13027 lines
383 KiB
C
13027 lines
383 KiB
C
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#ifdef newc
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#include <iostream>
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#include <iomanip>
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#include <fstream>
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#include <cstdlib>
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#include <cstdio>
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#include <string>
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#include <cmath>
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using namespace std;
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#else
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#include <iostream.h>
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#include <iomanip.h>
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#include <fstream.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#endif
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#define Power(x,y) (pow((double) (x), (double) (y)))
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#define Sqrt(x) sqrt(x)
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#define Log(x) log((double) (x))
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#define pow2(x) ((x)*(x))
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#define pow3(x) ((x)*(x)*(x))
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#define pow4(x) ((x)*(x)*(x)*(x))
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#define pow2inv(x) (1.0/((x)*(x)))
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#define Cal(x,y,z) ((x)?(y):(z))
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#define Tan(x) tan(x)
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#define ArcTan(x) atan(x)
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#define Sin(x) sin(x)
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#define Cos(x) cos(x)
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#define Csc(x) (1./sin(x))
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#define Abs(x) (fabs(x))
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#define sqrt2 (sqrt(2))
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#define Tanh(x) tanh(x)
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#define Sech(x) (1/cosh(x))
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extern "C" {
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#ifdef fortran1
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void cpbc_point
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#endif
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#ifdef fortran2
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void CPBC_POINT
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#endif
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#ifdef fortran3
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void cpbc_point_
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#endif
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(double & r,double & xp,double & yp,double & zp,
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double & Theta,double & chi,double & Khat,
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double & g11,double & g12,double & g13,double & g22,double & g23,double & g33,
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double & A11,double & A12,double & A13,double & A22,double & A23,double & A33,
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double & G1,double & G2,double & G3,
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double & alpha,double & beta1,double & beta2,double & beta3,
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double & da1,double & da2,double & da3,
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double & dda11,double & dda12,double & dda13,double & dda22,double & dda23,double & dda33,
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double & db11,double & db21,double & db31,
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double & db12,double & db22,double & db32,
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double & db13,double & db23,double & db33,
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double & ddb111,double & ddb121,double & ddb131,double & ddb221,double & ddb231,double & ddb331,
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double & ddb112,double & ddb122,double & ddb132,double & ddb222,double & ddb232,double & ddb332,
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double & ddb113,double & ddb123,double & ddb133,double & ddb223,double & ddb233,double & ddb333,
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double & dchi1,double & dchi2,double & dchi3,
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double & ddchi11,double & ddchi12,double & ddchi13,double & ddchi22,double & ddchi23,double & ddchi33,
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double & dg111,double & dg112,double & dg113,double & dg122,double & dg123,double & dg133,
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double & dg211,double & dg212,double & dg213,double & dg222,double & dg223,double & dg233,
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double & dg311,double & dg312,double & dg313,double & dg322,double & dg323,double & dg333,
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double & ddg1111,double & ddg1211,double & ddg1311,double & ddg2211,double & ddg2311,double & ddg3311,
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double & ddg1112,double & ddg1212,double & ddg1312,double & ddg2212,double & ddg2312,double & ddg3312,
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double & ddg1113,double & ddg1213,double & ddg1313,double & ddg2213,double & ddg2313,double & ddg3313,
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double & ddg1122,double & ddg1222,double & ddg1322,double & ddg2222,double & ddg2322,double & ddg3322,
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double & ddg1123,double & ddg1223,double & ddg1323,double & ddg2223,double & ddg2323,double & ddg3323,
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double & ddg1133,double & ddg1233,double & ddg1333,double & ddg2233,double & ddg2333,double & ddg3333,
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double & dKhat1,double & dKhat2,double & dKhat3,
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double & dA111,double & dA112,double & dA113,double & dA122,double & dA123,double & dA133,
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double & dA211,double & dA212,double & dA213,double & dA222,double & dA223,double & dA233,
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double & dA311,double & dA312,double & dA313,double & dA322,double & dA323,double & dA333,
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double & dG11,double & dG21,double & dG31,
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double & dG12,double & dG22,double & dG32,
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double & dG13,double & dG23,double & dG33,
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double & dTheta1,double & dTheta2,double & dTheta3,
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double & rKhat,double & rTheta,
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double & rA11,double & rA12,double & rA13,double & rA22,double & rA23,double & rA33,
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double & rG1,double & rG2,double & rG3,
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double &kappa1,double &kappa2,double &shiftdriver)
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{
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double AA11;
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double AA12;
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double AA13;
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double AA21;
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double AA22;
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double AA23;
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double AA31;
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double AA32;
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double AA33;
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double ADMginv11;
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double ADMginv12;
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double ADMginv13;
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double ADMginv22;
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double ADMginv23;
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double ADMginv33;
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double Ainv11;
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double Ainv12;
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double Ainv13;
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double Ainv22;
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double Ainv23;
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double Ainv33;
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double betaA1;
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double betaA2;
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double betaA3;
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double betas;
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double cdA111;
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double cdA112;
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double cdA113;
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double cdA122;
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double cdA123;
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double cdA133;
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double cdA211;
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double cdA212;
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double cdA213;
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double cdA222;
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double cdA223;
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double cdA233;
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double cdA311;
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double cdA312;
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double cdA313;
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double cdA322;
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double cdA323;
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double cdA333;
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double cdda11;
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double cdda12;
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double cdda13;
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double cdda22;
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double cdda23;
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double cdda33;
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double cddf11;
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double cddf12;
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double cddf13;
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double cddf22;
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double cddf23;
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double cddf33;
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const double chipsipower = -4;
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double Dalpha;
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double DbetaA1;
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double DbetaA2;
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double DbetaA3;
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double Dbetas;
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double ddf11;
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double ddf12;
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double ddf13;
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double ddf22;
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double ddf23;
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double ddf33;
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double detginv;
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double df1;
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double df2;
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double df3;
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double DGamA1;
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double DGamA2;
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double DGamA3;
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double DGams;
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double dGfromgdu11;
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double dGfromgdu12;
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double dGfromgdu13;
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double dGfromgdu21;
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double dGfromgdu22;
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double dGfromgdu23;
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double dGfromgdu31;
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double dGfromgdu32;
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double dGfromgdu33;
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double dginv111;
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double dginv112;
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double dginv113;
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double dginv122;
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double dginv123;
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double dginv133;
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double dginv211;
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double dginv212;
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double dginv213;
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double dginv222;
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double dginv223;
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double dginv233;
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double dginv311;
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double dginv312;
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double dginv313;
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double dginv322;
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double dginv323;
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double dginv333;
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double divbeta;
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double DK;
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double dK1;
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double dK2;
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double dK3;
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double DKhat;
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double DTheta;
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double f;
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double ff;
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double gADM11;
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double gADM12;
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double gADM13;
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double gADM21;
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double gADM22;
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double gADM23;
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double gADM31;
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double gADM32;
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double gADM33;
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double GamA1;
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double GamA2;
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double GamA3;
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double gamma111;
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double gamma112;
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double gamma113;
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double gamma122;
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double gamma123;
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double gamma133;
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double gamma211;
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double gamma212;
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double gamma213;
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double gamma222;
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double gamma223;
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double gamma233;
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double gamma311;
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double gamma312;
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double gamma313;
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double gamma322;
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double gamma323;
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double gamma333;
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double gammado111;
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double gammado112;
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double gammado113;
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double gammado122;
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double gammado123;
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double gammado133;
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double gammado211;
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double gammado212;
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double gammado213;
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double gammado222;
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double gammado223;
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double gammado233;
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double gammado311;
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double gammado312;
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double gammado313;
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double gammado322;
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double gammado323;
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double gammado333;
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double Gams;
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double Gfromg1;
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double Gfromg2;
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double Gfromg3;
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double ginv11;
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double ginv12;
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double ginv13;
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double ginv22;
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double ginv23;
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double ginv33;
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const bool givehPsi0 = false;
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const double hPsi0para = 0;
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const double hPsi0parb = 0;
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const double hPsi0parc = 0;
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double ImhPsi0;
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double K;
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double lieA11;
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double lieA12;
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double lieA13;
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double lieA22;
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double lieA23;
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double lieA33;
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double lieg11;
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double lieg12;
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double lieg13;
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double lieg22;
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double lieg23;
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double lieg33;
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double lienK;
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double lienKhat;
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double lienTheta;
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double modshatARG;
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double muL;
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double muStilde;
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double oochipsipower;
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double oomodshat;
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double psim4;
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double qdd11;
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double qdd12;
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double qdd13;
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double qdd22;
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double qdd23;
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double qdd33;
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double qPhysuudd1111;
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double qPhysuudd1112;
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double qPhysuudd1113;
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double qPhysuudd1122;
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double qPhysuudd1123;
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double qPhysuudd1133;
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double qPhysuudd1211;
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double qPhysuudd1212;
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double qPhysuudd1213;
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double qPhysuudd1222;
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double qPhysuudd1223;
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double qPhysuudd1233;
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double qPhysuudd1311;
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double qPhysuudd1312;
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double qPhysuudd1313;
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double qPhysuudd1322;
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double qPhysuudd1323;
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double qPhysuudd1333;
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double qPhysuudd2211;
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double qPhysuudd2212;
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double qPhysuudd2213;
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double qPhysuudd2222;
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double qPhysuudd2223;
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double qPhysuudd2233;
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double qPhysuudd2311;
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double qPhysuudd2312;
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double qPhysuudd2313;
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double qPhysuudd2322;
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double qPhysuudd2323;
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double qPhysuudd2333;
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double qPhysuudd3311;
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double qPhysuudd3312;
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double qPhysuudd3313;
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double qPhysuudd3322;
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double qPhysuudd3323;
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double qPhysuudd3333;
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double qud11;
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double qud12;
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double qud13;
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double qud21;
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double qud22;
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double qud23;
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double qud31;
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double qud32;
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double qud33;
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double quu11;
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double quu12;
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double quu13;
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double quu22;
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double quu23;
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double quu33;
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double R11;
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double R12;
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double R13;
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double R22;
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double R23;
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double R33;
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double rACABTF11;
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double rACABTF12;
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double rACABTF13;
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double rACABTF22;
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double rACABTF23;
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double rACABTF33;
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double rACqq;
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double rACsA1;
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double rACsA2;
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double rACsA3;
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double rACss;
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double RehPsi0;
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double Rf11;
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double Rf12;
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double Rf13;
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double Rf22;
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double Rf23;
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double Rf33;
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double rGamA1;
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double rGamA2;
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double rGamA3;
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double rGams;
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double Rhat;
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double Rphi11;
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double Rphi12;
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double Rphi13;
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double Rphi22;
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double Rphi23;
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double Rphi33;
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double sdotv;
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double sdotw;
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double sdown1;
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double sdown2;
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double sdown3;
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double shat1;
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double shat2;
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double shat3;
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double sup1;
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double sup2;
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double sup3;
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const double time = 0;
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double totdivbeta;
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double trcdda;
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double trcddf;
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double vbetaA;
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double vbetas;
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double vd1;
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double vd2;
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double vd3;
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double vdotv;
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double vdotw;
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double vu1;
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double vu2;
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double vu3;
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double wd1;
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double wd2;
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double wd3;
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double wdotw;
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double wu1;
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double wu2;
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double wu3;
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shat1=xp/r;shat2=yp/r;shat3=zp/r;
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#if 0
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// my code
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detginv
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=
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1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
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g11*pow2(g23))
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;
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ginv11
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=
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detginv*(g22*g33 - pow2(g23))
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;
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ginv12
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=
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detginv*(g13*g23 - g12*g33)
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;
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ginv13
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=
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detginv*(-(g13*g22) + g12*g23)
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;
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ginv22
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=
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detginv*(g11*g33 - pow2(g13))
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;
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ginv23
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=
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detginv*(g12*g13 - g11*g23)
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;
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ginv33
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=
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detginv*(g11*g22 - pow2(g12))
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;
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ADMginv11
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=
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chi*ginv11
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;
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ADMginv12
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=
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chi*ginv12
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;
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ADMginv13
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=
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chi*ginv13
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;
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ADMginv22
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=
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chi*ginv22
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;
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ADMginv23
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=
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chi*ginv23
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;
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ADMginv33
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=
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chi*ginv33
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;
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modshatARG
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=
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2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
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ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
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;
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if (modshatARG<0.00001) {
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printf("modshat is wrong (%e)\n",modshatARG);
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modshatARG = 0.00001;
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}oomodshat
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=
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1/sqrt(modshatARG)
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;
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sdown1
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=
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oomodshat*shat1
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;
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sdown2
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=
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oomodshat*shat2
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;
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sdown3
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=
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oomodshat*shat3
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;
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sup1
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=
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ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
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;
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sup2
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=
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ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
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;
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sup3
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=
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ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
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;
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qud11
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=
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1. - sdown1*sup1
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;
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qud12
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=
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-(sdown2*sup1)
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;
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qud13
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=
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-(sdown3*sup1)
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;
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qud21
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=
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-(sdown1*sup2)
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;
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qud22
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=
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|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
qdd11
|
|
=
|
|
g11/chi - pow2(sdown1)
|
|
;
|
|
|
|
qdd12
|
|
=
|
|
g12/chi - sdown1*sdown2
|
|
;
|
|
|
|
qdd13
|
|
=
|
|
g13/chi - sdown1*sdown3
|
|
;
|
|
|
|
qdd22
|
|
=
|
|
g22/chi - pow2(sdown2)
|
|
;
|
|
|
|
qdd23
|
|
=
|
|
g23/chi - sdown2*sdown3
|
|
;
|
|
|
|
qdd33
|
|
=
|
|
g33/chi - pow2(sdown3)
|
|
;
|
|
|
|
quu11
|
|
=
|
|
ADMginv11 - pow2(sup1)
|
|
;
|
|
|
|
quu12
|
|
=
|
|
ADMginv12 - sup1*sup2
|
|
;
|
|
|
|
quu13
|
|
=
|
|
ADMginv13 - sup1*sup3
|
|
;
|
|
|
|
quu22
|
|
=
|
|
ADMginv22 - pow2(sup2)
|
|
;
|
|
|
|
quu23
|
|
=
|
|
ADMginv23 - sup2*sup3
|
|
;
|
|
|
|
quu33
|
|
=
|
|
ADMginv33 - pow2(sup3)
|
|
;
|
|
|
|
qPhysuudd1111
|
|
=
|
|
-0.5*qdd11*quu11 + pow2(qud11)
|
|
;
|
|
|
|
qPhysuudd1112
|
|
=
|
|
qud11*qud12 - 0.5*qdd12*quu11
|
|
;
|
|
|
|
qPhysuudd1113
|
|
=
|
|
qud11*qud13 - 0.5*qdd13*quu11
|
|
;
|
|
|
|
qPhysuudd1122
|
|
=
|
|
-0.5*qdd22*quu11 + pow2(qud12)
|
|
;
|
|
|
|
qPhysuudd1123
|
|
=
|
|
qud12*qud13 - 0.5*qdd23*quu11
|
|
;
|
|
|
|
qPhysuudd1133
|
|
=
|
|
-0.5*qdd33*quu11 + pow2(qud13)
|
|
;
|
|
|
|
qPhysuudd1211
|
|
=
|
|
qud11*qud21 - 0.5*qdd11*quu12
|
|
;
|
|
|
|
qPhysuudd1212
|
|
=
|
|
0.5*(qud12*qud21 + qud11*qud22 - qdd12*quu12)
|
|
;
|
|
|
|
qPhysuudd1213
|
|
=
|
|
0.5*(qud13*qud21 + qud11*qud23 - qdd13*quu12)
|
|
;
|
|
|
|
qPhysuudd1222
|
|
=
|
|
qud12*qud22 - 0.5*qdd22*quu12
|
|
;
|
|
|
|
qPhysuudd1223
|
|
=
|
|
0.5*(qud13*qud22 + qud12*qud23 - qdd23*quu12)
|
|
;
|
|
|
|
qPhysuudd1233
|
|
=
|
|
qud13*qud23 - 0.5*qdd33*quu12
|
|
;
|
|
|
|
qPhysuudd1311
|
|
=
|
|
qud11*qud31 - 0.5*qdd11*quu13
|
|
;
|
|
|
|
qPhysuudd1312
|
|
=
|
|
0.5*(qud12*qud31 + qud11*qud32 - qdd12*quu13)
|
|
;
|
|
|
|
qPhysuudd1313
|
|
=
|
|
0.5*(qud13*qud31 + qud11*qud33 - qdd13*quu13)
|
|
;
|
|
|
|
qPhysuudd1322
|
|
=
|
|
qud12*qud32 - 0.5*qdd22*quu13
|
|
;
|
|
|
|
qPhysuudd1323
|
|
=
|
|
0.5*(qud13*qud32 + qud12*qud33 - qdd23*quu13)
|
|
;
|
|
|
|
qPhysuudd1333
|
|
=
|
|
qud13*qud33 - 0.5*qdd33*quu13
|
|
;
|
|
|
|
qPhysuudd2211
|
|
=
|
|
-0.5*qdd11*quu22 + pow2(qud21)
|
|
;
|
|
|
|
qPhysuudd2212
|
|
=
|
|
qud21*qud22 - 0.5*qdd12*quu22
|
|
;
|
|
|
|
qPhysuudd2213
|
|
=
|
|
qud21*qud23 - 0.5*qdd13*quu22
|
|
;
|
|
|
|
qPhysuudd2222
|
|
=
|
|
-0.5*qdd22*quu22 + pow2(qud22)
|
|
;
|
|
|
|
qPhysuudd2223
|
|
=
|
|
qud22*qud23 - 0.5*qdd23*quu22
|
|
;
|
|
|
|
qPhysuudd2233
|
|
=
|
|
-0.5*qdd33*quu22 + pow2(qud23)
|
|
;
|
|
|
|
qPhysuudd2311
|
|
=
|
|
qud21*qud31 - 0.5*qdd11*quu23
|
|
;
|
|
|
|
qPhysuudd2312
|
|
=
|
|
0.5*(qud22*qud31 + qud21*qud32 - qdd12*quu23)
|
|
;
|
|
|
|
qPhysuudd2313
|
|
=
|
|
0.5*(qud23*qud31 + qud21*qud33 - qdd13*quu23)
|
|
;
|
|
|
|
qPhysuudd2322
|
|
=
|
|
qud22*qud32 - 0.5*qdd22*quu23
|
|
;
|
|
|
|
qPhysuudd2323
|
|
=
|
|
0.5*(qud23*qud32 + qud22*qud33 - qdd23*quu23)
|
|
;
|
|
|
|
qPhysuudd2333
|
|
=
|
|
qud23*qud33 - 0.5*qdd33*quu23
|
|
;
|
|
|
|
qPhysuudd3311
|
|
=
|
|
-0.5*qdd11*quu33 + pow2(qud31)
|
|
;
|
|
|
|
qPhysuudd3312
|
|
=
|
|
qud31*qud32 - 0.5*qdd12*quu33
|
|
;
|
|
|
|
qPhysuudd3313
|
|
=
|
|
qud31*qud33 - 0.5*qdd13*quu33
|
|
;
|
|
|
|
qPhysuudd3322
|
|
=
|
|
-0.5*qdd22*quu33 + pow2(qud32)
|
|
;
|
|
|
|
qPhysuudd3323
|
|
=
|
|
qud32*qud33 - 0.5*qdd23*quu33
|
|
;
|
|
|
|
qPhysuudd3333
|
|
=
|
|
-0.5*qdd33*quu33 + pow2(qud33)
|
|
;
|
|
|
|
muL
|
|
=
|
|
2./alpha
|
|
;
|
|
|
|
muStilde
|
|
=
|
|
1/chi
|
|
;
|
|
|
|
vbetas
|
|
=
|
|
2.*sqrt(0.33333333333333333333*muStilde)
|
|
;
|
|
|
|
vbetaA
|
|
=
|
|
sqrt(muStilde)
|
|
;
|
|
|
|
K
|
|
=
|
|
Khat + 2.*Theta
|
|
;
|
|
|
|
dK1
|
|
=
|
|
dKhat1 + 2.*dTheta1
|
|
;
|
|
|
|
dK2
|
|
=
|
|
dKhat2 + 2.*dTheta2
|
|
;
|
|
|
|
dK3
|
|
=
|
|
dKhat3 + 2.*dTheta3
|
|
;
|
|
|
|
dginv111
|
|
=
|
|
-2.*(dg123*ginv12*ginv13 + ginv11*(dg112*ginv12 + dg113*ginv13)) -
|
|
dg111*pow2(ginv11) - dg122*pow2(ginv12) - dg133*pow2(ginv13)
|
|
;
|
|
|
|
dginv112
|
|
=
|
|
-(ginv11*(dg111*ginv12 + dg112*ginv22 + dg113*ginv23)) -
|
|
ginv12*(dg113*ginv13 + dg122*ginv22 + dg123*ginv23) -
|
|
ginv13*(dg123*ginv22 + dg133*ginv23) - dg112*pow2(ginv12)
|
|
;
|
|
|
|
dginv113
|
|
=
|
|
-(ginv11*(dg111*ginv13 + dg112*ginv23 + dg113*ginv33)) -
|
|
ginv12*(dg112*ginv13 + dg122*ginv23 + dg123*ginv33) -
|
|
ginv13*(dg123*ginv23 + dg133*ginv33) - dg113*pow2(ginv13)
|
|
;
|
|
|
|
dginv122
|
|
=
|
|
-2.*(dg123*ginv22*ginv23 + ginv12*(dg112*ginv22 + dg113*ginv23)) -
|
|
dg111*pow2(ginv12) - dg122*pow2(ginv22) - dg133*pow2(ginv23)
|
|
;
|
|
|
|
dginv123
|
|
=
|
|
-(ginv13*(dg112*ginv22 + dg113*ginv23)) - dg133*ginv23*ginv33 -
|
|
ginv12*(dg111*ginv13 + dg112*ginv23 + dg113*ginv33) -
|
|
ginv22*(dg122*ginv23 + dg123*ginv33) - dg123*pow2(ginv23)
|
|
;
|
|
|
|
dginv133
|
|
=
|
|
-2.*(dg123*ginv23*ginv33 + ginv13*(dg112*ginv23 + dg113*ginv33)) -
|
|
dg111*pow2(ginv13) - dg122*pow2(ginv23) - dg133*pow2(ginv33)
|
|
;
|
|
|
|
dginv211
|
|
=
|
|
-2.*(dg223*ginv12*ginv13 + ginv11*(dg212*ginv12 + dg213*ginv13)) -
|
|
dg211*pow2(ginv11) - dg222*pow2(ginv12) - dg233*pow2(ginv13)
|
|
;
|
|
|
|
dginv212
|
|
=
|
|
-(ginv11*(dg211*ginv12 + dg212*ginv22 + dg213*ginv23)) -
|
|
ginv12*(dg213*ginv13 + dg222*ginv22 + dg223*ginv23) -
|
|
ginv13*(dg223*ginv22 + dg233*ginv23) - dg212*pow2(ginv12)
|
|
;
|
|
|
|
dginv213
|
|
=
|
|
-(ginv11*(dg211*ginv13 + dg212*ginv23 + dg213*ginv33)) -
|
|
ginv12*(dg212*ginv13 + dg222*ginv23 + dg223*ginv33) -
|
|
ginv13*(dg223*ginv23 + dg233*ginv33) - dg213*pow2(ginv13)
|
|
;
|
|
|
|
dginv222
|
|
=
|
|
-2.*(dg223*ginv22*ginv23 + ginv12*(dg212*ginv22 + dg213*ginv23)) -
|
|
dg211*pow2(ginv12) - dg222*pow2(ginv22) - dg233*pow2(ginv23)
|
|
;
|
|
|
|
dginv223
|
|
=
|
|
-(ginv13*(dg212*ginv22 + dg213*ginv23)) - dg233*ginv23*ginv33 -
|
|
ginv12*(dg211*ginv13 + dg212*ginv23 + dg213*ginv33) -
|
|
ginv22*(dg222*ginv23 + dg223*ginv33) - dg223*pow2(ginv23)
|
|
;
|
|
|
|
dginv233
|
|
=
|
|
-2.*(dg223*ginv23*ginv33 + ginv13*(dg212*ginv23 + dg213*ginv33)) -
|
|
dg211*pow2(ginv13) - dg222*pow2(ginv23) - dg233*pow2(ginv33)
|
|
;
|
|
|
|
dginv311
|
|
=
|
|
-2.*(dg323*ginv12*ginv13 + ginv11*(dg312*ginv12 + dg313*ginv13)) -
|
|
dg311*pow2(ginv11) - dg322*pow2(ginv12) - dg333*pow2(ginv13)
|
|
;
|
|
|
|
dginv312
|
|
=
|
|
-(ginv11*(dg311*ginv12 + dg312*ginv22 + dg313*ginv23)) -
|
|
ginv12*(dg313*ginv13 + dg322*ginv22 + dg323*ginv23) -
|
|
ginv13*(dg323*ginv22 + dg333*ginv23) - dg312*pow2(ginv12)
|
|
;
|
|
|
|
dginv313
|
|
=
|
|
-(ginv11*(dg311*ginv13 + dg312*ginv23 + dg313*ginv33)) -
|
|
ginv12*(dg312*ginv13 + dg322*ginv23 + dg323*ginv33) -
|
|
ginv13*(dg323*ginv23 + dg333*ginv33) - dg313*pow2(ginv13)
|
|
;
|
|
|
|
dginv322
|
|
=
|
|
-2.*(dg323*ginv22*ginv23 + ginv12*(dg312*ginv22 + dg313*ginv23)) -
|
|
dg311*pow2(ginv12) - dg322*pow2(ginv22) - dg333*pow2(ginv23)
|
|
;
|
|
|
|
dginv323
|
|
=
|
|
-(ginv13*(dg312*ginv22 + dg313*ginv23)) - dg333*ginv23*ginv33 -
|
|
ginv12*(dg311*ginv13 + dg312*ginv23 + dg313*ginv33) -
|
|
ginv22*(dg322*ginv23 + dg323*ginv33) - dg323*pow2(ginv23)
|
|
;
|
|
|
|
dginv333
|
|
=
|
|
-2.*(dg323*ginv23*ginv33 + ginv13*(dg312*ginv23 + dg313*ginv33)) -
|
|
dg311*pow2(ginv13) - dg322*pow2(ginv23) - dg333*pow2(ginv33)
|
|
;
|
|
|
|
gammado111
|
|
=
|
|
0.5*dg111
|
|
;
|
|
|
|
gammado112
|
|
=
|
|
0.5*dg211
|
|
;
|
|
|
|
gammado113
|
|
=
|
|
0.5*dg311
|
|
;
|
|
|
|
gammado122
|
|
=
|
|
-0.5*dg122 + dg212
|
|
;
|
|
|
|
gammado123
|
|
=
|
|
0.5*(-dg123 + dg213 + dg312)
|
|
;
|
|
|
|
gammado133
|
|
=
|
|
-0.5*dg133 + dg313
|
|
;
|
|
|
|
gammado211
|
|
=
|
|
dg112 - 0.5*dg211
|
|
;
|
|
|
|
gammado212
|
|
=
|
|
0.5*dg122
|
|
;
|
|
|
|
gammado213
|
|
=
|
|
0.5*(dg123 - dg213 + dg312)
|
|
;
|
|
|
|
gammado222
|
|
=
|
|
0.5*dg222
|
|
;
|
|
|
|
gammado223
|
|
=
|
|
0.5*dg322
|
|
;
|
|
|
|
gammado233
|
|
=
|
|
-0.5*dg233 + dg323
|
|
;
|
|
|
|
gammado311
|
|
=
|
|
dg113 - 0.5*dg311
|
|
;
|
|
|
|
gammado312
|
|
=
|
|
0.5*(dg123 + dg213 - dg312)
|
|
;
|
|
|
|
gammado313
|
|
=
|
|
0.5*dg133
|
|
;
|
|
|
|
gammado322
|
|
=
|
|
dg223 - 0.5*dg322
|
|
;
|
|
|
|
gammado323
|
|
=
|
|
0.5*dg233
|
|
;
|
|
|
|
gammado333
|
|
=
|
|
0.5*dg333
|
|
;
|
|
|
|
gamma111
|
|
=
|
|
gammado111*ginv11 + gammado211*ginv12 + gammado311*ginv13
|
|
;
|
|
|
|
gamma112
|
|
=
|
|
gammado112*ginv11 + gammado212*ginv12 + gammado312*ginv13
|
|
;
|
|
|
|
gamma113
|
|
=
|
|
gammado113*ginv11 + gammado213*ginv12 + gammado313*ginv13
|
|
;
|
|
|
|
gamma122
|
|
=
|
|
gammado122*ginv11 + gammado222*ginv12 + gammado322*ginv13
|
|
;
|
|
|
|
gamma123
|
|
=
|
|
gammado123*ginv11 + gammado223*ginv12 + gammado323*ginv13
|
|
;
|
|
|
|
gamma133
|
|
=
|
|
gammado133*ginv11 + gammado233*ginv12 + gammado333*ginv13
|
|
;
|
|
|
|
gamma211
|
|
=
|
|
gammado111*ginv12 + gammado211*ginv22 + gammado311*ginv23
|
|
;
|
|
|
|
gamma212
|
|
=
|
|
gammado112*ginv12 + gammado212*ginv22 + gammado312*ginv23
|
|
;
|
|
|
|
gamma213
|
|
=
|
|
gammado113*ginv12 + gammado213*ginv22 + gammado313*ginv23
|
|
;
|
|
|
|
gamma222
|
|
=
|
|
gammado122*ginv12 + gammado222*ginv22 + gammado322*ginv23
|
|
;
|
|
|
|
gamma223
|
|
=
|
|
gammado123*ginv12 + gammado223*ginv22 + gammado323*ginv23
|
|
;
|
|
|
|
gamma233
|
|
=
|
|
gammado133*ginv12 + gammado233*ginv22 + gammado333*ginv23
|
|
;
|
|
|
|
gamma311
|
|
=
|
|
gammado111*ginv13 + gammado211*ginv23 + gammado311*ginv33
|
|
;
|
|
|
|
gamma312
|
|
=
|
|
gammado112*ginv13 + gammado212*ginv23 + gammado312*ginv33
|
|
;
|
|
|
|
gamma313
|
|
=
|
|
gammado113*ginv13 + gammado213*ginv23 + gammado313*ginv33
|
|
;
|
|
|
|
gamma322
|
|
=
|
|
gammado122*ginv13 + gammado222*ginv23 + gammado322*ginv33
|
|
;
|
|
|
|
gamma323
|
|
=
|
|
gammado123*ginv13 + gammado223*ginv23 + gammado323*ginv33
|
|
;
|
|
|
|
gamma333
|
|
=
|
|
gammado133*ginv13 + gammado233*ginv23 + gammado333*ginv33
|
|
;
|
|
|
|
Gfromg1
|
|
=
|
|
gamma111*ginv11 + gamma122*ginv22 +
|
|
2.*(gamma112*ginv12 + gamma113*ginv13 + gamma123*ginv23) + gamma133*ginv33
|
|
;
|
|
|
|
Gfromg2
|
|
=
|
|
gamma211*ginv11 + gamma222*ginv22 +
|
|
2.*(gamma212*ginv12 + gamma213*ginv13 + gamma223*ginv23) + gamma233*ginv33
|
|
;
|
|
|
|
Gfromg3
|
|
=
|
|
gamma311*ginv11 + gamma322*ginv22 +
|
|
