/* dcmut version of JTT model from http://www.ebi.ac.uk/goldman-srv/dayhoff/ */ 
double freqaa[20]={0.076862, 0.051057, 0.042546, 0.051269, 0.020279, 0.041061, 0.06182, 0.074714, 0.022983, 0.052569, 0.091111, 0.059498, 0.023414, 0.04053, 0.050532, 0.068225, 0.058518, 0.014336, 0.032303, 0.066374};     /* amino acid frequencies   */
double jttQmatrix[20][20] = {
{-1.246848850342, 0.027145883646, 0.023739263982, 0.042422277705, 0.011649839362, 0.022859685225, 0.06594221942, 0.130014239526, 0.00505557051, 0.019013366196, 0.028245047777, 0.021980762626, 0.01099041453, 0.00560501529, 0.099022456668, 0.265197056375, 0.26816253867, 0.001208940544, 0.004506010076, 0.194088262214},
{0.040865834436, -1.034887467504, 0.01919228787, 0.007941516831, 0.020681396197, 0.124086136695, 0.01968861906, 0.101585039528, 0.073790851593, 0.012574241955, 0.033917071971, 0.38847761399, 0.01009248763, 0.00264717642, 0.035902430148, 0.068330816975, 0.038053202076, 0.018034128896, 0.007610619103, 0.01141599613},
{0.042886459554, 0.023031557415, -1.296723756255, 0.28451885357, 0.006353633769, 0.031569092874, 0.0357390693, 0.057777307482, 0.092524455774, 0.025811536707, 0.012508538079, 0.150501202466, 0.00774347808, 0.00297818493, 0.006154999728, 0.3450795939, 0.137594017098, 0.0003971072, 0.022634485979, 0.01092018235},
{0.06359907759, 0.007908678243, 0.23611030338, -1.072295266232, 0.002141969375, 0.021419306406, 0.48012855374, 0.095068633876, 0.023726316186, 0.006096321792, 0.005602050946, 0.016806162068, 0.004448683414, 0.00131811666, 0.006425851248, 0.0402028093, 0.024879454362, 0.000823832576, 0.014664011456, 0.020925133614},
{0.044155528036, 0.052070124051, 0.013330129806, 0.005415288125, -0.548613339595, 0.003749033544, 0.00333253074, 0.040822907746, 0.016662629034, 0.007914736071, 0.014996232823, 0.002915937482, 0.009581055628, 0.02749291755, 0.006248433396, 0.147047457475, 0.027493102314, 0.015829538816, 0.068316064156, 0.041239692802},
{0.04279099695, 0.154293998715, 0.032710811364, 0.026744268774, 0.001851553816, -1.047356261971, 0.21128258492, 0.017280899916, 0.13063721064, 0.00411457563, 0.064598063444, 0.176514620536, 0.010697880014, 0.00185153199, 0.081261823032, 0.037442357575, 0.03065319135, 0.002468745216, 0.008229027735, 0.011932120354},
{0.081987235022, 0.016260786531, 0.02459648079, 0.398183610833, 0.001093180053, 0.140334426066, -0.960070519608, 0.083353329248, 0.005602519944, 0.005875794837, 0.008881955835, 0.103031734632, 0.004099416776, 0.00177638937, 0.009701840808, 0.021316833025, 0.019403632512, 0.001639766016, 0.002049689956, 0.030881897354},
{0.133752101058, 0.069419752164, 0.032901374898, 0.065236418746, 0.011080222531, 0.009497162934, 0.06896837024, -0.623424845046, 0.004635579168, 0.002826582561, 0.006331485612, 0.01605494032, 0.003052693906, 0.00203509236, 0.010514749092, 0.1278738446, 0.018542130516, 0.00780136448, 0.0016959075, 0.03120507236},
{0.01690733414, 0.163927229247, 0.171280750788, 0.052927141998, 0.014702234442, 0.23339400888, 0.01506973776, 0.015069514944, -1.134631228378, 0.009556413372, 0.049251964381, 0.031242161808, 0.00771865924, 0.01837743684, 0.057705573252, 0.05072242205, 0.02793385989, 0.001837774848, 0.1889208652, 0.008086145298},
