ffc_18.h

Dolfin provide a high-performance linear algebra library

    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] = \
    {{0.0288675134594813, 0.0130410132739325, 0.00752923252421043, 0.00532397137499949, 0.018298126367785, 0.014173667737846, 0.00818317088384971, 0.0115727512471569, 0.00668153104781061, 0.00472455591261533, -0.028347335475692, -0.0239578711874977, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197613, -0.0131222664791956, -0.00757614408414158, -0.00535714285714285},
    {0.0288675134594813, -0.0130410132739325, 0.00752923252421044, 0.00532397137499949, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.00668153104781061, 0.00472455591261533, 0.028347335475692, -0.0239578711874977, 0.0185576872239522, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414158, -0.00535714285714285},
    {0.0288675134594813, 0, -0.0150584650484208, 0.00532397137499949, 0, 0, 0.0245495126515491, 0, -0.0133630620956212, 0.00472455591261535, 0, 0, 0, 0.0428571428571429, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714286},
    {0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.0283473354756921, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},
    {0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -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, -0.0638876564999939, 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, -0.0535714285714285},
    {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, -0.0069160416896561, -0.0160714285714286, 0.0154647393532936, 0.00874817765279706, 0, -0.00535714285714286},
    {0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515491, -0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197612, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},
    {0, -0.0978075995544939, -0.0564692439315782, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -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, -0.0245495126515491, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714285},
    {0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515491, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197612, -0.00437408882639853, 0.00757614408414158, -0.00535714285714285},
    {0, -0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192486, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874978, -0.00618589574131742, -0.0107142857142857, 0.0207481250689683, -0.00535714285714286, -0.00927884361197613, -0.00437408882639852, -0.00757614408414158, -0.00535714285714285},
    {0, 0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.0334076552390531, 0.0236227795630767, -0.0850420064270761, 0.0239578711874977, 0.00618589574131741, -0.0107142857142857, 0.0207481250689683, 0.00535714285714286, -0.00927884361197613, 0.00437408882639853, -0.00757614408414158, -0.00535714285714285},
    {0.259807621135332, 0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829414, 0.0400891862868637, -0.0992156741649221, 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, 0.0400891862868637, -0.0992156741649221, 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, -0.143747227124987, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532936, 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},
    {3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 5.61248608016091, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.29128784747792, 0, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, -1.67332005306815, -1.18321595661992, 7.74596669241483, 0, 0.346410161513775, 0, 0.282842712474619, 0.200000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 2.44948974278318, 0, 0, 0, 7.09929573971954, 0, -0.414039335605415, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.8, 0, 4.38178046004133, -0.774596669241484, 0, 0, 4.76235235991626, 0, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 2.12132034355964, 0, 0, 0, 0, 0, 7.17137165600636, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.55884572681199, 0, 1.58113883008419, 2.45967477524977, 0, 0, 0, 0, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.27279220613579, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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},
    {1.58113883008419, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.73861278752583, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.47901994577491, 2.80624304008046, -0.540061724867321, -0.381881307912986, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.14564392373896, 3.62284418654736, 2.09165006633519, -0.295803989154979, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-1.3228756555323, 0, 4.83045891539648, 0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.935414346693486, 0, 0, 2.17370651192842, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.62018517460197, 0, 0, 3.76497011940334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.37477270848675, 2.89827534923789, -0.836660026534075, -0.591607978309961, 3.87298334620742, -0.6, 0.173205080756888, -0.489897948556636, 0.14142135623731, 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.16189500386223, 1.22474487139159, 1.41421356237309, -0.5, 4.58257569495584, 3.54964786985977, -1.02469507659596, -0.207019667802708, -0.239045721866878, 0.0845154254728521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.9, -2.84604989415154, 2.19089023002067, -0.387298334620743, 0, 5.49909083394701, 2.38117617995813, 0.481070235442363, -0.370328039909021, 0.065465367070798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.59807621135332, 0, -1.58113883008419, -1.1180339887499, 0, 0, 6.87386354243376, 0, 0.267261241912425, 0.188982236504615, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.00623058987491, 1.06066017177982, -0.204124145231931, 1.58771324027147, 0, 0, 0, 3.58568582800318, -0.690065559342354, -0.780720058358825, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.779422863405996, 1.36930639376292, 0.790569415042095, 1.22983738762489, 0, 0, 0, 4.62910049886276, 2.67261241912425, -0.604743156814763, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-0.9, 0, 1.82574185835055, -1.42009389360939, 0, 0, 0, 0, 6.17213399848368, 0.698297248755173, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.636396103067893, 0, 0, 1.91702895126808, 0, 0, 0, 0, 0, 2.59229627936314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.10227038425243, 0, 0, 3.3203915431768, 0, 0, 0, 0, 0, 4.48998886412873, 0, 0, 0, 0, 0, 0, 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},
    {1.58113883008419, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.912870929175277, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.58198889747161, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.47901994577491, 2.80624304008046, -0.54006172486732, -0.381881307912986, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.14564392373896, 0.724568837309473, 2.09165006633519, -0.29580398915498, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.661437827766147, 0, 1.93218356615859, -0.170782512765993, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.935414346693487, 3.54964786985977, 0, 2.17370651192842, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.540061724867322, 0, 3.54964786985977, 1.25499003980111, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {-1.90940653956493, 0, 0, 4.43705983732471, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.37477270848675, 2.89827534923789, -0.836660026534075, -0.59160797830996, 3.87298334620742, -0.599999999999999, 0.173205080756888, -0.489897948556635, 0.14142135623731, 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.16189500386223, 1.22474487139159, 1.4142135623731, -0.5, 0.654653670707977, 3.54964786985977, -1.02469507659596, -0.207019667802707, -0.239045721866878, 0.084515425472852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.900000000000001, 0.316227766016837, 2.19089023002067, -0.387298334620742, 0, 1.57116880969914, 2.38117617995813, -0.0534522483824848, -0.370328039909021, 0.0654653670707978, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.519615242270664, 0, 1.58113883008419, -0.22360679774998, 0, 0, 2.9459415181859, 0, -0.267261241912425, 0.0377964473009227, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.00623058987491, 1.06066017177982, -0.204124145231931, 1.58771324027147, 4.53557367611073, 0, 0, 3.58568582800318, -0.690065559342354, -0.780720058358825, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.779422863405996, 0.273861278752583, 0.790569415042095, 1.22983738762489, 0, 4.53557367611073, 0, 0.925820099772552, 2.67261241912425, -0.604743156814763, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.450000000000001, 0, 0.730296743340223, 0.710046946804693, 0, 0, 4.53557367611073, 0, 2.46885359939347, -0.349148624377588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.636396103067892, -3.13049516849971, 0, 1.91702895126808, 0, 0, 0, 5.29150262212918, 0, 2.59229627936314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0.367423461417478, 0, -3.13049516849971, 1.10679718105893, 0, 0, 0, 0, 5.29150262212918, 1.49666295470958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.85788383248865, 0, 0, -2.34787137637478, 0, 0, 0, 0, 0, 6.34980314655502, 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];
    
    // Declare coefficients
    double coeff0_0 = 0;
    double coeff0_1 = 0;
    double coeff0_2 = 0;
    double coeff0_3 = 0;
    double coeff0_4 = 0;
    double coeff0_5 = 0;