from __future__ import absolute_import, division, print_function
from six.moves import range
from rstbx.diffraction import rotation_angles
from cctbx.crystal_orientation import crystal_orientation,basis_type
from libtbx.test_utils import approx_equal

test_results=[
((-4, -3, -5),(-2.1644080756068704, 0.82603163906757826)),
((-4, -3, -4),(-2.1563824130204701, 0.83451621989551883)),
((-4, -3, -3),(-2.1476369882498436, 0.84275362492632477)),
((-4, -3, -2),(-2.1381420481925733, 0.85073212909354023)),
((-4, -3, -1),(-2.1278664357865269, 0.85843936020563638)),
((-4, -3, 0),(-2.1167775302687417, 0.86586226386067811)),
((-4, -3, 1),(-2.1048411851088034, 0.87298706505447998)),
((-4, -3, 2),(-2.0920216634827948, 0.87979922593866833)),
((-4, -2, -8),(-2.3517102079316765, 0.63998771713383507)),
((-4, -2, -7),(-2.3478281931611629, 0.64721041614149566)),
((-4, -2, -6),(-2.3433224076234787, 0.65416216116158055)),
((-4, -2, -5),(-2.338163187294632, 0.66082958483881171)),
((-4, -2, -4),(-2.3323190243690588, 0.66719843977099291)),
((-4, -2, -3),(-2.3257564359156206, 0.67325353443169111)),
((-4, -2, -2),(-2.3184398205079146, 0.67897866221111858)),
((-4, -2, -1),(-2.3103313013994797, 0.68435652253111579)),
((-4, -2, 0),(-2.3013905545938611, 0.68936863278894389)),
((-4, -2, 1),(-2.2915746198968177, 0.69399522963913585)),
((-4, -2, 2),(-2.2808376927234328, 0.69821515782199495)),
((-4, -2, 3),(-2.2691308940541397, 0.70200574437742413)),
((-4, -2, 4),(-2.2564020154745883, 0.70534265562555354)),
((-4, -2, 5),(-2.2425952356738228, 0.70819973372741496)),
((-4, -1, -9),(-2.5308098266764345, 0.46028415341980455)),
((-4, -1, -8),(-2.5302848214986784, 0.46514725234493398)),
((-4, -1, -7),(-2.5292342273209871, 0.46966628410773587)),
((-4, -1, -6),(-2.5276312561197014, 0.47382369995636803)),
((-4, -1, -5),(-2.5254472282330442, 0.47760069073118888)),
((-4, -1, -4),(-2.5226514099331481, 0.48097707866688094)),
((-4, -1, -3),(-2.5192108323762348, 0.4839311961914976)),
((-4, -1, -2),(-2.5150900891927819, 0.4864397496659289)),
((-4, -1, -1),(-2.5102511094811852, 0.48847766560364997)),
((-4, -1, 0),(-2.5046529023623023, 0.49001791641395342)),
((-4, -1, 1),(-2.4982512685115954, 0.49103132209800959)),
((-4, -1, 2),(-2.4909984731750785, 0.49148632356375704)),
((-4, -1, 3),(-2.4828428740492936, 0.49134872227079812)),
((-4, -1, 4),(-2.4737284960041088, 0.49058137971448473)),
((-4, -1, 5),(-2.4635945428704575, 0.48914386873456728)),
((-4, -1, 6),(-2.4523748342967511, 0.48699206668781031)),
((-4, 0, -9),(-2.7075479183479456, 0.28262514671259681)),
((-4, 0, -8),(-2.7099907535850076, 0.28453239000476199)),
((-4, 0, -7),(-2.712011168841761, 0.28599904122031838)),
((-4, 0, -6),(-2.7135874843901879, 0.28700247991898331)),
((-4, 0, -5),(-2.7146964449166768, 0.28751844401101351)),
((-4, 0, -4),(-2.7153130789933311, 0.28752088332609876)),
((-4, 0, -3),(-2.7154105413808369, 0.28698179536956087)),
((-4, 0, -2),(-2.7149599354532072, 0.28587104047261436)),
((-4, 0, -1),(-2.7139301125074402, 0.28415613300355697)),
((-4, 0, 0),(-2.7122874440734508, 0.28180200464428157)),