{0.027799755608, 0.012212579115, 0.020890213638, 0.005945563392, 0.003053185961, 0.00321384447, 0.00690980686, 0.004017297066, 0.004178033604, -1.284254008163, 0.212756849429, 0.012052033876, 0.113128627724, 0.0314954577, 0.00498144456, 0.027639243775, 0.149443619508, 0.00192833536, 0.009802183835, 0.632805932682},
{0.023827758034, 0.019006529877, 0.005841097794, 0.003152325734, 0.003337781447, 0.029112413244, 0.0060265227, 0.005192025288, 0.012423943293, 0.122755922091, -0.673299120831, 0.008715326538, 0.090305597084, 0.10133691582, 0.053589388128, 0.040424062975, 0.015946974252, 0.007602724864, 0.007788059482, 0.116913752186},
{0.028395666694, 0.333364172535, 0.107620830282, 0.014481749354, 0.000993853511, 0.121816982652, 0.10705270488, 0.02016082576, 0.012068281368, 0.010648481778, 0.013346030391, -0.897730486617, 0.014623939534, 0.00099383613, 0.01093234554, 0.03237126155, 0.056507380038, 0.001277825024, 0.002839562912, 0.008234756684},
{0.03607863849, 0.022007864565, 0.01407081312, 0.009741161269, 0.008298207358, 0.018760811961, 0.01082369288, 0.009741136606, 0.00757657578, 0.253995849954, 0.351406562566, 0.037161320338, -1.159570704377, 0.01767841593, 0.00829811238, 0.0194826039, 0.123749653104, 0.002886324224, 0.00613337061, 0.201679589342},
{0.010629476566, 0.003334736898, 0.003126322626, 0.001667370418, 0.013755955465, 0.001875789663, 0.00270950878, 0.003751539368, 0.010421135724, 0.04085084421, 0.227804286634, 0.001458950458, 0.010212741934, -0.635893041519, 0.007503142956, 0.064402421475, 0.008128384272, 0.007711649792, 0.177157275508, 0.039391508772},
{0.150618698338, 0.036275436873, 0.005182272984, 0.006519571116, 0.002507559187, 0.066031261686, 0.01186906908, 0.015546563834, 0.026245689663, 0.00518225202, 0.096623579944, 0.01287209481, 0.00384493001, 0.00601801599, -0.723172263287, 0.19023899935, 0.068873403798, 0.00100301824, 0.00367769655, 0.014042149814},
{0.29876989589, 0.051136189407, 0.215196136344, 0.030211181092, 0.043707957349, 0.022534564227, 0.01931559718, 0.140036151344, 0.017086895214, 0.021296700711, 0.053984269721, 0.028230492044, 0.006686195496, 0.03825914463, 0.140903731992, -1.458812726451, 0.279578347146, 0.004457449472, 0.020305924224, 0.027115902968},
{0.35222511103, 0.033201448074, 0.100038877806, 0.021797476771, 0.009527540617, 0.021508778325, 0.02049852288, 0.023674027468, 0.010971049965, 0.134251027614, 0.024829023054, 0.057453708218, 0.049514241392, 0.00562977912, 0.059474193252, 0.325954966575, -1.334131090979, 0.001154850816, 0.006495939482, 0.07593052852},
{0.006481695598, 0.064227714777, 0.0011785242, 0.002946224354, 0.022391686499, 0.007070950566, 0.00707103342, 0.04065786452, 0.002946259719, 0.00707105619, 0.048318349964, 0.005303294732, 0.004714034276, 0.02180197866, 0.00353547138, 0.021212994575, 0.004713976008, -0.311711816483, 0.024159058367, 0.015909648678},
{0.010721634104, 0.012029080257, 0.029811684378, 0.023273665088, 0.042887083708, 0.010460084445, 0.00392260264, 0.003922485, 0.1344137772, 0.015951800205, 0.021966315434, 0.005230112192, 0.00444561618, 0.22227608508, 0.0057530682, 0.0428867808, 0.011767618692, 0.010721736704, -0.623424335209, 0.010983104902},
