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 = 9*F01;

const auto helper_1 = 9*F02;

const auto helper_2 = F11*F22;

const auto helper_3 = F12*F21;

const auto helper_4 = F12*F20;

const auto helper_5 = F10*F21;

const auto helper_6 = F10*F22;

const auto helper_7 = F11*F20;

const auto helper_8 = F00*helper_2 - F00*helper_3 + F01*helper_4 - F01*helper_6 + F02*helper_5 - F02*helper_7;

const auto helper_9 = 1.0/helper_8;

const auto helper_10 = 6*pow(F00, 2) + 6*pow(F10, 2) + 6*pow(F20, 2) + 2*pow(F00 - 2*F01, 2) + 2*pow(F10 - 2*F11, 2) + 2*pow(F20 - 2*F21, 2) + pow(F00 + F01 - 3*F02, 2) + pow(F10 + F11 - 3*F12, 2) + pow(F20 + F21 - 3*F22, 2);

const auto helper_11 = helper_10*helper_9;

const auto helper_12 = (1.0/18.0)*pow(2, 2.0/3.0)/pow(helper_8, 2.0/3.0);

const auto helper_13 = 9*F00;

const auto helper_14 = 9*F11;

const auto helper_15 = 9*F12;

const auto helper_16 = 9*F10;

const auto helper_17 = 9*F21;

const auto helper_18 = 9*F22;

const auto helper_19 = 9*F20;

result_0[0] = -helper_12*(-27*F00 + helper_0 + helper_1 + helper_11*(helper_2 - helper_3));

result_0[1] = helper_12*(27*F01 - helper_1 + helper_10*helper_9*(-helper_4 + helper_6) - helper_13);

result_0[2] = -helper_12*(-27*F02 + helper_0 + helper_11*(helper_5 - helper_7) + helper_13);

result_0[3] = helper_12*(27*F10 + helper_11*(F01*F22 - F02*F21) - helper_14 - helper_15);

result_0[4] = -helper_12*(-27*F11 + helper_11*(F00*F22 - F02*F20) + helper_15 + helper_16);

result_0[5] = helper_12*(27*F12 + helper_10*helper_9*(F00*F21 - F01*F20) - helper_14 - helper_16);

result_0[6] = -helper_12*(-27*F20 + helper_11*(F01*F12 - F02*F11) + helper_17 + helper_18);

result_0[7] = helper_12*(27*F21 + helper_10*helper_9*(F00*F12 - F02*F10) - helper_18 - helper_19);

result_0[8] = -helper_12*(-27*F22 + helper_11*(F00*F11 - F01*F10) + helper_17 + helper_19);;

            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 = 3*F00;

const auto helper_1 = F01 + F02 - helper_0;

const auto helper_2 = F11*F22;

const auto helper_3 = F12*F21;

const auto helper_4 = helper_2 - helper_3;

const auto helper_5 = F12*F20;

const auto helper_6 = F10*F21;

const auto helper_7 = F10*F22;

const auto helper_8 = F11*F20;

const auto helper_9 = F00*helper_2 - F00*helper_3 + F01*helper_5 - F01*helper_7 + F02*helper_6 - F02*helper_8;

const auto helper_10 = 1.0/helper_9;

const auto helper_11 = 36*helper_10;

const auto helper_12 = pow(helper_9, -2);

const auto helper_13 = 3*F02;

const auto helper_14 = F00 + F01 - helper_13;

const auto helper_15 = 3*F12;

const auto helper_16 = F10 + F11 - helper_15;

const auto helper_17 = 3*F22;

const auto helper_18 = F20 + F21 - helper_17;

const auto helper_19 = 6*pow(F00, 2) + 6*pow(F10, 2) + 6*pow(F20, 2) + pow(helper_14, 2) + pow(helper_16, 2) + pow(helper_18, 2) + 2*pow(F00 - 2*F01, 2) + 2*pow(F10 - 2*F11, 2) + 2*pow(F20 - 2*F21, 2);