((-4, 0, 1),(-2.7099955625391106, 0.2787707349185628)),
((-4, 0, 2),(-2.7070150644101365, 0.2750212431429222)),
((-4, 0, 3),(-2.7033031692799137, 0.2705089347019079)),
((-4, 0, 4),(-2.6988133260168774, 0.26518529295327825)),
((-4, 0, 5),(-2.6934947556889823, 0.25899740604605698)),
((-4, 0, 6),(-2.6872919182034409, 0.25188741535194725)),
((-4, 1, -8),(-2.8796653646852977, 0.10938810433468421)),
((-4, 1, -7),(-2.8844290526903671, 0.10802314514838145)),
((-4, 1, -6),(-2.8888544340477269, 0.10612014605319227)),
((-4, 1, -5),(-2.8929247721042515, 0.10365257781794722)),
((-4, 1, -4),(-2.8966221726532195, 0.10059211225346927)),
((-4, 1, -3),(-2.8999274875451237, 0.096908473277887167)),
((-4, 1, -2),(-2.90282020686249, 0.09256927138710698)),
((-4, 1, -1),(-2.9052783378602522, 0.087539819143462594)),
((-4, 1, 0),(-2.9072782685237462, 0.081782924869921295)),
((-4, 1, 1),(-2.9087946131676299, 0.075258661221423648)),
((-4, 1, 2),(-2.9098000369706947, 0.067924104676897204)),
((-4, 1, 3),(-2.9102650556866623, 0.059733041226309229)),
((-4, 1, 4),(-2.9101578059546229, 0.050635632579456205)),
((-4, 1, 5),(-2.909443780608759, 0.040578036048329796)),
((-4, 2, -3),(-3.0621609181560006, -0.075176923028023243)),
((-4, 2, -2),(-3.0675200578810209, -0.081831067832066243)),
((-4, 2, -1),(-3.0725497629968923, -0.089189117263163406)),
((-4, 2, 0),(-3.0772340546619521, -0.097283839954712306)),
((-3, -4, -9),(-1.9186807978345002, 1.0678756183194666)),
((-3, -4, -8),(-1.9095408418739945, 1.0821170500791975)),
((-3, -4, -7),(-1.8996857140430228, 1.0962061655013031)),
((-3, -4, -6),(-1.8890926257610019, 1.1101336310873262)),
((-3, -4, -5),(-1.8777383483996397, 1.1238896353781627)),
((-3, -4, -4),(-1.8655992637788497, 1.1374638864261277)),
((-3, -4, -3),(-1.8526514223811588, 1.1508456108700291)),
((-3, -4, -2),(-1.8388706097467478, 1.1640235547087561)),
((-3, -4, -1),(-1.8242324214645822, 1.1769859858454257)),
((-3, -4, 0),(-1.8087123471112596, 1.189720698444829)),
((-3, -4, 1),(-1.7922858634060383, 1.2022150191114247)),
((-3, -4, 2),(-1.7749285367455292, 1.214455814852786)),
((-3, -4, 3),(-1.7566161351529119, 1.2264295027444108)),
((-3, -4, 4),(-1.7373247495219588, 1.2381220611555419)),
((-3, -4, 5),(-1.717030923854153, 1.249519042332484)),
((-3, -4, 6),(-1.6957117939762307, 1.2606055860656162)),
((-3, -3, -12),(-2.1014485380247865, 0.87645308424953716)),
((-3, -3, -11),(-2.0957357801431784, 0.89042140922191038)),
((-3, -3, -10),(-2.089318695933847, 0.90427646297309716)),
((-3, -3, -9),(-2.0821669686519959, 0.91801060121359623)),
((-3, -3, -8),(-2.0742488395849121, 0.93161559528854909)),
((-3, -3, -7),(-2.0655310728826279, 0.94508260617016893)),
((-3, -3, -6),(-2.0559789247649376, 0.9584021579863129)),
((-3, -3, -5),(-2.045556118199046, 0.97156411117071717)),
((-3, -3, -4),(-2.0342248242844101, 0.98455763532001472)),
((-3, -3, -3),(-2.0219456517325916, 0.99737118183784879)),
((-3, -3, -2),(-2.0086776459885258, 1.0099924564358937)),
((-3, -3, -1),(-1.9943782997027253, 1.0224083915437105)),
