L56">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.direct!-Tuple{Tuple}" href="#FastMultipole.direct!-Tuple{Tuple}"><code>FastMultipole.direct!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">direct!(systems; derivatives_switches)</code></pre><p>Applies all interactions of <code>systems</code> acting on itself without multipole acceleration.</p><p><strong>Arguments</strong></p><ul><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/direct.jl#L1-L19">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.drdx-Tuple{Any, Any, Any}" href="#FastMultipole.drdx-Tuple{Any, Any, Any}"><code>FastMultipole.drdx</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>dr<em>j/dx</em>i</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/derivatives.jl#L24-L26">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{Any}, Tuple{PE}} where PE" href="#FastMultipole.fmm!-Union{Tuple{Any}, Tuple{PE}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(systems; kwargs...)</code></pre><p>Apply all interactions of <code>systems</code> acting on itself using the fast multipole method. Assumes compatibility functions have been overloaded for both source and target systems.</p><p><strong>Arguments</strong></p><ul><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>expansion_order::Int</code>: the expansion order to be used</li><li><code>leaf_size::Int</code>: maximum number of bodies from <code>systems</code> allowed in a leaf-level branch</li><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (comuted without multipoles) interactions should be included in the direct_list</li><li><code>farfield::Bool</code>: indicates whether far-field (comuted with multipoles) interactions should be included in the m2l_list</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself in the direct_list</li><li><code>unsort_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>systems</code></li><li><code>shink_recenter::Bool</code>: indicates whether or not to resize branches for the octree after it is created to increase computational efficiency</li><li><code>save_tree::Bool</code>: indicates whether or not to save a VTK file for visualizing the octree</li><li><code>save_name::String</code>: name and path of the octree visualization if <code>save_tree == true</code></li><li><code>nearfield_user::Bool</code>: indicates whether or not the <code>nearfield_user!</code> function should be used for nearfield interactions</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/fmm.jl#L637-L669">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Any, Any}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Any, Any}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(target_systems, source_systems; kwargs...)</code></pre><p>Apply all interactions of <code>source_systems</code> acting on <code>target_systems</code> using the fast multipole method. Assumes compatibility functions have been overloaded for both source and target systems.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or - a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>expansion_order::Int</code>: the expansion order to be used</li><li><code>leaf_size_source::Int</code>: maximum number of bodies from <code>source_systems</code> allowed in a leaf-level branch</li><li><code>leaf_size_target::Int</code>: maximum number of bodies from <code>target_systems</code> allowed in a leaf-level branch</li><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>lamb_helmholtz::Bool</code>: determines whether or not to calculate the induced velocity due to a vector potential using the Lamb-Helmholtz decomposition; erroroneous velocity and gradient will result if <code>lamb_helmholtz==false</code> and a vector potential is used.</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (comuted without multipoles) interactions should be included</li><li><code>farfield::Bool</code>: indicates whether far-field (comuted with multipoles) interactions should be included</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself</li><li><code>unsort_source_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for the <code>source_systems</code></li><li><code>unsort_target_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for the <code>target_systems</code></li><li><code>source_shink_recenter::Bool</code>: indicates whether or not to resize branches for the <code>source_systems</code> octree after it is created to increase computational efficiency</li><li><code>target_shink_recenter::Bool</code>: indicates whether or not to resize branches for the <code>target_systems</code> octree after it is created to increase computational efficiency</li><li><code>save_tree_source::Bool</code>: indicates whether or not to save a VTK file for visualizing the source octree</li><li><code>save_tree_target::Bool</code>: indicates whether or not to save a VTK file for visualizing the target octree</li><li><code>save_name_source::String</code>: name and path of the source octree visualization if <code>save_tree == true</code></li><li><code>save_name_target::String</code>: name and path of the target octree visualization if <code>save_tree == true</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/fmm.jl#L557-L598">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Any, Any, Any, Val}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(tree, systems; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using an existing <code>::Tree</code>.</p><p><strong>Arguments</strong></p><ul><li><p><code>tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>m2l_list::Vector{SVector{2,Int32}}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which multipole expansions of the source branch are to be transformed to local expansions at the target branch</p></li><li><p><code>direct_list::Union{Vector{SVector{2,Int32}}, InteractionList}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which interactions are to be evaluted without multipole expansion (i.e., directly); if <code>typeof(direct_list) &lt;: InteractionList</code>, then prepared influence matrices are used rather than computing direct influences on the fly</p></li><li><p><code>derivatives_switches::Union{DerivativesSwitch, Tuple{&lt;:DerivativesSwitch,...}}</code>: switch determining which of scalar potential, vector potential, velocity, and/or velocity gradient are to be computed for each target system</p></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>unsort_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/fmm.jl#L832-L856">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any, Any, Any, Any, Val}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(target_tree, target_systems, source_tree, source_systems, m2l_list, direct_list, derivatives_switches; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using existing <code>::Tree</code> objects.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>target_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>source_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>m2l_list::Vector{SVector{2,Int32}}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which multipole expansions of the source branch are to be transformed to local expansions at the target branch</p></li><li><p><code>direct_list::Union{Vector{SVector{2,Int32}}, InteractionList}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which interactions are to be evaluted without multipole expansion (i.e., directly); if <code>typeof(direct_list) &lt;: InteractionList</code>, then prepared influence matrices are used rather than computing direct influences on the fly</p></li><li><p><code>derivatives_switches::Union{DerivativesSwitch, Tuple{&lt;:DerivativesSwitch,...}}</code>: switch determining which of scalar potential, vector potential, velocity, and/or velocity gradient are to be computed for each target system</p></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (comuted without multipoles) interactions should be included</li><li><code>farfield::Bool</code>: indicates whether far-field (comuted with multipoles) interactions should be included</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself</li><li><code>unsort_source_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>source_systems</code></li><li><code>unsort_target_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>target_systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/fmm.jl#L881-L919">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(target_tree, target_systems, source_tree, source_systems; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using existing <code>::Tree</code> objects.