2.*(gamma312*ginv12 + gamma313*ginv13 + gamma323*ginv23) + gamma333*ginv33
|
|
;
|
|
|
|
dGfromgdu11
|
|
=
|
|
-((dg122*(4.*dg112 + dg211) + 2.*dg112*dg212 + dg111*dg222)*
|
|
Power(ginv12,3)) - (dg133*(4.*dg113 + dg311) + 2.*dg113*dg313 +
|
|
dg111*dg333)*Power(ginv13,3) - 2.*Power(ginv11,3)*pow2(dg111) +
|
|
(ddg1111 - dg111*((8.*dg112 + 2.*dg211)*ginv12 +
|
|
(8.*dg113 + 2.*dg311)*ginv13) -
|
|
(dg113*(4.*dg112 + dg211) + dg112*dg311 + dg111*(dg213 + dg312))*
|
|
ginv23 - ginv22*(dg112*dg211 + dg111*dg212 + 2.*pow2(dg112)) -
|
|
ginv33*(dg113*dg311 + dg111*dg313 + 2.*pow2(dg113)))*pow2(ginv11) +
|
|
(ddg1122 + ddg1212 - (dg123*(8.*dg112 + 2.*dg211) +
|
|
dg113*(4.*dg122 + 2.*dg212) + dg122*dg311 +
|
|
2.*(dg111*dg223 + dg112*(dg213 + dg312)) + dg111*dg322)*ginv13 -
|
|
(dg123*(4.*dg122 + 2.*dg212) +
|
|
2.*(dg113*dg222 + dg122*(dg213 + dg312) + dg112*(dg223 + dg322)))*
|
|
ginv23 - ginv22*(3.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122)) -
|
|
ginv33*(dg123*(dg213 + dg312) + dg122*dg313 + dg113*(dg223 + dg322) +
|
|
dg112*dg323 + 2.*pow2(dg123)))*pow2(ginv12) +
|
|
(ddg1133 + ddg1313 - (dg133*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg313 + dg113*(dg233 + dg323) + dg112*dg333))*ginv23 -
|
|
ginv22*(dg133*dg212 + dg113*dg223 + dg123*(dg213 + dg312) +
|
|
dg112*(dg233 + dg323) + 2.*pow2(dg123)) -
|
|
ginv33*(3.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133)))*pow2(ginv13) \
|
|
+ ginv13*(ddg1333*ginv33 + ginv22*
|
|
(ddg1223 - (dg133*dg222 + dg123*(4.*dg223 + dg322) +
|
|
dg122*(dg233 + dg323))*ginv23 -
|
|
(dg133*dg223 + dg123*(dg233 + 2.*dg323))*ginv33) +
|
|
ginv23*(ddg1233 + ddg1323 -
|
|
(dg133*(2.*dg233 + 3.*dg323) + 3.*dg123*dg333)*ginv33) -
|
|
(dg123*dg222 + dg122*dg223)*pow2(ginv22) -
|
|
(dg133*dg322 + 2.*(dg133*dg223 + dg123*(dg233 + dg323)) +
|
|
dg122*dg333)*pow2(ginv23) - 2.*dg133*dg333*pow2(ginv33)) +
|
|
ginv11*(ddg1313*ginv33 + ginv12*
|
|
(2.*ddg1112 + ddg1211 -
|
|
(dg113*(12.*dg112 + 3.*dg211) + 3.*dg112*dg311 +
|
|
dg111*(8.*dg123 + 3.*(dg213 + dg312)))*ginv13 -
|
|
(dg122*(4.*dg112 + dg211) + 6.*dg112*dg212 + dg111*dg222)*ginv22 -
|
|
(dg123*dg211 + dg122*dg311 +
|
|
4.*(dg113*(dg122 + dg212) + dg112*(dg123 + dg213 + dg312)) +
|
|
dg111*(dg223 + dg322))*ginv23 -
|
|
(dg123*dg311 + dg113*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*dg112*dg313 + dg111*dg323)*ginv33) +
|
|
ginv22*(ddg1212 - (dg113*dg222 + 2.*(dg123*dg212 + dg112*dg223) +
|
|
dg122*(dg213 + dg312) + dg112*dg322)*ginv23 -
|
|
(dg113*dg223 + dg123*(dg213 + dg312) + dg112*dg323)*ginv33) +
|
|
ginv13*(2.*ddg1113 + ddg1311 -
|
|
(dg123*(4.*dg112 + dg211) + dg111*dg223 +
|
|
2.*(dg113*dg212 + dg112*(dg213 + dg312)))*ginv22 -
|
|
(dg133*dg211 + dg123*dg311 +
|
|
4.*(dg113*(dg123 + dg213 + dg312) + dg112*(dg133 + dg313)) +
|
|
dg111*(dg233 + dg323))*ginv23 -
|
|
(dg133*(4.*dg113 + dg311) + 6.*dg113*dg313 + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1213 + ddg1312 -
|
|
(dg133*(dg213 + dg312) + 2.*dg123*dg313 +
|
|
dg113*(dg233 + 2.*dg323) + dg112*dg333)*ginv33) -
|
|
(3.*dg112*dg211 + dg111*(4.*dg122 + 3.*dg212) + 6.*pow2(dg112))*
|
|
pow2(ginv12) - (3.*dg113*dg311 + dg111*(4.*dg133 + 3.*dg313) +
|
|
6.*pow2(dg113))*pow2(ginv13) -
|
|
(dg122*dg212 + dg112*dg222)*pow2(ginv22) -
|
|
(dg133*dg212 + dg123*(dg213 + dg312) + dg122*dg313 +
|
|
dg113*(dg223 + dg322) + dg112*(dg233 + dg323))*pow2(ginv23) -
|
|
(dg133*dg313 + dg113*dg333)*pow2(ginv33)) +
|
|
ginv12*(ddg1323*ginv33 + ginv22*
|
|
(ddg1222 - (3.*(dg123*dg222 + dg122*dg223) + 2.*dg122*dg322)*ginv23 -
|
|
(dg123*(2.*dg223 + dg322) + dg122*dg323)*ginv33) +
|
|
ginv23*(ddg1223 + ddg1322 -
|
|
(dg133*(dg223 + dg322) + dg123*(dg233 + 4.*dg323) + dg122*dg333)*
|
|
ginv33) + ginv13*(2.*ddg1123 + ddg1213 + ddg1312 -
|
|
(dg113*dg222 + 4.*(dg123*(dg122 + dg212) + dg112*dg223) +
|
|
dg122*(dg213 + dg312) + dg112*dg322)*ginv22 -
|
|
(dg133*(4.*dg123 + dg213 + dg312) + 4.*dg123*dg313 +
|
|
dg113*(dg233 + 4.*dg323) + dg112*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*dg212 + dg112*dg233 + dg122*dg313 +
|
|
dg113*dg322) + 4.*
|
|
(dg122*dg133 + dg113*dg223 + dg123*(dg213 + dg312) +
|
|
dg112*dg323 + pow2(dg123)))) -
|
|
(dg133*(4.*dg112 + dg211) + dg113*(8.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg311 + dg112*dg313) + dg111*(dg233 + 2.*dg323))*
|
|
pow2(ginv13) - 2.*dg122*dg222*pow2(ginv22) -
|
|
(dg133*dg222 + 2.*dg123*(dg223 + dg322) + dg122*(dg233 + 2.*dg323))*
|
|
pow2(ginv23) - (dg133*dg323 + dg123*dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu12
|
|
=
|
|
-((dg133*dg322 + 2.*(dg133*dg223 + dg123*(dg233 + dg323)) + dg122*dg333)*
|
|
Power(ginv23,3)) - 2.*(dg122*dg222*Power(ginv22,3) +
|
|
Power(ginv12,3)*(dg112*dg211 + dg111*(dg122 + dg212) + pow2(dg112)) +
|
|
(dg111*(dg112*ginv22 + dg113*ginv23) + ginv12*pow2(dg111))*pow2(ginv11)\
|
|
) + (ddg1112 + ddg1211 - (4.*(dg112*dg113 + dg111*dg123) +
|
|
2.*(dg113*dg211 + dg112*dg311 + dg111*(dg213 + dg312)))*ginv13 -
|
|
(dg122*(6.*dg112 + 2.*dg211) + 6.*dg112*dg212 + 2.*dg111*dg222)*
|
|
ginv22 - (4.*(dg113*(dg122 + dg212) + dg112*(dg123 + dg213)) +
|
|
dg122*dg311 + 2.*(dg123*dg211 + dg111*dg223 + dg112*dg312) +
|
|
dg111*dg322)*ginv23 -
|
|
(dg123*dg311 + dg113*(2.*(dg123 + dg213) + dg312) + dg112*dg313 +
|
|
dg111*dg323)*ginv33)*pow2(ginv12) -
|
|
((2.*(dg113*dg123 + dg112*dg133) + dg123*dg311 + dg113*dg312 +
|
|
dg112*dg313 + dg111*dg323)*ginv22 +
|
|
(dg133*(4.*dg113 + dg311) + 2.*dg113*dg313 + dg111*dg333)*ginv23)*
|
|
pow2(ginv13) + (ddg1222 - (4.*(dg123*dg222 + dg122*dg223) +
|
|
2.*dg122*dg322)*ginv23 -
|
|
(dg123*(2.*dg223 + dg322) + dg122*dg323)*ginv33)*pow2(ginv22) +
|
|
(ddg1233 + ddg1323 - (dg133*(2.*dg233 + 3.*dg323) + 3.*dg123*dg333)*
|
|
ginv33)*pow2(ginv23) + ginv11*
|
|
(ginv23*(ddg1113 - 2.*dg113*(dg133 + dg313)*ginv33) +
|
|
ginv22*(ddg1112 - (dg112*(4.*dg123 + 2.*dg213) +
|
|
2.*(dg113*(dg122 + dg212) + dg112*dg312))*ginv23 -
|
|
(dg113*(2.*dg123 + dg312) + dg112*dg313)*ginv33) +
|
|
ginv12*(ddg1111 - dg111*(6.*dg113 + 2.*dg311)*ginv13 -
|
|
(dg113*(8.*dg112 + 2.*dg211) + dg112*dg311 +
|
|
dg111*(2.*(dg123 + dg213) + dg312))*ginv23 -
|
|
ginv22*(2.*(dg112*dg211 + dg111*(dg122 + dg212)) +
|
|
6.*pow2(dg112)) - ginv33*
|
|
(dg113*dg311 + dg111*dg313 + 2.*pow2(dg113))) -
|
|
ginv13*((dg112*(4.*dg113 + dg311) + dg111*(2.*dg123 + dg312))*
|
|
ginv22 + ginv23*(dg113*dg311 + dg111*(2.*dg133 + dg313) +
|
|
4.*pow2(dg113))) - dg111*(6.*dg112 + 2.*dg211)*pow2(ginv12) -
|
|
2.*dg112*(dg122 + dg212)*pow2(ginv22) -
|
|
(2.*(dg112*dg133 + dg113*(dg123 + dg213)) + dg113*dg312 + dg112*dg313)*
|
|
pow2(ginv23)) + ginv13*(ginv22*
|
|
(ddg1123 + ddg1312 - (dg133*(2.*dg123 + dg312) +
|
|
2.*(dg123*dg313 + dg113*dg323) + dg112*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*(dg122 + dg212) + dg123*dg213 + dg113*dg223 +
|
|
dg112*dg233) + dg122*dg313 + dg113*dg322 +
|
|
4.*(dg123*dg312 + dg112*dg323 + pow2(dg123)))) +
|
|
ginv23*(ddg1133 + ddg1313 -
|
|
ginv33*(3.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133))) -
|
|
(2.*(dg123*(dg122 + dg212) + dg112*dg223) + dg122*dg312 +
|
|
dg112*dg322)*pow2(ginv22) -
|
|
(dg133*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg313 + dg113*(dg233 + dg323) + dg112*dg333))*pow2(ginv23)\
|
|
) + ginv23*(ddg1333*ginv33 - 2.*dg133*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg1313*ginv33 + ginv13*
|
|
(ddg1113 + ddg1311 - (2.*
|
|
(dg123*dg211 + dg113*(dg122 + dg212) + dg111*dg223) +
|
|
dg122*dg311 + dg112*(8.*dg123 + 2.*dg213 + 4.*dg312) +
|
|
dg111*dg322)*ginv22 -
|
|
(dg133*(4.*dg112 + 2.*dg211) +
|
|
dg113*(8.*dg123 + 4.*(dg213 + dg312)) + 4.*dg112*dg313 +
|
|
2.*(dg123*dg311 + dg111*(dg233 + dg323)))*ginv23 -
|
|
(dg133*(2.*dg113 + dg311) + 4.*dg113*dg313 + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1123 + 2.*ddg1213 + ddg1312 -
|
|
(2.*(dg133*(dg123 + dg213) + dg113*dg233) + dg133*dg312 +
|
|
4.*(dg123*dg313 + dg113*dg323) + dg112*dg333)*ginv33) +
|
|
ginv22*(ddg1122 + 2.*ddg1212 -
|
|
(4.*(dg122*dg213 + dg113*dg222) +
|
|
6.*(dg123*(dg122 + dg212) + dg112*dg223) +
|
|
3.*(dg122*dg312 + dg112*dg322))*ginv23 -
|
|
ginv33*(dg122*dg313 + dg113*dg322 +
|
|
2.*(dg113*dg223 + dg123*(dg213 + dg312) + dg112*dg323 +
|
|
pow2(dg123)))) -
|
|
2.*(dg113*dg311 + dg111*(dg133 + dg313) + pow2(dg113))*pow2(ginv13) -
|
|
(4.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122))*pow2(ginv22) -
|
|
(4.*(dg123*dg213 + dg113*dg223) +
|
|
2.*(dg133*(dg122 + dg212) + dg123*dg312 + dg122*dg313 +
|
|
dg113*dg322 + dg112*(dg233 + dg323) + pow2(dg123)))*pow2(ginv23) \
|
|
- (dg133*dg313 + dg113*dg333)*pow2(ginv33)) +
|
|
ginv22*(ddg1323*ginv33 + ginv23*
|
|
(2.*ddg1223 + ddg1322 - (2.*(dg133*dg223 + dg123*dg233) +
|
|
dg133*dg322 + 6.*dg123*dg323 + dg122*dg333)*ginv33) -
|
|
(2.*(dg133*dg222 + dg122*dg233) + dg123*(6.*dg223 + 3.*dg322) +
|
|
3.*dg122*dg323)*pow2(ginv23) -
|
|
(dg133*dg323 + dg123*dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu13
|
|
=
|
|
-((dg133*dg222 + 2.*dg123*(dg223 + dg322) + dg122*(dg233 + 2.*dg323))*
|
|
Power(ginv23,3)) - 2.*(dg133*dg333*Power(ginv33,3) +
|
|
Power(ginv13,3)*(dg113*dg311 + dg111*(dg133 + dg313) + pow2(dg113)) +
|
|
(dg111*(dg112*ginv23 + dg113*ginv33) + ginv13*pow2(dg111))*pow2(ginv11)\
|
|
) - ((dg122*(4.*dg112 + dg211) + 2.*dg112*dg212 + dg111*dg222)*ginv23 +
|
|
(2.*(dg113*dg122 + dg112*dg123) + dg123*dg211 + dg113*dg212 +
|
|
dg112*dg213 + dg111*dg223)*ginv33 +
|
|
2.*ginv13*(dg112*dg211 + dg111*(dg122 + dg212) + pow2(dg112)))*
|
|
pow2(ginv12) + (ddg1113 + ddg1311 -
|
|
(dg123*(2.*dg112 + dg211) + dg113*dg212 + dg111*dg223 +
|
|
dg112*(dg213 + 2.*dg312))*ginv22 -
|
|
(dg133*dg211 + 2.*(dg113*dg213 + dg123*dg311) +
|
|
4.*(dg113*(dg123 + dg312) + dg112*(dg133 + dg313)) +
|
|
dg111*(dg233 + 2.*dg323))*ginv23 -
|
|
(dg133*(6.*dg113 + 2.*dg311) + 6.*dg113*dg313 + 2.*dg111*dg333)*ginv33\
|
|
)*pow2(ginv13) - (2.*dg122*dg222*ginv23 +
|
|
(dg123*dg222 + dg122*dg223)*ginv33)*pow2(ginv22) +
|
|
(ddg1223 + ddg1322 - (3.*(dg133*dg223 + dg123*dg233) + 6.*dg123*dg323 +
|
|
2.*(dg133*dg322 + dg122*dg333))*ginv33)*pow2(ginv23) +
|
|
ddg1333*pow2(ginv33) + ginv11*
|
|
(ddg1113*ginv33 - ginv22*(2.*dg112*(dg122 + dg212)*ginv23 +
|
|
(dg113*dg212 + dg112*(2.*dg123 + dg213))*ginv33) +
|
|
ginv23*(ddg1112 - (dg113*(4.*dg123 + 2.*dg213) +
|
|
2.*(dg113*dg312 + dg112*(dg133 + dg313)))*ginv33) -
|
|
ginv12*(dg111*(6.*dg112 + 2.*dg211)*ginv13 +
|
|
(dg113*(4.*dg112 + dg211) + dg111*(2.*dg123 + dg213))*ginv33 +
|
|
ginv23*(dg112*dg211 + dg111*(2.*dg122 + dg212) + 4.*pow2(dg112))) +
|
|
ginv13*(ddg1111 - (dg113*(8.*dg112 + dg211) + 2.*dg112*dg311 +
|
|
dg111*(dg213 + 2.*(dg123 + dg312)))*ginv23 -
|
|
ginv22*(dg112*dg211 + dg111*dg212 + 2.*pow2(dg112)) -
|
|
ginv33*(2.*(dg113*dg311 + dg111*(dg133 + dg313)) + 6.*pow2(dg113))) \
|
|
- dg111*(6.*dg113 + 2.*dg311)*pow2(ginv13) -
|
|
(dg113*dg212 + dg112*dg213 +
|
|
2.*(dg113*dg122 + dg112*(dg123 + dg312)))*pow2(ginv23) -
|
|
2.*dg113*(dg133 + dg313)*pow2(ginv33)) +
|
|
ginv12*((ddg1123 + ddg1213)*ginv33 +
|
|
ginv13*(ddg1112 + ddg1211 -
|
|
(dg122*(2.*dg112 + dg211) + 4.*dg112*dg212 + dg111*dg222)*ginv22 -
|
|
(dg123*(8.*dg112 + 2.*dg211) +
|
|
4.*(dg113*(dg122 + dg212) + dg112*(dg213 + dg312)) +
|
|
2.*(dg122*dg311 + dg111*(dg223 + dg322)))*ginv23 -
|
|
(dg133*(2.*dg112 + dg211) +
|
|
dg113*(8.*dg123 + 4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg311 + dg112*dg313) + dg111*(dg233 + 2.*dg323))*
|
|
ginv33) - ginv22*((dg122*dg213 + dg113*dg222 +
|
|
2.*(dg123*(dg122 + dg212) + dg112*dg223))*ginv33 +
|
|
ginv23*(3.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122))) +
|
|
ginv23*(ddg1122 + ddg1212 -
|
|
ginv33*(dg133*(2.*dg122 + dg212) +
|
|
2.*(dg123*dg312 + dg122*dg313 + dg113*dg322) +
|
|
dg112*(dg233 + 2.*dg323) +
|
|
4.*(dg123*dg213 + dg113*dg223 + pow2(dg123)))) -
|
|
(4.*(dg112*dg113 + dg111*dg123) +
|
|
2.*(dg113*dg211 + dg112*dg311 + dg111*(dg213 + dg312)))*
|
|
pow2(ginv13) - (dg123*(4.*dg122 + 2.*dg212) +
|
|
2.*(dg113*dg222 + dg122*(dg213 + dg312) + dg112*(dg223 + dg322)))*
|
|
pow2(ginv23) - (dg133*(2.*dg123 + dg213) + 2.*dg123*dg313 +
|
|
dg113*(dg233 + 2.*dg323))*pow2(ginv33)) +
|
|
ginv22*(ddg1223*ginv33 + ginv23*
|
|
(ddg1222 - (dg133*dg222 + dg123*(6.*dg223 + 2.*dg322) +
|
|
dg122*(dg233 + 2.*dg323))*ginv33) -
|
|
(3.*(dg123*dg222 + dg122*dg223) + 2.*dg122*dg322)*pow2(ginv23) -
|
|
(dg133*dg223 + dg123*(dg233 + 2.*dg323))*pow2(ginv33)) +
|
|
ginv23*((ddg1233 + 2.*ddg1323)*ginv33 -
|
|
(dg133*(2.*dg233 + 4.*dg323) + 4.*dg123*dg333)*pow2(ginv33)) +
|
|
ginv13*((ddg1133 + 2.*ddg1313)*ginv33 +
|
|
ginv23*(ddg1123 + ddg1213 + 2.*ddg1312 -
|
|
(dg133*(6.*dg123 + 3.*dg213 + 4.*dg312) + 6.*dg123*dg313 +
|
|
dg113*(3.*dg233 + 6.*dg323) + 4.*dg112*dg333)*ginv33) +
|
|
ginv22*(ddg1212 - (dg123*(2.*dg122 + 4.*dg212) + dg113*dg222 +
|
|
dg122*(dg213 + 2.*dg312) + dg112*(4.*dg223 + 2.*dg322))*ginv23 -
|
|
ginv33*(dg133*dg212 + dg112*(dg233 + 2.*dg323) +
|
|
2.*(dg113*dg223 + dg123*(dg213 + dg312) + pow2(dg123)))) -
|
|
(dg122*dg212 + dg112*dg222)*pow2(ginv22) -
|
|
(4.*(dg123*dg312 + dg112*dg323) +
|
|
2.*(dg133*(dg122 + dg212) + dg123*dg213 + dg112*dg233 +
|
|
dg122*dg313 + dg113*(dg223 + dg322) + pow2(dg123)))*pow2(ginv23) \
|
|
- (4.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133))*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu21
|
|
=
|
|
-((dg233*dg311 + 2.*(dg113*dg233 + dg213*(dg133 + dg313)) + dg211*dg333)*
|
|
Power(ginv13,3)) - 2.*(dg111*dg211*Power(ginv11,3) +
|
|
Power(ginv12,3)*(dg122*dg212 + (dg112 + dg211)*dg222 + pow2(dg212))) +
|
|
(ddg1211 - (4.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*ginv13 -
|
|
2.*(dg112 + dg211)*dg212*ginv22 -
|
|
(2.*(dg113*dg212 + (dg112 + dg211)*dg213) + dg212*dg311 +
|
|
dg211*dg312)*ginv23 -
|
|
(dg213*(2.*dg113 + dg311) + dg211*dg313)*ginv33 -
|
|
ginv12*(4.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211)))*pow2(ginv11) \
|
|
+ (ddg1222 + ddg2212 - (4.*(dg212*(dg123 + dg213) +
|
|
(dg112 + dg211)*dg223) + dg222*dg311 +
|
|
2.*(dg122*dg213 + dg113*dg222 + dg212*dg312) + dg211*dg322)*ginv13 \
|
|
- (2.*dg122 + 6.*dg212)*dg222*ginv22 -
|
|
((2.*dg122 + 4.*dg212)*dg223 +
|
|
dg222*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*dg322)*ginv23 -
|
|
(dg223*(2.*(dg123 + dg213) + dg312) + dg222*dg313 + dg213*dg322 +
|
|
dg212*dg323)*ginv33)*pow2(ginv12) +
|
|
(ddg1233 + ddg2313 - (2.*((dg123 + dg213)*dg223 + dg212*dg233) +
|
|
dg223*dg312 + dg212*dg323)*ginv22 -
|
|
(dg233*(4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg233 + dg223*(dg133 + dg313) + dg213*dg323 +
|
|
dg212*dg333))*ginv23 -
|
|
(dg233*(2.*dg133 + 3.*dg313) + 3.*dg213*dg333)*ginv33)*pow2(ginv13) +
|
|
ginv11*(ddg2313*ginv33 + ginv22*
|
|
(ddg2212 - (dg222*(2.*dg213 + dg312) + dg212*(4.*dg223 + dg322))*
|
|
ginv23 - (dg223*(2.*dg213 + dg312) + dg212*dg323)*ginv33) +
|
|
ginv23*(ddg2213 + ddg2312 -
|
|
(dg233*(2.*dg213 + dg312) + 2.*(dg223*dg313 + dg213*dg323) +
|
|
dg212*dg333)*ginv33) +
|
|
ginv13*(2.*ddg1213 + ddg2311 -
|
|
(2.*(dg112 + dg211)*dg223 +
|
|
dg212*(4.*dg213 + 2.*(dg123 + dg312)))*ginv22 -
|
|
(2.*(dg133*dg213 + dg113*dg233) + dg233*dg311 + 6.*dg213*dg313 +
|
|
dg211*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*dg212 + dg123*dg213 + dg113*dg223 +
|
|
(dg112 + dg211)*dg233) + dg223*dg311 + dg211*dg323 +
|
|
4.*(dg213*dg312 + dg212*dg313 + pow2(dg213)))) +
|
|
ginv12*(2.*ddg1212 + ddg2211 -
|
|
(6.*(dg113*dg212 + dg112*dg213) + 4.*dg111*dg223 +
|
|
3.*dg212*dg311 + dg211*(4.*dg123 + 6.*dg213 + 3.*dg312))*ginv13 \
|
|
- (2.*(dg123*dg212 + dg122*dg213 + dg113*dg222 +
|
|
(dg112 + dg211)*dg223) + dg222*dg311 +
|
|
dg212*(8.*dg213 + 4.*dg312) + dg211*dg322)*ginv23 -
|
|
ginv22*(2.*(dg122*dg212 + (dg112 + dg211)*dg222) +
|
|
6.*pow2(dg212)) - ginv33*
|
|
(dg223*dg311 + dg211*dg323 +
|
|
2.*(dg113*dg223 + dg213*(dg123 + dg312) + dg212*dg313 +
|
|
pow2(dg213)))) -
|
|
(6.*dg112*dg212 + dg211*(2.*dg122 + 6.*dg212) + 2.*dg111*dg222)*
|
|
pow2(ginv12) - (2.*(dg133*dg211 + dg111*dg233) +
|
|
dg213*(6.*dg113 + 3.*dg311) + 3.*dg211*dg313)*pow2(ginv13) -
|
|
2.*dg212*dg222*pow2(ginv22) -
|
|
(2.*(dg213*dg223 + dg212*dg233) + dg223*dg312 + dg222*dg313 +
|
|
dg213*dg322 + dg212*dg323)*pow2(ginv23) -
|
|
(dg233*dg313 + dg213*dg333)*pow2(ginv33)) +
|
|
ginv12*(ddg2323*ginv33 + ginv13*
|
|
(2.*ddg1223 + ddg2213 + ddg2312 -
|
|
(2.*((dg123 + dg213)*dg222 + dg122*dg223) + dg222*dg312 +
|
|
dg212*(8.*dg223 + dg322))*ginv22 -
|
|
(dg223*(8.*dg213 + 4.*(dg123 + dg312)) +
|
|
2.*(dg122*dg233 + dg222*(dg133 + dg313) + dg213*dg322) +
|
|
4.*dg212*(dg233 + dg323))*ginv23 -
|
|
(2.*(dg133*dg223 + (dg123 + dg213)*dg233) + dg233*dg312 +
|
|
4.*(dg223*dg313 + dg213*dg323) + dg212*dg333)*ginv33) +
|
|
ginv23*(ddg2223 + ddg2322 -
|
|
(dg233*(2.*dg223 + dg322) + 4.*dg223*dg323 + dg222*dg333)*ginv33) +
|
|
ginv22*(ddg2222 - dg222*(6.*dg223 + 2.*dg322)*ginv23 -
|
|
ginv33*(dg223*dg322 + dg222*dg323 + 2.*pow2(dg223))) -
|
|
(4.*(dg123*dg213 + dg113*dg223) +
|
|
2.*((dg112 + dg211)*dg233 + dg223*dg311 + dg213*dg312 +
|
|
dg212*(dg133 + dg313) + dg211*dg323 + pow2(dg213)))*pow2(ginv13) \
|
|
- 2.*(pow2(dg222)*pow2(ginv22) +
|
|
(dg223*dg322 + dg222*(dg233 + dg323) + pow2(dg223))*pow2(ginv23)) -
|
|
(dg233*dg323 + dg223*dg333)*pow2(ginv33)) +
|
|
ginv13*(ddg2333*ginv33 + ginv22*
|
|
(ddg2223 - 2.*dg223*(dg233 + dg323)*ginv33 -
|
|
ginv23*(dg223*dg322 + dg222*(2.*dg233 + dg323) + 4.*pow2(dg223))) +
|
|
ginv23*(ddg2233 + ddg2323 -
|
|
ginv33*(3.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233))) -
|
|
(dg233*(4.*dg223 + dg322) + 2.*dg223*dg323 + dg222*dg333)*
|
|
pow2(ginv23) - 2.*(dg222*dg223*pow2(ginv22) + dg233*dg333*pow2(ginv33))\
|
|
)
|
|
;
|
|
|
|
dGfromgdu22
|
|
=
|
|
-((2.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*
|
|
Power(ginv12,3)) - (dg233*(4.*dg223 + dg322) + 2.*dg223*dg323 +
|
|
dg222*dg333)*Power(ginv23,3) - 2.*Power(ginv22,3)*pow2(dg222) -
|
|
(2.*dg111*dg211*ginv12 + (dg112*dg211 + dg111*dg212)*ginv22 +
|
|
(dg113*dg211 + dg111*dg213)*ginv23)*pow2(ginv11) +
|
|
(ddg1212 + ddg2211 - (2.*(dg123*dg211 + dg112*dg213 + dg111*dg223 +
|
|
dg212*(dg113 + dg311)) + dg211*(4.*dg213 + 2.*dg312))*ginv13 -
|
|
(2.*(dg123*dg212 + dg122*dg213 + dg113*dg222 + dg112*dg223) +
|
|
dg222*dg311 + dg212*(8.*dg213 + 2.*dg312) +
|
|
dg211*(4.*dg223 + dg322))*ginv23 -
|
|
ginv22*(4.*dg211*dg222 + 3.*(dg122*dg212 + dg112*dg222) +
|
|
6.*pow2(dg212)) - ginv33*
|
|
(dg223*(dg113 + dg311) + dg213*(dg123 + dg312) + dg212*dg313 +
|
|
dg211*dg323 + 2.*pow2(dg213)))*pow2(ginv12) -
|
|
((dg112*dg233 + dg223*(dg113 + dg311) + dg213*(dg123 + dg312) +
|
|
dg212*(dg133 + dg313) + dg211*dg323)*ginv22 +
|
|
(dg233*dg311 + 2.*(dg113*dg233 + dg213*(dg133 + dg313)) +
|
|
dg211*dg333)*ginv23)*pow2(ginv13) +
|
|
(ddg2222 - dg222*(8.*dg223 + 2.*dg322)*ginv23 -
|
|
ginv33*(dg223*dg322 + dg222*dg323 + 2.*pow2(dg223)))*pow2(ginv22) +
|
|
(ddg2233 + ddg2323 - ginv33*
|
|
(3.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233)))*pow2(ginv23) +
|
|
ginv13*(ginv22*(ddg1223 + ddg2312 -
|
|
(dg122*dg233 + dg222*(dg133 + dg313) + dg213*dg322 +
|
|
4.*(dg223*(dg123 + dg213 + dg312) + dg212*(dg233 + dg323)))*
|
|
ginv23 - (dg233*(dg123 + dg312) + dg223*(dg133 + 2.*dg313) +
|
|
2.*dg213*dg323 + dg212*dg333)*ginv33) +
|
|
ginv23*(ddg1233 + ddg2313 -
|
|
(dg233*(2.*dg133 + 3.*dg313) + 3.*dg213*dg333)*ginv33) -
|
|
((dg122 + 4.*dg212)*dg223 + dg222*(dg123 + dg312) + dg212*dg322)*
|
|
pow2(ginv22) - (dg233*(4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg233 + dg223*(dg133 + dg313) + dg213*dg323 +
|
|
dg212*dg333))*pow2(ginv23)) +
|
|
ginv11*(-(ginv13*((2.*(dg113*dg212 + dg112*dg213) + dg111*dg223 +
|
|
dg212*dg311 + dg211*(dg123 + dg312))*ginv22 +
|
|
(dg111*dg233 + dg213*(4.*dg113 + dg311) + dg211*(dg133 + dg313))*
|
|
ginv23)) + ginv12*(ddg1211 -
|
|
(3.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*ginv13 -
|
|
(6.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*ginv22 -
|
|
(4.*(dg113*dg212 + dg112*dg213) + dg111*dg223 + dg212*dg311 +
|
|
dg211*(dg123 + 4.*dg213 + dg312))*ginv23 -
|
|
(dg213*(2.*dg113 + dg311) + dg211*dg313)*ginv33) +
|
|
ginv22*(ddg1212 - (dg122*dg213 + dg113*dg222 + 2.*dg112*dg223 +
|
|
dg212*(4.*dg213 + 2.*(dg123 + dg312)))*ginv23 -
|
|
(dg113*dg223 + dg213*(dg123 + dg312) + dg212*dg313)*ginv33) +
|
|
ginv23*(ddg1213 - (dg113*dg233 + dg213*(dg133 + 2.*dg313))*ginv33) -
|
|
(3.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211))*pow2(ginv12) -
|
|
(dg122*dg212 + dg112*dg222 + 2.*pow2(dg212))*pow2(ginv22) -
|
|
(dg113*dg223 + dg112*dg233 + dg213*(dg123 + dg312) +
|
|
dg212*(dg133 + dg313) + 2.*pow2(dg213))*pow2(ginv23)) +
|
|
ginv23*(ddg2333*ginv33 - 2.*dg233*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg2313*ginv33 + ginv22*
|
|
(ddg1222 + 2.*ddg2212 -
|
|
((3.*dg122 + 12.*dg212)*dg223 +
|
|
dg222*(8.*dg213 + 3.*(dg123 + dg312)) + 3.*dg212*dg322)*ginv23 \
|
|
- (dg223*(4.*dg213 + 2.*(dg123 + dg312)) + dg222*dg313 + dg213*dg322 +
|
|
2.*dg212*dg323)*ginv33) +
|
|
ginv23*(ddg1223 + 2.*ddg2213 + ddg2312 -
|
|
(dg233*(dg123 + 4.*dg213 + dg312) + dg223*(dg133 + 4.*dg313) +
|
|
4.*dg213*dg323 + dg212*dg333)*ginv33) +
|
|
ginv13*(ddg1213 + ddg2311 -
|
|
(dg122*dg213 + dg222*(dg113 + dg311) +
|
|
4.*((dg112 + dg211)*dg223 + dg212*(dg123 + dg213 + dg312)) +
|
|
dg211*dg322)*ginv22 -
|
|
(dg233*(dg113 + dg311) + dg213*(dg133 + 4.*dg313) + dg211*dg333)*
|
|
ginv33 - ginv23*(2.*(dg133*dg212 + dg112*dg233 + dg223*dg311 +
|
|
dg211*dg323) + 4.*
|
|
(dg113*dg223 + dg211*dg233 + dg213*(dg123 + dg312) +
|
|
dg212*dg313 + pow2(dg213)))) -
|
|
(dg111*dg233 + 2.*dg213*(dg113 + dg311) + dg211*(dg133 + 2.*dg313))*
|
|
pow2(ginv13) - (2.*dg122 + 8.*dg212)*dg222*pow2(ginv22) -
|
|
((dg122 + 4.*dg212)*dg233 + dg223*(8.*dg213 + 2.*(dg123 + dg312)) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*(dg213*dg322 + dg212*dg323))*
|
|
pow2(ginv23) - (dg233*dg313 + dg213*dg333)*pow2(ginv33)) +
|
|
ginv22*(ddg2323*ginv33 + ginv23*
|
|
(2.*ddg2223 + ddg2322 - (dg233*(4.*dg223 + dg322) + 6.*dg223*dg323 +
|
|
dg222*dg333)*ginv33) -
|
|
(3.*dg223*dg322 + dg222*(4.*dg233 + 3.*dg323) + 6.*pow2(dg223))*
|
|
pow2(ginv23) - (dg233*dg323 + dg223*dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu23
|
|
=
|
|
-((dg111*dg233 + 2.*dg213*(dg113 + dg311) + dg211*(dg133 + 2.*dg313))*
|
|
Power(ginv13,3)) - (2.*dg111*dg211*ginv13 +
|
|
(dg112*dg211 + dg111*dg212)*ginv23 +
|
|
(dg113*dg211 + dg111*dg213)*ginv33)*pow2(ginv11) -
|
|
((2.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*ginv13 +
|
|
(dg122*dg213 + dg212*(dg123 + 2.*dg213) + dg113*dg222 +
|
|
(dg112 + 2.*dg211)*dg223)*ginv33 +
|
|
2.*ginv23*(dg122*dg212 + (dg112 + dg211)*dg222 + pow2(dg212)))*
|
|
pow2(ginv12) + (ddg1213 + ddg2311 -
|
|
((dg112 + 2.*dg211)*dg223 + dg212*(dg123 + 2.*(dg213 + dg312)))*
|
|
ginv22 - (3.*(dg133*dg213 + dg113*dg233) + 6.*dg213*dg313 +
|
|
2.*(dg233*dg311 + dg211*dg333))*ginv33 -
|
|
ginv23*(4.*(dg213*dg312 + dg212*dg313) +
|
|
2.*(dg133*dg212 + dg123*dg213 + (dg112 + dg211)*dg233 +
|
|
dg223*(dg113 + dg311) + dg211*dg323 + pow2(dg213))))*pow2(ginv13) \
|
|
- 2.*(dg233*dg333*Power(ginv33,3) +
|
|
Power(ginv23,3)*(dg223*dg322 + dg222*(dg233 + dg323) + pow2(dg223)) +
|
|
(dg222*dg223*ginv33 + ginv23*pow2(dg222))*pow2(ginv22)) +
|
|
(ddg2223 + ddg2322 - (dg233*(6.*dg223 + 2.*dg322) + 6.*dg223*dg323 +
|
|
2.*dg222*dg333)*ginv33)*pow2(ginv23) + ddg2333*pow2(ginv33) +
|
|
ginv11*(ddg1213*ginv33 + ginv13*
|
|
(ddg1211 - 2.*(dg112 + dg211)*dg212*ginv22 -
|
|
(4.*(dg113*dg212 + dg112*dg213) + dg111*dg223 + 2.*dg212*dg311 +
|
|
dg211*(dg123 + 2.*(dg213 + dg312)))*ginv23 -
|
|
(dg111*dg233 + dg213*(6.*dg113 + 2.*dg311) +
|
|
dg211*(dg133 + 2.*dg313))*ginv33) -
|
|
ginv12*((4.*dg112*dg212 + dg211*(dg122 + 2.*dg212) + dg111*dg222)*
|
|
ginv23 + (dg211*(dg123 + 2.*dg213) +
|
|
2.*(dg113*dg212 + dg112*dg213) + dg111*dg223)*ginv33 +
|
|
ginv13*(3.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211))) -
|
|
ginv22*((dg212*(dg123 + 2.*dg213) + dg112*dg223)*ginv33 +
|
|
ginv23*(dg122*dg212 + dg112*dg222 + 2.*pow2(dg212))) +
|
|
ginv23*(ddg1212 - ginv33*
|
|
(dg112*dg233 + dg212*(dg133 + 2.*dg313) +
|
|
2.*(dg113*dg223 + dg213*(dg123 + dg312) + pow2(dg213)))) -
|
|
(3.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*pow2(ginv13) -
|
|
(dg122*dg213 + dg113*dg222 + dg112*dg223 +
|
|
dg212*(dg123 + 2.*(dg213 + dg312)))*pow2(ginv23) -
|
|
(dg113*dg233 + dg213*(dg133 + 2.*dg313))*pow2(ginv33)) +
|
|
ginv22*(ddg2223*ginv33 + ginv23*
|
|
(ddg2222 - ginv33*(2.*(dg223*dg322 + dg222*(dg233 + dg323)) +
|
|
6.*pow2(dg223))) - dg222*(6.*dg223 + 2.*dg322)*pow2(ginv23) -
|
|
2.*dg223*(dg233 + dg323)*pow2(ginv33)) +
|
|
ginv12*((ddg1223 + ddg2213)*ginv33 -
|
|
ginv22*((2.*dg122 + 6.*dg212)*dg222*ginv23 +
|
|
((dg123 + 2.*dg213)*dg222 + (dg122 + 4.*dg212)*dg223)*ginv33) +
|
|
ginv23*(ddg1222 + ddg2212 -
|
|
((dg122 + 2.*dg212)*dg233 +
|
|
dg223*(4.*dg123 + 8.*dg213 + 2.*dg312) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*(dg213*dg322 + dg212*dg323))*
|
|
ginv33) + ginv13*(ddg1212 + ddg2211 -
|
|
(4.*(dg112 + dg211)*dg223 +
|
|
dg212*(8.*dg213 + 4.*(dg123 + dg312)) +
|
|
2.*(dg122*dg213 + dg222*(dg113 + dg311) + dg211*dg322))*ginv23 \
|
|
- ginv22*(dg122*dg212 + (dg112 + 2.*dg211)*dg222 + 4.*pow2(dg212)) -
|
|
ginv33*((dg112 + 2.*dg211)*dg233 + dg212*(dg133 + 2.*dg313) +
|
|
2.*(dg223*dg311 + dg213*dg312 + dg211*dg323) +
|
|
4.*(dg123*dg213 + dg113*dg223 + pow2(dg213)))) -
|
|
(2.*(dg123*dg211 + dg112*dg213 + dg111*dg223 +
|
|
dg212*(dg113 + dg311)) + dg211*(4.*dg213 + 2.*dg312))*
|
|
pow2(ginv13) - ((2.*dg122 + 4.*dg212)*dg223 +
|
|
dg222*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*dg322)*
|
|
pow2(ginv23) - ((dg123 + 2.*dg213)*dg233 +
|
|
dg223*(dg133 + 2.*dg313) + 2.*dg213*dg323)*pow2(ginv33)) +
|
|
ginv13*((ddg1233 + 2.*ddg2313)*ginv33 +
|
|
ginv22*(ddg2212 - ((dg122 + 8.*dg212)*dg223 +
|
|
dg222*(dg123 + 2.*(dg213 + dg312)) + 2.*dg212*dg322)*ginv23 -
|
|
(dg223*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*(dg233 + dg323))*
|
|
ginv33) + ginv23*(ddg1223 + ddg2213 + 2.*ddg2312 -
|
|
(3.*(dg133*dg223 + dg123*dg233) + dg233*(6.*dg213 + 4.*dg312) +
|
|
6.*(dg223*dg313 + dg213*dg323) + 4.*dg212*dg333)*ginv33) -
|
|
2.*dg212*dg222*pow2(ginv22) -
|
|
((dg122 + 4.*dg212)*dg233 + dg223*(2.*dg123 + 4.*(dg213 + dg312)) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*dg213*dg322 + 4.*dg212*dg323)*
|
|
pow2(ginv23) - (dg233*(2.*dg133 + 4.*dg313) + 4.*dg213*dg333)*
|
|
pow2(ginv33)) + ginv23*((ddg2233 + 2.*ddg2323)*ginv33 -
|
|
(4.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233))*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu31
|
|
=
|
|
-((dg222*dg311 + dg211*dg322 + 2.*((dg122 + dg212)*dg312 + dg112*dg322))*
|
|
Power(ginv12,3)) - 2.*(dg111*dg311*Power(ginv11,3) +
|
|
Power(ginv13,3)*(dg133*dg313 + (dg113 + dg311)*dg333 + pow2(dg313))) +
|
|
(ddg1311 - ((4.*dg112 + 2.*dg211)*dg311 + 4.*dg111*dg312)*ginv12 -
|
|
(dg212*dg311 + (2.*dg112 + dg211)*dg312)*ginv22 -
|
|
(dg311*(dg213 + 2.*dg312) + dg211*dg313 +
|
|
2.*(dg113*dg312 + dg112*dg313))*ginv23 -
|
|
2.*(dg113 + dg311)*dg313*ginv33 -
|
|
ginv13*(4.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311)))*pow2(ginv11) \
|
|
+ (ddg1322 + ddg2312 - (2.*dg122*dg322 + 3.*(dg222*dg312 + dg212*dg322))*
|
|
ginv22 - ((2.*dg213 + 4.*dg312)*dg322 +
|
|
2.*(dg223*dg312 + dg222*dg313 + dg123*dg322 +
|
|
(dg122 + dg212)*dg323))*ginv23 -
|
|
(dg313*(dg223 + 2.*dg322) + (dg213 + 2.*(dg123 + dg312))*dg323)*
|
|
ginv33 - ginv13*(4.*(dg123*dg312 + dg112*dg323) +
|
|
2.*(dg213*dg312 + (dg122 + dg212)*dg313 + dg113*dg322 +
|
|
dg311*(dg223 + dg322) + dg211*dg323 + pow2(dg312))))*pow2(ginv12) \
|
|
+ (ddg1333 + ddg3313 - (dg233*dg312 + dg223*dg313 +
|
|
(dg213 + 2.*(dg123 + dg312))*dg323 + dg212*dg333)*ginv22 -
|
|
(2.*(dg233*dg313 + dg133*dg323 + (dg123 + dg213)*dg333) +
|
|
4.*(dg313*dg323 + dg312*dg333))*ginv23 -
|
|
(2.*dg133 + 6.*dg313)*dg333*ginv33)*pow2(ginv13) +
|
|
ginv11*(ddg3313*ginv33 + ginv22*
|
|
(ddg2312 - (dg222*dg313 + dg213*dg322 +
|
|
2.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 -
|
|
(dg223*dg313 + (dg213 + 2.*dg312)*dg323)*ginv33) +
|
|
ginv23*(ddg2313 + ddg3312 -
|
|
(dg313*(dg233 + 4.*dg323) + (dg213 + 2.*dg312)*dg333)*ginv33) +
|
|
ginv12*(2.*ddg1312 + ddg2311 -
|
|
(dg311*(4.*dg123 + 3.*dg213 + 6.*dg312) + 3.*dg211*dg313 +
|
|
6.*(dg113*dg312 + dg112*dg313) + 4.*dg111*dg323)*ginv13 -
|
|
(dg222*dg311 + (2.*dg122 + 6.*dg212)*dg312 +
|
|
(2.*dg112 + dg211)*dg322)*ginv22 -
|
|
(4.*dg312*dg313 + 2.*((dg123 + dg213)*dg313 +
|
|
(dg113 + dg311)*dg323))*ginv33 -
|
|
ginv23*((2.*dg123 + 4.*dg213)*dg312 + dg311*(dg223 + 2.*dg322) +
|
|
dg211*dg323 + 2.*(dg122*dg313 + dg113*dg322 + dg112*dg323) +
|
|
4.*(dg212*dg313 + pow2(dg312)))) +
|
|
ginv13*(2.*ddg1313 + ddg3311 -
|
|
((4.*dg213 + 8.*dg312)*dg313 + dg311*(dg233 + 2.*dg323) +
|
|
dg211*dg333 + 2.*(dg133*dg312 + dg123*dg313 + dg113*dg323 +
|
|
dg112*dg333))*ginv23 -
|
|
ginv22*(dg223*dg311 + dg211*dg323 +
|
|
2.*((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323 +
|
|
pow2(dg312))) -
|
|
ginv33*(2.*(dg133*dg313 + (dg113 + dg311)*dg333) + 6.*pow2(dg313))) \
|
|
- ((2.*dg122 + 3.*dg212)*dg311 + (6.*dg112 + 3.*dg211)*dg312 +
|
|
2.*dg111*dg322)*pow2(ginv12) -
|
|
(6.*dg113*dg313 + dg311*(2.*dg133 + 6.*dg313) + 2.*dg111*dg333)*
|
|
pow2(ginv13) - (dg222*dg312 + dg212*dg322)*pow2(ginv22) -
|
|
(dg313*(dg223 + 2.*dg322) + dg213*dg323 + dg312*(dg233 + 2.*dg323) +
|
|
dg212*dg333)*pow2(ginv23) - 2.*dg313*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg3323*ginv33 + ginv13*
|
|
(2.*ddg1323 + ddg2313 + ddg3312 -
|
|
(dg222*dg313 + (2.*dg123 + dg213)*dg322 +
|
|
dg312*(4.*dg223 + 2.*dg322) + (2.*dg122 + 4.*dg212)*dg323)*
|
|
ginv22 - ((4.*dg213 + 8.*dg312)*dg323 +
|
|
4.*(dg313*(dg223 + dg322) + dg123*dg323) +
|
|
2.*(dg233*dg312 + dg133*dg322 + (dg122 + dg212)*dg333))*ginv23 \
|
|
- (dg313*(dg233 + 8.*dg323) + (dg213 + 2.*dg312)*dg333 +
|
|
2.*(dg133*dg323 + dg123*dg333))*ginv33) +
|
|
ginv22*(ddg2322 - 2.*(dg223 + dg322)*dg323*ginv33 -
|
|
ginv23*(3.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322))) +
|
|
ginv23*(ddg2323 + ddg3322 -
|
|
ginv33*(dg233*dg323 + (dg223 + 2.*dg322)*dg333 + 4.*pow2(dg323))) -
|
|
(dg311*(dg233 + 4.*dg323) +
|
|
4.*((dg123 + dg312)*dg313 + dg113*dg323) + dg211*dg333 +
|
|
2.*(dg133*dg312 + dg213*dg313 + dg112*dg333))*pow2(ginv13) -
|
|
(2.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*
|
|
pow2(ginv23) - 2.*(dg222*dg322*pow2(ginv22) +
|
|
dg323*dg333*pow2(ginv33))) +
|
|
ginv13*(ddg3333*ginv33 + ginv23*
|
|
(ddg2333 + ddg3323 - (2.*dg233 + 6.*dg323)*dg333*ginv33) +
|
|
ginv22*(ddg2323 - (4.*dg223*dg323 + dg322*(dg233 + 2.*dg323) +
|
|
dg222*dg333)*ginv23 -
|
|
ginv33*(dg233*dg323 + dg223*dg333 + 2.*pow2(dg323))) -
|
|
(dg223*dg322 + dg222*dg323)*pow2(ginv22) -
|
|
2.*((dg233*dg323 + (dg223 + dg322)*dg333 + pow2(dg323))*pow2(ginv23) +
|
|
pow2(dg333)*pow2(ginv33)))
|
|
;
|
|
|
|
dGfromgdu32
|
|
=
|
|
-(((dg122 + 2.*dg212)*dg311 + 2.*(dg112 + dg211)*dg312 + dg111*dg322)*
|
|
Power(ginv12,3)) - 2.*(dg222*dg322*Power(ginv22,3) +
|
|
Power(ginv23,3)*(dg233*dg323 + (dg223 + dg322)*dg333 + pow2(dg323))) -
|
|
(2.*dg111*dg311*ginv12 + (dg112*dg311 + dg111*dg312)*ginv22 +
|
|
(dg113*dg311 + dg111*dg313)*ginv23)*pow2(ginv11) +
|
|
(ddg1312 + ddg2311 - (4.*dg311*dg312 +
|
|
2.*((dg123 + dg213)*dg311 + dg113*dg312 +
|
|
(dg112 + dg211)*dg313 + dg111*dg323))*ginv13 -
|
|
((3.*dg122 + 6.*dg212)*dg312 + 3.*dg112*dg322 +
|
|
2.*(dg222*dg311 + dg211*dg322))*ginv22 -
|
|
((dg123 + 2.*(dg213 + dg312))*dg313 + (dg113 + 2.*dg311)*dg323)*
|
|
ginv33 - ginv23*(4.*(dg213*dg312 + dg212*dg313) +
|
|
2.*(dg123*dg312 + dg122*dg313 + dg113*dg322 +
|
|
dg311*(dg223 + dg322) + (dg112 + dg211)*dg323 + pow2(dg312))))*
|
|
pow2(ginv12) - ((dg123*dg313 + dg312*(dg133 + 2.*dg313) +
|
|
(dg113 + 2.*dg311)*dg323 + dg112*dg333)*ginv22 +
|
|
2.*ginv23*(dg133*dg313 + (dg113 + dg311)*dg333 + pow2(dg313)))*
|
|
pow2(ginv13) + (ddg2322 - 2.*(dg223 + dg322)*dg323*ginv33 -
|
|
ginv23*(4.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322)))*pow2(ginv22) \
|
|
+ (ddg2333 + ddg3323 - (2.*dg233 + 6.*dg323)*dg333*ginv33)*pow2(ginv23) +
|
|
ginv11*(-(ginv13*((dg311*(dg123 + 2.*dg312) +
|
|
2.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv22 +
|
|
(4.*dg113*dg313 + dg311*(dg133 + 2.*dg313) + dg111*dg333)*ginv23)\
|
|
) + ginv12*(ddg1311 - ((dg122 + 2.*dg212)*dg311 +
|
|
(6.*dg112 + 2.*dg211)*dg312 + dg111*dg322)*ginv22 -
|
|
(dg311*(dg123 + 2.*(dg213 + dg312)) + 2.*dg211*dg313 +
|
|
4.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv23 -
|
|
2.*(dg113 + dg311)*dg313*ginv33 -
|
|
ginv13*(3.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311))) +
|
|
ginv22*(ddg1312 - ((dg123 + 2.*dg312)*dg313 + dg113*dg323)*ginv33 -
|
|
ginv23*(dg122*dg313 + dg113*dg322 +
|
|
2.*((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323 +
|
|
pow2(dg312)))) +
|
|
ginv23*(ddg1313 - ginv33*
|
|
(dg133*dg313 + dg113*dg333 + 2.*pow2(dg313))) -
|
|
((3.*dg112 + 2.*dg211)*dg311 + 3.*dg111*dg312)*pow2(ginv12) -
|
|
((dg122 + 2.*dg212)*dg312 + dg112*dg322)*pow2(ginv22) -
|
|
(dg133*dg312 + (dg123 + 2.*(dg213 + dg312))*dg313 + dg113*dg323 +
|
|
dg112*dg333)*pow2(ginv23)) +
|
|
ginv13*(ginv23*(ddg1333 + ddg3313 - (2.*dg133 + 6.*dg313)*dg333*ginv33) +
|
|
ginv22*(ddg1323 + ddg3312 -
|
|
(dg133*dg322 + (4.*dg123 + 2.*dg213 + 8.*dg312)*dg323 +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg313*(dg223 + dg322) +
|
|
dg212*dg333))*ginv23 -
|
|
((dg133 + 4.*dg313)*dg323 + (dg123 + 2.*dg312)*dg333)*ginv33) -
|
|
(dg123*dg322 + dg122*dg323 +
|
|
2.*(dg312*(dg223 + dg322) + dg212*dg323))*pow2(ginv22) -
|
|
(2.*(dg233*dg313 + dg133*dg323 + (dg123 + dg213)*dg333) +
|
|
4.*(dg313*dg323 + dg312*dg333))*pow2(ginv23)) +
|
|
ginv12*(ddg3313*ginv33 + ginv22*
|
|
(ddg1322 + 2.*ddg2312 -
|
|
(4.*(dg222*dg313 + dg213*dg322) +
|
|
3.*(dg123*dg322 + dg122*dg323) +
|
|
6.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 -
|
|
((2.*dg213 + 4.*dg312)*dg323 +
|
|
2.*(dg313*(dg223 + dg322) + dg123*dg323))*ginv33) +
|
|
ginv23*(ddg1323 + 2.*ddg2313 + ddg3312 -
|
|
(dg133*dg323 + dg313*(2.*dg233 + 8.*dg323) +
|
|
(dg123 + 2.*(dg213 + dg312))*dg333)*ginv33) +
|
|
ginv13*(ddg1313 + ddg3311 -
|
|
(8.*dg312*dg313 + 4.*
|
|
((dg123 + dg213)*dg313 + (dg113 + dg311)*dg323) +
|
|
2.*(dg233*dg311 + dg133*dg312 + (dg112 + dg211)*dg333))*ginv23 \
|
|
- ginv22*(dg122*dg313 + dg113*dg322 +
|
|
2.*(dg213*dg312 + dg212*dg313 + dg311*(dg223 + dg322) +
|
|
dg211*dg323) + 4.*(dg123*dg312 + dg112*dg323 + pow2(dg312))) \
|
|
- ginv33*(dg133*dg313 + (dg113 + 2.*dg311)*dg333 + 4.*pow2(dg313))) -
|
|
(2.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*
|
|
pow2(ginv13) - (2.*dg122*dg322 + 4.*(dg222*dg312 + dg212*dg322))*
|
|
pow2(ginv22) - (dg133*dg322 +
|
|
4.*(dg313*(dg223 + dg322) + (dg213 + dg312)*dg323) +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg123*dg323 + dg212*dg333))*
|
|
pow2(ginv23) - 2.*dg313*dg333*pow2(ginv33)) +
|
|
ginv22*(ddg3323*ginv33 + ginv23*
|
|
(2.*ddg2323 + ddg3322 -
|
|
ginv33*(2.*(dg233*dg323 + (dg223 + dg322)*dg333) + 6.*pow2(dg323))) \
|
|
- (6.*dg223*dg323 + dg322*(2.*dg233 + 6.*dg323) + 2.*dg222*dg333)*
|
|
pow2(ginv23) - 2.*dg323*dg333*pow2(ginv33)) +
|
|
ginv23*(ddg3333*ginv33 - 2.*pow2(dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu33
|
|
=
|
|
-((2.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*
|
|
Power(ginv13,3)) - (2.*dg223*dg323 + dg322*(dg233 + 4.*dg323) +
|
|
dg222*dg333)*Power(ginv23,3) - 2.*Power(ginv33,3)*pow2(dg333) -
|
|
(2.*dg111*dg311*ginv13 + (dg112*dg311 + dg111*dg312)*ginv23 +
|
|
(dg113*dg311 + dg111*dg313)*ginv33)*pow2(ginv11) -
|
|
(((dg122 + 2.*dg212)*dg311 + 2.*(dg112 + dg211)*dg312 + dg111*dg322)*
|
|
ginv13 + (dg222*dg311 + dg211*dg322 +
|
|
2.*((dg122 + dg212)*dg312 + dg112*dg322))*ginv23 +
|
|
(dg223*dg311 + (dg123 + dg213)*dg312 + (dg122 + dg212)*dg313 +
|
|
dg113*dg322 + (dg112 + dg211)*dg323)*ginv33)*pow2(ginv12) +
|
|
(ddg1313 + ddg3311 - ((2.*dg213 + 8.*dg312)*dg313 +
|
|
dg311*(dg233 + 4.*dg323) + dg211*dg333 +
|
|
2.*(dg133*dg312 + dg123*dg313 + dg113*dg323 + dg112*dg333))*ginv23 \
|
|
- ginv22*(dg223*dg311 + (dg123 + dg213)*dg312 + dg212*dg313 +
|
|
(dg112 + dg211)*dg323 + 2.*pow2(dg312)) -
|
|
ginv33*(4.*dg311*dg333 + 3.*(dg133*dg313 + dg113*dg333) +
|
|
6.*pow2(dg313)))*pow2(ginv13) -
|
|
(2.*dg222*dg322*ginv23 + (dg223*dg322 + dg222*dg323)*ginv33)*
|
|
pow2(ginv22) + (ddg2323 + ddg3322 -
|
|
ginv33*(4.*dg322*dg333 + 3.*(dg233*dg323 + dg223*dg333) +
|
|
6.*pow2(dg323)))*pow2(ginv23) + ddg3333*pow2(ginv33) +
|
|
ginv13*((ddg1333 + 2.*ddg3313)*ginv33 +
|
|
ginv22*(ddg2312 - (dg222*dg313 + (dg123 + dg213)*dg322 +
|
|
dg122*dg323 + 4.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 \
|
|
- (dg312*(dg233 + 4.*dg323) + 2.*(dg223*dg313 + (dg123 + dg213)*dg323) +
|
|
dg212*dg333)*ginv33) +
|
|
ginv23*(ddg1323 + ddg2313 + 2.*ddg3312 -
|
|
(12.*dg313*dg323 + (3.*dg213 + 8.*dg312)*dg333 +
|
|
3.*(dg233*dg313 + dg133*dg323 + dg123*dg333))*ginv33) -
|
|
(dg222*dg312 + dg212*dg322)*pow2(ginv22) -
|
|
((dg133 + 4.*dg313)*dg322 + (2.*dg213 + 8.*dg312)*dg323 +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg223*dg313 + dg123*dg323 +
|
|
dg212*dg333))*pow2(ginv23) -
|
|
(2.*dg133 + 8.*dg313)*dg333*pow2(ginv33)) +
|
|
ginv23*((ddg2333 + 2.*ddg3323)*ginv33 -
|
|
(2.*dg233 + 8.*dg323)*dg333*pow2(ginv33)) +
|
|
ginv12*((ddg1323 + ddg2313)*ginv33 -
|
|
ginv22*((2.*dg122*dg322 + 3.*(dg222*dg312 + dg212*dg322))*ginv23 +
|
|
(dg222*dg313 + (dg123 + dg213)*dg322 + dg122*dg323 +
|
|
2.*(dg223*dg312 + dg212*dg323))*ginv33) +
|
|
ginv23*(ddg1322 + ddg2312 -
|
|
(dg233*dg312 + dg133*dg322 +
|
|
4.*(dg313*(dg223 + dg322) + (dg123 + dg213 + dg312)*dg323) +
|
|
(dg122 + dg212)*dg333)*ginv33) +
|
|
ginv13*(ddg1312 + ddg2311 -
|
|
(dg222*dg311 + (dg122 + 4.*dg212)*dg312 + (dg112 + dg211)*dg322)*
|
|
ginv22 - (dg133*dg312 + dg311*(dg233 + 4.*dg323) +
|
|
4.*((dg123 + dg213 + dg312)*dg313 + dg113*dg323) +
|
|
(dg112 + dg211)*dg333)*ginv33 -
|
|
ginv23*(2.*(dg223*dg311 + dg122*dg313 + dg113*dg322 +
|
|
dg211*dg323) + 4.*
|
|
((dg123 + dg213)*dg312 + dg212*dg313 + dg311*dg322 +
|
|
dg112*dg323 + pow2(dg312)))) -
|
|
(4.*dg311*dg312 + 2.*((dg123 + dg213)*dg311 + dg113*dg312 +
|
|
(dg112 + dg211)*dg313 + dg111*dg323))*pow2(ginv13) -
|
|
((2.*dg213 + 4.*dg312)*dg322 +
|
|
2.*(dg223*dg312 + dg222*dg313 + dg123*dg322 +
|
|
(dg122 + dg212)*dg323))*pow2(ginv23) -
|
|
(dg133*dg323 + dg313*(dg233 + 4.*dg323) + (dg123 + dg213)*dg333)*
|
|
pow2(ginv33)) + ginv11*(ddg1313*ginv33 -
|
|
ginv12*(((3.*dg112 + 2.*dg211)*dg311 + 3.*dg111*dg312)*ginv13 +
|
|
((dg122 + dg212)*dg311 + (4.*dg112 + dg211)*dg312 + dg111*dg322)*
|
|
ginv23 + ((dg123 + dg213)*dg311 + dg211*dg313 +
|
|
2.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv33) -
|
|
ginv22*(((dg122 + 2.*dg212)*dg312 + dg112*dg322)*ginv23 +
|
|
((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323)*ginv33) +
|
|
ginv13*(ddg1311 - (dg212*dg311 + (2.*dg112 + dg211)*dg312)*ginv22 -
|
|
((dg123 + dg213)*dg311 + 4.*(dg113 + dg311)*dg312 +
|
|
(4.*dg112 + dg211)*dg313 + dg111*dg323)*ginv23 -
|
|
(6.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1312 - (dg312*(dg133 + 4.*dg313) +
|
|
2.*((dg123 + dg213)*dg313 + dg113*dg323) + dg112*dg333)*ginv33) \
|
|
- (3.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311))*pow2(ginv13) -
|
|
((dg123 + dg213)*dg312 + (dg122 + dg212)*dg313 + dg113*dg322 +
|
|
dg112*dg323 + 2.*pow2(dg312))*pow2(ginv23) -
|
|
(dg133*dg313 + dg113*dg333 + 2.*pow2(dg313))*pow2(ginv33)) +
|
|
ginv22*(ddg2323*ginv33 + ginv23*
|
|
(ddg2322 - (6.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*
|
|
ginv33) - (3.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322))*
|
|
pow2(ginv23) - (dg233*dg323 + dg223*dg333 + 2.*pow2(dg323))*
|
|
pow2(ginv33))
|
|
;
|
|
|
|
R11
|
|
=
|
|
dG11*g11 + dG12*g12 + dG13*g13 + gammado111*Gfromg1 + gammado112*Gfromg2 +
|
|
gammado113*Gfromg3 + (-0.5*ddg1111 + 3.*gamma111*gammado111 +
|
|
2.*(gamma211*gammado112 + gamma311*gammado113) +
|
|
gamma211*gammado211 + gamma311*gammado311)*ginv11 +
|
|
(-ddg1211 + 3.*(gamma112*gammado111 + gamma111*gammado112) +
|
|
2.*(gamma212*gammado112 + gamma312*gammado113 +
|
|
gamma211*gammado122 + gamma311*gammado123) + gamma212*gammado211 +
|
|
gamma211*gammado212 + gamma312*gammado311 + gamma311*gammado312)*ginv12 \
|
|
+ (-ddg1311 + 3.*(gamma113*gammado111 + gamma111*gammado113) +
|
|
2.*(gamma213*gammado112 + gamma313*gammado113 +
|
|
gamma211*gammado123 + gamma311*gammado133) + gamma213*gammado211 +
|
|
gamma211*gammado213 + gamma313*gammado311 + gamma311*gammado313)*ginv13 \
|
|
+ (-0.5*ddg2211 + 3.*gamma112*gammado112 +
|
|
2.*(gamma212*gammado122 + gamma312*gammado123) +
|
|
gamma212*gammado212 + gamma312*gammado312)*ginv22 +
|
|
(-ddg2311 + 3.*(gamma113*gammado112 + gamma112*gammado113) +
|
|
2.*(gamma213*gammado122 + (gamma212 + gamma313)*gammado123 +
|
|
gamma312*gammado133) + gamma213*gammado212 + gamma212*gammado213 +
|
|
gamma313*gammado312 + gamma312*gammado313)*ginv23 +
|
|
(-0.5*ddg3311 + 3.*gamma113*gammado113 +
|
|
2.*(gamma213*gammado123 + gamma313*gammado133) + gamma213*gammado213 +
|
|
gamma313*gammado313)*ginv33
|
|
;
|
|
|
|
R12
|
|
=
|
|
0.5*(dG21*g11 + (dG11 + dG22)*g12 + dG23*g13 + dG12*g22 + dG13*g23 +
|
|
(gammado112 + gammado211)*Gfromg1 +
|
|
(gammado122 + gammado212)*Gfromg2 + (gammado123 + gammado213)*Gfromg3) \
|
|
+ (-0.5*ddg1112 + gamma112*gammado111 + (gamma111 + gamma212)*gammado112 +
|
|
gamma312*gammado113 + gamma111*gammado211 + 2.*gamma211*gammado212 +
|
|
gamma311*(gammado213 + gammado312))*ginv11 +
|
|
(-ddg1212 + gamma122*gammado111 + (2.*gamma112 + gamma222)*gammado112 +
|
|
gamma322*gammado113 + (gamma111 + gamma212)*gammado122 +
|
|
gamma112*gammado211 + (gamma111 + 2.*gamma212)*gammado212 +
|
|
2.*gamma211*gammado222 +
|
|
gamma312*(gammado123 + gammado213 + gammado312) +
|
|
gamma311*(gammado223 + gammado322))*ginv12 +
|
|
(-ddg1312 + gamma123*gammado111 + (gamma113 + gamma223)*gammado112 +
|
|
(gamma112 + gamma323)*gammado113 + (gamma111 + gamma212)*gammado123 +
|
|
gamma312*gammado133 + gamma113*gammado211 +
|
|
(gamma111 + gamma313)*gammado213 +
|
|
2.*(gamma213*gammado212 + gamma211*gammado223) +
|
|
gamma313*gammado312 + gamma311*(gammado233 + gammado323))*ginv13 +
|
|
(-0.5*ddg2212 + gamma122*gammado112 + (gamma112 + gamma222)*gammado122 +
|
|
gamma322*gammado123 + gamma112*gammado212 + 2.*gamma212*gammado222 +
|
|
gamma312*(gammado223 + gammado322))*ginv22 +
|
|
(-ddg2312 + gamma123*gammado112 + gamma122*gammado113 +
|
|
(gamma113 + gamma223)*gammado122 +
|
|
(gamma112 + gamma222 + gamma323)*gammado123 + gamma322*gammado133 +
|
|
gamma113*gammado212 + gamma112*gammado213 +
|
|
2.*(gamma213*gammado222 + gamma212*gammado223) +
|
|
gamma313*(gammado223 + gammado322) +
|
|
gamma312*(gammado233 + gammado323))*ginv23 +
|
|
(-0.5*ddg3312 + gamma123*gammado113 + (gamma113 + gamma223)*gammado123 +
|
|
gamma323*gammado133 + gamma113*gammado213 + 2.*gamma213*gammado223 +
|
|
gamma313*(gammado233 + gammado323))*ginv33
|
|
;
|
|
|
|
R13
|
|
=
|
|
0.5*(dG31*g11 + dG32*g12 + (dG11 + dG33)*g13 + dG12*g23 + dG13*g33 +
|
|
(gammado113 + gammado311)*Gfromg1 +
|
|
(gammado123 + gammado312)*Gfromg2 + (gammado133 + gammado313)*Gfromg3) \
|
|
+ (-0.5*ddg1113 + gamma113*gammado111 + gamma213*gammado112 +
|
|
(gamma111 + gamma313)*gammado113 + gamma111*gammado311 +
|
|
gamma211*(gammado213 + gammado312) + 2.*gamma311*gammado313)*ginv11 +
|
|
(-ddg1213 + gamma123*gammado111 + (gamma113 + gamma223)*gammado112 +
|
|
(gamma112 + gamma323)*gammado113 + gamma213*gammado122 +
|
|
(gamma111 + gamma313)*gammado123 + gamma112*gammado311 +
|
|
gamma111*gammado312 + gamma212*(gammado213 + gammado312) +
|
|
gamma211*(gammado223 + gammado322) +
|
|
2.*(gamma312*gammado313 + gamma311*gammado323))*ginv12 +
|
|
(-ddg1313 + gamma133*gammado111 + gamma233*gammado112 +
|
|
(2.*gamma113 + gamma333)*gammado113 +
|
|
(gamma111 + gamma313)*gammado133 + gamma113*gammado311 +
|
|
gamma213*(gammado123 + gammado213 + gammado312) +
|
|
(gamma111 + 2.*gamma313)*gammado313 +
|
|
gamma211*(gammado233 + gammado323) + 2.*gamma311*gammado333)*ginv13 +
|
|
(-0.5*ddg2213 + gamma123*gammado112 + gamma223*gammado122 +
|
|
(gamma112 + gamma323)*gammado123 + gamma112*gammado312 +
|
|
gamma212*(gammado223 + gammado322) + 2.*gamma312*gammado323)*ginv22 +
|
|
(-ddg2313 + gamma133*gammado112 + gamma123*gammado113 +
|
|
gamma233*gammado122 + (gamma113 + gamma223 + gamma333)*gammado123 +
|
|
(gamma112 + gamma323)*gammado133 + gamma113*gammado312 +
|
|
gamma112*gammado313 + gamma213*(gammado223 + gammado322) +
|
|
gamma212*(gammado233 + gammado323) +
|
|
2.*(gamma313*gammado323 + gamma312*gammado333))*ginv23 +
|
|
(-0.5*ddg3313 + gamma133*gammado113 + gamma233*gammado123 +
|
|
(gamma113 + gamma333)*gammado133 + gamma113*gammado313 +
|
|
gamma213*(gammado233 + gammado323) + 2.*gamma313*gammado333)*ginv33
|
|
;
|
|
|
|
R22
|
|
=
|
|
dG21*g12 + dG22*g22 + dG23*g23 + gammado212*Gfromg1 + gammado222*Gfromg2 +
|
|
gammado223*Gfromg3 + (-0.5*ddg1122 +
|
|
gamma112*(gammado112 + 2.*gammado211) + 3.*gamma212*gammado212 +
|
|
gamma312*(2.*gammado213 + gammado312))*ginv11 +
|
|
(-ddg1222 + gamma122*(gammado112 + 2.*gammado211) +
|
|
gamma112*(gammado122 + 2.*gammado212) +
|
|
3.*(gamma222*gammado212 + gamma212*gammado222) +
|
|
2.*(gamma322*gammado213 + gamma312*gammado223) +
|
|
gamma322*gammado312 + gamma312*gammado322)*ginv12 +
|
|
(-ddg1322 + gamma123*(gammado112 + 2.*gammado211) +
|
|
gamma112*(gammado123 + 2.*gammado213) +
|
|
3.*(gamma223*gammado212 + gamma212*gammado223) +
|
|
2.*(gamma323*gammado213 + gamma312*gammado233) +
|
|
gamma323*gammado312 + gamma312*gammado323)*ginv13 +
|
|
(-0.5*ddg2222 + gamma122*(gammado122 + 2.*gammado212) +
|
|
3.*gamma222*gammado222 + gamma322*(2.*gammado223 + gammado322))*ginv22 \
|
|
+ (-ddg2322 + gamma123*(gammado122 + 2.*gammado212) +
|
|
gamma122*(gammado123 + 2.*gammado213) +
|
|
3.*(gamma223*gammado222 + gamma222*gammado223) +
|
|
2.*(gamma323*gammado223 + gamma322*gammado233) +
|
|
gamma323*gammado322 + gamma322*gammado323)*ginv23 +
|
|
(-0.5*ddg3322 + gamma123*(gammado123 + 2.*gammado213) +
|
|
3.*gamma223*gammado223 + gamma323*(2.*gammado233 + gammado323))*ginv33
|
|
;
|
|
|
|
R23
|
|
=
|
|
0.5*(dG31*g12 + dG21*g13 + dG32*g22 + (dG22 + dG33)*g23 + dG23*g33 +
|
|
(gammado213 + gammado312)*Gfromg1 +
|
|
(gammado223 + gammado322)*Gfromg2 + (gammado233 + gammado323)*Gfromg3) \
|
|
+ (-0.5*ddg1123 + gamma113*gammado211 + gamma213*gammado212 +
|
|
(gamma212 + gamma313)*gammado213 +
|
|
gamma112*(gammado113 + gammado311) + gamma212*gammado312 +
|
|
2.*gamma312*gammado313)*ginv11 +
|
|
(-ddg1223 + gamma123*gammado211 + (gamma113 + gamma223)*gammado212 +
|
|
(gamma222 + gamma323)*gammado213 + gamma213*gammado222 +
|
|
(gamma212 + gamma313)*gammado223 +
|
|
gamma122*(gammado113 + gammado311) + gamma222*gammado312 +
|
|
gamma112*(gammado123 + gammado312) + gamma212*gammado322 +
|
|
2.*(gamma322*gammado313 + gamma312*gammado323))*ginv12 +