const auto helper_20 = 5*helper_19;

const auto helper_21 = helper_12*helper_20;

const auto helper_22 = (1.0/54.0)*pow(2, 2.0/3.0);

const auto helper_23 = helper_22/pow(helper_9, 2.0/3.0);

const auto helper_24 = -helper_5 + helper_7;

const auto helper_25 = 18*helper_1;

const auto helper_26 = helper_10*helper_25;

const auto helper_27 = 3*F01;

const auto helper_28 = F00 + F02 - helper_27;

const auto helper_29 = helper_21*helper_4;

const auto helper_30 = helper_23*(18*helper_10*helper_28*helper_4 - helper_24*helper_26 - helper_24*helper_29 - 27);

const auto helper_31 = helper_6 - helper_8;

const auto helper_32 = 18*helper_4;

const auto helper_33 = helper_23*(helper_10*helper_14*helper_32 + helper_26*helper_31 + helper_29*helper_31 - 27);

const auto helper_34 = F01*F22 - F02*F21;

const auto helper_35 = 3*F10;

const auto helper_36 = F11 + F12 - helper_35;

const auto helper_37 = helper_20*helper_4;

const auto helper_38 = helper_10*helper_37;

const auto helper_39 = helper_22/pow(helper_9, 5.0/3.0);

const auto helper_40 = helper_39*(-helper_25*helper_34 - helper_34*helper_38 + 18*helper_36*helper_4);

const auto helper_41 = F00*F22 - F02*F20;

const auto helper_42 = 3*F11;

const auto helper_43 = F10 + F12 - helper_42;

const auto helper_44 = helper_17*helper_19;

const auto helper_45 = helper_39*(helper_25*helper_41 + helper_32*helper_43 + helper_38*helper_41 - helper_44);

const auto helper_46 = F00*F21 - F01*F20;

const auto helper_47 = 3*F21;

const auto helper_48 = helper_19*helper_47;

const auto helper_49 = helper_10*helper_46;

const auto helper_50 = helper_39*(helper_16*helper_32 - helper_25*helper_46 - helper_37*helper_49 + helper_48);

const auto helper_51 = F01*F12 - F02*F11;

const auto helper_52 = 3*F20;

const auto helper_53 = F21 + F22 - helper_52;

const auto helper_54 = helper_39*(helper_25*helper_51 + helper_32*helper_53 + helper_38*helper_51);

const auto helper_55 = F00*F12 - F02*F10;

const auto helper_56 = F20 + F22 - helper_47;

const auto helper_57 = helper_15*helper_19;

const auto helper_58 = helper_39*(-helper_25*helper_55 + helper_32*helper_56 - helper_38*helper_55 + helper_57);

const auto helper_59 = F00*F11 - F01*F10;

const auto helper_60 = helper_19*helper_42;

const auto helper_61 = helper_39*(helper_18*helper_32 + helper_25*helper_59 + helper_38*helper_59 - helper_60);

const auto helper_62 = 18*helper_24;

const auto helper_63 = helper_23*(-helper_10*helper_14*helper_62 + 18*helper_10*helper_28*helper_31 - helper_21*helper_24*helper_31 - 27);

const auto helper_64 = 18*helper_28;

const auto helper_65 = helper_10*helper_20*helper_24;

const auto helper_66 = helper_39*(-helper_34*helper_64 + helper_34*helper_65 - helper_36*helper_62 + helper_44);

const auto helper_67 = helper_39*(18*helper_28*helper_41 - helper_41*helper_65 - helper_43*helper_62);

const auto helper_68 = helper_19*helper_52;

const auto helper_69 = helper_39*(5*helper_10*helper_19*helper_24*helper_46 - helper_16*helper_62 - helper_46*helper_64 - helper_68);

const auto helper_70 = helper_39*(18*helper_28*helper_51 - helper_51*helper_65 - helper_53*helper_62 - helper_57);

