correlation_integrals.hpp

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#pragma once
 
#include <map>
#include <array>
#include <cmath>
 
#include "teqp/types.hpp"
#include "teqp/exceptions.hpp"
 
namespace teqp {
namespace SAFTpolar{
 
// |x| = sqrt(x^2), the latter is well-suited to differentiation
template<typename X>
inline auto differentiable_abs(const X& x){
    return forceeval(sqrt(x*x));
};
 
static const std::map<int, std::array<double, 12>> Luckas_J_coeffs = {
    {4,  {-1.38410152e00,  -7.05792933e-01, 2.60947023e00,  1.96828333e01, 1.13619510e01, -2.98510490e01,  -3.15686398e01, -2.00943290e01,  5.11029320e01, 1.44194150e01, 9.40061069e00,  -2.36844608e01}},
    {5,  {-6.89702637e-01, -1.62382602e-01, 1.16302441e00,  1.42067443e01, 4.59642681e00, -1.81421003e01,  -2.45012804e01, -8.42839734e00,  3.25579587e01, 1.16339969e01, 4.00080085e00,  -1.54419815e01}},
    {6,  {-4.57433648e-01, -4.74592642e-02, 7.36156406e-01, 1.19830560e01, 2.52201906e00, -1.40252699e01,  -2.15154325e01, -4.69572629e00,  2.59035512e01, 1.04390419e01, 2.24160266e00,  -1.24580635e01}},
    {7,  {-3.46551277e-01, -8.67899015e-03, 5.41729996e-01, 1.07102246e01, 1.58762511e00, -1.19085356e01,  -1.98486869e01, -2.98067526e00,  2.25425086e01, 9.79650295e00, 1.42953263e00,  -1.09749041e01}},
    {8,  {-2.85932401e-01,  7.44866141e-03, 4.35471488e-01, 9.87890138e00, 1.08489226e00, -1.06280961e01,  -1.88507949e01, -2.04803671e00,  2.06131402e01, 9.44834359e00, 9.88551760e-01, -1.01576036e01}},
    {9,  {-2.50931500e-01,  1.49604396e-02, 3.71768229e-01, 9.29877256e00, 7.84100755e-01, -9.78235175e00, -1.82609129e01, -1.48667167e00,  1.94537822e01, 9.28527644e00, 7.24545266e-01, -9.70374243e00}},
    {10, {-2.30585563e-01,  1.86890174e-02, 3.31660880e-01, 8.88275358e00, 5.90996555e-01, -9.19786291e00, -1.79530632e01, -1.12502567e00,  1.87717642e01, 9.25235661e00, 5.55909350e-01, -9.47729033e00}},
    {11, {-2.19221482e-01,  2.05982865e-02, 3.05823216e-01, 8.58399185e00, 4.60555635e-01, -8.78667564e00, -1.78552884e01, -8.80186074e-01, 1.84146650e01, 9.31691675e00, 4.43027169e-01, -9.40608814e00}},
    {12, {-2.13591301e-01,  2.15809377e-02, 2.89113218e-01, 8.37291362e00, 3.68864477e-01, -8.49747359e00, -1.79188678e01, -7.07751483e-01, 1.82906357e01, 9.45598216e00, 3.64636215e-01, -9.44579903e00}},
    {13, {-2.11696363e-01,  2.20767096e-02, 2.78453228e-01, 8.23384704e00, 3.02478832e-01, -8.30238277e00, -1.81183432e01, -5.82685843e-01, 1.83497132e01, 9.65764061e00, 3.08765033e-01, -9.57226243e00}},
    {14, {-2.12238116e-01,  2.23157164e-02, 2.71883622e-01, 8.15208365e00, 2.53073339e-01, -8.17919021e00, -1.84273649e01, -4.89407317e-01, 1.85502740e01, 9.90906951e00, 2.67965960e-01, -9.76495200e00}},
    {15, {-2.14335965e-01,  2.24240261e-02, 2.68094773e-01, 8.11899188e00, 2.15506735e-01, -8.11465705e00, -1.88310645e01, -4.18309476e-01, 1.88679367e01, 1.02033085e01, 2.37674032e-01, -1.00120648e01}},
};
 
 
class LuckasJIntegral{
public:
    const int n;
    const std::array<double, 12> a;
    double a00,a01,a02,a10,a11,a12,a20,a21,a22,a30,a31,a32;
    
    LuckasJIntegral(int n) : n(n), a(Luckas_J_coeffs.at(n)){
        a00 = a[0]; a01 = a[1]; a02 = a[2];
        a10 = a[3]; a11 = a[4]; a12 = a[5];
        a20 = a[6]; a21 = a[7]; a22 = a[8];
        a30 = a[9]; a31 = a[10]; a32 = a[11];
    }
    
    template<typename TType, typename RhoType>
    auto get_J(const TType& Tstar, const RhoType& rhostar) const{
        double Z_1 = 0.3 + 0.05*n;
        double Z_2 = 1.0/n;
        RhoType A_0 = a00 + a10*rhostar + a20*rhostar*rhostar + a30*rhostar*rhostar*rhostar;
        RhoType A_1 = a01 + a11*rhostar + a21*rhostar*rhostar + a31*rhostar*rhostar*rhostar;
        RhoType A_2 = a02 + a12*rhostar + a22*rhostar*rhostar + a32*rhostar*rhostar*rhostar;
        std::common_type_t<TType, RhoType> out = (A_0 + A_1*pow(Tstar, Z_1) + A_2*pow(Tstar, Z_2))*exp(1.0/(Tstar + 4.0/pow(differentiable_abs(log(forceeval(rhostar/sqrt(2.0)))), 3.0)));
        return out;
    }
};
 
static const std::map<std::tuple<int, int>, std::array<double, 16>> Luckas_K_coeffs = {
    {{222,333},{  1.23746712e-02,  1.90127007e-04,  5.92861480e-03,  1.88387469e-04,  1.51499090e-01, -4.03661304e-03, -1.71653218e-01,  7.44958473e-02,  4.61939219e-01,  7.61527540e-03, -1.30641988e00,   7.63483402e-01,  7.36061418e-03, -3.14115085e-03, -2.62332295e-01,  2.99061150e-01}},
    {{233,344},{  3.51281055e-03,  2.12654833e-04,  3.26699985e-03,  1.71420492e-04,  9.78591707e-02, -3.24426472e-03, -9.85906322e-02,  4.31053752e-02,  2.68515490e-01,  6.25909413e-03, -7.46179517e-01,  4.10644114e-01,  1.28223189e-01, -2.54348393e-03, -5.40215100e-01,  4.50896967e-01}},
    {{334,445},{ -1.77119569e-03, -2.60437070e-04, -2.65044611e-03, -1.96937245e-04, -8.97801454e-02,  2.93120169e-03,  8.77755068e-02, -3.76799716e-02, -2.19892289e-01, -5.73110168e-03,  6.37326406e-01, -3.52780095e-01, -1.57228990e-01,  2.04489194e-03,  5.59739399e-01, -4.42956307e-01}},
    {{444,555},{  1.07862851e-03,  2.88647260e-04,  2.07369614e-03,  1.79600129e-04,  7.57084957e-02, -2.28761197e-03, -7.33670248e-02,  3.12736172e-02,  1.73518964e-01,  4.54174801e-03, -5.14488122e-01,  2.85483011e-01,  1.71670939e-01, -1.07503182e-03, -5.51880129e-01,  4.16887229e-01}}
};
 
class LuckasKIntegral{
public:
    
    const int n1, n2;
    const std::array<double, 16> a;
    double a00, a01, a02, a03, a10, a11, a12, a13, a20, a21, a22, a23, a30, a31, a32, a33;
    