((-3, -3, 0),(-1.979003576428247, 1.0346051186525971)),
((-3, -3, 1),(-1.962507949576102, 1.0465679405804109)),
((-3, -3, 2),(-1.9448444588120386, 1.0582813035928971)),
((-3, -3, 3),(-1.9259647862068898, 1.0697287692491899)),
((-3, -3, 4),(-1.9058193545508628, 1.0808929857519785)),
((-3, -3, 5),(-1.8843574502948603, 1.0917556584727153)),
((-3, -3, 6),(-1.8615273735714883, 1.1022975191852051)),
((-3, -3, 7),(-1.8372766176529489, 1.1124982933720182)),
((-3, -3, 8),(-1.8115520799964697, 1.1223366647620168)),
((-3, -3, 9),(-1.7843003066790657, 1.1317902360070144)),
((-3, -2, -13),(-2.2900278505333258, 0.68617749256662541)),
((-3, -2, -12),(-2.2875880980790106, 0.69829285391925877)),
((-3, -2, -11),(-2.2844906531541063, 0.71026682526633877)),
((-3, -2, -10),(-2.2807008820870909, 0.72209093411940517)),
((-3, -2, -9),(-2.2761817673439348, 0.73375597668886261)),
((-3, -2, -8),(-2.2708937381379699, 0.74525196591387977)),
((-3, -2, -7),(-2.2647944885152289, 0.75656807511358304)),
((-3, -2, -6),(-2.2578387821488413, 0.7676925768166255)),
((-3, -2, -5),(-2.2499782430721043, 0.77861277625440528)),
((-3, -2, -4),(-2.2411611315891755, 0.78931493891473092)),
((-3, -2, -3),(-2.2313321046291188, 0.79978421144347833)),
((-3, -2, -2),(-2.2204319598581872, 0.81000453504626735)),
((-3, -2, -1),(-2.2083973629420037, 0.81995855037294751)),
((-3, -2, 0),(-2.1951605574608921, 0.8296274926561944)),
((-3, -2, 1),(-2.1806490571347852, 0.83899107560948483)),
((-3, -2, 2),(-2.1647853202173759, 0.84802736225450637)),
((-3, -2, 3),(-2.1474864061802501, 0.85671262042368024)),
((-3, -2, 4),(-2.1286636151339779, 0.86502116014437558)),
((-3, -2, 5),(-2.1082221108293702, 0.87292514942377353)),
((-3, -2, 6),(-2.0860605285475167, 0.88039440407201508)),
((-3, -2, 7),(-2.0620705697121102, 0.88739614606635686)),
((-3, -2, 8),(-2.0361365856149476, 0.89389472348891319)),
((-3, -2, 9),(-2.008135153181632, 0.8998512831539176)),
((-3, -2, 10),(-1.9779346461214229, 0.90522338452333351)),
((-3, -2, 11),(-1.9453948049357528, 0.90996454017632245)),
((-3, -1, -14),(-2.4908850917087864, 0.47810695364223693)),
((-3, -1, -13),(-2.4926358998901077, 0.48715824176293415)),
((-3, -1, -12),(-2.4938666015936364, 0.49597167311988166)),
((-3, -1, -11),(-2.4945471313040022, 0.50453364205691342)),
((-3, -1, -10),(-2.4946449448748949, 0.5128293499299994)),
((-3, -1, -9),(-2.4941247840238758, 0.52084269550513662)),
((-3, -1, -8),(-2.492948412836181, 0.52855615217397856)),
((-3, -1, -7),(-2.4910743222639158, 0.53595063000129917)),
((-3, -1, -6),(-2.4884573979099538, 0.54300532023644543)),
((-3, -1, -5),(-2.4850485455454199, 0.54969751945004997)),
((-3, -1, -4),(-2.4807942677917314, 0.55600242987341009)),
((-3, -1, -3),(-2.4756361841590762, 0.56189293178957433)),
((-3, -1, -2),(-2.46951048511644, 0.56733932291033429)),
((-3, -1, -1),(-2.4623473090015806, 0.5723090185171017)),
((-3, -1, 0),(-2.4540700282669023, 0.57676620467101924)),
((-3, -1, 1),(-2.4445944286747676, 0.58067143490906037)),
((-3, -1, 2),(-2.4338277614360146, 0.58398115840023113)),