const auto helper_71 = helper_39*(5*helper_10*helper_19*helper_24*helper_55 - helper_55*helper_64 - helper_56*helper_62);

const auto helper_72 = helper_19*helper_35;

const auto helper_73 = helper_39*(-helper_18*helper_62 + helper_59*helper_64 - helper_59*helper_65 + helper_72);

const auto helper_74 = 18*helper_14;

const auto helper_75 = helper_10*helper_20*helper_31;

const auto helper_76 = helper_39*(18*helper_31*helper_36 - helper_34*helper_74 - helper_34*helper_75 - helper_48);

const auto helper_77 = 18*helper_31;

const auto helper_78 = helper_39*(helper_41*helper_74 + helper_41*helper_75 + helper_43*helper_77 + helper_68);

const auto helper_79 = helper_39*(18*helper_16*helper_31 - helper_46*helper_74 - helper_46*helper_75);

const auto helper_80 = helper_39*(helper_51*helper_74 + helper_51*helper_75 + helper_53*helper_77 + helper_60);

const auto helper_81 = helper_39*(18*helper_31*helper_56 - helper_55*helper_74 - helper_55*helper_75 - helper_72);

const auto helper_82 = helper_39*(helper_18*helper_77 + helper_59*helper_74 + helper_59*helper_75);

const auto helper_83 = 18*helper_34;

const auto helper_84 = helper_10*helper_83;

const auto helper_85 = helper_23*(18*helper_10*helper_36*helper_41 - helper_21*helper_34*helper_41 - helper_43*helper_84 - 27);

const auto helper_86 = 18*helper_36;

const auto helper_87 = helper_23*(-helper_10*helper_46*helper_86 + 5*helper_12*helper_19*helper_34*helper_46 - helper_16*helper_84 - 27);

const auto helper_88 = helper_10*helper_20;

const auto helper_89 = helper_34*helper_88;

const auto helper_90 = helper_39*(18*helper_36*helper_51 - helper_51*helper_89 - helper_53*helper_83);

const auto helper_91 = helper_13*helper_19;

const auto helper_92 = helper_39*(5*helper_10*helper_19*helper_34*helper_55 - helper_55*helper_86 - helper_56*helper_83 - helper_91);

const auto helper_93 = helper_19*helper_27;

const auto helper_94 = helper_39*(-helper_18*helper_83 + helper_59*helper_86 - helper_59*helper_89 + helper_93);

const auto helper_95 = 18*helper_43;

const auto helper_96 = helper_23*(18*helper_10*helper_16*helper_41 - helper_21*helper_41*helper_46 - helper_49*helper_95 - 27);

const auto helper_97 = 18*helper_41;

const auto helper_98 = helper_41*helper_88;

const auto helper_99 = helper_39*(helper_51*helper_95 + helper_51*helper_98 + helper_53*helper_97 + helper_91);

const auto helper_100 = helper_39*(18*helper_41*helper_56 - helper_55*helper_95 - helper_55*helper_98);

const auto helper_101 = helper_0*helper_19;

const auto helper_102 = helper_39*(-helper_101 + helper_18*helper_97 + helper_59*helper_95 + helper_59*helper_98);

const auto helper_103 = 18*helper_46;

const auto helper_104 = helper_20*helper_49;

const auto helper_105 = helper_39*(-helper_103*helper_53 - helper_104*helper_51 + 18*helper_16*helper_51 - helper_93);

const auto helper_106 = helper_39*(helper_101 - helper_103*helper_56 + helper_104*helper_55 - 18*helper_16*helper_55);

const auto helper_107 = helper_39*(-helper_103*helper_18 - helper_104*helper_59 + 18*helper_16*helper_59);

const auto helper_108 = 18*helper_10;

const auto helper_109 = helper_108*helper_53;

const auto helper_110 = helper_21*helper_51;

