poisson3d_3.h

利用C

    const double psitilde_bs_2_1 = 3.5*y + 2.5;
    const double psitilde_bs_3_0 = 1;
    
    // Compute psitilde_cs
    const double psitilde_cs_00_0 = 1;
    const double psitilde_cs_00_1 = 2*z + 1;
    const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
    const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;
    const double psitilde_cs_01_0 = 1;
    const double psitilde_cs_01_1 = 3*z + 2;
    const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;
    const double psitilde_cs_02_0 = 1;
    const double psitilde_cs_02_1 = 4*z + 3;
    const double psitilde_cs_03_0 = 1;
    const double psitilde_cs_10_0 = 1;
    const double psitilde_cs_10_1 = 3*z + 2;
    const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;
    const double psitilde_cs_11_0 = 1;
    const double psitilde_cs_11_1 = 4*z + 3;
    const double psitilde_cs_12_0 = 1;
    const double psitilde_cs_20_0 = 1;
    const double psitilde_cs_20_1 = 4*z + 3;
    const double psitilde_cs_21_0 = 1;
    const double psitilde_cs_30_0 = 1;
    
    // Compute basisvalues
    const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
    const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
    const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
    const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
    const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
    const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
    const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
    const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
    const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
    const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
    const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;
    const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;
    const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;
    const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;
    const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;
    const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;
    const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;
    const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;
    const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;
    const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;
    
    // Table(s) of coefficients
    const static double coefficients0[20][20] = \
    {{0.0288675134594814, 0.0130410132739325, 0.00752923252421041, 0.00532397137499948, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.00668153104781061, 0.00472455591261533, -0.028347335475692, -0.0239578711874977, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},
    {0.0288675134594812, -0.0130410132739326, 0.00752923252421044, 0.00532397137499954, 0.018298126367785, -0.014173667737846, 0.00818317088384973, -0.0115727512471569, 0.00668153104781061, 0.00472455591261533, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414159, -0.00535714285714286},
    {0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515491, 0, -0.0133630620956212, 0.00472455591261533, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714285},
    {0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},
    {0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912425, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731326, 0.0267857142857143},
    {0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},
    {0, 0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515492, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
    {0, -0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},
    {0, 0.0978075995544939, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -0.0245495126515492, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.00691604168965609, -0.0160714285714286, 0.0154647393532935, 0.00874817765279706, 0, -0.00535714285714287},
    {0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714286},
    {0, -0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515492, -0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
    {0, 0.0195615199108988, 0.0112938487863157, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714286},
    {0, -0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714286},
    {0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197614, -0.00437408882639853, 0.00757614408414158, -0.00535714285714286},
    {0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714285, -0.00927884361197612, -0.00437408882639851, -0.00757614408414159, -0.00535714285714287},
    {0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.0334076552390531, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.0061858957413174, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197612, 0.00437408882639851, -0.00757614408414159, -0.00535714285714285},
    {0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
    {0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829413, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
    {0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},
    {0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714286}};
    
    // Interesting (new) part
    // Tables of derivatives of the polynomial base (transpose)
    const static double dmats0[20][20] = \
    {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {6.32455532033677, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-1.47608043968248e-14, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.74165738677395, 0, 0, 8.69482604771367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.49909083394702, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.69282032302755, 0, 0.565685424949236, 0.400000000000002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.82807867121083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.6, 0, 8.76356092008267, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 4.24264068711928, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.54558441227156, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    
    const static double dmats1[20][20] = \
    {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.47722557505167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.9580398915498, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.29128784747791, 7.24568837309472, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-2.6457513110646, 0, 9.66091783079296, 0.683130051063972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.7495454169735, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474618, 0.200000000000002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733759, 0.169030850945705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.80000000000001, -5.69209978830308, 4.38178046004133, -0.774596669241487, 0, 10.998181667894, 4.76235235991627, 0.962140470884726, -0.740656079818042, 0.130930734141595, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.19615242270664, 0, -3.16227766016838, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.534522483824849, 0.377964473009229, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.01246117974981, 2.12132034355964, -0.408248290463863, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772552, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-1.80000000000001, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.27279220613578, 0, 0, 3.83405790253617, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    
    const static double dmats2[20][20] = \
    {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.82574185835056, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.16397779494323, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.9580398915498, 5.61248608016091, -1.08012344973464, -0.763762615825972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.29128784747792, 1.44913767461894, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.3228756555323, 0, 3.86436713231719, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.87082869338696, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.7495454169735, 5.79655069847577, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513776, -0.979795897113271, 0.282842712474618, 0.200000000000002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733758, 0.169030850945704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.8, 0.632455532033674, 4.38178046004133, -0.774596669241484, 0, 3.14233761939829, 4.76235235991627, -0.10690449676497, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018457, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.01246117974981, 2.12132034355964, -0.408248290463864, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.55884572681199, 0.547722557505165, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.899999999999997, 0, 1.46059348668045, 1.42009389360939, 0, 0, 9.07114735222146, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.27279220613579, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.734846922834951, 0, -6.26099033699942, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.71576766497729, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    
    // Compute reference derivatives
    // Declare pointer to array of derivatives on FIAT element
    double *derivatives = new double [num_derivatives];