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>target_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>source_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>reset_source_tree::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(source_systems)</code> indicating whether or not to reset the expansions of each source tree</li><li><code>reset_target_tree::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(source_systems)</code> indicating whether or not to reset the expansions of each target tree</li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (computed without multipoles) interactions should be included in the direct_list</li><li><code>farfield::Bool</code>: indicates whether far-field (computed with multipoles) interactions should be included in the m2l_list</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself in the direct_list</li><li><code>unsort_source_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>source_systems</code></li><li><code>unsort_target_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>target_systems</code></li><li><code>nearfield_user::Bool</code>: indicates whether or not the <code>nearfield_user!</code> function should be used for nearfield interactions</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/fmm.jl#L761-L798">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(tree, systems; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using an existing <code>::Tree</code>.</p><p><strong>Arguments</strong></p><ul><li><p><code>tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (computed without multipoles) interactions should be included in the direct_list</li><li><code>farfield::Bool</code>: indicates whether far-field (computed with multipoles) interactions should be included in the m2l_list</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself in the direct_list</li><li><code>unsort_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>systems</code></li><li><code>nearfield_user::Bool</code>: indicates whether or not the <code>nearfield_user!</code> function should be used for nearfield interactions</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/fmm.jl#L702-L730">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.get_P-Tuple{Any, Any, Any, Any, Any, Any, Any, Union{EqualSpheres, UnequalBoxes, UnequalSpheres}}" href="#FastMultipole.get_P-Tuple{Any, Any, Any, Any, Any, Any, Any, Union{EqualSpheres, UnequalBoxes, UnequalSpheres}}"><code>FastMultipole.get_P</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_P(r_min, r_max, ρ_min, ρ_max, ΔC2, Pmax, ε_rel, error_method)</code></pre><p>Returns the smallest expansion order not greater than <code>Pmax</code> and satisfying the specified relative error tolerance.</p><p><strong>Inputs</strong></p><ul><li><code>r_min::Flaot64</code>: distance from the multipole expansion to the closest target</li><li><code>r_max::Float64</code>: distance from the local expansion to the farthest target</li><li><code>ρ_min::Float64</code>: distance from the local expansion to the closest source</li><li><code>ρ_max::Float64</code>: distance from the multipole expansion to the farthest source</li><li><code>ΔC2::Float64</code>: distance squared between multipole and local centers</li><li><code>Pmax::Int64</code>: maximum allowable expansion order</li><li><code>ε_rel::Float64</code>: relative error tolerance</li><li><code>error_method::ErrorMethod</code>: type used to dispatch on the desired error method</li></ul><p><strong>Ouputs</strong></p><ul><li><code>P::Int</code>: the smallest expansion order to satisfy the error tolerance</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/interaction_list.jl#L31-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.local_to_local!-Union{Tuple{LH}, Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Val{P}, Val{LH}}} where {P, LH}" href="#FastMultipole.local_to_local!-Union{Tuple{LH}, Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Val{P}, Val{LH}}} where {P, LH}"><code>FastMultipole.local_to_local!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Expects ηs<em>mag and Hs</em>π2 to be precomputed. Ts and eimϕs are computed here.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/translate.jl#L343-L345">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.mirrored_source_to_vortex!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.mirrored_source_to_vortex!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.mirrored_source_to_vortex!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>my novel derivation</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/bodytomultipole.jl#L271-L273">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.multipole_to_local!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.multipole_to_local!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.multipole_to_local!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Expects ζs<em>mag, ηs</em>mag, and Hs_π2 to be computed a priori.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/translate.jl#L255-L257">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.reset!-Tuple{ProbeSystem}" href="#FastMultipole.reset!-Tuple{ProbeSystem}"><code>FastMultipole.reset!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reset!(probes)</code></pre><p>Zeroes all values (e.g. scalar/vector potential, velocity, and/or velocity gradient) of all probes.</p><p><strong>Arguments</strong></p><ul><li><code>probes::ProbeSystem</code>: a <code>::</code><a href="#FastMultipole.ProbeSystem"><code>ProbeSystem</code></a> object</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/probe.jl#L146-L154">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.resort!-Tuple{Tuple, MultiTree}" href="#FastMultipole.resort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.resort!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Performs the same sort operation as the tree. (Undoes <code>unsort!</code> operation.)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/tree.jl#L472-L474">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.rotate_multipole_y!-NTuple{8, Any}" href="#FastMultipole.rotate_multipole_y!-NTuple{8, Any}"><code>FastMultipole.rotate_multipole_y!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Rotate solid harmonic weights about the y axis by θ. Note that Hs<em>π2 and ζs</em>mag must be updated a priori, but Ts is updated en situ. Resets rotated_weights before computing.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/rotate.jl#L572-L574">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.rotate_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Performs a z-axis rotation of the supplied solid harmonic coefficients. Computes e^{imϕ} as well.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/rotate.jl#L304-L306">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.shrink_branch!-Tuple{Any, Any, Any}" href="#FastMultipole.shrink_branch!-Tuple{Any, Any, Any}"><code>FastMultipole.shrink_branch!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Computes the smallest bounding box to completely bound all child boxes.</p><p>Shrunk radii are merely the distance from the center to the corner of the box.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/tree.jl#L759-L763">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.source_to_dipole!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.source_to_dipole!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_dipole!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>assumes source expansion coefficients have already been calculated</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/bodytomultipole.jl#L239-L241">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.source_to_vortex_point!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.source_to_vortex_point!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_vortex_point!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>might be slightly faster than mirrored<em>source</em>to_vortex</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/bodytomultipole.jl#L327-L329">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.translate_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.translate_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_local_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Overwrites translated_weights</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/translate.jl#L298-L300">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.translate_multipole_to_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.translate_multipole_to_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_to_local_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Overwrites translated_weights</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/translate.jl#L181-L183">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.translate_multipole_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.translate_multipole_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Overwrites translated_weights</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/translate.jl#L3-L5">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.unsort!-Tuple{Tuple, MultiTree}" href="#FastMultipole.unsort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.unsort!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Undoes the sort operation performed by the tree.