const auto helper_111 = helper_23*(18*helper_10*helper_51*helper_56 - helper_109*helper_55 - helper_110*helper_55 - 27);

const auto helper_112 = helper_23*(helper_108*helper_18*helper_51 + helper_109*helper_59 + helper_110*helper_59 - 27);

const auto helper_113 = helper_23*(18*helper_10*helper_56*helper_59 - helper_108*helper_18*helper_55 - helper_21*helper_55*helper_59 - 27);

result_0[0] = helper_23*(helper_1*helper_11*helper_4 + helper_21*pow(helper_4, 2) + 81);

result_0[1] = helper_30;

result_0[2] = helper_33;

result_0[3] = helper_40;

result_0[4] = helper_45;

result_0[5] = helper_50;

result_0[6] = helper_54;

result_0[7] = helper_58;

result_0[8] = helper_61;

result_0[9] = helper_30;

result_0[10] = helper_23*(-helper_11*helper_24*helper_28 + helper_21*pow(helper_24, 2) + 81);

result_0[11] = helper_63;

result_0[12] = helper_66;

result_0[13] = helper_67;

result_0[14] = helper_69;

result_0[15] = helper_70;

result_0[16] = helper_71;

result_0[17] = helper_73;

result_0[18] = helper_33;

result_0[19] = helper_63;

result_0[20] = helper_23*(helper_11*helper_14*helper_31 + helper_21*pow(helper_31, 2) + 81);

result_0[21] = helper_76;

result_0[22] = helper_78;

result_0[23] = helper_79;

result_0[24] = helper_80;

result_0[25] = helper_81;

result_0[26] = helper_82;

result_0[27] = helper_40;

result_0[28] = helper_66;

result_0[29] = helper_76;

result_0[30] = helper_23*(-helper_11*helper_34*helper_36 + helper_21*pow(helper_34, 2) + 81);

result_0[31] = helper_85;

result_0[32] = helper_87;

result_0[33] = helper_90;

result_0[34] = helper_92;

result_0[35] = helper_94;

result_0[36] = helper_45;

result_0[37] = helper_67;

result_0[38] = helper_78;

result_0[39] = helper_85;

result_0[40] = helper_23*(helper_11*helper_41*helper_43 + helper_21*pow(helper_41, 2) + 81);

result_0[41] = helper_96;

result_0[42] = helper_99;

result_0[43] = helper_100;

result_0[44] = helper_102;

result_0[45] = helper_50;

result_0[46] = helper_69;

result_0[47] = helper_79;

result_0[48] = helper_87;

result_0[49] = helper_96;

result_0[50] = helper_23*(-helper_11*helper_16*helper_46 + helper_21*pow(helper_46, 2) + 81);

result_0[51] = helper_105;

result_0[52] = helper_106;

result_0[53] = helper_107;

result_0[54] = helper_54;

result_0[55] = helper_70;

result_0[56] = helper_80;

result_0[57] = helper_90;

result_0[58] = helper_99;

result_0[59] = helper_105;

result_0[60] = helper_23*(helper_11*helper_51*helper_53 + helper_21*pow(helper_51, 2) + 81);

result_0[61] = helper_111;

result_0[62] = helper_112;

result_0[63] = helper_58;

result_0[64] = helper_71;

result_0[65] = helper_81;

result_0[66] = helper_92;

result_0[67] = helper_100;

result_0[68] = helper_106;

result_0[69] = helper_111;

result_0[70] = helper_23*(-helper_11*helper_55*helper_56 + helper_21*pow(helper_55, 2) + 81);

result_0[71] = helper_113;

result_0[72] = helper_61;

result_0[73] = helper_73;

result_0[74] = helper_82;

result_0[75] = helper_94;

result_0[76] = helper_102;

result_0[77] = helper_107;

result_0[78] = helper_112;

result_0[79] = helper_113;

result_0[80] = helper_23*(helper_11*helper_18*helper_59 + helper_21*pow(helper_59, 2) + 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:60

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