((-3, -1, 3),(-2.4216676437051952, 0.58664716435076802)),
((-3, -1, 4),(-2.4080007770002441, 0.58861592325487977)),
((-3, -1, 5),(-2.3927014455838824, 0.58982780001598689)),
((-3, -1, 6),(-2.3756297470418053, 0.59021610647888945)),
((-3, -1, 7),(-2.3566294943870654, 0.58970595074380672)),
((-3, -1, 8),(-2.3355257118081156, 0.58821282663979757)),
((-3, -1, 9),(-2.3121216228927586, 0.58564086721481734)),
((-3, -1, 10),(-2.2861949981468088, 0.58188065845470027)),
((-3, -1, 11),(-2.2574936838111155, 0.57680646963619076)),
((-3, -1, 12),(-2.2257300699530007, 0.57027269833079075)),
((-3, 0, -14),(-2.6946178997817647, 0.27409042376715442)),
((-3, 0, -13),(-2.7002814312865349, 0.27922063173268452)),
((-3, 0, -12),(-2.7055804876639731, 0.28396543283279291)),
((-3, 0, -11),(-2.7104939026322081, 0.28830240392495621)),
((-3, 0, -10),(-2.7149986754165156, 0.29220718470089274)),
((-3, 0, -9),(-2.7190697882855615, 0.29565328452088058)),
((-3, 0, -8),(-2.7226800004707767, 0.29861186426422409)),
((-3, 0, -7),(-2.7257996146682943, 0.30105148918718122)),
((-3, 0, -6),(-2.7283962115666003, 0.30293784798635459)),
((-3, 0, -5),(-2.7304343469077001, 0.30423343228563537)),
((-3, 0, -4),(-2.7318752044252759, 0.30489716954650892)),
((-3, 0, -3),(-2.7326761965451589, 0.30488400087792644)),
((-3, 0, -2),(-2.7327905028944786, 0.30414439330309334)),
((-3, 0, -1),(-2.7321665343305295, 0.30262377360739312)),
((-3, 0, 0),(-2.7307473072116188, 0.30026186778244973)),
((-3, 0, 1),(-2.7284697087762617, 0.29699192607649683)),
((-3, 0, 2),(-2.7252636294791652, 0.29273980845810754)),
((-3, 0, 3),(-2.7210509315406544, 0.28742289847705527)),
((-3, 0, 4),(-2.7157442142198303, 0.28094880446869103)),
((-3, 0, 5),(-2.7092453245888524, 0.27321379494723746)),
((-3, 0, 6),(-2.7014435466590054, 0.2641008986382013)),
((-3, 0, 7),(-2.6922133798079226, 0.25347757709856139)),
((-3, 0, 8),(-2.6814117869099356, 0.24119284655150369)),
((-3, 0, 9),(-2.6688747492937166, 0.2270736812777692)),
((-3, 0, 10),(-2.6544129032694777, 0.2109204672045038)),
((-3, 0, 11),(-2.6378059413036521, 0.19250118092482396)),
((-3, 0, 12),(-2.6187953233011818, 0.17154382943920357)),
((-3, 1, -13),(-2.8959492178816468, 0.079382252936560108)),
((-3, 1, -12),(-2.9047325778546265, 0.080283095570497093)),
((-3, 1, -11),(-2.9132746229649684, 0.080648634296221502)),
((-3, 1, -10),(-2.9215619008626383, 0.080448946442102126)),
((-3, 1, -9),(-2.9295798367305146, 0.079651756780256378)),
((-3, 1, -8),(-2.9373126348700018, 0.07822222455894795)),
((-3, 1, -7),(-2.9447431688812951, 0.076122706402541637)),
((-3, 1, -6),(-2.9518528587543407, 0.073312491763175197)),
((-3, 1, -5),(-2.9586215328659113, 0.069747507052956362)),
((-3, 1, -4),(-2.96502727248384, 0.06537998391962753)),
((-3, 1, -3),(-2.9710462358917846, 0.060158086326600413)),
((-3, 1, -2),(-2.9766524586413388, 0.054025490127486135)),
((-3, 1, -1),(-2.9818176256792897, 0.046920907643934848)),
((-3, 1, 0),(-2.9865108101420965, 0.038777548310174062)),
((-3, 1, 1),(-2.990698172398043, 0.029522504668110922)),