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/da5ad007091f6b1897e99311cc1399897bcd9d8a/src/tree.jl#L442-L444">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../advanced_usage/">« Advanced 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title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Reference"><a class="docs-heading-anchor" href="#Reference">Reference</a><a id="Reference-1"></a><a class="docs-heading-anchor-permalink" href="#Reference" title="Permalink"></a></h1><ul><li><a href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool, Tuple}"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.DerivativesSwitch-Tuple{Any, Any, Any}"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.DerivativesSwitch"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool}"><code>FastMultipole.DerivativesSwitch</code></a></li><li><a href="#FastMultipole.ExpansionSwitch"><code>FastMultipole.ExpansionSwitch</code></a></li><li><a href="#FastMultipole.MultiBranch"><code>FastMultipole.MultiBranch</code></a></li><li><a href="#FastMultipole.MultiTree"><code>FastMultipole.MultiTree</code></a></li><li><a href="#FastMultipole.ProbeSystem-Union{Tuple{Array{StaticArraysCore.SVector{3, TF}, 1}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a></li><li><a href="#FastMultipole.ProbeSystem"><code>FastMultipole.ProbeSystem</code></a></li><li><a href="#FastMultipole.ProbeSystem-Union{Tuple{Matrix{TF}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a></li><li><a href="#FastMultipole.SingleBranch"><code>FastMultipole.SingleBranch</code></a></li><li><a href="#FastMultipole.SortWrapper-Tuple{Any}"><code>FastMultipole.SortWrapper</code></a></li><li><a href="#FastMultipole.Tree"><code>FastMultipole.Tree</code></a></li><li><a href="#FastMultipole.EmptyTree-Tuple{Any}"><code>FastMultipole.EmptyTree</code></a></li><li><a href="#FastMultipole.accumulate_charge!-Union{Tuple{TF}, Tuple{AbstractVector{&lt;:Branch{TF}}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge!</code></a></li><li><a href="#FastMultipole.accumulate_charge_bodies!-Union{Tuple{TF}, Tuple{Array{SingleBranch{TF}, 1}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge_bodies!</code></a></li><li><a href="#FastMultipole.add_line!-Tuple{ProbeSystem, Vararg{Any, 4}}"><code>FastMultipole.add_line!</code></a></li><li><a href="#FastMultipole.back_rotate_local_y!-NTuple{7, Any}"><code>FastMultipole.back_rotate_local_y!</code></a></li><li><a href="#FastMultipole.back_rotate_multipole_y!-NTuple{6, Any}"><code>FastMultipole.back_rotate_multipole_y!</code></a></li><li><a href="#FastMultipole.back_rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.back_rotate_z!</code></a></li><li><a href="#FastMultipole.calculate_ib!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_ib!</code></a></li><li><a href="#FastMultipole.calculate_pj!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_pj!</code></a></li><li><a href="#FastMultipole.d2rdx2-Tuple{Any, Any, Any}"><code>FastMultipole.d2rdx2</code></a></li><li><a href="#FastMultipole.direct!-Tuple{Tuple}"><code>FastMultipole.direct!</code></a></li><li><a href="#FastMultipole.direct!-Tuple{Any, Any}"><code>FastMultipole.direct!</code></a></li><li><a href="#FastMultipole.drdx-Tuple{Any, Any, Any}"><code>FastMultipole.drdx</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{Any}, Tuple{PE}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Any, Any}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a></li><li><a href="#FastMultipole.get_P-Tuple{Any, Any, Any, Any, Any, Any, Any, Union{EqualSpheres, UnequalBoxes, UnequalSpheres}}"><code>FastMultipole.get_P</code></a></li><li><a href="#FastMultipole.local_to_local!-Union{Tuple{LH}, Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Val{P}, Val{LH}}} where {P, LH}"><code>FastMultipole.local_to_local!</code></a></li><li><a href="#FastMultipole.mirrored_source_to_vortex!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.mirrored_source_to_vortex!</code></a></li><li><a href="#FastMultipole.multipole_to_local!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.multipole_to_local!</code></a></li><li><a href="#FastMultipole.reset!-Tuple{ProbeSystem}"><code>FastMultipole.reset!</code></a></li><li><a href="#FastMultipole.resort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.resort!</code></a></li><li><a href="#FastMultipole.rotate_multipole_y!-NTuple{8, Any}"><code>FastMultipole.rotate_multipole_y!</code></a></li><li><a href="#FastMultipole.rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.rotate_z!</code></a></li><li><a href="#FastMultipole.shrink_branch!-Tuple{Any, Any, Any}"><code>FastMultipole.shrink_branch!</code></a></li><li><a href="#FastMultipole.source_to_dipole!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_dipole!</code></a></li><li><a href="#FastMultipole.source_to_vortex_point!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_vortex_point!</code></a></li><li><a href="#FastMultipole.translate_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_local_z!</code></a></li><li><a href="#FastMultipole.translate_multipole_to_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_to_local_z!</code></a></li><li><a href="#FastMultipole.translate_multipole_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_z!</code></a></li><li><a href="#FastMultipole.unsort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.unsort!</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch" href="#FastMultipole.DerivativesSwitch"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch</code></pre><p>Switch indicating whether the scalar potential, vector potential, velocity, and/or velocity gradient should be computed for a target system. Information is stored as type parameters, allowing the compiler to compile away if statements.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L54-L58">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch-Tuple{Any, Any, Any}" href="#FastMultipole.DerivativesSwitch-Tuple{Any, Any, Any}"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch(scalar_potential, velocity, velocity_gradient)</code></pre><p>Constructs a tuple of <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> objects.</p><p><strong>Arguments</strong></p><ul><li><code>scalar_potential::Vector{Bool}</code>: a vector of <code>::Bool</code> indicating whether the scalar potential should be computed for each target system</li><li><code>velocity::Vector{Bool}</code>: a vector of <code>::Bool</code> indicating whether the velocity should be computed for each target system</li><li><code>velocity_gradient::Vector{Bool}</code>: a vector of <code>::Bool</code> indicating whether the velocity gradient should be computed for each target system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/derivativesswitch.jl#L1-L12">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool, Tuple}" href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool, Tuple}"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch(scalar_potential, velocity, velocity_gradient, target_systems)</code></pre><p>Constructs a <code>::Tuple</code> of indentical <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> objects of the same length as <code>target_systems</code> (if it is a <code>::Tuple</code>), or a single <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> (if <code>target_system</code> is not a <code>::Tuple</code>)</p><p><strong>Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: a <code>::Bool</code> indicating whether the scalar potential should be computed for each target system</li><li><code>velocity::Bool</code>: a <code>::Bool</code> indicating whether the velocity should be computed for each target system</li><li><code>velocity_gradient::Bool</code>: a <code>::Bool</code> indicating whether the velocity gradient should be computed for each target system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/derivativesswitch.jl#L33-L44">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool}" href="#FastMultipole.DerivativesSwitch-Tuple{Bool, Bool, Bool}"><code>FastMultipole.DerivativesSwitch</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DerivativesSwitch(scalar_potential, velocity, velocity_gradient)</code></pre><p>Constructs a single <a href="#FastMultipole.DerivativesSwitch"><code>DerivativesSwitch</code></a> object.