    LuckasKIntegral(const int n1, const int n2) : n1(n1), n2(n2), a(Luckas_K_coeffs.at({n1, n2})){
        a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
        a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
        a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
        a30 = a[12]; a31 = a[13]; a32 = a[14]; a33 = a[15];
    }
    
    template<typename TType, typename RhoType>
    auto get_K(const TType& Tstar, const RhoType& rhostar) const{
        double Z_1 = 2.0;
        double Z_2 = 3.0;
        double Z_3 = 4.0;
        RhoType b_0 = a00 + a10*rhostar + a20*rhostar*rhostar + a30*rhostar*rhostar*rhostar;
        RhoType b_1 = a01 + a11*rhostar + a21*rhostar*rhostar + a31*rhostar*rhostar*rhostar;
        RhoType b_2 = a02 + a12*rhostar + a22*rhostar*rhostar + a32*rhostar*rhostar*rhostar;
        RhoType b_3 = a03 + a13*rhostar + a23*rhostar*rhostar + a33*rhostar*rhostar*rhostar;
        std::common_type_t<TType, RhoType> out = b_0 + b_1*Tstar + b_2*pow(exp(pow(1.0-rhostar/sqrt(2.0),Z_3)), Z_1) + b_3*pow(exp(pow(1.0-rhostar/sqrt(2.0),Z_3)), Z_2);
        return out;
    }
};
 
static const std::map<int, std::array<double, 6>> GubbinsTwu_J_coeffs = {
    {4, {-0.257431, 0.439229, 0.414783, -0.457019, -0.145520,  0.299666}},
    {5, {-0.396724, 0.690721, 0.628935, -0.652622, -0.201462, -0.231635}},
    {6, {-0.488498, 0.863195, 0.761344, -0.750086, -0.218562, -0.538463}},
    {7, {-0.556600, 0.995172, 0.852903, -0.804710, -0.214736, -0.761700}},
    {8, {-0.611295, 1.103390, 0.921359, -0.838804, -0.197999, -0.940714}},
    {9, {-0.657866, 1.196189, 0.975721, -0.862346, -0.172526, -1.091678}},
    {10, {-0.698790, 1.278054, 1.020604, -0.880027, -0.140749, -1.222733}},
    {11, {-0.735855, 1.351533, 1.058986, -0.894024, -0.104174, -1.338626}},
    {12, {-0.769504, 1.418223, 1.092052, -0.905347, -0.063730, -1.442398}},
    {13, {-0.800934, 1.479538, 1.121453, -0.914864, -0.020150, -1.536070}},
    {14, {-0.829779, 1.535822, 1.147161, -0.922381,  0.026157, -1.621183}},
    {15, {-0.856655, 1.587957, 1.169885, -0.928269,  0.074849, -1.698853}},
    {16, {-0.881757, 1.636402, 1.190082, -0.932668,  0.125590, -1.769898}},
    {17, {-0.994998, 1.681421, 1.207610, -0.935419,  0.178283, -1.835070}},
    {18, {-0.926828, 1.723393, 1.223088, -0.936667,  0.232649, -1.894899}},
    {19, {-0.946773, 1.762571, 1.236007, -0.936403,  0.288687, -1.949858}},
    {20, {-0.965248, 1.799170, 1.246887, -0.934650,  0.346207, -2.000344}},
    {21, {-0.982191, 1.833319, 1.255610, -0.931384,  0.405158, -2.046682}},
    {22, {-0.997939, 1.865462, 1.262618, -0.926907,  0.465360, -2.089104}},
    {23, {-1.012232, 1.895591, 1.267649, -0.921117,  0.526812, -2.127879}},
    {24, {-1.025464, 1.924001, 1.271137, -0.914236,  0.589374, -2.163174}},
    {15, {-1.037283, 1.950746, 1.272812, -0.906279,  0.652984, -2.195140}},
    {16, {-1.048171, 1.976055, 1.273152, -0.897398,  0.717529, -2.223942}},
    {17, {-1.058118, 2.000177, 1.272334, -0.887913,  0.782867, -2.249616}},
    {18, {-1.067379, 2.023204, 1.270456, -0.877745,  0.848994, -2.272369}},
    {19, {-1.075455, 2.044986, 1.267349, -0.866935,  0.915713, -2.292167}},
    {30, {-1.683352, 2.066474, 1.264000, -0.856364,  0.982900, -2.309055}},
    {31, {-1.090542, 2.087049, 1.259912, -0.845434,  1.050527, -2.323154}},
    {32, {-1.097422, 2.107200, 1.255618, -0.834664,  1.118425, -2.334465}},
    {33, {-1.104213, 2.127189, 1.251457, -0.824397,  1.186445, -2.342962}},
    {34, {-1.110868, 2.147097, 1.247470, -0.814738,  1.254509, -2.348686}},
    {35, {-1.117701, 2.166994, 1.244047, -0.805790,  1.322469, -2.351658}},
    {36, {-1.124468, 2.186826, 1.241051, -0.797564,  1.390261, -2.351903}}
};
 
class GubbinsTwuJIntegral{
public:
    const int n;
    const std::array<double, 6> a;
    double A, B, C, D, E, F;
    
    GubbinsTwuJIntegral(int n) : n(n), a(GubbinsTwu_J_coeffs.at(n)){
        A = a[0]; B = a[1]; C = a[2]; D = a[3]; E = a[4]; F = a[5];
    }
    
    template<typename TType, typename RhoType>
    auto get_J(const TType& Tstar, const RhoType& rhostar) const{
        std::common_type_t<TType, RhoType> out = exp(A*rhostar*rhostar*log(Tstar) + B*rhostar*rhostar + C*rhostar*log(Tstar) + D*rhostar + E*log(Tstar) + F);
        return out;
    }
};
 
static const std::map<std::tuple<int, int>, std::array<double, 6>> GubbinsTwu_K_coeffs = {
    {{222,333}, {-1.050534, 1.747476, 1.749366, -1.999227, -0.661046, -3.028720}},
    {{233,344}, {-1.309550, 2.249120, 2.135877, -2.278530, -0.773166, -3.704690}},
    {{334,445}, {-1.490116, 2.619997, 2.404319, -2.420706, -0.829466, -3.930928}},
    {{444,555}, {-1.616385, 2.881007, 2.577600, -2.484990, -0.828596, -4.175589}},
    {{666,777}, {-1.940503, 3.552034, 2.940925, -2.593808, -0.724353, -4.899975}}
};
 
class GubbinsTwuKIntegral{
public:
    
    const int n1, n2;
    const std::array<double, 6> a;
    double A, B, C, D, E, F;
    double sign_term;
    