|
|
(-ddg1323 + gamma133*gammado211 + gamma233*gammado212 +
|
|
(gamma113 + gamma223 + gamma333)*gammado213 + gamma213*gammado223 +
|
|
(gamma212 + gamma313)*gammado233 +
|
|
gamma123*(gammado113 + gammado311) + gamma223*gammado312 +
|
|
gamma112*(gammado133 + gammado313) + gamma212*gammado323 +
|
|
2.*(gamma323*gammado313 + gamma312*gammado333))*ginv13 +
|
|
(-0.5*ddg2223 + gamma123*gammado212 + gamma223*gammado222 +
|
|
(gamma222 + gamma323)*gammado223 +
|
|
gamma122*(gammado123 + gammado312) + gamma222*gammado322 +
|
|
2.*gamma322*gammado323)*ginv22 +
|
|
(-ddg2323 + gamma133*gammado212 + gamma233*gammado222 +
|
|
(2.*gamma223 + gamma333)*gammado223 +
|
|
(gamma222 + gamma323)*gammado233 +
|
|
gamma123*(gammado123 + gammado213 + gammado312) +
|
|
gamma122*(gammado133 + gammado313) + gamma223*gammado322 +
|
|
(gamma222 + 2.*gamma323)*gammado323 + 2.*gamma322*gammado333)*ginv23 +
|
|
(-0.5*ddg3323 + gamma133*gammado213 + gamma233*gammado223 +
|
|
(gamma223 + gamma333)*gammado233 +
|
|
gamma123*(gammado133 + gammado313) + gamma223*gammado323 +
|
|
2.*gamma323*gammado333)*ginv33
|
|
;
|
|
|
|
R33
|
|
=
|
|
dG31*g13 + dG32*g23 + dG33*g33 + gammado313*Gfromg1 + gammado323*Gfromg2 +
|
|
gammado333*Gfromg3 + (-0.5*ddg1133 +
|
|
gamma113*(gammado113 + 2.*gammado311) +
|
|
gamma213*(gammado213 + 2.*gammado312) + 3.*gamma313*gammado313)*ginv11 \
|
|
+ (-ddg1233 + gamma123*(gammado113 + 2.*gammado311) +
|
|
gamma113*(gammado123 + 2.*gammado312) +
|
|
gamma223*(gammado213 + 2.*gammado312) +
|
|
gamma213*(gammado223 + 2.*gammado322) +
|
|
3.*(gamma323*gammado313 + gamma313*gammado323))*ginv12 +
|
|
(-ddg1333 + gamma133*(gammado113 + 2.*gammado311) +
|
|
gamma233*(gammado213 + 2.*gammado312) +
|
|
gamma113*(gammado133 + 2.*gammado313) +
|
|
gamma213*(gammado233 + 2.*gammado323) +
|
|
3.*(gamma333*gammado313 + gamma313*gammado333))*ginv13 +
|
|
(-0.5*ddg2233 + gamma123*(gammado123 + 2.*gammado312) +
|
|
gamma223*(gammado223 + 2.*gammado322) + 3.*gamma323*gammado323)*ginv22 \
|
|
+ (-ddg2333 + gamma133*(gammado123 + 2.*gammado312) +
|
|
gamma123*(gammado133 + 2.*gammado313) +
|
|
gamma233*(gammado223 + 2.*gammado322) +
|
|
gamma223*(gammado233 + 2.*gammado323) +
|
|
3.*(gamma333*gammado323 + gamma323*gammado333))*ginv23 +
|
|
(-0.5*ddg3333 + gamma133*(gammado133 + 2.*gammado313) +
|
|
gamma233*(gammado233 + 2.*gammado323) + 3.*gamma333*gammado333)*ginv33
|
|
;
|
|
|
|
ff
|
|
=
|
|
chi
|
|
;
|
|
|
|
oochipsipower
|
|
=
|
|
1/chipsipower
|
|
;
|
|
|
|
f
|
|
=
|
|
oochipsipower*log(ff)
|
|
;
|
|
|
|
psim4
|
|
=
|
|
exp(-4.*f)
|
|
;
|
|
|
|
df1
|
|
=
|
|
(dchi1*oochipsipower)/chi
|
|
;
|
|
|
|
df2
|
|
=
|
|
(dchi2*oochipsipower)/chi
|
|
;
|
|
|
|
df3
|
|
=
|
|
(dchi3*oochipsipower)/chi
|
|
;
|
|
|
|
ddf11
|
|
=
|
|
(ddchi11*oochipsipower)/chi - chipsipower*pow2(df1)
|
|
;
|
|
|
|
ddf12
|
|
=
|
|
-(chipsipower*df1*df2) + (ddchi12*oochipsipower)/chi
|
|
;
|
|
|
|
ddf13
|
|
=
|
|
-(chipsipower*df1*df3) + (ddchi13*oochipsipower)/chi
|
|
;
|
|
|
|
ddf22
|
|
=
|
|
(ddchi22*oochipsipower)/chi - chipsipower*pow2(df2)
|
|
;
|
|
|
|
ddf23
|
|
=
|
|
-(chipsipower*df2*df3) + (ddchi23*oochipsipower)/chi
|
|
;
|
|
|
|
ddf33
|
|
=
|
|
(ddchi33*oochipsipower)/chi - chipsipower*pow2(df3)
|
|
;
|
|
|
|
cddf11
|
|
=
|
|
ddf11 - df1*gamma111 - df2*gamma211 - df3*gamma311
|
|
;
|
|
|
|
cddf12
|
|
=
|
|
ddf12 - df1*gamma112 - df2*gamma212 - df3*gamma312
|
|
;
|
|
|
|
cddf13
|
|
=
|
|
ddf13 - df1*gamma113 - df2*gamma213 - df3*gamma313
|
|
;
|
|
|
|
cddf22
|
|
=
|
|
ddf22 - df1*gamma122 - df2*gamma222 - df3*gamma322
|
|
;
|
|
|
|
cddf23
|
|
=
|
|
ddf23 - df1*gamma123 - df2*gamma223 - df3*gamma323
|
|
;
|
|
|
|
cddf33
|
|
=
|
|
ddf33 - df1*gamma133 - df2*gamma233 - df3*gamma333
|
|
;
|
|
|
|
trcddf
|
|
=
|
|
cddf11*ginv11 + cddf22*ginv22 +
|
|
2.*(cddf12*ginv12 + cddf13*ginv13 + cddf23*ginv23) + cddf33*ginv33
|
|
;
|
|
|
|
Rphi11
|
|
=
|
|
-2.*(cddf11 + g11*trcddf) + (4. - 4.*g11*ginv11)*pow2(df1) -
|
|
g11*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi12
|
|
=
|
|
df1*df2*(4. - 8.*g12*ginv12) - 2.*(cddf12 + g12*trcddf) -
|
|
g12*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi13
|
|
=
|
|
df1*(4.*df3 - 8.*df2*g13*ginv12) - 2.*(cddf13 + g13*trcddf) -
|
|
g13*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi22
|
|
=
|
|
-2.*(cddf22 + g22*trcddf) + (4. - 4.*g22*ginv22)*pow2(df2) -
|
|
g22*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi23
|
|
=
|
|
df2*(-8.*df1*g23*ginv12 + df3*(4. - 8.*g23*ginv23)) -
|
|
2.*(cddf23 + g23*trcddf) - g23*
|
|
(8.*df1*df3*ginv13 + 4.*(ginv11*pow2(df1) + ginv22*pow2(df2) +
|
|
ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi33
|
|
=
|
|
-2.*(cddf33 + g33*trcddf) - g33*
|
|
(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2))) +
|
|
(4. - 4.*g33*ginv33)*pow2(df3)
|
|
;
|
|
|
|
Rf11
|
|
=
|
|
R11 + Rphi11
|
|
;
|
|
|
|
Rf12
|
|
=
|
|
R12 + Rphi12
|
|
;
|
|
|
|
Rf13
|
|
=
|
|
R13 + Rphi13
|
|
;
|
|
|
|
Rf22
|
|
=
|
|
R22 + Rphi22
|
|
;
|
|
|
|
Rf23
|
|
=
|
|
R23 + Rphi23
|
|
;
|
|
|
|
Rf33
|
|
=
|
|
R33 + Rphi33
|
|
;
|
|
|
|
Rhat
|
|
=
|
|
psim4*(ginv11*Rf11 + ginv22*Rf22 +
|
|
2.*(ginv12*Rf12 + ginv13*Rf13 + ginv23*Rf23) + ginv33*Rf33)
|
|
;
|
|
|
|
cdda11
|
|
=
|
|
dda11 - da2*gamma211 - da3*gamma311 +
|
|
da1*(-gamma111 + df1*(-4. + 2.*g11*ginv11)) +
|
|
2.*g11*((da2*df1 + da1*df2)*ginv12 + (da3*df1 + da1*df3)*ginv13 +
|
|
da2*df2*ginv22 + (da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)
|
|
;
|
|
|
|
cdda12
|
|
=
|
|
dda12 - da1*gamma112 - da2*gamma212 - da3*gamma312 +
|
|
2.*(-(da2*df1) - da1*df2 + g12*
|
|
(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33))
|
|
;
|
|
|
|
cdda13
|
|
=
|
|
dda13 - da1*gamma113 - da2*gamma213 - da3*gamma313 +
|
|
2.*(-(da3*df1) - da1*df3 + g13*
|
|
(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33))
|
|
;
|
|
|
|
cdda22
|
|
=
|
|
dda22 - da1*gamma122 - da2*(4.*df2 + gamma222) - da3*gamma322 +
|
|
2.*g22*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)
|
|
;
|
|
|
|
cdda23
|
|
=
|
|
dda23 - da1*gamma123 - da2*gamma223 - da3*gamma323 +
|
|
2.*(-(da3*df2) - da2*df3 + g23*
|
|
(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33))
|
|
;
|
|
|
|
cdda33
|
|
=
|
|
dda33 - da1*gamma133 - da2*gamma233 - da3*(4.*df3 + gamma333) +
|
|
2.*g33*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)
|
|
;
|
|
|
|
trcdda
|
|
=
|
|
(cdda11*ginv11 + cdda22*ginv22 +
|
|
2.*(cdda12*ginv12 + cdda13*ginv13 + cdda23*ginv23) + cdda33*ginv33)*psim4
|
|
;
|
|
|
|
AA11
|
|
=
|
|
2.*(A11*(A12*ginv12 + A13*ginv13) + A12*A13*ginv23) + ginv11*pow2(A11) +
|
|
ginv22*pow2(A12) + ginv33*pow2(A13)
|
|
;
|
|
|
|
AA12
|
|
=
|
|
(A12*A13 + A11*A23)*ginv13 + A12*(A11*ginv11 + A22*ginv22) +
|
|
(A13*A22 + A12*A23)*ginv23 + A13*A23*ginv33 + ginv12*(A11*A22 + pow2(A12))
|
|
;
|
|
|
|
AA13
|
|
=
|
|
(A12*A13 + A11*A23)*ginv12 + A12*A23*ginv22 + (A13*A23 + A12*A33)*ginv23 +
|
|
A13*(A11*ginv11 + A33*ginv33) + ginv13*(A11*A33 + pow2(A13))
|
|
;
|
|
|
|
AA21
|
|
=
|
|
(A12*A13 + A11*A23)*ginv13 + A12*(A11*ginv11 + A22*ginv22) +
|
|
(A13*A22 + A12*A23)*ginv23 + A13*A23*ginv33 + ginv12*(A11*A22 + pow2(A12))
|
|
;
|
|
|
|
AA22
|
|
=
|
|
2.*(A12*(A22*ginv12 + A23*ginv13) + A22*A23*ginv23) + ginv11*pow2(A12) +
|
|
ginv22*pow2(A22) + ginv33*pow2(A23)
|
|
;
|
|
|
|
AA23
|
|
=
|
|
A12*A13*ginv11 + (A13*A22 + A12*A23)*ginv12 + (A13*A23 + A12*A33)*ginv13 +
|
|
A23*(A22*ginv22 + A33*ginv33) + ginv23*(A22*A33 + pow2(A23))
|
|
;
|
|
|
|
AA31
|
|
=
|
|
(A12*A13 + A11*A23)*ginv12 + A12*A23*ginv22 + (A13*A23 + A12*A33)*ginv23 +
|
|
A13*(A11*ginv11 + A33*ginv33) + ginv13*(A11*A33 + pow2(A13))
|
|
;
|
|
|
|
AA32
|
|
=
|
|
A12*A13*ginv11 + (A13*A22 + A12*A23)*ginv12 + (A13*A23 + A12*A33)*ginv13 +
|
|
A23*(A22*ginv22 + A33*ginv33) + ginv23*(A22*A33 + pow2(A23))
|
|
;
|
|
|
|
AA33
|
|
=
|
|
2.*(A13*(A23*ginv12 + A33*ginv13) + A23*A33*ginv23) + ginv11*pow2(A13) +
|
|
ginv22*pow2(A23) + ginv33*pow2(A33)
|
|
;
|
|
|
|
Ainv11
|
|
=
|
|
2.*(A23*ginv12*ginv13 + ginv11*(A12*ginv12 + A13*ginv13)) +
|
|
A11*pow2(ginv11) + A22*pow2(ginv12) + A33*pow2(ginv13)
|
|
;
|
|
|
|
Ainv12
|
|
=
|
|
ginv11*(A11*ginv12 + A12*ginv22 + A13*ginv23) +
|
|
ginv12*(A13*ginv13 + A22*ginv22 + A23*ginv23) +
|
|
ginv13*(A23*ginv22 + A33*ginv23) + A12*pow2(ginv12)
|
|
;
|
|
|
|
Ainv13
|
|
=
|
|
ginv11*(A11*ginv13 + A12*ginv23 + A13*ginv33) +
|
|
ginv12*(A12*ginv13 + A22*ginv23 + A23*ginv33) +
|
|
ginv13*(A23*ginv23 + A33*ginv33) + A13*pow2(ginv13)
|
|
;
|
|
|
|
Ainv22
|
|
=
|
|
2.*(A23*ginv22*ginv23 + ginv12*(A12*ginv22 + A13*ginv23)) +
|
|
A11*pow2(ginv12) + A22*pow2(ginv22) + A33*pow2(ginv23)
|
|
;
|
|
|
|
Ainv23
|
|
=
|
|
ginv13*(A12*ginv22 + A13*ginv23) + A33*ginv23*ginv33 +
|
|
ginv12*(A11*ginv13 + A12*ginv23 + A13*ginv33) +
|
|
ginv22*(A22*ginv23 + A23*ginv33) + A23*pow2(ginv23)
|
|
;
|
|
|
|
Ainv33
|
|
=
|
|
2.*(A23*ginv23*ginv33 + ginv13*(A12*ginv23 + A13*ginv33)) +
|
|
A11*pow2(ginv13) + A22*pow2(ginv23) + A33*pow2(ginv33)
|
|
;
|
|
|
|
cdA111
|
|
=
|
|
dA111 - 2.*(A11*gamma111 + A12*gamma211 + A13*gamma311)
|
|
;
|
|
|
|
cdA112
|
|
=
|
|
dA112 - A11*gamma112 - A22*gamma211 - A12*(gamma111 + gamma212) -
|
|
A23*gamma311 - A13*gamma312
|
|
;
|
|
|
|
cdA113
|
|
=
|
|
dA113 - A11*gamma113 - A23*gamma211 - A12*gamma213 - A33*gamma311 -
|
|
A13*(gamma111 + gamma313)
|
|
;
|
|
|
|
cdA122
|
|
=
|
|
dA122 - 2.*(A12*gamma112 + A22*gamma212 + A23*gamma312)
|
|
;
|
|
|
|
cdA123
|
|
=
|
|
dA123 - A13*gamma112 - A12*gamma113 - A22*gamma213 - A33*gamma312 -
|
|
A23*(gamma212 + gamma313)
|
|
;
|
|
|
|
cdA133
|
|
=
|
|
dA133 - 2.*(A13*gamma113 + A23*gamma213 + A33*gamma313)
|
|
;
|
|
|
|
cdA211
|
|
=
|
|
dA211 - 2.*(A11*gamma112 + A12*gamma212 + A13*gamma312)
|
|
;
|
|
|
|
cdA212
|
|
=
|
|
dA212 - A11*gamma122 - A22*gamma212 - A12*(gamma112 + gamma222) -
|
|
A23*gamma312 - A13*gamma322
|
|
;
|
|
|
|
cdA213
|
|
=
|
|
dA213 - A11*gamma123 - A23*gamma212 - A12*gamma223 - A33*gamma312 -
|
|
A13*(gamma112 + gamma323)
|
|
;
|
|
|
|
cdA222
|
|
=
|
|
dA222 - 2.*(A12*gamma122 + A22*gamma222 + A23*gamma322)
|
|
;
|
|
|
|
cdA223
|
|
=
|
|
dA223 - A13*gamma122 - A12*gamma123 - A22*gamma223 - A33*gamma322 -
|
|
A23*(gamma222 + gamma323)
|
|
;
|
|
|
|
cdA233
|
|
=
|
|
dA233 - 2.*(A13*gamma123 + A23*gamma223 + A33*gamma323)
|
|
;
|
|
|
|
cdA311
|
|
=
|
|
dA311 - 2.*(A11*gamma113 + A12*gamma213 + A13*gamma313)
|
|
;
|
|
|
|
cdA312
|
|
=
|
|
dA312 - A11*gamma123 - A22*gamma213 - A12*(gamma113 + gamma223) -
|
|
A23*gamma313 - A13*gamma323
|
|
;
|
|
|
|
cdA313
|
|
=
|
|
dA313 - A11*gamma133 - A23*gamma213 - A12*gamma233 - A33*gamma313 -
|
|
A13*(gamma113 + gamma333)
|
|
;
|
|
|
|
cdA322
|
|
=
|
|
dA322 - 2.*(A12*gamma123 + A22*gamma223 + A23*gamma323)
|
|
;
|
|
|
|
cdA323
|
|
=
|
|
dA323 - A13*gamma123 - A12*gamma133 - A22*gamma233 - A33*gamma323 -
|
|
A23*(gamma223 + gamma333)
|
|
;
|
|
|
|
cdA333
|
|
=
|
|
dA333 - 2.*(A13*gamma133 + A23*gamma233 + A33*gamma333)
|
|
;
|
|
|
|
divbeta
|
|
=
|
|
db11 + db22 + db33
|
|
;
|
|
|
|
totdivbeta
|
|
=
|
|
0.66666666666666666667*divbeta
|
|
;
|
|
|
|
lieg11
|
|
=
|
|
beta1*dg111 + beta2*dg211 + beta3*dg311 +
|
|
2.*(db11*g11 + db12*g12 + db13*g13) - g11*totdivbeta
|
|
;
|
|
|
|
lieg12
|
|
=
|
|
beta1*dg112 + beta2*dg212 + beta3*dg312 + db21*g11 + db23*g13 + db12*g22 +
|
|
db13*g23 + g12*(db11 + db22 - totdivbeta)
|
|
;
|
|
|
|
lieg13
|
|
=
|
|
beta1*dg113 + beta2*dg213 + beta3*dg313 + db31*g11 + db32*g12 + db12*g23 +
|
|
db13*g33 + g13*(db11 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieg22
|
|
=
|
|
beta1*dg122 + beta2*dg222 + beta3*dg322 +
|
|
2.*(db21*g12 + db22*g22 + db23*g23) - g22*totdivbeta
|
|
;
|
|
|
|
lieg23
|
|
=
|
|
beta1*dg123 + beta2*dg223 + beta3*dg323 + db31*g12 + db21*g13 + db32*g22 +
|
|
db23*g33 + g23*(db22 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieg33
|
|
=
|
|
beta1*dg133 + beta2*dg233 + beta3*dg333 +
|
|
2.*(db31*g13 + db32*g23 + db33*g33) - g33*totdivbeta
|
|
;
|
|
|
|
lieA11
|
|
=
|
|
beta1*dA111 + beta2*dA211 + beta3*dA311 +
|
|
2.*(A11*db11 + A12*db12 + A13*db13) - A11*totdivbeta
|
|
;
|
|
|
|
lieA12
|
|
=
|
|
beta1*dA112 + beta2*dA212 + beta3*dA312 + A22*db12 + A23*db13 + A11*db21 +
|
|
A13*db23 + A12*(db11 + db22 - totdivbeta)
|
|
;
|
|
|
|
lieA13
|
|
=
|
|
beta1*dA113 + beta2*dA213 + beta3*dA313 + A23*db12 + A33*db13 + A11*db31 +
|
|
A12*db32 + A13*(db11 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieA22
|
|
=
|
|
beta1*dA122 + beta2*dA222 + beta3*dA322 +
|
|
2.*(A12*db21 + A22*db22 + A23*db23) - A22*totdivbeta
|
|
;
|
|
|
|
lieA23
|
|
=
|
|
beta1*dA123 + beta2*dA223 + beta3*dA323 + A13*db21 + A33*db23 + A12*db31 +
|
|
A22*db32 + A23*(db22 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieA33
|
|
=
|
|
beta1*dA133 + beta2*dA233 + beta3*dA333 +
|
|
2.*(A13*db31 + A23*db32 + A33*db33) - A33*totdivbeta
|
|
;
|
|
|
|
betas
|
|
=
|
|
beta1*sdown1 + beta2*sdown2 + beta3*sdown3
|
|
;
|
|
|
|
Dbetas
|
|
=
|
|
(db11*sdown1 + db12*sdown2 + db13*sdown3)*sup1 +
|
|
(db21*sdown1 + db22*sdown2 + db23*sdown3)*sup2 +
|
|
(db31*sdown1 + db32*sdown2 + db33*sdown3)*sup3
|
|
;
|
|
|
|
Dalpha
|
|
=
|
|
da1*sup1 + da2*sup2 + da3*sup3
|
|
;
|
|
|
|
DKhat
|
|
=
|
|
dKhat1*sup1 + dKhat2*sup2 + dKhat3*sup3
|
|
;
|
|
|
|
DK
|
|
=
|
|
dK1*sup1 + dK2*sup2 + dK3*sup3
|
|
;
|
|
|
|
DTheta
|
|
=
|
|
dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3
|
|
;
|
|
|
|
Gams
|
|
=
|
|
G1*sdown1 + G2*sdown2 + G3*sdown3
|
|
;
|
|
|
|
DGams
|
|
=
|
|
(dG11*sdown1 + dG12*sdown2 + dG13*sdown3)*sup1 +
|
|
(dG21*sdown1 + dG22*sdown2 + dG23*sdown3)*sup2 +
|
|
(dG31*sdown1 + dG32*sdown2 + dG33*sdown3)*sup3
|
|
;
|
|
|
|
GamA1
|
|
=
|
|
G1*qud11 + G2*qud12 + G3*qud13
|
|
;
|
|
|
|
GamA2
|
|
=
|
|
G1*qud21 + G2*qud22 + G3*qud23
|
|
;
|
|
|
|
GamA3
|
|
=
|
|
G1*qud31 + G2*qud32 + G3*qud33
|
|
;
|
|
|
|
DGamA1
|
|
=
|
|
(dG11*qud11 + dG12*qud12 + dG13*qud13)*sup1 +
|
|
(dG21*qud11 + dG22*qud12 + dG23*qud13)*sup2 +
|
|
(dG31*qud11 + dG32*qud12 + dG33*qud13)*sup3
|
|
;
|
|
|
|
DGamA2
|
|
=
|
|
(dG11*qud21 + dG12*qud22 + dG13*qud23)*sup1 +
|
|
(dG21*qud21 + dG22*qud22 + dG23*qud23)*sup2 +
|
|
(dG31*qud21 + dG32*qud22 + dG33*qud23)*sup3
|
|
;
|
|
|
|
DGamA3
|
|
=
|
|
(dG11*qud31 + dG12*qud32 + dG13*qud33)*sup1 +
|
|
(dG21*qud31 + dG22*qud32 + dG23*qud33)*sup2 +
|
|
(dG31*qud31 + dG32*qud32 + dG33*qud33)*sup3
|
|
;
|
|
|
|
betaA1
|
|
=
|
|
beta1*qud11 + beta2*qud12 + beta3*qud13
|
|
;
|
|
|
|
betaA2
|
|
=
|
|
beta1*qud21 + beta2*qud22 + beta3*qud23
|
|
;
|
|
|
|
betaA3
|
|
=
|
|
beta1*qud31 + beta2*qud32 + beta3*qud33
|
|
;
|
|
|
|
DbetaA1
|
|
=
|
|
(db11*qud11 + db12*qud12 + db13*qud13)*sup1 +
|
|
(db21*qud11 + db22*qud12 + db23*qud13)*sup2 +
|
|
(db31*qud11 + db32*qud12 + db33*qud13)*sup3
|
|
;
|
|
|
|
DbetaA2
|
|
=
|
|
(db11*qud21 + db12*qud22 + db13*qud23)*sup1 +
|
|
(db21*qud21 + db22*qud22 + db23*qud23)*sup2 +
|
|
(db31*qud21 + db32*qud22 + db33*qud23)*sup3
|
|
;
|
|
|
|
DbetaA3
|
|
=
|
|
(db11*qud31 + db12*qud32 + db13*qud33)*sup1 +
|
|
(db21*qud31 + db22*qud32 + db23*qud33)*sup2 +
|
|
(db31*qud31 + db32*qud32 + db33*qud33)*sup3
|
|
;
|
|
|
|
lienKhat
|
|
=
|
|
-((DKhat + Khat/r)*sqrt(muL))
|
|
;
|
|
|
|
lienTheta
|
|
=
|
|
-DTheta - (kappa1*(2. + kappa2) + 1/r)*Theta
|
|
;
|
|
|
|
lienK
|
|
=
|
|
lienKhat + 2.*lienTheta
|
|
;
|
|
|
|
rKhat
|
|
=
|
|
beta1*dKhat1 + beta2*dKhat2 + beta3*dKhat3 + alpha*lienKhat
|
|
;
|
|
|
|
#if 0
|
|
// David's new version
|
|
rGams
|
|
=
|
|
(beta1*dG11 + beta2*dG21 + beta3*dG31 +
|
|
(ddb111*quu11 + ddb221*quu22 +
|
|
2.*(ddb121*quu12 + ddb131*quu13 + ddb231*quu23) + ddb331*quu33)/chi\
|
|
)*sdown1 + (beta1*dG12 + beta2*dG22 + beta3*dG32 +
|
|
(ddb112*quu11 + ddb222*quu22 +
|
|
2.*(ddb122*quu12 + ddb132*quu13 + ddb232*quu23) + ddb332*quu33)/chi\
|
|
)*sdown2 + (beta1*dG13 + beta2*dG23 + beta3*dG33 +
|
|
(ddb113*quu11 + ddb223*quu22 +
|
|
2.*(ddb123*quu12 + ddb133*quu13 + ddb233*quu23) + ddb333*quu33)/chi\
|
|
)*sdown3 - ((ddb111*qud11 + ddb112*qud12 + ddb113*qud13 + ddb121*qud21 +
|
|
ddb122*qud22 + ddb123*qud23 + ddb131*qud31 + ddb132*qud32 +
|
|
ddb133*qud33)*sup1 + (ddb121*qud11 + ddb122*qud12 +
|
|
ddb123*qud13 + ddb221*qud21 + ddb222*qud22 + ddb223*qud23 +
|
|
ddb231*qud31 + ddb232*qud32 + ddb233*qud33)*sup2 +
|
|
(ddb131*qud11 + ddb132*qud12 + ddb133*qud13 + ddb231*qud21 +
|
|
ddb232*qud22 + ddb233*qud23 + ddb331*qud31 + ddb332*qud32 +
|
|
ddb333*qud33)*sup3)/chi - (dG11 + dG22 + dG33)*vbetas +
|
|
2.*((0.33333333333333333333*alpha*
|
|
(dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3))/(chi + chi*vbetas) +
|
|
((db11 + db22 + db33)*shiftdriver)/(vbetaA*sqrt(3.))) +
|
|
(1.3333333333333333333*alpha*(dKhat1*sup1 + dKhat2*sup2 + dKhat3*sup3)*
|
|
sqrt(muL))/(chi*(vbetas + sqrt(muL)))
|
|
;
|
|
#else
|
|
//David's old version
|
|
rGams
|
|
=
|
|
shiftdriver*((beta1*db11 + beta2*db21)*(db12*sdown2 + db13*sdown3) +
|
|
2.*beta1*((beta2*ddb121 + beta3*ddb131)*sdown1 +
|
|
(beta2*ddb122 + beta3*ddb132)*sdown2 +
|
|
(beta2*ddb123 + beta3*ddb133)*sdown3) +
|
|
sdown1*(db21*(beta1*db12 + beta2*(db11 + db22) + beta3*db32) +
|
|
db31*(beta1*db13 + beta2*db23 + beta3*(db11 + db33)) +
|
|
beta2*(2.*beta3*ddb231 + dG21) + beta3*dG31 + ddb111*pow2(beta1) +
|
|
ddb221*pow2(beta2) + ddb331*pow2(beta3) + beta1*(dG11 + pow2(db11))\
|
|
) + sdown2*(db12*(beta1*db22 + beta3*db31) +
|
|
db32*(beta1*db13 + beta2*db23 + beta3*(db22 + db33)) + beta1*dG12 +
|
|
beta3*dG32 + ddb112*pow2(beta1) + ddb222*pow2(beta2) +
|
|
ddb332*pow2(beta3) + beta2*(2.*beta3*ddb232 + dG22 + pow2(db22)))) -
|
|
((beta1*db11 + beta2*db21 + beta3*db31)*sdown1 +
|
|
(beta2*db22 + beta3*db32)*sdown2 + beta2*db23*sdown3 +
|
|
beta1*(db12*sdown2 + db13*sdown3))*pow2(shiftdriver) +
|
|
sdown3*(shiftdriver*((beta1*db12 + beta2*db22)*db23 + beta1*dG13 +
|
|
beta2*dG23 + ddb113*pow2(beta1) + ddb223*pow2(beta2) +
|
|
ddb333*pow2(beta3) + beta3*
|
|
(db13*db31 + db23*db32 + 2.*beta2*ddb233 + dG33 + pow2(db33))) +
|
|
db33*((beta1*db13 + beta2*db23)*shiftdriver - beta3*pow2(shiftdriver)))
|
|
;
|
|
#endif
|
|
|
|
rTheta
|
|
=
|
|
beta1*dTheta1 + beta2*dTheta2 + beta3*dTheta3 + alpha*lienTheta
|
|
;
|
|
|
|
rACss
|
|
=
|
|
2.*((A23*alpha*K + lieA23)*sup2*sup3 +
|
|
sup1*((A12*alpha*K + lieA12)*sup2 + A13*alpha*K*sup3) +
|
|
psim4*((-cdda23 + alpha*Rf23)*sup2*sup3 +
|
|
sup1*((-cdda12 + alpha*Rf12)*sup2 - cdda13*sup3))) +
|
|
0.66666666666666666667*(g13*sup1 + g23*sup2)*sup3*trcdda +
|
|
sup1*(2.*(-(AA31*alpha) + lieA13)*sup3 +
|
|
0.66666666666666666667*g12*sup2*trcdda) +
|
|
(lieA11 + psim4*(-cdda11 + alpha*Rf11) +
|
|
0.33333333333333333333*g11*(-(alpha*Rhat) + trcdda))*pow2(sup1) +
|
|
(lieA22 - cdda22*psim4 + alpha*
|
|
(A22*K + psim4*Rf22 - 0.33333333333333333333*g22*Rhat) +
|
|
0.33333333333333333333*g22*trcdda)*pow2(sup2) +
|
|
(lieA33 - cdda33*psim4 + alpha*
|
|
(A33*K + psim4*Rf33 - 0.33333333333333333333*g33*Rhat) +
|
|
0.33333333333333333333*g33*trcdda)*pow2(sup3) +
|
|
alpha*(ginv11*((-2.*cdA111*chi + 3.*A11*dchi1)*sup1 +
|
|
(-2.*cdA112*chi + 3.*A12*dchi1)*sup2 +
|
|
(-2.*cdA113*chi + 3.*A13*dchi1)*sup3) +
|
|
ginv22*((-2.*cdA212*chi + 3.*A12*dchi2)*sup1 +
|
|
(-2.*cdA222*chi + 3.*A22*dchi2)*sup2 +
|
|
(-2.*cdA223*chi + 3.*A23*dchi2)*sup3) +
|
|
ginv33*((-2.*cdA313*chi + 3.*A13*dchi3)*sup1 +
|
|
(-2.*cdA323*chi + 3.*A23*dchi3)*sup2 +
|
|
(-2.*cdA333*chi + 3.*A33*dchi3)*sup3) +
|
|
chi*(-2.*DTheta + 1.3333333333333333333*
|
|
(dK1*sup1 + dK2*sup2 + dK3*sup3)) +
|
|
ginv12*((-2.*cdA212*chi + 3.*A12*dchi2)*sup2 +
|
|
(-2.*cdA213*chi + 3.*A13*dchi2)*sup3 -
|
|
2.*chi*((cdA112 + cdA211)*sup1 + cdA122*sup2 + cdA123*sup3) +
|
|
3.*((A12*dchi1 + A11*dchi2)*sup1 + dchi1*(A22*sup2 + A23*sup3))) +
|
|
ginv13*((-2.*cdA312*chi + 3.*A12*dchi3)*sup2 +
|
|
(-2.*cdA313*chi + 3.*A13*dchi3)*sup3 -
|
|
2.*chi*((cdA113 + cdA311)*sup1 + cdA123*sup2 + cdA133*sup3) +
|
|
3.*((A13*dchi1 + A11*dchi3)*sup1 + dchi1*(A23*sup2 + A33*sup3))) +
|
|
ginv23*((-2.*cdA322*chi + 3.*A22*dchi3)*sup2 +
|
|
(-2.*cdA323*chi + 3.*A23*dchi3)*sup3 -
|
|
2.*chi*((cdA213 + cdA312)*sup1 + cdA223*sup2 + cdA233*sup3) +
|
|
3.*((A13*dchi2 + A12*dchi3)*sup1 + dchi2*(A23*sup2 + A33*sup3))) +
|
|
(0.33333333333333333333*((dG11 - dGfromgdu11)*qud11 +
|
|
(dG12 - dGfromgdu12)*qud12 + (dG13 - dGfromgdu13)*qud13 +
|
|
(dG21 - dGfromgdu21)*qud21 + (dG22 - dGfromgdu22)*qud22 +
|
|
(dG23 - dGfromgdu23)*qud23 + (dG31 - dGfromgdu31)*qud31 +
|
|
(dG32 - dGfromgdu32)*qud32 + (dG33 - dGfromgdu33)*qud33) +
|
|
kappa1*((G1 - Gfromg1)*sdown1 + (G2 - Gfromg2)*sdown2 +
|
|
(G3 - Gfromg3)*sdown3) +
|
|
0.66666666666666666667*
|
|
((dGfromgdu21*sdown1 + dGfromgdu22*sdown2)*sup2 +
|
|
sdown3*((-dG13 + dGfromgdu13)*sup1 - dG23*sup2 - dG33*sup3) +
|
|
sdown1*((-dG11 + dGfromgdu11)*sup1 - dG21*sup2 - dG31*sup3 +
|
|
dGfromgdu31*sup3) +
|
|
sdown2*((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3 +
|
|
dGfromgdu32*sup3)))*pow2(chi) +
|
|
0.66666666666666666667*sup2*
|
|
(-(Rhat*(g12*sup1 + g23*sup3)) + dGfromgdu23*sdown3*pow2(chi)) +
|
|
sup3*((2.*psim4*Rf13 - 0.66666666666666666667*g13*Rhat)*sup1 +
|
|
0.66666666666666666667*dGfromgdu33*sdown3*pow2(chi)) +
|
|
(-2.*AA11 + A11*K)*pow2(sup1) -
|
|
2.*((AA23 + AA32)*sup2*sup3 + sup1*((AA12 + AA21)*sup2 + AA13*sup3) +
|
|
AA22*pow2(sup2) + AA33*pow2(sup3)))
|
|
;
|
|
|
|
rACqq
|
|
=
|
|
chi*(-((4.*(A12*Ainv12 + A13*Ainv13 + A23*Ainv23) +
|
|
2.*(A11*Ainv11 + A22*Ainv22 + A33*Ainv33))*alpha) +
|
|
Ainv11*lieg11 + Ainv22*lieg22 +
|
|
2.*(Ainv12*lieg12 + Ainv13*lieg13 + Ainv23*lieg23) + Ainv33*lieg33) -
|
|
rACss
|
|
;
|
|
|
|
rGamA1
|
|
=
|
|
-(((dG21*qud11 + dG22*qud12 + dG23*qud13)*sup2 +
|
|
(dG31*qud11 + dG32*qud12 + dG33*qud13)*sup3)*vbetaA) +
|
|
qud11*(beta2*dG21 + beta3*dG31 +
|
|
(1.3333333333333333333*ddb111*quu11 +
|
|
2.3333333333333333333*(ddb121*quu12 + ddb131*quu13) +
|
|
ddb221*quu22 + ddb331*quu33 +
|
|
(shiftdriver*(db11*sup1 + db31*sup3))/vbetaA)/chi +
|
|
dG11*(beta1 - sup1*vbetaA)) +
|
|
qud12*(beta2*dG22 + beta3*dG32 +
|
|
(1.3333333333333333333*ddb112*quu11 +
|
|
2.3333333333333333333*(ddb122*quu12 + ddb132*quu13) +
|
|
ddb222*quu22 + 2.*ddb232*quu23 + ddb332*quu33 +
|
|
(shiftdriver*(db12*sup1 + db22*sup2 + db32*sup3))/vbetaA)/chi +
|
|
dG12*(beta1 - sup1*vbetaA)) +
|
|
qud13*(beta2*dG23 + beta3*dG33 +
|
|
(1.3333333333333333333*ddb113*quu11 +
|
|
2.3333333333333333333*(ddb123*quu12 + ddb133*quu13) +
|
|
ddb223*quu22 + 2.*ddb233*quu23 + ddb333*quu33 +
|
|
(shiftdriver*(db13*sup1 + db23*sup2 + db33*sup3))/vbetaA)/chi +
|
|
dG13*(beta1 - sup1*vbetaA)) +
|
|
(0.33333333333333333333*((ddb121*qud21 + ddb122*qud22 + ddb123*qud23 +
|
|
ddb131*qud31 + ddb132*qud32 + ddb133*qud33)*quu11 +
|
|
(ddb221*qud21 + ddb223*qud23 + ddb231*qud31 + ddb232*qud32 +
|
|
ddb233*qud33)*quu12 +
|
|
(ddb231*qud21 + ddb232*qud22 + ddb233*qud23 + ddb331*qud31 +
|
|
ddb332*qud32)*quu13) -
|
|
alpha*((1.3333333333333333333*dKhat1 +
|
|
0.66666666666666666667*dTheta1)*quu11 +
|
|
1.3333333333333333333*(dKhat2*quu12 + dKhat3*quu13)) +
|
|
1.3333333333333333333*((ddb132*quu13*sdown2 + ddb113*quu11*sdown3)*
|
|
sup1 + (quu13*(ddb231*sdown1 + ddb232*sdown2) +
|
|
quu12*(ddb222*sdown2 + ddb223*sdown3))*sup2 +
|
|
(quu12*(ddb232*sdown2 + ddb233*sdown3) +
|
|
quu13*(ddb331*sdown1 + ddb332*sdown2 + ddb333*sdown3))*sup3 +
|
|
sdown1*((ddb121*quu12 + ddb131*quu13)*sup1 + ddb221*quu12*sup2 +
|
|
ddb131*quu11*sup3) +
|
|
sdown2*((ddb112*quu11 + ddb122*quu12)*sup1 +
|
|
quu11*(ddb122*sup2 + ddb132*sup3)) +
|
|
sdown3*((ddb123*quu12 + ddb133*quu13)*sup1 +
|
|
quu11*(ddb123*sup2 + ddb133*sup3))) +
|
|
qud11*(2.*ddb231*quu23 + (db21*shiftdriver*sup2)/vbetaA) -
|
|
(((db11*quu11 + db21*quu12)*sdown1 +
|
|
(db12*quu11 + db22*quu12 + db32*quu13)*sdown2 +
|
|
(db13*quu11 + db23*quu12 + db33*quu13)*sdown3)*shiftdriver)/
|
|
vbetaA + ((dG22*quu12 + dG32*quu13)*sdown2 +
|
|
(dG13*quu11 + dG23*quu12)*sdown3)*vbetaA +
|
|
quu11*(1.3333333333333333333*sdown1*(ddb111*sup1 + ddb121*sup2) +
|
|
(dG11*sdown1 + dG12*sdown2)*vbetaA) +
|
|
quu12*(-0.66666666666666666667*alpha*dTheta2 +
|
|
0.33333333333333333333*ddb222*qud22 +
|
|
sdown1*(1.3333333333333333333*ddb231*sup3 + dG21*vbetaA)) +
|
|
quu13*(-0.66666666666666666667*alpha*dTheta3 +
|
|
0.33333333333333333333*ddb333*qud33 -
|
|
(db31*sdown1*shiftdriver)/vbetaA + dG31*sdown1*vbetaA +
|
|
sdown3*(1.3333333333333333333*ddb233*sup2 + dG33*vbetaA)))/chi
|
|
;
|
|
|
|
rGamA2
|
|
=
|
|
-(((dG21*qud21 + dG22*qud22 + dG23*qud23)*sup2 +
|
|
(dG31*qud21 + dG32*qud22 + dG33*qud23)*sup3)*vbetaA) +
|
|
qud21*(beta2*dG21 + beta3*dG31 +
|
|
(ddb111*quu11 + 2.*ddb131*quu13 +
|
|
1.3333333333333333333*ddb221*quu22 +
|
|
2.3333333333333333333*(ddb121*quu12 + ddb231*quu23) +
|
|
ddb331*quu33 + (shiftdriver*(db11*sup1 + db31*sup3))/vbetaA)/chi +
|
|
dG11*(beta1 - sup1*vbetaA)) +
|
|
qud22*(beta2*dG22 + beta3*dG32 +
|
|
(ddb112*quu11 + 2.*ddb132*quu13 +
|
|
1.3333333333333333333*ddb222*quu22 +
|
|
2.3333333333333333333*(ddb122*quu12 + ddb232*quu23) +
|
|
ddb332*quu33 + (shiftdriver*(db12*sup1 + db22*sup2 + db32*sup3))/
|
|
vbetaA)/chi + dG12*(beta1 - sup1*vbetaA)) +
|
|
qud23*(beta2*dG23 + beta3*dG33 +
|
|
(ddb113*quu11 + 2.*ddb133*quu13 +
|
|
1.3333333333333333333*ddb223*quu22 +
|
|
2.3333333333333333333*(ddb123*quu12 + ddb233*quu23) +
|
|
ddb333*quu33 + (shiftdriver*(db13*sup1 + db23*sup2 + db33*sup3))/
|
|
vbetaA)/chi + dG13*(beta1 - sup1*vbetaA)) +
|
|
(0.33333333333333333333*((ddb111*qud11 + ddb112*qud12 + ddb113*qud13 +
|
|
ddb131*qud31 + ddb132*qud32 + ddb133*qud33)*quu12 +
|
|
(ddb121*qud11 + ddb123*qud13 + ddb231*qud31 + ddb232*qud32 +
|
|
ddb233*qud33)*quu22 +
|
|
(ddb131*qud11 + ddb132*qud12 + ddb133*qud13 + ddb331*qud31 +
|
|
ddb332*qud32)*quu23) -
|
|
alpha*((1.3333333333333333333*dKhat1 +
|
|
0.66666666666666666667*dTheta1)*quu12 +
|
|
1.3333333333333333333*(dKhat2*quu22 + dKhat3*quu23)) +
|
|
1.3333333333333333333*((ddb132*quu23*sdown2 + ddb113*quu12*sdown3)*
|
|
sup1 + (quu23*(ddb231*sdown1 + ddb232*sdown2) +
|
|
quu22*(ddb222*sdown2 + ddb223*sdown3))*sup2 +
|
|
(quu22*(ddb232*sdown2 + ddb233*sdown3) +
|
|
quu23*(ddb331*sdown1 + ddb332*sdown2 + ddb333*sdown3))*sup3 +
|
|
sdown1*((ddb121*quu22 + ddb131*quu23)*sup1 + ddb221*quu22*sup2 +
|
|
ddb131*quu12*sup3) +
|
|
sdown2*((ddb112*quu12 + ddb122*quu22)*sup1 +
|
|
quu12*(ddb122*sup2 + ddb132*sup3)) +
|
|
sdown3*((ddb123*quu22 + ddb133*quu23)*sup1 +
|
|
quu12*(ddb123*sup2 + ddb133*sup3))) -
|
|
(((db11*quu12 + db21*quu22)*sdown1 +
|
|
(db12*quu12 + db22*quu22 + db32*quu23)*sdown2 +
|
|
(db13*quu12 + db23*quu22 + db33*quu23)*sdown3)*shiftdriver)/
|
|
vbetaA + (db21*qud21*shiftdriver*sup2)/vbetaA +
|
|
((dG22*quu22 + dG32*quu23)*sdown2 + (dG13*quu12 + dG23*quu22)*sdown3)*
|
|
vbetaA + quu12*(1.3333333333333333333*sdown1*
|
|
(ddb111*sup1 + ddb121*sup2) + (dG11*sdown1 + dG12*sdown2)*vbetaA) \
|
|
+ quu22*(-0.66666666666666666667*alpha*dTheta2 +
|
|
0.33333333333333333333*ddb122*qud12 +
|
|
sdown1*(1.3333333333333333333*ddb231*sup3 + dG21*vbetaA)) +
|
|
quu23*(-0.66666666666666666667*alpha*dTheta3 +
|
|
0.33333333333333333333*ddb333*qud33 -
|
|
(db31*sdown1*shiftdriver)/vbetaA + dG31*sdown1*vbetaA +
|
|
sdown3*(1.3333333333333333333*ddb233*sup2 + dG33*vbetaA)))/chi
|
|
;
|
|
|
|
rGamA3
|
|
=
|
|
-(((dG21*qud31 + dG22*qud32 + dG23*qud33)*sup2 +
|
|
(dG31*qud31 + dG32*qud32 + dG33*qud33)*sup3)*vbetaA) +
|
|
qud31*(beta2*dG21 + beta3*dG31 +
|
|
(ddb111*quu11 + 2.*ddb121*quu12 + ddb221*quu22 +
|
|
2.3333333333333333333*(ddb131*quu13 + ddb231*quu23) +
|
|
1.3333333333333333333*ddb331*quu33 +
|
|
(shiftdriver*(db11*sup1 + db31*sup3))/vbetaA)/chi +
|
|
dG11*(beta1 - sup1*vbetaA)) +
|
|
qud32*(beta2*dG22 + beta3*dG32 +
|
|
(ddb112*quu11 + 2.*ddb122*quu12 + ddb222*quu22 +
|
|
2.3333333333333333333*(ddb132*quu13 + ddb232*quu23) +
|
|
1.3333333333333333333*ddb332*quu33 +
|
|
(shiftdriver*(db12*sup1 + db22*sup2 + db32*sup3))/vbetaA)/chi +
|
|
dG12*(beta1 - sup1*vbetaA)) +
|
|
qud33*(beta2*dG23 + beta3*dG33 +
|
|
(ddb113*quu11 + 2.*ddb123*quu12 + ddb223*quu22 +
|
|
2.3333333333333333333*(ddb133*quu13 + ddb233*quu23) +
|
|
1.3333333333333333333*ddb333*quu33 +
|
|
(shiftdriver*(db13*sup1 + db23*sup2 + db33*sup3))/vbetaA)/chi +
|
|
dG13*(beta1 - sup1*vbetaA)) +
|
|
(0.33333333333333333333*((ddb111*qud11 + ddb112*qud12 + ddb113*qud13 +
|
|
ddb121*qud21 + ddb122*qud22 + ddb123*qud23)*quu13 +
|
|
(ddb121*qud11 + ddb123*qud13 + ddb221*qud21 + ddb222*qud22 +
|
|
ddb223*qud23)*quu23 +
|
|
(ddb131*qud11 + ddb132*qud12 + ddb133*qud13 + ddb231*qud21 +
|
|
ddb232*qud22)*quu33) -
|
|
alpha*((1.3333333333333333333*dKhat1 +
|
|
0.66666666666666666667*dTheta1)*quu13 +
|
|
1.3333333333333333333*(dKhat2*quu23 + dKhat3*quu33)) +
|
|
1.3333333333333333333*((ddb132*quu33*sdown2 + ddb113*quu13*sdown3)*
|
|
sup1 + (quu33*(ddb231*sdown1 + ddb232*sdown2) +
|
|
quu23*(ddb222*sdown2 + ddb223*sdown3))*sup2 +
|
|
(quu23*(ddb232*sdown2 + ddb233*sdown3) +
|
|
quu33*(ddb331*sdown1 + ddb332*sdown2 + ddb333*sdown3))*sup3 +
|
|
sdown1*((ddb121*quu23 + ddb131*quu33)*sup1 + ddb221*quu23*sup2 +
|
|
ddb131*quu13*sup3) +
|
|
sdown2*((ddb112*quu13 + ddb122*quu23)*sup1 +
|
|
quu13*(ddb122*sup2 + ddb132*sup3)) +
|
|
sdown3*((ddb123*quu23 + ddb133*quu33)*sup1 +
|
|
quu13*(ddb123*sup2 + ddb133*sup3))) -
|
|
(((db11*quu13 + db21*quu23)*sdown1 +
|
|
(db12*quu13 + db22*quu23 + db32*quu33)*sdown2 +
|
|
(db13*quu13 + db23*quu23 + db33*quu33)*sdown3)*shiftdriver)/
|
|
vbetaA + (db21*qud31*shiftdriver*sup2)/vbetaA +
|
|
((dG22*quu23 + dG32*quu33)*sdown2 + (dG13*quu13 + dG23*quu23)*sdown3)*
|
|
vbetaA + quu13*(1.3333333333333333333*sdown1*
|
|
(ddb111*sup1 + ddb121*sup2) + (dG11*sdown1 + dG12*sdown2)*vbetaA) \
|
|
+ quu33*(-0.66666666666666666667*alpha*dTheta3 +
|
|
ddb233*(0.33333333333333333333*qud23 +
|
|
1.3333333333333333333*sdown3*sup2) -
|
|
(db31*sdown1*shiftdriver)/vbetaA +
|
|
(dG31*sdown1 + dG33*sdown3)*vbetaA) +
|
|
quu23*(-0.66666666666666666667*alpha*dTheta2 +
|
|
0.33333333333333333333*ddb122*qud12 +
|
|
sdown1*(1.3333333333333333333*ddb231*sup3 + dG21*vbetaA)))/chi
|
|
;
|
|
|
|
rACsA1
|
|
=
|
|
(qud11*(lieA11 + alpha*chi*Rf11) +
|
|
qud21*(lieA12 + alpha*(-2.*AA12 + chi*Rf12)) +
|
|
qud31*(lieA13 + alpha*(-2.*AA13 + chi*Rf13)))*sup1 +
|
|
qud11*((-(cdda11*chi) + A11*alpha*K)*sup1 + lieA12*sup2 +
|
|
(A13*alpha*K + lieA13)*sup3 +
|
|
alpha*((-2.*AA21 + A12*K)*sup2 - 2.*AA31*sup3)) +
|
|
qud21*((-(cdda12*chi) + A12*alpha*K)*sup1 + lieA22*sup2 +
|
|
(A23*alpha*K + lieA23)*sup3 +
|
|
alpha*((-2.*AA22 + A22*K)*sup2 - 2.*AA32*sup3)) +
|
|
qud31*((-(cdda13*chi) + A13*alpha*K)*sup1 + lieA23*sup2 +
|
|
(A33*alpha*K + lieA33)*sup3 +
|
|
alpha*((-2.*AA23 + A23*K)*sup2 - 2.*AA33*sup3)) +
|
|
alpha*(ginv11*((-(cdA111*chi) + 1.5*A11*dchi1)*qud11 +
|
|
(-(cdA112*chi) + 1.5*A12*dchi1)*qud21 +
|
|
(-(cdA113*chi) + 1.5*A13*dchi1)*qud31) +
|
|
ginv22*((-(cdA212*chi) + 1.5*A12*dchi2)*qud11 +
|
|
(-(cdA222*chi) + 1.5*A22*dchi2)*qud21 +
|
|
(-(cdA223*chi) + 1.5*A23*dchi2)*qud31) +
|
|
ginv33*((-(cdA313*chi) + 1.5*A13*dchi3)*qud11 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud21 +
|
|
(-(cdA333*chi) + 1.5*A33*dchi3)*qud31) +
|
|
chi*((0.66666666666666666667*dK1 - dTheta1)*qud11 +
|
|
(0.66666666666666666667*dK2 - dTheta2)*qud21 +
|
|
(0.66666666666666666667*dK3 - dTheta3)*qud31) +
|
|
ginv12*((-(cdA212*chi) + 1.5*A12*dchi2)*qud21 +
|
|
(-(cdA213*chi) + 1.5*A13*dchi2)*qud31 -
|
|
chi*((cdA112 + cdA211)*qud11 + cdA122*qud21 + cdA123*qud31) +
|
|
1.5*((A12*dchi1 + A11*dchi2)*qud11 + dchi1*(A22*qud21 + A23*qud31))\
|
|
) + ginv13*((-(cdA312*chi) + 1.5*A12*dchi3)*qud21 +
|
|
(-(cdA313*chi) + 1.5*A13*dchi3)*qud31 -
|
|
chi*((cdA113 + cdA311)*qud11 + cdA123*qud21 + cdA133*qud31) +
|
|
1.5*((A13*dchi1 + A11*dchi3)*qud11 + dchi1*(A23*qud21 + A33*qud31))\
|
|
) + ginv23*((-(cdA322*chi) + 1.5*A22*dchi3)*qud21 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud31 -
|
|
chi*((cdA213 + cdA312)*qud11 + cdA223*qud21 + cdA233*qud31) +
|
|
1.5*((A13*dchi2 + A12*dchi3)*qud11 + dchi2*(A23*qud21 + A33*qud31))\
|
|
) + 0.5*(kappa1*((G1 - Gfromg1)*qdd11 + (G2 - Gfromg2)*qdd12 +
|
|
(G3 - Gfromg3)*qdd13) - dG13*qdd13*sup1 - dG21*qdd11*sup2 +
|
|
(dGfromgdu22*qdd12 - dG23*qdd13)*sup2 +
|
|
(dGfromgdu31*qdd11 + dGfromgdu32*qdd12 - dG33*qdd13)*sup3 +
|
|
qdd11*((-dG11 + dGfromgdu11)*sup1 + dGfromgdu21*sup2 -
|
|
dG31*sup3) + qdd12*
|
|
((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3))*pow2(chi) +
|
|
sup1*(-2.*AA11*qud11 + 0.5*dGfromgdu13*qdd13*pow2(chi))) +
|
|
sup2*(chi*(-(cdda12*qud11) - cdda22*qud21 - cdda23*qud31 +
|
|
alpha*qud21*Rf22) + alpha*
|
|
(chi*(qud11*Rf12 + qud31*Rf23) + 0.5*dGfromgdu23*qdd13*pow2(chi))) +
|
|
sup3*(chi*(-(cdda13*qud11) - cdda23*qud21 - cdda33*qud31 +
|
|
alpha*qud21*Rf23) + alpha*
|
|
(chi*(qud11*Rf13 + qud31*Rf33) + 0.5*dGfromgdu33*qdd13*pow2(chi)))
|
|
;
|
|
|
|
rACsA2
|
|
=
|
|
(qud12*(lieA11 + alpha*chi*Rf11) +
|
|
qud22*(lieA12 + alpha*(-2.*AA12 + chi*Rf12)) +
|
|
qud32*(lieA13 + alpha*(-2.*AA13 + chi*Rf13)))*sup1 +
|
|
qud12*((-(cdda11*chi) + A11*alpha*K)*sup1 + lieA12*sup2 +
|
|
(A13*alpha*K + lieA13)*sup3 +
|
|
alpha*((-2.*AA21 + A12*K)*sup2 - 2.*AA31*sup3)) +
|
|
qud22*((-(cdda12*chi) + A12*alpha*K)*sup1 + lieA22*sup2 +
|
|
(A23*alpha*K + lieA23)*sup3 +
|
|
alpha*((-2.*AA22 + A22*K)*sup2 - 2.*AA32*sup3)) +
|
|
qud32*((-(cdda13*chi) + A13*alpha*K)*sup1 + lieA23*sup2 +
|
|
(A33*alpha*K + lieA33)*sup3 +
|
|
alpha*((-2.*AA23 + A23*K)*sup2 - 2.*AA33*sup3)) +
|
|
alpha*(ginv11*((-(cdA111*chi) + 1.5*A11*dchi1)*qud12 +
|
|
(-(cdA112*chi) + 1.5*A12*dchi1)*qud22 +
|
|
(-(cdA113*chi) + 1.5*A13*dchi1)*qud32) +
|
|
ginv22*((-(cdA212*chi) + 1.5*A12*dchi2)*qud12 +
|
|
(-(cdA222*chi) + 1.5*A22*dchi2)*qud22 +
|
|
(-(cdA223*chi) + 1.5*A23*dchi2)*qud32) +
|
|
ginv33*((-(cdA313*chi) + 1.5*A13*dchi3)*qud12 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud22 +
|
|
(-(cdA333*chi) + 1.5*A33*dchi3)*qud32) +
|
|
chi*((0.66666666666666666667*dK1 - dTheta1)*qud12 +
|
|
(0.66666666666666666667*dK2 - dTheta2)*qud22 +
|
|
(0.66666666666666666667*dK3 - dTheta3)*qud32) +
|
|
ginv12*((-(cdA212*chi) + 1.5*A12*dchi2)*qud22 +
|
|
(-(cdA213*chi) + 1.5*A13*dchi2)*qud32 -
|
|
chi*((cdA112 + cdA211)*qud12 + cdA122*qud22 + cdA123*qud32) +
|
|
1.5*((A12*dchi1 + A11*dchi2)*qud12 + dchi1*(A22*qud22 + A23*qud32))\
|
|
) + ginv13*((-(cdA312*chi) + 1.5*A12*dchi3)*qud22 +
|
|
(-(cdA313*chi) + 1.5*A13*dchi3)*qud32 -
|
|
chi*((cdA113 + cdA311)*qud12 + cdA123*qud22 + cdA133*qud32) +
|
|
1.5*((A13*dchi1 + A11*dchi3)*qud12 + dchi1*(A23*qud22 + A33*qud32))\
|
|
) + ginv23*((-(cdA322*chi) + 1.5*A22*dchi3)*qud22 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud32 -
|
|
chi*((cdA213 + cdA312)*qud12 + cdA223*qud22 + cdA233*qud32) +
|
|
1.5*((A13*dchi2 + A12*dchi3)*qud12 + dchi2*(A23*qud22 + A33*qud32))\
|
|
) + 0.5*(kappa1*((G1 - Gfromg1)*qdd12 + (G2 - Gfromg2)*qdd22 +
|
|
(G3 - Gfromg3)*qdd23) - dG13*qdd23*sup1 - dG21*qdd12*sup2 +
|
|
(dGfromgdu22*qdd22 - dG23*qdd23)*sup2 +
|
|
(dGfromgdu31*qdd12 + dGfromgdu32*qdd22 - dG33*qdd23)*sup3 +
|
|
qdd12*((-dG11 + dGfromgdu11)*sup1 + dGfromgdu21*sup2 -
|
|
dG31*sup3) + qdd22*
|
|
((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3))*pow2(chi) +
|
|
sup1*(-2.*AA11*qud12 + 0.5*dGfromgdu13*qdd23*pow2(chi))) +
|
|
sup2*(chi*(-(cdda12*qud12) - cdda22*qud22 - cdda23*qud32 +
|
|
alpha*qud22*Rf22) + alpha*
|
|
(chi*(qud12*Rf12 + qud32*Rf23) + 0.5*dGfromgdu23*qdd23*pow2(chi))) +
|
|
sup3*(chi*(-(cdda13*qud12) - cdda23*qud22 - cdda33*qud32 +
|
|
alpha*qud22*Rf23) + alpha*
|
|
(chi*(qud12*Rf13 + qud32*Rf33) + 0.5*dGfromgdu33*qdd23*pow2(chi)))
|
|
;
|
|
|
|
rACsA3
|
|
=
|
|
(qud13*(lieA11 + alpha*chi*Rf11) +
|
|
qud23*(lieA12 + alpha*(-2.*AA12 + chi*Rf12)) +
|
|
qud33*(lieA13 + alpha*(-2.*AA13 + chi*Rf13)))*sup1 +
|
|
qud13*((-(cdda11*chi) + A11*alpha*K)*sup1 + lieA12*sup2 +
|
|
(A13*alpha*K + lieA13)*sup3 +
|
|
alpha*((-2.*AA21 + A12*K)*sup2 - 2.*AA31*sup3)) +
|
|
qud23*((-(cdda12*chi) + A12*alpha*K)*sup1 + lieA22*sup2 +
|
|
(A23*alpha*K + lieA23)*sup3 +
|
|
alpha*((-2.*AA22 + A22*K)*sup2 - 2.*AA32*sup3)) +
|
|
qud33*((-(cdda13*chi) + A13*alpha*K)*sup1 + lieA23*sup2 +
|
|
(A33*alpha*K + lieA33)*sup3 +
|
|
alpha*((-2.*AA23 + A23*K)*sup2 - 2.*AA33*sup3)) +
|
|
alpha*(ginv11*((-(cdA111*chi) + 1.5*A11*dchi1)*qud13 +
|
|
(-(cdA112*chi) + 1.5*A12*dchi1)*qud23 +
|
|
(-(cdA113*chi) + 1.5*A13*dchi1)*qud33) +
|
|
ginv22*((-(cdA212*chi) + 1.5*A12*dchi2)*qud13 +
|
|
(-(cdA222*chi) + 1.5*A22*dchi2)*qud23 +
|
|
(-(cdA223*chi) + 1.5*A23*dchi2)*qud33) +
|
|
ginv33*((-(cdA313*chi) + 1.5*A13*dchi3)*qud13 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud23 +
|
|
(-(cdA333*chi) + 1.5*A33*dchi3)*qud33) +
|
|
chi*((0.66666666666666666667*dK1 - dTheta1)*qud13 +
|
|
(0.66666666666666666667*dK2 - dTheta2)*qud23 +
|
|
(0.66666666666666666667*dK3 - dTheta3)*qud33) +
|
|
ginv12*((-(cdA212*chi) + 1.5*A12*dchi2)*qud23 +
|
|
(-(cdA213*chi) + 1.5*A13*dchi2)*qud33 -
|
|
chi*((cdA112 + cdA211)*qud13 + cdA122*qud23 + cdA123*qud33) +
|
|
1.5*((A12*dchi1 + A11*dchi2)*qud13 + dchi1*(A22*qud23 + A23*qud33))\
|
|
) + ginv13*((-(cdA312*chi) + 1.5*A12*dchi3)*qud23 +
|
|
(-(cdA313*chi) + 1.5*A13*dchi3)*qud33 -
|
|
chi*((cdA113 + cdA311)*qud13 + cdA123*qud23 + cdA133*qud33) +
|
|
1.5*((A13*dchi1 + A11*dchi3)*qud13 + dchi1*(A23*qud23 + A33*qud33))\
|
|
) + ginv23*((-(cdA322*chi) + 1.5*A22*dchi3)*qud23 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud33 -
|
|
chi*((cdA213 + cdA312)*qud13 + cdA223*qud23 + cdA233*qud33) +
|
|
1.5*((A13*dchi2 + A12*dchi3)*qud13 + dchi2*(A23*qud23 + A33*qud33))\
|
|
) + 0.5*(kappa1*((G1 - Gfromg1)*qdd13 + (G2 - Gfromg2)*qdd23 +
|
|
(G3 - Gfromg3)*qdd33) - dG13*qdd33*sup1 - dG21*qdd13*sup2 +
|
|
(dGfromgdu22*qdd23 - dG23*qdd33)*sup2 +
|
|
(dGfromgdu31*qdd13 + dGfromgdu32*qdd23 - dG33*qdd33)*sup3 +
|
|
qdd13*((-dG11 + dGfromgdu11)*sup1 + dGfromgdu21*sup2 -
|
|
dG31*sup3) + qdd23*
|
|
((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3))*pow2(chi) +
|
|
sup1*(-2.*AA11*qud13 + 0.5*dGfromgdu13*qdd33*pow2(chi))) +
|
|
sup2*(chi*(-(cdda12*qud13) - cdda22*qud23 - cdda23*qud33 +
|
|
alpha*qud23*Rf22) + alpha*
|
|
(chi*(qud13*Rf12 + qud33*Rf23) + 0.5*dGfromgdu23*qdd33*pow2(chi))) +
|
|
sup3*(chi*(-(cdda13*qud13) - cdda23*qud23 - cdda33*qud33 +
|
|
alpha*qud23*Rf23) + alpha*
|
|
(chi*(qud13*Rf13 + qud33*Rf33) + 0.5*dGfromgdu33*qdd33*pow2(chi)))
|
|
;
|
|
|
|
rACABTF11
|
|
=
|
|
-(qPhysuudd1211*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3311*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1111*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1211*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1311*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2211*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2311*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1311 + AA22*qPhysuudd2211 + AA23*qPhysuudd2311 +
|
|
AA33*qPhysuudd3311 + qPhysuudd1111*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1311 +
|
|
(0.5*(A12*dchi1*qPhysuudd1111 + A23*dchi3*qPhysuudd3311))/chi)*
|
|
sup2) - qPhysuudd3311*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1211*sup3 +
|
|
qPhysuudd1211*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1311*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2211*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2311*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2311*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1211 + A13*dchi2*qPhysuudd1311)*sup2 +
|
|
(A12*dchi3*qPhysuudd1211 -
|
|
0.5*dchi1*(A13*qPhysuudd1111 + A23*qPhysuudd1211))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1211 -
|
|
dchi3*(A11*qPhysuudd1311 + A12*qPhysuudd2311) +
|
|
dchi1*(A22*qPhysuudd2211 + A33*qPhysuudd3311))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1311) -
|
|
A22*dchi3*qPhysuudd2311 +
|
|
dchi2*(A11*qPhysuudd1111 + A33*qPhysuudd3311))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1311) +
|
|
A13*(-(dchi2*qPhysuudd1211) + dchi3*qPhysuudd1311) +
|
|
dchi3*(A11*qPhysuudd1111 + A22*qPhysuudd2211) +
|
|
A23*(-(dchi2*qPhysuudd2211) + dchi3*qPhysuudd2311))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF12
|
|
=
|
|
-(qPhysuudd1212*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3312*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1112*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1212*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1312*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2212*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2312*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1312 + AA22*qPhysuudd2212 + AA23*qPhysuudd2312 +
|
|
AA33*qPhysuudd3312 + qPhysuudd1112*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1312 +
|
|
(0.5*(A12*dchi1*qPhysuudd1112 + A23*dchi3*qPhysuudd3312))/chi)*
|
|
sup2) - qPhysuudd3312*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1212*sup3 +
|
|
qPhysuudd1212*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1312*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2212*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2312*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2312*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1212 + A13*dchi2*qPhysuudd1312)*sup2 +
|
|
(A12*dchi3*qPhysuudd1212 -
|
|
0.5*dchi1*(A13*qPhysuudd1112 + A23*qPhysuudd1212))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1212 -
|
|
dchi3*(A11*qPhysuudd1312 + A12*qPhysuudd2312) +
|
|
dchi1*(A22*qPhysuudd2212 + A33*qPhysuudd3312))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1312) -
|
|
A22*dchi3*qPhysuudd2312 +
|
|
dchi2*(A11*qPhysuudd1112 + A33*qPhysuudd3312))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1312) +
|
|
A13*(-(dchi2*qPhysuudd1212) + dchi3*qPhysuudd1312) +
|
|
dchi3*(A11*qPhysuudd1112 + A22*qPhysuudd2212) +
|
|
A23*(-(dchi2*qPhysuudd2212) + dchi3*qPhysuudd2312))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF13
|
|
=
|
|
-(qPhysuudd1213*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3313*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1113*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1213*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1313*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2213*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2313*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1313 + AA22*qPhysuudd2213 + AA23*qPhysuudd2313 +
|
|
AA33*qPhysuudd3313 + qPhysuudd1113*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1313 +
|
|
(0.5*(A12*dchi1*qPhysuudd1113 + A23*dchi3*qPhysuudd3313))/chi)*
|
|
sup2) - qPhysuudd3313*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1213*sup3 +
|
|
qPhysuudd1213*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1313*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2213*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2313*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2313*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1213 + A13*dchi2*qPhysuudd1313)*sup2 +
|
|
(A12*dchi3*qPhysuudd1213 -
|
|
0.5*dchi1*(A13*qPhysuudd1113 + A23*qPhysuudd1213))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1213 -
|
|
dchi3*(A11*qPhysuudd1313 + A12*qPhysuudd2313) +
|
|
dchi1*(A22*qPhysuudd2213 + A33*qPhysuudd3313))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1313) -
|
|
A22*dchi3*qPhysuudd2313 +
|
|
dchi2*(A11*qPhysuudd1113 + A33*qPhysuudd3313))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1313) +
|
|
A13*(-(dchi2*qPhysuudd1213) + dchi3*qPhysuudd1313) +
|
|
dchi3*(A11*qPhysuudd1113 + A22*qPhysuudd2213) +
|
|
A23*(-(dchi2*qPhysuudd2213) + dchi3*qPhysuudd2313))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF22
|
|
=
|
|
-(qPhysuudd1222*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3322*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1122*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1222*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1322*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2222*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2322*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1322 + AA22*qPhysuudd2222 + AA23*qPhysuudd2322 +
|
|
AA33*qPhysuudd3322 + qPhysuudd1122*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1322 +
|
|
(0.5*(A12*dchi1*qPhysuudd1122 + A23*dchi3*qPhysuudd3322))/chi)*
|
|
sup2) - qPhysuudd3322*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1222*sup3 +
|
|
qPhysuudd1222*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1322*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2222*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2322*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2322*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1222 + A13*dchi2*qPhysuudd1322)*sup2 +
|
|
(A12*dchi3*qPhysuudd1222 -
|
|
0.5*dchi1*(A13*qPhysuudd1122 + A23*qPhysuudd1222))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1222 -
|
|
dchi3*(A11*qPhysuudd1322 + A12*qPhysuudd2322) +
|
|
dchi1*(A22*qPhysuudd2222 + A33*qPhysuudd3322))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1322) -
|
|
A22*dchi3*qPhysuudd2322 +
|
|
dchi2*(A11*qPhysuudd1122 + A33*qPhysuudd3322))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1322) +
|
|
A13*(-(dchi2*qPhysuudd1222) + dchi3*qPhysuudd1322) +
|
|
dchi3*(A11*qPhysuudd1122 + A22*qPhysuudd2222) +
|
|
A23*(-(dchi2*qPhysuudd2222) + dchi3*qPhysuudd2322))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF23
|
|
=
|
|
-(qPhysuudd1223*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3323*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1123*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1223*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1323*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2223*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2323*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1323 + AA22*qPhysuudd2223 + AA23*qPhysuudd2323 +
|
|
AA33*qPhysuudd3323 + qPhysuudd1123*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1323 +
|
|
(0.5*(A12*dchi1*qPhysuudd1123 + A23*dchi3*qPhysuudd3323))/chi)*
|
|
sup2) - qPhysuudd3323*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1223*sup3 +
|
|
qPhysuudd1223*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1323*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2223*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2323*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2323*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1223 + A13*dchi2*qPhysuudd1323)*sup2 +
|
|
(A12*dchi3*qPhysuudd1223 -
|
|
0.5*dchi1*(A13*qPhysuudd1123 + A23*qPhysuudd1223))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1223 -
|
|
dchi3*(A11*qPhysuudd1323 + A12*qPhysuudd2323) +
|
|
dchi1*(A22*qPhysuudd2223 + A33*qPhysuudd3323))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1323) -
|
|
A22*dchi3*qPhysuudd2323 +
|
|
dchi2*(A11*qPhysuudd1123 + A33*qPhysuudd3323))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1323) +
|
|
A13*(-(dchi2*qPhysuudd1223) + dchi3*qPhysuudd1323) +
|
|
dchi3*(A11*qPhysuudd1123 + A22*qPhysuudd2223) +
|
|
A23*(-(dchi2*qPhysuudd2223) + dchi3*qPhysuudd2323))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF33
|
|
=
|
|
