polyfem/_volume_penalty3d_8hpp_source.html

// Auto-generated code for VolumePenalty3d energy

#pragma once

#include <Eigen/Dense>


namespace polyfem

{

    namespace autogen

    {


        Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> VolumePenalty3d_gradient(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> &F, const double k)

        {

            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 = F11 * F22;

            const auto helper_1 = F12 * F21;

            const auto helper_2 = F00 * helper_0;

            const auto helper_3 = F00 * helper_1;

            const auto helper_4 = F10 * F22;

            const auto helper_5 = F01 * helper_4;

            const auto helper_6 = F12 * F20;

            const auto helper_7 = F01 * helper_6;

            const auto helper_8 = F10 * F21;

            const auto helper_9 = F02 * helper_8;

            const auto helper_10 = F11 * F20;

            const auto helper_11 = F02 * helper_10;

            const auto helper_12 = 0.5 * k * (1.0 * helper_11 - 1.0 * helper_2 + 1.0 * helper_3 + 1.0 * helper_5 - 1.0 * helper_7 - 1.0 * helper_9 + 1.0 / (-helper_11 + helper_2 - helper_3 - helper_5 + helper_7 + helper_9));

            result_0[0] = -helper_12 * (helper_0 - helper_1);

            result_0[1] = helper_12 * (helper_4 - helper_6);

            result_0[2] = -helper_12 * (-helper_10 + helper_8);

            result_0[3] = helper_12 * (F01 * F22 - F02 * F21);

            result_0[4] = -helper_12 * (F00 * F22 - F02 * F20);

            result_0[5] = helper_12 * (F00 * F21 - F01 * F20);

            result_0[6] = -helper_12 * (F01 * F12 - F02 * F11);

            result_0[7] = helper_12 * (F00 * F12 - F02 * F10);

            result_0[8] = -helper_12 * (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> VolumePenalty3d_hessian(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> &F, const double k)

        {

            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 = F11 * F22;

            const auto helper_1 = F12 * F21;

            const auto helper_2 = helper_0 - helper_1;

            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_0 - F00 * helper_1 + F01 * helper_3 - F01 * helper_5 + F02 * helper_4 - F02 * helper_6;

            const auto helper_8 = pow(helper_7, -2);

            const auto helper_9 = 0.5 * k;

            const auto helper_10 = helper_9 * (helper_8 + 1.0);

            const auto helper_11 = -helper_3 + helper_5;

            const auto helper_12 = helper_10 * helper_2;

            const auto helper_13 = -helper_11 * helper_12;

            const auto helper_14 = helper_4 - helper_6;

            const auto helper_15 = helper_12 * helper_14;

            const auto helper_16 = F01 * F22 - F02 * F21;

            const auto helper_17 = -helper_12 * helper_16;

            const auto helper_18 = F00 * F22 - F02 * F20;

            const auto helper_19 = helper_18 * helper_2;

            const auto helper_20 = 1.0 * helper_7;

            const auto helper_21 = F22 * helper_20;

            const auto helper_22 = 1.0 / helper_7;

            const auto helper_23 = F22 * helper_22;

            const auto helper_24 = helper_9 * (helper_19 * helper_8 + 1.0 * helper_19 + helper_21 - helper_23);

            const auto helper_25 = F00 * F21 - F01 * F20;

            const auto helper_26 = helper_2 * helper_25;

            const auto helper_27 = F21 * helper_22;

            const auto helper_28 = -helper_9 * (F21 * helper_20 + helper_26 * helper_8 + 1.0 * helper_26 - helper_27);

            const auto helper_29 = F01 * F12 - F02 * F11;

            const auto helper_30 = helper_12 * helper_29;

            const auto helper_31 = F00 * F12 - F02 * F10;

            const auto helper_32 = helper_2 * helper_31;

            const auto helper_33 = F12 * helper_22;

            const auto helper_34 = -helper_9 * (F12 * helper_20 + helper_32 * helper_8 + 1.0 * helper_32 - helper_33);

            const auto helper_35 = F00 * F11 - F01 * F10;