</p><p><strong>Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: a <code>::Bool</code> indicating whether the scalar potential should be computed for the target system</li><li><code>velocity::Bool</code>: a <code>::Bool</code> indicating whether the velocity should be computed for the target system</li><li><code>velocity_gradient::Bool</code>: a <code>::Bool</code> indicating whether the velocity gradient should be computed for the target system</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/derivativesswitch.jl#L17-L28">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ExpansionSwitch" href="#FastMultipole.ExpansionSwitch"><code>FastMultipole.ExpansionSwitch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ExpansionSwitch</code></pre><p>Switch indicating which expansions should be used:</p><ol><li>scalar potential (<code>SP</code>)</li><li>vector potential via Lamb-Helmholtz decomposition (<code>VP</code>)</li></ol></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L61-L68">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.MultiBranch" href="#FastMultipole.MultiBranch"><code>FastMultipole.MultiBranch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">MultiBranch{TF,N} &lt;: Branch{TF}</code></pre><p>Branch object used to sort more than one system into an octree. Type parameters represent:</p><ul><li><code>TF</code>: the floating point type (would be a dual number if using algorithmic differentiation)</li><li><code>N</code>: the number of systems represented</li></ul><p><strong>Fields</strong></p><ul><li><code>bodies_index::Vector{UnitRange}</code>: vector of unit ranges indicating the index of bodies in each represented system, respectively</li><li><code>n_branches::Int</code>: number of child branches corresponding to this branch</li><li><code>branch_index::UnitRange</code>: indices of this branch&#39;s child branches</li><li><code>i_parent::Int</code>: index of this branch&#39;s parent</li><li><code>i_leaf::Int</code>: if this branch is a leaf, what is its index in its parent <code>&lt;:Tree</code>&#39;s <code>leaf_index</code> field</li><li><code>center::Vector{TF}</code>: center of this branch at which its multipole and local expansions are centered</li><li><code>source_radius::TF</code>: if this branch is a leaf, distance from <code>center</code> to the outer edge of farthest body contained in this branch; otherwise, this is the distance from <code>center</code> to the corner of its <code>source_box</code></li><li><code>target_radius::TF</code>: distance from <code>center</code> to the farthest body center contained in this branch</li><li><code>source_box::Vector{TF}</code>: vector of length 6 containing the distances from the center to faces of a rectangular prism completely enclosing all bodies with their finite radius in the negative x, positive x, negative y, positive y, negative z, and positive z directions, respectively</li><li><code>target_box::Vector{TF}</code>: vector of length 3 containing the distances from the center to faces of a rectangular prism completely enclosing all body centers in the x, y, and z direction, respectively</li><li>multipole_expansion::Array{TF,3}<code>: array of size (2,2,) containing the multipole expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li>local_expansion::Array{TF,3}<code>: array of size</code>(2,2,(p+1)(p+2)/2)<code>containing the local expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li><code>harmonics::Array{TF,3}</code>: array of size <code>(2,2,(p+1)(p+2)/2)</code> used as storage for regular harmonics, irregular harmonics, or whatever is needed, and is indexed as multipole and local expansions</li><li><code>lock::ReentrantLock</code>: lock used to avoid data race conditions when modifying this branch or its corresponding bodies</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L154-L179">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.MultiTree" href="#FastMultipole.MultiTree"><code>FastMultipole.MultiTree</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>bodies[index<em>list] is the same sort operation as performed by the tree sorted</em>bodies[inverse<em>index</em>list] undoes the sort operation performed by the tree</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L268-L271">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ProbeSystem" href="#FastMultipole.ProbeSystem"><code>FastMultipole.ProbeSystem</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ProbeSystem</code></pre><p>Convenience system for defining locations at which the potential, velocity, or velocity gradient may be desired.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L319-L323">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ProbeSystem-Union{Tuple{Array{StaticArraysCore.SVector{3, TF}, 1}}, Tuple{TF}} where TF" href="#FastMultipole.ProbeSystem-Union{Tuple{Array{StaticArraysCore.SVector{3, TF}, 1}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ProbeSystem(positions; kwargs...)</code></pre><p>A convenience system constructor for calculating the influence of source systems at locations not already described by a system object. It behaves like a system whose elements induce a null potential field.</p><p><strong>Arguments</strong></p><ul><li><code>positions::Vector{SVector{3,Float64}}</code>: a vector of position vectors of each probe</li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: whether or not to compute the scalar potential at each probe location</li><li><code>vector_potential::Bool</code>: whether or not to compute the vector potential at each probe location</li><li><code>velocity::Bool</code>: whether or not to compute the velocity at each probe location</li><li><code>velocity_gradient::Bool</code>: whether or not to compute the velocity gradient at each probe location</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/probe.jl#L9-L25">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.ProbeSystem-Union{Tuple{Matrix{TF}}, Tuple{TF}} where TF" href="#FastMultipole.ProbeSystem-Union{Tuple{Matrix{TF}}, Tuple{TF}} where TF"><code>FastMultipole.ProbeSystem</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ProbeSystem(positions; kwargs...)</code></pre><p>Dispatch of <a href="#FastMultipole.ProbeSystem"><code>ProbeSystem</code></a> accepting a matrix of horizontally concatenated column vectors describing the position of each probe. Optional arguments are identical.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/probe.jl#L35-L39">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.SingleBranch" href="#FastMultipole.SingleBranch"><code>FastMultipole.SingleBranch</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SingleBranch{TF} &lt;: Branch{TF}</code></pre><p>Branch object used to sort a single system into an octree. Type parameters represent:</p><ul><li><code>TF</code>: the floating point type (would be a dual number if using algorithmic differentiation)</li></ul><p><strong>Fields</strong></p><ul><li><code>bodies_index::UnitRange</code>: unit range indicating the index of bodies in the represented system</li><li><code>n_branches::Int</code>: number of child branches corresponding to this branch</li><li><code>branch_index::UnitRange</code>: indices of this branch&#39;s child branches</li><li><code>i_parent::Int</code>: index of this branch&#39;s parent</li><li><code>i_leaf::Int</code>: if this branch is a leaf, what is its index in its parent <code>&lt;:Tree</code>&#39;s <code>leaf_index</code> field</li><li><code>center::Vector{TF}</code>: center of this branch at which its multipole and local expansions are centered</li><li><code>source_radius::TF</code>: if this branch is a leaf, distance from <code>center</code> to the outer edge of farthest body contained in this branch; otherwise, this is the distance from <code>center</code> to the corner of its <code>source_box</code></li><li><code>target_radius::TF</code>: distance from <code>center</code> to the farthest body center contained in this branch</li><li><code>source_box::Vector{TF}</code>: vector of length 6 containing the distances from the center to faces of a rectangular prism completely enclosing all bodies with their finite radius in the negative x, positive x, negative y, positive y, negative z, and positive z directions, respectively</li><li><code>target_box::Vector{TF}</code>: vector of length 3 containing the distances from the center to faces of a rectangular prism completely enclosing all body centers in the x, y, and z direction, respectively</li><li>multipole_expansion::Array{TF,3}<code>: array of size (2,2,) containing the multipole expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li>local_expansion::Array{TF,3}<code>: array of size</code>(2,2,(p+1)(p+2)/2)<code>containing the local expansion coefficients; the first index indicates real or imaginary, the second index indicates scalar potential or the second component of the Lamb-Helmholtz decomposition, and the third index</code>k` indicates the expansion coefficient of degree <span>$n$</span> and order <span>$m$</span>, as <span>$k = p(p+1)/2 + m + 1$</span></li><li><code>harmonics::Array{TF,3}</code>: array of size <code>(2,2,(p+1)(p+2)/2)</code> used as storage for regular harmonics, irregular harmonics, or whatever is needed, and is indexed as multipole and local expansions</li><li><code>lock::ReentrantLock</code>: lock used to avoid data race conditions when modifying this branch or its corresponding bodies</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L208-L232">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.SortWrapper-Tuple{Any}" href="#FastMultipole.SortWrapper-Tuple{Any}"><code>FastMultipole.SortWrapper</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">SortWrapper(system)</code></pre><p>Convenience wrapper for systems whose elements cannot be sorted in-place (e.g. structured grids). The resulting object is treated like any other <code>system</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/sortwrapper.jl#L1-L5">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.Tree" href="#FastMultipole.Tree"><code>FastMultipole.Tree</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">abstract type Tree{TF,P} end</code></pre><p>Supertype of all octree structures with <code>TF</code> the floating point type and <code>P</code> the expansion order.