    GubbinsTwuKIntegral(const int n1, const int n2) : n1(n1), n2(n2), a(GubbinsTwu_K_coeffs.at({n1, n2})){
        A = a[0]; B = a[1]; C = a[2]; D = a[3]; E = a[4]; F = a[5];
        
        // The {334, 445} term has opposite sign to the others
        sign_term = ((n1==334) && (n2==445) ? -1 : 1);
    }
    
    template<typename TType, typename RhoType>
    auto get_K(const TType& Tstar, const RhoType& rhostar) const{
        std::common_type_t<TType, RhoType> out = sign_term*exp(A*rhostar*rhostar*log(Tstar) + B*rhostar*rhostar + C*rhostar*log(Tstar) + D*rhostar + E*log(Tstar) + F);
        return out;
    }
};
 
 
 
//Type    R^2    a[0, 0]    a[0, 1]    a[0,2]    a[0,3]    a[1, 0]    a[1, 1]    a[1,2]    a[1,3]    a[2, 0]    a[2, 1]    a[2,2]    a[2,3]    a[3, 0]    a[3, 1]    a[3,2]    a[3,3]    a[4, 0]    a[4, 1]    a[4,2]    a[4,3]    b[0, 0]    b[0, 1]    b[0,2]    b[1, 0]    b[1, 1]    b[1,2]    b[2, 0]    b[2, 1]    b[2,2]    b[3, 0]    b[3, 1]    b[3,2]    b[4, 0]    b[4, 1]    b[4,2]
static const std::map<int, std::array<double, 35>> Gottschalk_J_coeffs = {
    {{4}, {9.20762061490718E-01, 3.65233141807771E-01, 1.07871599009702E+00, 1.46531395339295E-06, -3.13549715576067E+01, -2.14347171035042E+02, -4.46936442221474E+02, -2.52046886389241E-05, 9.59476543889466E+01, 6.72066160042726E+02, 1.41943517935122E+03, 9.03007555165018E-05, -9.58398037269371E+01, -7.03598871905455E+02, -1.51155093398986E+03, -1.01437944136810E-04, 3.21143191531758E+01, 2.49283638814592E+02, 5.45458916686374E+02, 3.68350682469709E-05, -7.33315599725484E-02, 7.17782493862785E-01, -1.07882642679631E+00, 4.08068473857470E+01, -2.32614867704771E+02, 4.46937747749130E+02, -1.34367887089787E+02, 7.47459457204644E+02, -1.41943986985120E+03, 1.48945273699473E+02, -8.08058129527236E+02, 1.51155630097149E+03, -5.59295311120630E+01, 2.96215796243915E+02, -5.45460908392279E+02}},
    {{5}, {7.78317650769383E-01, 5.99206004305284E-01, 1.51505659599139E+00, 2.07056321821513E-06, -6.42594369009722E+00, -6.77626651470902E+01, -1.57366926125767E+02, -2.37414367157603E-05, 2.17188616679221E+01, 2.24978201318131E+02, 5.26347478618125E+02, 8.01470444174510E-05, -2.32101308927474E+01, -2.52180339267828E+02, -5.97690123563652E+02, -8.70761423184869E-05, 8.99504653938558E+00, 9.92714679182362E+01, 2.36531170237292E+02, 3.04151384860261E-05, -1.22862207731153E-01, 9.21021403876641E-01, -1.51520172786190E+00, 1.76561517446869E+01, -8.96285624361416E+01, 1.57368161594690E+02, -6.05832340349862E+01, 3.01449444216860E+02, -5.26351643127702E+02, 7.06451918826372E+01, -3.45599503965135E+02, 5.97694705736524E+02, -2.82773060418931E+01, 1.37292180369747E+02, -2.36532795134605E+02}},
    {{6}, {7.84353476631425E-01, 6.85720448356048E-01, 1.62670627229158E+00, 2.54936277034233E-06, 4.47099585508689E+00, -3.29222156231796E+00, -2.96976509772110E+01, -2.34149051622900E-05, -8.52898508169395E+00, 4.00527157292150E+01, 1.54598567397736E+02, 7.63141143915834E-05, 3.60780542310039E+00, -7.97013837912071E+01, -2.43669064947076E+02, -8.12331954077934E-05, 1.77013221710562E+00, 4.84574605762221E+01, 1.28748817040483E+02, 2.76192881583106E-05, -1.32142877177911E-01, 9.46992395582885E-01, -1.62688108898392E+00, 7.38465356236924E+00, -2.64295672330205E+01, 2.96988758329901E+01, -2.93410584260195E+01, 1.14622191952606E+02, -1.54602540528670E+02, 3.92213457881652E+01, -1.64050494048192E+02, 2.43673328746399E+02, -1.79349649900422E+01, 8.03201352469139E+01, -1.28750280199986E+02}},
    {{7}, {8.35923369473595E-01, 8.36677758858304E-01, 1.84012238540570E+00, 2.95158919217436E-06, 1.04308480601121E+01, 3.22575024923935E+01, 4.09254052998227E+01, -2.35327254022092E-05, -2.39853372239537E+01, -5.60420962515534E+01, -3.99584884375199E+01, 7.48886963971160E-05, 1.57078975270853E+01, 1.77837968441997E+00, -7.34290355928896E+01, -7.85879121919987E-05, -6.34595861538581E-01, 2.85721518805557E+01, 8.43682899717243E+01, 2.61866011224344E-05, -1.41092601741133E-01, 1.01019042121228E+00, -1.84032278125301E+00, 1.65577241238338E+00, 8.64349862727415E+00, -4.09241683798187E+01, -1.26779405410039E+01, 1.61586056544664E+01, 3.99545800444195E+01, 2.34403357454985E+01, -7.52869363354067E+01, 7.34331560029303E+01, -1.32014925766845E+01, 5.58228957439797E+01, -8.43696689061774E+01}},
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    {{36}, {1.94071903395404E+00, 4.30815630128459E+00, 7.41945486225346E+00, 8.04129819154619E-06, 3.12795677114849E+01, 1.54720456662477E+02, 2.82910138946970E+02, -4.51185370132462E-05, -6.76623878561680E+01, -3.26610593605394E+02, -5.89663763708538E+02, 1.30064679999137E-04, 3.14642018299911E+01, 1.33685768145537E+02, 2.24699835988089E+02, -1.28806673892190E-04, 7.67986766874738E+00, 5.20159122266596E+01, 1.07693298076419E+02, 3.96257342166686E-05, -3.83611089495781E-01, 3.12627897732626E+00, -7.41996323155748E+00, -1.77092249651606E+01, 1.28145532684806E+02, -2.82907795262461E+02, 3.50443877287770E+01, -2.62931112874138E+02, 5.89657091847996E+02, -9.31746233172336E+00, 9.08979636154349E+01, -2.24693319725730E+02, -9.72592470392138E+00, 5.57106237961232E+01, -1.07695254916667E+02}},
 