            const auto helper_36 = helper_2 * helper_35;

            const auto helper_37 = F11 * helper_20;

            const auto helper_38 = F11 * helper_22;

            const auto helper_39 = helper_9 * (helper_36 * helper_8 + 1.0 * helper_36 + helper_37 - helper_38);

            const auto helper_40 = helper_10 * helper_11;

            const auto helper_41 = -helper_14 * helper_40;

            const auto helper_42 = helper_11 * helper_16;

            const auto helper_43 = helper_9 * (-helper_21 + helper_23 + helper_42 * helper_8 + 1.0 * helper_42);

            const auto helper_44 = -helper_18 * helper_40;

            const auto helper_45 = helper_11 * helper_25;

            const auto helper_46 = F20 * helper_20;

            const auto helper_47 = F20 * helper_22;

            const auto helper_48 = helper_9 * (helper_45 * helper_8 + 1.0 * helper_45 + helper_46 - helper_47);

            const auto helper_49 = helper_11 * helper_29;

            const auto helper_50 = helper_9 * (1.0 * F12 * helper_7 - helper_33 - helper_49 * helper_8 - 1.0 * helper_49);

            const auto helper_51 = helper_31 * helper_40;

            const auto helper_52 = helper_11 * helper_35;

            const auto helper_53 = F10 * helper_22;

            const auto helper_54 = -helper_9 * (F10 * helper_20 + helper_52 * helper_8 + 1.0 * helper_52 - helper_53);

            const auto helper_55 = helper_14 * helper_16;

            const auto helper_56 = helper_9 * (1.0 * F21 * helper_7 - helper_27 - helper_55 * helper_8 - 1.0 * helper_55);

            const auto helper_57 = helper_14 * helper_18;

            const auto helper_58 = helper_9 * (-helper_46 + helper_47 + helper_57 * helper_8 + 1.0 * helper_57);

            const auto helper_59 = helper_10 * helper_14;

            const auto helper_60 = -helper_25 * helper_59;

            const auto helper_61 = helper_14 * helper_29;

            const auto helper_62 = helper_9 * (-helper_37 + helper_38 + helper_61 * helper_8 + 1.0 * helper_61);

            const auto helper_63 = helper_14 * helper_31;

            const auto helper_64 = helper_9 * (1.0 * F10 * helper_7 - helper_53 - helper_63 * helper_8 - 1.0 * helper_63);

            const auto helper_65 = helper_35 * helper_59;

            const auto helper_66 = helper_10 * helper_16;

            const auto helper_67 = -helper_18 * helper_66;

            const auto helper_68 = helper_25 * helper_66;

            const auto helper_69 = -helper_29 * helper_66;

            const auto helper_70 = helper_16 * helper_31;

            const auto helper_71 = F02 * helper_20;

            const auto helper_72 = F02 * helper_22;

            const auto helper_73 = helper_9 * (helper_70 * helper_8 + 1.0 * helper_70 + helper_71 - helper_72);

            const auto helper_74 = helper_16 * helper_35;

            const auto helper_75 = F01 * helper_22;

            const auto helper_76 = -helper_9 * (F01 * helper_20 + helper_74 * helper_8 + 1.0 * helper_74 - helper_75);

            const auto helper_77 = helper_10 * helper_18;

            const auto helper_78 = -helper_25 * helper_77;

            const auto helper_79 = helper_18 * helper_29;

            const auto helper_80 = helper_9 * (-helper_71 + helper_72 + helper_79 * helper_8 + 1.0 * helper_79);

            const auto helper_81 = -helper_31 * helper_77;

            const auto helper_82 = helper_18 * helper_35;

            const auto helper_83 = F00 * helper_20;

            const auto helper_84 = F00 * helper_22;

            const auto helper_85 = helper_9 * (helper_8 * helper_82 + 1.0 * helper_82 + helper_83 - helper_84);

            const auto helper_86 = helper_25 * helper_29;

            const auto helper_87 = helper_9 * (1.0 * F01 * helper_7 - helper_75 - helper_8 * helper_86 - 1.0 * helper_86);

