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;

        }


    }

}

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:54

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:7

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