};
 
class GottschalkJIntegral{
public:
    const int n;
    const std::array<double, 35> ab;
    
    GottschalkJIntegral(int n) : n(n), ab(Gottschalk_J_coeffs.at(n)){}
    
    template<typename TType, typename RhoType>
    auto get_J(const TType& Tstar, const RhoType& rhostar) const{
        std::common_type_t<TType, RhoType> summer = 0.0;
        for (auto i = 0; i <= 4; ++i){
            for (auto j = 0; j <= 3; ++j){
                auto I = 4*i + j;
                summer += ab[I]*pow(rhostar, i)*pow(Tstar, j);
            }
        }
        for (auto i = 0; i <= 4; ++i){
            for (auto j = 0; j <= 2; ++j){
                auto I = 20 + 3*i + j;
                summer += ab[I]*pow(rhostar, i)*pow(Tstar, j)*exp(1.0/Tstar);
            }
        }
        return pow(summer, n-2);
    }
};
 
 
 
// Type, a[0,1], a[0,2], a[1,1], a[1,2], a[2,1], a[2,2], a[3,1], a[3,2], b[0,1], b[0,2], b[1,1], b[1,2], b[2,1], b[2,2], b[3,1], b[3,2], c[0,1], c[0,2], c[0,3], c[0,4], c[1,0], c[1,1], c[1,2], c[1,3], c[2,0], c[2,1], c[2,2], c[2,3], c[3,0], c[3,1], c[3,2], c[3,3], c[4,0], c[4,1], c[4,2], c[4,3], c[5,0], c[5,1], c[5,2], c[5,3]
static const std::map<std::tuple<std::tuple<int,int,int>, std::tuple<int,int,int>>, std::array<double, 40>> Gottschalk_K_coeffs = {
    {{{2,2,2},{3,3,3}}, {5.42444082407911E+00, 1.99461721851827E+00, -7.79943499574988E+00, -5.95306423355890E+00, 1.14672051901995E+00, 5.96687355992124E+00, 1.57892985819129E+00, -1.99235454796223E+00, -5.41856353157736E+00, -1.99001117059474E+00, 1.08221237311497E+01, 2.88930400287336E+00, -7.71557411635195E+00, 5.18908612078444E-03, 2.12180709078436E+00, -1.09482382065437E+00, 6.36909816323590E-03, 2.79472187550309E-04, 1.92082140326594E-06, -1.74086067501819E-07, 3.92286590760404E-02, 2.01914799518260E-03, -1.24074155157559E-04, 2.80164785188307E-06, 6.19238462016263E-01, 7.17311000046791E-04, -4.51094217237624E-05, -2.01742036513682E-07, -5.55505371928574E-01, -1.49546202491092E-02, 9.02847562166521E-04, -1.62118687038889E-05, -9.31563262615475E-02, 1.93800947967539E-02, -1.18316966937579E-03, 2.24359377558566E-05, 3.31240818053268E-02, -6.81951409579061E-03, 4.25234801807147E-04, -8.28079417586071E-06}},
    {{{2,3,3},{3,4,4}}, {3.99742731639367E+00, 1.23579222175592E+00, -5.82727703962485E+00, -3.60508169240370E+00, 1.28231084254979E+00, 3.54340888289165E+00, 8.02274046417593E-01, -1.16362434398544E+00, -3.99685528163714E+00, -1.23243185481745E+00, 7.66286420532143E+00, 1.62072861591476E+00, -5.13713300256105E+00, 1.46021389124403E-01, 1.31704487280630E+00, -6.64215770115759E-01, 3.10121371171748E-03, 1.86206269763217E-04, 3.18435844304192E-06, -1.63867186774153E-07, 1.46001939047032E-01, 1.70625038283980E-03, -1.11890743211568E-04, 2.65557825596483E-06, 1.88071510223345E-01, -1.52422445555933E-03, 1.46336372199072E-04, -4.63927881946733E-06, -2.72182167645867E-01, -4.75990045635550E-03, 1.98565515993789E-04, -1.12062570555131E-06, -3.98107863229894E-02, 8.08708292057630E-03, -4.32515946570324E-04, 6.62645581034702E-06, 1.52986005217160E-02, -3.10128564214180E-03, 1.77857319979180E-04, -3.06965046638737E-06}},
    {{{2,4,4},{3,5,5}}, {7.66792089283848E-01, 2.75297951453362E-01, -1.14961767414510E+00, -8.33798059992107E-01, 3.39181596901623E-01, 8.59623929728455E-01, 1.90773779211133E-01, -2.96619248685997E-01, -7.66001709604301E-01, -2.74735677874936E-01, 1.56612732669654E+00, 4.08336841752989E-01, -1.27873004072718E+00, -4.34059094383595E-03, 3.77088433771990E-01, -1.96035798884472E-01, 1.30948394348354E-04, 1.06139307725294E-04, -1.55856479654891E-06, 1.49407162096004E-08, 9.60875316807800E-03, 1.83916452031763E-04, -3.05479964580661E-06, -4.31169678964768E-08, 8.51673307442435E-02, 8.37068146866005E-04, -6.89417943049662E-05, 1.78242509581761E-06, -6.21438631057473E-02, -3.04535608194716E-03, 2.20102808514677E-04, -5.14135739634171E-06, -1.45715095719363E-02, 3.33431639032812E-03, -2.32609567589275E-04, 5.24534888776091E-06, 5.30333556533054E-03, -1.15021340573145E-03, 7.93113478132349E-05, -1.76212435918817E-06}},
    {{{2,5,5},{3,6,6}}, {-1.87888594114787E+00, -3.98778496314823E-01, 2.78121043514766E+00, 1.07393815987908E+00, -5.82709875936336E-01, -9.46224511668149E-01, -1.84017464491590E-01, 2.73586115410880E-01, 1.88070012863321E+00, 3.97610068626671E-01, -3.32288593227971E+00, -3.59910905349272E-01, 1.52895362047230E+00, -1.87651821947185E-01, -1.93395713326451E-01, 9.70093774899509E-02, -1.67340512692621E-03, 5.75834788258873E-05, -6.99207163596071E-06, 1.72895835960648E-07, -1.68871652703438E-01, -1.18620808855092E-03, 8.69478929524077E-05, -2.08630774341105E-06, 1.72290885137602E-01, 3.52045298153230E-03, -2.86781557559445E-04, 7.18782667350350E-06, 1.97322734262047E-02, -4.36164922587827E-03, 3.83373415672240E-04, -1.01224194253523E-05, -4.56568358850074E-03, 1.94446731466216E-03, -2.04333883106063E-04, 5.91427305521251E-06, -8.36681540227123E-04, -2.00506952873583E-04, 3.47435171985320E-05, -1.18319408899513E-06}},
    {{{3,3,4},{4,4,5}}, {-4.21691301848977E+00, -1.16439325280820E+00, 6.03076249607683E+00, 3.31749501933008E+00, -1.38852182725105E+00, -3.18924643368820E+00, -6.77570732417047E-01, 1.02659354200590E+00, 4.21819503000668E+00, 1.16111673692155E+00, -7.72636214133521E+00, -1.38976901618504E+00, 4.81781255315698E+00, -2.23724748325620E-01, -1.14526858817650E+00, 5.75038384512084E-01, -3.13798823141918E-03, -1.55466617345853E-04, -7.37871412696050E-06, 2.64062708357487E-07, -2.27498081628574E-01, -2.18661192717513E-03, 1.53323548592840E-04, -3.79011880542242E-06, -4.49432271819262E-02, 3.51094733294940E-03, -3.41099016003576E-04, 9.87987234529542E-06, 2.17337788297072E-01, 2.66965317505575E-04, 1.86202219962895E-04, -8.77928754274318E-06, 2.29602946730767E-02, -4.42138580395699E-03, 1.29829969955861E-04, 1.05666955361128E-06, -1.09807185048123E-02, 2.12266918209122E-03, -9.64983334262941E-05, 9.97183436130033E-07}},
