polyfem/_a_m_i_p_s3d_8hpp_source.html

// Auto-generated code for AMIPS3d energy

#pragma once

#include <Eigen/Dense>


namespace polyfem

{

    namespace autogen

    {


        Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> AMIPS3d_gradient(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> &F)

        {

            Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> grad(3, 3);

            const double F00 = F(0, 0);

            const double F01 = F(0, 1);

            const double F02 = F(0, 2);

            const double F10 = F(1, 0);

            const double F11 = F(1, 1);

            const double F12 = F(1, 2);

            const double F20 = F(2, 0);

            const double F21 = F(2, 1);

            const double F22 = F(2, 2);

            std::array<double, 9> result_0;

            const auto helper_0 = 72 * F02;

            const auto helper_1 = F11 * F22;

            const auto helper_2 = F12 * F21;

            const auto helper_3 = F12 * F20;

            const auto helper_4 = F10 * F21;

            const auto helper_5 = F10 * F22;

            const auto helper_6 = F11 * F20;

            const auto helper_7 = F00 * helper_1 - F00 * helper_2 + F01 * helper_3 - F01 * helper_5 + F02 * helper_4 - F02 * helper_6;

            const auto helper_8 = 1.0 / helper_7;

            const auto helper_9 = 27 * pow(F00, 2) + 27 * pow(F10, 2) + 27 * pow(F20, 2) + 9 * pow(F00 - 2 * F01, 2) + 9 * pow(F10 - 2 * F11, 2) + 9 * pow(F20 - 2 * F21, 2) + 4 * pow(F00 + F01 - 3 * F02, 2) + 4 * pow(F10 + F11 - 3 * F12, 2) + 4 * pow(F20 + F21 - 3 * F22, 2);

            const auto helper_10 = 5 * helper_8 * helper_9;

            const auto helper_11 = (1.0 / 432.0) * pow(6, 2.0 / 3.0) / pow(helper_7, 5.0 / 3.0);

            const auto helper_12 = 72 * F12;

            const auto helper_13 = 72 * F22;

            result_0[0] = -helper_11 * (-240 * F00 + 84 * F01 + helper_0 + helper_10 * (helper_1 - helper_2));

            result_0[1] = helper_11 * (-84 * F00 + 240 * F01 - helper_0 + 5 * helper_8 * helper_9 * (-helper_3 + helper_5));

            result_0[2] = -helper_11 * (72 * F00 + 72 * F01 - 216 * F02 + helper_10 * (helper_4 - helper_6));

            result_0[3] = helper_11 * (240 * F10 - 84 * F11 + helper_10 * (F01 * F22 - F02 * F21) - helper_12);

            result_0[4] = -helper_11 * (84 * F10 - 240 * F11 + helper_10 * (F00 * F22 - F02 * F20) + helper_12);

            result_0[5] = helper_11 * (-72 * F10 - 72 * F11 + 216 * F12 + 5 * helper_8 * helper_9 * (F00 * F21 - F01 * F20));

            result_0[6] = -helper_11 * (-240 * F20 + 84 * F21 + helper_10 * (F01 * F12 - F02 * F11) + helper_13);

            result_0[7] = helper_11 * (-84 * F20 + 240 * F21 - helper_13 + 5 * helper_8 * helper_9 * (F00 * F12 - F02 * F10));

            result_0[8] = -helper_11 * (72 * F20 + 72 * F21 - 216 * F22 + helper_10 * (F00 * F11 - F01 * F10));

            ;

            grad(0, 0) = result_0[0];

            grad(0, 1) = result_0[1];

            grad(0, 2) = result_0[2];

            grad(1, 0) = result_0[3];

            grad(1, 1) = result_0[4];

            grad(1, 2) = result_0[5];

            grad(2, 0) = result_0[6];

            grad(2, 1) = result_0[7];

            grad(2, 2) = result_0[8];

            return grad;

        }


        inline Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9> AMIPS3d_hessian(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> &F)