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/containers.jl#L261-L265">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.EmptyTree-Tuple{Any}" href="#FastMultipole.EmptyTree-Tuple{Any}"><code>FastMultipole.EmptyTree</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">EmptyTree(system)</code></pre><p>Returns an empty tree. Used if <code>system</code> is empty.</p><p><strong>Arguments</strong></p><ul><li><code>system</code>: the system from which a tree is to be created</li></ul><p><strong>Returns</strong></p><ul><li><code>tree</code>: if <code>typeof(system)&lt;:Tuple</code>, a <code>::MultiTree</code> is returned; otherwise, a <code>::SingleTree</code> is returned</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/tree.jl#L105-L118">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.accumulate_charge!-Union{Tuple{TF}, Tuple{AbstractVector{&lt;:Branch{TF}}, Any, Any}} where TF" href="#FastMultipole.accumulate_charge!-Union{Tuple{TF}, Tuple{AbstractVector{&lt;:Branch{TF}}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">accumulate_charge!(branches, systems, branch_index)</code></pre><p>Computes the sum of the absolute value of body source strengths, as well as the sum of the L2 norm of the dipole strengths, and store them in each branch, inheriting values from child branches if available.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/tree.jl#L792-L797">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.accumulate_charge_bodies!-Union{Tuple{TF}, Tuple{Array{SingleBranch{TF}, 1}, Any, Any}} where TF" href="#FastMultipole.accumulate_charge_bodies!-Union{Tuple{TF}, Tuple{Array{SingleBranch{TF}, 1}, Any, Any}} where TF"><code>FastMultipole.accumulate_charge_bodies!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">accumulate_charge!(branch, systems)</code></pre><p>Computes the sum of the absolute value of body source strengths, as well as the sum of the L2 norm of the dipole strengths, based on source bodies directly, and store them in each branch.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/tree.jl#L824-L829">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.add_line!-Tuple{ProbeSystem, Vararg{Any, 4}}" href="#FastMultipole.add_line!-Tuple{ProbeSystem, Vararg{Any, 4}}"><code>FastMultipole.add_line!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">add_line!(probes::ProbeSystem, x1, x2, n_probes, i_last)</code></pre><p>Adds <code>n_probes</code> probes in a line between <code>x1</code> and <code>x2</code>. Specifically, they are added at the midpoint of equally partiti    oned segments of the line.</p><p><strong>Arguments</strong></p><ul><li><code>probes::ProbeSystem</code>: the probe system whose <code>.position</code> field is to be updated</li><li><code>x1::Vector{Float64}</code>: the first point defining the line along which probes are to be added</li><li><code>x2::Vector{Float64}</code>: the second point defining the line along which probes are to be added</li><li><code>n_probes::Int</code>: number of probes to be added</li><li><code>i_last::Int</code>: index of the last probe in <code>probes</code></li></ul><p><strong>Output</strong></p><ul><li><code>i_last::Int</code>: updated index of the last probe in <code>probes</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/probe.jl#L113-L130">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.back_rotate_local_y!-NTuple{7, Any}" href="#FastMultipole.back_rotate_local_y!-NTuple{7, Any}"><code>FastMultipole.back_rotate_local_y!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assumes Ts, Hs<em>π2, and ηs</em>mag have all been precomputed. Resets target_weights.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/rotate.jl#L784-L786">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.back_rotate_multipole_y!-NTuple{6, Any}" href="#FastMultipole.back_rotate_multipole_y!-NTuple{6, Any}"><code>FastMultipole.back_rotate_multipole_y!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assumes Ts, Hs<em>π2, and ζs</em>mag have all been precomputed. Resets target_weights.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/rotate.jl#L584-L586">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.back_rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.back_rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.back_rotate_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Assumes eimϕs have already been computed. DOES NOT overwrite rotated weights (unlike other rotate functions); rather, accumulates on top of it.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/rotate.jl#L345-L347">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.calculate_ib!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.calculate_ib!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_ib!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>assumes j has already been calculated</p><p>Note: if X0<em>real is replaced with X0</em>real + Xw_real, etc., this becomes bnm (as used for volumes) instead of inm (as used for panels)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/bodytomultipole.jl#L169-L173">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.calculate_pj!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.calculate_pj!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.calculate_pj!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>assumes q has already been calculated</p><p>If X0<em>real is replaced with X0</em>real + Xv_real, etc., the result becomes jnm instead of pnm, as used for panels.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/bodytomultipole.jl#L132-L136">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.d2rdx2-Tuple{Any, Any, Any}" href="#FastMultipole.d2rdx2-Tuple{Any, Any, Any}"><code>FastMultipole.d2rdx2</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>dr<em>k/dx</em>idx_j</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/derivatives.jl#L1-L3">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.direct!-Tuple{Any, Any}" href="#FastMultipole.direct!-Tuple{Any, Any}"><code>FastMultipole.direct!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">direct!(target_system, source_system; derivatives_switches)</code></pre><p>Applies all interactions of <code>source_system</code> acting on <code>target_system</code> without multipole acceleration.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_system</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_system</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/direct.jl#L33-L56">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.direct!-Tuple{Tuple}" href="#FastMultipole.direct!-Tuple{Tuple}"><code>FastMultipole.direct!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">direct!(systems; derivatives_switches)</code></pre><p>Applies all interactions of <code>systems</code> acting on itself without multipole acceleration.</p><p><strong>Arguments</strong></p><ul><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/direct.jl#L1-L19">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.drdx-Tuple{Any, Any, Any}" href="#FastMultipole.drdx-Tuple{Any, Any, Any}"><code>FastMultipole.drdx</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>dr<em>j/dx</em>i</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/derivatives.jl#L24-L26">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{Any}, Tuple{PE}} where PE" href="#FastMultipole.fmm!-Union{Tuple{Any}, Tuple{PE}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(systems; kwargs...)</code></pre><p>Apply all interactions of <code>systems</code> acting on itself using the fast multipole method. Assumes compatibility functions have been overloaded for both source and target systems.</p><p><strong>Arguments</strong></p><ul><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>expansion_order::Int</code>: the expansion order to be used</li><li><code>leaf_size::Int</code>: maximum number of bodies from <code>systems</code> allowed in a leaf-level branch</li><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (comuted without multipoles) interactions should be included in the direct_list</li><li><code>farfield::Bool</code>: indicates whether far-field (comuted with multipoles) interactions should be included in the m2l_list</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself in the direct_list</li><li><code>unsort_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>systems</code></li><li><code>shink_recenter::Bool</code>: indicates whether or not to resize branches for the octree after it is created to increase computational efficiency</li><li><code>save_tree::Bool</code>: indicates whether or not to save a VTK file for visualizing the octree</li><li><code>save_name::String</code>: name and path of the octree visualization if <code>save_tree == true</code></li><li><code>nearfield_user::Bool</code>: indicates whether or not the <code>nearfield_user!