    {{{3,4,5},{4,5,6}}, {-1.87855990843247E+00, -5.75022152153909E-01, 2.56326947679373E+00, 1.66202221341208E+00, -5.75969899254094E-01, -1.63807221446864E+00, -3.78452161265661E-01, 5.42906220485095E-01, 1.87899815614151E+00, 5.73413309667397E-01, -3.42230152470312E+00, -7.34559024393395E-01, 2.38025184286029E+00, -5.07481198955490E-02, -6.45580635846515E-01, 3.32460131454282E-01, -1.22971525041235E-03, -1.27068315490571E-04, -4.25980434500255E-06, 1.55615720658725E-07, -6.62090575792389E-02, -1.21573491901178E-03, 8.32731857639620E-05, -2.09727273955416E-06, -1.27600488929121E-01, 1.25532790674025E-03, -1.60397196949211E-04, 5.07160737707647E-06, 1.37753294972694E-01, 1.37209920872661E-03, 4.15123343754816E-05, -3.86928887350442E-06, 1.87254939648341E-02, -3.65839285590086E-03, 1.35891765079873E-04, -5.10958487388577E-07, -9.05447008188625E-03, 1.62841427456277E-03, -7.78079416794263E-05, 9.84642187550318E-07}},
    {{{3,5,6},{4,6,7}}, {5.38335404165607E-02, -1.65741037838703E-02, -1.33814036659934E-01, 6.19488310784084E-02, 3.65326991790176E-02, -8.19250914905983E-02, -3.01748955242906E-02, 3.46504157129119E-02, -5.40679568040414E-02, 1.65229992005511E-02, 1.00507102621880E-01, -4.91543004775631E-02, 7.13948616025876E-02, 3.06024072086538E-02, -6.33515239163259E-02, 3.32898983440077E-02, -9.74942651884560E-06, -4.30427313575326E-05, 4.30310988368452E-07, -9.40021705693541E-09, 2.03658137889129E-02, -7.06339662172058E-05, -2.20187760692210E-06, 1.46162457146041E-07, -5.63254788784857E-02, -2.04018244825023E-04, 2.64741552615823E-05, -9.28263294489165E-07, 2.17230134324291E-02, 5.67459951285132E-04, -6.15481638805597E-05, 1.93214021172590E-06, 4.65538957661885E-03, -7.29448873404259E-04, 6.32512865058604E-05, -1.77975109902218E-06, -2.18411916118892E-03, 3.07843071190017E-04, -2.32981002727147E-05, 6.00746707589970E-07}},
    {{{4,4,6},{5,5,7}}, {2.96764260657850E+00, 7.03092275890737E-01, -4.22799276319446E+00, -1.93798240899941E+00, 9.75913428063972E-01, 1.79126747499097E+00, 3.56756102281384E-01, -5.53623607171459E-01, -2.96955048327906E+00, -7.01234547867752E-01, 5.20683785048234E+00, 7.24538047246824E-01, -2.82320489117913E+00, 2.16237222473152E-01, 5.34316750117956E-01, -2.73623100163602E-01, 2.51067694055481E-03, 6.48121319346496E-05, 1.03813558872693E-05, -2.72926955102890E-07, 2.30022151841588E-01, 1.96394886387731E-03, -1.29387918388819E-04, 2.98540598178787E-06, -1.38590452460763E-01, -4.03811614043725E-03, 3.52382867454668E-04, -8.69687788260969E-06, -6.99559346356186E-02, 3.66886832331064E-03, -3.69164793734705E-04, 9.91160660064894E-06, -8.03236996487208E-03, 5.40971867915539E-04, 7.27854360508128E-05, -3.27263850871172E-06, 9.38208592331486E-03, -1.06228828205759E-03, 3.69836086799339E-05, -2.71732190829232E-07}},
    {{{4,5,7},{5,6,8}}, {1.42666820960381E+00, 3.45017865101772E-01, -1.96247550830271E+00, -9.46309065663811E-01, 4.18261135698539E-01, 8.72297454873067E-01, 1.80511045525248E-01, -2.68920187738143E-01, -1.42778416603253E+00, -3.44083083639850E-01, 2.44824471854885E+00, 3.54124895173016E-01, -1.33897167236516E+00, 9.82706489201847E-02, 2.71801448726778E-01, -1.36410348751957E-01, 1.49635868970185E-03, 2.06044447958276E-05, 9.64997907128668E-06, -2.57887631481684E-07, 1.02390983909847E-01, 1.58582512677763E-03, -1.18610853006776E-04, 3.09612761642116E-06, -3.36211720100163E-02, -4.08798525378858E-03, 3.98633052642793E-04, -1.10581010597377E-05, -5.54837181394803E-02, 5.29410031892766E-03, -5.57039406867244E-04, 1.63744825744623E-05, -4.50327460474820E-03, -1.74326489817204E-03, 2.91984200123208E-04, -9.85337179907661E-06, 8.13232243982234E-03, -1.87075034285800E-04, -4.14164874759782E-05, 1.94084307164858E-06}},
    {{{5,5,8},{6,6,9}}, {-2.45313680665222E+00, -5.03961693707401E-01, 3.61542108831159E+00, 1.34553581412146E+00, -9.00540909113099E-01, -1.18353980218140E+00, -1.81976304349185E-01, 3.43662749685603E-01, 2.45462386133280E+00, 5.02920854569119E-01, -4.28325510571952E+00, -4.36862799852705E-01, 2.05651578318504E+00, -2.39451761124711E-01, -2.83796201602616E-01, 1.39881038940765E-01, -1.88308167853915E-03, 1.12147181018812E-06, -1.44167141323138E-05, 3.79021486968717E-07, -2.35933494539367E-01, -2.18182485306358E-03, 1.62894043457942E-04, -4.50008247306596E-06, 2.46819798294457E-01, 6.47152799012847E-03, -6.06575109311945E-04, 1.73646290143768E-05, -5.69627938667923E-03, -9.76232489964938E-03, 9.26177434500812E-04, -2.75112120711887E-05, 9.05740553617230E-03, 4.49085125154577E-03, -5.49244411590428E-04, 1.79584150079129E-05, -1.47595392735166E-02, -3.76632235166816E-04, 1.02880075515404E-04, -4.00772991951897E-06}},
    {{{4,4,4},{5,5,5}}, {2.52469317017544E+00, 8.26177202122772E-01, -3.23475676438786E+00, -2.38752562438813E+00, 6.64751555690522E-01, 2.36720544055216E+00, 5.61020579897902E-01, -7.90752294769291E-01, -2.52563549516801E+00, -8.23601865216396E-01, 4.49270434521372E+00, 1.07436718641049E+00, -3.33558776232313E+00, 2.60645228363244E-02, 9.96483096208423E-01, -5.04055524736721E-01, 2.19308744326541E-03, 1.73436487656116E-04, 8.83524899927144E-06, -3.03344595365151E-07, 5.00925420993048E-02, 2.27928307397880E-03, -1.64388472223847E-04, 4.21196769901678E-06, 3.02727654223290E-01, -3.58144672504402E-03, 3.98974204945052E-04, -1.19830744460333E-05, -2.56870885978387E-01, 7.83095522029698E-04, -3.32816774037648E-04, 1.33383686051992E-05, -2.04241801271120E-02, 3.34064037151345E-03, 2.32132740739504E-06, -4.98030179368835E-06, 1.10108370256734E-02, -1.81425261633730E-03, 5.80093554272687E-05, 1.39552290257640E-07}},
    {{{4,5,5},{5,6,6}}, {2.73820204864218E+00, 7.00346534765638E-01, -3.69680446680593E+00, -1.93794572233433E+00, 8.25216049483546E-01, 1.81783550868196E+00, 3.72288286378053E-01, -5.73134804753511E-01, -2.74013224757890E+00, -6.98324464420398E-01, 4.69899890466331E+00, 7.54355332066654E-01, -2.77229320850403E+00, 1.55878886186388E-01, 6.36364810787289E-01, -3.16236796226066E-01, 2.79237676231657E-03, 7.52148076587529E-05, 1.39103460900121E-05, -3.88906729643374E-07, 1.74680215860077E-01, 2.62776627228451E-03, -1.92606222849564E-04, 4.85224043818134E-06, 3.94069617776020E-03, -6.21457325163260E-03, 5.98871575505814E-04, -1.62906364820491E-05, -1.36811818053603E-01, 7.09867493986490E-03, -7.74785192015546E-04, 2.27080125814711E-05, -3.21473595433954E-04, -1.79464065798033E-03, 3.65711004601243E-04, -1.27246062370887E-05, 7.22997515996539E-03, -4.53033813023508E-04, -4.11409808893549E-05, 2.27901440368552E-06}},