        {

            Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9> hess(9, 9);

            std::array<double, 81> result_0;

            const double F00 = F(0, 0);

            const double F01 = F(0, 1);

            const double F02 = F(0, 2);

            const double F10 = F(1, 0);

            const double F11 = F(1, 1);

            const double F12 = F(1, 2);

            const double F20 = F(2, 0);

            const double F21 = F(2, 1);

            const double F22 = F(2, 2);

            const auto helper_0 = 6 * F02;

            const auto helper_1 = -20 * F00 + 7 * F01 + helper_0;

            const auto helper_2 = 3 * helper_1;

            const auto helper_3 = F11 * F22;

            const auto helper_4 = F12 * F21;

            const auto helper_5 = helper_3 - helper_4;

            const auto helper_6 = F12 * F20;

            const auto helper_7 = F10 * F21;

            const auto helper_8 = F10 * F22;

            const auto helper_9 = F11 * F20;

            const auto helper_10 = F00 * helper_3 - F00 * helper_4 + F01 * helper_6 - F01 * helper_8 + F02 * helper_7 - F02 * helper_9;

            const auto helper_11 = 1.0 / helper_10;

            const auto helper_12 = helper_11 * helper_5;

            const auto helper_13 = pow(helper_10, -2);

            const auto helper_14 = 3 * F02;

            const auto helper_15 = F00 + F01 - helper_14;

            const auto helper_16 = 3 * F12;

            const auto helper_17 = F10 + F11 - helper_16;

            const auto helper_18 = 3 * F22;

            const auto helper_19 = F20 + F21 - helper_18;

            const auto helper_20 = 27 * pow(F00, 2) + 27 * pow(F10, 2) + 27 * pow(F20, 2) + 4 * pow(helper_15, 2) + 4 * pow(helper_17, 2) + 4 * pow(helper_19, 2) + 9 * pow(F00 - 2 * F01, 2) + 9 * pow(F10 - 2 * F11, 2) + 9 * pow(F20 - 2 * F21, 2);

            const auto helper_21 = helper_13 * helper_20;

            const auto helper_22 = pow(6, 2.0 / 3.0);

            const auto helper_23 = helper_22 / pow(helper_10, 5.0 / 3.0);

            const auto helper_24 = (5.0 / 162.0) * helper_23;

            const auto helper_25 = -helper_6 + helper_8;

            const auto helper_26 = helper_11 * helper_25;

            const auto helper_27 = 15 * helper_1;

            const auto helper_28 = 7 * F00 - 20 * F01 + helper_0;

            const auto helper_29 = 10 * helper_21;

            const auto helper_30 = helper_29 * helper_5;

            const auto helper_31 = (1.0 / 324.0) * helper_23;

            const auto helper_32 = helper_31 * (15 * helper_11 * helper_28 * helper_5 - helper_25 * helper_30 - helper_26 * helper_27 - 63);

            const auto helper_33 = 90 * helper_15;

            const auto helper_34 = helper_7 - helper_9;

            const auto helper_35 = helper_11 * helper_34;

            const auto helper_36 = helper_31 * (helper_12 * helper_33 + helper_27 * helper_35 + helper_30 * helper_34 - 54);

            const auto helper_37 = F01 * F22 - F02 * F21;

            const auto helper_38 = 6 * F12;

            const auto helper_39 = -20 * F10 + 7 * F11 + helper_38;

            const auto helper_40 = helper_12 * helper_20;

            const auto helper_41 = 2 * helper_40;

            const auto helper_42 = helper_22 / pow(helper_10, 8.0 / 3.0);

            const auto helper_43 = (5.0 / 324.0) * helper_42;

            const auto helper_44 = helper_43 * (-helper_2 * helper_37 - helper_37 * helper_41 + 3 * helper_39 * helper_5);

            const auto helper_45 = F00 * F22 - F02 * F20;

            const auto helper_46 = 12 * helper_1;

            const auto helper_47 = 7 * F10 - 20 * F11 + helper_38;

            const auto helper_48 = 12 * helper_5;

            const auto helper_49 = helper_18 * helper_20;

            const auto helper_50 = 8 * helper_40;