-(qPhysuudd1233*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3333*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1133*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1233*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1333*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2233*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2333*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1333 + AA22*qPhysuudd2233 + AA23*qPhysuudd2333 +
|
|
AA33*qPhysuudd3333 + qPhysuudd1133*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1333 +
|
|
(0.5*(A12*dchi1*qPhysuudd1133 + A23*dchi3*qPhysuudd3333))/chi)*
|
|
sup2) - qPhysuudd3333*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1233*sup3 +
|
|
qPhysuudd1233*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1333*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2233*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2333*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2333*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1233 + A13*dchi2*qPhysuudd1333)*sup2 +
|
|
(A12*dchi3*qPhysuudd1233 -
|
|
0.5*dchi1*(A13*qPhysuudd1133 + A23*qPhysuudd1233))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1233 -
|
|
dchi3*(A11*qPhysuudd1333 + A12*qPhysuudd2333) +
|
|
dchi1*(A22*qPhysuudd2233 + A33*qPhysuudd3333))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1333) -
|
|
A22*dchi3*qPhysuudd2333 +
|
|
dchi2*(A11*qPhysuudd1133 + A33*qPhysuudd3333))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1333) +
|
|
A13*(-(dchi2*qPhysuudd1233) + dchi3*qPhysuudd1333) +
|
|
dchi3*(A11*qPhysuudd1133 + A22*qPhysuudd2233) +
|
|
A23*(-(dchi2*qPhysuudd2233) + dchi3*qPhysuudd2333))*sup3))/chi)
|
|
;
|
|
|
|
|
|
if (givehPsi0) {
|
|
|
|
gADM11
|
|
=
|
|
g11/chi
|
|
;
|
|
|
|
gADM12
|
|
=
|
|
g12/chi
|
|
;
|
|
|
|
gADM13
|
|
=
|
|
g13/chi
|
|
;
|
|
|
|
gADM21
|
|
=
|
|
g12/chi
|
|
;
|
|
|
|
gADM22
|
|
=
|
|
g22/chi
|
|
;
|
|
|
|
gADM23
|
|
=
|
|
g23/chi
|
|
;
|
|
|
|
gADM31
|
|
=
|
|
g13/chi
|
|
;
|
|
|
|
gADM32
|
|
=
|
|
g23/chi
|
|
;
|
|
|
|
gADM33
|
|
=
|
|
g33/chi
|
|
;
|
|
|
|
vu1
|
|
=
|
|
-yp
|
|
;
|
|
|
|
vu2
|
|
=
|
|
xp
|
|
;
|
|
|
|
vu3
|
|
=
|
|
0
|
|
;
|
|
|
|
wu1
|
|
=
|
|
((-(ADMginv13*sup2) + ADMginv12*sup3)*vu1 +
|
|
(ADMginv13*sup1 - ADMginv11*sup3)*vu2 +
|
|
(-(ADMginv12*sup1) + ADMginv11*sup2)*vu3)/Power(chi,1.5)
|
|
;
|
|
|
|
wu2
|
|
=
|
|
((-(ADMginv23*sup2) + ADMginv22*sup3)*vu1 +
|
|
(ADMginv23*sup1 - ADMginv12*sup3)*vu2 +
|
|
(-(ADMginv22*sup1) + ADMginv12*sup2)*vu3)/Power(chi,1.5)
|
|
;
|
|
|
|
wu3
|
|
=
|
|
((-(ADMginv33*sup2) + ADMginv23*sup3)*vu1 +
|
|
(ADMginv33*sup1 - ADMginv13*sup3)*vu2 +
|
|
(-(ADMginv23*sup1) + ADMginv13*sup2)*vu3)/Power(chi,1.5)
|
|
;
|
|
|
|
sdotv
|
|
=
|
|
(gADM11*sup1 + gADM21*sup2 + gADM31*sup3)*vu1 +
|
|
(gADM12*sup1 + gADM22*sup2 + gADM32*sup3)*vu2 +
|
|
(gADM13*sup1 + gADM23*sup2 + gADM33*sup3)*vu3
|
|
;
|
|
|
|
vu1
|
|
=
|
|
-(sdotv*sup1) + vu1
|
|
;
|
|
|
|
vu2
|
|
=
|
|
-(sdotv*sup2) + vu2
|
|
;
|
|
|
|
vu3
|
|
=
|
|
-(sdotv*sup3) + vu3
|
|
;
|
|
|
|
vdotv
|
|
=
|
|
(gADM31*vu1 + (gADM23 + gADM32)*vu2)*vu3 +
|
|
vu1*((gADM12 + gADM21)*vu2 + gADM13*vu3) + gADM11*pow2(vu1) +
|
|
gADM22*pow2(vu2) + gADM33*pow2(vu3)
|
|
;
|
|
|
|
vu1
|
|
=
|
|
vu1/Sqrt(vdotv)
|
|
;
|
|
|
|
vu2
|
|
=
|
|
vu2/Sqrt(vdotv)
|
|
;
|
|
|
|
vu3
|
|
=
|
|
vu3/Sqrt(vdotv)
|
|
;
|
|
|
|
sdotw
|
|
=
|
|
(gADM11*sup1 + gADM21*sup2 + gADM31*sup3)*wu1 +
|
|
(gADM12*sup1 + gADM22*sup2 + gADM32*sup3)*wu2 +
|
|
(gADM13*sup1 + gADM23*sup2 + gADM33*sup3)*wu3
|
|
;
|
|
|
|
vdotw
|
|
=
|
|
(gADM11*vu1 + gADM21*vu2 + gADM31*vu3)*wu1 +
|
|
(gADM12*vu1 + gADM22*vu2 + gADM32*vu3)*wu2 +
|
|
(gADM13*vu1 + gADM23*vu2 + gADM33*vu3)*wu3
|
|
;
|
|
|
|
wu1
|
|
=
|
|
-(sdotw*sup1) - vdotw*vu1 + wu1
|
|
;
|
|
|
|
wu2
|
|
=
|
|
-(sdotw*sup2) - vdotw*vu2 + wu2
|
|
;
|
|
|
|
wu3
|
|
=
|
|
-(sdotw*sup3) - vdotw*vu3 + wu3
|
|
;
|
|
|
|
wdotw
|
|
=
|
|
(gADM31*wu1 + (gADM23 + gADM32)*wu2)*wu3 +
|
|
wu1*((gADM12 + gADM21)*wu2 + gADM13*wu3) + gADM11*pow2(wu1) +
|
|
gADM22*pow2(wu2) + gADM33*pow2(wu3)
|
|
;
|
|
|
|
wu1
|
|
=
|
|
wu1/Sqrt(wdotw)
|
|
;
|
|
|
|
wu2
|
|
=
|
|
wu2/Sqrt(wdotw)
|
|
;
|
|
|
|
wu3
|
|
=
|
|
wu3/Sqrt(wdotw)
|
|
;
|
|
|
|
vd1
|
|
=
|
|
gADM11*vu1 + gADM12*vu2 + gADM13*vu3
|
|
;
|
|
|
|
vd2
|
|
=
|
|
gADM21*vu1 + gADM22*vu2 + gADM23*vu3
|
|
;
|
|
|
|
vd3
|
|
=
|
|
gADM31*vu1 + gADM32*vu2 + gADM33*vu3
|
|
;
|
|
|
|
wd1
|
|
=
|
|
gADM11*wu1 + gADM12*wu2 + gADM13*wu3
|
|
;
|
|
|
|
wd2
|
|
=
|
|
gADM21*wu1 + gADM22*wu2 + gADM23*wu3
|
|
;
|
|
|
|
wd3
|
|
=
|
|
gADM31*wu1 + gADM32*wu2 + gADM33*wu3
|
|
;
|
|
|
|
RehPsi0
|
|
=
|
|
Power(2.7182818284590452354,pow2(hPsi0parb)*
|
|
(2.*hPsi0parc*time - pow2(hPsi0parc) - pow2(time)))*hPsi0para
|
|
;
|
|
|
|
ImhPsi0
|
|
=
|
|
0
|
|
;
|
|
|
|
rACABTF11
|
|
=
|
|
rACABTF11 + alpha*chi*(2.*ImhPsi0*vd1*wd1 + RehPsi0*(pow2(vd1) - pow2(wd1)))
|
|
;
|
|
|
|
rACABTF12
|
|
=
|
|
rACABTF12 + alpha*chi*(vd2*(RehPsi0*vd1 + ImhPsi0*wd1) +
|
|
(ImhPsi0*vd1 - RehPsi0*wd1)*wd2)
|
|
;
|
|
|
|
rACABTF13
|
|
=
|
|
rACABTF13 + alpha*chi*(vd3*(RehPsi0*vd1 + ImhPsi0*wd1) +
|
|
(ImhPsi0*vd1 - RehPsi0*wd1)*wd3)
|
|
;
|
|
|
|
rACABTF22
|
|
=
|
|
rACABTF22 + alpha*chi*(2.*ImhPsi0*vd2*wd2 + RehPsi0*(pow2(vd2) - pow2(wd2)))
|
|
;
|
|
|
|
rACABTF23
|
|
=
|
|
rACABTF23 + alpha*chi*(vd3*(RehPsi0*vd2 + ImhPsi0*wd2) +
|
|
(ImhPsi0*vd2 - RehPsi0*wd2)*wd3)
|
|
;
|
|
|
|
rACABTF33
|
|
=
|
|
rACABTF33 + alpha*chi*(2.*ImhPsi0*vd3*wd3 + RehPsi0*(pow2(vd3) - pow2(wd3)))
|
|
;
|
|
|
|
|
|
}
|
|
|
|
rA11
|
|
=
|
|
rACABTF11 + 0.5*qdd11*rACqq + 2.*
|
|
(qud11*rACsA1 + qud21*rACsA2 + qud31*rACsA3)*sdown1 + rACss*pow2(sdown1)
|
|
;
|
|
|
|
rA12
|
|
=
|
|
rACABTF12 + 0.5*qdd12*rACqq + (qud11*rACsA1 + qud21*rACsA2 + qud31*rACsA3)*
|
|
sdown2 + sdown1*(qud12*rACsA1 + qud22*rACsA2 + qud32*rACsA3 +
|
|
rACss*sdown2)
|
|
;
|
|
|
|
rA13
|
|
=
|
|
rACABTF13 + 0.5*qdd13*rACqq + (qud11*rACsA1 + qud21*rACsA2 + qud31*rACsA3)*
|
|
sdown3 + sdown1*(qud13*rACsA1 + qud23*rACsA2 + qud33*rACsA3 +
|
|
rACss*sdown3)
|
|
;
|
|
|
|
rA22
|
|
=
|
|
rACABTF22 + 0.5*qdd22*rACqq + 2.*
|
|
(qud12*rACsA1 + qud22*rACsA2 + qud32*rACsA3)*sdown2 + rACss*pow2(sdown2)
|
|
;
|
|
|
|
rA23
|
|
=
|
|
rACABTF23 + 0.5*qdd23*rACqq + (qud12*rACsA1 + qud22*rACsA2 + qud32*rACsA3)*
|
|
sdown3 + sdown2*(qud13*rACsA1 + qud23*rACsA2 + qud33*rACsA3 +
|
|
rACss*sdown3)
|
|
;
|
|
|
|
rA33
|
|
=
|
|
rACABTF33 + 0.5*qdd33*rACqq + 2.*
|
|
(qud13*rACsA1 + qud23*rACsA2 + qud33*rACsA3)*sdown3 + rACss*pow2(sdown3)
|
|
;
|
|
|
|
rG1
|
|
=
|
|
qud11*rGamA1 + qud12*rGamA2 + qud13*rGamA3 + rGams*sup1
|
|
;
|
|
|
|
rG2
|
|
=
|
|
qud21*rGamA1 + qud22*rGamA2 + qud23*rGamA3 + rGams*sup2
|
|
;
|
|
|
|
rG3
|
|
=
|
|
qud31*rGamA1 + qud32*rGamA2 + qud33*rGamA3 + rGams*sup3
|
|
;
|
|
#else
|
|
// code adapted from David 2012-8-18
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 + g11*g22*g33 -
|
|
g33*pow2(g12) - g22*pow2(g13) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
ginv11*chi
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
ginv12*chi
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
ginv13*chi
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
ginv22*chi
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
ginv23*chi
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
ginv33*chi
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
qdd11
|
|
=
|
|
g11/chi - pow2(sdown1)
|
|
;
|
|
|
|
qdd12
|
|
=
|
|
-(sdown1*sdown2) + g12/chi
|
|
;
|
|
|
|
qdd13
|
|
=
|
|
-(sdown1*sdown3) + g13/chi
|
|
;
|
|
|
|
qdd22
|
|
=
|
|
g22/chi - pow2(sdown2)
|
|
;
|
|
|
|
qdd23
|
|
=
|
|
-(sdown2*sdown3) + g23/chi
|
|
;
|
|
|
|
qdd33
|
|
=
|
|
g33/chi - pow2(sdown3)
|
|
;
|
|
|
|
quu11
|
|
=
|
|
ADMginv11 - pow2(sup1)
|
|
;
|
|
|
|
quu12
|
|
=
|
|
ADMginv12 - sup1*sup2
|
|
;
|
|
|
|
quu13
|
|
=
|
|
ADMginv13 - sup1*sup3
|
|
;
|
|
|
|
quu22
|
|
=
|
|
ADMginv22 - pow2(sup2)
|
|
;
|
|
|
|
quu23
|
|
=
|
|
ADMginv23 - sup2*sup3
|
|
;
|
|
|
|
quu33
|
|
=
|
|
ADMginv33 - pow2(sup3)
|
|
;
|
|
|
|
qPhysuudd1111
|
|
=
|
|
-0.5*qdd11*quu11 + pow2(qud11)
|
|
;
|
|
|
|
qPhysuudd1112
|
|
=
|
|
qud11*qud12 - 0.5*qdd12*quu11
|
|
;
|
|
|
|
qPhysuudd1113
|
|
=
|
|
qud11*qud13 - 0.5*qdd13*quu11
|
|
;
|
|
|
|
qPhysuudd1122
|
|
=
|
|
-0.5*qdd22*quu11 + pow2(qud12)
|
|
;
|
|
|
|
qPhysuudd1123
|
|
=
|
|
qud12*qud13 - 0.5*qdd23*quu11
|
|
;
|
|
|
|
qPhysuudd1133
|
|
=
|
|
-0.5*qdd33*quu11 + pow2(qud13)
|
|
;
|
|
|
|
qPhysuudd1211
|
|
=
|
|
qud11*qud21 - 0.5*qdd11*quu12
|
|
;
|
|
|
|
qPhysuudd1212
|
|
=
|
|
0.5*(qud12*qud21 + qud11*qud22 - qdd12*quu12)
|
|
;
|
|
|
|
qPhysuudd1213
|
|
=
|
|
0.5*(qud13*qud21 + qud11*qud23 - qdd13*quu12)
|
|
;
|
|
|
|
qPhysuudd1222
|
|
=
|
|
qud12*qud22 - 0.5*qdd22*quu12
|
|
;
|
|
|
|
qPhysuudd1223
|
|
=
|
|
0.5*(qud13*qud22 + qud12*qud23 - qdd23*quu12)
|
|
;
|
|
|
|
qPhysuudd1233
|
|
=
|
|
qud13*qud23 - 0.5*qdd33*quu12
|
|
;
|
|
|
|
qPhysuudd1311
|
|
=
|
|
qud11*qud31 - 0.5*qdd11*quu13
|
|
;
|
|
|
|
qPhysuudd1312
|
|
=
|
|
0.5*(qud12*qud31 + qud11*qud32 - qdd12*quu13)
|
|
;
|
|
|
|
qPhysuudd1313
|
|
=
|
|
0.5*(qud13*qud31 + qud11*qud33 - qdd13*quu13)
|
|
;
|
|
|
|
qPhysuudd1322
|
|
=
|
|
qud12*qud32 - 0.5*qdd22*quu13
|
|
;
|
|
|
|
qPhysuudd1323
|
|
=
|
|
0.5*(qud13*qud32 + qud12*qud33 - qdd23*quu13)
|
|
;
|
|
|
|
qPhysuudd1333
|
|
=
|
|
qud13*qud33 - 0.5*qdd33*quu13
|
|
;
|
|
|
|
qPhysuudd2211
|
|
=
|
|
-0.5*qdd11*quu22 + pow2(qud21)
|
|
;
|
|
|
|
qPhysuudd2212
|
|
=
|
|
qud21*qud22 - 0.5*qdd12*quu22
|
|
;
|
|
|
|
qPhysuudd2213
|
|
=
|
|
qud21*qud23 - 0.5*qdd13*quu22
|
|
;
|
|
|
|
qPhysuudd2222
|
|
=
|
|
-0.5*qdd22*quu22 + pow2(qud22)
|
|
;
|
|
|
|
qPhysuudd2223
|
|
=
|
|
qud22*qud23 - 0.5*qdd23*quu22
|
|
;
|
|
|
|
qPhysuudd2233
|
|
=
|
|
-0.5*qdd33*quu22 + pow2(qud23)
|
|
;
|
|
|
|
qPhysuudd2311
|
|
=
|
|
qud21*qud31 - 0.5*qdd11*quu23
|
|
;
|
|
|
|
qPhysuudd2312
|
|
=
|
|
0.5*(qud22*qud31 + qud21*qud32 - qdd12*quu23)
|
|
;
|
|
|
|
qPhysuudd2313
|
|
=
|
|
0.5*(qud23*qud31 + qud21*qud33 - qdd13*quu23)
|
|
;
|
|
|
|
qPhysuudd2322
|
|
=
|
|
qud22*qud32 - 0.5*qdd22*quu23
|
|
;
|
|
|
|
qPhysuudd2323
|
|
=
|
|
0.5*(qud23*qud32 + qud22*qud33 - qdd23*quu23)
|
|
;
|
|
|
|
qPhysuudd2333
|
|
=
|
|
qud23*qud33 - 0.5*qdd33*quu23
|
|
;
|
|
|
|
qPhysuudd3311
|
|
=
|
|
-0.5*qdd11*quu33 + pow2(qud31)
|
|
;
|
|
|
|
qPhysuudd3312
|
|
=
|
|
qud31*qud32 - 0.5*qdd12*quu33
|
|
;
|
|
|
|
qPhysuudd3313
|
|
=
|
|
qud31*qud33 - 0.5*qdd13*quu33
|
|
;
|
|
|
|
qPhysuudd3322
|
|
=
|
|
-0.5*qdd22*quu33 + pow2(qud32)
|
|
;
|
|
|
|
qPhysuudd3323
|
|
=
|
|
qud32*qud33 - 0.5*qdd23*quu33
|
|
;
|
|
|
|
qPhysuudd3333
|
|
=
|
|
-0.5*qdd33*quu33 + pow2(qud33)
|
|
;
|
|
|
|
muL
|
|
=
|
|
2./alpha
|
|
;
|
|
|
|
muStilde
|
|
=
|
|
1/chi
|
|
;
|
|
|
|
vbetas
|
|
=
|
|
2.*sqrt(0.33333333333333333333*muStilde)
|
|
;
|
|
|
|
vbetaA
|
|
=
|
|
sqrt(muStilde)
|
|
;
|
|
|
|
K
|
|
=
|
|
Khat + 2.*Theta
|
|
;
|
|
|
|
dK1
|
|
=
|
|
dKhat1 + 2.*dTheta1
|
|
;
|
|
|
|
dK2
|
|
=
|
|
dKhat2 + 2.*dTheta2
|
|
;
|
|
|
|
dK3
|
|
=
|
|
dKhat3 + 2.*dTheta3
|
|
;
|
|
|
|
dginv111
|
|
=
|
|
-2.*(dg123*ginv12*ginv13 + ginv11*(dg112*ginv12 + dg113*ginv13)) -
|
|
dg111*pow2(ginv11) - dg122*pow2(ginv12) - dg133*pow2(ginv13)
|
|
;
|
|
|
|
dginv112
|
|
=
|
|
-(ginv11*(dg111*ginv12 + dg112*ginv22 + dg113*ginv23)) -
|
|
ginv12*(dg113*ginv13 + dg122*ginv22 + dg123*ginv23) -
|
|
ginv13*(dg123*ginv22 + dg133*ginv23) - dg112*pow2(ginv12)
|
|
;
|
|
|
|
dginv113
|
|
=
|
|
-(ginv11*(dg111*ginv13 + dg112*ginv23 + dg113*ginv33)) -
|
|
ginv12*(dg112*ginv13 + dg122*ginv23 + dg123*ginv33) -
|
|
ginv13*(dg123*ginv23 + dg133*ginv33) - dg113*pow2(ginv13)
|
|
;
|
|
|
|
dginv122
|
|
=
|
|
-2.*(dg123*ginv22*ginv23 + ginv12*(dg112*ginv22 + dg113*ginv23)) -
|
|
dg111*pow2(ginv12) - dg122*pow2(ginv22) - dg133*pow2(ginv23)
|
|
;
|
|
|
|
dginv123
|
|
=
|
|
-(ginv13*(dg112*ginv22 + dg113*ginv23)) - dg133*ginv23*ginv33 -
|
|
ginv12*(dg111*ginv13 + dg112*ginv23 + dg113*ginv33) -
|
|
ginv22*(dg122*ginv23 + dg123*ginv33) - dg123*pow2(ginv23)
|
|
;
|
|
|
|
dginv133
|
|
=
|
|
-2.*(dg123*ginv23*ginv33 + ginv13*(dg112*ginv23 + dg113*ginv33)) -
|
|
dg111*pow2(ginv13) - dg122*pow2(ginv23) - dg133*pow2(ginv33)
|
|
;
|
|
|
|
dginv211
|
|
=
|
|
-2.*(dg223*ginv12*ginv13 + ginv11*(dg212*ginv12 + dg213*ginv13)) -
|
|
dg211*pow2(ginv11) - dg222*pow2(ginv12) - dg233*pow2(ginv13)
|
|
;
|
|
|
|
dginv212
|
|
=
|
|
-(ginv11*(dg211*ginv12 + dg212*ginv22 + dg213*ginv23)) -
|
|
ginv12*(dg213*ginv13 + dg222*ginv22 + dg223*ginv23) -
|
|
ginv13*(dg223*ginv22 + dg233*ginv23) - dg212*pow2(ginv12)
|
|
;
|
|
|
|
dginv213
|
|
=
|
|
-(ginv11*(dg211*ginv13 + dg212*ginv23 + dg213*ginv33)) -
|
|
ginv12*(dg212*ginv13 + dg222*ginv23 + dg223*ginv33) -
|
|
ginv13*(dg223*ginv23 + dg233*ginv33) - dg213*pow2(ginv13)
|
|
;
|
|
|
|
dginv222
|
|
=
|
|
-2.*(dg223*ginv22*ginv23 + ginv12*(dg212*ginv22 + dg213*ginv23)) -
|
|
dg211*pow2(ginv12) - dg222*pow2(ginv22) - dg233*pow2(ginv23)
|
|
;
|
|
|
|
dginv223
|
|
=
|
|
-(ginv13*(dg212*ginv22 + dg213*ginv23)) - dg233*ginv23*ginv33 -
|
|
ginv12*(dg211*ginv13 + dg212*ginv23 + dg213*ginv33) -
|
|
ginv22*(dg222*ginv23 + dg223*ginv33) - dg223*pow2(ginv23)
|
|
;
|
|
|
|
dginv233
|
|
=
|
|
-2.*(dg223*ginv23*ginv33 + ginv13*(dg212*ginv23 + dg213*ginv33)) -
|
|
dg211*pow2(ginv13) - dg222*pow2(ginv23) - dg233*pow2(ginv33)
|
|
;
|
|
|
|
dginv311
|
|
=
|
|
-2.*(dg323*ginv12*ginv13 + ginv11*(dg312*ginv12 + dg313*ginv13)) -
|
|
dg311*pow2(ginv11) - dg322*pow2(ginv12) - dg333*pow2(ginv13)
|
|
;
|
|
|
|
dginv312
|
|
=
|
|
-(ginv11*(dg311*ginv12 + dg312*ginv22 + dg313*ginv23)) -
|
|
ginv12*(dg313*ginv13 + dg322*ginv22 + dg323*ginv23) -
|
|
ginv13*(dg323*ginv22 + dg333*ginv23) - dg312*pow2(ginv12)
|
|
;
|
|
|
|
dginv313
|
|
=
|
|
-(ginv11*(dg311*ginv13 + dg312*ginv23 + dg313*ginv33)) -
|
|
ginv12*(dg312*ginv13 + dg322*ginv23 + dg323*ginv33) -
|
|
ginv13*(dg323*ginv23 + dg333*ginv33) - dg313*pow2(ginv13)
|
|
;
|
|
|
|
dginv322
|
|
=
|
|
-2.*(dg323*ginv22*ginv23 + ginv12*(dg312*ginv22 + dg313*ginv23)) -
|
|
dg311*pow2(ginv12) - dg322*pow2(ginv22) - dg333*pow2(ginv23)
|
|
;
|
|
|
|
dginv323
|
|
=
|
|
-(ginv13*(dg312*ginv22 + dg313*ginv23)) - dg333*ginv23*ginv33 -
|
|
ginv12*(dg311*ginv13 + dg312*ginv23 + dg313*ginv33) -
|
|
ginv22*(dg322*ginv23 + dg323*ginv33) - dg323*pow2(ginv23)
|
|
;
|
|
|
|
dginv333
|
|
=
|
|
-2.*(dg323*ginv23*ginv33 + ginv13*(dg312*ginv23 + dg313*ginv33)) -
|
|
dg311*pow2(ginv13) - dg322*pow2(ginv23) - dg333*pow2(ginv33)
|
|
;
|
|
|
|
gammado111
|
|
=
|
|
0.5*dg111
|
|
;
|
|
|
|
gammado112
|
|
=
|
|
0.5*dg211
|
|
;
|
|
|
|
gammado113
|
|
=
|
|
0.5*dg311
|
|
;
|
|
|
|
gammado122
|
|
=
|
|
-0.5*dg122 + dg212
|
|
;
|
|
|
|
gammado123
|
|
=
|
|
0.5*(-dg123 + dg213 + dg312)
|
|
;
|
|
|
|
gammado133
|
|
=
|
|
-0.5*dg133 + dg313
|
|
;
|
|
|
|
gammado211
|
|
=
|
|
dg112 - 0.5*dg211
|
|
;
|
|
|
|
gammado212
|
|
=
|
|
0.5*dg122
|
|
;
|
|
|
|
gammado213
|
|
=
|
|
0.5*(dg123 - dg213 + dg312)
|
|
;
|
|
|
|
gammado222
|
|
=
|
|
0.5*dg222
|
|
;
|
|
|
|
gammado223
|
|
=
|
|
0.5*dg322
|
|
;
|
|
|
|
gammado233
|
|
=
|
|
-0.5*dg233 + dg323
|
|
;
|
|
|
|
gammado311
|
|
=
|
|
dg113 - 0.5*dg311
|
|
;
|
|
|
|
gammado312
|
|
=
|
|
0.5*(dg123 + dg213 - dg312)
|
|
;
|
|
|
|
gammado313
|
|
=
|
|
0.5*dg133
|
|
;
|
|
|
|
gammado322
|
|
=
|
|
dg223 - 0.5*dg322
|
|
;
|
|
|
|
gammado323
|
|
=
|
|
0.5*dg233
|
|
;
|
|
|
|
gammado333
|
|
=
|
|
0.5*dg333
|
|
;
|
|
|
|
gamma111
|
|
=
|
|
gammado111*ginv11 + gammado211*ginv12 + gammado311*ginv13
|
|
;
|
|
|
|
gamma112
|
|
=
|
|
gammado112*ginv11 + gammado212*ginv12 + gammado312*ginv13
|
|
;
|
|
|
|
gamma113
|
|
=
|
|
gammado113*ginv11 + gammado213*ginv12 + gammado313*ginv13
|
|
;
|
|
|
|
gamma122
|
|
=
|
|
gammado122*ginv11 + gammado222*ginv12 + gammado322*ginv13
|
|
;
|
|
|
|
gamma123
|
|
=
|
|
gammado123*ginv11 + gammado223*ginv12 + gammado323*ginv13
|
|
;
|
|
|
|
gamma133
|
|
=
|
|
gammado133*ginv11 + gammado233*ginv12 + gammado333*ginv13
|
|
;
|
|
|
|
gamma211
|
|
=
|
|
gammado111*ginv12 + gammado211*ginv22 + gammado311*ginv23
|
|
;
|
|
|
|
gamma212
|
|
=
|
|
gammado112*ginv12 + gammado212*ginv22 + gammado312*ginv23
|
|
;
|
|
|
|
gamma213
|
|
=
|
|
gammado113*ginv12 + gammado213*ginv22 + gammado313*ginv23
|
|
;
|
|
|
|
gamma222
|
|
=
|
|
gammado122*ginv12 + gammado222*ginv22 + gammado322*ginv23
|
|
;
|
|
|
|
gamma223
|
|
=
|
|
gammado123*ginv12 + gammado223*ginv22 + gammado323*ginv23
|
|
;
|
|
|
|
gamma233
|
|
=
|
|
gammado133*ginv12 + gammado233*ginv22 + gammado333*ginv23
|
|
;
|
|
|
|
gamma311
|
|
=
|
|
gammado111*ginv13 + gammado211*ginv23 + gammado311*ginv33
|
|
;
|
|
|
|
gamma312
|
|
=
|
|
gammado112*ginv13 + gammado212*ginv23 + gammado312*ginv33
|
|
;
|
|
|
|
gamma313
|
|
=
|
|
gammado113*ginv13 + gammado213*ginv23 + gammado313*ginv33
|
|
;
|
|
|
|
gamma322
|
|
=
|
|
gammado122*ginv13 + gammado222*ginv23 + gammado322*ginv33
|
|
;
|
|
|
|
gamma323
|
|
=
|
|
gammado123*ginv13 + gammado223*ginv23 + gammado323*ginv33
|
|
;
|
|
|
|
gamma333
|
|
=
|
|
gammado133*ginv13 + gammado233*ginv23 + gammado333*ginv33
|
|
;
|
|
|
|
Gfromg1
|
|
=
|
|
gamma111*ginv11 + gamma122*ginv22 +
|
|
2.*(gamma112*ginv12 + gamma113*ginv13 + gamma123*ginv23) + gamma133*ginv33
|
|
;
|
|
|
|
Gfromg2
|
|
=
|
|
gamma211*ginv11 + gamma222*ginv22 +
|
|
2.*(gamma212*ginv12 + gamma213*ginv13 + gamma223*ginv23) + gamma233*ginv33
|
|
;
|
|
|
|
Gfromg3
|
|
=
|
|
gamma311*ginv11 + gamma322*ginv22 +
|
|
2.*(gamma312*ginv12 + gamma313*ginv13 + gamma323*ginv23) + gamma333*ginv33
|
|
;
|
|
|
|
dGfromgdu11
|
|
=
|
|
(ddg1111 - dg111*((8.*dg112 + 2.*dg211)*ginv12 +
|
|
(8.*dg113 + 2.*dg311)*ginv13) -
|
|
(dg113*(4.*dg112 + dg211) + dg112*dg311 + dg111*(dg213 + dg312))*
|
|
ginv23 - ginv22*(dg112*dg211 + dg111*dg212 + 2.*pow2(dg112)) -
|
|
ginv33*(dg113*dg311 + dg111*dg313 + 2.*pow2(dg113)))*pow2(ginv11) +
|
|
(ddg1122 + ddg1212 - (dg123*(8.*dg112 + 2.*dg211) +
|
|
dg113*(4.*dg122 + 2.*dg212) + dg122*dg311 +
|
|
2.*(dg111*dg223 + dg112*(dg213 + dg312)) + dg111*dg322)*ginv13 -
|
|
(dg123*(4.*dg122 + 2.*dg212) +
|
|
2.*(dg113*dg222 + dg122*(dg213 + dg312) + dg112*(dg223 + dg322)))*
|
|
ginv23 - ginv22*(3.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122)) -
|
|
ginv33*(dg123*(dg213 + dg312) + dg122*dg313 + dg113*(dg223 + dg322) +
|
|
dg112*dg323 + 2.*pow2(dg123)))*pow2(ginv12) +
|
|
(ddg1133 + ddg1313 - (dg133*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg313 + dg113*(dg233 + dg323) + dg112*dg333))*ginv23 -
|
|
ginv22*(dg133*dg212 + dg113*dg223 + dg123*(dg213 + dg312) +
|
|
dg112*(dg233 + dg323) + 2.*pow2(dg123)) -
|
|
ginv33*(3.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133)))*pow2(ginv13) \
|
|
+ ginv13*(ddg1333*ginv33 + ginv22*
|
|
(ddg1223 - (dg133*dg222 + dg123*(4.*dg223 + dg322) +
|
|
dg122*(dg233 + dg323))*ginv23 -
|
|
(dg133*dg223 + dg123*(dg233 + 2.*dg323))*ginv33) +
|
|
ginv23*(ddg1233 + ddg1323 -
|
|
(dg133*(2.*dg233 + 3.*dg323) + 3.*dg123*dg333)*ginv33) -
|
|
(dg123*dg222 + dg122*dg223)*pow2(ginv22) -
|
|
(dg133*dg322 + 2.*(dg133*dg223 + dg123*(dg233 + dg323)) +
|
|
dg122*dg333)*pow2(ginv23) - 2.*dg133*dg333*pow2(ginv33)) +
|
|
ginv11*(ddg1313*ginv33 + ginv12*
|
|
(2.*ddg1112 + ddg1211 - (dg113*(12.*dg112 + 3.*dg211) +
|
|
3.*dg112*dg311 + dg111*(8.*dg123 + 3.*(dg213 + dg312)))*ginv13 \
|
|
- (dg122*(4.*dg112 + dg211) + 6.*dg112*dg212 + dg111*dg222)*ginv22 -
|
|
(dg123*dg211 + dg122*dg311 +
|
|
4.*(dg113*(dg122 + dg212) + dg112*(dg123 + dg213 + dg312)) +
|
|
dg111*(dg223 + dg322))*ginv23 -
|
|
(dg123*dg311 + dg113*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*dg112*dg313 + dg111*dg323)*ginv33) +
|
|
ginv22*(ddg1212 - (dg113*dg222 + 2.*(dg123*dg212 + dg112*dg223) +
|
|
dg122*(dg213 + dg312) + dg112*dg322)*ginv23 -
|
|
(dg113*dg223 + dg123*(dg213 + dg312) + dg112*dg323)*ginv33) +
|
|
ginv13*(2.*ddg1113 + ddg1311 -
|
|
(dg123*(4.*dg112 + dg211) + dg111*dg223 +
|
|
2.*(dg113*dg212 + dg112*(dg213 + dg312)))*ginv22 -
|
|
(dg133*dg211 + dg123*dg311 +
|
|
4.*(dg113*(dg123 + dg213 + dg312) + dg112*(dg133 + dg313)) +
|
|
dg111*(dg233 + dg323))*ginv23 -
|
|
(dg133*(4.*dg113 + dg311) + 6.*dg113*dg313 + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1213 + ddg1312 -
|
|
(dg133*(dg213 + dg312) + 2.*dg123*dg313 +
|
|
dg113*(dg233 + 2.*dg323) + dg112*dg333)*ginv33) -
|
|
(3.*dg112*dg211 + dg111*(4.*dg122 + 3.*dg212) + 6.*pow2(dg112))*
|
|
pow2(ginv12) - (3.*dg113*dg311 + dg111*(4.*dg133 + 3.*dg313) +
|
|
6.*pow2(dg113))*pow2(ginv13) -
|
|
(dg122*dg212 + dg112*dg222)*pow2(ginv22) -
|
|
(dg133*dg212 + dg123*(dg213 + dg312) + dg122*dg313 +
|
|
dg113*(dg223 + dg322) + dg112*(dg233 + dg323))*pow2(ginv23) -
|
|
(dg133*dg313 + dg113*dg333)*pow2(ginv33)) +
|
|
ginv12*(ddg1323*ginv33 + ginv22*
|
|
(ddg1222 - (3.*(dg123*dg222 + dg122*dg223) + 2.*dg122*dg322)*
|
|
ginv23 - (dg123*(2.*dg223 + dg322) + dg122*dg323)*ginv33) +
|
|
ginv23*(ddg1223 + ddg1322 -
|
|
(dg133*(dg223 + dg322) + dg123*(dg233 + 4.*dg323) + dg122*dg333)*
|
|
ginv33) + ginv13*(2.*ddg1123 + ddg1213 + ddg1312 -
|
|
(dg113*dg222 + 4.*(dg123*(dg122 + dg212) + dg112*dg223) +
|
|
dg122*(dg213 + dg312) + dg112*dg322)*ginv22 -
|
|
(dg133*(4.*dg123 + dg213 + dg312) + 4.*dg123*dg313 +
|
|
dg113*(dg233 + 4.*dg323) + dg112*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*dg212 + dg112*dg233 + dg122*dg313 +
|
|
dg113*dg322) + 4.*
|
|
(dg122*dg133 + dg113*dg223 + dg123*(dg213 + dg312) +
|
|
dg112*dg323 + pow2(dg123)))) -
|
|
(dg133*(4.*dg112 + dg211) + dg113*(8.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg311 + dg112*dg313) + dg111*(dg233 + 2.*dg323))*
|
|
pow2(ginv13) - 2.*dg122*dg222*pow2(ginv22) -
|
|
(dg133*dg222 + 2.*dg123*(dg223 + dg322) + dg122*(dg233 + 2.*dg323))*
|
|
pow2(ginv23) - (dg133*dg323 + dg123*dg333)*pow2(ginv33)) -
|
|
2.*pow2(dg111)*pow3(ginv11) -
|
|
(dg122*(4.*dg112 + dg211) + 2.*dg112*dg212 + dg111*dg222)*pow3(ginv12) -
|
|
(dg133*(4.*dg113 + dg311) + 2.*dg113*dg313 + dg111*dg333)*pow3(ginv13)
|
|
;
|
|
|
|
dGfromgdu12
|
|
=
|
|
(ddg1112 + ddg1211 - (4.*(dg112*dg113 + dg111*dg123) +
|
|
2.*(dg113*dg211 + dg112*dg311 + dg111*(dg213 + dg312)))*ginv13 -
|
|
(dg122*(6.*dg112 + 2.*dg211) + 6.*dg112*dg212 + 2.*dg111*dg222)*
|
|
ginv22 - (4.*(dg113*(dg122 + dg212) + dg112*(dg123 + dg213)) +
|
|
dg122*dg311 + 2.*(dg123*dg211 + dg111*dg223 + dg112*dg312) +
|
|
dg111*dg322)*ginv23 - (dg123*dg311 +
|
|
dg113*(2.*(dg123 + dg213) + dg312) + dg112*dg313 + dg111*dg323)*
|
|
ginv33)*pow2(ginv12) - ((2.*(dg113*dg123 + dg112*dg133) +
|
|
dg123*dg311 + dg113*dg312 + dg112*dg313 + dg111*dg323)*ginv22 +
|
|
(dg133*(4.*dg113 + dg311) + 2.*dg113*dg313 + dg111*dg333)*ginv23)*
|
|
pow2(ginv13) + (ddg1222 - (4.*(dg123*dg222 + dg122*dg223) +
|
|
2.*dg122*dg322)*ginv23 -
|
|
(dg123*(2.*dg223 + dg322) + dg122*dg323)*ginv33)*pow2(ginv22) +
|
|
(ddg1233 + ddg1323 - (dg133*(2.*dg233 + 3.*dg323) + 3.*dg123*dg333)*
|
|
ginv33)*pow2(ginv23) + ginv11*
|
|
(ginv23*(ddg1113 - 2.*dg113*(dg133 + dg313)*ginv33) +
|
|
ginv22*(ddg1112 - (dg112*(4.*dg123 + 2.*dg213) +
|
|
2.*(dg113*(dg122 + dg212) + dg112*dg312))*ginv23 -
|
|
(dg113*(2.*dg123 + dg312) + dg112*dg313)*ginv33) +
|
|
ginv12*(ddg1111 - dg111*(6.*dg113 + 2.*dg311)*ginv13 -
|
|
(dg113*(8.*dg112 + 2.*dg211) + dg112*dg311 +
|
|
dg111*(2.*(dg123 + dg213) + dg312))*ginv23 -
|
|
ginv22*(2.*(dg112*dg211 + dg111*(dg122 + dg212)) +
|
|
6.*pow2(dg112)) - ginv33*
|
|
(dg113*dg311 + dg111*dg313 + 2.*pow2(dg113))) -
|
|
ginv13*((dg112*(4.*dg113 + dg311) + dg111*(2.*dg123 + dg312))*
|
|
ginv22 + ginv23*(dg113*dg311 + dg111*(2.*dg133 + dg313) +
|
|
4.*pow2(dg113))) - dg111*(6.*dg112 + 2.*dg211)*pow2(ginv12) -
|
|
2.*dg112*(dg122 + dg212)*pow2(ginv22) -
|
|
(2.*(dg112*dg133 + dg113*(dg123 + dg213)) + dg113*dg312 + dg112*dg313)*
|
|
pow2(ginv23)) + ginv13*(ginv22*
|
|
(ddg1123 + ddg1312 - (dg133*(2.*dg123 + dg312) +
|
|
2.*(dg123*dg313 + dg113*dg323) + dg112*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*(dg122 + dg212) + dg123*dg213 + dg113*dg223 +
|
|
dg112*dg233) + dg122*dg313 + dg113*dg322 +
|
|
4.*(dg123*dg312 + dg112*dg323 + pow2(dg123)))) +
|
|
ginv23*(ddg1133 + ddg1313 -
|
|
ginv33*(3.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133))) -
|
|
(2.*(dg123*(dg122 + dg212) + dg112*dg223) + dg122*dg312 +
|
|
dg112*dg322)*pow2(ginv22) -
|
|
(dg133*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg313 + dg113*(dg233 + dg323) + dg112*dg333))*pow2(ginv23)\
|
|
) + ginv23*(ddg1333*ginv33 - 2.*dg133*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg1313*ginv33 + ginv13*
|
|
(ddg1113 + ddg1311 - (2.*
|
|
(dg123*dg211 + dg113*(dg122 + dg212) + dg111*dg223) +
|
|
dg122*dg311 + dg112*(8.*dg123 + 2.*dg213 + 4.*dg312) +
|
|
dg111*dg322)*ginv22 -
|
|
(dg133*(4.*dg112 + 2.*dg211) +
|
|
dg113*(8.*dg123 + 4.*(dg213 + dg312)) + 4.*dg112*dg313 +
|
|
2.*(dg123*dg311 + dg111*(dg233 + dg323)))*ginv23 -
|
|
(dg133*(2.*dg113 + dg311) + 4.*dg113*dg313 + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1123 + 2.*ddg1213 + ddg1312 -
|
|
(2.*(dg133*(dg123 + dg213) + dg113*dg233) + dg133*dg312 +
|
|
4.*(dg123*dg313 + dg113*dg323) + dg112*dg333)*ginv33) +
|
|
ginv22*(ddg1122 + 2.*ddg1212 -
|
|
(4.*(dg122*dg213 + dg113*dg222) +
|
|
6.*(dg123*(dg122 + dg212) + dg112*dg223) +
|
|
3.*(dg122*dg312 + dg112*dg322))*ginv23 -
|
|
ginv33*(dg122*dg313 + dg113*dg322 +
|
|
2.*(dg113*dg223 + dg123*(dg213 + dg312) + dg112*dg323 +
|
|
pow2(dg123)))) -
|
|
2.*(dg113*dg311 + dg111*(dg133 + dg313) + pow2(dg113))*pow2(ginv13) -
|
|
(4.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122))*pow2(ginv22) -
|
|
(4.*(dg123*dg213 + dg113*dg223) +
|
|
2.*(dg133*(dg122 + dg212) + dg123*dg312 + dg122*dg313 +
|
|
dg113*dg322 + dg112*(dg233 + dg323) + pow2(dg123)))*pow2(ginv23) \
|
|
- (dg133*dg313 + dg113*dg333)*pow2(ginv33)) +
|
|
ginv22*(ddg1323*ginv33 + ginv23*
|
|
(2.*ddg1223 + ddg1322 - (2.*(dg133*dg223 + dg123*dg233) +
|
|
dg133*dg322 + 6.*dg123*dg323 + dg122*dg333)*ginv33) -
|
|
(2.*(dg133*dg222 + dg122*dg233) + dg123*(6.*dg223 + 3.*dg322) +
|
|
3.*dg122*dg323)*pow2(ginv23) -
|
|
(dg133*dg323 + dg123*dg333)*pow2(ginv33)) -
|
|
2.*((dg111*(dg112*ginv22 + dg113*ginv23) + ginv12*pow2(dg111))*
|
|
pow2(ginv11) + (dg112*dg211 + dg111*(dg122 + dg212) + pow2(dg112))*
|
|
pow3(ginv12) + dg122*dg222*pow3(ginv22)) -
|
|
(dg133*dg322 + 2.*(dg133*dg223 + dg123*(dg233 + dg323)) + dg122*dg333)*
|
|
pow3(ginv23)
|
|
;
|
|
|
|
dGfromgdu13
|
|
=
|
|
-(((dg122*(4.*dg112 + dg211) + 2.*dg112*dg212 + dg111*dg222)*ginv23 +
|
|
(2.*(dg113*dg122 + dg112*dg123) + dg123*dg211 + dg113*dg212 +
|
|
dg112*dg213 + dg111*dg223)*ginv33 +
|
|
2.*ginv13*(dg112*dg211 + dg111*(dg122 + dg212) + pow2(dg112)))*
|
|
pow2(ginv12)) + (ddg1113 + ddg1311 -
|
|
(dg123*(2.*dg112 + dg211) + dg113*dg212 + dg111*dg223 +
|
|
dg112*(dg213 + 2.*dg312))*ginv22 -
|
|
(dg133*dg211 + 2.*(dg113*dg213 + dg123*dg311) +
|
|
4.*(dg113*(dg123 + dg312) + dg112*(dg133 + dg313)) +
|
|
dg111*(dg233 + 2.*dg323))*ginv23 -
|
|
(dg133*(6.*dg113 + 2.*dg311) + 6.*dg113*dg313 + 2.*dg111*dg333)*ginv33\
|
|
)*pow2(ginv13) - (2.*dg122*dg222*ginv23 +
|
|
(dg123*dg222 + dg122*dg223)*ginv33)*pow2(ginv22) +
|
|
(ddg1223 + ddg1322 - (3.*(dg133*dg223 + dg123*dg233) + 6.*dg123*dg323 +
|
|
2.*(dg133*dg322 + dg122*dg333))*ginv33)*pow2(ginv23) +
|
|
ddg1333*pow2(ginv33) + ginv11*
|
|
(ddg1113*ginv33 - ginv22*(2.*dg112*(dg122 + dg212)*ginv23 +
|
|
(dg113*dg212 + dg112*(2.*dg123 + dg213))*ginv33) +
|
|
ginv23*(ddg1112 - (dg113*(4.*dg123 + 2.*dg213) +
|
|
2.*(dg113*dg312 + dg112*(dg133 + dg313)))*ginv33) -
|
|
ginv12*(dg111*(6.*dg112 + 2.*dg211)*ginv13 +
|
|
(dg113*(4.*dg112 + dg211) + dg111*(2.*dg123 + dg213))*ginv33 +
|
|
ginv23*(dg112*dg211 + dg111*(2.*dg122 + dg212) + 4.*pow2(dg112))) +
|
|
ginv13*(ddg1111 - (dg113*(8.*dg112 + dg211) + 2.*dg112*dg311 +
|
|
dg111*(dg213 + 2.*(dg123 + dg312)))*ginv23 -
|
|
ginv22*(dg112*dg211 + dg111*dg212 + 2.*pow2(dg112)) -
|
|
ginv33*(2.*(dg113*dg311 + dg111*(dg133 + dg313)) + 6.*pow2(dg113))) \
|
|
- dg111*(6.*dg113 + 2.*dg311)*pow2(ginv13) -
|
|
(dg113*dg212 + dg112*dg213 +
|
|
2.*(dg113*dg122 + dg112*(dg123 + dg312)))*pow2(ginv23) -
|
|
2.*dg113*(dg133 + dg313)*pow2(ginv33)) +
|
|
ginv12*((ddg1123 + ddg1213)*ginv33 +
|
|
ginv13*(ddg1112 + ddg1211 -
|
|
(dg122*(2.*dg112 + dg211) + 4.*dg112*dg212 + dg111*dg222)*ginv22 -
|
|
(dg123*(8.*dg112 + 2.*dg211) +
|
|
4.*(dg113*(dg122 + dg212) + dg112*(dg213 + dg312)) +
|
|
2.*(dg122*dg311 + dg111*(dg223 + dg322)))*ginv23 -
|
|
(dg133*(2.*dg112 + dg211) +
|
|
dg113*(8.*dg123 + 4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg311 + dg112*dg313) + dg111*(dg233 + 2.*dg323))*
|
|
ginv33) - ginv22*((dg122*dg213 + dg113*dg222 +
|
|
2.*(dg123*(dg122 + dg212) + dg112*dg223))*ginv33 +
|
|
ginv23*(3.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122))) +
|
|
ginv23*(ddg1122 + ddg1212 -
|
|
ginv33*(dg133*(2.*dg122 + dg212) +
|
|
2.*(dg123*dg312 + dg122*dg313 + dg113*dg322) +
|
|
dg112*(dg233 + 2.*dg323) +
|
|
4.*(dg123*dg213 + dg113*dg223 + pow2(dg123)))) -
|
|
(4.*(dg112*dg113 + dg111*dg123) +
|
|
2.*(dg113*dg211 + dg112*dg311 + dg111*(dg213 + dg312)))*
|
|
pow2(ginv13) - (dg123*(4.*dg122 + 2.*dg212) +
|
|
2.*(dg113*dg222 + dg122*(dg213 + dg312) + dg112*(dg223 + dg322)))*
|
|
pow2(ginv23) - (dg133*(2.*dg123 + dg213) + 2.*dg123*dg313 +
|
|
dg113*(dg233 + 2.*dg323))*pow2(ginv33)) +
|
|
ginv22*(ddg1223*ginv33 + ginv23*
|
|
(ddg1222 - (dg133*dg222 + dg123*(6.*dg223 + 2.*dg322) +
|
|
dg122*(dg233 + 2.*dg323))*ginv33) -
|
|
(3.*(dg123*dg222 + dg122*dg223) + 2.*dg122*dg322)*pow2(ginv23) -
|
|
(dg133*dg223 + dg123*(dg233 + 2.*dg323))*pow2(ginv33)) +
|
|
ginv23*((ddg1233 + 2.*ddg1323)*ginv33 -
|
|
(dg133*(2.*dg233 + 4.*dg323) + 4.*dg123*dg333)*pow2(ginv33)) +
|
|
ginv13*((ddg1133 + 2.*ddg1313)*ginv33 +
|
|
ginv23*(ddg1123 + ddg1213 + 2.*ddg1312 -
|
|
(dg133*(6.*dg123 + 3.*dg213 + 4.*dg312) + 6.*dg123*dg313 +
|
|
dg113*(3.*dg233 + 6.*dg323) + 4.*dg112*dg333)*ginv33) +
|
|
ginv22*(ddg1212 - (dg123*(2.*dg122 + 4.*dg212) + dg113*dg222 +
|
|
dg122*(dg213 + 2.*dg312) + dg112*(4.*dg223 + 2.*dg322))*ginv23 \
|
|
- ginv33*(dg133*dg212 + dg112*(dg233 + 2.*dg323) +
|
|
2.*(dg113*dg223 + dg123*(dg213 + dg312) + pow2(dg123)))) -
|
|
(dg122*dg212 + dg112*dg222)*pow2(ginv22) -
|
|
(4.*(dg123*dg312 + dg112*dg323) +
|
|
2.*(dg133*(dg122 + dg212) + dg123*dg213 + dg112*dg233 +
|
|
dg122*dg313 + dg113*(dg223 + dg322) + pow2(dg123)))*pow2(ginv23) \
|
|
- (4.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133))*pow2(ginv33)) -
|
|
(dg133*dg222 + 2.*dg123*(dg223 + dg322) + dg122*(dg233 + 2.*dg323))*
|
|
pow3(ginv23) - 2.*((dg111*(dg112*ginv23 + dg113*ginv33) +
|
|
ginv13*pow2(dg111))*pow2(ginv11) +
|
|
(dg113*dg311 + dg111*(dg133 + dg313) + pow2(dg113))*pow3(ginv13) +
|
|
dg133*dg333*pow3(ginv33))
|
|
;
|
|
|
|
dGfromgdu21
|
|
=
|
|
(ddg1211 - (4.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*ginv13 -
|
|
2.*(dg112 + dg211)*dg212*ginv22 -
|
|
(2.*(dg113*dg212 + (dg112 + dg211)*dg213) + dg212*dg311 +
|
|
dg211*dg312)*ginv23 - (dg213*(2.*dg113 + dg311) + dg211*dg313)*
|
|
ginv33 - ginv12*(4.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211)))*
|
|
pow2(ginv11) + (ddg1222 + ddg2212 -
|
|
(4.*(dg212*(dg123 + dg213) + (dg112 + dg211)*dg223) + dg222*dg311 +
|
|
2.*(dg122*dg213 + dg113*dg222 + dg212*dg312) + dg211*dg322)*ginv13 \
|
|
- (2.*dg122 + 6.*dg212)*dg222*ginv22 -
|
|
((2.*dg122 + 4.*dg212)*dg223 +
|
|
dg222*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*dg322)*ginv23 -
|
|
(dg223*(2.*(dg123 + dg213) + dg312) + dg222*dg313 + dg213*dg322 +
|
|
dg212*dg323)*ginv33)*pow2(ginv12) +
|
|
(ddg1233 + ddg2313 - (2.*((dg123 + dg213)*dg223 + dg212*dg233) +
|
|
dg223*dg312 + dg212*dg323)*ginv22 -
|
|
(dg233*(4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg233 + dg223*(dg133 + dg313) + dg213*dg323 +
|
|
dg212*dg333))*ginv23 -
|
|
(dg233*(2.*dg133 + 3.*dg313) + 3.*dg213*dg333)*ginv33)*pow2(ginv13) +
|
|
ginv11*(ddg2313*ginv33 + ginv22*
|
|
(ddg2212 - (dg222*(2.*dg213 + dg312) + dg212*(4.*dg223 + dg322))*
|
|
ginv23 - (dg223*(2.*dg213 + dg312) + dg212*dg323)*ginv33) +
|
|
ginv23*(ddg2213 + ddg2312 -
|
|
(dg233*(2.*dg213 + dg312) + 2.*(dg223*dg313 + dg213*dg323) +
|
|
dg212*dg333)*ginv33) +
|
|
ginv13*(2.*ddg1213 + ddg2311 -
|
|
(2.*(dg112 + dg211)*dg223 +
|
|
dg212*(4.*dg213 + 2.*(dg123 + dg312)))*ginv22 -
|
|
(2.*(dg133*dg213 + dg113*dg233) + dg233*dg311 + 6.*dg213*dg313 +
|
|
dg211*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*dg212 + dg123*dg213 + dg113*dg223 +
|
|
(dg112 + dg211)*dg233) + dg223*dg311 + dg211*dg323 +
|
|
4.*(dg213*dg312 + dg212*dg313 + pow2(dg213)))) +
|
|
ginv12*(2.*ddg1212 + ddg2211 -
|
|
(6.*(dg113*dg212 + dg112*dg213) + 4.*dg111*dg223 +
|
|
3.*dg212*dg311 + dg211*(4.*dg123 + 6.*dg213 + 3.*dg312))*ginv13 \
|
|
- (2.*(dg123*dg212 + dg122*dg213 + dg113*dg222 +
|
|
(dg112 + dg211)*dg223) + dg222*dg311 +
|
|
dg212*(8.*dg213 + 4.*dg312) + dg211*dg322)*ginv23 -
|
|
ginv22*(2.*(dg122*dg212 + (dg112 + dg211)*dg222) +
|
|
6.*pow2(dg212)) - ginv33*
|
|
(dg223*dg311 + dg211*dg323 +
|
|
2.*(dg113*dg223 + dg213*(dg123 + dg312) + dg212*dg313 +
|
|
pow2(dg213)))) -
|
|
(6.*dg112*dg212 + dg211*(2.*dg122 + 6.*dg212) + 2.*dg111*dg222)*
|
|
pow2(ginv12) - (2.*(dg133*dg211 + dg111*dg233) +
|
|
dg213*(6.*dg113 + 3.*dg311) + 3.*dg211*dg313)*pow2(ginv13) -
|
|
2.*dg212*dg222*pow2(ginv22) -
|
|
(2.*(dg213*dg223 + dg212*dg233) + dg223*dg312 + dg222*dg313 +
|
|
dg213*dg322 + dg212*dg323)*pow2(ginv23) -
|
|
(dg233*dg313 + dg213*dg333)*pow2(ginv33)) +
|
|
ginv12*(ddg2323*ginv33 + ginv13*
|
|
(2.*ddg1223 + ddg2213 + ddg2312 -
|
|
(2.*((dg123 + dg213)*dg222 + dg122*dg223) + dg222*dg312 +
|
|
dg212*(8.*dg223 + dg322))*ginv22 -
|
|
(dg223*(8.*dg213 + 4.*(dg123 + dg312)) +
|
|
2.*(dg122*dg233 + dg222*(dg133 + dg313) + dg213*dg322) +
|
|
4.*dg212*(dg233 + dg323))*ginv23 -
|
|
(2.*(dg133*dg223 + (dg123 + dg213)*dg233) + dg233*dg312 +
|
|
4.*(dg223*dg313 + dg213*dg323) + dg212*dg333)*ginv33) +
|
|
ginv23*(ddg2223 + ddg2322 -
|
|
(dg233*(2.*dg223 + dg322) + 4.*dg223*dg323 + dg222*dg333)*ginv33) +
|
|
ginv22*(ddg2222 - dg222*(6.*dg223 + 2.*dg322)*ginv23 -
|
|
ginv33*(dg223*dg322 + dg222*dg323 + 2.*pow2(dg223))) -
|
|
(4.*(dg123*dg213 + dg113*dg223) +
|
|
2.*((dg112 + dg211)*dg233 + dg223*dg311 + dg213*dg312 +
|
|
dg212*(dg133 + dg313) + dg211*dg323 + pow2(dg213)))*pow2(ginv13) \
|
|
- 2.*(pow2(dg222)*pow2(ginv22) +
|
|
(dg223*dg322 + dg222*(dg233 + dg323) + pow2(dg223))*pow2(ginv23)) -
|
|
(dg233*dg323 + dg223*dg333)*pow2(ginv33)) +
|
|
ginv13*(ddg2333*ginv33 + ginv22*
|
|
(ddg2223 - 2.*dg223*(dg233 + dg323)*ginv33 -
|
|
ginv23*(dg223*dg322 + dg222*(2.*dg233 + dg323) + 4.*pow2(dg223))) +
|
|
ginv23*(ddg2233 + ddg2323 -
|
|
ginv33*(3.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233))) -
|
|
(dg233*(4.*dg223 + dg322) + 2.*dg223*dg323 + dg222*dg333)*
|
|
pow2(ginv23) - 2.*(dg222*dg223*pow2(ginv22) +
|
|
dg233*dg333*pow2(ginv33))) -
|
|
2.*(dg111*dg211*pow3(ginv11) +
|
|
(dg122*dg212 + (dg112 + dg211)*dg222 + pow2(dg212))*pow3(ginv12)) -
|
|
(dg233*dg311 + 2.*(dg113*dg233 + dg213*(dg133 + dg313)) + dg211*dg333)*
|
|
pow3(ginv13)
|
|
;
|
|
|
|
dGfromgdu22
|
|
=
|
|
-((2.*dg111*dg211*ginv12 + (dg112*dg211 + dg111*dg212)*ginv22 +
|
|
(dg113*dg211 + dg111*dg213)*ginv23)*pow2(ginv11)) +
|
|
(ddg1212 + ddg2211 - (2.*(dg123*dg211 + dg112*dg213 + dg111*dg223 +
|
|
dg212*(dg113 + dg311)) + dg211*(4.*dg213 + 2.*dg312))*ginv13 -
|
|
(2.*(dg123*dg212 + dg122*dg213 + dg113*dg222 + dg112*dg223) +
|
|
dg222*dg311 + dg212*(8.*dg213 + 2.*dg312) +
|
|
dg211*(4.*dg223 + dg322))*ginv23 -
|
|
ginv22*(4.*dg211*dg222 + 3.*(dg122*dg212 + dg112*dg222) +
|
|
6.*pow2(dg212)) - ginv33*
|
|
(dg223*(dg113 + dg311) + dg213*(dg123 + dg312) + dg212*dg313 +
|
|
dg211*dg323 + 2.*pow2(dg213)))*pow2(ginv12) -
|
|
((dg112*dg233 + dg223*(dg113 + dg311) + dg213*(dg123 + dg312) +
|
|
dg212*(dg133 + dg313) + dg211*dg323)*ginv22 +
|
|
(dg233*dg311 + 2.*(dg113*dg233 + dg213*(dg133 + dg313)) +
|
|
dg211*dg333)*ginv23)*pow2(ginv13) +
|
|
(ddg2222 - dg222*(8.*dg223 + 2.*dg322)*ginv23 -
|
|
ginv33*(dg223*dg322 + dg222*dg323 + 2.*pow2(dg223)))*pow2(ginv22) +
|
|
(ddg2233 + ddg2323 - ginv33*(3.*(dg233*dg323 + dg223*dg333) +
|
|
2.*pow2(dg233)))*pow2(ginv23) +
|
|
ginv13*(ginv22*(ddg1223 + ddg2312 -
|
|
(dg122*dg233 + dg222*(dg133 + dg313) + dg213*dg322 +
|
|
4.*(dg223*(dg123 + dg213 + dg312) + dg212*(dg233 + dg323)))*
|
|
ginv23 - (dg233*(dg123 + dg312) + dg223*(dg133 + 2.*dg313) +
|
|
2.*dg213*dg323 + dg212*dg333)*ginv33) +
|
|
ginv23*(ddg1233 + ddg2313 -
|
|
(dg233*(2.*dg133 + 3.*dg313) + 3.*dg213*dg333)*ginv33) -
|
|
((dg122 + 4.*dg212)*dg223 + dg222*(dg123 + dg312) + dg212*dg322)*
|
|
pow2(ginv22) - (dg233*(4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg233 + dg223*(dg133 + dg313) + dg213*dg323 +
|
|
dg212*dg333))*pow2(ginv23)) +
|
|
ginv11*(-(ginv13*((2.*(dg113*dg212 + dg112*dg213) + dg111*dg223 +
|
|
dg212*dg311 + dg211*(dg123 + dg312))*ginv22 +
|
|
(dg111*dg233 + dg213*(4.*dg113 + dg311) + dg211*(dg133 + dg313))*
|
|
ginv23)) + ginv12*(ddg1211 -
|
|
(3.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*ginv13 -
|
|
(6.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*ginv22 -
|
|
(4.*(dg113*dg212 + dg112*dg213) + dg111*dg223 + dg212*dg311 +
|
|
dg211*(dg123 + 4.*dg213 + dg312))*ginv23 -
|
|
(dg213*(2.*dg113 + dg311) + dg211*dg313)*ginv33) +
|
|
ginv22*(ddg1212 - (dg122*dg213 + dg113*dg222 + 2.*dg112*dg223 +
|
|
dg212*(4.*dg213 + 2.*(dg123 + dg312)))*ginv23 -
|
|
(dg113*dg223 + dg213*(dg123 + dg312) + dg212*dg313)*ginv33) +
|
|
ginv23*(ddg1213 - (dg113*dg233 + dg213*(dg133 + 2.*dg313))*ginv33) -
|
|
(3.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211))*pow2(ginv12) -
|
|
(dg122*dg212 + dg112*dg222 + 2.*pow2(dg212))*pow2(ginv22) -
|
|
(dg113*dg223 + dg112*dg233 + dg213*(dg123 + dg312) +
|
|
dg212*(dg133 + dg313) + 2.*pow2(dg213))*pow2(ginv23)) +
|
|
ginv23*(ddg2333*ginv33 - 2.*dg233*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg2313*ginv33 + ginv22*
|
|
(ddg1222 + 2.*ddg2212 - ((3.*dg122 + 12.*dg212)*dg223 +
|
|
dg222*(8.*dg213 + 3.*(dg123 + dg312)) + 3.*dg212*dg322)*ginv23 \
|
|
- (dg223*(4.*dg213 + 2.*(dg123 + dg312)) + dg222*dg313 + dg213*dg322 +
|
|
2.*dg212*dg323)*ginv33) +
|
|
ginv23*(ddg1223 + 2.*ddg2213 + ddg2312 -
|
|
(dg233*(dg123 + 4.*dg213 + dg312) + dg223*(dg133 + 4.*dg313) +
|
|
4.*dg213*dg323 + dg212*dg333)*ginv33) +
|
|
ginv13*(ddg1213 + ddg2311 -
|
|
(dg122*dg213 + dg222*(dg113 + dg311) +
|
|
4.*((dg112 + dg211)*dg223 + dg212*(dg123 + dg213 + dg312)) +
|
|
dg211*dg322)*ginv22 -
|
|
(dg233*(dg113 + dg311) + dg213*(dg133 + 4.*dg313) + dg211*dg333)*
|
|
ginv33 - ginv23*(2.*(dg133*dg212 + dg112*dg233 + dg223*dg311 +
|
|
dg211*dg323) + 4.*
|
|
(dg113*dg223 + dg211*dg233 + dg213*(dg123 + dg312) +
|
|
dg212*dg313 + pow2(dg213)))) -
|
|
(dg111*dg233 + 2.*dg213*(dg113 + dg311) + dg211*(dg133 + 2.*dg313))*
|
|
pow2(ginv13) - (2.*dg122 + 8.*dg212)*dg222*pow2(ginv22) -
|
|
((dg122 + 4.*dg212)*dg233 + dg223*(8.*dg213 + 2.*(dg123 + dg312)) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*(dg213*dg322 + dg212*dg323))*
|
|
pow2(ginv23) - (dg233*dg313 + dg213*dg333)*pow2(ginv33)) +
|
|
ginv22*(ddg2323*ginv33 + ginv23*
|
|
(2.*ddg2223 + ddg2322 - (dg233*(4.*dg223 + dg322) +
|
|
6.*dg223*dg323 + dg222*dg333)*ginv33) -
|
|
(3.*dg223*dg322 + dg222*(4.*dg233 + 3.*dg323) + 6.*pow2(dg223))*
|
|
pow2(ginv23) - (dg233*dg323 + dg223*dg333)*pow2(ginv33)) -
|
|
(2.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*pow3(ginv12) -
|
|
2.*pow2(dg222)*pow3(ginv22) -
|
|
(dg233*(4.*dg223 + dg322) + 2.*dg223*dg323 + dg222*dg333)*pow3(ginv23)
|
|
;
|
|
|
|
dGfromgdu23
|
|
=
|
|
-((2.*dg111*dg211*ginv13 + (dg112*dg211 + dg111*dg212)*ginv23 +
|
|
(dg113*dg211 + dg111*dg213)*ginv33)*pow2(ginv11)) -
|
|
((2.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*ginv13 +
|
|
(dg122*dg213 + dg212*(dg123 + 2.*dg213) + dg113*dg222 +
|
|
(dg112 + 2.*dg211)*dg223)*ginv33 +
|
|
2.*ginv23*(dg122*dg212 + (dg112 + dg211)*dg222 + pow2(dg212)))*
|
|
pow2(ginv12) + (ddg1213 + ddg2311 -
|
|
((dg112 + 2.*dg211)*dg223 + dg212*(dg123 + 2.*(dg213 + dg312)))*
|
|
ginv22 - (3.*(dg133*dg213 + dg113*dg233) + 6.*dg213*dg313 +
|
|
2.*(dg233*dg311 + dg211*dg333))*ginv33 -
|
|
ginv23*(4.*(dg213*dg312 + dg212*dg313) +
|
|
2.*(dg133*dg212 + dg123*dg213 + (dg112 + dg211)*dg233 +
|
|
dg223*(dg113 + dg311) + dg211*dg323 + pow2(dg213))))*pow2(ginv13) \
|
|
+ (ddg2223 + ddg2322 - (dg233*(6.*dg223 + 2.*dg322) + 6.*dg223*dg323 +
|
|
2.*dg222*dg333)*ginv33)*pow2(ginv23) + ddg2333*pow2(ginv33) +
|
|
ginv11*(ddg1213*ginv33 + ginv13*
|
|
(ddg1211 - 2.*(dg112 + dg211)*dg212*ginv22 -
|
|
(4.*(dg113*dg212 + dg112*dg213) + dg111*dg223 + 2.*dg212*dg311 +
|
|
dg211*(dg123 + 2.*(dg213 + dg312)))*ginv23 -
|
|
(dg111*dg233 + dg213*(6.*dg113 + 2.*dg311) +
|
|
dg211*(dg133 + 2.*dg313))*ginv33) -
|
|
ginv12*((4.*dg112*dg212 + dg211*(dg122 + 2.*dg212) + dg111*dg222)*
|
|
ginv23 + (dg211*(dg123 + 2.*dg213) +
|
|
2.*(dg113*dg212 + dg112*dg213) + dg111*dg223)*ginv33 +
|
|
ginv13*(3.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211))) -
|
|
ginv22*((dg212*(dg123 + 2.*dg213) + dg112*dg223)*ginv33 +
|
|
ginv23*(dg122*dg212 + dg112*dg222 + 2.*pow2(dg212))) +
|
|
ginv23*(ddg1212 - ginv33*(dg112*dg233 + dg212*(dg133 + 2.*dg313) +
|
|
2.*(dg113*dg223 + dg213*(dg123 + dg312) + pow2(dg213)))) -
|
|
(3.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*pow2(ginv13) -
|
|
(dg122*dg213 + dg113*dg222 + dg112*dg223 +
|
|
dg212*(dg123 + 2.*(dg213 + dg312)))*pow2(ginv23) -
|
|
(dg113*dg233 + dg213*(dg133 + 2.*dg313))*pow2(ginv33)) +
|
|
ginv22*(ddg2223*ginv33 + ginv23*
|
|
(ddg2222 - ginv33*(2.*(dg223*dg322 + dg222*(dg233 + dg323)) +
|
|
6.*pow2(dg223))) - dg222*(6.*dg223 + 2.*dg322)*pow2(ginv23) -
|
|
2.*dg223*(dg233 + dg323)*pow2(ginv33)) +
|
|
ginv12*((ddg1223 + ddg2213)*ginv33 -
|
|
ginv22*((2.*dg122 + 6.*dg212)*dg222*ginv23 +
|
|
((dg123 + 2.*dg213)*dg222 + (dg122 + 4.*dg212)*dg223)*ginv33) +
|
|
ginv23*(ddg1222 + ddg2212 -
|
|
((dg122 + 2.*dg212)*dg233 +
|
|
dg223*(4.*dg123 + 8.*dg213 + 2.*dg312) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*(dg213*dg322 + dg212*dg323))*
|
|
ginv33) + ginv13*(ddg1212 + ddg2211 -
|
|
(4.*(dg112 + dg211)*dg223 +
|
|
dg212*(8.*dg213 + 4.*(dg123 + dg312)) +
|
|
2.*(dg122*dg213 + dg222*(dg113 + dg311) + dg211*dg322))*ginv23 \
|
|
- ginv22*(dg122*dg212 + (dg112 + 2.*dg211)*dg222 + 4.*pow2(dg212)) -
|
|
ginv33*((dg112 + 2.*dg211)*dg233 + dg212*(dg133 + 2.*dg313) +
|
|
2.*(dg223*dg311 + dg213*dg312 + dg211*dg323) +
|
|
4.*(dg123*dg213 + dg113*dg223 + pow2(dg213)))) -
|
|
(2.*(dg123*dg211 + dg112*dg213 + dg111*dg223 +
|
|
dg212*(dg113 + dg311)) + dg211*(4.*dg213 + 2.*dg312))*
|
|
pow2(ginv13) - ((2.*dg122 + 4.*dg212)*dg223 +
|
|
dg222*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*dg322)*
|
|
pow2(ginv23) - ((dg123 + 2.*dg213)*dg233 +
|
|
dg223*(dg133 + 2.*dg313) + 2.*dg213*dg323)*pow2(ginv33)) +
|
|
ginv13*((ddg1233 + 2.*ddg2313)*ginv33 +
|
|
ginv22*(ddg2212 - ((dg122 + 8.*dg212)*dg223 +
|
|
dg222*(dg123 + 2.*(dg213 + dg312)) + 2.*dg212*dg322)*ginv23 -
|
|
(dg223*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*(dg233 + dg323))*
|
|
ginv33) + ginv23*(ddg1223 + ddg2213 + 2.*ddg2312 -
|
|
(3.*(dg133*dg223 + dg123*dg233) + dg233*(6.*dg213 + 4.*dg312) +
|
|
6.*(dg223*dg313 + dg213*dg323) + 4.*dg212*dg333)*ginv33) -
|
|
2.*dg212*dg222*pow2(ginv22) -
|
|
((dg122 + 4.*dg212)*dg233 + dg223*(2.*dg123 + 4.*(dg213 + dg312)) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*dg213*dg322 + 4.*dg212*dg323)*
|
|
pow2(ginv23) - (dg233*(2.*dg133 + 4.*dg313) + 4.*dg213*dg333)*
|
|
pow2(ginv33)) + ginv23*((ddg2233 + 2.*ddg2323)*ginv33 -
|
|
(4.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233))*pow2(ginv33)) -
|
|
(dg111*dg233 + 2.*dg213*(dg113 + dg311) + dg211*(dg133 + 2.*dg313))*
|
|
pow3(ginv13) - 2.*((dg222*dg223*ginv33 + ginv23*pow2(dg222))*
|
|
pow2(ginv22) + (dg223*dg322 + dg222*(dg233 + dg323) + pow2(dg223))*
|
|
pow3(ginv23) + dg233*dg333*pow3(ginv33))
|
|
;
|
|
|
|
dGfromgdu31
|
|
=
|
|
(ddg1311 - ((4.*dg112 + 2.*dg211)*dg311 + 4.*dg111*dg312)*ginv12 -
|
|
(dg212*dg311 + (2.*dg112 + dg211)*dg312)*ginv22 -
|
|
(dg311*(dg213 + 2.*dg312) + dg211*dg313 +
|
|
2.*(dg113*dg312 + dg112*dg313))*ginv23 -
|
|
2.*(dg113 + dg311)*dg313*ginv33 -
|
|
ginv13*(4.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311)))*pow2(ginv11) \
|
|
+ (ddg1322 + ddg2312 - (2.*dg122*dg322 + 3.*(dg222*dg312 + dg212*dg322))*
|
|
ginv22 - ((2.*dg213 + 4.*dg312)*dg322 +
|
|
2.*(dg223*dg312 + dg222*dg313 + dg123*dg322 +
|
|
(dg122 + dg212)*dg323))*ginv23 -
|
|
(dg313*(dg223 + 2.*dg322) + (dg213 + 2.*(dg123 + dg312))*dg323)*
|
|
ginv33 - ginv13*(4.*(dg123*dg312 + dg112*dg323) +
|
|
2.*(dg213*dg312 + (dg122 + dg212)*dg313 + dg113*dg322 +
|
|
dg311*(dg223 + dg322) + dg211*dg323 + pow2(dg312))))*pow2(ginv12) \
|
|
+ (ddg1333 + ddg3313 - (dg233*dg312 + dg223*dg313 +
|
|
(dg213 + 2.*(dg123 + dg312))*dg323 + dg212*dg333)*ginv22 -
|
|
(2.*(dg233*dg313 + dg133*dg323 + (dg123 + dg213)*dg333) +
|
|
4.*(dg313*dg323 + dg312*dg333))*ginv23 -
|
|
(2.*dg133 + 6.*dg313)*dg333*ginv33)*pow2(ginv13) +
|
|
ginv11*(ddg3313*ginv33 + ginv22*
|
|
(ddg2312 - (dg222*dg313 + dg213*dg322 +
|
|
2.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 -
|
|
(dg223*dg313 + (dg213 + 2.*dg312)*dg323)*ginv33) +
|
|
ginv23*(ddg2313 + ddg3312 -
|
|
(dg313*(dg233 + 4.*dg323) + (dg213 + 2.*dg312)*dg333)*ginv33) +
|
|
ginv12*(2.*ddg1312 + ddg2311 -
|
|
(dg311*(4.*dg123 + 3.*dg213 + 6.*dg312) + 3.*dg211*dg313 +
|
|
6.*(dg113*dg312 + dg112*dg313) + 4.*dg111*dg323)*ginv13 -
|
|
(dg222*dg311 + (2.*dg122 + 6.*dg212)*dg312 +
|
|
(2.*dg112 + dg211)*dg322)*ginv22 -
|
|
(4.*dg312*dg313 + 2.*((dg123 + dg213)*dg313 +
|
|
(dg113 + dg311)*dg323))*ginv33 -
|
|
ginv23*((2.*dg123 + 4.*dg213)*dg312 + dg311*(dg223 + 2.*dg322) +
|
|
dg211*dg323 + 2.*(dg122*dg313 + dg113*dg322 + dg112*dg323) +
|
|
4.*(dg212*dg313 + pow2(dg312)))) +
|
|
ginv13*(2.*ddg1313 + ddg3311 -
|
|
((4.*dg213 + 8.*dg312)*dg313 + dg311*(dg233 + 2.*dg323) +
|
|
dg211*dg333 + 2.*(dg133*dg312 + dg123*dg313 + dg113*dg323 +
|
|
dg112*dg333))*ginv23 -
|
|
ginv22*(dg223*dg311 + dg211*dg323 +
|
|
2.*((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323 +
|
|
pow2(dg312))) - ginv33*
|
|
(2.*(dg133*dg313 + (dg113 + dg311)*dg333) + 6.*pow2(dg313))) -
|
|
((2.*dg122 + 3.*dg212)*dg311 + (6.*dg112 + 3.*dg211)*dg312 +
|
|
2.*dg111*dg322)*pow2(ginv12) -
|
|
(6.*dg113*dg313 + dg311*(2.*dg133 + 6.*dg313) + 2.*dg111*dg333)*
|
|
pow2(ginv13) - (dg222*dg312 + dg212*dg322)*pow2(ginv22) -
|
|
(dg313*(dg223 + 2.*dg322) + dg213*dg323 + dg312*(dg233 + 2.*dg323) +
|
|
dg212*dg333)*pow2(ginv23) - 2.*dg313*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg3323*ginv33 + ginv13*
|
|
(2.*ddg1323 + ddg2313 + ddg3312 -
|
|
(dg222*dg313 + (2.*dg123 + dg213)*dg322 +
|
|
dg312*(4.*dg223 + 2.*dg322) + (2.*dg122 + 4.*dg212)*dg323)*
|
|
ginv22 - ((4.*dg213 + 8.*dg312)*dg323 +
|
|
4.*(dg313*(dg223 + dg322) + dg123*dg323) +
|
|
2.*(dg233*dg312 + dg133*dg322 + (dg122 + dg212)*dg333))*ginv23 \
|
|
- (dg313*(dg233 + 8.*dg323) + (dg213 + 2.*dg312)*dg333 +
|
|
2.*(dg133*dg323 + dg123*dg333))*ginv33) +
|
|
ginv22*(ddg2322 - 2.*(dg223 + dg322)*dg323*ginv33 -
|
|
ginv23*(3.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322))) +
|
|
ginv23*(ddg2323 + ddg3322 -
|
|
ginv33*(dg233*dg323 + (dg223 + 2.*dg322)*dg333 + 4.*pow2(dg323))) -
|
|
(dg311*(dg233 + 4.*dg323) +
|
|
4.*((dg123 + dg312)*dg313 + dg113*dg323) + dg211*dg333 +
|
|