((-3, 1, 2),(-2.9943426113709446, 0.019076050791998238)),
((-3, 1, 3),(-2.9974033581898958, 0.0073508374699347455)),
((-3, 1, 4),(-2.9998354996303429, -0.0057490349911365375)),
((-3, 1, 5),(-3.0015894154387355, -0.020329089859899077)),
((-3, 1, 6),(-3.0026101091808122, -0.036505722117989456)),
((-3, 1, 7),(-3.002836406317571, -0.054407658055330113)),
((-3, 1, 8),(-3.0021999852119077, -0.074177672256026353)),
((-3, 1, 9),(-3.0006241958554454, -0.09597462052503887)),
((-3, 1, 10),(-2.9980226060242305, -0.11997586427498406)),
((-3, 1, 11),(-2.9942971934337583, -0.14638018508015721)),
((-3, 2, -12),(-3.07808083517271, -0.10157678587130563)),
((-3, 2, -11),(-3.088995129959494, -0.10416656658978136)),
((-3, 2, -10),(-3.0997387566944417, -0.10737234131068603)),
((-3, 2, -9),(-3.1103025410616842, -0.11122425520833933)),
((-3, 2, -8),(-3.1206766168492766, -0.11575437696165745)),
((-3, 2, -7),(-3.1308503808521446, -0.12099682538634071)),
((-3, 2, -6),(-3.1408124440644722, -0.12698790509229746)),
((-3, 2, -5),(3.1326347284295228, -0.13376625179038171)),
((-3, 2, -4),(3.123133646273303, -0.14137298791237843)),
((-3, 2, -3),(3.1138836996314532, -0.14985188924979251)),
((-3, 2, -2),(3.1048999990498225, -0.15924956336065643)),
((-3, 2, -1),(3.0961987578933035, -0.16961564053966618)),
((-3, 2, 0),(3.0877973752665762, -0.18100297819589323)),
((-3, 2, 1),(3.0797145277853075, -0.19346787953534081)),
((-3, 2, 2),(3.0719702716401334, -0.20707032750446822)),
((-3, 2, 3),(3.0645861567123447, -0.22187423501832021)),
((-3, 2, 4),(3.0575853548956911, -0.23794771257793224)),
((-3, 2, 5),(3.0509928052745892, -0.25536335448362563)),
((-3, 2, 6),(3.0448353794335929, -0.27419854498545915)),
((-3, 2, 7),(3.0391420709631691, -0.29453578589718205)),
((-3, 2, 8),(3.0339442142326489, -0.31646304746364151)),
((-3, 2, 9),(3.0292757387887681, -0.34007414465511288)),
((-3, 2, 10),(3.0251734673983983, -0.36546914162936717)),
((-3, 3, -9),(3.0266036406275112, -0.2714343471465524)),
((-3, 3, -8),(3.0150146400279647, -0.27770919088120244)),
((-3, 3, -7),(3.0035939871263553, -0.28465701480251288)),
((-3, 3, -6),(2.9923505381928734, -0.29230513049554352)),
((-3, 3, -5),(2.9812936847289455, -0.30068207717481887)),
((-3, 3, -4),(2.9704333750156682, -0.30981765584878845)),
((-3, 3, -3),(2.9597801364827814, -0.31974296179984474)),
((-3, 3, -2),(2.9493450989868197, -0.33049041490526571)),
((-3, 3, -1),(2.9391400191170254, -0.34209378727285161)),
((-3, 3, 0),(2.9291773056849482, -0.35458822761224001)),
((-3, 3, 1),(2.9194700465998551, -0.36801028171004563)),
((-3, 3, 2),(2.9100320373888535, -0.38239790832589482)),
((-3, 3, 3),(2.9008778116898419, -0.39779048977904935)),
((-3, 3, 4),(2.8920226741297621, -0.41422883645512371)),
((-3, 3, 5),(2.8834827361025943, -0.43175518443287592)),
((-3, 3, 6),(2.8752749550850796, -0.4504131854179832)),
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((3, 1, 6),(0.65313525567983921, -2.5985873333533478)),
((3, 1, 7),(0.65051833132587744, -2.6056420235884943)),
((3, 1, 8),(0.64864424075361238, -2.6130365014158148)),