            const auto helper_51 = (5.0 / 1296.0) * helper_42;

            const auto helper_52 = helper_51 * (helper_45 * helper_46 + helper_45 * helper_50 + helper_47 * helper_48 - helper_49);

            const auto helper_53 = 72 * helper_5;

            const auto helper_54 = F00 * F21 - F01 * F20;

            const auto helper_55 = 3 * helper_20;

            const auto helper_56 = F21 * helper_55;

            const auto helper_57 = helper_51 * (helper_17 * helper_53 - helper_46 * helper_54 - helper_50 * helper_54 + helper_56);

            const auto helper_58 = F01 * F12 - F02 * F11;

            const auto helper_59 = 6 * F22;

            const auto helper_60 = -20 * F20 + 7 * F21 + helper_59;

            const auto helper_61 = helper_43 * (helper_2 * helper_58 + helper_41 * helper_58 + 3 * helper_5 * helper_60);

            const auto helper_62 = F00 * F12 - F02 * F10;

            const auto helper_63 = 7 * F20 - 20 * F21 + helper_59;

            const auto helper_64 = helper_16 * helper_20;

            const auto helper_65 = helper_51 * (-helper_46 * helper_62 + helper_48 * helper_63 - helper_50 * helper_62 + helper_64);

            const auto helper_66 = F00 * F11 - F01 * F10;

            const auto helper_67 = F11 * helper_55;

            const auto helper_68 = helper_20 * helper_66;

            const auto helper_69 = 8 * helper_68;

            const auto helper_70 = helper_51 * (helper_12 * helper_69 + helper_19 * helper_53 + helper_46 * helper_66 - helper_67);

            const auto helper_71 = 3 * helper_25;

            const auto helper_72 = helper_31 * (15 * helper_11 * helper_28 * helper_34 - helper_25 * helper_29 * helper_34 - helper_26 * helper_33 - 54);

            const auto helper_73 = 12 * helper_28;

            const auto helper_74 = 12 * helper_25;

            const auto helper_75 = helper_20 * helper_26;

            const auto helper_76 = 8 * helper_37;

            const auto helper_77 = helper_51 * (-helper_37 * helper_73 - helper_39 * helper_74 + helper_49 + helper_75 * helper_76);

            const auto helper_78 = helper_43 * (3 * helper_28 * helper_45 - 2 * helper_45 * helper_75 - helper_47 * helper_71);

            const auto helper_79 = 72 * helper_25;

            const auto helper_80 = F20 * helper_55;

            const auto helper_81 = helper_51 * (8 * helper_11 * helper_20 * helper_25 * helper_54 - helper_17 * helper_79 - helper_54 * helper_73 - helper_80);

            const auto helper_82 = helper_51 * (12 * helper_28 * helper_58 - 8 * helper_58 * helper_75 - helper_60 * helper_74 - helper_64);

            const auto helper_83 = helper_43 * (2 * helper_11 * helper_20 * helper_25 * helper_62 - 3 * helper_28 * helper_62 - helper_63 * helper_71);

            const auto helper_84 = F10 * helper_55;

            const auto helper_85 = helper_51 * (-helper_19 * helper_79 - helper_26 * helper_69 + helper_66 * helper_73 + helper_84);

            const auto helper_86 = 5 * helper_21;

            const auto helper_87 = (1.0 / 162.0) * helper_23;

            const auto helper_88 = 72 * helper_15;

            const auto helper_89 = helper_20 * helper_35;

            const auto helper_90 = helper_51 * (12 * helper_34 * helper_39 - helper_37 * helper_88 - helper_56 - helper_76 * helper_89);

            const auto helper_91 = 12 * helper_34;

            const auto helper_92 = 8 * helper_89;

            const auto helper_93 = helper_51 * (helper_45 * helper_88 + helper_45 * helper_92 + helper_47 * helper_91 + helper_80);

            const auto helper_94 = 9 * helper_15;

            const auto helper_95 = (5.0 / 162.0) * helper_42;

            const auto helper_96 = helper_95 * (9 * helper_17 * helper_34 - helper_54 * helper_89 - helper_54 * helper_94);

