polyfem/_a_m_i_p_s3drest_8hpp_source.html

// Auto-generated code for AMIPS3drest energy

#pragma once

#include <Eigen/Dense>


namespace polyfem

{

    namespace autogen

    {


        Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3> AMIPS3drest_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 = F11 * F22;

            const auto helper_1 = F12 * F21;

            const auto helper_2 = F12 * F20;

            const auto helper_3 = F10 * F21;

            const auto helper_4 = F10 * F22;

            const auto helper_5 = F11 * F20;

            const auto helper_6 = F00 * helper_0 - F00 * helper_1 + F01 * helper_2 - F01 * helper_4 + F02 * helper_3 - F02 * helper_5;

            const auto helper_7 = (1.0 / 3.0) * (pow(F00, 2) + pow(F01, 2) + pow(F02, 2) + pow(F10, 2) + pow(F11, 2) + pow(F12, 2) + pow(F20, 2) + pow(F21, 2) + pow(F22, 2)) / helper_6;

            const auto helper_8 = 2 / pow(helper_6, 2.0 / 3.0);

            result_0[0] = helper_8 * (F00 - helper_7 * (helper_0 - helper_1));

            result_0[1] = helper_8 * (F01 + helper_7 * (-helper_2 + helper_4));

            result_0[2] = helper_8 * (F02 - helper_7 * (helper_3 - helper_5));

            result_0[3] = helper_8 * (F10 + helper_7 * (F01 * F22 - F02 * F21));

            result_0[4] = helper_8 * (F11 - helper_7 * (F00 * F22 - F02 * F20));

            result_0[5] = helper_8 * (F12 + helper_7 * (F00 * F21 - F01 * F20));

            result_0[6] = helper_8 * (F20 - helper_7 * (F01 * F12 - F02 * F11));

            result_0[7] = helper_8 * (F21 + helper_7 * (F00 * F12 - F02 * F10));

            result_0[8] = helper_8 * (F22 - helper_7 * (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> AMIPS3drest_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 = 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 = 1.0 / helper_7;

            const auto helper_9 = (4.0 / 3.0) * helper_8;

            const auto helper_10 = pow(F00, 2) + pow(F01, 2) + pow(F02, 2) + pow(F10, 2) + pow(F11, 2) + pow(F12, 2) + pow(F20, 2) + pow(F21, 2) + pow(F22, 2);

            const auto helper_11 = (5.0 / 9.0) * helper_10 / pow(helper_7, 2);

            const auto helper_12 = 2 / pow(helper_7, 2.0 / 3.0);

            const auto helper_13 = -helper_3 + helper_5;

            const auto helper_14 = 6 * helper_2;

            const auto helper_15 = 5 * helper_10 * helper_8;

            const auto helper_16 = helper_15 * helper_2;

            const auto helper_17 = (2.0 / 9.0) / pow(helper_7, 5.0 / 3.0);

            const auto helper_18 = helper_17 * (6 * F00 * helper_13 - F01 * helper_14 - helper_13 * helper_16);

            const auto helper_19 = helper_4 - helper_6;

            const auto helper_20 = 6 * F00;

            const auto helper_21 = helper_17 * (-F02 * helper_14 + 5 * helper_10 * helper_19 * helper_2 * helper_8 - helper_19 * helper_20);

            const auto helper_22 = F01 * F22 - F02 * F21;

            const auto helper_23 = helper_17 * (6 * F00 * helper_22 - F10 * helper_14 - helper_16 * helper_22);

            const auto helper_24 = F00 * F22 - F02 * F20;

            const auto helper_25 = 3 * helper_10;

            const auto helper_26 = F22 * helper_25;

            const auto helper_27 = helper_17 * (-F11 * helper_14 + 5 * helper_10 * helper_2 * helper_24 * helper_8 - helper_20 * helper_24 - helper_26);

            const auto helper_28 = F00 * F21 - F01 * F20;

            const auto helper_29 = F21 * helper_25;

            const auto helper_30 = helper_17 * (-F12 * helper_14 - helper_16 * helper_28 + helper_20 * helper_28 + helper_29);

            const auto helper_31 = F01 * F12 - F02 * F11;

            const auto helper_32 = helper_17 * (-F20 * helper_14 + 5 * helper_10 * helper_2 * helper_31 * helper_8 - helper_20 * helper_31);

            const auto helper_33 = F00 * F12 - F02 * F10;

            const auto helper_34 = F12 * helper_25;

            const auto helper_35 = helper_17 * (-F21 * helper_14 - helper_16 * helper_33 + helper_20 * helper_33 + helper_34);

            const auto helper_36 = F00 * F11 - F01 * F10;

            const auto helper_37 = F11 * helper_25;