((3, 1, 9),(0.64746786956591751, -2.6207499580846565)),
((3, 1, 10),(0.64694770871489848, -2.6287633036597939)),
((3, 1, 11),(0.64704552228579104, -2.6370590115328798)),
((3, 1, 12),(0.64772605199615707, -2.6456209804699116)),
((3, 1, 13),(0.64895675369968531, -2.654434411826859)),
((3, 1, 14),(0.65070756188100687, -2.6634856999475565)),
((3, 2, -11),(1.1961978486540406, -2.2316281134134708)),
((3, 2, -10),(1.1636580074683704, -2.2363692690664596)),
((3, 2, -9),(1.1334575004081613, -2.2417413704358755)),
((3, 2, -8),(1.1054560679748455, -2.2476979301008799)),
((3, 2, -7),(1.0795220838776829, -2.2541965075234365)),
((3, 2, -6),(1.0555321250422767, -2.2611982495177783)),
((3, 2, -5),(1.0333705427604229, -2.2686675041660198)),
((3, 2, -4),(1.0129290384558152, -2.2765714934454175)),
((3, 2, -3),(0.99410624740954312, -2.2848800331661132)),
((3, 2, -2),(0.97680733337241732, -2.2935652913352871)),
((3, 2, -1),(0.96094359645500826, -2.3026015779803082)),
((3, 2, 0),(0.94643209612890089, -2.3119651609335987)),
((3, 2, 1),(0.93319529064778928, -2.3216341032168457)),
((3, 2, 2),(0.92116069373160625, -2.3315881185435257)),
((3, 2, 3),(0.91026054896067465, -2.341808442146315)),
((3, 2, 4),(0.90043152200061793, -2.3522777146750622)),
((3, 2, 5),(0.89161441051768886, -2.3629798773353881)),
((3, 2, 6),(0.88375387144095185, -2.3739000767731677)),
((3, 2, 7),(0.87679816507456454, -2.3850245784762101)),
((3, 2, 8),(0.87069891545182321, -2.3963406876759135)),
((3, 2, 9),(0.86541088624585827, -2.4078366769009305)),
((3, 2, 10),(0.86089177150270246, -2.4195017194703881)),
((3, 2, 11),(0.85710200043568696, -2.4313258283234545)),
((3, 2, 12),(0.85400455551078269, -2.4432997996705343)),
((3, 2, 13),(0.85156480305646742, -2.4554151610231676)),
((3, 3, -9),(1.3572923469107276, -2.0098024175827787)),
((3, 3, -8),(1.3300405735933236, -2.0192559888277763)),
((3, 3, -7),(1.3043160359368444, -2.0290943602177749)),
((3, 3, -6),(1.2800652800183048, -2.039295134404588)),
((3, 3, -5),(1.2572352032949328, -2.0498369951170781)),
((3, 3, -4),(1.2357732990389303, -2.0606996678378149)),
((3, 3, -3),(1.2156278673829035, -2.0718638843406034)),
((3, 3, -2),(1.1967481947777547, -2.083311349996896)),
((3, 3, -1),(1.1790847040136911, -2.0950247130093822)),
((3, 3, 0),(1.1625890771615464, -2.106987534937196)),
((3, 3, 1),(1.1472143538870681, -2.1191842620460828)),
((3, 3, 2),(1.1329150076012675, -2.1316001971538996)),
((3, 3, 3),(1.1196470018572016, -2.1442214717519446)),
((3, 3, 4),(1.1073678293053832, -2.1570350182697786)),
((3, 3, 5),(1.0960365353907473, -2.1700285424190762)),
((3, 3, 6),(1.0856137288248557, -2.1831904956034802)),
((3, 3, 7),(1.0760615807071654, -2.1965100474196242)),
((3, 3, 8),(1.0673438140048812, -2.2099770583012441)),
((3, 3, 9),(1.0594256849377974, -2.2235820523761971)),
((3, 3, 10),(1.0522739576559463, -2.2373161906166961)),
((3, 3, 11),(1.0458568734466149, -2.2511712443678831)),
((3, 3, 12),(1.0401441155650066, -2.2651395693402563)),
((3, 4, -6),(1.4458808596135624, -1.8809870675241769)),