2.*(dg133*dg312 + dg213*dg313 + dg112*dg333))*pow2(ginv13) -
|
|
(2.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*
|
|
pow2(ginv23) - 2.*(dg222*dg322*pow2(ginv22) +
|
|
dg323*dg333*pow2(ginv33))) +
|
|
ginv13*(ddg3333*ginv33 + ginv23*
|
|
(ddg2333 + ddg3323 - (2.*dg233 + 6.*dg323)*dg333*ginv33) +
|
|
ginv22*(ddg2323 - (4.*dg223*dg323 + dg322*(dg233 + 2.*dg323) +
|
|
dg222*dg333)*ginv23 -
|
|
ginv33*(dg233*dg323 + dg223*dg333 + 2.*pow2(dg323))) -
|
|
(dg223*dg322 + dg222*dg323)*pow2(ginv22) -
|
|
2.*((dg233*dg323 + (dg223 + dg322)*dg333 + pow2(dg323))*pow2(ginv23) +
|
|
pow2(dg333)*pow2(ginv33))) -
|
|
(dg222*dg311 + dg211*dg322 + 2.*((dg122 + dg212)*dg312 + dg112*dg322))*
|
|
pow3(ginv12) - 2.*(dg111*dg311*pow3(ginv11) +
|
|
(dg133*dg313 + (dg113 + dg311)*dg333 + pow2(dg313))*pow3(ginv13))
|
|
;
|
|
|
|
dGfromgdu32
|
|
=
|
|
-((2.*dg111*dg311*ginv12 + (dg112*dg311 + dg111*dg312)*ginv22 +
|
|
(dg113*dg311 + dg111*dg313)*ginv23)*pow2(ginv11)) +
|
|
(ddg1312 + ddg2311 - (4.*dg311*dg312 +
|
|
2.*((dg123 + dg213)*dg311 + dg113*dg312 +
|
|
(dg112 + dg211)*dg313 + dg111*dg323))*ginv13 -
|
|
((3.*dg122 + 6.*dg212)*dg312 + 3.*dg112*dg322 +
|
|
2.*(dg222*dg311 + dg211*dg322))*ginv22 -
|
|
((dg123 + 2.*(dg213 + dg312))*dg313 + (dg113 + 2.*dg311)*dg323)*
|
|
ginv33 - ginv23*(4.*(dg213*dg312 + dg212*dg313) +
|
|
2.*(dg123*dg312 + dg122*dg313 + dg113*dg322 +
|
|
dg311*(dg223 + dg322) + (dg112 + dg211)*dg323 + pow2(dg312))))*
|
|
pow2(ginv12) - ((dg123*dg313 + dg312*(dg133 + 2.*dg313) +
|
|
(dg113 + 2.*dg311)*dg323 + dg112*dg333)*ginv22 +
|
|
2.*ginv23*(dg133*dg313 + (dg113 + dg311)*dg333 + pow2(dg313)))*
|
|
pow2(ginv13) + (ddg2322 - 2.*(dg223 + dg322)*dg323*ginv33 -
|
|
ginv23*(4.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322)))*pow2(ginv22) \
|
|
+ (ddg2333 + ddg3323 - (2.*dg233 + 6.*dg323)*dg333*ginv33)*pow2(ginv23) +
|
|
ginv11*(-(ginv13*((dg311*(dg123 + 2.*dg312) +
|
|
2.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv22 +
|
|
(4.*dg113*dg313 + dg311*(dg133 + 2.*dg313) + dg111*dg333)*ginv23)\
|
|
) + ginv12*(ddg1311 - ((dg122 + 2.*dg212)*dg311 +
|
|
(6.*dg112 + 2.*dg211)*dg312 + dg111*dg322)*ginv22 -
|
|
(dg311*(dg123 + 2.*(dg213 + dg312)) + 2.*dg211*dg313 +
|
|
4.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv23 -
|
|
2.*(dg113 + dg311)*dg313*ginv33 -
|
|
ginv13*(3.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311))) +
|
|
ginv22*(ddg1312 - ((dg123 + 2.*dg312)*dg313 + dg113*dg323)*ginv33 -
|
|
ginv23*(dg122*dg313 + dg113*dg322 +
|
|
2.*((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323 +
|
|
pow2(dg312)))) +
|
|
ginv23*(ddg1313 - ginv33*
|
|
(dg133*dg313 + dg113*dg333 + 2.*pow2(dg313))) -
|
|
((3.*dg112 + 2.*dg211)*dg311 + 3.*dg111*dg312)*pow2(ginv12) -
|
|
((dg122 + 2.*dg212)*dg312 + dg112*dg322)*pow2(ginv22) -
|
|
(dg133*dg312 + (dg123 + 2.*(dg213 + dg312))*dg313 + dg113*dg323 +
|
|
dg112*dg333)*pow2(ginv23)) +
|
|
ginv13*(ginv23*(ddg1333 + ddg3313 - (2.*dg133 + 6.*dg313)*dg333*ginv33) +
|
|
ginv22*(ddg1323 + ddg3312 -
|
|
(dg133*dg322 + (4.*dg123 + 2.*dg213 + 8.*dg312)*dg323 +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg313*(dg223 + dg322) +
|
|
dg212*dg333))*ginv23 -
|
|
((dg133 + 4.*dg313)*dg323 + (dg123 + 2.*dg312)*dg333)*ginv33) -
|
|
(dg123*dg322 + dg122*dg323 +
|
|
2.*(dg312*(dg223 + dg322) + dg212*dg323))*pow2(ginv22) -
|
|
(2.*(dg233*dg313 + dg133*dg323 + (dg123 + dg213)*dg333) +
|
|
4.*(dg313*dg323 + dg312*dg333))*pow2(ginv23)) +
|
|
ginv12*(ddg3313*ginv33 + ginv22*
|
|
(ddg1322 + 2.*ddg2312 - (4.*(dg222*dg313 + dg213*dg322) +
|
|
3.*(dg123*dg322 + dg122*dg323) +
|
|
6.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 -
|
|
((2.*dg213 + 4.*dg312)*dg323 +
|
|
2.*(dg313*(dg223 + dg322) + dg123*dg323))*ginv33) +
|
|
ginv23*(ddg1323 + 2.*ddg2313 + ddg3312 -
|
|
(dg133*dg323 + dg313*(2.*dg233 + 8.*dg323) +
|
|
(dg123 + 2.*(dg213 + dg312))*dg333)*ginv33) +
|
|
ginv13*(ddg1313 + ddg3311 -
|
|
(8.*dg312*dg313 + 4.*
|
|
((dg123 + dg213)*dg313 + (dg113 + dg311)*dg323) +
|
|
2.*(dg233*dg311 + dg133*dg312 + (dg112 + dg211)*dg333))*ginv23 \
|
|
- ginv22*(dg122*dg313 + dg113*dg322 +
|
|
2.*(dg213*dg312 + dg212*dg313 + dg311*(dg223 + dg322) +
|
|
dg211*dg323) + 4.*(dg123*dg312 + dg112*dg323 + pow2(dg312))) \
|
|
- ginv33*(dg133*dg313 + (dg113 + 2.*dg311)*dg333 + 4.*pow2(dg313))) -
|
|
(2.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*
|
|
pow2(ginv13) - (2.*dg122*dg322 + 4.*(dg222*dg312 + dg212*dg322))*
|
|
pow2(ginv22) - (dg133*dg322 +
|
|
4.*(dg313*(dg223 + dg322) + (dg213 + dg312)*dg323) +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg123*dg323 + dg212*dg333))*
|
|
pow2(ginv23) - 2.*dg313*dg333*pow2(ginv33)) +
|
|
ginv22*(ddg3323*ginv33 + ginv23*
|
|
(2.*ddg2323 + ddg3322 - ginv33*
|
|
(2.*(dg233*dg323 + (dg223 + dg322)*dg333) + 6.*pow2(dg323))) -
|
|
(6.*dg223*dg323 + dg322*(2.*dg233 + 6.*dg323) + 2.*dg222*dg333)*
|
|
pow2(ginv23) - 2.*dg323*dg333*pow2(ginv33)) +
|
|
ginv23*(ddg3333*ginv33 - 2.*pow2(dg333)*pow2(ginv33)) -
|
|
((dg122 + 2.*dg212)*dg311 + 2.*(dg112 + dg211)*dg312 + dg111*dg322)*
|
|
pow3(ginv12) - 2.*(dg222*dg322*pow3(ginv22) +
|
|
(dg233*dg323 + (dg223 + dg322)*dg333 + pow2(dg323))*pow3(ginv23))
|
|
;
|
|
|
|
dGfromgdu33
|
|
=
|
|
-((2.*dg111*dg311*ginv13 + (dg112*dg311 + dg111*dg312)*ginv23 +
|
|
(dg113*dg311 + dg111*dg313)*ginv33)*pow2(ginv11)) -
|
|
(((dg122 + 2.*dg212)*dg311 + 2.*(dg112 + dg211)*dg312 + dg111*dg322)*
|
|
ginv13 + (dg222*dg311 + dg211*dg322 +
|
|
2.*((dg122 + dg212)*dg312 + dg112*dg322))*ginv23 +
|
|
(dg223*dg311 + (dg123 + dg213)*dg312 + (dg122 + dg212)*dg313 +
|
|
dg113*dg322 + (dg112 + dg211)*dg323)*ginv33)*pow2(ginv12) +
|
|
(ddg1313 + ddg3311 - ((2.*dg213 + 8.*dg312)*dg313 +
|
|
dg311*(dg233 + 4.*dg323) + dg211*dg333 +
|
|
2.*(dg133*dg312 + dg123*dg313 + dg113*dg323 + dg112*dg333))*ginv23 \
|
|
- ginv22*(dg223*dg311 + (dg123 + dg213)*dg312 + dg212*dg313 +
|
|
(dg112 + dg211)*dg323 + 2.*pow2(dg312)) -
|
|
ginv33*(4.*dg311*dg333 + 3.*(dg133*dg313 + dg113*dg333) +
|
|
6.*pow2(dg313)))*pow2(ginv13) -
|
|
(2.*dg222*dg322*ginv23 + (dg223*dg322 + dg222*dg323)*ginv33)*
|
|
pow2(ginv22) + (ddg2323 + ddg3322 -
|
|
ginv33*(4.*dg322*dg333 + 3.*(dg233*dg323 + dg223*dg333) +
|
|
6.*pow2(dg323)))*pow2(ginv23) + ddg3333*pow2(ginv33) +
|
|
ginv13*((ddg1333 + 2.*ddg3313)*ginv33 +
|
|
ginv22*(ddg2312 - (dg222*dg313 + (dg123 + dg213)*dg322 +
|
|
dg122*dg323 + 4.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 \
|
|
- (dg312*(dg233 + 4.*dg323) + 2.*(dg223*dg313 + (dg123 + dg213)*dg323) +
|
|
dg212*dg333)*ginv33) +
|
|
ginv23*(ddg1323 + ddg2313 + 2.*ddg3312 -
|
|
(12.*dg313*dg323 + (3.*dg213 + 8.*dg312)*dg333 +
|
|
3.*(dg233*dg313 + dg133*dg323 + dg123*dg333))*ginv33) -
|
|
(dg222*dg312 + dg212*dg322)*pow2(ginv22) -
|
|
((dg133 + 4.*dg313)*dg322 + (2.*dg213 + 8.*dg312)*dg323 +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg223*dg313 + dg123*dg323 +
|
|
dg212*dg333))*pow2(ginv23) -
|
|
(2.*dg133 + 8.*dg313)*dg333*pow2(ginv33)) +
|
|
ginv23*((ddg2333 + 2.*ddg3323)*ginv33 -
|
|
(2.*dg233 + 8.*dg323)*dg333*pow2(ginv33)) +
|
|
ginv12*((ddg1323 + ddg2313)*ginv33 -
|
|
ginv22*((2.*dg122*dg322 + 3.*(dg222*dg312 + dg212*dg322))*ginv23 +
|
|
(dg222*dg313 + (dg123 + dg213)*dg322 + dg122*dg323 +
|
|
2.*(dg223*dg312 + dg212*dg323))*ginv33) +
|
|
ginv23*(ddg1322 + ddg2312 -
|
|
(dg233*dg312 + dg133*dg322 +
|
|
4.*(dg313*(dg223 + dg322) + (dg123 + dg213 + dg312)*dg323) +
|
|
(dg122 + dg212)*dg333)*ginv33) +
|
|
ginv13*(ddg1312 + ddg2311 -
|
|
(dg222*dg311 + (dg122 + 4.*dg212)*dg312 + (dg112 + dg211)*dg322)*
|
|
ginv22 - (dg133*dg312 + dg311*(dg233 + 4.*dg323) +
|
|
4.*((dg123 + dg213 + dg312)*dg313 + dg113*dg323) +
|
|
(dg112 + dg211)*dg333)*ginv33 -
|
|
ginv23*(2.*(dg223*dg311 + dg122*dg313 + dg113*dg322 +
|
|
dg211*dg323) + 4.*
|
|
((dg123 + dg213)*dg312 + dg212*dg313 + dg311*dg322 +
|
|
dg112*dg323 + pow2(dg312)))) -
|
|
(4.*dg311*dg312 + 2.*((dg123 + dg213)*dg311 + dg113*dg312 +
|
|
(dg112 + dg211)*dg313 + dg111*dg323))*pow2(ginv13) -
|
|
((2.*dg213 + 4.*dg312)*dg322 +
|
|
2.*(dg223*dg312 + dg222*dg313 + dg123*dg322 +
|
|
(dg122 + dg212)*dg323))*pow2(ginv23) -
|
|
(dg133*dg323 + dg313*(dg233 + 4.*dg323) + (dg123 + dg213)*dg333)*
|
|
pow2(ginv33)) + ginv11*(ddg1313*ginv33 -
|
|
ginv12*(((3.*dg112 + 2.*dg211)*dg311 + 3.*dg111*dg312)*ginv13 +
|
|
((dg122 + dg212)*dg311 + (4.*dg112 + dg211)*dg312 + dg111*dg322)*
|
|
ginv23 + ((dg123 + dg213)*dg311 + dg211*dg313 +
|
|
2.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv33) -
|
|
ginv22*(((dg122 + 2.*dg212)*dg312 + dg112*dg322)*ginv23 +
|
|
((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323)*ginv33) +
|
|
ginv13*(ddg1311 - (dg212*dg311 + (2.*dg112 + dg211)*dg312)*ginv22 -
|
|
((dg123 + dg213)*dg311 + 4.*(dg113 + dg311)*dg312 +
|
|
(4.*dg112 + dg211)*dg313 + dg111*dg323)*ginv23 -
|
|
(6.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1312 - (dg312*(dg133 + 4.*dg313) +
|
|
2.*((dg123 + dg213)*dg313 + dg113*dg323) + dg112*dg333)*ginv33) \
|
|
- (3.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311))*pow2(ginv13) -
|
|
((dg123 + dg213)*dg312 + (dg122 + dg212)*dg313 + dg113*dg322 +
|
|
dg112*dg323 + 2.*pow2(dg312))*pow2(ginv23) -
|
|
(dg133*dg313 + dg113*dg333 + 2.*pow2(dg313))*pow2(ginv33)) +
|
|
ginv22*(ddg2323*ginv33 + ginv23*
|
|
(ddg2322 - (6.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*
|
|
ginv33) - (3.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322))*
|
|
pow2(ginv23) - (dg233*dg323 + dg223*dg333 + 2.*pow2(dg323))*
|
|
pow2(ginv33)) - (2.*dg113*dg313 + dg311*(dg133 + 4.*dg313) +
|
|
dg111*dg333)*pow3(ginv13) -
|
|
(2.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*pow3(ginv23) -
|
|
2.*pow2(dg333)*pow3(ginv33)
|
|
;
|
|
|
|
R11
|
|
=
|
|
gammado111*Gfromg1 + gammado112*Gfromg2 + gammado113*Gfromg3 +
|
|
(-0.5*ddg1111 + 3.*gamma111*gammado111 +
|
|
2.*(gamma211*gammado112 + gamma311*gammado113) +
|
|
gamma211*gammado211 + gamma311*gammado311)*ginv11 +
|
|
(-ddg1211 + 3.*(gamma112*gammado111 + gamma111*gammado112) +
|
|
2.*(gamma212*gammado112 + gamma312*gammado113 +
|
|
gamma211*gammado122 + gamma311*gammado123) + gamma212*gammado211 +
|
|
gamma211*gammado212 + gamma312*gammado311 + gamma311*gammado312)*ginv12 \
|
|
+ (-ddg1311 + 3.*(gamma113*gammado111 + gamma111*gammado113) +
|
|
2.*(gamma213*gammado112 + gamma313*gammado113 +
|
|
gamma211*gammado123 + gamma311*gammado133) + gamma213*gammado211 +
|
|
gamma211*gammado213 + gamma313*gammado311 + gamma311*gammado313)*ginv13 \
|
|
+ (-0.5*ddg2211 + 3.*gamma112*gammado112 +
|
|
2.*(gamma212*gammado122 + gamma312*gammado123) +
|
|
gamma212*gammado212 + gamma312*gammado312)*ginv22 +
|
|
(-ddg2311 + 3.*(gamma113*gammado112 + gamma112*gammado113) +
|
|
2.*(gamma213*gammado122 + (gamma212 + gamma313)*gammado123 +
|
|
gamma312*gammado133) + gamma213*gammado212 + gamma212*gammado213 +
|
|
gamma313*gammado312 + gamma312*gammado313)*ginv23 +
|
|
(-0.5*ddg3311 + 3.*gamma113*gammado113 +
|
|
2.*(gamma213*gammado123 + gamma313*gammado133) +
|
|
gamma213*gammado213 + gamma313*gammado313)*ginv33 + dG11*g11 +
|
|
dG12*g12 + dG13*g13
|
|
;
|
|
|
|
R12
|
|
=
|
|
(-0.5*ddg1112 + gamma112*gammado111 + (gamma111 + gamma212)*gammado112 +
|
|
gamma312*gammado113 + gamma111*gammado211 + 2.*gamma211*gammado212 +
|
|
gamma311*(gammado213 + gammado312))*ginv11 +
|
|
(-ddg1212 + gamma122*gammado111 + (2.*gamma112 + gamma222)*gammado112 +
|
|
gamma322*gammado113 + (gamma111 + gamma212)*gammado122 +
|
|
gamma112*gammado211 + (gamma111 + 2.*gamma212)*gammado212 +
|
|
2.*gamma211*gammado222 + gamma312*
|
|
(gammado123 + gammado213 + gammado312) +
|
|
gamma311*(gammado223 + gammado322))*ginv12 +
|
|
(-ddg1312 + gamma123*gammado111 + (gamma113 + gamma223)*gammado112 +
|
|
(gamma112 + gamma323)*gammado113 + (gamma111 + gamma212)*gammado123 +
|
|
gamma312*gammado133 + gamma113*gammado211 +
|
|
(gamma111 + gamma313)*gammado213 +
|
|
2.*(gamma213*gammado212 + gamma211*gammado223) +
|
|
gamma313*gammado312 + gamma311*(gammado233 + gammado323))*ginv13 +
|
|
(-0.5*ddg2212 + gamma122*gammado112 + (gamma112 + gamma222)*gammado122 +
|
|
gamma322*gammado123 + gamma112*gammado212 + 2.*gamma212*gammado222 +
|
|
gamma312*(gammado223 + gammado322))*ginv22 +
|
|
(-ddg2312 + gamma123*gammado112 + gamma122*gammado113 +
|
|
(gamma113 + gamma223)*gammado122 +
|
|
(gamma112 + gamma222 + gamma323)*gammado123 + gamma322*gammado133 +
|
|
gamma113*gammado212 + gamma112*gammado213 +
|
|
2.*(gamma213*gammado222 + gamma212*gammado223) +
|
|
gamma313*(gammado223 + gammado322) +
|
|
gamma312*(gammado233 + gammado323))*ginv23 +
|
|
(-0.5*ddg3312 + gamma123*gammado113 + (gamma113 + gamma223)*gammado123 +
|
|
gamma323*gammado133 + gamma113*gammado213 + 2.*gamma213*gammado223 +
|
|
gamma313*(gammado233 + gammado323))*ginv33 +
|
|
0.5*((gammado112 + gammado211)*Gfromg1 +
|
|
(gammado122 + gammado212)*Gfromg2 + (gammado123 + gammado213)*Gfromg3 +
|
|
dG21*g11 + (dG11 + dG22)*g12 + dG23*g13 +
|
|
dG12*g22 + dG13*g23)
|
|
;
|
|
|
|
R13
|
|
=
|
|
(-0.5*ddg1113 + gamma113*gammado111 + gamma213*gammado112 +
|
|
(gamma111 + gamma313)*gammado113 + gamma111*gammado311 +
|
|
gamma211*(gammado213 + gammado312) + 2.*gamma311*gammado313)*ginv11 +
|
|
(-ddg1213 + gamma123*gammado111 + (gamma113 + gamma223)*gammado112 +
|
|
(gamma112 + gamma323)*gammado113 + gamma213*gammado122 +
|
|
(gamma111 + gamma313)*gammado123 + gamma112*gammado311 +
|
|
gamma111*gammado312 + gamma212*(gammado213 + gammado312) +
|
|
gamma211*(gammado223 + gammado322) +
|
|
2.*(gamma312*gammado313 + gamma311*gammado323))*ginv12 +
|
|
(-ddg1313 + gamma133*gammado111 + gamma233*gammado112 +
|
|
(2.*gamma113 + gamma333)*gammado113 +
|
|
(gamma111 + gamma313)*gammado133 + gamma113*gammado311 +
|
|
gamma213*(gammado123 + gammado213 + gammado312) +
|
|
(gamma111 + 2.*gamma313)*gammado313 +
|
|
gamma211*(gammado233 + gammado323) + 2.*gamma311*gammado333)*ginv13 +
|
|
(-0.5*ddg2213 + gamma123*gammado112 + gamma223*gammado122 +
|
|
(gamma112 + gamma323)*gammado123 + gamma112*gammado312 +
|
|
gamma212*(gammado223 + gammado322) + 2.*gamma312*gammado323)*ginv22 +
|
|
(-ddg2313 + gamma133*gammado112 + gamma123*gammado113 +
|
|
gamma233*gammado122 + (gamma113 + gamma223 + gamma333)*gammado123 +
|
|
(gamma112 + gamma323)*gammado133 + gamma113*gammado312 +
|
|
gamma112*gammado313 + gamma213*(gammado223 + gammado322) +
|
|
gamma212*(gammado233 + gammado323) +
|
|
2.*(gamma313*gammado323 + gamma312*gammado333))*ginv23 +
|
|
(-0.5*ddg3313 + gamma133*gammado113 + gamma233*gammado123 +
|
|
(gamma113 + gamma333)*gammado133 + gamma113*gammado313 +
|
|
gamma213*(gammado233 + gammado323) + 2.*gamma313*gammado333)*ginv33 +
|
|
0.5*((gammado113 + gammado311)*Gfromg1 +
|
|
(gammado123 + gammado312)*Gfromg2 + (gammado133 + gammado313)*Gfromg3 +
|
|
dG31*g11 + dG32*g12 + (dG11 + dG33)*g13 +
|
|
dG12*g23 + dG13*g33)
|
|
;
|
|
|
|
R22
|
|
=
|
|
gammado212*Gfromg1 + gammado222*Gfromg2 + gammado223*Gfromg3 +
|
|
(-0.5*ddg1122 + gamma112*(gammado112 + 2.*gammado211) +
|
|
3.*gamma212*gammado212 + gamma312*(2.*gammado213 + gammado312))*ginv11 \
|
|
+ (-ddg1222 + gamma122*(gammado112 + 2.*gammado211) +
|
|
gamma112*(gammado122 + 2.*gammado212) +
|
|
3.*(gamma222*gammado212 + gamma212*gammado222) +
|
|
2.*(gamma322*gammado213 + gamma312*gammado223) +
|
|
gamma322*gammado312 + gamma312*gammado322)*ginv12 +
|
|
(-ddg1322 + gamma123*(gammado112 + 2.*gammado211) +
|
|
gamma112*(gammado123 + 2.*gammado213) +
|
|
3.*(gamma223*gammado212 + gamma212*gammado223) +
|
|
2.*(gamma323*gammado213 + gamma312*gammado233) +
|
|
gamma323*gammado312 + gamma312*gammado323)*ginv13 +
|
|
(-0.5*ddg2222 + gamma122*(gammado122 + 2.*gammado212) +
|
|
3.*gamma222*gammado222 + gamma322*(2.*gammado223 + gammado322))*ginv22 \
|
|
+ (-ddg2322 + gamma123*(gammado122 + 2.*gammado212) +
|
|
gamma122*(gammado123 + 2.*gammado213) +
|
|
3.*(gamma223*gammado222 + gamma222*gammado223) +
|
|
2.*(gamma323*gammado223 + gamma322*gammado233) +
|
|
gamma323*gammado322 + gamma322*gammado323)*ginv23 +
|
|
(-0.5*ddg3322 + gamma123*(gammado123 + 2.*gammado213) +
|
|
3.*gamma223*gammado223 + gamma323*(2.*gammado233 + gammado323))*ginv33 \
|
|
+ dG21*g12 + dG22*g22 + dG23*g23
|
|
;
|
|
|
|
R23
|
|
=
|
|
(-0.5*ddg1123 + gamma113*gammado211 + gamma213*gammado212 +
|
|
(gamma212 + gamma313)*gammado213 +
|
|
gamma112*(gammado113 + gammado311) + gamma212*gammado312 +
|
|
2.*gamma312*gammado313)*ginv11 +
|
|
(-ddg1223 + gamma123*gammado211 + (gamma113 + gamma223)*gammado212 +
|
|
(gamma222 + gamma323)*gammado213 + gamma213*gammado222 +
|
|
(gamma212 + gamma313)*gammado223 +
|
|
gamma122*(gammado113 + gammado311) + gamma222*gammado312 +
|
|
gamma112*(gammado123 + gammado312) + gamma212*gammado322 +
|
|
2.*(gamma322*gammado313 + gamma312*gammado323))*ginv12 +
|
|
(-ddg1323 + gamma133*gammado211 + gamma233*gammado212 +
|
|
(gamma113 + gamma223 + gamma333)*gammado213 + gamma213*gammado223 +
|
|
(gamma212 + gamma313)*gammado233 +
|
|
gamma123*(gammado113 + gammado311) + gamma223*gammado312 +
|
|
gamma112*(gammado133 + gammado313) + gamma212*gammado323 +
|
|
2.*(gamma323*gammado313 + gamma312*gammado333))*ginv13 +
|
|
(-0.5*ddg2223 + gamma123*gammado212 + gamma223*gammado222 +
|
|
(gamma222 + gamma323)*gammado223 +
|
|
gamma122*(gammado123 + gammado312) + gamma222*gammado322 +
|
|
2.*gamma322*gammado323)*ginv22 +
|
|
(-ddg2323 + gamma133*gammado212 + gamma233*gammado222 +
|
|
(2.*gamma223 + gamma333)*gammado223 +
|
|
(gamma222 + gamma323)*gammado233 +
|
|
gamma123*(gammado123 + gammado213 + gammado312) +
|
|
gamma122*(gammado133 + gammado313) + gamma223*gammado322 +
|
|
(gamma222 + 2.*gamma323)*gammado323 + 2.*gamma322*gammado333)*ginv23 +
|
|
(-0.5*ddg3323 + gamma133*gammado213 + gamma233*gammado223 +
|
|
(gamma223 + gamma333)*gammado233 +
|
|
gamma123*(gammado133 + gammado313) + gamma223*gammado323 +
|
|
2.*gamma323*gammado333)*ginv33 +
|
|
0.5*((gammado213 + gammado312)*Gfromg1 +
|
|
(gammado223 + gammado322)*Gfromg2 + (gammado233 + gammado323)*Gfromg3 +
|
|
dG31*g12 + dG21*g13 + dG32*g22 +
|
|
(dG22 + dG33)*g23 + dG23*g33)
|
|
;
|
|
|
|
R33
|
|
=
|
|
gammado313*Gfromg1 + gammado323*Gfromg2 + gammado333*Gfromg3 +
|
|
(-0.5*ddg1133 + gamma113*(gammado113 + 2.*gammado311) +
|
|
gamma213*(gammado213 + 2.*gammado312) + 3.*gamma313*gammado313)*ginv11 \
|
|
+ (-ddg1233 + gamma123*(gammado113 + 2.*gammado311) +
|
|
gamma113*(gammado123 + 2.*gammado312) +
|
|
gamma223*(gammado213 + 2.*gammado312) +
|
|
gamma213*(gammado223 + 2.*gammado322) +
|
|
3.*(gamma323*gammado313 + gamma313*gammado323))*ginv12 +
|
|
(-ddg1333 + gamma133*(gammado113 + 2.*gammado311) +
|
|
gamma233*(gammado213 + 2.*gammado312) +
|
|
gamma113*(gammado133 + 2.*gammado313) +
|
|
gamma213*(gammado233 + 2.*gammado323) +
|
|
3.*(gamma333*gammado313 + gamma313*gammado333))*ginv13 +
|
|
(-0.5*ddg2233 + gamma123*(gammado123 + 2.*gammado312) +
|
|
gamma223*(gammado223 + 2.*gammado322) + 3.*gamma323*gammado323)*ginv22 \
|
|
+ (-ddg2333 + gamma133*(gammado123 + 2.*gammado312) +
|
|
gamma123*(gammado133 + 2.*gammado313) +
|
|
gamma233*(gammado223 + 2.*gammado322) +
|
|
gamma223*(gammado233 + 2.*gammado323) +
|
|
3.*(gamma333*gammado323 + gamma323*gammado333))*ginv23 +
|
|
(-0.5*ddg3333 + gamma133*(gammado133 + 2.*gammado313) +
|
|
gamma233*(gammado233 + 2.*gammado323) + 3.*gamma333*gammado333)*ginv33 \
|
|
+ dG31*g13 + dG32*g23 + dG33*g33
|
|
;
|
|
|
|
ff
|
|
=
|
|
chi
|
|
;
|
|
|
|
oochipsipower
|
|
=
|
|
1/chipsipower
|
|
;
|
|
|
|
f
|
|
=
|
|
oochipsipower*log(ff)
|
|
;
|
|
|
|
psim4
|
|
=
|
|
exp(-4.*f)
|
|
;
|
|
|
|
df1
|
|
=
|
|
(dchi1*oochipsipower)/chi
|
|
;
|
|
|
|
df2
|
|
=
|
|
(dchi2*oochipsipower)/chi
|
|
;
|
|
|
|
df3
|
|
=
|
|
(dchi3*oochipsipower)/chi
|
|
;
|
|
|
|
ddf11
|
|
=
|
|
(ddchi11*oochipsipower)/chi - chipsipower*pow2(df1)
|
|
;
|
|
|
|
ddf12
|
|
=
|
|
-(chipsipower*df1*df2) + (ddchi12*oochipsipower)/chi
|
|
;
|
|
|
|
ddf13
|
|
=
|
|
-(chipsipower*df1*df3) + (ddchi13*oochipsipower)/chi
|
|
;
|
|
|
|
ddf22
|
|
=
|
|
(ddchi22*oochipsipower)/chi - chipsipower*pow2(df2)
|
|
;
|
|
|
|
ddf23
|
|
=
|
|
-(chipsipower*df2*df3) + (ddchi23*oochipsipower)/chi
|
|
;
|
|
|
|
ddf33
|
|
=
|
|
(ddchi33*oochipsipower)/chi - chipsipower*pow2(df3)
|
|
;
|
|
|
|
cddf11
|
|
=
|
|
ddf11 - df1*gamma111 - df2*gamma211 - df3*gamma311
|
|
;
|
|
|
|
cddf12
|
|
=
|
|
ddf12 - df1*gamma112 - df2*gamma212 - df3*gamma312
|
|
;
|
|
|
|
cddf13
|
|
=
|
|
ddf13 - df1*gamma113 - df2*gamma213 - df3*gamma313
|
|
;
|
|
|
|
cddf22
|
|
=
|
|
ddf22 - df1*gamma122 - df2*gamma222 - df3*gamma322
|
|
;
|
|
|
|
cddf23
|
|
=
|
|
ddf23 - df1*gamma123 - df2*gamma223 - df3*gamma323
|
|
;
|
|
|
|
cddf33
|
|
=
|
|
ddf33 - df1*gamma133 - df2*gamma233 - df3*gamma333
|
|
;
|
|
|
|
trcddf
|
|
=
|
|
cddf11*ginv11 + cddf22*ginv22 +
|
|
2.*(cddf12*ginv12 + cddf13*ginv13 + cddf23*ginv23) + cddf33*ginv33
|
|
;
|
|
|
|
Rphi11
|
|
=
|
|
-2.*(cddf11 + trcddf*g11) + (4. - 4.*ginv11*g11)*pow2(df1) -
|
|
g11*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi12
|
|
=
|
|
df1*df2*(4. - 8.*ginv12*g12) - 2.*(cddf12 + trcddf*g12) -
|
|
g12*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi13
|
|
=
|
|
df1*(4.*df3 - 8.*df2*ginv12*g13) - 2.*(cddf13 + trcddf*g13) -
|
|
g13*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi22
|
|
=
|
|
-2.*(cddf22 + trcddf*g22) + (4. - 4.*ginv22*g22)*pow2(df2) -
|
|
g22*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi23
|
|
=
|
|
df2*(4.*df3 - 8.*df1*ginv12*g23) - 2.*(cddf23 + trcddf*g23) -
|
|
g23*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi33
|
|
=
|
|
-2.*(cddf33 + trcddf*g33) -
|
|
g33*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2))) +
|
|
(4. - 4.*ginv33*g33)*pow2(df3)
|
|
;
|
|
|
|
Rf11
|
|
=
|
|
R11 + Rphi11
|
|
;
|
|
|
|
Rf12
|
|
=
|
|
R12 + Rphi12
|
|
;
|
|
|
|
Rf13
|
|
=
|
|
R13 + Rphi13
|
|
;
|
|
|
|
Rf22
|
|
=
|
|
R22 + Rphi22
|
|
;
|
|
|
|
Rf23
|
|
=
|
|
R23 + Rphi23
|
|
;
|
|
|
|
Rf33
|
|
=
|
|
R33 + Rphi33
|
|
;
|
|
|
|
Rhat
|
|
=
|
|
psim4*(ginv11*Rf11 + ginv22*Rf22 +
|
|
2.*(ginv12*Rf12 + ginv13*Rf13 + ginv23*Rf23) + ginv33*Rf33)
|
|
;
|
|
|
|
cdda11
|
|
=
|
|
dda11 - da2*gamma211 - da3*gamma311 +
|
|
2.*((da2*df1 + da1*df2)*ginv12 + (da3*df1 + da1*df3)*ginv13 +
|
|
da2*df2*ginv22 + (da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g11 \
|
|
+ da1*(-4.*df1 - gamma111 + 2.*df1*ginv11*g11)
|
|
;
|
|
|
|
cdda12
|
|
=
|
|
dda12 - 2.*(da2*df1 + da1*df2) - da1*gamma112 - da2*gamma212 -
|
|
da3*gamma312 + 2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g12
|
|
;
|
|
|
|
cdda13
|
|
=
|
|
dda13 - 2.*(da3*df1 + da1*df3) - da1*gamma113 - da2*gamma213 -
|
|
da3*gamma313 + 2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g13
|
|
;
|
|
|
|
cdda22
|
|
=
|
|
dda22 - da1*gamma122 - da3*gamma322 +
|
|
2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + (da3*df2 + da2*df3)*ginv23 +
|
|
da3*df3*ginv33)*g22 +
|
|
da2*(-4.*df2 - gamma222 + 2.*df2*ginv22*g22)
|
|
;
|
|
|
|
cdda23
|
|
=
|
|
dda23 - 2.*(da3*df2 + da2*df3) - da1*gamma123 - da2*gamma223 -
|
|
da3*gamma323 + 2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g23
|
|
;
|
|
|
|
cdda33
|
|
=
|
|
dda33 - da1*gamma133 - da2*gamma233 +
|
|
2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23)*g33 +
|
|
da3*(-4.*df3 - gamma333 + 2.*df3*ginv33*g33)
|
|
;
|
|
|
|
dda12
|
|
=
|
|
dda12 - 2.*(da2*df1 + da1*df2) - da1*gamma112 - da2*gamma212 -
|
|
da3*gamma312 + 2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g12
|
|
;
|
|
|
|
dda13
|
|
=
|
|
dda13 - 2.*(da3*df1 + da1*df3) - da1*gamma113 - da2*gamma213 -
|
|
da3*gamma313 + 2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g13
|
|
;
|
|
|
|
dda23
|
|
=
|
|
dda23 - 2.*(da3*df2 + da2*df3) - da1*gamma123 - da2*gamma223 -
|
|
da3*gamma323 + 2.*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)*g23
|
|
;
|
|
|
|
trcdda
|
|
=
|
|
(cdda11*ginv11 + (cdda12 + dda12)*ginv12 + (cdda13 + dda13)*ginv13 +
|
|
cdda22*ginv22 + (cdda23 + dda23)*ginv23 + cdda33*ginv33)*psim4
|
|
;
|
|
|
|
AA11
|
|
=
|
|
2.*(ginv23*A12*A13 +
|
|
A11*(ginv12*A12 + ginv13*A13)) + ginv11*pow2(A11) +
|
|
ginv22*pow2(A12) + ginv33*pow2(A13)
|
|
;
|
|
|
|
AA12
|
|
=
|
|
A12*(ginv11*A11 + ginv22*A22) + ginv33*A13*A23 +
|
|
ginv13*(A12*A13 + A11*A23) +
|
|
ginv23*(A13*A22 + A12*A23) +
|
|
ginv12*(A11*A22 + pow2(A12))
|
|
;
|
|
|
|
AA13
|
|
=
|
|
ginv22*A12*A23 + ginv12*(A12*A13 + A11*A23) +
|
|
A13*(ginv11*A11 + ginv33*A33) +
|
|
ginv23*(A13*A23 + A12*A33) +
|
|
ginv13*(A11*A33 + pow2(A13))
|
|
;
|
|
|
|
AA21
|
|
=
|
|
A12*(ginv11*A11 + ginv22*A22) + ginv33*A13*A23 +
|
|
ginv13*(A12*A13 + A11*A23) +
|
|
ginv23*(A13*A22 + A12*A23) +
|
|
ginv12*(A11*A22 + pow2(A12))
|
|
;
|
|
|
|
AA22
|
|
=
|
|
2.*(ginv23*A22*A23 +
|
|
A12*(ginv12*A22 + ginv13*A23)) + ginv11*pow2(A12) +
|
|
ginv22*pow2(A22) + ginv33*pow2(A23)
|
|
;
|
|
|
|
AA23
|
|
=
|
|
ginv11*A12*A13 + ginv12*(A13*A22 + A12*A23) +
|
|
A23*(ginv22*A22 + ginv33*A33) +
|
|
ginv13*(A13*A23 + A12*A33) +
|
|
ginv23*(A22*A33 + pow2(A23))
|
|
;
|
|
|
|
AA31
|
|
=
|
|
ginv22*A12*A23 + ginv12*(A12*A13 + A11*A23) +
|
|
A13*(ginv11*A11 + ginv33*A33) +
|
|
ginv23*(A13*A23 + A12*A33) +
|
|
ginv13*(A11*A33 + pow2(A13))
|
|
;
|
|
|
|
AA32
|
|
=
|
|
ginv11*A12*A13 + ginv12*(A13*A22 + A12*A23) +
|
|
A23*(ginv22*A22 + ginv33*A33) +
|
|
ginv13*(A13*A23 + A12*A33) +
|
|
ginv23*(A22*A33 + pow2(A23))
|
|
;
|
|
|
|
AA33
|
|
=
|
|
2.*(ginv23*A23*A33 +
|
|
A13*(ginv12*A23 + ginv13*A33)) + ginv11*pow2(A13) +
|
|
ginv22*pow2(A23) + ginv33*pow2(A33)
|
|
;
|
|
|
|
Ainv11
|
|
=
|
|
2.*(ginv11*(ginv12*A12 + ginv13*A13) + ginv12*ginv13*A23) +
|
|
A11*pow2(ginv11) + A22*pow2(ginv12) + A33*pow2(ginv13)
|
|
;
|
|
|
|
Ainv12
|
|
=
|
|
ginv11*(ginv12*A11 + ginv22*A12 + ginv23*A13) +
|
|
ginv12*(ginv13*A13 + ginv22*A22 + ginv23*A23) +
|
|
ginv13*(ginv22*A23 + ginv23*A33) + A12*pow2(ginv12)
|
|
;
|
|
|
|
Ainv13
|
|
=
|
|
ginv11*(ginv13*A11 + ginv23*A12 + ginv33*A13) +
|
|
ginv12*(ginv13*A12 + ginv23*A22 + ginv33*A23) +
|
|
ginv13*(ginv23*A23 + ginv33*A33) + A13*pow2(ginv13)
|
|
;
|
|
|
|
Ainv22
|
|
=
|
|
2.*(ginv12*(ginv22*A12 + ginv23*A13) + ginv22*ginv23*A23) +
|
|
A11*pow2(ginv12) + A22*pow2(ginv22) + A33*pow2(ginv23)
|
|
;
|
|
|
|
Ainv23
|
|
=
|
|
ginv13*(ginv22*A12 + ginv23*A13) +
|
|
ginv12*(ginv13*A11 + ginv23*A12 + ginv33*A13) +
|
|
ginv22*(ginv23*A22 + ginv33*A23) + ginv23*ginv33*A33 +
|
|
A23*pow2(ginv23)
|
|
;
|
|
|
|
Ainv33
|
|
=
|
|
2.*(ginv13*(ginv23*A12 + ginv33*A13) + ginv23*ginv33*A23) +
|
|
A11*pow2(ginv13) + A22*pow2(ginv23) + A33*pow2(ginv33)
|
|
;
|
|
|
|
cdA111
|
|
=
|
|
dA111 - 2.*(gamma111*A11 + gamma211*A12 + gamma311*A13)
|
|
;
|
|
|
|
cdA112
|
|
=
|
|
dA112 - gamma112*A11 - (gamma111 + gamma212)*A12 -
|
|
gamma312*A13 - gamma211*A22 - gamma311*A23
|
|
;
|
|
|
|
cdA113
|
|
=
|
|
dA113 - gamma113*A11 - gamma213*A12 -
|
|
(gamma111 + gamma313)*A13 - gamma211*A23 - gamma311*A33
|
|
;
|
|
|
|
cdA122
|
|
=
|
|
dA122 - 2.*(gamma112*A12 + gamma212*A22 + gamma312*A23)
|
|
;
|
|
|
|
cdA123
|
|
=
|
|
dA123 - gamma113*A12 - gamma112*A13 - gamma213*A22 -
|
|
(gamma212 + gamma313)*A23 - gamma312*A33
|
|
;
|
|
|
|
cdA133
|
|
=
|
|
dA133 - 2.*(gamma113*A13 + gamma213*A23 + gamma313*A33)
|
|
;
|
|
|
|
cdA211
|
|
=
|
|
dA211 - 2.*(gamma112*A11 + gamma212*A12 + gamma312*A13)
|
|
;
|
|
|
|
cdA212
|
|
=
|
|
dA212 - gamma122*A11 - (gamma112 + gamma222)*A12 -
|
|
gamma322*A13 - gamma212*A22 - gamma312*A23
|
|
;
|
|
|
|
cdA213
|
|
=
|
|
dA213 - gamma123*A11 - gamma223*A12 -
|
|
(gamma112 + gamma323)*A13 - gamma212*A23 - gamma312*A33
|
|
;
|
|
|
|
cdA222
|
|
=
|
|
dA222 - 2.*(gamma122*A12 + gamma222*A22 + gamma322*A23)
|
|
;
|
|
|
|
cdA223
|
|
=
|
|
dA223 - gamma123*A12 - gamma122*A13 - gamma223*A22 -
|
|
(gamma222 + gamma323)*A23 - gamma322*A33
|
|
;
|
|
|
|
cdA233
|
|
=
|
|
dA233 - 2.*(gamma123*A13 + gamma223*A23 + gamma323*A33)
|
|
;
|
|
|
|
cdA311
|
|
=
|
|
dA311 - 2.*(gamma113*A11 + gamma213*A12 + gamma313*A13)
|
|
;
|
|
|
|
cdA312
|
|
=
|
|
dA312 - gamma123*A11 - (gamma113 + gamma223)*A12 -
|
|
gamma323*A13 - gamma213*A22 - gamma313*A23
|
|
;
|
|
|
|
cdA313
|
|
=
|
|
dA313 - gamma133*A11 - gamma233*A12 -
|
|
(gamma113 + gamma333)*A13 - gamma213*A23 - gamma313*A33
|
|
;
|
|
|
|
cdA322
|
|
=
|
|
dA322 - 2.*(gamma123*A12 + gamma223*A22 + gamma323*A23)
|
|
;
|
|
|
|
cdA323
|
|
=
|
|
dA323 - gamma133*A12 - gamma123*A13 - gamma233*A22 -
|
|
(gamma223 + gamma333)*A23 - gamma323*A33
|
|
;
|
|
|
|
cdA333
|
|
=
|
|
dA333 - 2.*(gamma133*A13 + gamma233*A23 + gamma333*A33)
|
|
;
|
|
|
|
divbeta
|
|
=
|
|
db11 + db22 + db33
|
|
;
|
|
|
|
totdivbeta
|
|
=
|
|
0.66666666666666666667*divbeta
|
|
;
|
|
|
|
lieg11
|
|
=
|
|
dg111*beta1 + dg211*beta2 + dg311*beta3 +
|
|
(2.*db11 - totdivbeta)*g11 + 2.*(db12*g12 + db13*g13)
|
|
;
|
|
|
|
lieg12
|
|
=
|
|
dg112*beta1 + dg212*beta2 + dg312*beta3 + db21*g11 +
|
|
(db11 + db22 - totdivbeta)*g12 + db23*g13 + db12*g22 +
|
|
db13*g23
|
|
;
|
|
|
|
lieg13
|
|
=
|
|
dg113*beta1 + dg213*beta2 + dg313*beta3 + db31*g11 +
|
|
db32*g12 + (db11 + db33 - totdivbeta)*g13 + db12*g23 +
|
|
db13*g33
|
|
;
|
|
|
|
lieg22
|
|
=
|
|
dg122*beta1 + dg222*beta2 + dg322*beta3 -
|
|
totdivbeta*g22 + 2.*(db21*g12 + db22*g22 + db23*g23)
|
|
;
|
|
|
|
lieg23
|
|
=
|
|
dg123*beta1 + dg223*beta2 + dg323*beta3 + db31*g12 +
|
|
db21*g13 + db32*g22 + (db22 + db33 - totdivbeta)*g23 +
|
|
db23*g33
|
|
;
|
|
|
|
lieg33
|
|
=
|
|
dg133*beta1 + dg233*beta2 + dg333*beta3 -
|
|
totdivbeta*g33 + 2.*(db31*g13 + db32*g23 + db33*g33)
|
|
;
|
|
|
|
lieA11
|
|
=
|
|
(2.*db11 - totdivbeta)*A11 + 2.*(db12*A12 + db13*A13) +
|
|
dA111*beta1 + dA211*beta2 + dA311*beta3
|
|
;
|
|
|
|
lieA12
|
|
=
|
|
db21*A11 + (db11 + db22 - totdivbeta)*A12 + db23*A13 +
|
|
db12*A22 + db13*A23 + dA112*beta1 + dA212*beta2 +
|
|
dA312*beta3
|
|
;
|
|
|
|
lieA13
|
|
=
|
|
db31*A11 + db32*A12 + (db11 + db33 - totdivbeta)*A13 +
|
|
db12*A23 + db13*A33 + dA113*beta1 + dA213*beta2 +
|
|
dA313*beta3
|
|
;
|
|
|
|
lieA22
|
|
=
|
|
-(totdivbeta*A22) + 2.*(db21*A12 + db22*A22 +
|
|
db23*A23) + dA122*beta1 + dA222*beta2 + dA322*beta3
|
|
;
|
|
|
|
lieA23
|
|
=
|
|
db31*A12 + db21*A13 + db32*A22 +
|
|
(db22 + db33 - totdivbeta)*A23 + db23*A33 + dA123*beta1 +
|
|
dA223*beta2 + dA323*beta3
|
|
;
|
|
|
|
lieA33
|
|
=
|
|
-(totdivbeta*A33) + 2.*(db31*A13 + db32*A23 +
|
|
db33*A33) + dA133*beta1 + dA233*beta2 + dA333*beta3
|
|
;
|
|
|
|
betas
|
|
=
|
|
sdown1*beta1 + sdown2*beta2 + sdown3*beta3
|
|
;
|
|
|
|
Dbetas
|
|
=
|
|
(db11*sdown1 + db12*sdown2 + db13*sdown3)*sup1 +
|
|
(db21*sdown1 + db22*sdown2 + db23*sdown3)*sup2 +
|
|
(db31*sdown1 + db32*sdown2 + db33*sdown3)*sup3
|
|
;
|
|
|
|
Dalpha
|
|
=
|
|
da1*sup1 + da2*sup2 + da3*sup3
|
|
;
|
|
|
|
DKhat
|
|
=
|
|
dKhat1*sup1 + dKhat2*sup2 + dKhat3*sup3
|
|
;
|
|
|
|
DK
|
|
=
|
|
dK1*sup1 + dK2*sup2 + dK3*sup3
|
|
;
|
|
|
|
DTheta
|
|
=
|
|
dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3
|
|
;
|
|
|
|
Gams
|
|
=
|
|
sdown1*G1 + sdown2*G2 + sdown3*G3
|
|
;
|
|
|
|
DGams
|
|
=
|
|
(dG11*sdown1 + dG12*sdown2 + dG13*sdown3)*sup1 +
|
|
(dG21*sdown1 + dG22*sdown2 + dG23*sdown3)*sup2 +
|
|
(dG31*sdown1 + dG32*sdown2 + dG33*sdown3)*sup3
|
|
;
|
|
|
|
GamA1
|
|
=
|
|
qud11*G1 + qud12*G2 + qud13*G3
|
|
;
|
|
|
|
GamA2
|
|
=
|
|
qud21*G1 + qud22*G2 + qud23*G3
|
|
;
|
|
|
|
GamA3
|
|
=
|
|
qud31*G1 + qud32*G2 + qud33*G3
|
|
;
|
|
|
|
DGamA1
|
|
=
|
|
(dG11*qud11 + dG12*qud12 + dG13*qud13)*sup1 +
|
|
(dG21*qud11 + dG22*qud12 + dG23*qud13)*sup2 +
|
|
(dG31*qud11 + dG32*qud12 + dG33*qud13)*sup3
|
|
;
|
|
|
|
DGamA2
|
|
=
|
|
(dG11*qud21 + dG12*qud22 + dG13*qud23)*sup1 +
|
|
(dG21*qud21 + dG22*qud22 + dG23*qud23)*sup2 +
|
|
(dG31*qud21 + dG32*qud22 + dG33*qud23)*sup3
|
|
;
|
|
|
|
DGamA3
|
|
=
|
|
(dG11*qud31 + dG12*qud32 + dG13*qud33)*sup1 +
|
|
(dG21*qud31 + dG22*qud32 + dG23*qud33)*sup2 +
|
|
(dG31*qud31 + dG32*qud32 + dG33*qud33)*sup3
|
|
;
|
|
|
|
betaA1
|
|
=
|
|
qud11*beta1 + qud12*beta2 + qud13*beta3
|
|
;
|
|
|
|
betaA2
|
|
=
|
|
qud21*beta1 + qud22*beta2 + qud23*beta3
|
|
;
|
|
|
|
betaA3
|
|
=
|
|
qud31*beta1 + qud32*beta2 + qud33*beta3
|
|
;
|
|
|
|
DbetaA1
|
|
=
|
|
(db11*qud11 + db12*qud12 + db13*qud13)*sup1 +
|
|
(db21*qud11 + db22*qud12 + db23*qud13)*sup2 +
|
|
(db31*qud11 + db32*qud12 + db33*qud13)*sup3
|
|
;
|
|
|
|
DbetaA2
|
|
=
|
|
(db11*qud21 + db12*qud22 + db13*qud23)*sup1 +
|
|
(db21*qud21 + db22*qud22 + db23*qud23)*sup2 +
|
|
(db31*qud21 + db32*qud22 + db33*qud23)*sup3
|
|
;
|
|
|
|
DbetaA3
|
|
=
|
|
(db11*qud31 + db12*qud32 + db13*qud33)*sup1 +
|
|
(db21*qud31 + db22*qud32 + db23*qud33)*sup2 +
|
|
(db31*qud31 + db32*qud32 + db33*qud33)*sup3
|
|
;
|
|
|
|
lienKhat
|
|
=
|
|
-((DKhat + Khat/r)*sqrt(muL))
|
|
;
|
|
|
|
lienTheta
|
|
=
|
|
-DTheta - (kappa1*(2. + kappa2) + 1/r)*Theta
|
|
;
|
|
|
|
lienK
|
|
=
|
|
lienKhat + 2.*lienTheta
|
|
;
|
|
|
|
rKhat
|
|
=
|
|
lienKhat*alpha + dKhat1*beta1 + dKhat2*beta2 +
|
|
dKhat3*beta3
|
|
;
|
|
|
|
rGams
|
|
=
|
|
-(((db11*sdown1 + db12*sdown2)*beta1 +
|
|
(db21*sdown1 + db22*sdown2 + db23*sdown3)*beta2 +
|
|
db31*sdown1*beta3)*pow2(shiftdriver)) +
|
|
beta3*(2.*ddb231*sdown1*shiftdriver*beta2 +
|
|
sdown2*(2.*ddb132*shiftdriver*beta1 - db32*pow2(shiftdriver)) +
|
|
sdown3*(shiftdriver*(dG33 + 2.*ddb133*beta1) -
|
|
db33*pow2(shiftdriver))) +
|
|
sdown3*(db13*(db21*shiftdriver*beta2 -
|
|
beta1*pow2(shiftdriver)) +
|
|
shiftdriver*((db12*db23 + db13*(db11 + db33) + dG13)*beta1 +
|
|
(db23*db33 + dG23)*beta2 +
|
|
beta3*(db13*db31 + db23*db32 + pow2(db33)) +
|
|
ddb113*pow2(beta1))) +
|
|
shiftdriver*((dG22*sdown2 + db22*(db21*sdown1 + db23*sdown3) +
|
|
2.*ddb123*sdown3*beta1)*beta2 +
|
|
2.*((ddb232*sdown2 + ddb233*sdown3)*beta2*beta3 +
|
|
beta1*((ddb121*sdown1 + ddb122*sdown2)*beta2 +
|
|
ddb131*sdown1*beta3)) +
|
|
sdown2*((db13*db32 + dG12)*beta1 +
|
|
(db32*(db22 + db33) + dG32)*beta3 +
|
|
db12*((db11 + db22)*beta1 + db31*beta3) +
|
|
beta2*(db12*db21 + db23*db32 + pow2(db22))) +
|
|
(ddb111*sdown1 + ddb112*sdown2)*pow2(beta1) +
|
|
(ddb221*sdown1 + ddb222*sdown2 + ddb223*sdown3)*pow2(beta2) +
|
|
(ddb332*sdown2 + ddb333*sdown3)*pow2(beta3) +
|
|
sdown1*((db11*db21 + db23*db31 + dG21)*beta2 +
|
|
(db21*db32 + db31*(db11 + db33) + dG31)*beta3 +
|
|
beta1*(db12*db21 + db13*db31 + dG11 + pow2(db11)) +
|
|
ddb331*pow2(beta3)))
|
|
;
|
|
|
|
rTheta
|
|
=
|
|
lienTheta*alpha + dTheta1*beta1 + dTheta2*beta2 +
|
|
dTheta3*beta3
|
|
;
|
|
|
|
rACss
|
|
=
|
|
sup1*(2.*lieA13*sup3 + 1.3333333333333333333*dK1*alpha*chi +
|
|
sup2*(-(cdda12*psim4) + 2.*(lieA12 - AA12*alpha) +
|
|
0.66666666666666666667*trcdda*g12)) +
|
|
sup3*(2.*((psim4*Rf13*sup1 - AA23*sup2)*alpha +
|
|
sup2*(lieA23 + (-AA32 + psim4*Rf23)*alpha)) +
|
|
1.3333333333333333333*dK3*alpha*chi +
|
|
sup1*(-(dda13*psim4) - 2.*AA13*alpha +
|
|
0.66666666666666666667*trcdda*g13)) +
|
|
(lieA11 - cdda11*psim4 - 2.*AA11*alpha +
|
|
0.33333333333333333333*trcdda*g11)*pow2(sup1) +
|
|
(lieA22 - 2.*AA22*alpha + 0.33333333333333333333*trcdda*g22)*
|
|
pow2(sup2) - psim4*((cdda23 + dda23)*sup2*sup3 +
|
|
sup1*(dda12*sup2 + cdda13*sup3) + cdda22*pow2(sup2)) +
|
|
(lieA33 - cdda33*psim4 - 2.*AA33*alpha +
|
|
0.33333333333333333333*trcdda*g33)*pow2(sup3) -
|
|
alpha*(sup2*(2.*AA21*sup1 +
|
|
0.66666666666666666667*Rhat*sup3*g23) +
|
|
0.33333333333333333333*(Rhat*g11*pow2(sup1) +
|
|
dGfromgdu11*qud11*pow2(chi))) +
|
|
alpha*(1.3333333333333333333*dK2*sup2*chi +
|
|
2.*(sup1*(-(AA31*sup3) + K*sup2*A12) + K*sup2*sup3*A23 -
|
|
DTheta*chi) + ginv11*
|
|
(3.*dchi1*(sup1*A11 + sup2*A12 + sup3*A13) -
|
|
2.*(cdA111*sup1 + cdA112*sup2 + cdA113*sup3)*chi) +
|
|
ginv12*(3.*(sup1*(dchi2*A11 + dchi1*A12) +
|
|
dchi2*(sup2*A12 + sup3*A13) +
|
|
dchi1*(sup2*A22 + sup3*A23)) -
|
|
2.*((cdA112 + cdA211)*sup1 + (cdA122 + cdA212)*sup2 +
|
|
(cdA123 + cdA213)*sup3)*chi) +
|
|
ginv22*(3.*dchi2*(sup1*A12 + sup2*A22 + sup3*A23) -
|
|
2.*(cdA212*sup1 + cdA222*sup2 + cdA223*sup3)*chi) +
|
|
ginv13*(3.*(dchi3*(sup1*A11 + sup2*A12) +
|
|
(dchi1*sup1 + dchi3*sup3)*A13 +
|
|
dchi1*(sup2*A23 + sup3*A33)) -
|
|
2.*((cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 + cdA313)*sup3)*chi) +
|
|
ginv23*(3.*(sup1*(dchi3*A12 + dchi2*A13) +
|
|
sup2*(dchi3*A22 + dchi2*A23) +
|
|
sup3*(dchi3*A23 + dchi2*A33)) -
|
|
2.*((cdA213 + cdA312)*sup1 + (cdA223 + cdA322)*sup2 +
|
|
(cdA233 + cdA323)*sup3)*chi) +
|
|
ginv33*(3.*dchi3*(sup1*A13 + sup2*A23 + sup3*A33) -
|
|
2.*(cdA313*sup1 + cdA323*sup2 + cdA333*sup3)*chi) -
|
|
0.66666666666666666667*Rhat*sup1*sup3*g13 +
|
|
psim4*(2.*Rf12*sup1*sup2 + Rf11*pow2(sup1) + Rf22*pow2(sup2) +
|
|
Rf33*pow2(sup3)) + K*(2.*sup1*sup3*A13 +
|
|
A11*pow2(sup1) + A22*pow2(sup2) + A33*pow2(sup3)) +
|
|
(0.33333333333333333333*dG11*qud11 -
|
|
sdown3*(Gfromg3*kappa1 + 0.66666666666666666667*dG33*sup3) +
|
|
sdown1*(0.66666666666666666667*dGfromgdu11*sup1 +
|
|
kappa1*G1) + kappa1*
|
|
(-(Gfromg1*sdown1) - Gfromg2*sdown2 + sdown2*G2 +
|
|
sdown3*G3))*pow2(chi) +
|
|
0.33333333333333333333*(-(Rhat*
|
|
(g22*pow2(sup2) + g33*pow2(sup3))) +
|
|
((dG12 - dGfromgdu12)*qud12 + (dG13 - dGfromgdu13)*qud13 +
|
|
(dG21 - dGfromgdu21)*qud21 + (dG22 - dGfromgdu22)*qud22 +
|
|
(dG23 - dGfromgdu23)*qud23 + (dG31 - dGfromgdu31)*qud31 +
|
|
(dG32 - dGfromgdu32)*qud32 + (dG33 - dGfromgdu33)*qud33)*
|
|
pow2(chi))) + 0.66666666666666666667*
|
|
(sup2*(sup3*trcdda*g23 +
|
|
(-(dG21*sdown1) - dG22*sdown2 + dGfromgdu22*sdown2 +
|
|
dGfromgdu23*sdown3)*alpha*pow2(chi)) +
|
|
alpha*((-(sdown3*(dG13*sup1 + dG23*sup2)) +
|
|
(-(dG31*sdown1) - dG32*sdown2 + dGfromgdu32*sdown2 +
|
|
dGfromgdu33*sdown3)*sup3 +
|
|
sdown1*(dGfromgdu21*sup2 + dGfromgdu31*sup3))*pow2(chi) +
|
|
sup1*(-(Rhat*sup2*g12) +
|
|
(-(dG11*sdown1) - dG12*sdown2 + dGfromgdu12*sdown2 +
|
|
dGfromgdu13*sdown3)*pow2(chi))))
|
|
;
|
|
|
|
rACqq
|
|
=
|
|
-rACss + (Ainv22*lieg22 + 2.*(Ainv12*lieg12 + Ainv13*lieg13 +
|
|
Ainv23*lieg23) - (2.*Ainv22*A22 +
|
|
4.*(Ainv12*A12 + Ainv13*A13 + Ainv23*A23))*
|
|
alpha + Ainv11*(lieg11 - 2.*A11*alpha) +
|
|
Ainv33*(lieg33 - 2.*A33*alpha))*chi
|
|
;
|
|
|
|
rGamA1
|
|
=
|
|
-(((dG11*qud11 + dG12*qud12 + dG13*qud13)*sup1 +
|
|
(dG22*qud12 + dG23*qud13)*sup2 + (dG32*qud12 + dG33*qud13)*sup3 +
|
|
qud11*(dG21*sup2 + dG31*sup3))*vbetaA) +
|
|
(dG11*qud11 + dG12*qud12 + dG13*qud13)*beta1 +
|
|
(dG21*qud11 + dG22*qud12 + dG23*qud13)*beta2 +
|
|
(dG31*qud11 + dG32*qud12 + dG33*qud13)*beta3 -
|
|
((((db11*quu11 + db21*quu12 + db31*quu13)*sdown1 +
|
|
(db12*quu11 + db22*quu12 + db32*quu13)*sdown2 +
|
|
(db13*quu11 + db23*quu12)*sdown3)*shiftdriver)/vbetaA +
|
|
(0.66666666666666666667*dTheta1*quu11 +
|
|
(1.3333333333333333333*dKhat2 + 0.66666666666666666667*dTheta2)*
|
|
quu12)*alpha + quu13*
|
|
((db33*sdown3*shiftdriver)/vbetaA +
|
|
1.3333333333333333333*dKhat3*alpha))/chi +
|
|
(2.3333333333333333333*((ddb121*qud11 + ddb122*qud12 + ddb123*qud13)*
|
|
quu12 + (ddb131*qud11 + ddb132*qud12 + ddb133*qud13)*quu13) +
|
|
0.33333333333333333333*((ddb122*qud22 + ddb123*qud23 +
|
|
ddb131*qud31 + ddb132*qud32)*quu11 +
|
|
(ddb221*qud21 + ddb222*qud22 + ddb223*qud23 + ddb231*qud31 +
|
|
ddb232*qud32 + ddb233*qud33)*quu12 +
|
|
(ddb231*qud21 + ddb232*qud22 + ddb233*qud23 + ddb331*qud31 +
|
|
ddb332*qud32 + ddb333*qud33)*quu13) +
|
|
(ddb221*qud11 + ddb222*qud12 + ddb223*qud13)*quu22 +
|
|
2.*(ddb231*qud11 + ddb232*qud12 + ddb233*qud13)*quu23 +
|
|
(ddb331*qud11 + ddb332*qud12 + ddb333*qud13)*quu33 +
|
|
1.3333333333333333333*((ddb111*qud11 + ddb112*qud12)*quu11 +
|
|
(ddb132*quu13*sdown2 + ddb113*quu11*sdown3)*sup1 +
|
|
(ddb232*quu13*sdown2 + ddb123*quu11*sdown3)*sup2 +
|
|
(ddb332*quu13*sdown2 + ddb133*quu11*sdown3)*sup3 +
|
|
sdown2*((ddb112*quu11 + ddb122*quu12)*sup1 +
|
|
(ddb122*quu11 + ddb222*quu12)*sup2 +
|
|
(ddb132*quu11 + ddb232*quu12)*sup3) +
|
|
sdown1*((ddb121*quu12 + ddb131*quu13)*sup1 +
|
|
(ddb221*quu12 + ddb231*quu13)*sup2 +
|
|
(ddb231*quu12 + ddb331*quu13)*sup3) +
|
|
sdown3*((ddb123*quu12 + ddb133*quu13)*sup1 +
|
|
(ddb223*quu12 + ddb233*quu13)*sup2 +
|
|
(ddb233*quu12 + ddb333*quu13)*sup3)) +
|
|
(shiftdriver*((db11*qud11 + db12*qud12 + db13*qud13)*sup1 +
|
|
(db21*qud11 + db22*qud12 + db23*qud13)*sup2 +
|
|
(db31*qud11 + db32*qud12 + db33*qud13)*sup3))/vbetaA +
|
|
((dG21*quu12 + dG31*quu13)*sdown1 +
|
|
(dG12*quu11 + dG22*quu12 + dG32*quu13)*sdown2 +
|
|
(dG13*quu11 + dG23*quu12 + dG33*quu13)*sdown3)*vbetaA -
|
|
0.66666666666666666667*dTheta3*quu13*alpha +
|
|
quu11*(0.33333333333333333333*(ddb121*qud21 + ddb133*qud33) +
|
|
dG11*sdown1*vbetaA + 1.3333333333333333333*
|
|
(ddb113*qud13 + sdown1*(ddb111*sup1 + ddb121*sup2 + ddb131*sup3) -
|
|
dKhat1*alpha)))/chi
|
|
;
|
|
|
|
rGamA2
|
|
=
|
|
-(((dG11*qud21 + dG12*qud22 + dG13*qud23)*sup1 +
|
|
(dG22*qud22 + dG23*qud23)*sup2 + (dG32*qud22 + dG33*qud23)*sup3 +
|
|
qud21*(dG21*sup2 + dG31*sup3))*vbetaA) +
|
|
(dG11*qud21 + dG12*qud22 + dG13*qud23)*beta1 +
|
|
(dG21*qud21 + dG22*qud22 + dG23*qud23)*beta2 +
|
|
(dG31*qud21 + dG32*qud22 + dG33*qud23)*beta3 -
|
|
((((db11*quu12 + db21*quu22 + db31*quu23)*sdown1 +
|
|
(db12*quu12 + db22*quu22 + db32*quu23)*sdown2 +
|
|
(db13*quu12 + db23*quu22)*sdown3)*shiftdriver)/vbetaA +
|
|
(0.66666666666666666667*dTheta1*quu12 +
|
|
(1.3333333333333333333*dKhat2 + 0.66666666666666666667*dTheta2)*
|
|
quu22)*alpha + quu23*
|
|
((db33*sdown3*shiftdriver)/vbetaA +
|
|
1.3333333333333333333*dKhat3*alpha))/chi +
|
|
((ddb111*qud21 + ddb112*qud22)*quu11 +
|
|
2.*(ddb131*qud21 + ddb132*qud22 + ddb133*qud23)*quu13 +
|
|
(1.3333333333333333333*ddb223*qud23 +
|
|
0.33333333333333333333*(ddb121*qud11 + ddb231*qud31))*quu22 +
|
|
2.3333333333333333333*((ddb121*qud21 + ddb122*qud22)*quu12 +
|
|
(ddb231*qud21 + ddb232*qud22)*quu23) +
|
|
0.33333333333333333333*((ddb112*qud12 + ddb113*qud13 +
|
|
ddb132*qud32 + ddb133*qud33)*quu12 +
|
|
(ddb122*qud12 + ddb123*qud13 + ddb232*qud32 + ddb233*qud33)*
|
|
quu22 + (ddb132*qud12 + ddb133*qud13 + ddb332*qud32 +
|
|
ddb333*qud33)*quu23) +
|
|
(ddb331*qud21 + ddb332*qud22 + ddb333*qud23)*quu33 +
|
|
1.3333333333333333333*((ddb221*qud21 + ddb222*qud22)*quu22 +
|
|
(ddb132*quu23*sdown2 + ddb113*quu12*sdown3)*sup1 +
|
|
(ddb232*quu23*sdown2 + ddb123*quu12*sdown3)*sup2 +
|
|
(ddb332*quu23*sdown2 + ddb133*quu12*sdown3)*sup3 +
|
|
sdown2*((ddb112*quu12 + ddb122*quu22)*sup1 +
|
|
(ddb122*quu12 + ddb222*quu22)*sup2 +
|
|
(ddb132*quu12 + ddb232*quu22)*sup3) +
|
|
sdown1*((ddb121*quu22 + ddb131*quu23)*sup1 +
|
|
(ddb221*quu22 + ddb231*quu23)*sup2 +
|
|
(ddb231*quu22 + ddb331*quu23)*sup3) +
|
|
sdown3*((ddb123*quu22 + ddb133*quu23)*sup1 +
|
|
(ddb223*quu22 + ddb233*quu23)*sup2 +
|
|
(ddb233*quu22 + ddb333*quu23)*sup3)) +
|
|
qud23*(ddb113*quu11 + (db33*shiftdriver*sup3)/vbetaA) +
|
|
(shiftdriver*((db11*qud21 + db12*qud22 + db13*qud23)*sup1 +
|
|
(db21*qud21 + db22*qud22 + db23*qud23)*sup2 +
|
|
(db31*qud21 + db32*qud22)*sup3))/vbetaA +
|
|
((dG21*quu22 + dG31*quu23)*sdown1 +
|
|
(dG12*quu12 + dG22*quu22 + dG32*quu23)*sdown2 +
|
|
(dG13*quu12 + dG23*quu22 + dG33*quu23)*sdown3)*vbetaA +
|
|
quu23*(2.3333333333333333333*ddb233*qud23 +
|
|
0.33333333333333333333*(ddb131*qud11 + ddb331*qud31) -
|
|
0.66666666666666666667*dTheta3*alpha) +
|
|
quu12*(2.3333333333333333333*ddb123*qud23 +
|
|
0.33333333333333333333*(ddb111*qud11 + ddb131*qud31) +
|
|
dG11*sdown1*vbetaA + 1.3333333333333333333*
|
|
(sdown1*(ddb111*sup1 + ddb121*sup2 + ddb131*sup3) -
|
|
dKhat1*alpha)))/chi
|
|
;
|
|
|
|
rGamA3
|
|
=
|
|
-(((dG11*qud31 + dG12*qud32 + dG13*qud33)*sup1 +
|
|
(dG22*qud32 + dG23*qud33)*sup2 + (dG32*qud32 + dG33*qud33)*sup3 +
|
|
qud31*(dG21*sup2 + dG31*sup3))*vbetaA) +
|
|
(dG11*qud31 + dG12*qud32 + dG13*qud33)*beta1 +
|
|
(dG21*qud31 + dG22*qud32 + dG23*qud33)*beta2 +
|
|
(dG31*qud31 + dG32*qud32 + dG33*qud33)*beta3 -
|
|
((((db11*quu13 + db21*quu23 + db31*quu33)*sdown1 +
|
|
(db12*quu13 + db22*quu23 + db32*quu33)*sdown2 +
|
|
(db13*quu13 + db23*quu23)*sdown3)*shiftdriver)/vbetaA +
|
|
(0.66666666666666666667*dTheta1*quu13 +
|
|
(1.3333333333333333333*dKhat2 + 0.66666666666666666667*dTheta2)*
|
|
quu23)*alpha + quu33*
|
|
((db33*sdown3*shiftdriver)/vbetaA +
|
|
1.3333333333333333333*dKhat3*alpha))/chi +
|
|
((ddb111*qud31 + ddb112*qud32)*quu11 +
|
|
2.*(ddb122*qud32 + ddb123*qud33)*quu12 +
|
|
(ddb222*qud32 + ddb223*qud33)*quu22 +
|
|
qud31*(2.*ddb121*quu12 + ddb221*quu22) +
|
|
(0.33333333333333333333*(ddb121*qud11 + ddb223*qud23) +
|
|
2.3333333333333333333*ddb231*qud31)*quu23 +
|
|
2.3333333333333333333*((ddb132*qud32 + ddb133*qud33)*quu13 +
|
|
(ddb232*qud32 + ddb233*qud33)*quu23) +
|
|
0.33333333333333333333*((ddb112*qud12 + ddb113*qud13 +
|
|
ddb121*qud21 + ddb122*qud22)*quu13 +
|
|
(ddb122*qud12 + ddb123*qud13 + ddb221*qud21 + ddb222*qud22)*
|
|
quu23 + (ddb132*qud12 + ddb133*qud13 + ddb231*qud21 +
|
|
ddb232*qud22)*quu33) +
|
|
1.3333333333333333333*((ddb332*qud32 + ddb333*qud33)*quu33 +
|
|
(ddb132*quu33*sdown2 + ddb113*quu13*sdown3)*sup1 +
|
|
(ddb232*quu33*sdown2 + ddb123*quu13*sdown3)*sup2 +
|
|
(ddb332*quu33*sdown2 + ddb133*quu13*sdown3)*sup3 +
|
|
sdown2*((ddb112*quu13 + ddb122*quu23)*sup1 +
|
|
(ddb122*quu13 + ddb222*quu23)*sup2 +
|
|
(ddb132*quu13 + ddb232*quu23)*sup3) +
|
|
sdown1*((ddb121*quu23 + ddb131*quu33)*sup1 +
|
|
(ddb221*quu23 + ddb231*quu33)*sup2 +
|
|
(ddb231*quu23 + ddb331*quu33)*sup3) +
|
|
sdown3*((ddb123*quu23 + ddb133*quu33)*sup1 +
|
|
(ddb223*quu23 + ddb233*quu33)*sup2 +
|
|
(ddb233*quu23 + ddb333*quu33)*sup3)) +
|
|
qud33*(ddb113*quu11 + (db33*shiftdriver*sup3)/vbetaA) +
|
|
(shiftdriver*((db11*qud31 + db12*qud32 + db13*qud33)*sup1 +
|
|
(db21*qud31 + db22*qud32 + db23*qud33)*sup2 +
|
|
(db31*qud31 + db32*qud32)*sup3))/vbetaA +
|
|
((dG21*quu23 + dG31*quu33)*sdown1 +
|
|
(dG12*quu13 + dG22*quu23 + dG32*quu33)*sdown2 +
|
|
(dG13*quu13 + dG23*quu23 + dG33*quu33)*sdown3)*vbetaA +
|
|
quu33*(0.33333333333333333333*(ddb131*qud11 + ddb233*qud23) +
|
|
1.3333333333333333333*ddb331*qud31 -
|
|
0.66666666666666666667*dTheta3*alpha) +
|
|
quu13*(0.33333333333333333333*(ddb111*qud11 + ddb123*qud23) +
|
|
ddb131*(2.3333333333333333333*qud31 +
|
|
1.3333333333333333333*sdown1*sup3) + dG11*sdown1*vbetaA +
|
|
1.3333333333333333333*(sdown1*(ddb111*sup1 + ddb121*sup2) -
|
|
dKhat1*alpha)))/chi
|
|
;
|
|
|
|
rACsA1
|
|
=
|
|
-2.*((AA12*qud21 + AA13*qud31)*sup1 + (AA22*qud21 + AA23*qud31)*sup2 +
|
|
(AA32*qud21 + AA33*qud31)*sup3)*alpha -
|
|
((cdda12*qud21 + cdda13*qud31)*sup1 +
|
|
(cdda22*qud21 + cdda23*qud31)*sup2 + dda23*qud21*sup3)*chi +
|
|
(-(cdda33*qud31*sup3) + 0.66666666666666666667*dK1*qud11*alpha)*
|
|
chi + sup1*(qud11*(lieA11 - 2.*AA11*alpha - cdda11*chi) +
|
|
qud21*(lieA12 + Rf12*alpha*chi) +
|
|
qud31*(lieA13 + Rf13*alpha*chi)) +
|
|
sup2*(lieA23*qud31 + qud11*(lieA12 - 2.*AA21*alpha -
|
|
dda12*chi + Rf12*alpha*chi) +
|
|
qud21*(lieA22 + Rf22*alpha*chi)) +
|
|
sup3*(qud11*(lieA13 - 2.*AA31*alpha - dda13*chi) +
|
|
qud21*(lieA23 + Rf23*alpha*chi) +
|
|
qud31*(lieA33 + alpha*(K*A33 + Rf33*chi)) -
|
|
0.5*dG33*qdd13*alpha*pow2(chi)) +
|
|
alpha*(K*(sup1*(qud11*A11 + qud21*A12 + qud31*A13) +
|
|
qud11*(sup2*A12 + sup3*A13) + qud21*sup3*A23 +
|
|
sup2*(qud21*A22 + qud31*A23)) +
|
|
(-(dTheta1*qud11) - dTheta2*qud21 - dTheta3*qud31 +
|
|
0.66666666666666666667*(dK2*qud21 + dK3*qud31) + qud31*Rf23*sup2 +
|
|
qud11*(Rf11*sup1 + Rf13*sup3))*chi +
|
|