            const auto helper_97 = helper_51 * (helper_58 * helper_88 + helper_58 * helper_92 + helper_60 * helper_91 + helper_67);

            const auto helper_98 = helper_51 * (12 * helper_34 * helper_63 - helper_62 * helper_88 - helper_62 * helper_92 - helper_84);

            const auto helper_99 = helper_95 * (9 * helper_19 * helper_34 + helper_66 * helper_89 + helper_66 * helper_94);

            const auto helper_100 = 3 * helper_37;

            const auto helper_101 = helper_11 * helper_39;

            const auto helper_102 = helper_11 * helper_37;

            const auto helper_103 = 15 * helper_47;

            const auto helper_104 = helper_31 * (-helper_102 * helper_103 + 15 * helper_11 * helper_39 * helper_45 - helper_29 * helper_37 * helper_45 - 63);

            const auto helper_105 = 90 * helper_17;

            const auto helper_106 = helper_31 * (-15 * helper_101 * helper_54 - helper_102 * helper_105 + 10 * helper_13 * helper_20 * helper_37 * helper_54 - 54);

            const auto helper_107 = helper_43 * (-helper_100 * helper_60 - 2 * helper_102 * helper_20 * helper_58 + 3 * helper_39 * helper_58);

            const auto helper_108 = 12 * helper_39;

            const auto helper_109 = 12 * helper_63;

            const auto helper_110 = helper_14 * helper_20;

            const auto helper_111 = helper_51 * (-helper_108 * helper_62 - helper_109 * helper_37 + 8 * helper_11 * helper_20 * helper_37 * helper_62 - helper_110);

            const auto helper_112 = 72 * helper_19;

            const auto helper_113 = F01 * helper_55;

            const auto helper_114 = helper_51 * (-helper_102 * helper_69 + helper_108 * helper_66 - helper_112 * helper_37 + helper_113);

            const auto helper_115 = 3 * helper_47;

            const auto helper_116 = helper_11 * helper_45;

            const auto helper_117 = helper_11 * helper_54;

            const auto helper_118 = helper_31 * (-helper_103 * helper_117 + 90 * helper_11 * helper_17 * helper_45 - helper_29 * helper_45 * helper_54 - 54);

            const auto helper_119 = 12 * helper_60;

            const auto helper_120 = 12 * helper_47;

            const auto helper_121 = helper_116 * helper_20;

            const auto helper_122 = 8 * helper_58;

            const auto helper_123 = helper_51 * (helper_110 + helper_119 * helper_45 + helper_120 * helper_58 + helper_121 * helper_122);

            const auto helper_124 = helper_43 * (-helper_115 * helper_62 - 2 * helper_121 * helper_62 + 3 * helper_45 * helper_63);

            const auto helper_125 = F00 * helper_55;

            const auto helper_126 = helper_51 * (helper_112 * helper_45 + helper_116 * helper_69 + helper_120 * helper_66 - helper_125);

            const auto helper_127 = helper_117 * helper_20;

            const auto helper_128 = helper_51 * (-helper_113 - helper_119 * helper_54 - helper_122 * helper_127 + 72 * helper_17 * helper_58);

            const auto helper_129 = helper_51 * (-helper_109 * helper_54 + helper_125 + 8 * helper_127 * helper_62 - 72 * helper_17 * helper_62);

            const auto helper_130 = helper_95 * (-helper_117 * helper_68 + 9 * helper_17 * helper_66 - 9 * helper_19 * helper_54);

            const auto helper_131 = helper_11 * helper_60;

            const auto helper_132 = 15 * helper_131;

            const auto helper_133 = helper_29 * helper_58;

            const auto helper_134 = helper_31 * (15 * helper_11 * helper_58 * helper_63 - helper_132 * helper_62 - helper_133 * helper_62 - 63);

            const auto helper_135 = 90 * helper_19;

            const auto helper_136 = helper_31 * (helper_11 * helper_135 * helper_58 + helper_132 * helper_66 + helper_133 * helper_66 - 54);