{0.224756862782, 0.008781548715, 0.00699988065, 0.016163116209, 0.012599809117, 0.007381577031, 0.02876305322, 0.03512603996, 0.002799949941, 0.501189849567, 0.160486468729, 0.007381678868, 0.071144211662, 0.02405366334, 0.010690600452, 0.0278720957, 0.06694342164, 0.003436296192, 0.005345274319, -1.221915398094}
};
double eigmat[] ={0, -1.81721720738768, -1.87965834528617, -1.61403121885431, -1.5389660844375, -1.40486966367848, -1.30995061286931, -1.24668414819041, -1.17179756521289, -0.310333209874637, -0.346028378570345, -1.06031718484613, -0.999006029871051, -0.455767748889474, -0.860144034346771, -0.545694327352957, -0.768669565718611, -0.605935892953267, -0.65119724379348, -0.70249806480753};
double probmat[20][20] ={
{0.07686196157, 0.05105697447, 0.04254597873, 0.05126897437, 0.02027898986, 0.04106097947, 0.06181996909, 0.07471396264, 0.02298298851, 0.05256897372, 0.09111095444, 0.05949797025, 0.02341398829, 0.04052997974, 0.05053197473, 0.06822496589, 0.05851797074, 0.01433599283, 0.03230298385, 0.06637396681},
{0.0444579512, 0.01557336503, 0.09314817364, -0.044113721, 0.005111787251, -0.001884724275, 0.02176250428, 0.01330231089, -0.01004072642, -0.02707838224, 0.007850390507, -0.02238829876, -0.002574707035, 0.005103116996, 0.01727154263, -0.2007423533, 0.07236268503, 0.0001269011602, 0.002159746644, 0.01059243778},
{-0.09480046389, -0.0008265840581, -0.01530023104, 0.006399090427, -0.001606056021, -0.0003589664291, -0.001991613184, 0.002204828557, 0.00112601328, -0.1484020177, 0.00344295715, 0.001239762867, 0.004393999428, -0.0003247878571, 0.001042702664, 0.02596605592, 0.05645800567, -0.0002231990317, 0.0002279227183, 0.1613325805},
{-0.06924141195, -0.01816245289, -0.08104005811, 0.08985697111, 0.002796590179, 0.01083740323, -0.06449599336, 0.01794514261, 0.01036809142, 0.0428350445, 0.006344722738, 0.02339134834, -0.01748667848, 0.001618591063, 0.006224864325, -0.05854130196, 0.1508372866, 0.0003073375766, -0.001437395222, -0.05295810172},
{-0.1463794892, 0.02029296324, 0.02615316895, -0.1031153856, -0.001834127445, -0.02589124657, 0.1107367385, 0.008485817284, 0.001060577919, 0.05530240733, -0.0003153350695, -0.03124002869, -0.01533984125, -0.002887173373, 0.002727874106, 0.06300929916, 0.07920438311, -0.0004133528241, -0.000116488734, -0.03944076085},
{-0.05558229087, 0.08935293782, 0.04869509589, 0.04856877989, -0.002538360477, 0.07651693958, -0.06342453535, -0.00777376246, -0.08570270267, 0.01943016474, -0.005995165269, -0.09157595009, -0.003977351557, -0.004400938637, -0.002329980569, 0.02979967701, -0.004772994859, -0.001440117953, 0.01795114942, -0.0008005935923},
{0.05807741645, 0.1465429242, -0.06724975334, 0.02159062347, -0.003390855183, -0.06829036786, 0.03520631903, -0.02766062718, 0.03485632707, -0.02436836692, -0.003975660036, -0.1009548864, 0.02456887654, 0.003817641171, -0.009062613402, -0.01043058066, 0.01651199514, -0.002104172208, -0.00872508521, -0.01495915463},