ginv11*(1.5*dchi1*(qud11*A11 + qud21*A12 + qud31*A13) -
|
|
(cdA111*qud11 + cdA112*qud21 + cdA113*qud31)*chi) +
|
|
ginv12*(1.5*(qud11*(dchi2*A11 + dchi1*A12) +
|
|
dchi2*(qud21*A12 + qud31*A13) +
|
|
dchi1*(qud21*A22 + qud31*A23)) -
|
|
((cdA112 + cdA211)*qud11 + (cdA122 + cdA212)*qud21 +
|
|
(cdA123 + cdA213)*qud31)*chi) +
|
|
ginv22*(1.5*dchi2*(qud11*A12 + qud21*A22 + qud31*A23) -
|
|
(cdA212*qud11 + cdA222*qud21 + cdA223*qud31)*chi) +
|
|
ginv13*(1.5*(dchi3*(qud11*A11 + qud21*A12) +
|
|
(dchi1*qud11 + dchi3*qud31)*A13 +
|
|
dchi1*(qud21*A23 + qud31*A33)) -
|
|
((cdA113 + cdA311)*qud11 + (cdA123 + cdA312)*qud21 +
|
|
(cdA133 + cdA313)*qud31)*chi) +
|
|
ginv23*(1.5*(qud11*(dchi3*A12 + dchi2*A13) +
|
|
qud21*(dchi3*A22 + dchi2*A23) +
|
|
qud31*(dchi3*A23 + dchi2*A33)) -
|
|
((cdA213 + cdA312)*qud11 + (cdA223 + cdA322)*qud21 +
|
|
(cdA233 + cdA323)*qud31)*chi) +
|
|
ginv33*(1.5*dchi3*(qud11*A13 + qud21*A23 + qud31*A33) -
|
|
(cdA313*qud11 + cdA323*qud21 + cdA333*qud31)*chi) +
|
|
0.5*((-(dG11*qdd11) - dG12*qdd12 + dGfromgdu12*qdd12 +
|
|
dGfromgdu13*qdd13)*sup1 +
|
|
(-(dG21*qdd11) - dG22*qdd12 + dGfromgdu22*qdd12 +
|
|
dGfromgdu23*qdd13)*sup2 -
|
|
qdd13*(Gfromg3*kappa1 + dG13*sup1 + dG23*sup2) +
|
|
(-(dG31*qdd11) - dG32*qdd12 + dGfromgdu32*qdd12 +
|
|
dGfromgdu33*qdd13)*sup3 +
|
|
qdd11*(dGfromgdu11*sup1 + dGfromgdu21*sup2 + dGfromgdu31*sup3) +
|
|
kappa1*(-(Gfromg1*qdd11) - Gfromg2*qdd12 + qdd11*G1 +
|
|
qdd12*G2 + qdd13*G3))*pow2(chi))
|
|
;
|
|
|
|
rACsA2
|
|
=
|
|
-2.*((AA12*qud22 + AA13*qud32)*sup1 + (AA22*qud22 + AA23*qud32)*sup2 +
|
|
(AA32*qud22 + AA33*qud32)*sup3)*alpha -
|
|
((cdda12*qud22 + cdda13*qud32)*sup1 +
|
|
(cdda22*qud22 + cdda23*qud32)*sup2 + dda23*qud22*sup3)*chi +
|
|
(-(cdda33*qud32*sup3) + 0.66666666666666666667*dK1*qud12*alpha)*
|
|
chi + sup1*(qud12*(lieA11 - 2.*AA11*alpha - cdda11*chi) +
|
|
qud22*(lieA12 + Rf12*alpha*chi) +
|
|
qud32*(lieA13 + Rf13*alpha*chi)) +
|
|
sup2*(lieA23*qud32 + qud12*(lieA12 - 2.*AA21*alpha -
|
|
dda12*chi + Rf12*alpha*chi) +
|
|
qud22*(lieA22 + Rf22*alpha*chi)) +
|
|
sup3*(qud12*(lieA13 - 2.*AA31*alpha - dda13*chi) +
|
|
qud22*(lieA23 + Rf23*alpha*chi) +
|
|
qud32*(lieA33 + alpha*(K*A33 + Rf33*chi)) -
|
|
0.5*dG33*qdd23*alpha*pow2(chi)) +
|
|
alpha*(K*(sup1*(qud12*A11 + qud22*A12 + qud32*A13) +
|
|
qud12*(sup2*A12 + sup3*A13) + qud22*sup3*A23 +
|
|
sup2*(qud22*A22 + qud32*A23)) +
|
|
(-(dTheta1*qud12) - dTheta2*qud22 - dTheta3*qud32 +
|
|
0.66666666666666666667*(dK2*qud22 + dK3*qud32) + qud32*Rf23*sup2 +
|
|
qud12*(Rf11*sup1 + Rf13*sup3))*chi +
|
|
ginv11*(1.5*dchi1*(qud12*A11 + qud22*A12 + qud32*A13) -
|
|
(cdA111*qud12 + cdA112*qud22 + cdA113*qud32)*chi) +
|
|
ginv12*(1.5*(qud12*(dchi2*A11 + dchi1*A12) +
|
|
dchi2*(qud22*A12 + qud32*A13) +
|
|
dchi1*(qud22*A22 + qud32*A23)) -
|
|
((cdA112 + cdA211)*qud12 + (cdA122 + cdA212)*qud22 +
|
|
(cdA123 + cdA213)*qud32)*chi) +
|
|
ginv22*(1.5*dchi2*(qud12*A12 + qud22*A22 + qud32*A23) -
|
|
(cdA212*qud12 + cdA222*qud22 + cdA223*qud32)*chi) +
|
|
ginv13*(1.5*(dchi3*(qud12*A11 + qud22*A12) +
|
|
(dchi1*qud12 + dchi3*qud32)*A13 +
|
|
dchi1*(qud22*A23 + qud32*A33)) -
|
|
((cdA113 + cdA311)*qud12 + (cdA123 + cdA312)*qud22 +
|
|
(cdA133 + cdA313)*qud32)*chi) +
|
|
ginv23*(1.5*(qud12*(dchi3*A12 + dchi2*A13) +
|
|
qud22*(dchi3*A22 + dchi2*A23) +
|
|
qud32*(dchi3*A23 + dchi2*A33)) -
|
|
((cdA213 + cdA312)*qud12 + (cdA223 + cdA322)*qud22 +
|
|
(cdA233 + cdA323)*qud32)*chi) +
|
|
ginv33*(1.5*dchi3*(qud12*A13 + qud22*A23 + qud32*A33) -
|
|
(cdA313*qud12 + cdA323*qud22 + cdA333*qud32)*chi) +
|
|
0.5*((-(dG11*qdd12) - dG12*qdd22 + dGfromgdu12*qdd22 +
|
|
dGfromgdu13*qdd23)*sup1 +
|
|
(-(dG21*qdd12) - dG22*qdd22 + dGfromgdu22*qdd22 +
|
|
dGfromgdu23*qdd23)*sup2 -
|
|
qdd23*(Gfromg3*kappa1 + dG13*sup1 + dG23*sup2) +
|
|
(-(dG31*qdd12) - dG32*qdd22 + dGfromgdu32*qdd22 +
|
|
dGfromgdu33*qdd23)*sup3 +
|
|
qdd12*(dGfromgdu11*sup1 + dGfromgdu21*sup2 + dGfromgdu31*sup3) +
|
|
kappa1*(-(Gfromg1*qdd12) - Gfromg2*qdd22 + qdd12*G1 +
|
|
qdd22*G2 + qdd23*G3))*pow2(chi))
|
|
;
|
|
|
|
rACsA3
|
|
=
|
|
-2.*((AA12*qud23 + AA13*qud33)*sup1 + (AA22*qud23 + AA23*qud33)*sup2 +
|
|
(AA32*qud23 + AA33*qud33)*sup3)*alpha -
|
|
((cdda12*qud23 + cdda13*qud33)*sup1 +
|
|
(cdda22*qud23 + cdda23*qud33)*sup2 + dda23*qud23*sup3)*chi +
|
|
(-(cdda33*qud33*sup3) + 0.66666666666666666667*dK1*qud13*alpha)*
|
|
chi + sup1*(qud13*(lieA11 - 2.*AA11*alpha - cdda11*chi) +
|
|
qud23*(lieA12 + Rf12*alpha*chi) +
|
|
qud33*(lieA13 + Rf13*alpha*chi)) +
|
|
sup2*(lieA23*qud33 + qud13*(lieA12 - 2.*AA21*alpha -
|
|
dda12*chi + Rf12*alpha*chi) +
|
|
qud23*(lieA22 + Rf22*alpha*chi)) +
|
|
sup3*(qud13*(lieA13 - 2.*AA31*alpha - dda13*chi) +
|
|
qud23*(lieA23 + Rf23*alpha*chi) +
|
|
qud33*(lieA33 + alpha*(K*A33 + Rf33*chi)) -
|
|
0.5*dG33*qdd33*alpha*pow2(chi)) +
|
|
alpha*(K*(sup1*(qud13*A11 + qud23*A12 + qud33*A13) +
|
|
qud13*(sup2*A12 + sup3*A13) + qud23*sup3*A23 +
|
|
sup2*(qud23*A22 + qud33*A23)) +
|
|
(-(dTheta1*qud13) - dTheta2*qud23 - dTheta3*qud33 +
|
|
0.66666666666666666667*(dK2*qud23 + dK3*qud33) + qud33*Rf23*sup2 +
|
|
qud13*(Rf11*sup1 + Rf13*sup3))*chi +
|
|
ginv11*(1.5*dchi1*(qud13*A11 + qud23*A12 + qud33*A13) -
|
|
(cdA111*qud13 + cdA112*qud23 + cdA113*qud33)*chi) +
|
|
ginv12*(1.5*(qud13*(dchi2*A11 + dchi1*A12) +
|
|
dchi2*(qud23*A12 + qud33*A13) +
|
|
dchi1*(qud23*A22 + qud33*A23)) -
|
|
((cdA112 + cdA211)*qud13 + (cdA122 + cdA212)*qud23 +
|
|
(cdA123 + cdA213)*qud33)*chi) +
|
|
ginv22*(1.5*dchi2*(qud13*A12 + qud23*A22 + qud33*A23) -
|
|
(cdA212*qud13 + cdA222*qud23 + cdA223*qud33)*chi) +
|
|
ginv13*(1.5*(dchi3*(qud13*A11 + qud23*A12) +
|
|
(dchi1*qud13 + dchi3*qud33)*A13 +
|
|
dchi1*(qud23*A23 + qud33*A33)) -
|
|
((cdA113 + cdA311)*qud13 + (cdA123 + cdA312)*qud23 +
|
|
(cdA133 + cdA313)*qud33)*chi) +
|
|
ginv23*(1.5*(qud13*(dchi3*A12 + dchi2*A13) +
|
|
qud23*(dchi3*A22 + dchi2*A23) +
|
|
qud33*(dchi3*A23 + dchi2*A33)) -
|
|
((cdA213 + cdA312)*qud13 + (cdA223 + cdA322)*qud23 +
|
|
(cdA233 + cdA323)*qud33)*chi) +
|
|
ginv33*(1.5*dchi3*(qud13*A13 + qud23*A23 + qud33*A33) -
|
|
(cdA313*qud13 + cdA323*qud23 + cdA333*qud33)*chi) +
|
|
0.5*((-(dG11*qdd13) - dG12*qdd23 + dGfromgdu12*qdd23 +
|
|
dGfromgdu13*qdd33)*sup1 +
|
|
(-(dG21*qdd13) - dG22*qdd23 + dGfromgdu22*qdd23 +
|
|
dGfromgdu23*qdd33)*sup2 -
|
|
qdd33*(Gfromg3*kappa1 + dG13*sup1 + dG23*sup2) +
|
|
(-(dG31*qdd13) - dG32*qdd23 + dGfromgdu32*qdd23 +
|
|
dGfromgdu33*qdd33)*sup3 +
|
|
qdd13*(dGfromgdu11*sup1 + dGfromgdu21*sup2 + dGfromgdu31*sup3) +
|
|
kappa1*(-(Gfromg1*qdd13) - Gfromg2*qdd23 + qdd13*G1 +
|
|
qdd23*G2 + qdd33*G3))*pow2(chi))
|
|
;
|
|
|
|
rACABTF11
|
|
=
|
|
2.*(lieA12*qPhysuudd1211 + lieA13*qPhysuudd1311 +
|
|
qPhysuudd2311*(lieA23 - cdA123*sup1*alpha)) +
|
|
qPhysuudd1111*(lieA11 + alpha*
|
|
(-AA11 - cdA211*sup2 + sup2*(cdA112 - (0.5*dchi1*A12)/chi))) \
|
|
+ alpha*(qPhysuudd1111*(cdA113*sup3 +
|
|
0.66666666666666666667*K*A11) +
|
|
1.3333333333333333333*K*(qPhysuudd1211*A12 +
|
|
qPhysuudd1311*A13 + qPhysuudd2311*A23) +
|
|
qPhysuudd3311*(-(cdA233*sup2) + 0.66666666666666666667*K*A33) +
|
|
sup3*(cdA123*qPhysuudd1211 +
|
|
qPhysuudd1111*(-cdA311 + (0.5*dchi3*A11)/chi)) +
|
|
qPhysuudd2211*A22*(0.66666666666666666667*K +
|
|
(0.5*dchi3*sup3)/chi) +
|
|
sup2*(-2.*cdA213*qPhysuudd1311 - cdA223*qPhysuudd2311 +
|
|
cdA322*qPhysuudd2311 + cdA323*qPhysuudd3311 +
|
|
(0.5*dchi2*qPhysuudd1111*A11)/chi) +
|
|
(dchi3*(-0.5*qPhysuudd1311*sup2 + qPhysuudd1211*sup3)*A12 +
|
|
(-0.5*dchi3*qPhysuudd3311*sup1 + dchi2*qPhysuudd1311*sup2)*
|
|
A13 + sup1*(-0.5*dchi2*qPhysuudd1211*A11 +
|
|
dchi1*qPhysuudd2311*A23) +
|
|
0.5*((-(dchi3*qPhysuudd2311*sup1) + dchi2*qPhysuudd1211*sup2)*
|
|
A12 + dchi3*qPhysuudd1311*sup3*A13 -
|
|
(dchi1*qPhysuudd1211 + dchi3*qPhysuudd2311)*sup2*A22 +
|
|
sup1*((dchi1*qPhysuudd1211 - dchi2*qPhysuudd2211)*A12 +
|
|
(dchi1*qPhysuudd1311 - dchi2*qPhysuudd2311)*A13 +
|
|
dchi1*qPhysuudd2211*A22) -
|
|
(dchi3*qPhysuudd3311*sup2 + dchi1*qPhysuudd1211*sup3)*
|
|
A23 + ((-(dchi1*qPhysuudd1311) + dchi2*qPhysuudd2311)*
|
|
sup2 + (-(dchi2*qPhysuudd2211) + dchi3*qPhysuudd2311)*sup3\
|
|
)*A23 + qPhysuudd3311*(dchi1*sup1 + dchi2*sup2)*A33 -
|
|
sup3*((dchi1*qPhysuudd1111 + dchi2*qPhysuudd1211)*A13 +
|
|
(dchi1*qPhysuudd1311 + dchi2*qPhysuudd2311)*A33)))/
|
|
chi) - cdda11*qPhysuudd1111*chi +
|
|
qPhysuudd1211*(((-cdA112 + cdA211)*sup1 + (cdA122 - cdA212)*sup2 +
|
|
(cdA213 - 2.*cdA312)*sup3)*alpha - cdda12*chi) +
|
|
qPhysuudd1311*(((-cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 - cdA313)*sup3)*alpha - cdda13*chi) +
|
|
qPhysuudd2211*(lieA22 + (-AA22 - cdA122*sup1 + cdA212*sup1 +
|
|
cdA223*sup3 - cdA322*sup3)*alpha - cdda22*chi) +
|
|
qPhysuudd2311*(((cdA213 + cdA312)*sup1 + (cdA233 - cdA323)*sup3)*
|
|
alpha - cdda23*chi) +
|
|
qPhysuudd3311*(lieA33 + (-AA33 - cdA133*sup1 + cdA313*sup1)*alpha -
|
|
cdda33*chi) - qPhysuudd1211*
|
|
((AA12 + AA21)*alpha + dda12*chi) -
|
|
qPhysuudd1311*(alpha*(AA13 + AA31 +
|
|
(0.5*dchi3*sup1*A11)/chi) + dda13*chi) -
|
|
qPhysuudd2311*((AA23 + AA32)*alpha + dda23*chi)
|
|
;
|
|
|
|
rACABTF12
|
|
=
|
|
2.*(lieA12*qPhysuudd1212 + lieA13*qPhysuudd1312 +
|
|
qPhysuudd2312*(lieA23 - cdA123*sup1*alpha)) +
|
|
qPhysuudd1112*(lieA11 + alpha*
|
|
(-AA11 - cdA211*sup2 + sup2*(cdA112 - (0.5*dchi1*A12)/chi))) \
|
|
+ alpha*(qPhysuudd1112*(cdA113*sup3 +
|
|
0.66666666666666666667*K*A11) +
|
|
1.3333333333333333333*K*(qPhysuudd1212*A12 +
|
|
qPhysuudd1312*A13 + qPhysuudd2312*A23) +
|
|
qPhysuudd3312*(-(cdA233*sup2) + 0.66666666666666666667*K*A33) +
|
|
sup3*(cdA123*qPhysuudd1212 +
|
|
qPhysuudd1112*(-cdA311 + (0.5*dchi3*A11)/chi)) +
|
|
qPhysuudd2212*A22*(0.66666666666666666667*K +
|
|
(0.5*dchi3*sup3)/chi) +
|
|
sup2*(-2.*cdA213*qPhysuudd1312 - cdA223*qPhysuudd2312 +
|
|
cdA322*qPhysuudd2312 + cdA323*qPhysuudd3312 +
|
|
(0.5*dchi2*qPhysuudd1112*A11)/chi) +
|
|
(dchi3*(-0.5*qPhysuudd1312*sup2 + qPhysuudd1212*sup3)*A12 +
|
|
(-0.5*dchi3*qPhysuudd3312*sup1 + dchi2*qPhysuudd1312*sup2)*
|
|
A13 + sup1*(-0.5*dchi2*qPhysuudd1212*A11 +
|
|
dchi1*qPhysuudd2312*A23) +
|
|
0.5*((-(dchi3*qPhysuudd2312*sup1) + dchi2*qPhysuudd1212*sup2)*
|
|
A12 + dchi3*qPhysuudd1312*sup3*A13 -
|
|
(dchi1*qPhysuudd1212 + dchi3*qPhysuudd2312)*sup2*A22 +
|
|
sup1*((dchi1*qPhysuudd1212 - dchi2*qPhysuudd2212)*A12 +
|
|
(dchi1*qPhysuudd1312 - dchi2*qPhysuudd2312)*A13 +
|
|
dchi1*qPhysuudd2212*A22) -
|
|
(dchi3*qPhysuudd3312*sup2 + dchi1*qPhysuudd1212*sup3)*
|
|
A23 + ((-(dchi1*qPhysuudd1312) + dchi2*qPhysuudd2312)*
|
|
sup2 + (-(dchi2*qPhysuudd2212) + dchi3*qPhysuudd2312)*sup3\
|
|
)*A23 + qPhysuudd3312*(dchi1*sup1 + dchi2*sup2)*A33 -
|
|
sup3*((dchi1*qPhysuudd1112 + dchi2*qPhysuudd1212)*A13 +
|
|
(dchi1*qPhysuudd1312 + dchi2*qPhysuudd2312)*A33)))/
|
|
chi) - cdda11*qPhysuudd1112*chi +
|
|
qPhysuudd1212*(((-cdA112 + cdA211)*sup1 + (cdA122 - cdA212)*sup2 +
|
|
(cdA213 - 2.*cdA312)*sup3)*alpha - cdda12*chi) +
|
|
qPhysuudd1312*(((-cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 - cdA313)*sup3)*alpha - cdda13*chi) +
|
|
qPhysuudd2212*(lieA22 + (-AA22 - cdA122*sup1 + cdA212*sup1 +
|
|
cdA223*sup3 - cdA322*sup3)*alpha - cdda22*chi) +
|
|
qPhysuudd2312*(((cdA213 + cdA312)*sup1 + (cdA233 - cdA323)*sup3)*
|
|
alpha - cdda23*chi) +
|
|
qPhysuudd3312*(lieA33 + (-AA33 - cdA133*sup1 + cdA313*sup1)*alpha -
|
|
cdda33*chi) - qPhysuudd1212*
|
|
((AA12 + AA21)*alpha + dda12*chi) -
|
|
qPhysuudd1312*(alpha*(AA13 + AA31 +
|
|
(0.5*dchi3*sup1*A11)/chi) + dda13*chi) -
|
|
qPhysuudd2312*((AA23 + AA32)*alpha + dda23*chi)
|
|
;
|
|
|
|
rACABTF13
|
|
=
|
|
2.*(lieA12*qPhysuudd1213 + lieA13*qPhysuudd1313 +
|
|
qPhysuudd2313*(lieA23 - cdA123*sup1*alpha)) +
|
|
qPhysuudd1113*(lieA11 + alpha*
|
|
(-AA11 - cdA211*sup2 + sup2*(cdA112 - (0.5*dchi1*A12)/chi))) \
|
|
+ alpha*(qPhysuudd1113*(cdA113*sup3 +
|
|
0.66666666666666666667*K*A11) +
|
|
1.3333333333333333333*K*(qPhysuudd1213*A12 +
|
|
qPhysuudd1313*A13 + qPhysuudd2313*A23) +
|
|
qPhysuudd3313*(-(cdA233*sup2) + 0.66666666666666666667*K*A33) +
|
|
sup3*(cdA123*qPhysuudd1213 +
|
|
qPhysuudd1113*(-cdA311 + (0.5*dchi3*A11)/chi)) +
|
|
qPhysuudd2213*A22*(0.66666666666666666667*K +
|
|
(0.5*dchi3*sup3)/chi) +
|
|
sup2*(-2.*cdA213*qPhysuudd1313 - cdA223*qPhysuudd2313 +
|
|
cdA322*qPhysuudd2313 + cdA323*qPhysuudd3313 +
|
|
(0.5*dchi2*qPhysuudd1113*A11)/chi) +
|
|
(dchi3*(-0.5*qPhysuudd1313*sup2 + qPhysuudd1213*sup3)*A12 +
|
|
(-0.5*dchi3*qPhysuudd3313*sup1 + dchi2*qPhysuudd1313*sup2)*
|
|
A13 + sup1*(-0.5*dchi2*qPhysuudd1213*A11 +
|
|
dchi1*qPhysuudd2313*A23) +
|
|
0.5*((-(dchi3*qPhysuudd2313*sup1) + dchi2*qPhysuudd1213*sup2)*
|
|
A12 + dchi3*qPhysuudd1313*sup3*A13 -
|
|
(dchi1*qPhysuudd1213 + dchi3*qPhysuudd2313)*sup2*A22 +
|
|
sup1*((dchi1*qPhysuudd1213 - dchi2*qPhysuudd2213)*A12 +
|
|
(dchi1*qPhysuudd1313 - dchi2*qPhysuudd2313)*A13 +
|
|
dchi1*qPhysuudd2213*A22) -
|
|
(dchi3*qPhysuudd3313*sup2 + dchi1*qPhysuudd1213*sup3)*
|
|
A23 + ((-(dchi1*qPhysuudd1313) + dchi2*qPhysuudd2313)*
|
|
sup2 + (-(dchi2*qPhysuudd2213) + dchi3*qPhysuudd2313)*sup3\
|
|
)*A23 + qPhysuudd3313*(dchi1*sup1 + dchi2*sup2)*A33 -
|
|
sup3*((dchi1*qPhysuudd1113 + dchi2*qPhysuudd1213)*A13 +
|
|
(dchi1*qPhysuudd1313 + dchi2*qPhysuudd2313)*A33)))/
|
|
chi) - cdda11*qPhysuudd1113*chi +
|
|
qPhysuudd1213*(((-cdA112 + cdA211)*sup1 + (cdA122 - cdA212)*sup2 +
|
|
(cdA213 - 2.*cdA312)*sup3)*alpha - cdda12*chi) +
|
|
qPhysuudd1313*(((-cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 - cdA313)*sup3)*alpha - cdda13*chi) +
|
|
qPhysuudd2213*(lieA22 + (-AA22 - cdA122*sup1 + cdA212*sup1 +
|
|
cdA223*sup3 - cdA322*sup3)*alpha - cdda22*chi) +
|
|
qPhysuudd2313*(((cdA213 + cdA312)*sup1 + (cdA233 - cdA323)*sup3)*
|
|
alpha - cdda23*chi) +
|
|
qPhysuudd3313*(lieA33 + (-AA33 - cdA133*sup1 + cdA313*sup1)*alpha -
|
|
cdda33*chi) - qPhysuudd1213*
|
|
((AA12 + AA21)*alpha + dda12*chi) -
|
|
qPhysuudd1313*(alpha*(AA13 + AA31 +
|
|
(0.5*dchi3*sup1*A11)/chi) + dda13*chi) -
|
|
qPhysuudd2313*((AA23 + AA32)*alpha + dda23*chi)
|
|
;
|
|
|
|
rACABTF22
|
|
=
|
|
2.*(lieA12*qPhysuudd1222 + lieA13*qPhysuudd1322 +
|
|
qPhysuudd2322*(lieA23 - cdA123*sup1*alpha)) +
|
|
qPhysuudd1122*(lieA11 + alpha*
|
|
(-AA11 - cdA211*sup2 + sup2*(cdA112 - (0.5*dchi1*A12)/chi))) \
|
|
+ alpha*(qPhysuudd1122*(cdA113*sup3 +
|
|
0.66666666666666666667*K*A11) +
|
|
1.3333333333333333333*K*(qPhysuudd1222*A12 +
|
|
qPhysuudd1322*A13 + qPhysuudd2322*A23) +
|
|
qPhysuudd3322*(-(cdA233*sup2) + 0.66666666666666666667*K*A33) +
|
|
sup3*(cdA123*qPhysuudd1222 +
|
|
qPhysuudd1122*(-cdA311 + (0.5*dchi3*A11)/chi)) +
|
|
qPhysuudd2222*A22*(0.66666666666666666667*K +
|
|
(0.5*dchi3*sup3)/chi) +
|
|
sup2*(-2.*cdA213*qPhysuudd1322 - cdA223*qPhysuudd2322 +
|
|
cdA322*qPhysuudd2322 + cdA323*qPhysuudd3322 +
|
|
(0.5*dchi2*qPhysuudd1122*A11)/chi) +
|
|
(dchi3*(-0.5*qPhysuudd1322*sup2 + qPhysuudd1222*sup3)*A12 +
|
|
(-0.5*dchi3*qPhysuudd3322*sup1 + dchi2*qPhysuudd1322*sup2)*
|
|
A13 + sup1*(-0.5*dchi2*qPhysuudd1222*A11 +
|
|
dchi1*qPhysuudd2322*A23) +
|
|
0.5*((-(dchi3*qPhysuudd2322*sup1) + dchi2*qPhysuudd1222*sup2)*
|
|
A12 + dchi3*qPhysuudd1322*sup3*A13 -
|
|
(dchi1*qPhysuudd1222 + dchi3*qPhysuudd2322)*sup2*A22 +
|
|
sup1*((dchi1*qPhysuudd1222 - dchi2*qPhysuudd2222)*A12 +
|
|
(dchi1*qPhysuudd1322 - dchi2*qPhysuudd2322)*A13 +
|
|
dchi1*qPhysuudd2222*A22) -
|
|
(dchi3*qPhysuudd3322*sup2 + dchi1*qPhysuudd1222*sup3)*
|
|
A23 + ((-(dchi1*qPhysuudd1322) + dchi2*qPhysuudd2322)*
|
|
sup2 + (-(dchi2*qPhysuudd2222) + dchi3*qPhysuudd2322)*sup3\
|
|
)*A23 + qPhysuudd3322*(dchi1*sup1 + dchi2*sup2)*A33 -
|
|
sup3*((dchi1*qPhysuudd1122 + dchi2*qPhysuudd1222)*A13 +
|
|
(dchi1*qPhysuudd1322 + dchi2*qPhysuudd2322)*A33)))/
|
|
chi) - cdda11*qPhysuudd1122*chi +
|
|
qPhysuudd1222*(((-cdA112 + cdA211)*sup1 + (cdA122 - cdA212)*sup2 +
|
|
(cdA213 - 2.*cdA312)*sup3)*alpha - cdda12*chi) +
|
|
qPhysuudd1322*(((-cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 - cdA313)*sup3)*alpha - cdda13*chi) +
|
|
qPhysuudd2222*(lieA22 + (-AA22 - cdA122*sup1 + cdA212*sup1 +
|
|
cdA223*sup3 - cdA322*sup3)*alpha - cdda22*chi) +
|
|
qPhysuudd2322*(((cdA213 + cdA312)*sup1 + (cdA233 - cdA323)*sup3)*
|
|
alpha - cdda23*chi) +
|
|
qPhysuudd3322*(lieA33 + (-AA33 - cdA133*sup1 + cdA313*sup1)*alpha -
|
|
cdda33*chi) - qPhysuudd1222*
|
|
((AA12 + AA21)*alpha + dda12*chi) -
|
|
qPhysuudd1322*(alpha*(AA13 + AA31 +
|
|
(0.5*dchi3*sup1*A11)/chi) + dda13*chi) -
|
|
qPhysuudd2322*((AA23 + AA32)*alpha + dda23*chi)
|
|
;
|
|
|
|
rACABTF23
|
|
=
|
|
2.*(lieA12*qPhysuudd1223 + lieA13*qPhysuudd1323 +
|
|
qPhysuudd2323*(lieA23 - cdA123*sup1*alpha)) +
|
|
qPhysuudd1123*(lieA11 + alpha*
|
|
(-AA11 - cdA211*sup2 + sup2*(cdA112 - (0.5*dchi1*A12)/chi))) \
|
|
+ alpha*(qPhysuudd1123*(cdA113*sup3 +
|
|
0.66666666666666666667*K*A11) +
|
|
1.3333333333333333333*K*(qPhysuudd1223*A12 +
|
|
qPhysuudd1323*A13 + qPhysuudd2323*A23) +
|
|
qPhysuudd3323*(-(cdA233*sup2) + 0.66666666666666666667*K*A33) +
|
|
sup3*(cdA123*qPhysuudd1223 +
|
|
qPhysuudd1123*(-cdA311 + (0.5*dchi3*A11)/chi)) +
|
|
qPhysuudd2223*A22*(0.66666666666666666667*K +
|
|
(0.5*dchi3*sup3)/chi) +
|
|
sup2*(-2.*cdA213*qPhysuudd1323 - cdA223*qPhysuudd2323 +
|
|
cdA322*qPhysuudd2323 + cdA323*qPhysuudd3323 +
|
|
(0.5*dchi2*qPhysuudd1123*A11)/chi) +
|
|
(dchi3*(-0.5*qPhysuudd1323*sup2 + qPhysuudd1223*sup3)*A12 +
|
|
(-0.5*dchi3*qPhysuudd3323*sup1 + dchi2*qPhysuudd1323*sup2)*
|
|
A13 + sup1*(-0.5*dchi2*qPhysuudd1223*A11 +
|
|
dchi1*qPhysuudd2323*A23) +
|
|
0.5*((-(dchi3*qPhysuudd2323*sup1) + dchi2*qPhysuudd1223*sup2)*
|
|
A12 + dchi3*qPhysuudd1323*sup3*A13 -
|
|
(dchi1*qPhysuudd1223 + dchi3*qPhysuudd2323)*sup2*A22 +
|
|
sup1*((dchi1*qPhysuudd1223 - dchi2*qPhysuudd2223)*A12 +
|
|
(dchi1*qPhysuudd1323 - dchi2*qPhysuudd2323)*A13 +
|
|
dchi1*qPhysuudd2223*A22) -
|
|
(dchi3*qPhysuudd3323*sup2 + dchi1*qPhysuudd1223*sup3)*
|
|
A23 + ((-(dchi1*qPhysuudd1323) + dchi2*qPhysuudd2323)*
|
|
sup2 + (-(dchi2*qPhysuudd2223) + dchi3*qPhysuudd2323)*sup3\
|
|
)*A23 + qPhysuudd3323*(dchi1*sup1 + dchi2*sup2)*A33 -
|
|
sup3*((dchi1*qPhysuudd1123 + dchi2*qPhysuudd1223)*A13 +
|
|
(dchi1*qPhysuudd1323 + dchi2*qPhysuudd2323)*A33)))/
|
|
chi) - cdda11*qPhysuudd1123*chi +
|
|
qPhysuudd1223*(((-cdA112 + cdA211)*sup1 + (cdA122 - cdA212)*sup2 +
|
|
(cdA213 - 2.*cdA312)*sup3)*alpha - cdda12*chi) +
|
|
qPhysuudd1323*(((-cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 - cdA313)*sup3)*alpha - cdda13*chi) +
|
|
qPhysuudd2223*(lieA22 + (-AA22 - cdA122*sup1 + cdA212*sup1 +
|
|
cdA223*sup3 - cdA322*sup3)*alpha - cdda22*chi) +
|
|
qPhysuudd2323*(((cdA213 + cdA312)*sup1 + (cdA233 - cdA323)*sup3)*
|
|
alpha - cdda23*chi) +
|
|
qPhysuudd3323*(lieA33 + (-AA33 - cdA133*sup1 + cdA313*sup1)*alpha -
|
|
cdda33*chi) - qPhysuudd1223*
|
|
((AA12 + AA21)*alpha + dda12*chi) -
|
|
qPhysuudd1323*(alpha*(AA13 + AA31 +
|
|
(0.5*dchi3*sup1*A11)/chi) + dda13*chi) -
|
|
qPhysuudd2323*((AA23 + AA32)*alpha + dda23*chi)
|
|
;
|
|
|
|
rACABTF33
|
|
=
|
|
2.*(lieA12*qPhysuudd1233 + lieA13*qPhysuudd1333 +
|
|
qPhysuudd2333*(lieA23 - cdA123*sup1*alpha)) +
|
|
qPhysuudd1133*(lieA11 + alpha*
|
|
(-AA11 - cdA211*sup2 + sup2*(cdA112 - (0.5*dchi1*A12)/chi))) \
|
|
+ alpha*(qPhysuudd1133*(cdA113*sup3 +
|
|
0.66666666666666666667*K*A11) +
|
|
1.3333333333333333333*K*(qPhysuudd1233*A12 +
|
|
qPhysuudd1333*A13 + qPhysuudd2333*A23) +
|
|
qPhysuudd3333*(-(cdA233*sup2) + 0.66666666666666666667*K*A33) +
|
|
sup3*(cdA123*qPhysuudd1233 +
|
|
qPhysuudd1133*(-cdA311 + (0.5*dchi3*A11)/chi)) +
|
|
qPhysuudd2233*A22*(0.66666666666666666667*K +
|
|
(0.5*dchi3*sup3)/chi) +
|
|
sup2*(-2.*cdA213*qPhysuudd1333 - cdA223*qPhysuudd2333 +
|
|
cdA322*qPhysuudd2333 + cdA323*qPhysuudd3333 +
|
|
(0.5*dchi2*qPhysuudd1133*A11)/chi) +
|
|
(dchi3*(-0.5*qPhysuudd1333*sup2 + qPhysuudd1233*sup3)*A12 +
|
|
(-0.5*dchi3*qPhysuudd3333*sup1 + dchi2*qPhysuudd1333*sup2)*
|
|
A13 + sup1*(-0.5*dchi2*qPhysuudd1233*A11 +
|
|
dchi1*qPhysuudd2333*A23) +
|
|
0.5*((-(dchi3*qPhysuudd2333*sup1) + dchi2*qPhysuudd1233*sup2)*
|
|
A12 + dchi3*qPhysuudd1333*sup3*A13 -
|
|
(dchi1*qPhysuudd1233 + dchi3*qPhysuudd2333)*sup2*A22 +
|
|
sup1*((dchi1*qPhysuudd1233 - dchi2*qPhysuudd2233)*A12 +
|
|
(dchi1*qPhysuudd1333 - dchi2*qPhysuudd2333)*A13 +
|
|
dchi1*qPhysuudd2233*A22) -
|
|
(dchi3*qPhysuudd3333*sup2 + dchi1*qPhysuudd1233*sup3)*
|
|
A23 + ((-(dchi1*qPhysuudd1333) + dchi2*qPhysuudd2333)*
|
|
sup2 + (-(dchi2*qPhysuudd2233) + dchi3*qPhysuudd2333)*sup3\
|
|
)*A23 + qPhysuudd3333*(dchi1*sup1 + dchi2*sup2)*A33 -
|
|
sup3*((dchi1*qPhysuudd1133 + dchi2*qPhysuudd1233)*A13 +
|
|
(dchi1*qPhysuudd1333 + dchi2*qPhysuudd2333)*A33)))/
|
|
chi) - cdda11*qPhysuudd1133*chi +
|
|
qPhysuudd1233*(((-cdA112 + cdA211)*sup1 + (cdA122 - cdA212)*sup2 +
|
|
(cdA213 - 2.*cdA312)*sup3)*alpha - cdda12*chi) +
|
|
qPhysuudd1333*(((-cdA113 + cdA311)*sup1 + (cdA123 + cdA312)*sup2 +
|
|
(cdA133 - cdA313)*sup3)*alpha - cdda13*chi) +
|
|
qPhysuudd2233*(lieA22 + (-AA22 - cdA122*sup1 + cdA212*sup1 +
|
|
cdA223*sup3 - cdA322*sup3)*alpha - cdda22*chi) +
|
|
qPhysuudd2333*(((cdA213 + cdA312)*sup1 + (cdA233 - cdA323)*sup3)*
|
|
alpha - cdda23*chi) +
|
|
qPhysuudd3333*(lieA33 + (-AA33 - cdA133*sup1 + cdA313*sup1)*alpha -
|
|
cdda33*chi) - qPhysuudd1233*
|
|
((AA12 + AA21)*alpha + dda12*chi) -
|
|
qPhysuudd1333*(alpha*(AA13 + AA31 +
|
|
(0.5*dchi3*sup1*A11)/chi) + dda13*chi) -
|
|
qPhysuudd2333*((AA23 + AA32)*alpha + dda23*chi)
|
|
;
|
|
|
|
|
|
if (givehPsi0) {
|
|
|
|
gADM11
|
|
=
|
|
g11/chi
|
|
;
|
|
|
|
gADM12
|
|
=
|
|
g12/chi
|
|
;
|
|
|
|
gADM13
|
|
=
|
|
g13/chi
|
|
;
|
|
|
|
gADM21
|
|
=
|
|
g12/chi
|
|
;
|
|
|
|
gADM22
|
|
=
|
|
g22/chi
|
|
;
|
|
|
|
gADM23
|
|
=
|
|
g23/chi
|
|
;
|
|
|
|
gADM31
|
|
=
|
|
g13/chi
|
|
;
|
|
|
|
gADM32
|
|
=
|
|
g23/chi
|
|
;
|
|
|
|
gADM33
|
|
=
|
|
g33/chi
|
|
;
|
|
|
|
vu1
|
|
=
|
|
-yp
|
|
;
|
|
|
|
vu2
|
|
=
|
|
xp
|
|
;
|
|
|
|
vu3
|
|
=
|
|
0
|
|
;
|
|
|
|
wu1
|
|
=
|
|
((-(ADMginv13*sup2) + ADMginv12*sup3)*vu1 +
|
|
(ADMginv13*sup1 - ADMginv11*sup3)*vu2 +
|
|
(-(ADMginv12*sup1) + ADMginv11*sup2)*vu3)/Power(chi,1.5)
|
|
;
|
|
|
|
wu2
|
|
=
|
|
((-(ADMginv23*sup2) + ADMginv22*sup3)*vu1 +
|
|
(ADMginv23*sup1 - ADMginv12*sup3)*vu2 +
|
|
(-(ADMginv22*sup1) + ADMginv12*sup2)*vu3)/Power(chi,1.5)
|
|
;
|
|
|
|
wu3
|
|
=
|
|
((-(ADMginv33*sup2) + ADMginv23*sup3)*vu1 +
|
|
(ADMginv33*sup1 - ADMginv13*sup3)*vu2 +
|
|
(-(ADMginv23*sup1) + ADMginv13*sup2)*vu3)/Power(chi,1.5)
|
|
;
|
|
|
|
sdotv
|
|
=
|
|
(gADM11*sup1 + gADM21*sup2 + gADM31*sup3)*vu1 +
|
|
(gADM12*sup1 + gADM22*sup2 + gADM32*sup3)*vu2 +
|
|
(gADM13*sup1 + gADM23*sup2 + gADM33*sup3)*vu3
|
|
;
|
|
|
|
vu1
|
|
=
|
|
-(sdotv*sup1) + vu1
|
|
;
|
|
|
|
vu2
|
|
=
|
|
-(sdotv*sup2) + vu2
|
|
;
|
|
|
|
vu3
|
|
=
|
|
-(sdotv*sup3) + vu3
|
|
;
|
|
|
|
vdotv
|
|
=
|
|
(gADM31*vu1 + (gADM23 + gADM32)*vu2)*vu3 +
|
|
vu1*((gADM12 + gADM21)*vu2 + gADM13*vu3) + gADM11*pow2(vu1) +
|
|
gADM22*pow2(vu2) + gADM33*pow2(vu3)
|
|
;
|
|
|
|
vu1
|
|
=
|
|
vu1/Sqrt(vdotv)
|
|
;
|
|
|
|
vu2
|
|
=
|
|
vu2/Sqrt(vdotv)
|
|
;
|
|
|
|
vu3
|
|
=
|
|
vu3/Sqrt(vdotv)
|
|
;
|
|
|
|
sdotw
|
|
=
|
|
(gADM11*sup1 + gADM21*sup2 + gADM31*sup3)*wu1 +
|
|
(gADM12*sup1 + gADM22*sup2 + gADM32*sup3)*wu2 +
|
|
(gADM13*sup1 + gADM23*sup2 + gADM33*sup3)*wu3
|
|
;
|
|
|
|
vdotw
|
|
=
|
|
(gADM11*vu1 + gADM21*vu2 + gADM31*vu3)*wu1 +
|
|
(gADM12*vu1 + gADM22*vu2 + gADM32*vu3)*wu2 +
|
|
(gADM13*vu1 + gADM23*vu2 + gADM33*vu3)*wu3
|
|
;
|
|
|
|
wu1
|
|
=
|
|
-(sdotw*sup1) - vdotw*vu1 + wu1
|
|
;
|
|
|
|
wu2
|
|
=
|
|
-(sdotw*sup2) - vdotw*vu2 + wu2
|
|
;
|
|
|
|
wu3
|
|
=
|
|
-(sdotw*sup3) - vdotw*vu3 + wu3
|
|
;
|
|
|
|
wdotw
|
|
=
|
|
(gADM31*wu1 + (gADM23 + gADM32)*wu2)*wu3 +
|
|
wu1*((gADM12 + gADM21)*wu2 + gADM13*wu3) + gADM11*pow2(wu1) +
|
|
gADM22*pow2(wu2) + gADM33*pow2(wu3)
|
|
;
|
|
|
|
wu1
|
|
=
|
|
wu1/Sqrt(wdotw)
|
|
;
|
|
|
|
wu2
|
|
=
|
|
wu2/Sqrt(wdotw)
|
|
;
|
|
|
|
wu3
|
|
=
|
|
wu3/Sqrt(wdotw)
|
|
;
|
|
|
|
vd1
|
|
=
|
|
gADM11*vu1 + gADM12*vu2 + gADM13*vu3
|
|
;
|
|
|
|
vd2
|
|
=
|
|
gADM21*vu1 + gADM22*vu2 + gADM23*vu3
|
|
;
|
|
|
|
vd3
|
|
=
|
|
gADM31*vu1 + gADM32*vu2 + gADM33*vu3
|
|
;
|
|
|
|
wd1
|
|
=
|
|
gADM11*wu1 + gADM12*wu2 + gADM13*wu3
|
|
;
|
|
|
|
wd2
|
|
=
|
|
gADM21*wu1 + gADM22*wu2 + gADM23*wu3
|
|
;
|
|
|
|
wd3
|
|
=
|
|
gADM31*wu1 + gADM32*wu2 + gADM33*wu3
|
|
;
|
|
|
|
RehPsi0
|
|
=
|
|
Power(2.7182818284590452354,pow2(hPsi0parb)*
|
|
(2.*hPsi0parc*time - pow2(hPsi0parc) - pow2(time)))*hPsi0para
|
|
;
|
|
|
|
ImhPsi0
|
|
=
|
|
0
|
|
;
|
|
|
|
rACABTF11
|
|
=
|
|
rACABTF11 + alpha*chi*
|
|
(2.*ImhPsi0*vd1*wd1 + RehPsi0*(pow2(vd1) - pow2(wd1)))
|
|
;
|
|
|
|
rACABTF12
|
|
=
|
|
rACABTF12 + (vd2*(RehPsi0*vd1 + ImhPsi0*wd1) +
|
|
(ImhPsi0*vd1 - RehPsi0*wd1)*wd2)*alpha*chi
|
|
;
|
|
|
|
rACABTF13
|
|
=
|
|
rACABTF13 + (vd3*(RehPsi0*vd1 + ImhPsi0*wd1) +
|
|
(ImhPsi0*vd1 - RehPsi0*wd1)*wd3)*alpha*chi
|
|
;
|
|
|
|
rACABTF22
|
|
=
|
|
rACABTF22 + alpha*chi*
|
|
(2.*ImhPsi0*vd2*wd2 + RehPsi0*(pow2(vd2) - pow2(wd2)))
|
|
;
|
|
|
|
rACABTF23
|
|
=
|
|
rACABTF23 + (vd3*(RehPsi0*vd2 + ImhPsi0*wd2) +
|
|
(ImhPsi0*vd2 - RehPsi0*wd2)*wd3)*alpha*chi
|
|
;
|
|
|
|
rACABTF33
|
|
=
|
|
rACABTF33 + alpha*chi*
|
|
(2.*ImhPsi0*vd3*wd3 + RehPsi0*(pow2(vd3) - pow2(wd3)))
|
|
;
|
|
|
|
|
|
}
|
|
|
|
rA11
|
|
=
|
|
rACABTF11 + 0.5*qdd11*rACqq + 2.*
|
|
(qud11*rACsA1 + qud21*rACsA2 + qud31*rACsA3)*sdown1 + rACss*pow2(sdown1)
|
|
;
|
|
|
|
rA12
|
|
=
|
|
rACABTF12 + 0.5*qdd12*rACqq + (qud11*rACsA1 + qud21*rACsA2 + qud31*rACsA3)*
|
|
sdown2 + sdown1*(qud12*rACsA1 + qud22*rACsA2 + qud32*rACsA3 +
|
|
rACss*sdown2)
|
|
;
|
|
|
|
rA13
|
|
=
|
|
rACABTF13 + 0.5*qdd13*rACqq + (qud11*rACsA1 + qud21*rACsA2 + qud31*rACsA3)*
|
|
sdown3 + sdown1*(qud13*rACsA1 + qud23*rACsA2 + qud33*rACsA3 +
|
|
rACss*sdown3)
|
|
;
|
|
|
|
rA22
|
|
=
|
|
rACABTF22 + 0.5*qdd22*rACqq + 2.*
|
|
(qud12*rACsA1 + qud22*rACsA2 + qud32*rACsA3)*sdown2 + rACss*pow2(sdown2)
|
|
;
|
|
|
|
rA23
|
|
=
|
|
rACABTF23 + 0.5*qdd23*rACqq + (qud12*rACsA1 + qud22*rACsA2 + qud32*rACsA3)*
|
|
sdown3 + sdown2*(qud13*rACsA1 + qud23*rACsA2 + qud33*rACsA3 +
|
|
rACss*sdown3)
|
|
;
|
|
|
|
rA33
|
|
=
|
|
rACABTF33 + 0.5*qdd33*rACqq + 2.*
|
|
(qud13*rACsA1 + qud23*rACsA2 + qud33*rACsA3)*sdown3 + rACss*pow2(sdown3)
|
|
;
|
|
|
|
rG1
|
|
=
|
|
qud11*rGamA1 + qud12*rGamA2 + qud13*rGamA3 + rGams*sup1
|
|
;
|
|
|
|
rG2
|
|
=
|
|
qud21*rGamA1 + qud22*rGamA2 + qud23*rGamA3 + rGams*sup2
|
|
;
|
|
|
|
rG3
|
|
=
|
|
qud31*rGamA1 + qud32*rGamA2 + qud33*rGamA3 + rGams*sup3
|
|
;
|
|
|
|
#if 0
|
|
rG1 -= kappa1*(G1-Gfromg1);
|
|
rG2 -= kappa1*(G2-Gfromg2);
|
|
rG3 -= kappa1*(G3-Gfromg3);
|
|
|
|
rA11 -= kappa1*A11/r;
|
|
rA12 -= kappa1*A12/r;
|
|
rA13 -= kappa1*A13/r;
|
|
rA22 -= kappa1*A22/r;
|
|
rA23 -= kappa1*A23/r;
|
|
rA33 -= kappa1*A33/r;
|
|
#endif
|
|
|
|
#endif
|
|
} /* function */
|
|
// f and tof are uper index
|
|
#ifdef fortran1
|
|
void decompose2p1_1
|
|
#endif
|
|
#ifdef fortran2
|
|
void DECOMPOSE2P1_1
|
|
#endif
|
|
#ifdef fortran3
|
|
void decompose2p1_1_
|
|
#endif
|
|
(double & r,double & xp,double & yp,double & zp,double & chi,
|
|
double & g11,double & g12,double & g13,double & g22,double & g23,double & g33,
|
|
double & f1,double & f2,double & f3,double & tofs,double & tof1,double & tof2,double & tof3)
|
|
{
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double modshatARG;
|
|
double oomodshat;
|
|
double qud11;
|
|
double qud12;
|
|
double qud13;
|
|
double qud21;
|
|
double qud22;
|
|
double qud23;
|
|
double qud31;
|
|
double qud32;
|
|
double qud33;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
tofs
|
|
=
|
|
f1*sdown1 + f2*sdown2 + f3*sdown3
|
|
;
|
|
|
|
tof1
|
|
=
|
|
f1*qud11 + f2*qud12 + f3*qud13
|
|
;
|
|
|
|
tof2
|
|
=
|
|
f1*qud21 + f2*qud22 + f3*qud23
|
|
;
|
|
|
|
tof3
|
|
=
|
|
f1*qud31 + f2*qud32 + f3*qud33
|
|
;
|
|
} /* function */
|
|
// f and tof are lower index
|
|
#ifdef fortran1
|
|
void decompose2p1_2
|
|
#endif
|
|
#ifdef fortran2
|
|
void DECOMPOSE2P1_2
|
|
#endif
|
|
#ifdef fortran3
|
|
void decompose2p1_2_
|
|
#endif
|
|
(double & r,double & xp,double & yp,double & zp,double & chi,
|
|
double & g11,double & g12,double & g13,double & g22,double & g23,double & g33,
|
|
double & f11,double & f12,double & f13,double & f22,double & f23,double & f33,
|
|
double & tofqq,double & tofss,double & tofs1,double & tofs2,double & tofs3,
|
|
double & tof11,double & tof12,double & tof13,double & tof22,double & tof23,double & tof33)
|
|
{
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double modshatARG;
|
|
double oomodshat;
|
|
double qdd11;
|
|
double qdd12;
|
|
double qdd13;
|
|
double qdd22;
|
|
double qdd23;
|
|
double qdd33;
|
|
double qPhysuudd1111;
|
|
double qPhysuudd1112;
|
|
double qPhysuudd1113;
|
|
double qPhysuudd1122;
|
|
double qPhysuudd1123;
|
|
double qPhysuudd1133;
|
|
double qPhysuudd1211;
|
|
double qPhysuudd1212;
|
|
double qPhysuudd1213;
|
|
double qPhysuudd1222;
|
|
double qPhysuudd1223;
|
|
double qPhysuudd1233;
|
|
double qPhysuudd1311;
|
|
double qPhysuudd1312;
|
|
double qPhysuudd1313;
|
|
double qPhysuudd1322;
|
|
double qPhysuudd1323;
|
|
double qPhysuudd1333;
|
|
double qPhysuudd2211;
|
|
double qPhysuudd2212;
|
|
double qPhysuudd2213;
|
|
double qPhysuudd2222;
|
|
double qPhysuudd2223;
|
|
double qPhysuudd2233;
|
|
double qPhysuudd2311;
|
|
double qPhysuudd2312;
|
|
double qPhysuudd2313;
|
|
double qPhysuudd2322;
|
|
double qPhysuudd2323;
|
|
double qPhysuudd2333;
|
|
double qPhysuudd3311;
|
|
double qPhysuudd3312;
|
|
double qPhysuudd3313;
|
|
double qPhysuudd3322;
|
|
double qPhysuudd3323;
|
|
double qPhysuudd3333;
|
|
double qud11;
|
|
double qud12;
|
|
double qud13;
|
|
double qud21;
|
|
double qud22;
|
|
double qud23;
|
|
double qud31;
|
|
double qud32;
|
|
double qud33;
|
|
double quu11;
|
|
double quu12;
|
|
double quu13;
|
|
double quu22;
|
|
double quu23;
|
|
double quu33;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
qdd11
|
|
=
|
|
g11/chi - pow2(sdown1)
|
|
;
|
|
|
|
qdd12
|
|
=
|
|
g12/chi - sdown1*sdown2
|
|
;
|
|
|
|
qdd13
|
|
=
|
|
g13/chi - sdown1*sdown3
|
|
;
|
|
|
|
qdd22
|
|
=
|
|
g22/chi - pow2(sdown2)
|
|
;
|
|
|
|
qdd23
|
|
=
|
|
g23/chi - sdown2*sdown3
|
|
;
|
|
|
|
qdd33
|
|
=
|
|
g33/chi - pow2(sdown3)
|
|
;
|
|
|
|
quu11
|
|
=
|
|
ADMginv11 - pow2(sup1)
|
|
;
|
|
|
|
quu12
|
|
=
|
|
ADMginv12 - sup1*sup2
|
|
;
|
|
|
|
quu13
|
|
=
|
|
ADMginv13 - sup1*sup3
|
|
;
|
|
|
|
quu22
|
|
=
|
|
ADMginv22 - pow2(sup2)
|
|
;
|
|
|
|
quu23
|
|
=
|
|
ADMginv23 - sup2*sup3
|
|
;
|
|
|
|
quu33
|
|
=
|
|
ADMginv33 - pow2(sup3)
|
|
;
|
|
|
|
qPhysuudd1111
|
|
=
|
|
-0.5*qdd11*quu11 + pow2(qud11)
|
|
;
|
|
|
|
qPhysuudd1112
|
|
=
|
|
qud11*qud12 - 0.5*qdd12*quu11
|
|
;
|
|
|
|
qPhysuudd1113
|
|
=
|
|
qud11*qud13 - 0.5*qdd13*quu11
|
|
;
|
|
|
|
qPhysuudd1122
|
|
=
|
|
-0.5*qdd22*quu11 + pow2(qud12)
|
|
;
|
|
|
|
qPhysuudd1123
|
|
=
|
|
qud12*qud13 - 0.5*qdd23*quu11
|
|
;
|
|
|
|
qPhysuudd1133
|
|
=
|
|
-0.5*qdd33*quu11 + pow2(qud13)
|
|
;
|
|
|
|
qPhysuudd1211
|
|
=
|
|
qud11*qud21 - 0.5*qdd11*quu12
|
|
;
|
|
|
|
qPhysuudd1212
|
|
=
|
|
0.5*(qud12*qud21 + qud11*qud22 - qdd12*quu12)
|
|
;
|
|
|
|
qPhysuudd1213
|
|
=
|
|
0.5*(qud13*qud21 + qud11*qud23 - qdd13*quu12)
|
|
;
|
|
|
|
qPhysuudd1222
|
|
=
|
|
qud12*qud22 - 0.5*qdd22*quu12
|
|
;
|
|
|
|
qPhysuudd1223
|
|
=
|
|
0.5*(qud13*qud22 + qud12*qud23 - qdd23*quu12)
|
|
;
|
|
|
|
qPhysuudd1233
|
|
=
|
|
qud13*qud23 - 0.5*qdd33*quu12
|
|
;
|
|
|
|
qPhysuudd1311
|
|
=
|
|
qud11*qud31 - 0.5*qdd11*quu13
|
|
;
|
|
|
|
qPhysuudd1312
|
|
=
|
|
0.5*(qud12*qud31 + qud11*qud32 - qdd12*quu13)
|
|
;
|
|
|
|
qPhysuudd1313
|
|
=
|
|
0.5*(qud13*qud31 + qud11*qud33 - qdd13*quu13)
|
|
;
|
|
|
|
qPhysuudd1322
|
|
=
|
|
qud12*qud32 - 0.5*qdd22*quu13
|
|
;
|
|
|
|
qPhysuudd1323
|
|
=
|
|
0.5*(qud13*qud32 + qud12*qud33 - qdd23*quu13)
|
|
;
|
|
|
|
qPhysuudd1333
|
|
=
|
|
qud13*qud33 - 0.5*qdd33*quu13
|
|
;
|
|
|
|
qPhysuudd2211
|
|
=
|
|
-0.5*qdd11*quu22 + pow2(qud21)
|
|
;
|
|
|
|
qPhysuudd2212
|
|
=
|
|
qud21*qud22 - 0.5*qdd12*quu22
|
|
;
|
|
|
|
qPhysuudd2213
|
|
=
|
|
qud21*qud23 - 0.5*qdd13*quu22
|
|
;
|
|
|
|
qPhysuudd2222
|
|
=
|
|
-0.5*qdd22*quu22 + pow2(qud22)
|
|
;
|
|
|
|
qPhysuudd2223
|
|
=
|
|
qud22*qud23 - 0.5*qdd23*quu22
|
|
;
|
|
|
|
qPhysuudd2233
|
|
=
|
|
-0.5*qdd33*quu22 + pow2(qud23)
|
|
;
|
|
|
|
qPhysuudd2311
|
|
=
|
|
qud21*qud31 - 0.5*qdd11*quu23
|
|
;
|
|
|
|
qPhysuudd2312
|
|
=
|
|
0.5*(qud22*qud31 + qud21*qud32 - qdd12*quu23)
|
|
;
|
|
|
|
qPhysuudd2313
|
|
=
|
|
0.5*(qud23*qud31 + qud21*qud33 - qdd13*quu23)
|
|
;
|
|
|
|
qPhysuudd2322
|
|
=
|
|
qud22*qud32 - 0.5*qdd22*quu23
|
|
;
|
|
|
|
qPhysuudd2323
|
|
=
|
|
0.5*(qud23*qud32 + qud22*qud33 - qdd23*quu23)
|
|
;
|
|
|
|
qPhysuudd2333
|
|
=
|
|
qud23*qud33 - 0.5*qdd33*quu23
|
|
;
|
|
|
|
qPhysuudd3311
|
|
=
|
|
-0.5*qdd11*quu33 + pow2(qud31)
|
|
;
|
|
|
|
qPhysuudd3312
|
|
=
|
|
qud31*qud32 - 0.5*qdd12*quu33
|
|
;
|
|
|
|
qPhysuudd3313
|
|
=
|
|
qud31*qud33 - 0.5*qdd13*quu33
|
|
;
|
|
|
|
qPhysuudd3322
|
|
=
|
|
-0.5*qdd22*quu33 + pow2(qud32)
|
|
;
|
|
|
|
qPhysuudd3323
|
|
=
|
|
qud32*qud33 - 0.5*qdd23*quu33
|
|
;
|
|
|
|
qPhysuudd3333
|
|
=
|
|
-0.5*qdd33*quu33 + pow2(qud33)
|
|
;
|
|
|
|
tofss
|
|
=
|
|
2.*(f23*sup2*sup3 + sup1*(f12*sup2 + f13*sup3)) + f11*pow2(sup1) +
|
|
f22*pow2(sup2) + f33*pow2(sup3)
|
|
;
|
|
|
|
tofqq
|
|
=
|
|
f12*quu12 + f13*quu13 + f23*quu23 + 0.5*(f11*quu11 + f22*quu22 + f33*quu33)
|
|
;
|
|
|
|
tofs1
|
|
=
|
|
(f11*qud11 + f12*qud21 + f13*qud31)*sup1 +
|
|
(f12*qud11 + f22*qud21 + f23*qud31)*sup2 +
|
|
(f13*qud11 + f23*qud21 + f33*qud31)*sup3
|
|
;
|
|
|
|
tofs2
|
|
=
|
|
(f11*qud12 + f12*qud22 + f13*qud32)*sup1 +
|
|
(f12*qud12 + f22*qud22 + f23*qud32)*sup2 +
|
|
(f13*qud12 + f23*qud22 + f33*qud32)*sup3
|
|
;
|
|
|
|
tofs3
|
|
=
|
|
(f11*qud13 + f12*qud23 + f13*qud33)*sup1 +
|
|
(f12*qud13 + f22*qud23 + f23*qud33)*sup2 +
|
|
(f13*qud13 + f23*qud23 + f33*qud33)*sup3
|
|
;
|
|
|
|
tof11
|
|
=
|
|
f11*qPhysuudd1111 + f22*qPhysuudd2211 +
|
|
2.*(f12*qPhysuudd1211 + f13*qPhysuudd1311 + f23*qPhysuudd2311) +
|
|
f33*qPhysuudd3311
|
|
;
|
|
|
|
tof12
|
|
=
|
|
f11*qPhysuudd1112 + f22*qPhysuudd2212 +
|
|
2.*(f12*qPhysuudd1212 + f13*qPhysuudd1312 + f23*qPhysuudd2312) +
|
|
f33*qPhysuudd3312
|
|
;
|
|
|
|
tof13
|
|
=
|
|
f11*qPhysuudd1113 + f22*qPhysuudd2213 +
|
|
2.*(f12*qPhysuudd1213 + f13*qPhysuudd1313 + f23*qPhysuudd2313) +
|
|
f33*qPhysuudd3313
|
|
;
|
|
|
|
tof22
|
|
=
|
|
f11*qPhysuudd1122 + f22*qPhysuudd2222 +
|
|
2.*(f12*qPhysuudd1222 + f13*qPhysuudd1322 + f23*qPhysuudd2322) +
|
|
f33*qPhysuudd3322
|
|
;
|
|
|
|
tof23
|
|
=
|
|
f11*qPhysuudd1123 + f22*qPhysuudd2223 +
|
|
2.*(f12*qPhysuudd1223 + f13*qPhysuudd1323 + f23*qPhysuudd2323) +
|
|
f33*qPhysuudd3323
|
|
;
|
|
|
|
tof33
|
|
=
|
|
f11*qPhysuudd1133 + f22*qPhysuudd2233 +
|
|
2.*(f12*qPhysuudd1233 + f13*qPhysuudd1333 + f23*qPhysuudd2333) +
|
|
f33*qPhysuudd3333
|
|
;
|
|
} /*function */
|
|
// f and tof are uper index
|
|
#ifdef fortran1
|
|
void compose2p1_1
|
|
#endif
|
|
#ifdef fortran2
|
|
void COMPOSE2P1_1
|
|
#endif
|
|
#ifdef fortran3
|
|
void compose2p1_1_
|
|
#endif
|
|
(double & r,double & xp,double & yp,double & zp,double & chi,
|
|
double & g11,double & g12,double & g13,double & g22,double & g23,double & g33,
|
|
double & f1,double & f2,double & f3,double & tofs,double & tof1,double & tof2,double & tof3)
|
|
{
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double modshatARG;
|
|
double oomodshat;
|
|
double qud11;
|
|
double qud12;
|
|
double qud13;
|
|
double qud21;
|
|
double qud22;
|
|
double qud23;
|
|
double qud31;
|
|
double qud32;
|
|
double qud33;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
f1
|
|
=
|
|
qud11*tof1 + qud12*tof2 + qud13*tof3 + sup1*tofs
|
|
;
|
|
|
|
f2
|
|
=
|
|
qud21*tof1 + qud22*tof2 + qud23*tof3 + sup2*tofs
|
|
;
|
|
|
|
f3
|
|
=
|
|
qud31*tof1 + qud32*tof2 + qud33*tof3 + sup3*tofs
|
|
;
|
|
} /* function */
|
|
// f and tof are lower index
|
|
#ifdef fortran1
|
|
void compose2p1_2
|
|
#endif
|
|
#ifdef fortran2
|
|
void COMPOSE2P1_2
|
|
#endif
|
|
#ifdef fortran3
|
|
void compose2p1_2_
|
|
#endif
|
|
(double & r,double & xp,double & yp,double & zp,double & chi,
|
|
double & g11,double & g12,double & g13,double & g22,double & g23,double & g33,
|
|
double & f11,double & f12,double & f13,double & f22,double & f23,double & f33,
|
|
double & tofqq,double & tofss,double & tofs1,double & tofs2,double & tofs3,
|
|
double & tof11,double & tof12,double & tof13,double & tof22,double & tof23,double & tof33)
|
|
{
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double modshatARG;
|
|
double oomodshat;
|
|
double qdd11;
|
|
double qdd12;
|
|
double qdd13;
|
|
double qdd22;
|
|
double qdd23;
|
|
double qdd33;
|
|
double qPhysuudd1111;
|
|
double qPhysuudd1112;
|
|
double qPhysuudd1113;
|
|
double qPhysuudd1122;
|
|
double qPhysuudd1123;
|
|
double qPhysuudd1133;
|
|
double qPhysuudd1211;
|
|
double qPhysuudd1212;
|
|
double qPhysuudd1213;
|
|
double qPhysuudd1222;
|
|
double qPhysuudd1223;
|
|
double qPhysuudd1233;
|
|
double qPhysuudd1311;
|
|
double qPhysuudd1312;
|
|
double qPhysuudd1313;
|
|
double qPhysuudd1322;
|
|
double qPhysuudd1323;
|
|
double qPhysuudd1333;
|
|
double qPhysuudd2211;
|
|
double qPhysuudd2212;
|
|
double qPhysuudd2213;
|
|
double qPhysuudd2222;
|
|
double qPhysuudd2223;
|
|
double qPhysuudd2233;
|
|
double qPhysuudd2311;
|
|
double qPhysuudd2312;
|
|
double qPhysuudd2313;
|
|
double qPhysuudd2322;
|
|
double qPhysuudd2323;
|
|
double qPhysuudd2333;
|
|
double qPhysuudd3311;
|
|
double qPhysuudd3312;
|
|
double qPhysuudd3313;
|
|
double qPhysuudd3322;
|
|
double qPhysuudd3323;
|
|
double qPhysuudd3333;
|
|
double qud11;
|
|
double qud12;
|
|
double qud13;
|
|
double qud21;
|
|
double qud22;
|
|
double qud23;
|
|
double qud31;
|
|
double qud32;
|
|
double qud33;
|
|
double quu11;
|
|
double quu12;
|
|
double quu13;
|
|
double quu22;
|
|
double quu23;
|
|
double quu33;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
|
|
|
|
|
|
shat1
|
|
=
|
|
0
|
|
;
|
|
|
|
shat2
|
|
=
|
|
0
|
|
;
|
|
|
|
shat3
|
|
=
|
|
0
|
|
;
|
|
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
qdd11
|
|
=
|
|
g11/chi - pow2(sdown1)
|
|
;
|
|
|
|
qdd12
|
|
=
|
|
g12/chi - sdown1*sdown2
|
|
;
|
|
|
|
qdd13
|
|
=
|
|
g13/chi - sdown1*sdown3
|
|
;
|
|
|
|
qdd22
|
|
=
|
|
g22/chi - pow2(sdown2)
|
|
;
|
|
|
|
qdd23
|
|
=
|
|
g23/chi - sdown2*sdown3
|
|
;
|
|
|
|
qdd33
|
|
=
|
|
g33/chi - pow2(sdown3)
|
|
;
|
|
|
|
quu11
|
|
=
|
|
ADMginv11 - pow2(sup1)
|
|
;
|
|
|
|
quu12
|
|
=
|
|
ADMginv12 - sup1*sup2
|
|
;
|
|
|
|
quu13
|
|
=
|
|
ADMginv13 - sup1*sup3
|
|
;
|
|
|
|
quu22
|
|
=
|
|
ADMginv22 - pow2(sup2)
|
|
;
|
|
|
|
quu23
|
|
=
|
|
ADMginv23 - sup2*sup3
|
|
;
|
|
|
|
quu33
|
|
=
|
|
ADMginv33 - pow2(sup3)
|
|
;
|
|
|
|
qPhysuudd1111
|
|
=
|
|
-0.5*qdd11*quu11 + pow2(qud11)
|
|
;
|
|
|
|
qPhysuudd1112
|
|
=
|
|
qud11*qud12 - 0.5*qdd12*quu11
|
|
;
|
|
|
|
qPhysuudd1113
|
|
=
|
|
qud11*qud13 - 0.5*qdd13*quu11
|
|
;
|
|
|
|
qPhysuudd1122
|
|
=
|
|
-0.5*qdd22*quu11 + pow2(qud12)
|
|
;
|
|
|
|
qPhysuudd1123
|
|
=
|
|
qud12*qud13 - 0.5*qdd23*quu11
|
|
;
|
|
|
|
qPhysuudd1133
|
|
=
|
|
-0.5*qdd33*quu11 + pow2(qud13)
|
|
;
|
|
|
|
qPhysuudd1211
|
|
=
|
|
qud11*qud21 - 0.5*qdd11*quu12
|
|
;
|
|
|
|
qPhysuudd1212
|
|
=
|
|
0.5*(qud12*qud21 + qud11*qud22 - qdd12*quu12)
|
|
;
|
|
|
|
qPhysuudd1213
|
|
=
|
|
0.5*(qud13*qud21 + qud11*qud23 - qdd13*quu12)
|
|
;
|
|
|
|
qPhysuudd1222
|
|
=
|
|
qud12*qud22 - 0.5*qdd22*quu12
|
|
;
|
|
|
|
qPhysuudd1223
|
|
=
|
|
0.5*(qud13*qud22 + qud12*qud23 - qdd23*quu12)
|
|
;
|
|
|
|
qPhysuudd1233
|
|
=
|
|
qud13*qud23 - 0.5*qdd33*quu12
|
|
;
|
|
|
|
qPhysuudd1311
|
|
=
|
|
qud11*qud31 - 0.5*qdd11*quu13
|
|
;
|
|
|
|
qPhysuudd1312
|
|
=
|
|
0.5*(qud12*qud31 + qud11*qud32 - qdd12*quu13)
|
|
;
|
|
|
|
qPhysuudd1313
|
|
=
|
|
0.5*(qud13*qud31 + qud11*qud33 - qdd13*quu13)
|
|
;
|
|
|
|
qPhysuudd1322
|
|
=
|
|
qud12*qud32 - 0.5*qdd22*quu13
|
|
;
|
|
|
|
qPhysuudd1323
|
|
=
|
|
0.5*(qud13*qud32 + qud12*qud33 - qdd23*quu13)
|
|
;
|
|
|
|
qPhysuudd1333
|
|
=
|
|
qud13*qud33 - 0.5*qdd33*quu13
|
|
;
|
|
|
|
qPhysuudd2211
|
|
=
|
|
-0.5*qdd11*quu22 + pow2(qud21)
|
|
;
|
|
|
|
qPhysuudd2212
|
|
=
|
|
qud21*qud22 - 0.5*qdd12*quu22
|
|
;
|
|
|
|
qPhysuudd2213
|
|
=
|
|
qud21*qud23 - 0.5*qdd13*quu22
|
|
;
|
|
|
|
qPhysuudd2222
|
|
=
|
|
-0.5*qdd22*quu22 + pow2(qud22)
|
|
;
|
|
|
|
qPhysuudd2223
|
|
=
|
|
qud22*qud23 - 0.5*qdd23*quu22
|
|
;
|
|
|
|
qPhysuudd2233
|
|
=
|
|
-0.5*qdd33*quu22 + pow2(qud23)
|
|
;
|
|
|
|
qPhysuudd2311
|
|
=
|
|
qud21*qud31 - 0.5*qdd11*quu23
|
|
;
|
|
|
|
qPhysuudd2312
|
|
=
|
|
0.5*(qud22*qud31 + qud21*qud32 - qdd12*quu23)
|
|
;
|
|
|
|
qPhysuudd2313
|
|
=
|
|
0.5*(qud23*qud31 + qud21*qud33 - qdd13*quu23)
|
|
;
|
|
|
|
qPhysuudd2322
|
|
=
|
|
qud22*qud32 - 0.5*qdd22*quu23
|
|
;
|
|
|
|
qPhysuudd2323
|
|
=
|
|
0.5*(qud23*qud32 + qud22*qud33 - qdd23*quu23)
|
|
;
|
|
|
|
qPhysuudd2333
|
|
=
|
|
qud23*qud33 - 0.5*qdd33*quu23
|
|
;
|
|
|
|
qPhysuudd3311
|
|
=
|
|
-0.5*qdd11*quu33 + pow2(qud31)
|
|
;
|
|
|
|
qPhysuudd3312
|
|
=
|
|
qud31*qud32 - 0.5*qdd12*quu33
|
|
;
|
|
|
|
qPhysuudd3313
|
|
=
|
|
qud31*qud33 - 0.5*qdd13*quu33
|
|
;
|
|
|
|
qPhysuudd3322
|
|
=
|
|
-0.5*qdd22*quu33 + pow2(qud32)
|
|
;
|
|
|
|
qPhysuudd3323
|
|
=
|
|
qud32*qud33 - 0.5*qdd23*quu33
|
|
;
|
|
|
|
qPhysuudd3333
|
|
=
|
|
-0.5*qdd33*quu33 + pow2(qud33)
|
|
;
|
|
|
|
// my equations
|
|
#if 0
|
|
f11
|
|
=
|
|
qPhysuudd1111*tof11 + qPhysuudd2211*tof22 +
|
|
2.*(qPhysuudd1211*tof12 + qPhysuudd1311*tof13 + qPhysuudd2311*tof23) +
|
|
qPhysuudd3311*tof33 + qdd11*tofqq +
|
|
1.*sdown1*(qud11*tofs1 + qud21*tofs2 + qud31*tofs3) + tofss*pow2(sdown1)
|
|
;
|
|
|
|
f12
|
|
=
|
|
qPhysuudd1112*tof11 + qPhysuudd2212*tof22 +
|
|
2.*(qPhysuudd1212*tof12 + qPhysuudd1312*tof13 + qPhysuudd2312*tof23) +
|
|
qPhysuudd3312*tof33 + qdd12*tofqq +
|
|
0.5*((qud12*sdown1 + qud11*sdown2)*tofs1 +
|
|
(qud22*sdown1 + qud21*sdown2)*tofs2 +
|
|
(qud32*sdown1 + qud31*sdown2)*tofs3) + sdown1*sdown2*tofss
|
|
;
|
|
|
|
f13
|
|
=
|
|
qPhysuudd1113*tof11 + qPhysuudd2213*tof22 +
|
|
2.*(qPhysuudd1213*tof12 + qPhysuudd1313*tof13 + qPhysuudd2313*tof23) +
|
|
qPhysuudd3313*tof33 + qdd13*tofqq +
|
|
0.5*((qud13*sdown1 + qud11*sdown3)*tofs1 +
|
|
(qud23*sdown1 + qud21*sdown3)*tofs2 +
|
|
(qud33*sdown1 + qud31*sdown3)*tofs3) + sdown1*sdown3*tofss
|
|
;
|
|
|
|
f22
|
|
=
|
|
qPhysuudd1122*tof11 + qPhysuudd2222*tof22 +
|
|
2.*(qPhysuudd1222*tof12 + qPhysuudd1322*tof13 + qPhysuudd2322*tof23) +
|
|
qPhysuudd3322*tof33 + qdd22*tofqq +
|
|
1.*sdown2*(qud12*tofs1 + qud22*tofs2 + qud32*tofs3) + tofss*pow2(sdown2)
|
|
;
|
|
|
|
f23
|
|
=
|
|
qPhysuudd1123*tof11 + qPhysuudd2223*tof22 +
|
|
2.*(qPhysuudd1223*tof12 + qPhysuudd1323*tof13 + qPhysuudd2323*tof23) +
|
|
qPhysuudd3323*tof33 + qdd23*tofqq +
|
|
0.5*((qud13*sdown2 + qud12*sdown3)*tofs1 +
|
|
(qud23*sdown2 + qud22*sdown3)*tofs2 +
|
|
(qud33*sdown2 + qud32*sdown3)*tofs3) + sdown2*sdown3*tofss
|
|
;
|
|
|
|
f33
|
|
=
|
|
qPhysuudd1133*tof11 + qPhysuudd2233*tof22 +
|
|
2.*(qPhysuudd1233*tof12 + qPhysuudd1333*tof13 + qPhysuudd2333*tof23) +
|
|
qPhysuudd3333*tof33 + qdd33*tofqq +
|
|
1.*sdown3*(qud13*tofs1 + qud23*tofs2 + qud33*tofs3) + tofss*pow2(sdown3)
|
|
;
|
|
// David's equations
|
|
#else
|
|
f11
|
|
=
|
|
tof11 + 0.5*qdd11*tofqq + 2.*sdown1*
|
|
(qud11*tofs1 + qud21*tofs2 + qud31*tofs3) + tofss*pow2(sdown1)
|
|
;
|
|
|
|
f12
|
|
=
|
|
tof12 + 0.5*qdd12*tofqq + (qud12*sdown1 + qud11*sdown2)*tofs1 +
|
|
(qud22*sdown1 + qud21*sdown2)*tofs2 +
|
|
(qud32*sdown1 + qud31*sdown2)*tofs3 + sdown1*sdown2*tofss
|
|
;
|
|
|
|
f13
|
|
=
|
|
tof13 + 0.5*qdd13*tofqq + (qud13*sdown1 + qud11*sdown3)*tofs1 +
|
|
(qud23*sdown1 + qud21*sdown3)*tofs2 +
|
|
(qud33*sdown1 + qud31*sdown3)*tofs3 + sdown1*sdown3*tofss
|
|
;
|
|
|
|
f22
|
|
=
|
|
tof22 + 0.5*qdd22*tofqq + 2.*sdown2*
|
|
(qud12*tofs1 + qud22*tofs2 + qud32*tofs3) + tofss*pow2(sdown2)
|
|
;
|
|
|
|
f23
|
|
=
|
|
tof23 + 0.5*qdd23*tofqq + (qud13*sdown2 + qud12*sdown3)*tofs1 +
|
|
(qud23*sdown2 + qud22*sdown3)*tofs2 +
|
|
(qud33*sdown2 + qud32*sdown3)*tofs3 + sdown2*sdown3*tofss
|
|
;
|
|
|
|
f33
|
|
=
|
|
tof33 + 0.5*qdd33*tofqq + 2.*sdown3*
|
|
(qud13*tofs1 + qud23*tofs2 + qud33*tofs3) + tofss*pow2(sdown3)
|
|
;
|
|
#endif
|
|
|
|
} /* function */
|
|
#ifdef fortran1
|
|
void racqq_point
|
|
#endif
|
|
#ifdef fortran2
|
|
void RACQQ_POINT
|
|
#endif
|
|
#ifdef fortran3
|
|
void racqq_point_
|
|
#endif
|
|
(double &A11,
|
|
double &A12,
|
|
double &A13,
|
|
double &A22,
|
|
double &A23,
|
|
double &A33,
|
|
double &alpha,
|
|
double &beta1,
|
|
double &beta2,
|
|
double &beta3,
|
|
double &chi,
|
|
double &db11,
|
|
double &db12,
|
|
double &db13,
|
|
double &db21,
|
|
double &db22,
|
|
double &db23,
|
|
double &db31,
|
|
double &db32,
|
|
double &db33,
|
|
double &dg111,
|
|
double &dg112,
|
|
double &dg113,
|
|
double &dg122,
|
|
double &dg123,
|
|
double &dg133,
|
|
double &dg211,
|
|
double &dg212,
|
|
double &dg213,
|
|
double &dg222,
|
|
double &dg223,
|
|
double &dg233,
|
|
double &dg311,
|
|
double &dg312,
|
|
double &dg313,
|
|
double &dg322,
|
|
double &dg323,
|
|
double &dg333,
|
|
double &g11,
|
|
double &g12,
|
|
double &g13,
|
|
double &g22,
|
|
double &g23,
|
|
double &g33,
|
|
double &rACqq,
|
|
double &rACss)
|
|
{
|
|
|
|
double Ainv11;
|
|
double Ainv12;
|
|
double Ainv13;
|
|
double Ainv22;
|
|
double Ainv23;
|
|
double Ainv33;
|
|
double detginv;
|
|
double divbeta;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double lieg11;
|
|
double lieg12;
|
|
double lieg13;
|
|
double lieg22;
|
|
double lieg23;
|
|
double lieg33;
|
|
double totdivbeta;
|
|
|
|
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
divbeta
|
|
=
|
|
db11 + db22 + db33
|
|
;
|
|
|
|
totdivbeta
|
|
=
|
|
0.66666666666666666667*divbeta
|
|
;
|
|
|
|
Ainv11
|
|
=
|
|
2.*(A23*ginv12*ginv13 + ginv11*(A12*ginv12 + A13*ginv13)) +
|
|
A11*pow2(ginv11) + A22*pow2(ginv12) + A33*pow2(ginv13)
|
|
;
|
|
|
|
Ainv12
|
|
=
|
|
ginv11*(A11*ginv12 + A12*ginv22 + A13*ginv23) +
|
|
ginv12*(A13*ginv13 + A22*ginv22 + A23*ginv23) +
|
|
ginv13*(A23*ginv22 + A33*ginv23) + A12*pow2(ginv12)
|
|
;
|
|
|
|
Ainv13
|
|
=
|
|
ginv11*(A11*ginv13 + A12*ginv23 + A13*ginv33) +
|
|
ginv12*(A12*ginv13 + A22*ginv23 + A23*ginv33) +
|
|
ginv13*(A23*ginv23 + A33*ginv33) + A13*pow2(ginv13)
|
|
;
|
|
|
|
Ainv22
|
|
=
|
|
2.*(A23*ginv22*ginv23 + ginv12*(A12*ginv22 + A13*ginv23)) +
|
|
A11*pow2(ginv12) + A22*pow2(ginv22) + A33*pow2(ginv23)
|
|
;
|
|
|
|
Ainv23
|
|
=
|
|
ginv13*(A12*ginv22 + A13*ginv23) + A33*ginv23*ginv33 +
|
|
ginv12*(A11*ginv13 + A12*ginv23 + A13*ginv33) +
|
|
ginv22*(A22*ginv23 + A23*ginv33) + A23*pow2(ginv23)
|
|
;
|
|
|
|
Ainv33
|
|
=
|
|
2.*(A23*ginv23*ginv33 + ginv13*(A12*ginv23 + A13*ginv33)) +
|
|
A11*pow2(ginv13) + A22*pow2(ginv23) + A33*pow2(ginv33)
|
|
;
|
|
|
|
lieg11
|
|
=
|
|
beta1*dg111 + beta2*dg211 + beta3*dg311 +
|
|
2.*(db11*g11 + db12*g12 + db13*g13) - g11*totdivbeta
|
|
;
|
|
|
|
lieg12
|
|
=
|
|
beta1*dg112 + beta2*dg212 + beta3*dg312 + db21*g11 + db23*g13 + db12*g22 +
|
|
db13*g23 + g12*(db11 + db22 - totdivbeta)
|
|
;
|
|
|
|
lieg13
|
|
=
|
|
beta1*dg113 + beta2*dg213 + beta3*dg313 + db31*g11 + db32*g12 + db12*g23 +
|
|
db13*g33 + g13*(db11 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieg22
|
|
=
|
|