            const auto helper_137 = helper_11 * helper_62;

            const auto helper_138 = helper_31 * (15 * helper_11 * helper_63 * helper_66 - helper_135 * helper_137 - helper_29 * helper_62 * helper_66 - 54);

            result_0[0] = helper_24 * (helper_12 * helper_2 + helper_21 * pow(helper_5, 2) + 18);

            result_0[1] = helper_32;

            result_0[2] = helper_36;

            result_0[3] = helper_44;

            result_0[4] = helper_52;

            result_0[5] = helper_57;

            result_0[6] = helper_61;

            result_0[7] = helper_65;

            result_0[8] = helper_70;

            result_0[9] = helper_32;

            result_0[10] = helper_24 * (-helper_11 * helper_28 * helper_71 + helper_21 * pow(helper_25, 2) + 18);

            result_0[11] = helper_72;

            result_0[12] = helper_77;

            result_0[13] = helper_78;

            result_0[14] = helper_81;

            result_0[15] = helper_82;

            result_0[16] = helper_83;

            result_0[17] = helper_85;

            result_0[18] = helper_36;

            result_0[19] = helper_72;

            result_0[20] = helper_87 * (helper_33 * helper_35 + pow(helper_34, 2) * helper_86 + 81);

            result_0[21] = helper_90;

            result_0[22] = helper_93;

            result_0[23] = helper_96;

            result_0[24] = helper_97;

            result_0[25] = helper_98;

            result_0[26] = helper_99;

            result_0[27] = helper_44;

            result_0[28] = helper_77;

            result_0[29] = helper_90;

            result_0[30] = helper_24 * (-helper_100 * helper_101 + helper_21 * pow(helper_37, 2) + 18);

            result_0[31] = helper_104;

            result_0[32] = helper_106;

            result_0[33] = helper_107;

            result_0[34] = helper_111;

            result_0[35] = helper_114;

            result_0[36] = helper_52;

            result_0[37] = helper_78;

            result_0[38] = helper_93;

            result_0[39] = helper_104;

            result_0[40] = helper_24 * (helper_115 * helper_116 + helper_21 * pow(helper_45, 2) + 18);

            result_0[41] = helper_118;

            result_0[42] = helper_123;

            result_0[43] = helper_124;

            result_0[44] = helper_126;

            result_0[45] = helper_57;

            result_0[46] = helper_81;

            result_0[47] = helper_96;

            result_0[48] = helper_106;

            result_0[49] = helper_118;

            result_0[50] = helper_87 * (-helper_105 * helper_117 + pow(helper_54, 2) * helper_86 + 81);

            result_0[51] = helper_128;

            result_0[52] = helper_129;

            result_0[53] = helper_130;

            result_0[54] = helper_61;

            result_0[55] = helper_82;

            result_0[56] = helper_97;

            result_0[57] = helper_107;

            result_0[58] = helper_123;

            result_0[59] = helper_128;

            result_0[60] = helper_24 * (3 * helper_131 * helper_58 + helper_21 * pow(helper_58, 2) + 18);

            result_0[61] = helper_134;

            result_0[62] = helper_136;

            result_0[63] = helper_65;

            result_0[64] = helper_83;

            result_0[65] = helper_98;

            result_0[66] = helper_111;

            result_0[67] = helper_124;

            result_0[68] = helper_129;

            result_0[69] = helper_134;

            result_0[70] = helper_24 * (-3 * helper_137 * helper_63 + helper_21 * pow(helper_62, 2) + 18);

            result_0[71] = helper_138;

            result_0[72] = helper_70;

            result_0[73] = helper_85;

            result_0[74] = helper_99;

            result_0[75] = helper_114;

            result_0[76] = helper_126;

            result_0[77] = helper_130;

            result_0[78] = helper_136;

            result_0[79] = helper_138;

            result_0[80] = helper_87 * (helper_11 * helper_135 * helper_66 + pow(helper_66, 2) * helper_86 + 81);