{0.02564617107, 0.02960554611, -0.0005235674877, 0.009892678173, -0.0004403417214, -0.02279910635, -0.003637683565, -0.01086345666, 0.012297218, 0.02633650143, 0.06282966784, -0.007344864999, -0.1386393631, -0.009938919434, -0.006553096823, -0.002451917883, -0.02431633806, -0.0006855403152, -0.001213838589, 0.0628002524},
{0.1136242825, -0.02080375718, -0.08802750967, -0.06531316372, -0.001666260583, 0.06846081717, 0.07007301248, -0.01713112937, -0.05900588795, -0.04497159138, 0.04222484637, 0.001290431785, -0.01550337252, -0.01553102164, -0.04363429852, 0.01600063778, 0.05787328926, -8.265841118e-05, 0.02870014573, -0.02657681215},
{0.01840541227, 0.006101590188, 0.01368080422, 0.02383751807, -0.009235168942, 0.01209943151, 0.02906782189, 0.01992384905, 0.001973235683, 0.0001753141542, -0.01796698382, 0.01887083963, -0.0006333588673, -0.02365277335, 0.01209445088, 0.01308086448, 0.01286727242, -0.1142035898, -0.01886991701, 0.002383387286},
{-0.01100105032, -0.04250695865, -0.02554356701, -0.05473632079, 0.007259064699, -0.03003724918, -0.07051526125, -0.06939439879, -0.002858830561, 0.05334304125, 0.1283924185, -0.05883473754, 0.02424304967, 0.09134510778, -0.002260033472, -0.01280041778, -0.002079883056, -0.02957493909, 0.05290385687, 0.05465710875},
{-0.01421274522, 0.02074863338, -0.01006411986, 0.03319995456, -5.371699269e-05, -0.1226604646, 0.02419847063, -0.004411687066, -0.08299118738, -0.003232309135, 0.0295403512, 0.09212856796, 0.007186356273, -0.02706936116, 0.0447317328, -0.01274357635, -0.01395862741, -0.0007153884868, 0.04767640013, -0.00729728327},
{-0.03797680968, 0.01280286509, -0.08614616553, -0.01781049963, 0.006743199901, 0.04208667755, 0.05991325708, 0.0358101566, -0.0152981671, 0.06885987925, -0.1171912048, -0.0001433366381, 0.0007433678425, 0.02893416406, 0.0746615136, -0.08182016471, -0.06581536578, -0.000181959765, 0.00167443595, 0.09015415668},
{0.035777268, -0.02139253448, -0.01137813538, -0.01954939203, -0.04028242802, -0.01777500032, -0.02106862264, 0.004651996583, -0.02824805813, 0.06618860062, 0.08437791758, -0.02533125946, 0.02806344655, -0.06970805798, 0.02328376969, 0.006929923333, 0.02751392122, 0.01148722813, -0.1113040433, 0.07776346001},
{0.06014297925, 0.00711674356, 0.02424493473, -0.0003246435316, -0.003212218476, -0.03257969054, -0.01072805771, -0.06892027924, -0.03326534128, 0.01558838624, -0.1379423768, 0.04292623057, -0.01375763233, 0.1112515377, -0.03510076082, 0.04531670713, 0.06170413486, 0.001820236821, -0.05979891872, 0.02551802851},
{0.03515069992, -0.02310847228, -0.004744935486, -0.02787717003, 0.1203832968, -0.03178473522, -0.04445111601, 0.05334957493, -0.01290386678, 0.003760641716, -0.03996642738, -0.04777677296, -0.002336892006, -0.03917715405, 0.01755598278, 0.03389088626, 0.02180780263, -0.004734020439, -0.01964539477, 0.01260807238},
{-0.04120428254, 0.0006271716498, -0.01688703579, 0.0168577691, 0.02102702094, 0.01295781834, 0.03541815979, 0.03968150445, -0.02073122711, -0.0693224735, 0.1169631424, -0.003225237658, -0.01280515661, 0.08717664266, 0.06297225079, -0.0129050178, -0.04693925077, -0.001776536754, -0.08407812138, -0.08380714022},