((3, 4, -5),(1.4245617297356401, -1.8920736112573091)),
((3, 4, -4),(1.4042679040678343, -1.9034705924342512)),
((3, 4, -3),(1.3849765184368814, -1.9151631508453824)),
((3, 4, -2),(1.3666641168442639, -1.9271368387370071)),
((3, 4, -1),(1.3493067901837548, -1.9393776344783686)),
((3, 4, 0),(1.3328803064785337, -1.9518719551449641)),
((3, 4, 1),(1.3173602321252111, -1.9646066677443677)),
((3, 4, 2),(1.3027220438430454, -1.977569098881037)),
((3, 4, 3),(1.2889412312086344, -1.9907470427197642)),
((3, 4, 4),(1.2759933898109437, -2.0041287671636656)),
((3, 4, 5),(1.2638543051901536, -2.0177030182116305)),
((3, 4, 6),(1.2525000278287912, -2.0314590225024669)),
((3, 4, 7),(1.2419069395467706, -2.0453864880884902)),
((3, 4, 8),(1.2320518117157988, -2.0594756035105957)),
((3, 4, 9),(1.2229118557552929, -2.0737170352703265)),
((4, -2, 0),(0.06435859892784096, 3.0443088136350811)),
((4, -2, 1),(0.069042890592901043, 3.0524035363266298)),
((4, -2, 2),(0.074072595708772337, 3.0597615857577272)),
((4, -2, 3),(0.079431735433792561, 3.0664157305617699)),
((4, -1, -5),(0.23214887298103432, -3.1010146175414635)),
((4, -1, -4),(0.23143484763517025, -3.090957021010337)),
((4, -1, -3),(0.23132759790313087, -3.081859612363484)),
((4, -1, -2),(0.23179261661909864, -3.0736685489128961)),
((4, -1, -1),(0.2327980404221634, -3.0663339923683695)),
((4, -1, 0),(0.2343143850660469, -3.059809728719872)),
((4, -1, 1),(0.23631431572954079, -3.0540528344463307)),
((4, -1, 2),(0.23877244672730308, -3.0490233822026864)),
((4, -1, 3),(0.24166516604466937, -3.044684180311906)),
((4, -1, 4),(0.24497048093657392, -3.0410005413363241)),
((4, -1, 5),(0.24866788148554173, -3.037940075771846)),
((4, -1, 6),(0.25273821954206654, -3.0354725075366011)),
((4, -1, 7),(0.25716360089942614, -3.0335695084414116)),
((4, -1, 8),(0.26192728890449551, -3.0322045492551091)),
((4, 0, -6),(0.45430073538635213, -2.8897052382378461)),
((4, 0, -5),(0.44809789790081089, -2.8825952475437364)),
((4, 0, -4),(0.44277932757291577, -2.8764073606365148)),
((4, 0, -3),(0.43828948430987963, -2.8710837188878853)),
((4, 0, -2),(0.4345775891796565, -2.8665714104468711)),
((4, 0, -1),(0.43159709105068261, -2.8628219186712305)),
((4, 0, 0),(0.42930520951634238, -2.8597906489455118)),
((4, 0, 1),(0.42766254108235296, -2.8574365205862362)),
((4, 0, 2),(0.42663271813658615, -2.8557216131171788)),
((4, 0, 3),(0.42618211220895647, -2.8546108582202323)),
((4, 0, 4),(0.42627957459646199, -2.8540717702636944)),
((4, 0, 5),(0.42689620867311634, -2.8540742095787799)),
((4, 0, 6),(0.42800516919960535, -2.8545901736708101)),
((4, 0, 7),(0.42958148474803215, -2.855593612369475)),
((4, 0, 8),(0.4316019000047856, -2.8570602635850313)),
((4, 0, 9),(0.4340447352418475, -2.8589675068771965)),
((4, 1, -6),(0.68921781929304227, -2.6546005869019829)),
((4, 1, -5),(0.6779981107193358, -2.6524487848552258)),
((4, 1, -4),(0.66786415758568451, -2.6510112738753087)),
((4, 1, -3),(0.65874977954049951, -2.6502439313189949)),
((4, 1, -2),(0.65059418041471451, -2.6501063300260363)),
((4, 1, -1),(0.64334138507819771, -2.6505613314917835)),