</code> function should be used for nearfield interactions</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/fmm.jl#L637-L669">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Any, Any}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Any, Any}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(target_systems, source_systems; kwargs...)</code></pre><p>Apply all interactions of <code>source_systems</code> acting on <code>target_systems</code> using the fast multipole method. Assumes compatibility functions have been overloaded for both source and target systems.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or - a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>expansion_order::Int</code>: the expansion order to be used</li><li><code>leaf_size_source::Int</code>: maximum number of bodies from <code>source_systems</code> allowed in a leaf-level branch</li><li><code>leaf_size_target::Int</code>: maximum number of bodies from <code>target_systems</code> allowed in a leaf-level branch</li><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>lamb_helmholtz::Bool</code>: determines whether or not to calculate the induced velocity due to a vector potential using the Lamb-Helmholtz decomposition; erroroneous velocity and gradient will result if <code>lamb_helmholtz==false</code> and a vector potential is used.</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (comuted without multipoles) interactions should be included</li><li><code>farfield::Bool</code>: indicates whether far-field (comuted with multipoles) interactions should be included</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself</li><li><code>unsort_source_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for the <code>source_systems</code></li><li><code>unsort_target_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for the <code>target_systems</code></li><li><code>source_shink_recenter::Bool</code>: indicates whether or not to resize branches for the <code>source_systems</code> octree after it is created to increase computational efficiency</li><li><code>target_shink_recenter::Bool</code>: indicates whether or not to resize branches for the <code>target_systems</code> octree after it is created to increase computational efficiency</li><li><code>save_tree_source::Bool</code>: indicates whether or not to save a VTK file for visualizing the source octree</li><li><code>save_tree_target::Bool</code>: indicates whether or not to save a VTK file for visualizing the target octree</li><li><code>save_name_source::String</code>: name and path of the source octree visualization if <code>save_tree == true</code></li><li><code>save_name_target::String</code>: name and path of the target octree visualization if <code>save_tree == true</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/fmm.jl#L557-L598">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Any, Any, Any, Val}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(tree, systems; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using an existing <code>::Tree</code>.</p><p><strong>Arguments</strong></p><ul><li><p><code>tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>m2l_list::Vector{SVector{2,Int32}}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which multipole expansions of the source branch are to be transformed to local expansions at the target branch</p></li><li><p><code>direct_list::Union{Vector{SVector{2,Int32}}, InteractionList}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which interactions are to be evaluted without multipole expansion (i.e., directly); if <code>typeof(direct_list) &lt;: InteractionList</code>, then prepared influence matrices are used rather than computing direct influences on the fly</p></li><li><p><code>derivatives_switches::Union{DerivativesSwitch, Tuple{&lt;:DerivativesSwitch,...}}</code>: switch determining which of scalar potential, vector potential, velocity, and/or velocity gradient are to be computed for each target system</p></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>unsort_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/fmm.jl#L832-L856">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any, Any, Any, Any, Val}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any, Any, Any, Any, Val}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(target_tree, target_systems, source_tree, source_systems, m2l_list, direct_list, derivatives_switches; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using existing <code>::Tree</code> objects.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>target_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>source_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>m2l_list::Vector{SVector{2,Int32}}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which multipole expansions of the source branch are to be transformed to local expansions at the target branch</p></li><li><p><code>direct_list::Union{Vector{SVector{2,Int32}}, InteractionList}</code>: list of branch index pairs <code>[i_target, i_source]</code> for which interactions are to be evaluted without multipole expansion (i.e., directly); if <code>typeof(direct_list) &lt;: InteractionList</code>, then prepared influence matrices are used rather than computing direct influences on the fly</p></li><li><p><code>derivatives_switches::Union{DerivativesSwitch, Tuple{&lt;:DerivativesSwitch,...}}</code>: switch determining which of scalar potential, vector potential, velocity, and/or velocity gradient are to be computed for each target system</p></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (comuted without multipoles) interactions should be included</li><li><code>farfield::Bool</code>: indicates whether far-field (comuted with multipoles) interactions should be included</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself</li><li><code>unsort_source_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>source_systems</code></li><li><code>unsort_target_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>target_systems</code></li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/fmm.jl#L881-L919">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any, Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(target_tree, target_systems, source_tree, source_systems; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using existing <code>::Tree</code> objects.</p><p><strong>Arguments</strong></p><ul><li><p><code>target_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>target_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li><li><p><code>source_tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>source_systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(target_systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>reset_source_tree::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(source_systems)</code> indicating whether or not to reset the expansions of each source tree</li><li><code>reset_target_tree::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(source_systems)</code> indicating whether or not to reset the expansions of each target tree</li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (computed without multipoles) interactions should be included in the direct_list</li><li><code>farfield::Bool</code>: indicates whether far-field (computed with multipoles) interactions should be included in the m2l_list</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself in the direct_list</li><li><code>unsort_source_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>source_systems</code></li><li><code>unsort_target_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>target_systems</code></li><li><code>nearfield_user::Bool</code>: indicates whether or not the <code>nearfield_user!</code> function should be used for nearfield interactions</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/fmm.jl#L761-L798">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any}} where PE" href="#FastMultipole.fmm!-Union{Tuple{PE}, Tuple{Tree, Any}} where PE"><code>FastMultipole.fmm!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">fmm!(tree, systems; kwargs...)</code></pre><p>Dispatches <code>fmm!</code> using an existing <code>::Tree</code>.