beta1*dg122 + beta2*dg222 + beta3*dg322 +
|
|
2.*(db21*g12 + db22*g22 + db23*g23) - g22*totdivbeta
|
|
;
|
|
|
|
lieg23
|
|
=
|
|
beta1*dg123 + beta2*dg223 + beta3*dg323 + db31*g12 + db21*g13 + db32*g22 +
|
|
db23*g33 + g23*(db22 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieg33
|
|
=
|
|
beta1*dg133 + beta2*dg233 + beta3*dg333 +
|
|
2.*(db31*g13 + db32*g23 + db33*g33) - g33*totdivbeta
|
|
;
|
|
|
|
rACqq
|
|
=
|
|
chi*(-((4.*(A12*Ainv12 + A13*Ainv13 + A23*Ainv23) +
|
|
2.*(A11*Ainv11 + A22*Ainv22 + A33*Ainv33))*alpha) +
|
|
Ainv11*lieg11 + Ainv22*lieg22 +
|
|
2.*(Ainv12*lieg12 + Ainv13*lieg13 + Ainv23*lieg23) + Ainv33*lieg33) -
|
|
rACss
|
|
;
|
|
|
|
} /* function */
|
|
#ifdef fortran1
|
|
void rkhat_point
|
|
#endif
|
|
#ifdef fortran2
|
|
void RKHAT_POINT
|
|
#endif
|
|
#ifdef fortran3
|
|
void rkhat_point_
|
|
#endif
|
|
(double &alpha,
|
|
double &beta1,
|
|
double &beta2,
|
|
double &beta3,
|
|
double &chi,
|
|
double &dKhat1,
|
|
double &dKhat2,
|
|
double &dKhat3,
|
|
double &dTheta1,
|
|
double &dTheta2,
|
|
double &dTheta3,
|
|
double &g11,
|
|
double &g12,
|
|
double &g13,
|
|
double &g22,
|
|
double &g23,
|
|
double &g33,
|
|
double &kappa1,
|
|
double &kappa2,
|
|
double &Khat,
|
|
double &r,
|
|
double &rKhat,
|
|
double &Theta,
|
|
double &xp,
|
|
double &yp,
|
|
double &zp)
|
|
{
|
|
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double DKhat;
|
|
double DTheta;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double lienK;
|
|
double lienKhat;
|
|
double lienTheta;
|
|
double modshatARG;
|
|
double muL;
|
|
double oomodshat;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
muL
|
|
=
|
|
2./alpha
|
|
;
|
|
|
|
DKhat
|
|
=
|
|
dKhat1*sup1 + dKhat2*sup2 + dKhat3*sup3
|
|
;
|
|
|
|
DTheta
|
|
=
|
|
dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3
|
|
;
|
|
|
|
lienKhat
|
|
=
|
|
-((DKhat + Khat/r)*sqrt(muL))
|
|
;
|
|
|
|
lienTheta
|
|
=
|
|
-DTheta - (kappa1*(2. + kappa2) + 1/r)*Theta
|
|
;
|
|
|
|
lienK
|
|
=
|
|
lienKhat + 2.*lienTheta
|
|
;
|
|
|
|
rKhat
|
|
=
|
|
beta1*dKhat1 + beta2*dKhat2 + beta3*dKhat3 + alpha*lienKhat
|
|
;
|
|
|
|
} /* function */
|
|
#ifdef fortran1
|
|
void rtheta_point
|
|
#endif
|
|
#ifdef fortran2
|
|
void RTHETA_POINT
|
|
#endif
|
|
#ifdef fortran3
|
|
void rtheta_point_
|
|
#endif
|
|
(double &alpha,
|
|
double &beta1,
|
|
double &beta2,
|
|
double &beta3,
|
|
double &chi,
|
|
double &dTheta1,
|
|
double &dTheta2,
|
|
double &dTheta3,
|
|
double &g11,
|
|
double &g12,
|
|
double &g13,
|
|
double &g22,
|
|
double &g23,
|
|
double &g33,
|
|
double &kappa1,
|
|
double &kappa2,
|
|
double &r,
|
|
double &rTheta,
|
|
double &Theta,
|
|
double &xp,
|
|
double &yp,
|
|
double &zp)
|
|
{
|
|
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double DTheta;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double lienTheta;
|
|
double modshatARG;
|
|
double oomodshat;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
|
|
|
|
|
|
shat1
|
|
=
|
|
0
|
|
;
|
|
|
|
shat2
|
|
=
|
|
0
|
|
;
|
|
|
|
shat3
|
|
=
|
|
0
|
|
;
|
|
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
DTheta
|
|
=
|
|
dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3
|
|
;
|
|
|
|
lienTheta
|
|
=
|
|
-DTheta - (kappa1*(2. + kappa2) + 1/r)*Theta
|
|
;
|
|
|
|
rTheta
|
|
=
|
|
beta1*dTheta1 + beta2*dTheta2 + beta3*dTheta3 + alpha*lienTheta
|
|
;
|
|
|
|
} /* function */
|
|
|
|
#ifdef fortran1
|
|
void rgam_point
|
|
#endif
|
|
#ifdef fortran2
|
|
void RGAM_POINT
|
|
#endif
|
|
#ifdef fortran3
|
|
void rgam_point_
|
|
#endif
|
|
(double &alpha,
|
|
double &beta1,
|
|
double &beta2,
|
|
double &beta3,
|
|
double &chi,
|
|
double &db11,
|
|
double &db12,
|
|
double &db13,
|
|
double &db21,
|
|
double &db22,
|
|
double &db23,
|
|
double &db31,
|
|
double &db32,
|
|
double &db33,
|
|
double &ddb111,
|
|
double &ddb112,
|
|
double &ddb113,
|
|
double &ddb121,
|
|
double &ddb122,
|
|
double &ddb123,
|
|
double &ddb131,
|
|
double &ddb132,
|
|
double &ddb133,
|
|
double &ddb221,
|
|
double &ddb222,
|
|
double &ddb223,
|
|
double &ddb231,
|
|
double &ddb232,
|
|
double &ddb233,
|
|
double &ddb331,
|
|
double &ddb332,
|
|
double &ddb333,
|
|
double &dG11,
|
|
double &dG12,
|
|
double &dG13,
|
|
double &dG21,
|
|
double &dG22,
|
|
double &dG23,
|
|
double &dG31,
|
|
double &dG32,
|
|
double &dG33,
|
|
double &dKhat1,
|
|
double &dKhat2,
|
|
double &dKhat3,
|
|
double &dTheta1,
|
|
double &dTheta2,
|
|
double &dTheta3,
|
|
double &g11,
|
|
double &g12,
|
|
double &g13,
|
|
double &g22,
|
|
double &g23,
|
|
double &g33,
|
|
double &r,
|
|
double &rGamA1,
|
|
double &rGamA2,
|
|
double &rGamA3,
|
|
double &rGams,
|
|
double &shiftdriver,
|
|
double &xp,
|
|
double &yp,
|
|
double &zp)
|
|
{
|
|
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double detginv;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double modshatARG;
|
|
double muL;
|
|
double muStilde;
|
|
double oomodshat;
|
|
double qdd11;
|
|
double qdd12;
|
|
double qdd13;
|
|
double qdd22;
|
|
double qdd23;
|
|
double qdd33;
|
|
double qud11;
|
|
double qud12;
|
|
double qud13;
|
|
double qud21;
|
|
double qud22;
|
|
double qud23;
|
|
double qud31;
|
|
double qud32;
|
|
double qud33;
|
|
double quu11;
|
|
double quu12;
|
|
double quu13;
|
|
double quu22;
|
|
double quu23;
|
|
double quu33;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
double vbetaA;
|
|
double vbetas;
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
qdd11
|
|
=
|
|
g11/chi - pow2(sdown1)
|
|
;
|
|
|
|
qdd12
|
|
=
|
|
g12/chi - sdown1*sdown2
|
|
;
|
|
|
|
qdd13
|
|
=
|
|
g13/chi - sdown1*sdown3
|
|
;
|
|
|
|
qdd22
|
|
=
|
|
g22/chi - pow2(sdown2)
|
|
;
|
|
|
|
qdd23
|
|
=
|
|
g23/chi - sdown2*sdown3
|
|
;
|
|
|
|
qdd33
|
|
=
|
|
g33/chi - pow2(sdown3)
|
|
;
|
|
|
|
quu11
|
|
=
|
|
ADMginv11 - pow2(sup1)
|
|
;
|
|
|
|
quu12
|
|
=
|
|
ADMginv12 - sup1*sup2
|
|
;
|
|
|
|
quu13
|
|
=
|
|
ADMginv13 - sup1*sup3
|
|
;
|
|
|
|
quu22
|
|
=
|
|
ADMginv22 - pow2(sup2)
|
|
;
|
|
|
|
quu23
|
|
=
|
|
ADMginv23 - sup2*sup3
|
|
;
|
|
|
|
quu33
|
|
=
|
|
ADMginv33 - pow2(sup3)
|
|
;
|
|
|
|
muL
|
|
=
|
|
2./alpha
|
|
;
|
|
|
|
muStilde
|
|
=
|
|
1/chi
|
|
;
|
|
|
|
vbetas
|
|
=
|
|
2.*sqrt(0.33333333333333333333*muStilde)
|
|
;
|
|
|
|
vbetaA
|
|
=
|
|
sqrt(muStilde)
|
|
;
|
|
|
|
rGams
|
|
=
|
|
(beta1*dG11 + beta2*dG21 + beta3*dG31 +
|
|
(ddb111*quu11 + ddb221*quu22 +
|
|
2.*(ddb121*quu12 + ddb131*quu13 + ddb231*quu23) + ddb331*quu33)/chi\
|
|
)*sdown1 + (beta1*dG12 + beta2*dG22 + beta3*dG32 +
|
|
(ddb112*quu11 + ddb222*quu22 +
|
|
2.*(ddb122*quu12 + ddb132*quu13 + ddb232*quu23) + ddb332*quu33)/chi\
|
|
)*sdown2 + (beta1*dG13 + beta2*dG23 + beta3*dG33 +
|
|
(ddb113*quu11 + ddb223*quu22 +
|
|
2.*(ddb123*quu12 + ddb133*quu13 + ddb233*quu23) + ddb333*quu33)/chi\
|
|
)*sdown3 - ((ddb111*qud11 + ddb112*qud12 + ddb113*qud13 + ddb121*qud21 +
|
|
ddb122*qud22 + ddb123*qud23 + ddb131*qud31 + ddb132*qud32 +
|
|
ddb133*qud33)*sup1 + (ddb121*qud11 + ddb122*qud12 +
|
|
ddb123*qud13 + ddb221*qud21 + ddb222*qud22 + ddb223*qud23 +
|
|
ddb231*qud31 + ddb232*qud32 + ddb233*qud33)*sup2 +
|
|
(ddb131*qud11 + ddb132*qud12 + ddb133*qud13 + ddb231*qud21 +
|
|
ddb232*qud22 + ddb233*qud23 + ddb331*qud31 + ddb332*qud32 +
|
|
ddb333*qud33)*sup3)/chi - (dG11 + dG22 + dG33)*vbetas +
|
|
2.*((0.33333333333333333333*alpha*
|
|
(dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3))/(chi + chi*vbetas) +
|
|
((db11 + db22 + db33)*shiftdriver)/(vbetaA*sqrt(3.))) +
|
|
(1.3333333333333333333*alpha*(dKhat1*sup1 + dKhat2*sup2 + dKhat3*sup3)*
|
|
sqrt(muL))/(chi*(vbetas + sqrt(muL)))
|
|
;
|
|
|
|
rGamA1
|
|
=
|
|
-(((dG21*qud11 + dG22*qud12 + dG23*qud13)*sup2 +
|
|
(dG31*qud11 + dG32*qud12 + dG33*qud13)*sup3)*vbetaA) +
|
|
qud11*(beta2*dG21 + beta3*dG31 +
|
|
(1.3333333333333333333*ddb111*quu11 +
|
|
2.3333333333333333333*(ddb121*quu12 + ddb131*quu13) +
|
|
ddb221*quu22 + ddb331*quu33 +
|
|
(shiftdriver*(db11*sup1 + db31*sup3))/vbetaA)/chi +
|
|
dG11*(beta1 - sup1*vbetaA)) +
|
|
qud12*(beta2*dG22 + beta3*dG32 +
|
|
(1.3333333333333333333*ddb112*quu11 +
|
|
2.3333333333333333333*(ddb122*quu12 + ddb132*quu13) +
|
|
ddb222*quu22 + 2.*ddb232*quu23 + ddb332*quu33 +
|
|
(shiftdriver*(db12*sup1 + db22*sup2 + db32*sup3))/vbetaA)/chi +
|
|
dG12*(beta1 - sup1*vbetaA)) +
|
|
qud13*(beta2*dG23 + beta3*dG33 +
|
|
(1.3333333333333333333*ddb113*quu11 +
|
|
2.3333333333333333333*(ddb123*quu12 + ddb133*quu13) +
|
|
ddb223*quu22 + 2.*ddb233*quu23 + ddb333*quu33 +
|
|
(shiftdriver*(db13*sup1 + db23*sup2 + db33*sup3))/vbetaA)/chi +
|
|
dG13*(beta1 - sup1*vbetaA)) +
|
|
(0.33333333333333333333*((ddb121*qud21 + ddb122*qud22 + ddb123*qud23 +
|
|
ddb131*qud31 + ddb132*qud32 + ddb133*qud33)*quu11 +
|
|
(ddb221*qud21 + ddb223*qud23 + ddb231*qud31 + ddb232*qud32 +
|
|
ddb233*qud33)*quu12 +
|
|
(ddb231*qud21 + ddb232*qud22 + ddb233*qud23 + ddb331*qud31 +
|
|
ddb332*qud32)*quu13) -
|
|
alpha*((1.3333333333333333333*dKhat1 +
|
|
0.66666666666666666667*dTheta1)*quu11 +
|
|
1.3333333333333333333*(dKhat2*quu12 + dKhat3*quu13)) +
|
|
1.3333333333333333333*((ddb132*quu13*sdown2 + ddb113*quu11*sdown3)*
|
|
sup1 + (quu13*(ddb231*sdown1 + ddb232*sdown2) +
|
|
quu12*(ddb222*sdown2 + ddb223*sdown3))*sup2 +
|
|
(quu12*(ddb232*sdown2 + ddb233*sdown3) +
|
|
quu13*(ddb331*sdown1 + ddb332*sdown2 + ddb333*sdown3))*sup3 +
|
|
sdown1*((ddb121*quu12 + ddb131*quu13)*sup1 + ddb221*quu12*sup2 +
|
|
ddb131*quu11*sup3) +
|
|
sdown2*((ddb112*quu11 + ddb122*quu12)*sup1 +
|
|
quu11*(ddb122*sup2 + ddb132*sup3)) +
|
|
sdown3*((ddb123*quu12 + ddb133*quu13)*sup1 +
|
|
quu11*(ddb123*sup2 + ddb133*sup3))) +
|
|
qud11*(2.*ddb231*quu23 + (db21*shiftdriver*sup2)/vbetaA) -
|
|
(((db11*quu11 + db21*quu12)*sdown1 +
|
|
(db12*quu11 + db22*quu12 + db32*quu13)*sdown2 +
|
|
(db13*quu11 + db23*quu12 + db33*quu13)*sdown3)*shiftdriver)/
|
|
vbetaA + ((dG22*quu12 + dG32*quu13)*sdown2 +
|
|
(dG13*quu11 + dG23*quu12)*sdown3)*vbetaA +
|
|
quu11*(1.3333333333333333333*sdown1*(ddb111*sup1 + ddb121*sup2) +
|
|
(dG11*sdown1 + dG12*sdown2)*vbetaA) +
|
|
quu12*(-0.66666666666666666667*alpha*dTheta2 +
|
|
0.33333333333333333333*ddb222*qud22 +
|
|
sdown1*(1.3333333333333333333*ddb231*sup3 + dG21*vbetaA)) +
|
|
quu13*(-0.66666666666666666667*alpha*dTheta3 +
|
|
0.33333333333333333333*ddb333*qud33 -
|
|
(db31*sdown1*shiftdriver)/vbetaA + dG31*sdown1*vbetaA +
|
|
sdown3*(1.3333333333333333333*ddb233*sup2 + dG33*vbetaA)))/chi
|
|
;
|
|
|
|
rGamA2
|
|
=
|
|
-(((dG21*qud21 + dG22*qud22 + dG23*qud23)*sup2 +
|
|
(dG31*qud21 + dG32*qud22 + dG33*qud23)*sup3)*vbetaA) +
|
|
qud21*(beta2*dG21 + beta3*dG31 +
|
|
(ddb111*quu11 + 2.*ddb131*quu13 +
|
|
1.3333333333333333333*ddb221*quu22 +
|
|
2.3333333333333333333*(ddb121*quu12 + ddb231*quu23) +
|
|
ddb331*quu33 + (shiftdriver*(db11*sup1 + db31*sup3))/vbetaA)/chi +
|
|
dG11*(beta1 - sup1*vbetaA)) +
|
|
qud22*(beta2*dG22 + beta3*dG32 +
|
|
(ddb112*quu11 + 2.*ddb132*quu13 +
|
|
1.3333333333333333333*ddb222*quu22 +
|
|
2.3333333333333333333*(ddb122*quu12 + ddb232*quu23) +
|
|
ddb332*quu33 + (shiftdriver*(db12*sup1 + db22*sup2 + db32*sup3))/
|
|
vbetaA)/chi + dG12*(beta1 - sup1*vbetaA)) +
|
|
qud23*(beta2*dG23 + beta3*dG33 +
|
|
(ddb113*quu11 + 2.*ddb133*quu13 +
|
|
1.3333333333333333333*ddb223*quu22 +
|
|
2.3333333333333333333*(ddb123*quu12 + ddb233*quu23) +
|
|
ddb333*quu33 + (shiftdriver*(db13*sup1 + db23*sup2 + db33*sup3))/
|
|
vbetaA)/chi + dG13*(beta1 - sup1*vbetaA)) +
|
|
(0.33333333333333333333*((ddb111*qud11 + ddb112*qud12 + ddb113*qud13 +
|
|
ddb131*qud31 + ddb132*qud32 + ddb133*qud33)*quu12 +
|
|
(ddb121*qud11 + ddb123*qud13 + ddb231*qud31 + ddb232*qud32 +
|
|
ddb233*qud33)*quu22 +
|
|
(ddb131*qud11 + ddb132*qud12 + ddb133*qud13 + ddb331*qud31 +
|
|
ddb332*qud32)*quu23) -
|
|
alpha*((1.3333333333333333333*dKhat1 +
|
|
0.66666666666666666667*dTheta1)*quu12 +
|
|
1.3333333333333333333*(dKhat2*quu22 + dKhat3*quu23)) +
|
|
1.3333333333333333333*((ddb132*quu23*sdown2 + ddb113*quu12*sdown3)*
|
|
sup1 + (quu23*(ddb231*sdown1 + ddb232*sdown2) +
|
|
quu22*(ddb222*sdown2 + ddb223*sdown3))*sup2 +
|
|
(quu22*(ddb232*sdown2 + ddb233*sdown3) +
|
|
quu23*(ddb331*sdown1 + ddb332*sdown2 + ddb333*sdown3))*sup3 +
|
|
sdown1*((ddb121*quu22 + ddb131*quu23)*sup1 + ddb221*quu22*sup2 +
|
|
ddb131*quu12*sup3) +
|
|
sdown2*((ddb112*quu12 + ddb122*quu22)*sup1 +
|
|
quu12*(ddb122*sup2 + ddb132*sup3)) +
|
|
sdown3*((ddb123*quu22 + ddb133*quu23)*sup1 +
|
|
quu12*(ddb123*sup2 + ddb133*sup3))) -
|
|
(((db11*quu12 + db21*quu22)*sdown1 +
|
|
(db12*quu12 + db22*quu22 + db32*quu23)*sdown2 +
|
|
(db13*quu12 + db23*quu22 + db33*quu23)*sdown3)*shiftdriver)/
|
|
vbetaA + (db21*qud21*shiftdriver*sup2)/vbetaA +
|
|
((dG22*quu22 + dG32*quu23)*sdown2 + (dG13*quu12 + dG23*quu22)*sdown3)*
|
|
vbetaA + quu12*(1.3333333333333333333*sdown1*
|
|
(ddb111*sup1 + ddb121*sup2) + (dG11*sdown1 + dG12*sdown2)*vbetaA) \
|
|
+ quu22*(-0.66666666666666666667*alpha*dTheta2 +
|
|
0.33333333333333333333*ddb122*qud12 +
|
|
sdown1*(1.3333333333333333333*ddb231*sup3 + dG21*vbetaA)) +
|
|
quu23*(-0.66666666666666666667*alpha*dTheta3 +
|
|
0.33333333333333333333*ddb333*qud33 -
|
|
(db31*sdown1*shiftdriver)/vbetaA + dG31*sdown1*vbetaA +
|
|
sdown3*(1.3333333333333333333*ddb233*sup2 + dG33*vbetaA)))/chi
|
|
;
|
|
|
|
rGamA3
|
|
=
|
|
-(((dG21*qud31 + dG22*qud32 + dG23*qud33)*sup2 +
|
|
(dG31*qud31 + dG32*qud32 + dG33*qud33)*sup3)*vbetaA) +
|
|
qud31*(beta2*dG21 + beta3*dG31 +
|
|
(ddb111*quu11 + 2.*ddb121*quu12 + ddb221*quu22 +
|
|
2.3333333333333333333*(ddb131*quu13 + ddb231*quu23) +
|
|
1.3333333333333333333*ddb331*quu33 +
|
|
(shiftdriver*(db11*sup1 + db31*sup3))/vbetaA)/chi +
|
|
dG11*(beta1 - sup1*vbetaA)) +
|
|
qud32*(beta2*dG22 + beta3*dG32 +
|
|
(ddb112*quu11 + 2.*ddb122*quu12 + ddb222*quu22 +
|
|
2.3333333333333333333*(ddb132*quu13 + ddb232*quu23) +
|
|
1.3333333333333333333*ddb332*quu33 +
|
|
(shiftdriver*(db12*sup1 + db22*sup2 + db32*sup3))/vbetaA)/chi +
|
|
dG12*(beta1 - sup1*vbetaA)) +
|
|
qud33*(beta2*dG23 + beta3*dG33 +
|
|
(ddb113*quu11 + 2.*ddb123*quu12 + ddb223*quu22 +
|
|
2.3333333333333333333*(ddb133*quu13 + ddb233*quu23) +
|
|
1.3333333333333333333*ddb333*quu33 +
|
|
(shiftdriver*(db13*sup1 + db23*sup2 + db33*sup3))/vbetaA)/chi +
|
|
dG13*(beta1 - sup1*vbetaA)) +
|
|
(0.33333333333333333333*((ddb111*qud11 + ddb112*qud12 + ddb113*qud13 +
|
|
ddb121*qud21 + ddb122*qud22 + ddb123*qud23)*quu13 +
|
|
(ddb121*qud11 + ddb123*qud13 + ddb221*qud21 + ddb222*qud22 +
|
|
ddb223*qud23)*quu23 +
|
|
(ddb131*qud11 + ddb132*qud12 + ddb133*qud13 + ddb231*qud21 +
|
|
ddb232*qud22)*quu33) -
|
|
alpha*((1.3333333333333333333*dKhat1 +
|
|
0.66666666666666666667*dTheta1)*quu13 +
|
|
1.3333333333333333333*(dKhat2*quu23 + dKhat3*quu33)) +
|
|
1.3333333333333333333*((ddb132*quu33*sdown2 + ddb113*quu13*sdown3)*
|
|
sup1 + (quu33*(ddb231*sdown1 + ddb232*sdown2) +
|
|
quu23*(ddb222*sdown2 + ddb223*sdown3))*sup2 +
|
|
(quu23*(ddb232*sdown2 + ddb233*sdown3) +
|
|
quu33*(ddb331*sdown1 + ddb332*sdown2 + ddb333*sdown3))*sup3 +
|
|
sdown1*((ddb121*quu23 + ddb131*quu33)*sup1 + ddb221*quu23*sup2 +
|
|
ddb131*quu13*sup3) +
|
|
sdown2*((ddb112*quu13 + ddb122*quu23)*sup1 +
|
|
quu13*(ddb122*sup2 + ddb132*sup3)) +
|
|
sdown3*((ddb123*quu23 + ddb133*quu33)*sup1 +
|
|
quu13*(ddb123*sup2 + ddb133*sup3))) -
|
|
(((db11*quu13 + db21*quu23)*sdown1 +
|
|
(db12*quu13 + db22*quu23 + db32*quu33)*sdown2 +
|
|
(db13*quu13 + db23*quu23 + db33*quu33)*sdown3)*shiftdriver)/
|
|
vbetaA + (db21*qud31*shiftdriver*sup2)/vbetaA +
|
|
((dG22*quu23 + dG32*quu33)*sdown2 + (dG13*quu13 + dG23*quu23)*sdown3)*
|
|
vbetaA + quu13*(1.3333333333333333333*sdown1*
|
|
(ddb111*sup1 + ddb121*sup2) + (dG11*sdown1 + dG12*sdown2)*vbetaA) \
|
|
+ quu33*(-0.66666666666666666667*alpha*dTheta3 +
|
|
ddb233*(0.33333333333333333333*qud23 +
|
|
1.3333333333333333333*sdown3*sup2) -
|
|
(db31*sdown1*shiftdriver)/vbetaA +
|
|
(dG31*sdown1 + dG33*sdown3)*vbetaA) +
|
|
quu23*(-0.66666666666666666667*alpha*dTheta2 +
|
|
0.33333333333333333333*ddb122*qud12 +
|
|
sdown1*(1.3333333333333333333*ddb231*sup3 + dG21*vbetaA)))/chi
|
|
;
|
|
|
|
} /* function */
|
|
#ifdef fortran1
|
|
void ra_point
|
|
#endif
|
|
#ifdef fortran2
|
|
void RA_POINT
|
|
#endif
|
|
#ifdef fortran3
|
|
void ra_point_
|
|
#endif
|
|
(double &A11,
|
|
double &A12,
|
|
double &A13,
|
|
double &A22,
|
|
double &A23,
|
|
double &A33,
|
|
double &alpha,
|
|
double &beta1,
|
|
double &beta2,
|
|
double &beta3,
|
|
double &chi,
|
|
double &da1,
|
|
double &dA111,
|
|
double &dA112,
|
|
double &dA113,
|
|
double &dA122,
|
|
double &dA123,
|
|
double &dA133,
|
|
double &da2,
|
|
double &dA211,
|
|
double &dA212,
|
|
double &dA213,
|
|
double &dA222,
|
|
double &dA223,
|
|
double &dA233,
|
|
double &da3,
|
|
double &dA311,
|
|
double &dA312,
|
|
double &dA313,
|
|
double &dA322,
|
|
double &dA323,
|
|
double &dA333,
|
|
double &db11,
|
|
double &db12,
|
|
double &db13,
|
|
double &db21,
|
|
double &db22,
|
|
double &db23,
|
|
double &db31,
|
|
double &db32,
|
|
double &db33,
|
|
double &dchi1,
|
|
double &dchi2,
|
|
double &dchi3,
|
|
double &dda11,
|
|
double &dda12,
|
|
double &dda13,
|
|
double &dda22,
|
|
double &dda23,
|
|
double &dda33,
|
|
double &ddb111,
|
|
double &ddb112,
|
|
double &ddb113,
|
|
double &ddb121,
|
|
double &ddb122,
|
|
double &ddb123,
|
|
double &ddb131,
|
|
double &ddb132,
|
|
double &ddb133,
|
|
double &ddb221,
|
|
double &ddb222,
|
|
double &ddb223,
|
|
double &ddb231,
|
|
double &ddb232,
|
|
double &ddb233,
|
|
double &ddb331,
|
|
double &ddb332,
|
|
double &ddb333,
|
|
double &ddchi11,
|
|
double &ddchi12,
|
|
double &ddchi13,
|
|
double &ddchi22,
|
|
double &ddchi23,
|
|
double &ddchi33,
|
|
double &ddg1111,
|
|
double &ddg1112,
|
|
double &ddg1113,
|
|
double &ddg1122,
|
|
double &ddg1123,
|
|
double &ddg1133,
|
|
double &ddg1211,
|
|
double &ddg1212,
|
|
double &ddg1213,
|
|
double &ddg1222,
|
|
double &ddg1223,
|
|
double &ddg1233,
|
|
double &ddg1311,
|
|
double &ddg1312,
|
|
double &ddg1313,
|
|
double &ddg1322,
|
|
double &ddg1323,
|
|
double &ddg1333,
|
|
double &ddg2211,
|
|
double &ddg2212,
|
|
double &ddg2213,
|
|
double &ddg2222,
|
|
double &ddg2223,
|
|
double &ddg2233,
|
|
double &ddg2311,
|
|
double &ddg2312,
|
|
double &ddg2313,
|
|
double &ddg2322,
|
|
double &ddg2323,
|
|
double &ddg2333,
|
|
double &ddg3311,
|
|
double &ddg3312,
|
|
double &ddg3313,
|
|
double &ddg3322,
|
|
double &ddg3323,
|
|
double &ddg3333,
|
|
double &dG11,
|
|
double &dg111,
|
|
double &dg112,
|
|
double &dg113,
|
|
double &dG12,
|
|
double &dg122,
|
|
double &dg123,
|
|
double &dG13,
|
|
double &dg133,
|
|
double &dG21,
|
|
double &dg211,
|
|
double &dg212,
|
|
double &dg213,
|
|
double &dG22,
|
|
double &dg222,
|
|
double &dg223,
|
|
double &dG23,
|
|
double &dg233,
|
|
double &dG31,
|
|
double &dg311,
|
|
double &dg312,
|
|
double &dg313,
|
|
double &dG32,
|
|
double &dg322,
|
|
double &dg323,
|
|
double &dG33,
|
|
double &dg333,
|
|
double &dKhat1,
|
|
double &dKhat2,
|
|
double &dKhat3,
|
|
double &dTheta1,
|
|
double &dTheta2,
|
|
double &dTheta3,
|
|
double &G1,
|
|
double &g11,
|
|
double &g12,
|
|
double &g13,
|
|
double &G2,
|
|
double &g22,
|
|
double &g23,
|
|
double &G3,
|
|
double &g33,
|
|
double &kappa1,
|
|
double &Khat,
|
|
double &r,
|
|
double &rACABTF11,
|
|
double &rACABTF12,
|
|
double &rACABTF13,
|
|
double &rACABTF22,
|
|
double &rACABTF23,
|
|
double &rACABTF33,
|
|
double &rACsA1,
|
|
double &rACsA2,
|
|
double &rACsA3,
|
|
double &rACss,
|
|
double &Theta,
|
|
double &xp,
|
|
double &yp,
|
|
double &zp)
|
|
{
|
|
|
|
double AA11;
|
|
double AA12;
|
|
double AA13;
|
|
double AA21;
|
|
double AA22;
|
|
double AA23;
|
|
double AA31;
|
|
double AA32;
|
|
double AA33;
|
|
double ADMginv11;
|
|
double ADMginv12;
|
|
double ADMginv13;
|
|
double ADMginv22;
|
|
double ADMginv23;
|
|
double ADMginv33;
|
|
double cdA111;
|
|
double cdA112;
|
|
double cdA113;
|
|
double cdA122;
|
|
double cdA123;
|
|
double cdA133;
|
|
double cdA211;
|
|
double cdA212;
|
|
double cdA213;
|
|
double cdA222;
|
|
double cdA223;
|
|
double cdA233;
|
|
double cdA311;
|
|
double cdA312;
|
|
double cdA313;
|
|
double cdA322;
|
|
double cdA323;
|
|
double cdA333;
|
|
double cdda11;
|
|
double cdda12;
|
|
double cdda13;
|
|
double cdda22;
|
|
double cdda23;
|
|
double cdda33;
|
|
double cddf11;
|
|
double cddf12;
|
|
double cddf13;
|
|
double cddf22;
|
|
double cddf23;
|
|
double cddf33;
|
|
double chipsipower;
|
|
double ddf11;
|
|
double ddf12;
|
|
double ddf13;
|
|
double ddf22;
|
|
double ddf23;
|
|
double ddf33;
|
|
double detginv;
|
|
double df1;
|
|
double df2;
|
|
double df3;
|
|
double dGfromgdu11;
|
|
double dGfromgdu12;
|
|
double dGfromgdu13;
|
|
double dGfromgdu21;
|
|
double dGfromgdu22;
|
|
double dGfromgdu23;
|
|
double dGfromgdu31;
|
|
double dGfromgdu32;
|
|
double dGfromgdu33;
|
|
double divbeta;
|
|
double dK1;
|
|
double dK2;
|
|
double dK3;
|
|
double DTheta;
|
|
double f;
|
|
double ff;
|
|
double gamma111;
|
|
double gamma112;
|
|
double gamma113;
|
|
double gamma122;
|
|
double gamma123;
|
|
double gamma133;
|
|
double gamma211;
|
|
double gamma212;
|
|
double gamma213;
|
|
double gamma222;
|
|
double gamma223;
|
|
double gamma233;
|
|
double gamma311;
|
|
double gamma312;
|
|
double gamma313;
|
|
double gamma322;
|
|
double gamma323;
|
|
double gamma333;
|
|
double gammado111;
|
|
double gammado112;
|
|
double gammado113;
|
|
double gammado122;
|
|
double gammado123;
|
|
double gammado133;
|
|
double gammado211;
|
|
double gammado212;
|
|
double gammado213;
|
|
double gammado222;
|
|
double gammado223;
|
|
double gammado233;
|
|
double gammado311;
|
|
double gammado312;
|
|
double gammado313;
|
|
double gammado322;
|
|
double gammado323;
|
|
double gammado333;
|
|
double Gfromg1;
|
|
double Gfromg2;
|
|
double Gfromg3;
|
|
double ginv11;
|
|
double ginv12;
|
|
double ginv13;
|
|
double ginv22;
|
|
double ginv23;
|
|
double ginv33;
|
|
double K;
|
|
double lieA11;
|
|
double lieA12;
|
|
double lieA13;
|
|
double lieA22;
|
|
double lieA23;
|
|
double lieA33;
|
|
double modshatARG;
|
|
double oochipsipower;
|
|
double oomodshat;
|
|
double psim4;
|
|
double qdd11;
|
|
double qdd12;
|
|
double qdd13;
|
|
double qdd22;
|
|
double qdd23;
|
|
double qdd33;
|
|
double qPhysuudd1111;
|
|
double qPhysuudd1112;
|
|
double qPhysuudd1113;
|
|
double qPhysuudd1122;
|
|
double qPhysuudd1123;
|
|
double qPhysuudd1133;
|
|
double qPhysuudd1211;
|
|
double qPhysuudd1212;
|
|
double qPhysuudd1213;
|
|
double qPhysuudd1222;
|
|
double qPhysuudd1223;
|
|
double qPhysuudd1233;
|
|
double qPhysuudd1311;
|
|
double qPhysuudd1312;
|
|
double qPhysuudd1313;
|
|
double qPhysuudd1322;
|
|
double qPhysuudd1323;
|
|
double qPhysuudd1333;
|
|
double qPhysuudd2211;
|
|
double qPhysuudd2212;
|
|
double qPhysuudd2213;
|
|
double qPhysuudd2222;
|
|
double qPhysuudd2223;
|
|
double qPhysuudd2233;
|
|
double qPhysuudd2311;
|
|
double qPhysuudd2312;
|
|
double qPhysuudd2313;
|
|
double qPhysuudd2322;
|
|
double qPhysuudd2323;
|
|
double qPhysuudd2333;
|
|
double qPhysuudd3311;
|
|
double qPhysuudd3312;
|
|
double qPhysuudd3313;
|
|
double qPhysuudd3322;
|
|
double qPhysuudd3323;
|
|
double qPhysuudd3333;
|
|
double qud11;
|
|
double qud12;
|
|
double qud13;
|
|
double qud21;
|
|
double qud22;
|
|
double qud23;
|
|
double qud31;
|
|
double qud32;
|
|
double qud33;
|
|
double quu11;
|
|
double quu12;
|
|
double quu13;
|
|
double quu22;
|
|
double quu23;
|
|
double quu33;
|
|
double R11;
|
|
double R12;
|
|
double R13;
|
|
double R22;
|
|
double R23;
|
|
double R33;
|
|
double Rf11;
|
|
double Rf12;
|
|
double Rf13;
|
|
double Rf22;
|
|
double Rf23;
|
|
double Rf33;
|
|
double Rhat;
|
|
double Rphi11;
|
|
double Rphi12;
|
|
double Rphi13;
|
|
double Rphi22;
|
|
double Rphi23;
|
|
double Rphi33;
|
|
double sdown1;
|
|
double sdown2;
|
|
double sdown3;
|
|
double shat1;
|
|
double shat2;
|
|
double shat3;
|
|
double sup1;
|
|
double sup2;
|
|
double sup3;
|
|
double totdivbeta;
|
|
double trcdda;
|
|
double trcddf;
|
|
|
|
|
|
|
|
chipsipower
|
|
=
|
|
-4.
|
|
;
|
|
|
|
shat1=xp/r;shat2=yp/r;shat3=zp/r;
|
|
|
|
detginv
|
|
=
|
|
1/(2.*g12*g13*g23 - g33*pow2(g12) + g22*(g11*g33 - pow2(g13)) -
|
|
g11*pow2(g23))
|
|
;
|
|
|
|
ginv11
|
|
=
|
|
detginv*(g22*g33 - pow2(g23))
|
|
;
|
|
|
|
ginv12
|
|
=
|
|
detginv*(g13*g23 - g12*g33)
|
|
;
|
|
|
|
ginv13
|
|
=
|
|
detginv*(-(g13*g22) + g12*g23)
|
|
;
|
|
|
|
ginv22
|
|
=
|
|
detginv*(g11*g33 - pow2(g13))
|
|
;
|
|
|
|
ginv23
|
|
=
|
|
detginv*(g12*g13 - g11*g23)
|
|
;
|
|
|
|
ginv33
|
|
=
|
|
detginv*(g11*g22 - pow2(g12))
|
|
;
|
|
|
|
ADMginv11
|
|
=
|
|
chi*ginv11
|
|
;
|
|
|
|
ADMginv12
|
|
=
|
|
chi*ginv12
|
|
;
|
|
|
|
ADMginv13
|
|
=
|
|
chi*ginv13
|
|
;
|
|
|
|
ADMginv22
|
|
=
|
|
chi*ginv22
|
|
;
|
|
|
|
ADMginv23
|
|
=
|
|
chi*ginv23
|
|
;
|
|
|
|
ADMginv33
|
|
=
|
|
chi*ginv33
|
|
;
|
|
|
|
modshatARG
|
|
=
|
|
2.*(ADMginv23*shat2*shat3 + shat1*(ADMginv12*shat2 + ADMginv13*shat3)) +
|
|
ADMginv11*pow2(shat1) + ADMginv22*pow2(shat2) + ADMginv33*pow2(shat3)
|
|
;
|
|
|
|
|
|
if (modshatARG<0.00001) {
|
|
printf("modshat is wrong (%e)\n",modshatARG);
|
|
modshatARG = 0.00001;
|
|
}oomodshat
|
|
=
|
|
1/sqrt(modshatARG)
|
|
;
|
|
|
|
sdown1
|
|
=
|
|
oomodshat*shat1
|
|
;
|
|
|
|
sdown2
|
|
=
|
|
oomodshat*shat2
|
|
;
|
|
|
|
sdown3
|
|
=
|
|
oomodshat*shat3
|
|
;
|
|
|
|
sup1
|
|
=
|
|
ADMginv11*sdown1 + ADMginv12*sdown2 + ADMginv13*sdown3
|
|
;
|
|
|
|
sup2
|
|
=
|
|
ADMginv12*sdown1 + ADMginv22*sdown2 + ADMginv23*sdown3
|
|
;
|
|
|
|
sup3
|
|
=
|
|
ADMginv13*sdown1 + ADMginv23*sdown2 + ADMginv33*sdown3
|
|
;
|
|
|
|
qud11
|
|
=
|
|
1. - sdown1*sup1
|
|
;
|
|
|
|
qud12
|
|
=
|
|
-(sdown2*sup1)
|
|
;
|
|
|
|
qud13
|
|
=
|
|
-(sdown3*sup1)
|
|
;
|
|
|
|
qud21
|
|
=
|
|
-(sdown1*sup2)
|
|
;
|
|
|
|
qud22
|
|
=
|
|
1. - sdown2*sup2
|
|
;
|
|
|
|
qud23
|
|
=
|
|
-(sdown3*sup2)
|
|
;
|
|
|
|
qud31
|
|
=
|
|
-(sdown1*sup3)
|
|
;
|
|
|
|
qud32
|
|
=
|
|
-(sdown2*sup3)
|
|
;
|
|
|
|
qud33
|
|
=
|
|
1. - sdown3*sup3
|
|
;
|
|
|
|
qdd11
|
|
=
|
|
g11/chi - pow2(sdown1)
|
|
;
|
|
|
|
qdd12
|
|
=
|
|
g12/chi - sdown1*sdown2
|
|
;
|
|
|
|
qdd13
|
|
=
|
|
g13/chi - sdown1*sdown3
|
|
;
|
|
|
|
qdd22
|
|
=
|
|
g22/chi - pow2(sdown2)
|
|
;
|
|
|
|
qdd23
|
|
=
|
|
g23/chi - sdown2*sdown3
|
|
;
|
|
|
|
qdd33
|
|
=
|
|
g33/chi - pow2(sdown3)
|
|
;
|
|
|
|
quu11
|
|
=
|
|
ADMginv11 - pow2(sup1)
|
|
;
|
|
|
|
quu12
|
|
=
|
|
ADMginv12 - sup1*sup2
|
|
;
|
|
|
|
quu13
|
|
=
|
|
ADMginv13 - sup1*sup3
|
|
;
|
|
|
|
quu22
|
|
=
|
|
ADMginv22 - pow2(sup2)
|
|
;
|
|
|
|
quu23
|
|
=
|
|
ADMginv23 - sup2*sup3
|
|
;
|
|
|
|
quu33
|
|
=
|
|
ADMginv33 - pow2(sup3)
|
|
;
|
|
|
|
qPhysuudd1111
|
|
=
|
|
-0.5*qdd11*quu11 + pow2(qud11)
|
|
;
|
|
|
|
qPhysuudd1112
|
|
=
|
|
qud11*qud12 - 0.5*qdd12*quu11
|
|
;
|
|
|
|
qPhysuudd1113
|
|
=
|
|
qud11*qud13 - 0.5*qdd13*quu11
|
|
;
|
|
|
|
qPhysuudd1122
|
|
=
|
|
-0.5*qdd22*quu11 + pow2(qud12)
|
|
;
|
|
|
|
qPhysuudd1123
|
|
=
|
|
qud12*qud13 - 0.5*qdd23*quu11
|
|
;
|
|
|
|
qPhysuudd1133
|
|
=
|
|
-0.5*qdd33*quu11 + pow2(qud13)
|
|
;
|
|
|
|
qPhysuudd1211
|
|
=
|
|
qud11*qud21 - 0.5*qdd11*quu12
|
|
;
|
|
|
|
qPhysuudd1212
|
|
=
|
|
0.5*(qud12*qud21 + qud11*qud22 - qdd12*quu12)
|
|
;
|
|
|
|
qPhysuudd1213
|
|
=
|
|
0.5*(qud13*qud21 + qud11*qud23 - qdd13*quu12)
|
|
;
|
|
|
|
qPhysuudd1222
|
|
=
|
|
qud12*qud22 - 0.5*qdd22*quu12
|
|
;
|
|
|
|
qPhysuudd1223
|
|
=
|
|
0.5*(qud13*qud22 + qud12*qud23 - qdd23*quu12)
|
|
;
|
|
|
|
qPhysuudd1233
|
|
=
|
|
qud13*qud23 - 0.5*qdd33*quu12
|
|
;
|
|
|
|
qPhysuudd1311
|
|
=
|
|
qud11*qud31 - 0.5*qdd11*quu13
|
|
;
|
|
|
|
qPhysuudd1312
|
|
=
|
|
0.5*(qud12*qud31 + qud11*qud32 - qdd12*quu13)
|
|
;
|
|
|
|
qPhysuudd1313
|
|
=
|
|
0.5*(qud13*qud31 + qud11*qud33 - qdd13*quu13)
|
|
;
|
|
|
|
qPhysuudd1322
|
|
=
|
|
qud12*qud32 - 0.5*qdd22*quu13
|
|
;
|
|
|
|
qPhysuudd1323
|
|
=
|
|
0.5*(qud13*qud32 + qud12*qud33 - qdd23*quu13)
|
|
;
|
|
|
|
qPhysuudd1333
|
|
=
|
|
qud13*qud33 - 0.5*qdd33*quu13
|
|
;
|
|
|
|
qPhysuudd2211
|
|
=
|
|
-0.5*qdd11*quu22 + pow2(qud21)
|
|
;
|
|
|
|
qPhysuudd2212
|
|
=
|
|
qud21*qud22 - 0.5*qdd12*quu22
|
|
;
|
|
|
|
qPhysuudd2213
|
|
=
|
|
qud21*qud23 - 0.5*qdd13*quu22
|
|
;
|
|
|
|
qPhysuudd2222
|
|
=
|
|
-0.5*qdd22*quu22 + pow2(qud22)
|
|
;
|
|
|
|
qPhysuudd2223
|
|
=
|
|
qud22*qud23 - 0.5*qdd23*quu22
|
|
;
|
|
|
|
qPhysuudd2233
|
|
=
|
|
-0.5*qdd33*quu22 + pow2(qud23)
|
|
;
|
|
|
|
qPhysuudd2311
|
|
=
|
|
qud21*qud31 - 0.5*qdd11*quu23
|
|
;
|
|
|
|
qPhysuudd2312
|
|
=
|
|
0.5*(qud22*qud31 + qud21*qud32 - qdd12*quu23)
|
|
;
|
|
|
|
qPhysuudd2313
|
|
=
|
|
0.5*(qud23*qud31 + qud21*qud33 - qdd13*quu23)
|
|
;
|
|
|
|
qPhysuudd2322
|
|
=
|
|
qud22*qud32 - 0.5*qdd22*quu23
|
|
;
|
|
|
|
qPhysuudd2323
|
|
=
|
|
0.5*(qud23*qud32 + qud22*qud33 - qdd23*quu23)
|
|
;
|
|
|
|
qPhysuudd2333
|
|
=
|
|
qud23*qud33 - 0.5*qdd33*quu23
|
|
;
|
|
|
|
qPhysuudd3311
|
|
=
|
|
-0.5*qdd11*quu33 + pow2(qud31)
|
|
;
|
|
|
|
qPhysuudd3312
|
|
=
|
|
qud31*qud32 - 0.5*qdd12*quu33
|
|
;
|
|
|
|
qPhysuudd3313
|
|
=
|
|
qud31*qud33 - 0.5*qdd13*quu33
|
|
;
|
|
|
|
qPhysuudd3322
|
|
=
|
|
-0.5*qdd22*quu33 + pow2(qud32)
|
|
;
|
|
|
|
qPhysuudd3323
|
|
=
|
|
qud32*qud33 - 0.5*qdd23*quu33
|
|
;
|
|
|
|
qPhysuudd3333
|
|
=
|
|
-0.5*qdd33*quu33 + pow2(qud33)
|
|
;
|
|
|
|
K
|
|
=
|
|
Khat + 2.*Theta
|
|
;
|
|
|
|
dK1
|
|
=
|
|
dKhat1 + 2.*dTheta1
|
|
;
|
|
|
|
dK2
|
|
=
|
|
dKhat2 + 2.*dTheta2
|
|
;
|
|
|
|
dK3
|
|
=
|
|
dKhat3 + 2.*dTheta3
|
|
;
|
|
|
|
gammado111
|
|
=
|
|
0.5*dg111
|
|
;
|
|
|
|
gammado112
|
|
=
|
|
0.5*dg211
|
|
;
|
|
|
|
gammado113
|
|
=
|
|
0.5*dg311
|
|
;
|
|
|
|
gammado122
|
|
=
|
|
-0.5*dg122 + dg212
|
|
;
|
|
|
|
gammado123
|
|
=
|
|
0.5*(-dg123 + dg213 + dg312)
|
|
;
|
|
|
|
gammado133
|
|
=
|
|
-0.5*dg133 + dg313
|
|
;
|
|
|
|
gammado211
|
|
=
|
|
dg112 - 0.5*dg211
|
|
;
|
|
|
|
gammado212
|
|
=
|
|
0.5*dg122
|
|
;
|
|
|
|
gammado213
|
|
=
|
|
0.5*(dg123 - dg213 + dg312)
|
|
;
|
|
|
|
gammado222
|
|
=
|
|
0.5*dg222
|
|
;
|
|
|
|
gammado223
|
|
=
|
|
0.5*dg322
|
|
;
|
|
|
|
gammado233
|
|
=
|
|
-0.5*dg233 + dg323
|
|
;
|
|
|
|
gammado311
|
|
=
|
|
dg113 - 0.5*dg311
|
|
;
|
|
|
|
gammado312
|
|
=
|
|
0.5*(dg123 + dg213 - dg312)
|
|
;
|
|
|
|
gammado313
|
|
=
|
|
0.5*dg133
|
|
;
|
|
|
|
gammado322
|
|
=
|
|
dg223 - 0.5*dg322
|
|
;
|
|
|
|
gammado323
|
|
=
|
|
0.5*dg233
|
|
;
|
|
|
|
gammado333
|
|
=
|
|
0.5*dg333
|
|
;
|
|
|
|
gamma111
|
|
=
|
|
gammado111*ginv11 + gammado211*ginv12 + gammado311*ginv13
|
|
;
|
|
|
|
gamma112
|
|
=
|
|
gammado112*ginv11 + gammado212*ginv12 + gammado312*ginv13
|
|
;
|
|
|
|
gamma113
|
|
=
|
|
gammado113*ginv11 + gammado213*ginv12 + gammado313*ginv13
|
|
;
|
|
|
|
gamma122
|
|
=
|
|
gammado122*ginv11 + gammado222*ginv12 + gammado322*ginv13
|
|
;
|
|
|
|
gamma123
|
|
=
|
|
gammado123*ginv11 + gammado223*ginv12 + gammado323*ginv13
|
|
;
|
|
|
|
gamma133
|
|
=
|
|
gammado133*ginv11 + gammado233*ginv12 + gammado333*ginv13
|
|
;
|
|
|
|
gamma211
|
|
=
|
|
gammado111*ginv12 + gammado211*ginv22 + gammado311*ginv23
|
|
;
|
|
|
|
gamma212
|
|
=
|
|
gammado112*ginv12 + gammado212*ginv22 + gammado312*ginv23
|
|
;
|
|
|
|
gamma213
|
|
=
|
|
gammado113*ginv12 + gammado213*ginv22 + gammado313*ginv23
|
|
;
|
|
|
|
gamma222
|
|
=
|
|
gammado122*ginv12 + gammado222*ginv22 + gammado322*ginv23
|
|
;
|
|
|
|
gamma223
|
|
=
|
|
gammado123*ginv12 + gammado223*ginv22 + gammado323*ginv23
|
|
;
|
|
|
|
gamma233
|
|
=
|
|
gammado133*ginv12 + gammado233*ginv22 + gammado333*ginv23
|
|
;
|
|
|
|
gamma311
|
|
=
|
|
gammado111*ginv13 + gammado211*ginv23 + gammado311*ginv33
|
|
;
|
|
|
|
gamma312
|
|
=
|
|
gammado112*ginv13 + gammado212*ginv23 + gammado312*ginv33
|
|
;
|
|
|
|
gamma313
|
|
=
|
|
gammado113*ginv13 + gammado213*ginv23 + gammado313*ginv33
|
|
;
|
|
|
|
gamma322
|
|
=
|
|
gammado122*ginv13 + gammado222*ginv23 + gammado322*ginv33
|
|
;
|
|
|
|
gamma323
|
|
=
|
|
gammado123*ginv13 + gammado223*ginv23 + gammado323*ginv33
|
|
;
|
|
|
|
gamma333
|
|
=
|
|
gammado133*ginv13 + gammado233*ginv23 + gammado333*ginv33
|
|
;
|
|
|
|
Gfromg1
|
|
=
|
|
gamma111*ginv11 + gamma122*ginv22 +
|
|
2.*(gamma112*ginv12 + gamma113*ginv13 + gamma123*ginv23) + gamma133*ginv33
|
|
;
|
|
|
|
Gfromg2
|
|
=
|
|
gamma211*ginv11 + gamma222*ginv22 +
|
|
2.*(gamma212*ginv12 + gamma213*ginv13 + gamma223*ginv23) + gamma233*ginv33
|
|
;
|
|
|
|
Gfromg3
|
|
=
|
|
gamma311*ginv11 + gamma322*ginv22 +
|
|
2.*(gamma312*ginv12 + gamma313*ginv13 + gamma323*ginv23) + gamma333*ginv33
|
|
;
|
|
|
|
dGfromgdu11
|
|
=
|
|
-((dg122*(4.*dg112 + dg211) + 2.*dg112*dg212 + dg111*dg222)*
|
|
Power(ginv12,3)) - (dg133*(4.*dg113 + dg311) + 2.*dg113*dg313 +
|
|
dg111*dg333)*Power(ginv13,3) - 2.*Power(ginv11,3)*pow2(dg111) +
|
|
(ddg1111 - dg111*((8.*dg112 + 2.*dg211)*ginv12 +
|
|
(8.*dg113 + 2.*dg311)*ginv13) -
|
|
(dg113*(4.*dg112 + dg211) + dg112*dg311 + dg111*(dg213 + dg312))*
|
|
ginv23 - ginv22*(dg112*dg211 + dg111*dg212 + 2.*pow2(dg112)) -
|
|
ginv33*(dg113*dg311 + dg111*dg313 + 2.*pow2(dg113)))*pow2(ginv11) +
|
|
(ddg1122 + ddg1212 - (dg123*(8.*dg112 + 2.*dg211) +
|
|
dg113*(4.*dg122 + 2.*dg212) + dg122*dg311 +
|
|
2.*(dg111*dg223 + dg112*(dg213 + dg312)) + dg111*dg322)*ginv13 -
|
|
(dg123*(4.*dg122 + 2.*dg212) +
|
|
2.*(dg113*dg222 + dg122*(dg213 + dg312) + dg112*(dg223 + dg322)))*
|
|
ginv23 - ginv22*(3.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122)) -
|
|
ginv33*(dg123*(dg213 + dg312) + dg122*dg313 + dg113*(dg223 + dg322) +
|
|
dg112*dg323 + 2.*pow2(dg123)))*pow2(ginv12) +
|
|
(ddg1133 + ddg1313 - (dg133*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg313 + dg113*(dg233 + dg323) + dg112*dg333))*ginv23 -
|
|
ginv22*(dg133*dg212 + dg113*dg223 + dg123*(dg213 + dg312) +
|
|
dg112*(dg233 + dg323) + 2.*pow2(dg123)) -
|
|
ginv33*(3.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133)))*pow2(ginv13) \
|
|
+ ginv13*(ddg1333*ginv33 + ginv22*
|
|
(ddg1223 - (dg133*dg222 + dg123*(4.*dg223 + dg322) +
|
|
dg122*(dg233 + dg323))*ginv23 -
|
|
(dg133*dg223 + dg123*(dg233 + 2.*dg323))*ginv33) +
|
|
ginv23*(ddg1233 + ddg1323 -
|
|
(dg133*(2.*dg233 + 3.*dg323) + 3.*dg123*dg333)*ginv33) -
|
|
(dg123*dg222 + dg122*dg223)*pow2(ginv22) -
|
|
(dg133*dg322 + 2.*(dg133*dg223 + dg123*(dg233 + dg323)) +
|
|
dg122*dg333)*pow2(ginv23) - 2.*dg133*dg333*pow2(ginv33)) +
|
|
ginv11*(ddg1313*ginv33 + ginv12*
|
|
(2.*ddg1112 + ddg1211 -
|
|
(dg113*(12.*dg112 + 3.*dg211) + 3.*dg112*dg311 +
|
|
dg111*(8.*dg123 + 3.*(dg213 + dg312)))*ginv13 -
|
|
(dg122*(4.*dg112 + dg211) + 6.*dg112*dg212 + dg111*dg222)*ginv22 -
|
|
(dg123*dg211 + dg122*dg311 +
|
|
4.*(dg113*(dg122 + dg212) + dg112*(dg123 + dg213 + dg312)) +
|
|
dg111*(dg223 + dg322))*ginv23 -
|
|
(dg123*dg311 + dg113*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*dg112*dg313 + dg111*dg323)*ginv33) +
|
|
ginv22*(ddg1212 - (dg113*dg222 + 2.*(dg123*dg212 + dg112*dg223) +
|
|
dg122*(dg213 + dg312) + dg112*dg322)*ginv23 -
|
|
(dg113*dg223 + dg123*(dg213 + dg312) + dg112*dg323)*ginv33) +
|
|
ginv13*(2.*ddg1113 + ddg1311 -
|
|
(dg123*(4.*dg112 + dg211) + dg111*dg223 +
|
|
2.*(dg113*dg212 + dg112*(dg213 + dg312)))*ginv22 -
|
|
(dg133*dg211 + dg123*dg311 +
|
|
4.*(dg113*(dg123 + dg213 + dg312) + dg112*(dg133 + dg313)) +
|
|
dg111*(dg233 + dg323))*ginv23 -
|
|
(dg133*(4.*dg113 + dg311) + 6.*dg113*dg313 + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1213 + ddg1312 -
|
|
(dg133*(dg213 + dg312) + 2.*dg123*dg313 +
|
|
dg113*(dg233 + 2.*dg323) + dg112*dg333)*ginv33) -
|
|
(3.*dg112*dg211 + dg111*(4.*dg122 + 3.*dg212) + 6.*pow2(dg112))*
|
|
pow2(ginv12) - (3.*dg113*dg311 + dg111*(4.*dg133 + 3.*dg313) +
|
|
6.*pow2(dg113))*pow2(ginv13) -
|
|
(dg122*dg212 + dg112*dg222)*pow2(ginv22) -
|
|
(dg133*dg212 + dg123*(dg213 + dg312) + dg122*dg313 +
|
|
dg113*(dg223 + dg322) + dg112*(dg233 + dg323))*pow2(ginv23) -
|
|
(dg133*dg313 + dg113*dg333)*pow2(ginv33)) +
|
|
ginv12*(ddg1323*ginv33 + ginv22*
|
|
(ddg1222 - (3.*(dg123*dg222 + dg122*dg223) + 2.*dg122*dg322)*ginv23 -
|
|
(dg123*(2.*dg223 + dg322) + dg122*dg323)*ginv33) +
|
|
ginv23*(ddg1223 + ddg1322 -
|
|
(dg133*(dg223 + dg322) + dg123*(dg233 + 4.*dg323) + dg122*dg333)*
|
|
ginv33) + ginv13*(2.*ddg1123 + ddg1213 + ddg1312 -
|
|
(dg113*dg222 + 4.*(dg123*(dg122 + dg212) + dg112*dg223) +
|
|
dg122*(dg213 + dg312) + dg112*dg322)*ginv22 -
|
|
(dg133*(4.*dg123 + dg213 + dg312) + 4.*dg123*dg313 +
|
|
dg113*(dg233 + 4.*dg323) + dg112*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*dg212 + dg112*dg233 + dg122*dg313 +
|
|
dg113*dg322) + 4.*
|
|
(dg122*dg133 + dg113*dg223 + dg123*(dg213 + dg312) +
|
|
dg112*dg323 + pow2(dg123)))) -
|
|
(dg133*(4.*dg112 + dg211) + dg113*(8.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg311 + dg112*dg313) + dg111*(dg233 + 2.*dg323))*
|
|
pow2(ginv13) - 2.*dg122*dg222*pow2(ginv22) -
|
|
(dg133*dg222 + 2.*dg123*(dg223 + dg322) + dg122*(dg233 + 2.*dg323))*
|
|
pow2(ginv23) - (dg133*dg323 + dg123*dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu12
|
|
=
|
|
-((dg133*dg322 + 2.*(dg133*dg223 + dg123*(dg233 + dg323)) + dg122*dg333)*
|
|
Power(ginv23,3)) - 2.*(dg122*dg222*Power(ginv22,3) +
|
|
Power(ginv12,3)*(dg112*dg211 + dg111*(dg122 + dg212) + pow2(dg112)) +
|
|
(dg111*(dg112*ginv22 + dg113*ginv23) + ginv12*pow2(dg111))*pow2(ginv11)\
|
|
) + (ddg1112 + ddg1211 - (4.*(dg112*dg113 + dg111*dg123) +
|
|
2.*(dg113*dg211 + dg112*dg311 + dg111*(dg213 + dg312)))*ginv13 -
|
|
(dg122*(6.*dg112 + 2.*dg211) + 6.*dg112*dg212 + 2.*dg111*dg222)*
|
|
ginv22 - (4.*(dg113*(dg122 + dg212) + dg112*(dg123 + dg213)) +
|
|
dg122*dg311 + 2.*(dg123*dg211 + dg111*dg223 + dg112*dg312) +
|
|
dg111*dg322)*ginv23 -
|
|
(dg123*dg311 + dg113*(2.*(dg123 + dg213) + dg312) + dg112*dg313 +
|
|
dg111*dg323)*ginv33)*pow2(ginv12) -
|
|
((2.*(dg113*dg123 + dg112*dg133) + dg123*dg311 + dg113*dg312 +
|
|
dg112*dg313 + dg111*dg323)*ginv22 +
|
|
(dg133*(4.*dg113 + dg311) + 2.*dg113*dg313 + dg111*dg333)*ginv23)*
|
|
pow2(ginv13) + (ddg1222 - (4.*(dg123*dg222 + dg122*dg223) +
|
|
2.*dg122*dg322)*ginv23 -
|
|
(dg123*(2.*dg223 + dg322) + dg122*dg323)*ginv33)*pow2(ginv22) +
|
|
(ddg1233 + ddg1323 - (dg133*(2.*dg233 + 3.*dg323) + 3.*dg123*dg333)*
|
|
ginv33)*pow2(ginv23) + ginv11*
|
|
(ginv23*(ddg1113 - 2.*dg113*(dg133 + dg313)*ginv33) +
|
|
ginv22*(ddg1112 - (dg112*(4.*dg123 + 2.*dg213) +
|
|
2.*(dg113*(dg122 + dg212) + dg112*dg312))*ginv23 -
|
|
(dg113*(2.*dg123 + dg312) + dg112*dg313)*ginv33) +
|
|
ginv12*(ddg1111 - dg111*(6.*dg113 + 2.*dg311)*ginv13 -
|
|
(dg113*(8.*dg112 + 2.*dg211) + dg112*dg311 +
|
|
dg111*(2.*(dg123 + dg213) + dg312))*ginv23 -
|
|
ginv22*(2.*(dg112*dg211 + dg111*(dg122 + dg212)) +
|
|
6.*pow2(dg112)) - ginv33*
|
|
(dg113*dg311 + dg111*dg313 + 2.*pow2(dg113))) -
|
|
ginv13*((dg112*(4.*dg113 + dg311) + dg111*(2.*dg123 + dg312))*
|
|
ginv22 + ginv23*(dg113*dg311 + dg111*(2.*dg133 + dg313) +
|
|
4.*pow2(dg113))) - dg111*(6.*dg112 + 2.*dg211)*pow2(ginv12) -
|
|
2.*dg112*(dg122 + dg212)*pow2(ginv22) -
|
|
(2.*(dg112*dg133 + dg113*(dg123 + dg213)) + dg113*dg312 + dg112*dg313)*
|
|
pow2(ginv23)) + ginv13*(ginv22*
|
|
(ddg1123 + ddg1312 - (dg133*(2.*dg123 + dg312) +
|
|
2.*(dg123*dg313 + dg113*dg323) + dg112*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*(dg122 + dg212) + dg123*dg213 + dg113*dg223 +
|
|
dg112*dg233) + dg122*dg313 + dg113*dg322 +
|
|
4.*(dg123*dg312 + dg112*dg323 + pow2(dg123)))) +
|
|
ginv23*(ddg1133 + ddg1313 -
|
|
ginv33*(3.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133))) -
|
|
(2.*(dg123*(dg122 + dg212) + dg112*dg223) + dg122*dg312 +
|
|
dg112*dg322)*pow2(ginv22) -
|
|
(dg133*(4.*dg123 + 2.*(dg213 + dg312)) +
|
|
2.*(dg123*dg313 + dg113*(dg233 + dg323) + dg112*dg333))*pow2(ginv23)\
|
|
) + ginv23*(ddg1333*ginv33 - 2.*dg133*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg1313*ginv33 + ginv13*
|
|
(ddg1113 + ddg1311 - (2.*
|
|
(dg123*dg211 + dg113*(dg122 + dg212) + dg111*dg223) +
|
|
dg122*dg311 + dg112*(8.*dg123 + 2.*dg213 + 4.*dg312) +
|
|
dg111*dg322)*ginv22 -
|
|
(dg133*(4.*dg112 + 2.*dg211) +
|
|
dg113*(8.*dg123 + 4.*(dg213 + dg312)) + 4.*dg112*dg313 +
|
|
2.*(dg123*dg311 + dg111*(dg233 + dg323)))*ginv23 -
|
|
(dg133*(2.*dg113 + dg311) + 4.*dg113*dg313 + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1123 + 2.*ddg1213 + ddg1312 -
|
|
(2.*(dg133*(dg123 + dg213) + dg113*dg233) + dg133*dg312 +
|
|
4.*(dg123*dg313 + dg113*dg323) + dg112*dg333)*ginv33) +
|
|
ginv22*(ddg1122 + 2.*ddg1212 -
|
|
(4.*(dg122*dg213 + dg113*dg222) +
|
|
6.*(dg123*(dg122 + dg212) + dg112*dg223) +
|
|
3.*(dg122*dg312 + dg112*dg322))*ginv23 -
|
|
ginv33*(dg122*dg313 + dg113*dg322 +
|
|
2.*(dg113*dg223 + dg123*(dg213 + dg312) + dg112*dg323 +
|
|
pow2(dg123)))) -
|
|
2.*(dg113*dg311 + dg111*(dg133 + dg313) + pow2(dg113))*pow2(ginv13) -
|
|
(4.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122))*pow2(ginv22) -
|
|
(4.*(dg123*dg213 + dg113*dg223) +
|
|
2.*(dg133*(dg122 + dg212) + dg123*dg312 + dg122*dg313 +
|
|
dg113*dg322 + dg112*(dg233 + dg323) + pow2(dg123)))*pow2(ginv23) \
|
|
- (dg133*dg313 + dg113*dg333)*pow2(ginv33)) +
|
|
ginv22*(ddg1323*ginv33 + ginv23*
|
|
(2.*ddg1223 + ddg1322 - (2.*(dg133*dg223 + dg123*dg233) +
|
|
dg133*dg322 + 6.*dg123*dg323 + dg122*dg333)*ginv33) -
|
|
(2.*(dg133*dg222 + dg122*dg233) + dg123*(6.*dg223 + 3.*dg322) +
|
|
3.*dg122*dg323)*pow2(ginv23) -
|
|
(dg133*dg323 + dg123*dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu13
|
|
=
|
|
-((dg133*dg222 + 2.*dg123*(dg223 + dg322) + dg122*(dg233 + 2.*dg323))*
|
|
Power(ginv23,3)) - 2.*(dg133*dg333*Power(ginv33,3) +
|
|
Power(ginv13,3)*(dg113*dg311 + dg111*(dg133 + dg313) + pow2(dg113)) +
|
|
(dg111*(dg112*ginv23 + dg113*ginv33) + ginv13*pow2(dg111))*pow2(ginv11)\
|
|
) - ((dg122*(4.*dg112 + dg211) + 2.*dg112*dg212 + dg111*dg222)*ginv23 +
|
|
(2.*(dg113*dg122 + dg112*dg123) + dg123*dg211 + dg113*dg212 +
|
|
dg112*dg213 + dg111*dg223)*ginv33 +
|
|
2.*ginv13*(dg112*dg211 + dg111*(dg122 + dg212) + pow2(dg112)))*
|
|
pow2(ginv12) + (ddg1113 + ddg1311 -
|
|
(dg123*(2.*dg112 + dg211) + dg113*dg212 + dg111*dg223 +
|
|
dg112*(dg213 + 2.*dg312))*ginv22 -
|
|
(dg133*dg211 + 2.*(dg113*dg213 + dg123*dg311) +
|
|
4.*(dg113*(dg123 + dg312) + dg112*(dg133 + dg313)) +
|
|
dg111*(dg233 + 2.*dg323))*ginv23 -
|
|
(dg133*(6.*dg113 + 2.*dg311) + 6.*dg113*dg313 + 2.*dg111*dg333)*ginv33\
|
|
)*pow2(ginv13) - (2.*dg122*dg222*ginv23 +
|
|
(dg123*dg222 + dg122*dg223)*ginv33)*pow2(ginv22) +
|
|
(ddg1223 + ddg1322 - (3.*(dg133*dg223 + dg123*dg233) + 6.*dg123*dg323 +
|
|
2.*(dg133*dg322 + dg122*dg333))*ginv33)*pow2(ginv23) +
|
|
ddg1333*pow2(ginv33) + ginv11*
|
|
(ddg1113*ginv33 - ginv22*(2.*dg112*(dg122 + dg212)*ginv23 +
|
|
(dg113*dg212 + dg112*(2.*dg123 + dg213))*ginv33) +
|
|
ginv23*(ddg1112 - (dg113*(4.*dg123 + 2.*dg213) +
|
|
2.*(dg113*dg312 + dg112*(dg133 + dg313)))*ginv33) -
|
|
ginv12*(dg111*(6.*dg112 + 2.*dg211)*ginv13 +
|
|
(dg113*(4.*dg112 + dg211) + dg111*(2.*dg123 + dg213))*ginv33 +
|
|
ginv23*(dg112*dg211 + dg111*(2.*dg122 + dg212) + 4.*pow2(dg112))) +
|
|
ginv13*(ddg1111 - (dg113*(8.*dg112 + dg211) + 2.*dg112*dg311 +
|
|
dg111*(dg213 + 2.*(dg123 + dg312)))*ginv23 -
|
|
ginv22*(dg112*dg211 + dg111*dg212 + 2.*pow2(dg112)) -
|
|
ginv33*(2.*(dg113*dg311 + dg111*(dg133 + dg313)) + 6.*pow2(dg113))) \
|
|
- dg111*(6.*dg113 + 2.*dg311)*pow2(ginv13) -
|
|
(dg113*dg212 + dg112*dg213 +
|
|
2.*(dg113*dg122 + dg112*(dg123 + dg312)))*pow2(ginv23) -
|
|
2.*dg113*(dg133 + dg313)*pow2(ginv33)) +
|
|
ginv12*((ddg1123 + ddg1213)*ginv33 +
|
|
ginv13*(ddg1112 + ddg1211 -
|
|
(dg122*(2.*dg112 + dg211) + 4.*dg112*dg212 + dg111*dg222)*ginv22 -
|
|
(dg123*(8.*dg112 + 2.*dg211) +
|
|
4.*(dg113*(dg122 + dg212) + dg112*(dg213 + dg312)) +
|
|
2.*(dg122*dg311 + dg111*(dg223 + dg322)))*ginv23 -
|
|
(dg133*(2.*dg112 + dg211) +
|
|
dg113*(8.*dg123 + 4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg311 + dg112*dg313) + dg111*(dg233 + 2.*dg323))*
|
|
ginv33) - ginv22*((dg122*dg213 + dg113*dg222 +
|
|
2.*(dg123*(dg122 + dg212) + dg112*dg223))*ginv33 +
|
|
ginv23*(3.*(dg122*dg212 + dg112*dg222) + 2.*pow2(dg122))) +
|
|
ginv23*(ddg1122 + ddg1212 -
|
|
ginv33*(dg133*(2.*dg122 + dg212) +
|
|
2.*(dg123*dg312 + dg122*dg313 + dg113*dg322) +
|
|
dg112*(dg233 + 2.*dg323) +
|
|
4.*(dg123*dg213 + dg113*dg223 + pow2(dg123)))) -
|
|
(4.*(dg112*dg113 + dg111*dg123) +
|
|
2.*(dg113*dg211 + dg112*dg311 + dg111*(dg213 + dg312)))*
|
|
pow2(ginv13) - (dg123*(4.*dg122 + 2.*dg212) +
|
|
2.*(dg113*dg222 + dg122*(dg213 + dg312) + dg112*(dg223 + dg322)))*
|
|
pow2(ginv23) - (dg133*(2.*dg123 + dg213) + 2.*dg123*dg313 +
|
|
dg113*(dg233 + 2.*dg323))*pow2(ginv33)) +
|
|
ginv22*(ddg1223*ginv33 + ginv23*
|
|
(ddg1222 - (dg133*dg222 + dg123*(6.*dg223 + 2.*dg322) +
|
|
dg122*(dg233 + 2.*dg323))*ginv33) -
|
|
(3.*(dg123*dg222 + dg122*dg223) + 2.*dg122*dg322)*pow2(ginv23) -
|
|
(dg133*dg223 + dg123*(dg233 + 2.*dg323))*pow2(ginv33)) +
|
|
ginv23*((ddg1233 + 2.*ddg1323)*ginv33 -
|
|
(dg133*(2.*dg233 + 4.*dg323) + 4.*dg123*dg333)*pow2(ginv33)) +
|
|
ginv13*((ddg1133 + 2.*ddg1313)*ginv33 +
|
|
ginv23*(ddg1123 + ddg1213 + 2.*ddg1312 -
|
|
(dg133*(6.*dg123 + 3.*dg213 + 4.*dg312) + 6.*dg123*dg313 +
|
|
dg113*(3.*dg233 + 6.*dg323) + 4.*dg112*dg333)*ginv33) +
|
|
ginv22*(ddg1212 - (dg123*(2.*dg122 + 4.*dg212) + dg113*dg222 +
|
|
dg122*(dg213 + 2.*dg312) + dg112*(4.*dg223 + 2.*dg322))*ginv23 -
|
|
ginv33*(dg133*dg212 + dg112*(dg233 + 2.*dg323) +
|
|
2.*(dg113*dg223 + dg123*(dg213 + dg312) + pow2(dg123)))) -
|
|
(dg122*dg212 + dg112*dg222)*pow2(ginv22) -
|
|
(4.*(dg123*dg312 + dg112*dg323) +
|
|
2.*(dg133*(dg122 + dg212) + dg123*dg213 + dg112*dg233 +
|
|
dg122*dg313 + dg113*(dg223 + dg322) + pow2(dg123)))*pow2(ginv23) \
|
|
- (4.*(dg133*dg313 + dg113*dg333) + 2.*pow2(dg133))*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu21
|
|
=
|
|
-((dg233*dg311 + 2.*(dg113*dg233 + dg213*(dg133 + dg313)) + dg211*dg333)*
|
|
Power(ginv13,3)) - 2.*(dg111*dg211*Power(ginv11,3) +
|
|
Power(ginv12,3)*(dg122*dg212 + (dg112 + dg211)*dg222 + pow2(dg212))) +
|
|
(ddg1211 - (4.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*ginv13 -
|
|
2.*(dg112 + dg211)*dg212*ginv22 -
|
|
(2.*(dg113*dg212 + (dg112 + dg211)*dg213) + dg212*dg311 +
|
|
dg211*dg312)*ginv23 -
|
|
(dg213*(2.*dg113 + dg311) + dg211*dg313)*ginv33 -
|
|
ginv12*(4.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211)))*pow2(ginv11) \
|
|
+ (ddg1222 + ddg2212 - (4.*(dg212*(dg123 + dg213) +
|
|
(dg112 + dg211)*dg223) + dg222*dg311 +
|
|
2.*(dg122*dg213 + dg113*dg222 + dg212*dg312) + dg211*dg322)*ginv13 \
|
|
- (2.*dg122 + 6.*dg212)*dg222*ginv22 -
|
|
((2.*dg122 + 4.*dg212)*dg223 +
|
|
dg222*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*dg322)*ginv23 -
|
|
(dg223*(2.*(dg123 + dg213) + dg312) + dg222*dg313 + dg213*dg322 +
|
|
dg212*dg323)*ginv33)*pow2(ginv12) +
|
|
(ddg1233 + ddg2313 - (2.*((dg123 + dg213)*dg223 + dg212*dg233) +
|
|
dg223*dg312 + dg212*dg323)*ginv22 -
|
|
(dg233*(4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg233 + dg223*(dg133 + dg313) + dg213*dg323 +
|
|
dg212*dg333))*ginv23 -
|
|
(dg233*(2.*dg133 + 3.*dg313) + 3.*dg213*dg333)*ginv33)*pow2(ginv13) +
|
|
ginv11*(ddg2313*ginv33 + ginv22*
|
|
(ddg2212 - (dg222*(2.*dg213 + dg312) + dg212*(4.*dg223 + dg322))*
|
|
ginv23 - (dg223*(2.*dg213 + dg312) + dg212*dg323)*ginv33) +