{0.03138655229, -0.09052573757, 0.008742022194, 0.06060593729, -0.03426076652, -0.04832468257, 0.04735628794, 0.1450465374, -0.01709111334, -0.002787942154, -0.03513813821, -0.1169029483, -0.008362649026, 0.03270980973, -0.0258776413, 0.01638786059, 0.004854998225, 0.00305477087, 0.02295754527, 0.00616929723},
{-0.04898722042, -0.01460879657, 0.00508708857, 0.07730497806, 0.04252420017, 0.004842325803, 0.09861807969, -0.05169447907, -0.009178209079, 0.03679081047, 0.04998537113, 0.00769330212, 0.01805447684, -0.00498723245, -0.1414841618, -0.0517028176, -0.03230723311, -0.0003289067264, -0.02363523072, 0.03801365472},
{-0.02047562162, 0.0693378178, -0.02101117885, -0.06841945875, -0.008609675727, -0.008866502716, -0.07185241332, 0.1670368436, -0.006358475817, 0.008114789138, 0.01847205842, 0.06700967949, 0.005966073762, 0.02318239241, -0.1055295854, -0.01980199748, -0.02003785382, -0.005933924302, -0.009653910336, 0.007430943497}
};
double JTTeigenvect[20][20] ={
{1, -0.592366593520456, 1.26647770789007, 0.886548263786341, 1.97187647935208, 0.623522602802228, -0.700599455245314, -0.243940332948806, 1.37262281583815, 0.132339564200332, -0.139152627888942, -0.151960565192892, -0.503558304887216, 0.401286734811512, 0.770512572823075, -0.334122413123515, -0.511333615314838, 0.406698878874955, -0.608502721368149, -0.273471289767494},
{0.999999999999997, -0.312377658232602, 0.0166238074664203, 0.350080045748139, -0.411529844419508, -1.50897131070414, -2.66123819501591, -0.423926476977996, -0.378336484172162, 0.0660455518422499, -0.8094195350236, 0.333963354053788, 0.255561154846341, -0.361215400358873, 0.137256366220071, 0.330673395557778, 0.011716686083756, -1.76586631688791, -0.273181041364839, 1.39412334862137},
{1, -2.24216930527457, 0.369264894195805, 1.87451602378843, -0.636468250238205, -0.9868563256527, 1.46556858621415, 0.00899677154544075, -1.92110640720711, 0.177708713779254, -0.583702764592654, -0.194393471138667, -2.06357463590868, -0.230553474503508, 0.561136806849582, 0.0814807258907599, -0.378589318590149, 0.204641736635929, 0.114156848605826, -0.50696503584266},
{1, 0.881194220629092, -0.128162853723553, -1.72482515732893, 2.08247494132467, -0.816826439094774, -0.390467169640111, -0.141069066537029, -1.18287162801248, 0.256957926983144, -1.03798170192714, 0.532166157869003, -0.35404969272057, -0.328728773598177, -0.0062353147433961, 0.397262115164214, 0.313630956986789, 1.17733856273331, 1.43960724124326, -1.36997017368483},
{1, -0.258154101781237, 0.0813229122708902, -0.135715809717887, 0.0936470572711403, 0.107928017952226, 0.155037549213443, 0.015875084986608, -0.0762936031627112, -0.25168314986691, 0.348019095706172, -0.00217685632466558, 0.338892895856344, -1.71249146198339, -0.155978598396295, -4.3371357011773, 0.989019559896644, -1.68264145260302, 2.00207815257825, -0.435839496079438},
{0.999999999999999, 0.0470079267000042, 0.00897683166227234, -0.259743004459053, 0.652881855399199, -1.60677663958138, 1.54207010413757, 0.405939264674604, 1.54811884497737, 0.162851316874628, -0.711212821866371, -2.45493328107362, 1.04461939816656, -0.373198084292936, -0.781310940835223, 0.565551800255901, 0.301006610925809, -1.17214282025618, 0.112594167029802, -0.221671139535885},
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