</p><p><strong>Arguments</strong></p><ul><li><p><code>tree::Tree</code>: a <code>&lt;:Tree</code> object (see <a href="#FastMultipole.Tree"><code>Tree</code></a>)</p></li><li><p><code>systems</code>: either</p><ul><li>a system object for which compatibility functions have been overloaded, or</li><li>a tuple of system objects for which compatibility functions have been overloaded</li></ul></li></ul><p><strong>Optional Arguments</strong></p><ul><li><code>multipole_threshold::Float64</code>: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)</li><li><code>scalar_potential::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a scalar potential from <code>source_systems</code></li><li><code>velocity::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity from <code>source_systems</code></li><li><code>velocity_gradient::Bool</code>: either a <code>::Bool</code> or a <code>::AbstractVector{Bool}</code> of length <code>length(systems)</code> indicating whether each system should receive a velocity gradient from <code>source_systems</code></li><li><code>upward_pass::Bool</code>: whether or not to form the multipole expansions from source bodies and translate them upward in the source tree</li><li><code>horizontal_pass::Bool</code>: whether or not to transform multipole expansions from the source tree into local expansions in the target tree</li><li><code>downward_pass::Bool</code>: whether or not to translate local expansions down to the leaf level of the target tree and evaluate them</li><li><code>nearfield::Bool</code>: indicates whether near-field (computed without multipoles) interactions should be included in the direct_list</li><li><code>farfield::Bool</code>: indicates whether far-field (computed with multipoles) interactions should be included in the m2l_list</li><li><code>self_induced::Bool</code>: indicates whether to include the interactions of each leaf-level branch on itself in the direct_list</li><li><code>unsort_bodies::Bool</code>: indicates whether or not to undo the sort operation used to generate the octree for <code>systems</code></li><li><code>nearfield_user::Bool</code>: indicates whether or not the <code>nearfield_user!</code> function should be used for nearfield interactions</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/fmm.jl#L702-L730">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.get_P-Tuple{Any, Any, Any, Any, Any, Any, Any, Union{EqualSpheres, UnequalBoxes, UnequalSpheres}}" href="#FastMultipole.get_P-Tuple{Any, Any, Any, Any, Any, Any, Any, Union{EqualSpheres, UnequalBoxes, UnequalSpheres}}"><code>FastMultipole.get_P</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">get_P(r_min, r_max, ρ_min, ρ_max, ΔC2, Pmax, ε_rel, error_method)</code></pre><p>Returns the smallest expansion order not greater than <code>Pmax</code> and satisfying the specified relative error tolerance.</p><p><strong>Inputs</strong></p><ul><li><code>r_min::Flaot64</code>: distance from the multipole expansion to the closest target</li><li><code>r_max::Float64</code>: distance from the local expansion to the farthest target</li><li><code>ρ_min::Float64</code>: distance from the local expansion to the closest source</li><li><code>ρ_max::Float64</code>: distance from the multipole expansion to the farthest source</li><li><code>ΔC2::Float64</code>: distance squared between multipole and local centers</li><li><code>Pmax::Int64</code>: maximum allowable expansion order</li><li><code>ε_rel::Float64</code>: relative error tolerance</li><li><code>error_method::ErrorMethod</code>: type used to dispatch on the desired error method</li></ul><p><strong>Ouputs</strong></p><ul><li><code>P::Int</code>: the smallest expansion order to satisfy the error tolerance</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/interaction_list.jl#L31-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.local_to_local!-Union{Tuple{LH}, Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Val{P}, Val{LH}}} where {P, LH}" href="#FastMultipole.local_to_local!-Union{Tuple{LH}, Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Val{P}, Val{LH}}} where {P, LH}"><code>FastMultipole.local_to_local!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Expects ηs<em>mag and Hs</em>π2 to be precomputed. Ts and eimϕs are computed here.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/translate.jl#L343-L345">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.mirrored_source_to_vortex!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.mirrored_source_to_vortex!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.mirrored_source_to_vortex!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>my novel derivation</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/bodytomultipole.jl#L271-L273">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.multipole_to_local!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.multipole_to_local!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.multipole_to_local!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Expects ζs<em>mag, ηs</em>mag, and Hs_π2 to be computed a priori.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/translate.jl#L255-L257">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.reset!-Tuple{ProbeSystem}" href="#FastMultipole.reset!-Tuple{ProbeSystem}"><code>FastMultipole.reset!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">reset!(probes)</code></pre><p>Zeroes all values (e.g. scalar/vector potential, velocity, and/or velocity gradient) of all probes.</p><p><strong>Arguments</strong></p><ul><li><code>probes::ProbeSystem</code>: a <code>::</code><a href="#FastMultipole.ProbeSystem"><code>ProbeSystem</code></a> object</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/probe.jl#L146-L154">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.resort!-Tuple{Tuple, MultiTree}" href="#FastMultipole.resort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.resort!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Performs the same sort operation as the tree. (Undoes <code>unsort!</code> operation.)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/tree.jl#L472-L474">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.rotate_multipole_y!-NTuple{8, Any}" href="#FastMultipole.rotate_multipole_y!-NTuple{8, Any}"><code>FastMultipole.rotate_multipole_y!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Rotate solid harmonic weights about the y axis by θ. Note that Hs<em>π2 and ζs</em>mag must be updated a priori, but Ts is updated en situ. Resets rotated_weights before computing.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/rotate.jl#L572-L574">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.rotate_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.rotate_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Performs a z-axis rotation of the supplied solid harmonic coefficients. Computes e^{imϕ} as well.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/rotate.jl#L304-L306">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.shrink_branch!-Tuple{Any, Any, Any}" href="#FastMultipole.shrink_branch!-Tuple{Any, Any, Any}"><code>FastMultipole.shrink_branch!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Computes the smallest bounding box to completely bound all child boxes.</p><p>Shrunk radii are merely the distance from the center to the corner of the box.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/tree.jl#L759-L763">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.source_to_dipole!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.source_to_dipole!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_dipole!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>assumes source expansion coefficients have already been calculated</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/bodytomultipole.jl#L239-L241">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.source_to_vortex_point!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P" href="#FastMultipole.source_to_vortex_point!-Union{Tuple{P}, Tuple{Any, Any, Any, Any, Any, Any, Val{P}}} where P"><code>FastMultipole.source_to_vortex_point!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>might be slightly faster than mirrored<em>source</em>to_vortex</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/bodytomultipole.jl#L327-L329">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.translate_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.translate_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_local_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Overwrites translated_weights</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/translate.jl#L298-L300">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.translate_multipole_to_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.translate_multipole_to_local_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_to_local_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Overwrites translated_weights</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/translate.jl#L181-L183">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.translate_multipole_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH" href="#FastMultipole.translate_multipole_z!-Union{Tuple{LH}, Tuple{Any, Any, Any, Any, Val{LH}}} where LH"><code>FastMultipole.translate_multipole_z!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Overwrites translated_weights</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/translate.jl#L3-L5">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="FastMultipole.unsort!-Tuple{Tuple, MultiTree}" href="#FastMultipole.unsort!-Tuple{Tuple, MultiTree}"><code>FastMultipole.unsort!</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><p>Undoes the sort operation performed by the tree.