    {{{4,6,6},{5,7,7}}, {1.29384111976256E+00, 3.01517415634568E-01, -1.76756306901941E+00, -8.17177638396490E-01, 4.06092887383488E-01, 7.45911581200192E-01, 1.39258891654649E-01, -2.28144489592101E-01, -1.29462075268880E+00, -3.00788030952428E-01, 2.18542099110323E+00, 2.94503416259083E-01, -1.18187057671453E+00, 9.11775908280628E-02, 2.35930048111630E-01, -1.15561543388573E-01, 1.23370962460381E-03, 3.06126369696466E-05, 8.49249637361334E-06, -2.25826798863090E-07, 1.01270814266103E-01, 1.41550535056254E-03, -1.06540811690883E-04, 2.74608894832916E-06, -4.58219033219442E-02, -3.82736622037145E-03, 3.71623212815945E-04, -1.00620224936095E-05, -4.36422521174610E-02, 5.37359451521211E-03, -5.43490638078690E-04, 1.53057095265201E-05, 1.40350030776433E-03, -2.31316350038478E-03, 3.09825182261389E-04, -9.57845012022372E-06, 4.48634087204837E-03, 1.35983530300042E-04, -5.52343464494581E-05, 2.03145282341050E-06}},
    {{{5,5,6},{6,6,7}}, {-3.70136634997501E+00, -8.10855126735133E-01, 5.20584279748819E+00, 2.17538463560367E+00, -1.25290061325714E+00, -1.95114578106181E+00, -3.33377734863412E-01, 5.84087353611391E-01, 3.70355160458242E+00, 8.08998614652183E-01, -6.30544778456261E+00, -7.42950589586770E-01, 3.22045238641642E+00, -3.02546701632756E-01, -5.50322328660079E-01, 2.70679560180526E-01, -3.07443194411638E-03, -3.98526991641814E-05, -2.03801728378170E-05, 5.35291050968957E-07, -3.24755755656466E-01, -3.34519617378408E-03, 2.51927589021366E-04, -6.46234145685049E-06, 2.49563591899944E-01, 9.25591305745302E-03, -8.85469388980841E-04, 2.38065873858153E-05, 5.91751755698874E-02, -1.30690035985908E-02, 1.29773257574842E-03, -3.62619054851207E-05, -6.02166776558070E-03, 5.76085993845291E-03, -7.41147689973064E-04, 2.26785848956448E-05, -9.28350093327664E-03, -4.48391258275365E-04, 1.34423638886403E-04, -4.82980395961881E-06}},
    {{{5,6,7},{6,7,8}}, {-2.16051327067444E+00, -4.80111541627028E-01, 3.04027396436748E+00, 1.28681816461933E+00, -7.82337073832730E-01, -1.15450727968039E+00, -1.73350593577900E-01, 3.45715807031252E-01, 2.16208403704912E+00, 4.78954418133244E-01, -3.69782986235047E+00, -4.41890147756103E-01, 1.96392264267039E+00, -1.79135190778744E-01, -3.64209223797836E-01, 1.72728271464056E-01, -2.18970386473126E-03, -2.43824809151223E-05, -1.70509750062217E-05, 4.28889831532858E-07, -1.80659211409240E-01, -2.62934062938358E-03, 1.90488189648742E-04, -4.97464288360169E-06, 1.24961161973692E-01, 7.53575059443721E-03, -7.00275926403793E-04, 1.89311236001922E-05, 4.19514602248622E-02, -1.15177604921240E-02, 1.07142440971427E-03, -2.98262647941179E-05, -1.22864231493349E-03, 5.68239521516594E-03, -6.49631468593113E-04, 1.94858861833733E-05, -1.07479233657747E-02, -7.58308433462482E-04, 1.31022979210949E-04, -4.40646205435013E-06}},
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    {{{4,6,6},{12,7,7}}, {5.40563537699066E-01, 1.55976455058877E-01, -8.27733195457660E-01, -4.29740375927118E-01, 4.51124796337535E-01, 4.06505204391334E-01, -3.31706250797056E-02, -1.29500876509379E-01, -5.41836945752523E-01, -1.55307512111538E-01, 1.06344286882181E+00, 1.74573269934750E-01, -9.11222603539796E-01, 4.07371043962413E-02, 2.83602994300583E-01, -1.12737260630446E-01, 2.09603874128016E-03, 3.40818129601407E-05, 2.72505148084715E-05, -5.45621772132865E-07, 1.03266353540452E-02, 3.06794661085578E-03, -1.94627230669998E-04, 5.11952106063117E-06, 4.65351809683254E-02, -9.87825994217385E-03, 8.58485442087632E-04, -2.18131269620980E-05, -5.67380316298969E-02, 1.86444916055620E-02, -1.48173779876088E-03, 3.76838430491165E-05, 2.79170039709121E-02, -1.31236355539612E-02, 1.11244841861670E-03, -2.84636477704387E-05, 2.11724033593322E-04, 3.90890106515983E-03, -3.09621400067450E-04, 7.76417199868740E-06}},
    {{{4,4,4},{5,5,6}}, {2.09066876605832E+00, 7.00305205172485E-01, -2.54115357145426E+00, -2.01562017178018E+00, 4.96538161564588E-01, 2.00073937529836E+00, 4.78308733653519E-01, -6.70612155222510E-01, -2.09178807779157E+00, -6.98038010355779E-01, 3.61494826543358E+00, 9.08203460857226E-01, -2.78112700540170E+00, 1.10653993888038E-03, 8.73587259399374E-01, -4.38949044796251E-01, 2.23609909490268E-03, 1.51097149111709E-04, 1.10129442736985E-05, -3.46497092406433E-07, 2.75027898201453E-02, 2.49274624191111E-03, -1.81122954291999E-04, 4.62993965153250E-06, 3.10142998400761E-01, -4.61775057635349E-03, 4.90298288981350E-04, -1.41874991849013E-05, -2.44600437119987E-01, 3.19935104647825E-03, -5.22836980952936E-04, 1.77924022347532E-05, -1.31979368622931E-02, 1.42374002051063E-03, 1.54957724813348E-04, -8.56575845178011E-06, 9.77789945810810E-03, -1.31302112850423E-03, 1.66839380182426E-05, 1.12259833971293E-06}},
    {{{4,4,4},{5,6,6}}, {2.80825409360361E+00, 7.39179789219227E-01, -3.76182467763305E+00, -2.05608849322845E+00, 8.72931022177130E-01, 1.94689147277941E+00, 3.96059198907514E-01, -6.21110048424397E-01, -2.81015642039096E+00, -7.37000079487816E-01, 4.82659470268327E+00, 8.16989465713922E-01, -2.96785161615455E+00, 1.40786168543780E-01, 7.14981706463392E-01, -3.56363894847830E-01, 2.88489296900762E-03, 1.16533067840323E-04, 1.28735532974487E-05, -3.53474440931333E-07, 1.68041027431493E-01, 2.55357679081748E-03, -1.74563202217657E-04, 4.14910780586812E-06, 3.62387895130795E-02, -5.31315224693507E-03, 4.96723853295863E-04, -1.27611915321588E-05, -1.45739904279344E-01, 5.31541387304452E-03, -5.77233744262706E-04, 1.60783611176464E-05, -4.59436039826276E-03, -2.33715590420514E-04, 2.00607668599704E-04, -7.33576025833301E-06, 8.39032029004200E-03, -9.12582433497657E-04, 7.30098242948148E-06, 7.17137042849203E-07}},