            ;

            hess(0, 0) = result_0[0];

            hess(0, 1) = result_0[1];

            hess(0, 2) = result_0[2];

            hess(0, 3) = result_0[3];

            hess(0, 4) = result_0[4];

            hess(0, 5) = result_0[5];

            hess(0, 6) = result_0[6];

            hess(0, 7) = result_0[7];

            hess(0, 8) = result_0[8];

            hess(1, 0) = result_0[9];

            hess(1, 1) = result_0[10];

            hess(1, 2) = result_0[11];

            hess(1, 3) = result_0[12];

            hess(1, 4) = result_0[13];

            hess(1, 5) = result_0[14];

            hess(1, 6) = result_0[15];

            hess(1, 7) = result_0[16];

            hess(1, 8) = result_0[17];

            hess(2, 0) = result_0[18];

            hess(2, 1) = result_0[19];

            hess(2, 2) = result_0[20];

            hess(2, 3) = result_0[21];

            hess(2, 4) = result_0[22];

            hess(2, 5) = result_0[23];

            hess(2, 6) = result_0[24];

            hess(2, 7) = result_0[25];

            hess(2, 8) = result_0[26];

            hess(3, 0) = result_0[27];

            hess(3, 1) = result_0[28];

            hess(3, 2) = result_0[29];

            hess(3, 3) = result_0[30];

            hess(3, 4) = result_0[31];

            hess(3, 5) = result_0[32];

            hess(3, 6) = result_0[33];

            hess(3, 7) = result_0[34];

            hess(3, 8) = result_0[35];

            hess(4, 0) = result_0[36];

            hess(4, 1) = result_0[37];

            hess(4, 2) = result_0[38];

            hess(4, 3) = result_0[39];

            hess(4, 4) = result_0[40];

            hess(4, 5) = result_0[41];

            hess(4, 6) = result_0[42];

            hess(4, 7) = result_0[43];

            hess(4, 8) = result_0[44];

            hess(5, 0) = result_0[45];

            hess(5, 1) = result_0[46];

            hess(5, 2) = result_0[47];

            hess(5, 3) = result_0[48];

            hess(5, 4) = result_0[49];

            hess(5, 5) = result_0[50];

            hess(5, 6) = result_0[51];

            hess(5, 7) = result_0[52];

            hess(5, 8) = result_0[53];

            hess(6, 0) = result_0[54];

            hess(6, 1) = result_0[55];

            hess(6, 2) = result_0[56];

            hess(6, 3) = result_0[57];

            hess(6, 4) = result_0[58];

            hess(6, 5) = result_0[59];

            hess(6, 6) = result_0[60];

            hess(6, 7) = result_0[61];

            hess(6, 8) = result_0[62];

            hess(7, 0) = result_0[63];

            hess(7, 1) = result_0[64];

            hess(7, 2) = result_0[65];

            hess(7, 3) = result_0[66];

            hess(7, 4) = result_0[67];

            hess(7, 5) = result_0[68];

            hess(7, 6) = result_0[69];

            hess(7, 7) = result_0[70];

            hess(7, 8) = result_0[71];

            hess(8, 0) = result_0[72];

            hess(8, 1) = result_0[73];

            hess(8, 2) = result_0[74];

            hess(8, 3) = result_0[75];

            hess(8, 4) = result_0[76];

            hess(8, 5) = result_0[77];

            hess(8, 6) = result_0[78];

            hess(8, 7) = result_0[79];

            hess(8, 8) = result_0[80];

            return hess;

        }


    } // namespace autogen

} // namespace polyfem

polyfem::autogen::AMIPS3d_hessian
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9 > AMIPS3d_hessian(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &F)
Definition AMIPS3d.hpp:58

polyfem::autogen::AMIPS3d_gradient
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > AMIPS3d_gradient(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &F)
Definition AMIPS3d.hpp:9

polyfem
Definition ActiveFiber.cpp:4

polyfem::ElasticityTensorType::F
@ F

polyfem::RowVectorNd
Eigen::Matrix< double, 1, Eigen::Dynamic, Eigen::RowMajor, 1, 3 > RowVectorNd
Definition Types.hpp:13