            const auto helper_38 = helper_17 * (-F22 * helper_14 + 5 * helper_10 * helper_2 * helper_36 * helper_8 - helper_20 * helper_36 - helper_37);

            const auto helper_39 = 6 * F01;

            const auto helper_40 = helper_13 * helper_15;

            const auto helper_41 = helper_17 * (6 * F02 * helper_13 - helper_19 * helper_39 - helper_19 * helper_40);

            const auto helper_42 = 6 * helper_13;

            const auto helper_43 = helper_17 * (F10 * helper_42 + helper_22 * helper_39 + helper_22 * helper_40 + helper_26);

            const auto helper_44 = helper_17 * (6 * F11 * helper_13 - helper_24 * helper_39 - helper_24 * helper_40);

            const auto helper_45 = -F20 * helper_25;

            const auto helper_46 = helper_17 * (F12 * helper_42 + helper_28 * helper_39 + helper_28 * helper_40 + helper_45);

            const auto helper_47 = helper_17 * (6 * F20 * helper_13 - helper_31 * helper_39 - helper_31 * helper_40 - helper_34);

            const auto helper_48 = helper_17 * (F21 * helper_42 + helper_33 * helper_39 + helper_33 * helper_40);

            const auto helper_49 = F10 * helper_25;

            const auto helper_50 = helper_17 * (6 * F22 * helper_13 - helper_36 * helper_39 - helper_36 * helper_40 + helper_49);

            const auto helper_51 = 6 * helper_19;

            const auto helper_52 = helper_15 * helper_19;

            const auto helper_53 = helper_17 * (6 * F02 * helper_22 - F10 * helper_51 - helper_22 * helper_52 - helper_29);

            const auto helper_54 = 6 * F02;

            const auto helper_55 = helper_17 * (-F11 * helper_51 + 5 * helper_10 * helper_19 * helper_24 * helper_8 - helper_24 * helper_54 - helper_45);

            const auto helper_56 = helper_17 * (6 * F02 * helper_28 - F12 * helper_51 - helper_28 * helper_52);

            const auto helper_57 = helper_17 * (-F20 * helper_51 + 5 * helper_10 * helper_19 * helper_31 * helper_8 - helper_31 * helper_54 + helper_37);

            const auto helper_58 = helper_17 * (6 * F02 * helper_33 - F21 * helper_51 - helper_33 * helper_52 - helper_49);

            const auto helper_59 = helper_17 * (-F22 * helper_51 + 5 * helper_10 * helper_19 * helper_36 * helper_8 - helper_36 * helper_54);

            const auto helper_60 = 6 * F10;

            const auto helper_61 = helper_15 * helper_22;

            const auto helper_62 = helper_17 * (6 * F11 * helper_22 - helper_24 * helper_60 - helper_24 * helper_61);

            const auto helper_63 = 6 * helper_22;

            const auto helper_64 = helper_17 * (F12 * helper_63 + helper_28 * helper_60 + helper_28 * helper_61);

            const auto helper_65 = helper_17 * (6 * F20 * helper_22 - helper_31 * helper_60 - helper_31 * helper_61);

            const auto helper_66 = F02 * helper_25;

            const auto helper_67 = helper_17 * (F21 * helper_63 + helper_33 * helper_60 + helper_33 * helper_61 - helper_66);

            const auto helper_68 = F01 * helper_25;

            const auto helper_69 = helper_17 * (F22 * helper_63 - helper_36 * helper_60 - helper_36 * helper_61 + helper_68);

            const auto helper_70 = 6 * helper_24;

            const auto helper_71 = helper_15 * helper_24;

            const auto helper_72 = helper_17 * (6 * F11 * helper_28 - F12 * helper_70 - helper_28 * helper_71);

            const auto helper_73 = 6 * F11;

            const auto helper_74 = helper_17 * (-F20 * helper_70 + helper_31 * helper_71 - helper_31 * helper_73 + helper_66);

            const auto helper_75 = helper_17 * (6 * F11 * helper_33 - F21 * helper_70 - helper_33 * helper_71);

            const auto helper_76 = F00 * helper_25;

            const auto helper_77 = helper_17 * (-F22 * helper_70 + 5 * helper_10 * helper_24 * helper_36 * helper_8 - helper_36 * helper_73 - helper_76);

            const auto helper_78 = 6 * F12;

            const auto helper_79 = helper_15 * helper_28;

            const auto helper_80 = helper_17 * (6 * F20 * helper_28 - helper_31 * helper_78 - helper_31 * helper_79 - helper_68);

            const auto helper_81 = helper_17 * (6 * F21 * helper_28 + helper_33 * helper_78 + helper_33 * helper_79 + helper_76);