    {{{4,4,4},{6,6,6}}, {2.28704453837613E+00, 6.23420825294131E-01, -2.89528161745118E+00, -1.72381779815866E+00, 6.22915421870956E-01, 1.63137937904704E+00, 3.37902828221505E-01, -5.21233955663722E-01, -2.28892637878413E+00, -6.21510448410470E-01, 3.80685542335907E+00, 6.87672520994337E-01, -2.42454925399041E+00, 9.51147799877874E-02, 6.40634945624372E-01, -3.11685020389269E-01, 2.87786540442824E-03, 7.68627613323565E-05, 1.73187684811669E-05, -4.72055988872222E-07, 1.16004646388561E-01, 3.15185773271094E-03, -2.32754957021284E-04, 5.89360269386325E-06, 1.11576752739526E-01, -7.96450031776757E-03, 7.65609339541767E-04, -2.06702227528153E-05, -1.72425051475457E-01, 1.02901229020937E-02, -1.06582145230674E-03, 3.03444717002926E-05, 5.71433069158774E-03, -3.98560591008706E-03, 5.78317963837617E-04, -1.83981068308176E-05, 6.66905997806971E-03, 1.02789098862284E-04, -9.70900352819812E-05, 3.78994297070215E-06}},
    {{{4,4,4},{5,5,12}}, {2.10400894065802E+00, 4.93471285717820E-01, -2.83098150780710E+00, -1.31427690455168E+00, 8.13961432762250E-01, 1.18552784412553E+00, 1.33355656625135E-01, -3.59118498161605E-01, -2.10623366060073E+00, -4.92024462655871E-01, 3.52369358580079E+00, 4.59498392000066E-01, -2.07639096804941E+00, 1.54210358796116E-01, 4.80841121983828E-01, -2.11098605159052E-01, 3.33840719415964E-03, 3.27061547765378E-05, 2.89247018994803E-05, -6.95443282249669E-07, 1.49912729692413E-01, 4.27315980884394E-03, -3.08479511514747E-04, 7.92278379809873E-06, -2.88608694823691E-02, -1.30103203937724E-02, 1.19435122299884E-03, -3.13120442226453E-05, -1.01605880615255E-01, 2.14619773413301E-02, -1.92441421050299E-03, 5.11979259215601E-05, 2.70994004824335E-02, -1.27457500746471E-02, 1.28042470962859E-03, -3.54197457589606E-05, 4.58723590953162E-03, 2.75066935143207E-03, -3.03407264968036E-04, 8.71799262022716E-06}},
    {{{4,4,4},{5,6,12}}, {1.59300279608019E+00, 3.95102847027918E-01, -2.12076977465298E+00, -1.05555001918619E+00, 6.64634454767674E-01, 9.58535721592745E-01, 8.31826662459624E-02, -2.92383367716455E-01, -1.59523668135097E+00, -3.93789428769852E-01, 2.69047003495230E+00, 3.81209875872025E-01, -1.72231319846553E+00, 1.13115541031027E-01, 4.50535980418951E-01, -1.90422624329005E-01, 3.31086179143518E-03, 6.13810751290889E-06, 3.10095953822199E-05, -7.24836772170480E-07, 9.14915601377041E-02, 4.45146427192873E-03, -3.17637933448040E-04, 8.17690892951840E-06, 3.66640661401226E-02, -1.40256027033470E-02, 1.26264036268026E-03, -3.28772560392929E-05, -1.13736964975119E-01, 2.38241244034205E-02, -2.07619946851404E-03, 5.46529037238005E-05, 3.01018179774281E-02, -1.49369798309964E-02, 1.43054247368578E-03, -3.87846791001815E-05, 4.63103279378705E-03, 3.55897086509373E-03, -3.56093288754370E-04, 9.86514996492390E-06}},
    {{{4,4,4},{5,12,12}}, {9.74262492073940E-01, 2.15316799537894E-01, -1.69830685959792E+00, -5.71803601804710E-01, 8.80773535430457E-01, 5.00684929238419E-01, -1.29333470581557E-01, -1.43169931354522E-01, -9.76111403498654E-01, -2.14521012575412E-01, 1.99880364574604E+00, 1.92352460501930E-01, -1.39594676838876E+00, 1.33485981967122E-01, 3.44008824416384E-01, -1.21452496451217E-01, 2.75340241894652E-03, -3.83273699342290E-05, 3.91661848944953E-05, -7.25940777389933E-07, 6.68672924837183E-02, 4.36631715626199E-03, -2.43960521475298E-04, 7.21140327308856E-06, -7.05529670878929E-02, -1.72940394570158E-02, 1.28448903013590E-03, -3.38287543445531E-05, -2.87845837773862E-02, 3.67872914497333E-02, -2.46248423019562E-03, 6.36815941423171E-05, 4.59160706049164E-02, -3.08495302928968E-02, 2.12833679946650E-03, -5.34803919887172E-05, 1.22522646638219E-03, 1.08292435977975E-02, -6.76563990898527E-04, 1.62277691331570E-05}},
    {{{4,4,4},{6,6,12}}, {1.79557081651173E+00, 3.96650891685617E-01, -2.57041641719956E+00, -1.04385265812719E+00, 8.41018217806218E-01, 9.17521038702766E-01, 3.50979650004940E-02, -2.67644268913609E-01, -1.79795285932241E+00, -3.95419771097876E-01, 3.11853215645453E+00, 3.44474276275012E-01, -1.79955285449388E+00, 1.68028314554513E-01, 3.90775838023980E-01, -1.56774229630813E-01, 3.45869933286992E-03, -3.08282769500949E-05, 3.39256973214047E-05, -7.71368381277000E-07, 1.37755366311106E-01, 4.65724894356797E-03, -3.31873163675224E-04, 8.59688597826895E-06, -7.37799593649695E-02, -1.56171533743718E-02, 1.38006137841154E-03, -3.56748028406545E-05, -7.36109738039040E-02, 2.77550733169148E-02, -2.34593866686369E-03, 6.09033831962381E-05, 3.74434870034333E-02, -1.86089302631072E-02, 1.68714383537472E-03, -4.45973141194451E-05, 3.26158780389532E-03, 4.84895256562969E-03, -4.41539021109030E-04, 1.17487048463485E-05}},
    {{{4,4,4},{6,12,12}}, {5.26585016899371E-01, 1.40290200037086E-01, -9.71161151794264E-01, -3.71417425361688E-01, 6.71635769757586E-01, 3.27384210270523E-01, -1.52402322285805E-01, -9.37306790186619E-02, -5.28508272956277E-01, -1.39533870487960E-01, 1.18470643391164E+00, 1.36360417391982E-01, -1.05355010002278E+00, 8.28582093897455E-02, 3.35284321968435E-01, -1.11127677454377E-01, 2.84815896047565E-03, -7.21529614889717E-05, 4.19235564039182E-05, -7.52171366244631E-07, 8.17552465576421E-03, 4.65134583625585E-03, -2.53661202703718E-04, 7.69820041095422E-06, 2.52765622631305E-02, -1.92526265203718E-02, 1.37693471821187E-03, -3.63863168392371E-05, -6.77965068743374E-02, 4.16297133807668E-02, -2.68090811469273E-03, 6.92855994315965E-05, 5.56656714454914E-02, -3.62860655519681E-02, 2.39170262475949E-03, -5.94668104376819E-05, -1.99395204912831E-03, 1.31144138047660E-02, -7.79717463888969E-04, 1.84139233254138E-05}},
    {{{4,4,4},{12,12,12}}, {-1.24210310396193E+00, -1.59725506553029E-01, 2.60193506680308E+00, 5.19196839945744E-01, -5.58524229711173E-01, -4.97671212949024E-01, -2.24037592516291E-01, 1.53912839719329E-01, 1.23991437175522E+00, 1.60352910196943E-01, -2.74736064114001E+00, -1.76852482240692E-01, 8.19569366011630E-01, -1.83741422310728E-01, 2.46990474653860E-01, -4.22660445922953E-02, 3.18186809874449E-03, -1.93750789084718E-04, 5.16422217935972E-05, -5.94605128815383E-07, -2.13308206670970E-01, 5.31405896303429E-03, -1.34971509208458E-04, 8.14206816038753E-06, 4.97720726322018E-01, -2.87360094000296E-02, 1.24557723472852E-03, -3.86435412404371E-05, -2.89460246687436E-01, 7.06325150391368E-02, -2.72692995047770E-03, 7.78119390318640E-05, 1.28913776365168E-01, -7.40551432237739E-02, 3.06414023723629E-03, -7.48608079884618E-05, -3.16231452267994E-02, 3.03214856750955E-02, -1.11407204002267E-03, 2.46950448755328E-05}},
};
 