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/byuflowlab/FastMultipole/blob/3f103db676f9cf843ffa5c818a8ccad3e988cf15/src/tree.jl#L442-L444">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../advanced_usage/">« Advanced Usage</a><a class="docs-footer-nextpage" href="../theory/">Theory »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option 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-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Theory · FastMultipole.jl</title><meta name="title" content="Theory · FastMultipole.jl"/><meta property="og:title" content="Theory · FastMultipole.jl"/><meta property="twitter:title" content="Theory · FastMultipole.jl"/><meta name="description" content="Documentation for FastMultipole.jl."/><meta property="og:description" content="Documentation for FastMultipole.jl."/><meta property="twitter:description" content="Documentation for FastMultipole.jl."/><meta property="og:url" content="https://flow.byu.edu/FastMultipole/theory/"/><meta property="twitter:url" content="https://flow.byu.edu/FastMultipole/theory/"/><link rel="canonical" href="https://flow.byu.edu/FastMultipole/theory/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" 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class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Theory"><a class="docs-heading-anchor" href="#Theory">Theory</a><a id="Theory-1"></a><a class="docs-heading-anchor-permalink" href="#Theory" title="Permalink"></a></h1><p>In a nutshell, <code>FastMultipole</code> operates by forming series expansions of a kernel function, and translating and combining those expansions to obtain optimal compression. You can get a sense for how this works in the following figure.</p><img src="multipole_expansions.png" width="660px"/><p>Here, we see how each body&#39;s influence can be expressed as a series expansion. These series expansions can be translated and combined such that an entire cluster of bodies is represented by a single series expansion. This is what is known as a multipole expansion. Multipole expansions only converge outside of a finite radius of convergence, as illustrated by the red dotted line. Multipole expansions can only be used for interactions that are farther apart than this circl. The accuracy of the expansion gets better and better the farther away we go, so we can control the accuracy by imposing a cutoff radius (dotted blue line), and only use multipole expansions for interactions that are farther away than the blue circle. Multipole expansions are very helpful for reducing the cost of the N-body problem; in fact, we can reduce the scaling of the N-body problem to O(NlogN) by only considering multipole expansions.</p><p>Local expansions are very similar to multipole expansions, but they converge inside of a finite radius rather than outside. These provide the additional required compression to achieve fully O(N) scaling. In the next figure, we see how local expansions can reduce the number of times an expansion need be evaluated.</p><img src="local_expansions.png" width="660px"/><p>More details of the fast multipole method (FMM) can be found in the original work by Greengard and Rokhlin.[<a href="#greengard1987fast">4</a>]</p><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="GUMEROV2023112118">N. A. Gumerov, S. Kaneko and R. Duraiswami. <em>Recursive computation of the multipole expansions of layer potential integrals over simplices for efficient fast multipole accelerated boundary elements</em>. Journal of Computational Physics <strong>486</strong>, 112118 (2023).</div></dd><dt>[2]</dt><dd><div id="gumerov2013efficient">N. A. Gumerov and R. Duraiswami. <em>Efficient FMM accelerated vortex methods in three dimensions via the Lamb–Helmholtz decomposition</em>. Journal of Computational Physics <strong>240</strong>, 310–328 (2013).</div></dd><dt>[3]</dt><dd><div id="DENG2021265">S. DENG, C. JIANG, Y. WANG and H. WANG. <a href="https://www.sciencedirect.com/science/article/pii/S1000936120303204"><em>Acceleration of unsteady vortex lattice method via dipole panel fast multipole method</em></a>. <a href="https://doi.org/10.1016/j.cja.2020.06.029">Chinese Journal of Aeronautics <strong>34</strong>, 265–278</a> (2021).</div></dd><dt>[4]</dt><dd><div id="greengard1987fast">L. Greengard and V. Rokhlin. <em>A fast algorithm for particle simulations</em>. Journal of computational physics <strong>73</strong>, 325–348 (1987).</div></dd></dl></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reference/">« Reference</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 11 November 2024 20:47">Monday 11 November 2024</span>. 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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Theory · FastMultipole.jl</title><meta name="title" content="Theory · FastMultipole.jl"/><meta property="og:title" content="Theory · FastMultipole.jl"/><meta property="twitter:title" content="Theory · FastMultipole.jl"/><meta name="description" content="Documentation for FastMultipole.jl."/><meta property="og:description" content="Documentation for FastMultipole.jl."/><meta property="twitter:description" content="Documentation for FastMultipole.jl."/><meta property="og:url" content="https://flow.byu.edu/FastMultipole/theory/"/><meta property="twitter:url" content="https://flow.byu.edu/FastMultipole/theory/"/><link rel="canonical" href="https://flow.byu.edu/FastMultipole/theory/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" 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class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Theory"><a class="docs-heading-anchor" href="#Theory">Theory</a><a id="Theory-1"></a><a class="docs-heading-anchor-permalink" href="#Theory" title="Permalink"></a></h1><p>In a nutshell, <code>FastMultipole</code> operates by forming series expansions of a kernel function, and translating and combining those expansions to obtain optimal compression. You can get a sense for how this works in the following figure.</p><img src="multipole_expansions.png" width="660px"/><p>Here, we see how each body&#39;s influence can be expressed as a series expansion. These series expansions can be translated and combined such that an entire cluster of bodies is represented by a single series expansion. This is what is known as a multipole expansion. Multipole expansions only converge outside of a finite radius of convergence, as illustrated by the red dotted line. Multipole expansions can only be used for interactions that are farther apart than this circl. The accuracy of the expansion gets better and better the farther away we go, so we can control the accuracy by imposing a cutoff radius (dotted blue line), and only use multipole expansions for interactions that are farther away than the blue circle. Multipole expansions are very helpful for reducing the cost of the N-body problem; in fact, we can reduce the scaling of the N-body problem to O(NlogN) by only considering multipole expansions.</p><p>Local expansions are very similar to multipole expansions, but they converge inside of a finite radius rather than outside. These provide the additional required compression to achieve fully O(N) scaling. In the next figure, we see how local expansions can reduce the number of times an expansion need be evaluated.</p><img src="local_expansions.png" width="660px"/><p>More details of the fast multipole method (FMM) can be found in the original work by Greengard and Rokhlin.[<a href="#greengard1987fast">4</a>]</p><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><div class="citation canonical"><dl><dt>[1]</dt><dd><div id="GUMEROV2023112118">N. A. Gumerov, S. Kaneko and R. Duraiswami. <em>Recursive computation of the multipole expansions of layer potential integrals over simplices for efficient fast multipole accelerated boundary elements</em>. Journal of Computational Physics <strong>486</strong>, 112118 (2023).</div></dd><dt>[2]</dt><dd><div id="gumerov2013efficient">N. A. Gumerov and R. Duraiswami. <em>Efficient FMM accelerated vortex methods in three dimensions via the Lamb–Helmholtz decomposition</em>. Journal of Computational Physics <strong>240</strong>, 310–328 (2013).</div></dd><dt>[3]</dt><dd><div id="DENG2021265">S. DENG, C. JIANG, Y. WANG and H. WANG. <a href="https://www.sciencedirect.com/science/article/pii/S1000936120303204"><em>Acceleration of unsteady vortex lattice method via dipole panel fast multipole method</em></a>. <a href="https://doi.org/10.1016/j.cja.2020.06.029">Chinese Journal of Aeronautics <strong>34</strong>, 265–278</a> (2021).</div></dd><dt>[4]</dt><dd><div id="greengard1987fast">L. Greengard and V. Rokhlin. <em>A fast algorithm for particle simulations</em>. Journal of computational physics <strong>73</strong>, 325–348 (1987).</div></dd></dl></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../reference/">« Reference</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 11 November 2024 22:07">Monday 11 November 2024</span>. 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