            const auto helper_82 = helper_17 * (6 * F22 * helper_28 - helper_36 * helper_78 - helper_36 * helper_79);

            const auto helper_83 = 6 * helper_31;

            const auto helper_84 = helper_17 * (6 * F20 * helper_33 - F21 * helper_83 - helper_15 * helper_31 * helper_33);

            const auto helper_85 = helper_17 * (-6 * F20 * helper_36 - F22 * helper_83 + 5 * helper_10 * helper_31 * helper_36 * helper_8);

            const auto helper_86 = helper_17 * (-6 * F21 * helper_36 + 6 * F22 * helper_33 - helper_15 * helper_33 * helper_36);

            result_0[0] = helper_12 * (-F00 * helper_2 * helper_9 + helper_11 * pow(helper_2, 2) + 1);

            result_0[1] = helper_18;

            result_0[2] = helper_21;

            result_0[3] = helper_23;

            result_0[4] = helper_27;

            result_0[5] = helper_30;

            result_0[6] = helper_32;

            result_0[7] = helper_35;

            result_0[8] = helper_38;

            result_0[9] = helper_18;

            result_0[10] = helper_12 * (F01 * helper_13 * helper_9 + helper_11 * pow(helper_13, 2) + 1);

            result_0[11] = helper_41;

            result_0[12] = helper_43;

            result_0[13] = helper_44;

            result_0[14] = helper_46;

            result_0[15] = helper_47;

            result_0[16] = helper_48;

            result_0[17] = helper_50;

            result_0[18] = helper_21;

            result_0[19] = helper_41;

            result_0[20] = helper_12 * (-F02 * helper_19 * helper_9 + helper_11 * pow(helper_19, 2) + 1);

            result_0[21] = helper_53;

            result_0[22] = helper_55;

            result_0[23] = helper_56;

            result_0[24] = helper_57;

            result_0[25] = helper_58;

            result_0[26] = helper_59;

            result_0[27] = helper_23;

            result_0[28] = helper_43;

            result_0[29] = helper_53;

            result_0[30] = helper_12 * (F10 * helper_22 * helper_9 + helper_11 * pow(helper_22, 2) + 1);

            result_0[31] = helper_62;

            result_0[32] = helper_64;

            result_0[33] = helper_65;

            result_0[34] = helper_67;

            result_0[35] = helper_69;

            result_0[36] = helper_27;

            result_0[37] = helper_44;

            result_0[38] = helper_55;

            result_0[39] = helper_62;

            result_0[40] = helper_12 * (-F11 * helper_24 * helper_9 + helper_11 * pow(helper_24, 2) + 1);

            result_0[41] = helper_72;

            result_0[42] = helper_74;

            result_0[43] = helper_75;

            result_0[44] = helper_77;

            result_0[45] = helper_30;

            result_0[46] = helper_46;

            result_0[47] = helper_56;

            result_0[48] = helper_64;

            result_0[49] = helper_72;

            result_0[50] = helper_12 * (F12 * helper_28 * helper_9 + helper_11 * pow(helper_28, 2) + 1);

            result_0[51] = helper_80;

            result_0[52] = helper_81;

            result_0[53] = helper_82;

            result_0[54] = helper_32;

            result_0[55] = helper_47;

            result_0[56] = helper_57;

            result_0[57] = helper_65;

            result_0[58] = helper_74;

            result_0[59] = helper_80;

            result_0[60] = helper_12 * (-F20 * helper_31 * helper_9 + helper_11 * pow(helper_31, 2) + 1);

            result_0[61] = helper_84;

            result_0[62] = helper_85;

            result_0[63] = helper_35;

            result_0[64] = helper_48;

            result_0[65] = helper_58;

            result_0[66] = helper_67;

            result_0[67] = helper_75;

            result_0[68] = helper_81;

            result_0[69] = helper_84;

            result_0[70] = helper_12 * (F21 * helper_33 * helper_9 + helper_11 * pow(helper_33, 2) + 1);

            result_0[71] = helper_86;

            result_0[72] = helper_38;

            result_0[73] = helper_50;

            result_0[74] = helper_59;

            result_0[75] = helper_69;

            result_0[76] = helper_77;

            result_0[77] = helper_82;

            result_0[78] = helper_85;

            result_0[79] = helper_86;

            result_0[80] = helper_12 * (-F22 * helper_36 * helper_9 + helper_11 * pow(helper_36, 2) + 1);

            ;

            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::AMIPS3drest_gradient
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > AMIPS3drest_gradient(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &F)
Definition AMIPS3drest.hpp:9

polyfem::autogen::AMIPS3drest_hessian
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 9, 9 > AMIPS3drest_hessian(const RowVectorNd &p, const double t, const int el_id, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &F)
Definition AMIPS3drest.hpp:53

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