class GottschalkKIntegral{
private:
    std::tuple<int,int,int> int2key(int i){
        if (i < 222){
            throw teqp::InvalidArgument("");
        }
        if (i > 999){
            throw teqp::InvalidArgument("");
        }
        return std::make_tuple(i / 100 % 10, i / 10 % 10, i % 10);
    }
public:
    const std::tuple<int,int,int> k1, k2;
    const std::array<double, 40> abc;
    
    GottschalkKIntegral(std::tuple<int,int,int> k1, std::tuple<int,int,int> k2) : k1(k1), k2(k2), abc(Gottschalk_K_coeffs.at({k1, k2})){}
    GottschalkKIntegral(int k1, int k2) : k1(int2key(k1)), k2(int2key(k2)), abc(Gottschalk_K_coeffs.at({this->k1, this->k2})){}
    
    template<typename TType, typename RhoType>
    auto get_K(const TType& Tstar, const RhoType& rhostar) const{
        std::common_type_t<TType, RhoType> summer = 0.0;
        int N1 = 8, N2 = 8; // N3 = 24
        
        for (auto i = 0; i <= 3; ++i){
            for (auto j = 1; j <= 2; ++j){
                auto I = 2*i + (j-1); // 2 entries in j for each i
                summer += abc[I]*pow(rhostar, i)*pow(exp((1.0-rhostar/3.0)/Tstar), j);
            }
        }
        for (auto i = 0; i <= 3; ++i){
            for (auto j = 1; j <= 2; ++j){
                auto I = N1 + 2*i + (j-1); // 2 entries in j for each i
                summer += abc[I]*pow(rhostar, i)*pow(exp((1.0-rhostar/3.0)*(1.0-rhostar/3.0)/Tstar), j);
            }
        }
        for (auto i = 0; i <= 5; ++i){
            for (auto j = 0; j <= 3; ++j){
                auto I = N1 + N2 + 4*i + j; // 4 entries in j for each i
                summer += abc[I]*pow(rhostar, i)*pow(Tstar, j);
            }
        }
        return summer;
    }
};
 
}
}