            const auto helper_88 = helper_25 * helper_31;

            const auto helper_89 = helper_9 * (helper_8 * helper_88 - helper_83 + helper_84 + 1.0 * helper_88);

            const auto helper_90 = helper_10 * helper_35;

            const auto helper_91 = -helper_25 * helper_90;

            const auto helper_92 = -helper_10 * helper_29 * helper_31;

            const auto helper_93 = helper_29 * helper_90;

            const auto helper_94 = -helper_31 * helper_90;

            result_0[0] = helper_10 * pow(helper_2, 2);

            result_0[1] = helper_13;

            result_0[2] = helper_15;

            result_0[3] = helper_17;

            result_0[4] = helper_24;

            result_0[5] = helper_28;

            result_0[6] = helper_30;

            result_0[7] = helper_34;

            result_0[8] = helper_39;

            result_0[9] = helper_13;

            result_0[10] = helper_10 * pow(helper_11, 2);

            result_0[11] = helper_41;

            result_0[12] = helper_43;

            result_0[13] = helper_44;

            result_0[14] = helper_48;

            result_0[15] = helper_50;

            result_0[16] = helper_51;

            result_0[17] = helper_54;

            result_0[18] = helper_15;

            result_0[19] = helper_41;

            result_0[20] = helper_10 * pow(helper_14, 2);

            result_0[21] = helper_56;

            result_0[22] = helper_58;

            result_0[23] = helper_60;

            result_0[24] = helper_62;

            result_0[25] = helper_64;

            result_0[26] = helper_65;

            result_0[27] = helper_17;

            result_0[28] = helper_43;

            result_0[29] = helper_56;

            result_0[30] = helper_10 * pow(helper_16, 2);

            result_0[31] = helper_67;

            result_0[32] = helper_68;

            result_0[33] = helper_69;

            result_0[34] = helper_73;

            result_0[35] = helper_76;

            result_0[36] = helper_24;

            result_0[37] = helper_44;

            result_0[38] = helper_58;

            result_0[39] = helper_67;

            result_0[40] = helper_10 * pow(helper_18, 2);

            result_0[41] = helper_78;

            result_0[42] = helper_80;

            result_0[43] = helper_81;

            result_0[44] = helper_85;

            result_0[45] = helper_28;

            result_0[46] = helper_48;

            result_0[47] = helper_60;

            result_0[48] = helper_68;

            result_0[49] = helper_78;

            result_0[50] = helper_10 * pow(helper_25, 2);

            result_0[51] = helper_87;

            result_0[52] = helper_89;

            result_0[53] = helper_91;

            result_0[54] = helper_30;

            result_0[55] = helper_50;

            result_0[56] = helper_62;

            result_0[57] = helper_69;

            result_0[58] = helper_80;

            result_0[59] = helper_87;

            result_0[60] = helper_10 * pow(helper_29, 2);

            result_0[61] = helper_92;

            result_0[62] = helper_93;

            result_0[63] = helper_34;

            result_0[64] = helper_51;

            result_0[65] = helper_64;

            result_0[66] = helper_73;

            result_0[67] = helper_81;

            result_0[68] = helper_89;

            result_0[69] = helper_92;

            result_0[70] = helper_10 * pow(helper_31, 2);

            result_0[71] = helper_94;

            result_0[72] = helper_39;

            result_0[73] = helper_54;

            result_0[74] = helper_65;

            result_0[75] = helper_76;

            result_0[76] = helper_85;

            result_0[77] = helper_91;

            result_0[78] = helper_93;

            result_0[79] = helper_94;

            result_0[80] = helper_10 * pow(helper_35, 2);

            ;

            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::VolumePenalty3d_gradient
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > VolumePenalty3d_gradient(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &F, const double k)
Definition VolumePenalty3d.hpp:9

polyfem::autogen::VolumePenalty3d_hessian
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9 > VolumePenalty3d_hessian(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &F, const double k)
Definition VolumePenalty3d.hpp:57

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