((4, 1, 0),(0.63693975122749091, -2.65157473717584)),
((4, 1, 1),(0.63134154410860788, -2.6531149879861431)),
((4, 1, 2),(0.62650256439701135, -2.6551529039238644)),
((4, 1, 3),(0.62238182121355845, -2.6576614573982957)),
((4, 1, 4),(0.61894124365664538, -2.6606155749229123)),
((4, 1, 5),(0.61614542535674921, -2.6639919628586042)),
((4, 1, 6),(0.61396139747009182, -2.6677689536334253)),
((4, 1, 7),(0.6123584262688061, -2.6719263694820574)),
((4, 1, 8),(0.61130783209111506, -2.6764454012448593)),
((4, 1, 9),(0.61078282691335861, -2.6813085001699886)),
((4, 2, -5),(0.89899741791597043, -2.4333929198623783)),
((4, 2, -4),(0.88519063811520515, -2.4362499979642398)),
((4, 2, -3),(0.87246175953565352, -2.4395869092123692)),
((4, 2, -2),(0.86075496086636039, -2.4433774957677983)),
((4, 2, -1),(0.85001803369297546, -2.4475974239506573)),
((4, 2, 0),(0.84020209899593201, -2.4522240208008492)),
((4, 2, 1),(0.83126135219031361, -2.4572361310586777)),
((4, 2, 2),(0.82315283308187859, -2.4626139913786744)),
((4, 2, 3),(0.81583621767417269, -2.4683391191581023)),
((4, 2, 4),(0.80927362922073443, -2.4743942138188002)),
((4, 2, 5),(0.80342946629516132, -2.4807630687509814)),
((4, 2, 6),(0.79827024596631457, -2.4874304924282127)),
((4, 2, 7),(0.79376446042863036, -2.4943822374482973)),
((4, 2, 8),(0.78988244565811649, -2.5016049364559581)),
((4, 3, -2),(1.0495709901069983, -2.2617934276511251)),
((4, 3, -1),(1.0367514684809902, -2.2686055885353134)),
((4, 3, 0),(1.0248151233210518, -2.275730389729115)),
((4, 3, 1),(1.0137262178032664, -2.283153293384157)),
((4, 3, 2),(1.0034506053972199, -2.290860524496253)),
((4, 3, 3),(0.99395566533994972, -2.2988390286634686)),
((4, 3, 4),(0.98521024056932294, -2.3070764336942742)),
((4, 3, 5),(0.97718457798292291, -2.3155610145222152)),
]

def test_ewald_sphere_model():
  # direct space orientation matrix
  orientation = (24.67303504408280, -8.27539755075503, 12.97853642392082,
        -13.21765114237159, -0.18925842832666, 35.37258184706041,
         39.24485466996793, 107.21509370974169, 20.28943160079353)
  limiting_resolution = 6.429576016992
  wavelength = 0.979454000
  axial_direction = (0,1,0)

  # rotation_angles object must be instantiated with reciprocal-space orientation matrix
  CO = crystal_orientation(orientation,basis_type.direct)
  MM = CO.unit_cell().max_miller_indices(limiting_resolution)
  RA = rotation_angles(limiting_resolution,CO.reciprocal_matrix(),wavelength,axial_direction)

  maxh = MM[0];
  maxk = MM[1];
  maxl = MM[2];

  ptr=0
  for h in range(-maxh, maxh+1):
    for k in range(-maxk, maxk+1):
      for l in range(-maxl, maxl+1):
        if RA((h,k,l)):
          assert test_results[ptr][0]==(h,k,l)
          assert approx_equal(
            test_results[ptr][1],RA.get_intersection_angles(),eps = 1.E-10, multiplier=1.e-10)
          ptr+=1
          #print "(%s,%s),"%(str((h,k,l)),RA.get_intersection_angles())
  assert(ptr == len(test_results))

if __name__=="__main__":

  test_ewald_sphere_model()
  print("OK")