|
|
ginv23*(ddg2213 + ddg2312 -
|
|
(dg233*(2.*dg213 + dg312) + 2.*(dg223*dg313 + dg213*dg323) +
|
|
dg212*dg333)*ginv33) +
|
|
ginv13*(2.*ddg1213 + ddg2311 -
|
|
(2.*(dg112 + dg211)*dg223 +
|
|
dg212*(4.*dg213 + 2.*(dg123 + dg312)))*ginv22 -
|
|
(2.*(dg133*dg213 + dg113*dg233) + dg233*dg311 + 6.*dg213*dg313 +
|
|
dg211*dg333)*ginv33 -
|
|
ginv23*(2.*(dg133*dg212 + dg123*dg213 + dg113*dg223 +
|
|
(dg112 + dg211)*dg233) + dg223*dg311 + dg211*dg323 +
|
|
4.*(dg213*dg312 + dg212*dg313 + pow2(dg213)))) +
|
|
ginv12*(2.*ddg1212 + ddg2211 -
|
|
(6.*(dg113*dg212 + dg112*dg213) + 4.*dg111*dg223 +
|
|
3.*dg212*dg311 + dg211*(4.*dg123 + 6.*dg213 + 3.*dg312))*ginv13 \
|
|
- (2.*(dg123*dg212 + dg122*dg213 + dg113*dg222 +
|
|
(dg112 + dg211)*dg223) + dg222*dg311 +
|
|
dg212*(8.*dg213 + 4.*dg312) + dg211*dg322)*ginv23 -
|
|
ginv22*(2.*(dg122*dg212 + (dg112 + dg211)*dg222) +
|
|
6.*pow2(dg212)) - ginv33*
|
|
(dg223*dg311 + dg211*dg323 +
|
|
2.*(dg113*dg223 + dg213*(dg123 + dg312) + dg212*dg313 +
|
|
pow2(dg213)))) -
|
|
(6.*dg112*dg212 + dg211*(2.*dg122 + 6.*dg212) + 2.*dg111*dg222)*
|
|
pow2(ginv12) - (2.*(dg133*dg211 + dg111*dg233) +
|
|
dg213*(6.*dg113 + 3.*dg311) + 3.*dg211*dg313)*pow2(ginv13) -
|
|
2.*dg212*dg222*pow2(ginv22) -
|
|
(2.*(dg213*dg223 + dg212*dg233) + dg223*dg312 + dg222*dg313 +
|
|
dg213*dg322 + dg212*dg323)*pow2(ginv23) -
|
|
(dg233*dg313 + dg213*dg333)*pow2(ginv33)) +
|
|
ginv12*(ddg2323*ginv33 + ginv13*
|
|
(2.*ddg1223 + ddg2213 + ddg2312 -
|
|
(2.*((dg123 + dg213)*dg222 + dg122*dg223) + dg222*dg312 +
|
|
dg212*(8.*dg223 + dg322))*ginv22 -
|
|
(dg223*(8.*dg213 + 4.*(dg123 + dg312)) +
|
|
2.*(dg122*dg233 + dg222*(dg133 + dg313) + dg213*dg322) +
|
|
4.*dg212*(dg233 + dg323))*ginv23 -
|
|
(2.*(dg133*dg223 + (dg123 + dg213)*dg233) + dg233*dg312 +
|
|
4.*(dg223*dg313 + dg213*dg323) + dg212*dg333)*ginv33) +
|
|
ginv23*(ddg2223 + ddg2322 -
|
|
(dg233*(2.*dg223 + dg322) + 4.*dg223*dg323 + dg222*dg333)*ginv33) +
|
|
ginv22*(ddg2222 - dg222*(6.*dg223 + 2.*dg322)*ginv23 -
|
|
ginv33*(dg223*dg322 + dg222*dg323 + 2.*pow2(dg223))) -
|
|
(4.*(dg123*dg213 + dg113*dg223) +
|
|
2.*((dg112 + dg211)*dg233 + dg223*dg311 + dg213*dg312 +
|
|
dg212*(dg133 + dg313) + dg211*dg323 + pow2(dg213)))*pow2(ginv13) \
|
|
- 2.*(pow2(dg222)*pow2(ginv22) +
|
|
(dg223*dg322 + dg222*(dg233 + dg323) + pow2(dg223))*pow2(ginv23)) -
|
|
(dg233*dg323 + dg223*dg333)*pow2(ginv33)) +
|
|
ginv13*(ddg2333*ginv33 + ginv22*
|
|
(ddg2223 - 2.*dg223*(dg233 + dg323)*ginv33 -
|
|
ginv23*(dg223*dg322 + dg222*(2.*dg233 + dg323) + 4.*pow2(dg223))) +
|
|
ginv23*(ddg2233 + ddg2323 -
|
|
ginv33*(3.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233))) -
|
|
(dg233*(4.*dg223 + dg322) + 2.*dg223*dg323 + dg222*dg333)*
|
|
pow2(ginv23) - 2.*(dg222*dg223*pow2(ginv22) + dg233*dg333*pow2(ginv33))\
|
|
)
|
|
;
|
|
|
|
dGfromgdu22
|
|
=
|
|
-((2.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*
|
|
Power(ginv12,3)) - (dg233*(4.*dg223 + dg322) + 2.*dg223*dg323 +
|
|
dg222*dg333)*Power(ginv23,3) - 2.*Power(ginv22,3)*pow2(dg222) -
|
|
(2.*dg111*dg211*ginv12 + (dg112*dg211 + dg111*dg212)*ginv22 +
|
|
(dg113*dg211 + dg111*dg213)*ginv23)*pow2(ginv11) +
|
|
(ddg1212 + ddg2211 - (2.*(dg123*dg211 + dg112*dg213 + dg111*dg223 +
|
|
dg212*(dg113 + dg311)) + dg211*(4.*dg213 + 2.*dg312))*ginv13 -
|
|
(2.*(dg123*dg212 + dg122*dg213 + dg113*dg222 + dg112*dg223) +
|
|
dg222*dg311 + dg212*(8.*dg213 + 2.*dg312) +
|
|
dg211*(4.*dg223 + dg322))*ginv23 -
|
|
ginv22*(4.*dg211*dg222 + 3.*(dg122*dg212 + dg112*dg222) +
|
|
6.*pow2(dg212)) - ginv33*
|
|
(dg223*(dg113 + dg311) + dg213*(dg123 + dg312) + dg212*dg313 +
|
|
dg211*dg323 + 2.*pow2(dg213)))*pow2(ginv12) -
|
|
((dg112*dg233 + dg223*(dg113 + dg311) + dg213*(dg123 + dg312) +
|
|
dg212*(dg133 + dg313) + dg211*dg323)*ginv22 +
|
|
(dg233*dg311 + 2.*(dg113*dg233 + dg213*(dg133 + dg313)) +
|
|
dg211*dg333)*ginv23)*pow2(ginv13) +
|
|
(ddg2222 - dg222*(8.*dg223 + 2.*dg322)*ginv23 -
|
|
ginv33*(dg223*dg322 + dg222*dg323 + 2.*pow2(dg223)))*pow2(ginv22) +
|
|
(ddg2233 + ddg2323 - ginv33*
|
|
(3.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233)))*pow2(ginv23) +
|
|
ginv13*(ginv22*(ddg1223 + ddg2312 -
|
|
(dg122*dg233 + dg222*(dg133 + dg313) + dg213*dg322 +
|
|
4.*(dg223*(dg123 + dg213 + dg312) + dg212*(dg233 + dg323)))*
|
|
ginv23 - (dg233*(dg123 + dg312) + dg223*(dg133 + 2.*dg313) +
|
|
2.*dg213*dg323 + dg212*dg333)*ginv33) +
|
|
ginv23*(ddg1233 + ddg2313 -
|
|
(dg233*(2.*dg133 + 3.*dg313) + 3.*dg213*dg333)*ginv33) -
|
|
((dg122 + 4.*dg212)*dg223 + dg222*(dg123 + dg312) + dg212*dg322)*
|
|
pow2(ginv22) - (dg233*(4.*dg213 + 2.*dg312) +
|
|
2.*(dg123*dg233 + dg223*(dg133 + dg313) + dg213*dg323 +
|
|
dg212*dg333))*pow2(ginv23)) +
|
|
ginv11*(-(ginv13*((2.*(dg113*dg212 + dg112*dg213) + dg111*dg223 +
|
|
dg212*dg311 + dg211*(dg123 + dg312))*ginv22 +
|
|
(dg111*dg233 + dg213*(4.*dg113 + dg311) + dg211*(dg133 + dg313))*
|
|
ginv23)) + ginv12*(ddg1211 -
|
|
(3.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*ginv13 -
|
|
(6.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*ginv22 -
|
|
(4.*(dg113*dg212 + dg112*dg213) + dg111*dg223 + dg212*dg311 +
|
|
dg211*(dg123 + 4.*dg213 + dg312))*ginv23 -
|
|
(dg213*(2.*dg113 + dg311) + dg211*dg313)*ginv33) +
|
|
ginv22*(ddg1212 - (dg122*dg213 + dg113*dg222 + 2.*dg112*dg223 +
|
|
dg212*(4.*dg213 + 2.*(dg123 + dg312)))*ginv23 -
|
|
(dg113*dg223 + dg213*(dg123 + dg312) + dg212*dg313)*ginv33) +
|
|
ginv23*(ddg1213 - (dg113*dg233 + dg213*(dg133 + 2.*dg313))*ginv33) -
|
|
(3.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211))*pow2(ginv12) -
|
|
(dg122*dg212 + dg112*dg222 + 2.*pow2(dg212))*pow2(ginv22) -
|
|
(dg113*dg223 + dg112*dg233 + dg213*(dg123 + dg312) +
|
|
dg212*(dg133 + dg313) + 2.*pow2(dg213))*pow2(ginv23)) +
|
|
ginv23*(ddg2333*ginv33 - 2.*dg233*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg2313*ginv33 + ginv22*
|
|
(ddg1222 + 2.*ddg2212 -
|
|
((3.*dg122 + 12.*dg212)*dg223 +
|
|
dg222*(8.*dg213 + 3.*(dg123 + dg312)) + 3.*dg212*dg322)*ginv23 \
|
|
- (dg223*(4.*dg213 + 2.*(dg123 + dg312)) + dg222*dg313 + dg213*dg322 +
|
|
2.*dg212*dg323)*ginv33) +
|
|
ginv23*(ddg1223 + 2.*ddg2213 + ddg2312 -
|
|
(dg233*(dg123 + 4.*dg213 + dg312) + dg223*(dg133 + 4.*dg313) +
|
|
4.*dg213*dg323 + dg212*dg333)*ginv33) +
|
|
ginv13*(ddg1213 + ddg2311 -
|
|
(dg122*dg213 + dg222*(dg113 + dg311) +
|
|
4.*((dg112 + dg211)*dg223 + dg212*(dg123 + dg213 + dg312)) +
|
|
dg211*dg322)*ginv22 -
|
|
(dg233*(dg113 + dg311) + dg213*(dg133 + 4.*dg313) + dg211*dg333)*
|
|
ginv33 - ginv23*(2.*(dg133*dg212 + dg112*dg233 + dg223*dg311 +
|
|
dg211*dg323) + 4.*
|
|
(dg113*dg223 + dg211*dg233 + dg213*(dg123 + dg312) +
|
|
dg212*dg313 + pow2(dg213)))) -
|
|
(dg111*dg233 + 2.*dg213*(dg113 + dg311) + dg211*(dg133 + 2.*dg313))*
|
|
pow2(ginv13) - (2.*dg122 + 8.*dg212)*dg222*pow2(ginv22) -
|
|
((dg122 + 4.*dg212)*dg233 + dg223*(8.*dg213 + 2.*(dg123 + dg312)) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*(dg213*dg322 + dg212*dg323))*
|
|
pow2(ginv23) - (dg233*dg313 + dg213*dg333)*pow2(ginv33)) +
|
|
ginv22*(ddg2323*ginv33 + ginv23*
|
|
(2.*ddg2223 + ddg2322 - (dg233*(4.*dg223 + dg322) + 6.*dg223*dg323 +
|
|
dg222*dg333)*ginv33) -
|
|
(3.*dg223*dg322 + dg222*(4.*dg233 + 3.*dg323) + 6.*pow2(dg223))*
|
|
pow2(ginv23) - (dg233*dg323 + dg223*dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu23
|
|
=
|
|
-((dg111*dg233 + 2.*dg213*(dg113 + dg311) + dg211*(dg133 + 2.*dg313))*
|
|
Power(ginv13,3)) - (2.*dg111*dg211*ginv13 +
|
|
(dg112*dg211 + dg111*dg212)*ginv23 +
|
|
(dg113*dg211 + dg111*dg213)*ginv33)*pow2(ginv11) -
|
|
((2.*dg112*dg212 + dg211*(dg122 + 4.*dg212) + dg111*dg222)*ginv13 +
|
|
(dg122*dg213 + dg212*(dg123 + 2.*dg213) + dg113*dg222 +
|
|
(dg112 + 2.*dg211)*dg223)*ginv33 +
|
|
2.*ginv23*(dg122*dg212 + (dg112 + dg211)*dg222 + pow2(dg212)))*
|
|
pow2(ginv12) + (ddg1213 + ddg2311 -
|
|
((dg112 + 2.*dg211)*dg223 + dg212*(dg123 + 2.*(dg213 + dg312)))*
|
|
ginv22 - (3.*(dg133*dg213 + dg113*dg233) + 6.*dg213*dg313 +
|
|
2.*(dg233*dg311 + dg211*dg333))*ginv33 -
|
|
ginv23*(4.*(dg213*dg312 + dg212*dg313) +
|
|
2.*(dg133*dg212 + dg123*dg213 + (dg112 + dg211)*dg233 +
|
|
dg223*(dg113 + dg311) + dg211*dg323 + pow2(dg213))))*pow2(ginv13) \
|
|
- 2.*(dg233*dg333*Power(ginv33,3) +
|
|
Power(ginv23,3)*(dg223*dg322 + dg222*(dg233 + dg323) + pow2(dg223)) +
|
|
(dg222*dg223*ginv33 + ginv23*pow2(dg222))*pow2(ginv22)) +
|
|
(ddg2223 + ddg2322 - (dg233*(6.*dg223 + 2.*dg322) + 6.*dg223*dg323 +
|
|
2.*dg222*dg333)*ginv33)*pow2(ginv23) + ddg2333*pow2(ginv33) +
|
|
ginv11*(ddg1213*ginv33 + ginv13*
|
|
(ddg1211 - 2.*(dg112 + dg211)*dg212*ginv22 -
|
|
(4.*(dg113*dg212 + dg112*dg213) + dg111*dg223 + 2.*dg212*dg311 +
|
|
dg211*(dg123 + 2.*(dg213 + dg312)))*ginv23 -
|
|
(dg111*dg233 + dg213*(6.*dg113 + 2.*dg311) +
|
|
dg211*(dg133 + 2.*dg313))*ginv33) -
|
|
ginv12*((4.*dg112*dg212 + dg211*(dg122 + 2.*dg212) + dg111*dg222)*
|
|
ginv23 + (dg211*(dg123 + 2.*dg213) +
|
|
2.*(dg113*dg212 + dg112*dg213) + dg111*dg223)*ginv33 +
|
|
ginv13*(3.*(dg112*dg211 + dg111*dg212) + 2.*pow2(dg211))) -
|
|
ginv22*((dg212*(dg123 + 2.*dg213) + dg112*dg223)*ginv33 +
|
|
ginv23*(dg122*dg212 + dg112*dg222 + 2.*pow2(dg212))) +
|
|
ginv23*(ddg1212 - ginv33*
|
|
(dg112*dg233 + dg212*(dg133 + 2.*dg313) +
|
|
2.*(dg113*dg223 + dg213*(dg123 + dg312) + pow2(dg213)))) -
|
|
(3.*(dg113*dg211 + dg111*dg213) + 2.*dg211*dg311)*pow2(ginv13) -
|
|
(dg122*dg213 + dg113*dg222 + dg112*dg223 +
|
|
dg212*(dg123 + 2.*(dg213 + dg312)))*pow2(ginv23) -
|
|
(dg113*dg233 + dg213*(dg133 + 2.*dg313))*pow2(ginv33)) +
|
|
ginv22*(ddg2223*ginv33 + ginv23*
|
|
(ddg2222 - ginv33*(2.*(dg223*dg322 + dg222*(dg233 + dg323)) +
|
|
6.*pow2(dg223))) - dg222*(6.*dg223 + 2.*dg322)*pow2(ginv23) -
|
|
2.*dg223*(dg233 + dg323)*pow2(ginv33)) +
|
|
ginv12*((ddg1223 + ddg2213)*ginv33 -
|
|
ginv22*((2.*dg122 + 6.*dg212)*dg222*ginv23 +
|
|
((dg123 + 2.*dg213)*dg222 + (dg122 + 4.*dg212)*dg223)*ginv33) +
|
|
ginv23*(ddg1222 + ddg2212 -
|
|
((dg122 + 2.*dg212)*dg233 +
|
|
dg223*(4.*dg123 + 8.*dg213 + 2.*dg312) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*(dg213*dg322 + dg212*dg323))*
|
|
ginv33) + ginv13*(ddg1212 + ddg2211 -
|
|
(4.*(dg112 + dg211)*dg223 +
|
|
dg212*(8.*dg213 + 4.*(dg123 + dg312)) +
|
|
2.*(dg122*dg213 + dg222*(dg113 + dg311) + dg211*dg322))*ginv23 \
|
|
- ginv22*(dg122*dg212 + (dg112 + 2.*dg211)*dg222 + 4.*pow2(dg212)) -
|
|
ginv33*((dg112 + 2.*dg211)*dg233 + dg212*(dg133 + 2.*dg313) +
|
|
2.*(dg223*dg311 + dg213*dg312 + dg211*dg323) +
|
|
4.*(dg123*dg213 + dg113*dg223 + pow2(dg213)))) -
|
|
(2.*(dg123*dg211 + dg112*dg213 + dg111*dg223 +
|
|
dg212*(dg113 + dg311)) + dg211*(4.*dg213 + 2.*dg312))*
|
|
pow2(ginv13) - ((2.*dg122 + 4.*dg212)*dg223 +
|
|
dg222*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*dg322)*
|
|
pow2(ginv23) - ((dg123 + 2.*dg213)*dg233 +
|
|
dg223*(dg133 + 2.*dg313) + 2.*dg213*dg323)*pow2(ginv33)) +
|
|
ginv13*((ddg1233 + 2.*ddg2313)*ginv33 +
|
|
ginv22*(ddg2212 - ((dg122 + 8.*dg212)*dg223 +
|
|
dg222*(dg123 + 2.*(dg213 + dg312)) + 2.*dg212*dg322)*ginv23 -
|
|
(dg223*(4.*dg213 + 2.*(dg123 + dg312)) + 2.*dg212*(dg233 + dg323))*
|
|
ginv33) + ginv23*(ddg1223 + ddg2213 + 2.*ddg2312 -
|
|
(3.*(dg133*dg223 + dg123*dg233) + dg233*(6.*dg213 + 4.*dg312) +
|
|
6.*(dg223*dg313 + dg213*dg323) + 4.*dg212*dg333)*ginv33) -
|
|
2.*dg212*dg222*pow2(ginv22) -
|
|
((dg122 + 4.*dg212)*dg233 + dg223*(2.*dg123 + 4.*(dg213 + dg312)) +
|
|
dg222*(dg133 + 2.*dg313) + 2.*dg213*dg322 + 4.*dg212*dg323)*
|
|
pow2(ginv23) - (dg233*(2.*dg133 + 4.*dg313) + 4.*dg213*dg333)*
|
|
pow2(ginv33)) + ginv23*((ddg2233 + 2.*ddg2323)*ginv33 -
|
|
(4.*(dg233*dg323 + dg223*dg333) + 2.*pow2(dg233))*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu31
|
|
=
|
|
-((dg222*dg311 + dg211*dg322 + 2.*((dg122 + dg212)*dg312 + dg112*dg322))*
|
|
Power(ginv12,3)) - 2.*(dg111*dg311*Power(ginv11,3) +
|
|
Power(ginv13,3)*(dg133*dg313 + (dg113 + dg311)*dg333 + pow2(dg313))) +
|
|
(ddg1311 - ((4.*dg112 + 2.*dg211)*dg311 + 4.*dg111*dg312)*ginv12 -
|
|
(dg212*dg311 + (2.*dg112 + dg211)*dg312)*ginv22 -
|
|
(dg311*(dg213 + 2.*dg312) + dg211*dg313 +
|
|
2.*(dg113*dg312 + dg112*dg313))*ginv23 -
|
|
2.*(dg113 + dg311)*dg313*ginv33 -
|
|
ginv13*(4.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311)))*pow2(ginv11) \
|
|
+ (ddg1322 + ddg2312 - (2.*dg122*dg322 + 3.*(dg222*dg312 + dg212*dg322))*
|
|
ginv22 - ((2.*dg213 + 4.*dg312)*dg322 +
|
|
2.*(dg223*dg312 + dg222*dg313 + dg123*dg322 +
|
|
(dg122 + dg212)*dg323))*ginv23 -
|
|
(dg313*(dg223 + 2.*dg322) + (dg213 + 2.*(dg123 + dg312))*dg323)*
|
|
ginv33 - ginv13*(4.*(dg123*dg312 + dg112*dg323) +
|
|
2.*(dg213*dg312 + (dg122 + dg212)*dg313 + dg113*dg322 +
|
|
dg311*(dg223 + dg322) + dg211*dg323 + pow2(dg312))))*pow2(ginv12) \
|
|
+ (ddg1333 + ddg3313 - (dg233*dg312 + dg223*dg313 +
|
|
(dg213 + 2.*(dg123 + dg312))*dg323 + dg212*dg333)*ginv22 -
|
|
(2.*(dg233*dg313 + dg133*dg323 + (dg123 + dg213)*dg333) +
|
|
4.*(dg313*dg323 + dg312*dg333))*ginv23 -
|
|
(2.*dg133 + 6.*dg313)*dg333*ginv33)*pow2(ginv13) +
|
|
ginv11*(ddg3313*ginv33 + ginv22*
|
|
(ddg2312 - (dg222*dg313 + dg213*dg322 +
|
|
2.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 -
|
|
(dg223*dg313 + (dg213 + 2.*dg312)*dg323)*ginv33) +
|
|
ginv23*(ddg2313 + ddg3312 -
|
|
(dg313*(dg233 + 4.*dg323) + (dg213 + 2.*dg312)*dg333)*ginv33) +
|
|
ginv12*(2.*ddg1312 + ddg2311 -
|
|
(dg311*(4.*dg123 + 3.*dg213 + 6.*dg312) + 3.*dg211*dg313 +
|
|
6.*(dg113*dg312 + dg112*dg313) + 4.*dg111*dg323)*ginv13 -
|
|
(dg222*dg311 + (2.*dg122 + 6.*dg212)*dg312 +
|
|
(2.*dg112 + dg211)*dg322)*ginv22 -
|
|
(4.*dg312*dg313 + 2.*((dg123 + dg213)*dg313 +
|
|
(dg113 + dg311)*dg323))*ginv33 -
|
|
ginv23*((2.*dg123 + 4.*dg213)*dg312 + dg311*(dg223 + 2.*dg322) +
|
|
dg211*dg323 + 2.*(dg122*dg313 + dg113*dg322 + dg112*dg323) +
|
|
4.*(dg212*dg313 + pow2(dg312)))) +
|
|
ginv13*(2.*ddg1313 + ddg3311 -
|
|
((4.*dg213 + 8.*dg312)*dg313 + dg311*(dg233 + 2.*dg323) +
|
|
dg211*dg333 + 2.*(dg133*dg312 + dg123*dg313 + dg113*dg323 +
|
|
dg112*dg333))*ginv23 -
|
|
ginv22*(dg223*dg311 + dg211*dg323 +
|
|
2.*((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323 +
|
|
pow2(dg312))) -
|
|
ginv33*(2.*(dg133*dg313 + (dg113 + dg311)*dg333) + 6.*pow2(dg313))) \
|
|
- ((2.*dg122 + 3.*dg212)*dg311 + (6.*dg112 + 3.*dg211)*dg312 +
|
|
2.*dg111*dg322)*pow2(ginv12) -
|
|
(6.*dg113*dg313 + dg311*(2.*dg133 + 6.*dg313) + 2.*dg111*dg333)*
|
|
pow2(ginv13) - (dg222*dg312 + dg212*dg322)*pow2(ginv22) -
|
|
(dg313*(dg223 + 2.*dg322) + dg213*dg323 + dg312*(dg233 + 2.*dg323) +
|
|
dg212*dg333)*pow2(ginv23) - 2.*dg313*dg333*pow2(ginv33)) +
|
|
ginv12*(ddg3323*ginv33 + ginv13*
|
|
(2.*ddg1323 + ddg2313 + ddg3312 -
|
|
(dg222*dg313 + (2.*dg123 + dg213)*dg322 +
|
|
dg312*(4.*dg223 + 2.*dg322) + (2.*dg122 + 4.*dg212)*dg323)*
|
|
ginv22 - ((4.*dg213 + 8.*dg312)*dg323 +
|
|
4.*(dg313*(dg223 + dg322) + dg123*dg323) +
|
|
2.*(dg233*dg312 + dg133*dg322 + (dg122 + dg212)*dg333))*ginv23 \
|
|
- (dg313*(dg233 + 8.*dg323) + (dg213 + 2.*dg312)*dg333 +
|
|
2.*(dg133*dg323 + dg123*dg333))*ginv33) +
|
|
ginv22*(ddg2322 - 2.*(dg223 + dg322)*dg323*ginv33 -
|
|
ginv23*(3.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322))) +
|
|
ginv23*(ddg2323 + ddg3322 -
|
|
ginv33*(dg233*dg323 + (dg223 + 2.*dg322)*dg333 + 4.*pow2(dg323))) -
|
|
(dg311*(dg233 + 4.*dg323) +
|
|
4.*((dg123 + dg312)*dg313 + dg113*dg323) + dg211*dg333 +
|
|
2.*(dg133*dg312 + dg213*dg313 + dg112*dg333))*pow2(ginv13) -
|
|
(2.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*
|
|
pow2(ginv23) - 2.*(dg222*dg322*pow2(ginv22) +
|
|
dg323*dg333*pow2(ginv33))) +
|
|
ginv13*(ddg3333*ginv33 + ginv23*
|
|
(ddg2333 + ddg3323 - (2.*dg233 + 6.*dg323)*dg333*ginv33) +
|
|
ginv22*(ddg2323 - (4.*dg223*dg323 + dg322*(dg233 + 2.*dg323) +
|
|
dg222*dg333)*ginv23 -
|
|
ginv33*(dg233*dg323 + dg223*dg333 + 2.*pow2(dg323))) -
|
|
(dg223*dg322 + dg222*dg323)*pow2(ginv22) -
|
|
2.*((dg233*dg323 + (dg223 + dg322)*dg333 + pow2(dg323))*pow2(ginv23) +
|
|
pow2(dg333)*pow2(ginv33)))
|
|
;
|
|
|
|
dGfromgdu32
|
|
=
|
|
-(((dg122 + 2.*dg212)*dg311 + 2.*(dg112 + dg211)*dg312 + dg111*dg322)*
|
|
Power(ginv12,3)) - 2.*(dg222*dg322*Power(ginv22,3) +
|
|
Power(ginv23,3)*(dg233*dg323 + (dg223 + dg322)*dg333 + pow2(dg323))) -
|
|
(2.*dg111*dg311*ginv12 + (dg112*dg311 + dg111*dg312)*ginv22 +
|
|
(dg113*dg311 + dg111*dg313)*ginv23)*pow2(ginv11) +
|
|
(ddg1312 + ddg2311 - (4.*dg311*dg312 +
|
|
2.*((dg123 + dg213)*dg311 + dg113*dg312 +
|
|
(dg112 + dg211)*dg313 + dg111*dg323))*ginv13 -
|
|
((3.*dg122 + 6.*dg212)*dg312 + 3.*dg112*dg322 +
|
|
2.*(dg222*dg311 + dg211*dg322))*ginv22 -
|
|
((dg123 + 2.*(dg213 + dg312))*dg313 + (dg113 + 2.*dg311)*dg323)*
|
|
ginv33 - ginv23*(4.*(dg213*dg312 + dg212*dg313) +
|
|
2.*(dg123*dg312 + dg122*dg313 + dg113*dg322 +
|
|
dg311*(dg223 + dg322) + (dg112 + dg211)*dg323 + pow2(dg312))))*
|
|
pow2(ginv12) - ((dg123*dg313 + dg312*(dg133 + 2.*dg313) +
|
|
(dg113 + 2.*dg311)*dg323 + dg112*dg333)*ginv22 +
|
|
2.*ginv23*(dg133*dg313 + (dg113 + dg311)*dg333 + pow2(dg313)))*
|
|
pow2(ginv13) + (ddg2322 - 2.*(dg223 + dg322)*dg323*ginv33 -
|
|
ginv23*(4.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322)))*pow2(ginv22) \
|
|
+ (ddg2333 + ddg3323 - (2.*dg233 + 6.*dg323)*dg333*ginv33)*pow2(ginv23) +
|
|
ginv11*(-(ginv13*((dg311*(dg123 + 2.*dg312) +
|
|
2.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv22 +
|
|
(4.*dg113*dg313 + dg311*(dg133 + 2.*dg313) + dg111*dg333)*ginv23)\
|
|
) + ginv12*(ddg1311 - ((dg122 + 2.*dg212)*dg311 +
|
|
(6.*dg112 + 2.*dg211)*dg312 + dg111*dg322)*ginv22 -
|
|
(dg311*(dg123 + 2.*(dg213 + dg312)) + 2.*dg211*dg313 +
|
|
4.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv23 -
|
|
2.*(dg113 + dg311)*dg313*ginv33 -
|
|
ginv13*(3.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311))) +
|
|
ginv22*(ddg1312 - ((dg123 + 2.*dg312)*dg313 + dg113*dg323)*ginv33 -
|
|
ginv23*(dg122*dg313 + dg113*dg322 +
|
|
2.*((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323 +
|
|
pow2(dg312)))) +
|
|
ginv23*(ddg1313 - ginv33*
|
|
(dg133*dg313 + dg113*dg333 + 2.*pow2(dg313))) -
|
|
((3.*dg112 + 2.*dg211)*dg311 + 3.*dg111*dg312)*pow2(ginv12) -
|
|
((dg122 + 2.*dg212)*dg312 + dg112*dg322)*pow2(ginv22) -
|
|
(dg133*dg312 + (dg123 + 2.*(dg213 + dg312))*dg313 + dg113*dg323 +
|
|
dg112*dg333)*pow2(ginv23)) +
|
|
ginv13*(ginv23*(ddg1333 + ddg3313 - (2.*dg133 + 6.*dg313)*dg333*ginv33) +
|
|
ginv22*(ddg1323 + ddg3312 -
|
|
(dg133*dg322 + (4.*dg123 + 2.*dg213 + 8.*dg312)*dg323 +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg313*(dg223 + dg322) +
|
|
dg212*dg333))*ginv23 -
|
|
((dg133 + 4.*dg313)*dg323 + (dg123 + 2.*dg312)*dg333)*ginv33) -
|
|
(dg123*dg322 + dg122*dg323 +
|
|
2.*(dg312*(dg223 + dg322) + dg212*dg323))*pow2(ginv22) -
|
|
(2.*(dg233*dg313 + dg133*dg323 + (dg123 + dg213)*dg333) +
|
|
4.*(dg313*dg323 + dg312*dg333))*pow2(ginv23)) +
|
|
ginv12*(ddg3313*ginv33 + ginv22*
|
|
(ddg1322 + 2.*ddg2312 -
|
|
(4.*(dg222*dg313 + dg213*dg322) +
|
|
3.*(dg123*dg322 + dg122*dg323) +
|
|
6.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 -
|
|
((2.*dg213 + 4.*dg312)*dg323 +
|
|
2.*(dg313*(dg223 + dg322) + dg123*dg323))*ginv33) +
|
|
ginv23*(ddg1323 + 2.*ddg2313 + ddg3312 -
|
|
(dg133*dg323 + dg313*(2.*dg233 + 8.*dg323) +
|
|
(dg123 + 2.*(dg213 + dg312))*dg333)*ginv33) +
|
|
ginv13*(ddg1313 + ddg3311 -
|
|
(8.*dg312*dg313 + 4.*
|
|
((dg123 + dg213)*dg313 + (dg113 + dg311)*dg323) +
|
|
2.*(dg233*dg311 + dg133*dg312 + (dg112 + dg211)*dg333))*ginv23 \
|
|
- ginv22*(dg122*dg313 + dg113*dg322 +
|
|
2.*(dg213*dg312 + dg212*dg313 + dg311*(dg223 + dg322) +
|
|
dg211*dg323) + 4.*(dg123*dg312 + dg112*dg323 + pow2(dg312))) \
|
|
- ginv33*(dg133*dg313 + (dg113 + 2.*dg311)*dg333 + 4.*pow2(dg313))) -
|
|
(2.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*
|
|
pow2(ginv13) - (2.*dg122*dg322 + 4.*(dg222*dg312 + dg212*dg322))*
|
|
pow2(ginv22) - (dg133*dg322 +
|
|
4.*(dg313*(dg223 + dg322) + (dg213 + dg312)*dg323) +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg123*dg323 + dg212*dg333))*
|
|
pow2(ginv23) - 2.*dg313*dg333*pow2(ginv33)) +
|
|
ginv22*(ddg3323*ginv33 + ginv23*
|
|
(2.*ddg2323 + ddg3322 -
|
|
ginv33*(2.*(dg233*dg323 + (dg223 + dg322)*dg333) + 6.*pow2(dg323))) \
|
|
- (6.*dg223*dg323 + dg322*(2.*dg233 + 6.*dg323) + 2.*dg222*dg333)*
|
|
pow2(ginv23) - 2.*dg323*dg333*pow2(ginv33)) +
|
|
ginv23*(ddg3333*ginv33 - 2.*pow2(dg333)*pow2(ginv33))
|
|
;
|
|
|
|
dGfromgdu33
|
|
=
|
|
-((2.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*
|
|
Power(ginv13,3)) - (2.*dg223*dg323 + dg322*(dg233 + 4.*dg323) +
|
|
dg222*dg333)*Power(ginv23,3) - 2.*Power(ginv33,3)*pow2(dg333) -
|
|
(2.*dg111*dg311*ginv13 + (dg112*dg311 + dg111*dg312)*ginv23 +
|
|
(dg113*dg311 + dg111*dg313)*ginv33)*pow2(ginv11) -
|
|
(((dg122 + 2.*dg212)*dg311 + 2.*(dg112 + dg211)*dg312 + dg111*dg322)*
|
|
ginv13 + (dg222*dg311 + dg211*dg322 +
|
|
2.*((dg122 + dg212)*dg312 + dg112*dg322))*ginv23 +
|
|
(dg223*dg311 + (dg123 + dg213)*dg312 + (dg122 + dg212)*dg313 +
|
|
dg113*dg322 + (dg112 + dg211)*dg323)*ginv33)*pow2(ginv12) +
|
|
(ddg1313 + ddg3311 - ((2.*dg213 + 8.*dg312)*dg313 +
|
|
dg311*(dg233 + 4.*dg323) + dg211*dg333 +
|
|
2.*(dg133*dg312 + dg123*dg313 + dg113*dg323 + dg112*dg333))*ginv23 \
|
|
- ginv22*(dg223*dg311 + (dg123 + dg213)*dg312 + dg212*dg313 +
|
|
(dg112 + dg211)*dg323 + 2.*pow2(dg312)) -
|
|
ginv33*(4.*dg311*dg333 + 3.*(dg133*dg313 + dg113*dg333) +
|
|
6.*pow2(dg313)))*pow2(ginv13) -
|
|
(2.*dg222*dg322*ginv23 + (dg223*dg322 + dg222*dg323)*ginv33)*
|
|
pow2(ginv22) + (ddg2323 + ddg3322 -
|
|
ginv33*(4.*dg322*dg333 + 3.*(dg233*dg323 + dg223*dg333) +
|
|
6.*pow2(dg323)))*pow2(ginv23) + ddg3333*pow2(ginv33) +
|
|
ginv13*((ddg1333 + 2.*ddg3313)*ginv33 +
|
|
ginv22*(ddg2312 - (dg222*dg313 + (dg123 + dg213)*dg322 +
|
|
dg122*dg323 + 4.*(dg312*(dg223 + dg322) + dg212*dg323))*ginv23 \
|
|
- (dg312*(dg233 + 4.*dg323) + 2.*(dg223*dg313 + (dg123 + dg213)*dg323) +
|
|
dg212*dg333)*ginv33) +
|
|
ginv23*(ddg1323 + ddg2313 + 2.*ddg3312 -
|
|
(12.*dg313*dg323 + (3.*dg213 + 8.*dg312)*dg333 +
|
|
3.*(dg233*dg313 + dg133*dg323 + dg123*dg333))*ginv33) -
|
|
(dg222*dg312 + dg212*dg322)*pow2(ginv22) -
|
|
((dg133 + 4.*dg313)*dg322 + (2.*dg213 + 8.*dg312)*dg323 +
|
|
dg122*dg333 + 2.*(dg233*dg312 + dg223*dg313 + dg123*dg323 +
|
|
dg212*dg333))*pow2(ginv23) -
|
|
(2.*dg133 + 8.*dg313)*dg333*pow2(ginv33)) +
|
|
ginv23*((ddg2333 + 2.*ddg3323)*ginv33 -
|
|
(2.*dg233 + 8.*dg323)*dg333*pow2(ginv33)) +
|
|
ginv12*((ddg1323 + ddg2313)*ginv33 -
|
|
ginv22*((2.*dg122*dg322 + 3.*(dg222*dg312 + dg212*dg322))*ginv23 +
|
|
(dg222*dg313 + (dg123 + dg213)*dg322 + dg122*dg323 +
|
|
2.*(dg223*dg312 + dg212*dg323))*ginv33) +
|
|
ginv23*(ddg1322 + ddg2312 -
|
|
(dg233*dg312 + dg133*dg322 +
|
|
4.*(dg313*(dg223 + dg322) + (dg123 + dg213 + dg312)*dg323) +
|
|
(dg122 + dg212)*dg333)*ginv33) +
|
|
ginv13*(ddg1312 + ddg2311 -
|
|
(dg222*dg311 + (dg122 + 4.*dg212)*dg312 + (dg112 + dg211)*dg322)*
|
|
ginv22 - (dg133*dg312 + dg311*(dg233 + 4.*dg323) +
|
|
4.*((dg123 + dg213 + dg312)*dg313 + dg113*dg323) +
|
|
(dg112 + dg211)*dg333)*ginv33 -
|
|
ginv23*(2.*(dg223*dg311 + dg122*dg313 + dg113*dg322 +
|
|
dg211*dg323) + 4.*
|
|
((dg123 + dg213)*dg312 + dg212*dg313 + dg311*dg322 +
|
|
dg112*dg323 + pow2(dg312)))) -
|
|
(4.*dg311*dg312 + 2.*((dg123 + dg213)*dg311 + dg113*dg312 +
|
|
(dg112 + dg211)*dg313 + dg111*dg323))*pow2(ginv13) -
|
|
((2.*dg213 + 4.*dg312)*dg322 +
|
|
2.*(dg223*dg312 + dg222*dg313 + dg123*dg322 +
|
|
(dg122 + dg212)*dg323))*pow2(ginv23) -
|
|
(dg133*dg323 + dg313*(dg233 + 4.*dg323) + (dg123 + dg213)*dg333)*
|
|
pow2(ginv33)) + ginv11*(ddg1313*ginv33 -
|
|
ginv12*(((3.*dg112 + 2.*dg211)*dg311 + 3.*dg111*dg312)*ginv13 +
|
|
((dg122 + dg212)*dg311 + (4.*dg112 + dg211)*dg312 + dg111*dg322)*
|
|
ginv23 + ((dg123 + dg213)*dg311 + dg211*dg313 +
|
|
2.*(dg113*dg312 + dg112*dg313) + dg111*dg323)*ginv33) -
|
|
ginv22*(((dg122 + 2.*dg212)*dg312 + dg112*dg322)*ginv23 +
|
|
((dg123 + dg213)*dg312 + dg212*dg313 + dg112*dg323)*ginv33) +
|
|
ginv13*(ddg1311 - (dg212*dg311 + (2.*dg112 + dg211)*dg312)*ginv22 -
|
|
((dg123 + dg213)*dg311 + 4.*(dg113 + dg311)*dg312 +
|
|
(4.*dg112 + dg211)*dg313 + dg111*dg323)*ginv23 -
|
|
(6.*dg113*dg313 + dg311*(dg133 + 4.*dg313) + dg111*dg333)*ginv33) +
|
|
ginv23*(ddg1312 - (dg312*(dg133 + 4.*dg313) +
|
|
2.*((dg123 + dg213)*dg313 + dg113*dg323) + dg112*dg333)*ginv33) \
|
|
- (3.*(dg113*dg311 + dg111*dg313) + 2.*pow2(dg311))*pow2(ginv13) -
|
|
((dg123 + dg213)*dg312 + (dg122 + dg212)*dg313 + dg113*dg322 +
|
|
dg112*dg323 + 2.*pow2(dg312))*pow2(ginv23) -
|
|
(dg133*dg313 + dg113*dg333 + 2.*pow2(dg313))*pow2(ginv33)) +
|
|
ginv22*(ddg2323*ginv33 + ginv23*
|
|
(ddg2322 - (6.*dg223*dg323 + dg322*(dg233 + 4.*dg323) + dg222*dg333)*
|
|
ginv33) - (3.*(dg223*dg322 + dg222*dg323) + 2.*pow2(dg322))*
|
|
pow2(ginv23) - (dg233*dg323 + dg223*dg333 + 2.*pow2(dg323))*
|
|
pow2(ginv33))
|
|
;
|
|
|
|
R11
|
|
=
|
|
dG11*g11 + dG12*g12 + dG13*g13 + gammado111*Gfromg1 + gammado112*Gfromg2 +
|
|
gammado113*Gfromg3 + (-0.5*ddg1111 + 3.*gamma111*gammado111 +
|
|
2.*(gamma211*gammado112 + gamma311*gammado113) +
|
|
gamma211*gammado211 + gamma311*gammado311)*ginv11 +
|
|
(-ddg1211 + 3.*(gamma112*gammado111 + gamma111*gammado112) +
|
|
2.*(gamma212*gammado112 + gamma312*gammado113 +
|
|
gamma211*gammado122 + gamma311*gammado123) + gamma212*gammado211 +
|
|
gamma211*gammado212 + gamma312*gammado311 + gamma311*gammado312)*ginv12 \
|
|
+ (-ddg1311 + 3.*(gamma113*gammado111 + gamma111*gammado113) +
|
|
2.*(gamma213*gammado112 + gamma313*gammado113 +
|
|
gamma211*gammado123 + gamma311*gammado133) + gamma213*gammado211 +
|
|
gamma211*gammado213 + gamma313*gammado311 + gamma311*gammado313)*ginv13 \
|
|
+ (-0.5*ddg2211 + 3.*gamma112*gammado112 +
|
|
2.*(gamma212*gammado122 + gamma312*gammado123) +
|
|
gamma212*gammado212 + gamma312*gammado312)*ginv22 +
|
|
(-ddg2311 + 3.*(gamma113*gammado112 + gamma112*gammado113) +
|
|
2.*(gamma213*gammado122 + (gamma212 + gamma313)*gammado123 +
|
|
gamma312*gammado133) + gamma213*gammado212 + gamma212*gammado213 +
|
|
gamma313*gammado312 + gamma312*gammado313)*ginv23 +
|
|
(-0.5*ddg3311 + 3.*gamma113*gammado113 +
|
|
2.*(gamma213*gammado123 + gamma313*gammado133) + gamma213*gammado213 +
|
|
gamma313*gammado313)*ginv33
|
|
;
|
|
|
|
R12
|
|
=
|
|
0.5*(dG21*g11 + (dG11 + dG22)*g12 + dG23*g13 + dG12*g22 + dG13*g23 +
|
|
(gammado112 + gammado211)*Gfromg1 +
|
|
(gammado122 + gammado212)*Gfromg2 + (gammado123 + gammado213)*Gfromg3) \
|
|
+ (-0.5*ddg1112 + gamma112*gammado111 + (gamma111 + gamma212)*gammado112 +
|
|
gamma312*gammado113 + gamma111*gammado211 + 2.*gamma211*gammado212 +
|
|
gamma311*(gammado213 + gammado312))*ginv11 +
|
|
(-ddg1212 + gamma122*gammado111 + (2.*gamma112 + gamma222)*gammado112 +
|
|
gamma322*gammado113 + (gamma111 + gamma212)*gammado122 +
|
|
gamma112*gammado211 + (gamma111 + 2.*gamma212)*gammado212 +
|
|
2.*gamma211*gammado222 +
|
|
gamma312*(gammado123 + gammado213 + gammado312) +
|
|
gamma311*(gammado223 + gammado322))*ginv12 +
|
|
(-ddg1312 + gamma123*gammado111 + (gamma113 + gamma223)*gammado112 +
|
|
(gamma112 + gamma323)*gammado113 + (gamma111 + gamma212)*gammado123 +
|
|
gamma312*gammado133 + gamma113*gammado211 +
|
|
(gamma111 + gamma313)*gammado213 +
|
|
2.*(gamma213*gammado212 + gamma211*gammado223) +
|
|
gamma313*gammado312 + gamma311*(gammado233 + gammado323))*ginv13 +
|
|
(-0.5*ddg2212 + gamma122*gammado112 + (gamma112 + gamma222)*gammado122 +
|
|
gamma322*gammado123 + gamma112*gammado212 + 2.*gamma212*gammado222 +
|
|
gamma312*(gammado223 + gammado322))*ginv22 +
|
|
(-ddg2312 + gamma123*gammado112 + gamma122*gammado113 +
|
|
(gamma113 + gamma223)*gammado122 +
|
|
(gamma112 + gamma222 + gamma323)*gammado123 + gamma322*gammado133 +
|
|
gamma113*gammado212 + gamma112*gammado213 +
|
|
2.*(gamma213*gammado222 + gamma212*gammado223) +
|
|
gamma313*(gammado223 + gammado322) +
|
|
gamma312*(gammado233 + gammado323))*ginv23 +
|
|
(-0.5*ddg3312 + gamma123*gammado113 + (gamma113 + gamma223)*gammado123 +
|
|
gamma323*gammado133 + gamma113*gammado213 + 2.*gamma213*gammado223 +
|
|
gamma313*(gammado233 + gammado323))*ginv33
|
|
;
|
|
|
|
R13
|
|
=
|
|
0.5*(dG31*g11 + dG32*g12 + (dG11 + dG33)*g13 + dG12*g23 + dG13*g33 +
|
|
(gammado113 + gammado311)*Gfromg1 +
|
|
(gammado123 + gammado312)*Gfromg2 + (gammado133 + gammado313)*Gfromg3) \
|
|
+ (-0.5*ddg1113 + gamma113*gammado111 + gamma213*gammado112 +
|
|
(gamma111 + gamma313)*gammado113 + gamma111*gammado311 +
|
|
gamma211*(gammado213 + gammado312) + 2.*gamma311*gammado313)*ginv11 +
|
|
(-ddg1213 + gamma123*gammado111 + (gamma113 + gamma223)*gammado112 +
|
|
(gamma112 + gamma323)*gammado113 + gamma213*gammado122 +
|
|
(gamma111 + gamma313)*gammado123 + gamma112*gammado311 +
|
|
gamma111*gammado312 + gamma212*(gammado213 + gammado312) +
|
|
gamma211*(gammado223 + gammado322) +
|
|
2.*(gamma312*gammado313 + gamma311*gammado323))*ginv12 +
|
|
(-ddg1313 + gamma133*gammado111 + gamma233*gammado112 +
|
|
(2.*gamma113 + gamma333)*gammado113 +
|
|
(gamma111 + gamma313)*gammado133 + gamma113*gammado311 +
|
|
gamma213*(gammado123 + gammado213 + gammado312) +
|
|
(gamma111 + 2.*gamma313)*gammado313 +
|
|
gamma211*(gammado233 + gammado323) + 2.*gamma311*gammado333)*ginv13 +
|
|
(-0.5*ddg2213 + gamma123*gammado112 + gamma223*gammado122 +
|
|
(gamma112 + gamma323)*gammado123 + gamma112*gammado312 +
|
|
gamma212*(gammado223 + gammado322) + 2.*gamma312*gammado323)*ginv22 +
|
|
(-ddg2313 + gamma133*gammado112 + gamma123*gammado113 +
|
|
gamma233*gammado122 + (gamma113 + gamma223 + gamma333)*gammado123 +
|
|
(gamma112 + gamma323)*gammado133 + gamma113*gammado312 +
|
|
gamma112*gammado313 + gamma213*(gammado223 + gammado322) +
|
|
gamma212*(gammado233 + gammado323) +
|
|
2.*(gamma313*gammado323 + gamma312*gammado333))*ginv23 +
|
|
(-0.5*ddg3313 + gamma133*gammado113 + gamma233*gammado123 +
|
|
(gamma113 + gamma333)*gammado133 + gamma113*gammado313 +
|
|
gamma213*(gammado233 + gammado323) + 2.*gamma313*gammado333)*ginv33
|
|
;
|
|
|
|
R22
|
|
=
|
|
dG21*g12 + dG22*g22 + dG23*g23 + gammado212*Gfromg1 + gammado222*Gfromg2 +
|
|
gammado223*Gfromg3 + (-0.5*ddg1122 +
|
|
gamma112*(gammado112 + 2.*gammado211) + 3.*gamma212*gammado212 +
|
|
gamma312*(2.*gammado213 + gammado312))*ginv11 +
|
|
(-ddg1222 + gamma122*(gammado112 + 2.*gammado211) +
|
|
gamma112*(gammado122 + 2.*gammado212) +
|
|
3.*(gamma222*gammado212 + gamma212*gammado222) +
|
|
2.*(gamma322*gammado213 + gamma312*gammado223) +
|
|
gamma322*gammado312 + gamma312*gammado322)*ginv12 +
|
|
(-ddg1322 + gamma123*(gammado112 + 2.*gammado211) +
|
|
gamma112*(gammado123 + 2.*gammado213) +
|
|
3.*(gamma223*gammado212 + gamma212*gammado223) +
|
|
2.*(gamma323*gammado213 + gamma312*gammado233) +
|
|
gamma323*gammado312 + gamma312*gammado323)*ginv13 +
|
|
(-0.5*ddg2222 + gamma122*(gammado122 + 2.*gammado212) +
|
|
3.*gamma222*gammado222 + gamma322*(2.*gammado223 + gammado322))*ginv22 \
|
|
+ (-ddg2322 + gamma123*(gammado122 + 2.*gammado212) +
|
|
gamma122*(gammado123 + 2.*gammado213) +
|
|
3.*(gamma223*gammado222 + gamma222*gammado223) +
|
|
2.*(gamma323*gammado223 + gamma322*gammado233) +
|
|
gamma323*gammado322 + gamma322*gammado323)*ginv23 +
|
|
(-0.5*ddg3322 + gamma123*(gammado123 + 2.*gammado213) +
|
|
3.*gamma223*gammado223 + gamma323*(2.*gammado233 + gammado323))*ginv33
|
|
;
|
|
|
|
R23
|
|
=
|
|
0.5*(dG31*g12 + dG21*g13 + dG32*g22 + (dG22 + dG33)*g23 + dG23*g33 +
|
|
(gammado213 + gammado312)*Gfromg1 +
|
|
(gammado223 + gammado322)*Gfromg2 + (gammado233 + gammado323)*Gfromg3) \
|
|
+ (-0.5*ddg1123 + gamma113*gammado211 + gamma213*gammado212 +
|
|
(gamma212 + gamma313)*gammado213 +
|
|
gamma112*(gammado113 + gammado311) + gamma212*gammado312 +
|
|
2.*gamma312*gammado313)*ginv11 +
|
|
(-ddg1223 + gamma123*gammado211 + (gamma113 + gamma223)*gammado212 +
|
|
(gamma222 + gamma323)*gammado213 + gamma213*gammado222 +
|
|
(gamma212 + gamma313)*gammado223 +
|
|
gamma122*(gammado113 + gammado311) + gamma222*gammado312 +
|
|
gamma112*(gammado123 + gammado312) + gamma212*gammado322 +
|
|
2.*(gamma322*gammado313 + gamma312*gammado323))*ginv12 +
|
|
(-ddg1323 + gamma133*gammado211 + gamma233*gammado212 +
|
|
(gamma113 + gamma223 + gamma333)*gammado213 + gamma213*gammado223 +
|
|
(gamma212 + gamma313)*gammado233 +
|
|
gamma123*(gammado113 + gammado311) + gamma223*gammado312 +
|
|
gamma112*(gammado133 + gammado313) + gamma212*gammado323 +
|
|
2.*(gamma323*gammado313 + gamma312*gammado333))*ginv13 +
|
|
(-0.5*ddg2223 + gamma123*gammado212 + gamma223*gammado222 +
|
|
(gamma222 + gamma323)*gammado223 +
|
|
gamma122*(gammado123 + gammado312) + gamma222*gammado322 +
|
|
2.*gamma322*gammado323)*ginv22 +
|
|
(-ddg2323 + gamma133*gammado212 + gamma233*gammado222 +
|
|
(2.*gamma223 + gamma333)*gammado223 +
|
|
(gamma222 + gamma323)*gammado233 +
|
|
gamma123*(gammado123 + gammado213 + gammado312) +
|
|
gamma122*(gammado133 + gammado313) + gamma223*gammado322 +
|
|
(gamma222 + 2.*gamma323)*gammado323 + 2.*gamma322*gammado333)*ginv23 +
|
|
(-0.5*ddg3323 + gamma133*gammado213 + gamma233*gammado223 +
|
|
(gamma223 + gamma333)*gammado233 +
|
|
gamma123*(gammado133 + gammado313) + gamma223*gammado323 +
|
|
2.*gamma323*gammado333)*ginv33
|
|
;
|
|
|
|
R33
|
|
=
|
|
dG31*g13 + dG32*g23 + dG33*g33 + gammado313*Gfromg1 + gammado323*Gfromg2 +
|
|
gammado333*Gfromg3 + (-0.5*ddg1133 +
|
|
gamma113*(gammado113 + 2.*gammado311) +
|
|
gamma213*(gammado213 + 2.*gammado312) + 3.*gamma313*gammado313)*ginv11 \
|
|
+ (-ddg1233 + gamma123*(gammado113 + 2.*gammado311) +
|
|
gamma113*(gammado123 + 2.*gammado312) +
|
|
gamma223*(gammado213 + 2.*gammado312) +
|
|
gamma213*(gammado223 + 2.*gammado322) +
|
|
3.*(gamma323*gammado313 + gamma313*gammado323))*ginv12 +
|
|
(-ddg1333 + gamma133*(gammado113 + 2.*gammado311) +
|
|
gamma233*(gammado213 + 2.*gammado312) +
|
|
gamma113*(gammado133 + 2.*gammado313) +
|
|
gamma213*(gammado233 + 2.*gammado323) +
|
|
3.*(gamma333*gammado313 + gamma313*gammado333))*ginv13 +
|
|
(-0.5*ddg2233 + gamma123*(gammado123 + 2.*gammado312) +
|
|
gamma223*(gammado223 + 2.*gammado322) + 3.*gamma323*gammado323)*ginv22 \
|
|
+ (-ddg2333 + gamma133*(gammado123 + 2.*gammado312) +
|
|
gamma123*(gammado133 + 2.*gammado313) +
|
|
gamma233*(gammado223 + 2.*gammado322) +
|
|
gamma223*(gammado233 + 2.*gammado323) +
|
|
3.*(gamma333*gammado323 + gamma323*gammado333))*ginv23 +
|
|
(-0.5*ddg3333 + gamma133*(gammado133 + 2.*gammado313) +
|
|
gamma233*(gammado233 + 2.*gammado323) + 3.*gamma333*gammado333)*ginv33
|
|
;
|
|
|
|
ff
|
|
=
|
|
chi
|
|
;
|
|
|
|
oochipsipower
|
|
=
|
|
1/chipsipower
|
|
;
|
|
|
|
f
|
|
=
|
|
oochipsipower*log(ff)
|
|
;
|
|
|
|
psim4
|
|
=
|
|
exp(-4.*f)
|
|
;
|
|
|
|
df1
|
|
=
|
|
(dchi1*oochipsipower)/chi
|
|
;
|
|
|
|
df2
|
|
=
|
|
(dchi2*oochipsipower)/chi
|
|
;
|
|
|
|
df3
|
|
=
|
|
(dchi3*oochipsipower)/chi
|
|
;
|
|
|
|
ddf11
|
|
=
|
|
(ddchi11*oochipsipower)/chi - chipsipower*pow2(df1)
|
|
;
|
|
|
|
ddf12
|
|
=
|
|
-(chipsipower*df1*df2) + (ddchi12*oochipsipower)/chi
|
|
;
|
|
|
|
ddf13
|
|
=
|
|
-(chipsipower*df1*df3) + (ddchi13*oochipsipower)/chi
|
|
;
|
|
|
|
ddf22
|
|
=
|
|
(ddchi22*oochipsipower)/chi - chipsipower*pow2(df2)
|
|
;
|
|
|
|
ddf23
|
|
=
|
|
-(chipsipower*df2*df3) + (ddchi23*oochipsipower)/chi
|
|
;
|
|
|
|
ddf33
|
|
=
|
|
(ddchi33*oochipsipower)/chi - chipsipower*pow2(df3)
|
|
;
|
|
|
|
cddf11
|
|
=
|
|
ddf11 - df1*gamma111 - df2*gamma211 - df3*gamma311
|
|
;
|
|
|
|
cddf12
|
|
=
|
|
ddf12 - df1*gamma112 - df2*gamma212 - df3*gamma312
|
|
;
|
|
|
|
cddf13
|
|
=
|
|
ddf13 - df1*gamma113 - df2*gamma213 - df3*gamma313
|
|
;
|
|
|
|
cddf22
|
|
=
|
|
ddf22 - df1*gamma122 - df2*gamma222 - df3*gamma322
|
|
;
|
|
|
|
cddf23
|
|
=
|
|
ddf23 - df1*gamma123 - df2*gamma223 - df3*gamma323
|
|
;
|
|
|
|
cddf33
|
|
=
|
|
ddf33 - df1*gamma133 - df2*gamma233 - df3*gamma333
|
|
;
|
|
|
|
trcddf
|
|
=
|
|
cddf11*ginv11 + cddf22*ginv22 +
|
|
2.*(cddf12*ginv12 + cddf13*ginv13 + cddf23*ginv23) + cddf33*ginv33
|
|
;
|
|
|
|
Rphi11
|
|
=
|
|
-2.*(cddf11 + g11*trcddf) + (4. - 4.*g11*ginv11)*pow2(df1) -
|
|
g11*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi12
|
|
=
|
|
df1*df2*(4. - 8.*g12*ginv12) - 2.*(cddf12 + g12*trcddf) -
|
|
g12*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi13
|
|
=
|
|
df1*(4.*df3 - 8.*df2*g13*ginv12) - 2.*(cddf13 + g13*trcddf) -
|
|
g13*(8.*df3*(df1*ginv13 + df2*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi22
|
|
=
|
|
-2.*(cddf22 + g22*trcddf) + (4. - 4.*g22*ginv22)*pow2(df2) -
|
|
g22*(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi23
|
|
=
|
|
df2*(-8.*df1*g23*ginv12 + df3*(4. - 8.*g23*ginv23)) -
|
|
2.*(cddf23 + g23*trcddf) - g23*
|
|
(8.*df1*df3*ginv13 + 4.*(ginv11*pow2(df1) + ginv22*pow2(df2) +
|
|
ginv33*pow2(df3)))
|
|
;
|
|
|
|
Rphi33
|
|
=
|
|
-2.*(cddf33 + g33*trcddf) - g33*
|
|
(8.*(df1*(df2*ginv12 + df3*ginv13) + df2*df3*ginv23) +
|
|
4.*(ginv11*pow2(df1) + ginv22*pow2(df2))) +
|
|
(4. - 4.*g33*ginv33)*pow2(df3)
|
|
;
|
|
|
|
Rf11
|
|
=
|
|
R11 + Rphi11
|
|
;
|
|
|
|
Rf12
|
|
=
|
|
R12 + Rphi12
|
|
;
|
|
|
|
Rf13
|
|
=
|
|
R13 + Rphi13
|
|
;
|
|
|
|
Rf22
|
|
=
|
|
R22 + Rphi22
|
|
;
|
|
|
|
Rf23
|
|
=
|
|
R23 + Rphi23
|
|
;
|
|
|
|
Rf33
|
|
=
|
|
R33 + Rphi33
|
|
;
|
|
|
|
Rhat
|
|
=
|
|
psim4*(ginv11*Rf11 + ginv22*Rf22 +
|
|
2.*(ginv12*Rf12 + ginv13*Rf13 + ginv23*Rf23) + ginv33*Rf33)
|
|
;
|
|
|
|
cdda11
|
|
=
|
|
dda11 - da2*gamma211 - da3*gamma311 +
|
|
da1*(-gamma111 + df1*(-4. + 2.*g11*ginv11)) +
|
|
2.*g11*((da2*df1 + da1*df2)*ginv12 + (da3*df1 + da1*df3)*ginv13 +
|
|
da2*df2*ginv22 + (da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)
|
|
;
|
|
|
|
cdda12
|
|
=
|
|
dda12 - da1*gamma112 - da2*gamma212 - da3*gamma312 +
|
|
2.*(-(da2*df1) - da1*df2 + g12*
|
|
(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33))
|
|
;
|
|
|
|
cdda13
|
|
=
|
|
dda13 - da1*gamma113 - da2*gamma213 - da3*gamma313 +
|
|
2.*(-(da3*df1) - da1*df3 + g13*
|
|
(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33))
|
|
;
|
|
|
|
cdda22
|
|
=
|
|
dda22 - da1*gamma122 - da2*(4.*df2 + gamma222) - da3*gamma322 +
|
|
2.*g22*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)
|
|
;
|
|
|
|
cdda23
|
|
=
|
|
dda23 - da1*gamma123 - da2*gamma223 - da3*gamma323 +
|
|
2.*(-(da3*df2) - da2*df3 + g23*
|
|
(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33))
|
|
;
|
|
|
|
cdda33
|
|
=
|
|
dda33 - da1*gamma133 - da2*gamma233 - da3*(4.*df3 + gamma333) +
|
|
2.*g33*(da1*df1*ginv11 + (da2*df1 + da1*df2)*ginv12 +
|
|
(da3*df1 + da1*df3)*ginv13 + da2*df2*ginv22 +
|
|
(da3*df2 + da2*df3)*ginv23 + da3*df3*ginv33)
|
|
;
|
|
|
|
trcdda
|
|
=
|
|
(cdda11*ginv11 + cdda22*ginv22 +
|
|
2.*(cdda12*ginv12 + cdda13*ginv13 + cdda23*ginv23) + cdda33*ginv33)*psim4
|
|
;
|
|
|
|
AA11
|
|
=
|
|
2.*(A11*(A12*ginv12 + A13*ginv13) + A12*A13*ginv23) + ginv11*pow2(A11) +
|
|
ginv22*pow2(A12) + ginv33*pow2(A13)
|
|
;
|
|
|
|
AA12
|
|
=
|
|
(A12*A13 + A11*A23)*ginv13 + A12*(A11*ginv11 + A22*ginv22) +
|
|
(A13*A22 + A12*A23)*ginv23 + A13*A23*ginv33 + ginv12*(A11*A22 + pow2(A12))
|
|
;
|
|
|
|
AA13
|
|
=
|
|
(A12*A13 + A11*A23)*ginv12 + A12*A23*ginv22 + (A13*A23 + A12*A33)*ginv23 +
|
|
A13*(A11*ginv11 + A33*ginv33) + ginv13*(A11*A33 + pow2(A13))
|
|
;
|
|
|
|
AA21
|
|
=
|
|
(A12*A13 + A11*A23)*ginv13 + A12*(A11*ginv11 + A22*ginv22) +
|
|
(A13*A22 + A12*A23)*ginv23 + A13*A23*ginv33 + ginv12*(A11*A22 + pow2(A12))
|
|
;
|
|
|
|
AA22
|
|
=
|
|
2.*(A12*(A22*ginv12 + A23*ginv13) + A22*A23*ginv23) + ginv11*pow2(A12) +
|
|
ginv22*pow2(A22) + ginv33*pow2(A23)
|
|
;
|
|
|
|
AA23
|
|
=
|
|
A12*A13*ginv11 + (A13*A22 + A12*A23)*ginv12 + (A13*A23 + A12*A33)*ginv13 +
|
|
A23*(A22*ginv22 + A33*ginv33) + ginv23*(A22*A33 + pow2(A23))
|
|
;
|
|
|
|
AA31
|
|
=
|
|
(A12*A13 + A11*A23)*ginv12 + A12*A23*ginv22 + (A13*A23 + A12*A33)*ginv23 +
|
|
A13*(A11*ginv11 + A33*ginv33) + ginv13*(A11*A33 + pow2(A13))
|
|
;
|
|
|
|
AA32
|
|
=
|
|
A12*A13*ginv11 + (A13*A22 + A12*A23)*ginv12 + (A13*A23 + A12*A33)*ginv13 +
|
|
A23*(A22*ginv22 + A33*ginv33) + ginv23*(A22*A33 + pow2(A23))
|
|
;
|
|
|
|
AA33
|
|
=
|
|
2.*(A13*(A23*ginv12 + A33*ginv13) + A23*A33*ginv23) + ginv11*pow2(A13) +
|
|
ginv22*pow2(A23) + ginv33*pow2(A33)
|
|
;
|
|
|
|
cdA111
|
|
=
|
|
dA111 - 2.*(A11*gamma111 + A12*gamma211 + A13*gamma311)
|
|
;
|
|
|
|
cdA112
|
|
=
|
|
dA112 - A11*gamma112 - A22*gamma211 - A12*(gamma111 + gamma212) -
|
|
A23*gamma311 - A13*gamma312
|
|
;
|
|
|
|
cdA113
|
|
=
|
|
dA113 - A11*gamma113 - A23*gamma211 - A12*gamma213 - A33*gamma311 -
|
|
A13*(gamma111 + gamma313)
|
|
;
|
|
|
|
cdA122
|
|
=
|
|
dA122 - 2.*(A12*gamma112 + A22*gamma212 + A23*gamma312)
|
|
;
|
|
|
|
cdA123
|
|
=
|
|
dA123 - A13*gamma112 - A12*gamma113 - A22*gamma213 - A33*gamma312 -
|
|
A23*(gamma212 + gamma313)
|
|
;
|
|
|
|
cdA133
|
|
=
|
|
dA133 - 2.*(A13*gamma113 + A23*gamma213 + A33*gamma313)
|
|
;
|
|
|
|
cdA211
|
|
=
|
|
dA211 - 2.*(A11*gamma112 + A12*gamma212 + A13*gamma312)
|
|
;
|
|
|
|
cdA212
|
|
=
|
|
dA212 - A11*gamma122 - A22*gamma212 - A12*(gamma112 + gamma222) -
|
|
A23*gamma312 - A13*gamma322
|
|
;
|
|
|
|
cdA213
|
|
=
|
|
dA213 - A11*gamma123 - A23*gamma212 - A12*gamma223 - A33*gamma312 -
|
|
A13*(gamma112 + gamma323)
|
|
;
|
|
|
|
cdA222
|
|
=
|
|
dA222 - 2.*(A12*gamma122 + A22*gamma222 + A23*gamma322)
|
|
;
|
|
|
|
cdA223
|
|
=
|
|
dA223 - A13*gamma122 - A12*gamma123 - A22*gamma223 - A33*gamma322 -
|
|
A23*(gamma222 + gamma323)
|
|
;
|
|
|
|
cdA233
|
|
=
|
|
dA233 - 2.*(A13*gamma123 + A23*gamma223 + A33*gamma323)
|
|
;
|
|
|
|
cdA311
|
|
=
|
|
dA311 - 2.*(A11*gamma113 + A12*gamma213 + A13*gamma313)
|
|
;
|
|
|
|
cdA312
|
|
=
|
|
dA312 - A11*gamma123 - A22*gamma213 - A12*(gamma113 + gamma223) -
|
|
A23*gamma313 - A13*gamma323
|
|
;
|
|
|
|
cdA313
|
|
=
|
|
dA313 - A11*gamma133 - A23*gamma213 - A12*gamma233 - A33*gamma313 -
|
|
A13*(gamma113 + gamma333)
|
|
;
|
|
|
|
cdA322
|
|
=
|
|
dA322 - 2.*(A12*gamma123 + A22*gamma223 + A23*gamma323)
|
|
;
|
|
|
|
cdA323
|
|
=
|
|
dA323 - A13*gamma123 - A12*gamma133 - A22*gamma233 - A33*gamma323 -
|
|
A23*(gamma223 + gamma333)
|
|
;
|
|
|
|
cdA333
|
|
=
|
|
dA333 - 2.*(A13*gamma133 + A23*gamma233 + A33*gamma333)
|
|
;
|
|
|
|
divbeta
|
|
=
|
|
db11 + db22 + db33
|
|
;
|
|
|
|
totdivbeta
|
|
=
|
|
0.66666666666666666667*divbeta
|
|
;
|
|
|
|
lieA11
|
|
=
|
|
beta1*dA111 + beta2*dA211 + beta3*dA311 +
|
|
2.*(A11*db11 + A12*db12 + A13*db13) - A11*totdivbeta
|
|
;
|
|
|
|
lieA12
|
|
=
|
|
beta1*dA112 + beta2*dA212 + beta3*dA312 + A22*db12 + A23*db13 + A11*db21 +
|
|
A13*db23 + A12*(db11 + db22 - totdivbeta)
|
|
;
|
|
|
|
lieA13
|
|
=
|
|
beta1*dA113 + beta2*dA213 + beta3*dA313 + A23*db12 + A33*db13 + A11*db31 +
|
|
A12*db32 + A13*(db11 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieA22
|
|
=
|
|
beta1*dA122 + beta2*dA222 + beta3*dA322 +
|
|
2.*(A12*db21 + A22*db22 + A23*db23) - A22*totdivbeta
|
|
;
|
|
|
|
lieA23
|
|
=
|
|
beta1*dA123 + beta2*dA223 + beta3*dA323 + A13*db21 + A33*db23 + A12*db31 +
|
|
A22*db32 + A23*(db22 + db33 - totdivbeta)
|
|
;
|
|
|
|
lieA33
|
|
=
|
|
beta1*dA133 + beta2*dA233 + beta3*dA333 +
|
|
2.*(A13*db31 + A23*db32 + A33*db33) - A33*totdivbeta
|
|
;
|
|
|
|
DTheta
|
|
=
|
|
dTheta1*sup1 + dTheta2*sup2 + dTheta3*sup3
|
|
;
|
|
|
|
rACss
|
|
=
|
|
2.*((A23*alpha*K + lieA23)*sup2*sup3 +
|
|
sup1*((A12*alpha*K + lieA12)*sup2 + A13*alpha*K*sup3) +
|
|
psim4*((-cdda23 + alpha*Rf23)*sup2*sup3 +
|
|
sup1*((-cdda12 + alpha*Rf12)*sup2 - cdda13*sup3))) +
|
|
0.66666666666666666667*(g13*sup1 + g23*sup2)*sup3*trcdda +
|
|
sup1*(2.*(-(AA31*alpha) + lieA13)*sup3 +
|
|
0.66666666666666666667*g12*sup2*trcdda) +
|
|
(lieA11 + psim4*(-cdda11 + alpha*Rf11) +
|
|
0.33333333333333333333*g11*(-(alpha*Rhat) + trcdda))*pow2(sup1) +
|
|
(lieA22 - cdda22*psim4 + alpha*
|
|
(A22*K + psim4*Rf22 - 0.33333333333333333333*g22*Rhat) +
|
|
0.33333333333333333333*g22*trcdda)*pow2(sup2) +
|
|
(lieA33 - cdda33*psim4 + alpha*
|
|
(A33*K + psim4*Rf33 - 0.33333333333333333333*g33*Rhat) +
|
|
0.33333333333333333333*g33*trcdda)*pow2(sup3) +
|
|
alpha*(ginv11*((-2.*cdA111*chi + 3.*A11*dchi1)*sup1 +
|
|
(-2.*cdA112*chi + 3.*A12*dchi1)*sup2 +
|
|
(-2.*cdA113*chi + 3.*A13*dchi1)*sup3) +
|
|
ginv22*((-2.*cdA212*chi + 3.*A12*dchi2)*sup1 +
|
|
(-2.*cdA222*chi + 3.*A22*dchi2)*sup2 +
|
|
(-2.*cdA223*chi + 3.*A23*dchi2)*sup3) +
|
|
ginv33*((-2.*cdA313*chi + 3.*A13*dchi3)*sup1 +
|
|
(-2.*cdA323*chi + 3.*A23*dchi3)*sup2 +
|
|
(-2.*cdA333*chi + 3.*A33*dchi3)*sup3) +
|
|
chi*(-2.*DTheta + 1.3333333333333333333*
|
|
(dK1*sup1 + dK2*sup2 + dK3*sup3)) +
|
|
ginv12*((-2.*cdA212*chi + 3.*A12*dchi2)*sup2 +
|
|
(-2.*cdA213*chi + 3.*A13*dchi2)*sup3 -
|
|
2.*chi*((cdA112 + cdA211)*sup1 + cdA122*sup2 + cdA123*sup3) +
|
|
3.*((A12*dchi1 + A11*dchi2)*sup1 + dchi1*(A22*sup2 + A23*sup3))) +
|
|
ginv13*((-2.*cdA312*chi + 3.*A12*dchi3)*sup2 +
|
|
(-2.*cdA313*chi + 3.*A13*dchi3)*sup3 -
|
|
2.*chi*((cdA113 + cdA311)*sup1 + cdA123*sup2 + cdA133*sup3) +
|
|
3.*((A13*dchi1 + A11*dchi3)*sup1 + dchi1*(A23*sup2 + A33*sup3))) +
|
|
ginv23*((-2.*cdA322*chi + 3.*A22*dchi3)*sup2 +
|
|
(-2.*cdA323*chi + 3.*A23*dchi3)*sup3 -
|
|
2.*chi*((cdA213 + cdA312)*sup1 + cdA223*sup2 + cdA233*sup3) +
|
|
3.*((A13*dchi2 + A12*dchi3)*sup1 + dchi2*(A23*sup2 + A33*sup3))) +
|
|
(0.33333333333333333333*((dG11 - dGfromgdu11)*qud11 +
|
|
(dG12 - dGfromgdu12)*qud12 + (dG13 - dGfromgdu13)*qud13 +
|
|
(dG21 - dGfromgdu21)*qud21 + (dG22 - dGfromgdu22)*qud22 +
|
|
(dG23 - dGfromgdu23)*qud23 + (dG31 - dGfromgdu31)*qud31 +
|
|
(dG32 - dGfromgdu32)*qud32 + (dG33 - dGfromgdu33)*qud33) +
|
|
kappa1*((G1 - Gfromg1)*sdown1 + (G2 - Gfromg2)*sdown2 +
|
|
(G3 - Gfromg3)*sdown3) +
|
|
0.66666666666666666667*
|
|
((dGfromgdu21*sdown1 + dGfromgdu22*sdown2)*sup2 +
|
|
sdown3*((-dG13 + dGfromgdu13)*sup1 - dG23*sup2 - dG33*sup3) +
|
|
sdown1*((-dG11 + dGfromgdu11)*sup1 - dG21*sup2 - dG31*sup3 +
|
|
dGfromgdu31*sup3) +
|
|
sdown2*((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3 +
|
|
dGfromgdu32*sup3)))*pow2(chi) +
|
|
0.66666666666666666667*sup2*
|
|
(-(Rhat*(g12*sup1 + g23*sup3)) + dGfromgdu23*sdown3*pow2(chi)) +
|
|
sup3*((2.*psim4*Rf13 - 0.66666666666666666667*g13*Rhat)*sup1 +
|
|
0.66666666666666666667*dGfromgdu33*sdown3*pow2(chi)) +
|
|
(-2.*AA11 + A11*K)*pow2(sup1) -
|
|
2.*((AA23 + AA32)*sup2*sup3 + sup1*((AA12 + AA21)*sup2 + AA13*sup3) +
|
|
AA22*pow2(sup2) + AA33*pow2(sup3)))
|
|
;
|
|
|
|
rACsA1
|
|
=
|
|
(qud11*(lieA11 + alpha*chi*Rf11) +
|
|
qud21*(lieA12 + alpha*(-2.*AA12 + chi*Rf12)) +
|
|
qud31*(lieA13 + alpha*(-2.*AA13 + chi*Rf13)))*sup1 +
|
|
qud11*((-(cdda11*chi) + A11*alpha*K)*sup1 + lieA12*sup2 +
|
|
(A13*alpha*K + lieA13)*sup3 +
|
|
alpha*((-2.*AA21 + A12*K)*sup2 - 2.*AA31*sup3)) +
|
|
qud21*((-(cdda12*chi) + A12*alpha*K)*sup1 + lieA22*sup2 +
|
|
(A23*alpha*K + lieA23)*sup3 +
|
|
alpha*((-2.*AA22 + A22*K)*sup2 - 2.*AA32*sup3)) +
|
|
qud31*((-(cdda13*chi) + A13*alpha*K)*sup1 + lieA23*sup2 +
|
|
(A33*alpha*K + lieA33)*sup3 +
|
|
alpha*((-2.*AA23 + A23*K)*sup2 - 2.*AA33*sup3)) +
|
|
alpha*(ginv11*((-(cdA111*chi) + 1.5*A11*dchi1)*qud11 +
|
|
(-(cdA112*chi) + 1.5*A12*dchi1)*qud21 +
|
|
(-(cdA113*chi) + 1.5*A13*dchi1)*qud31) +
|
|
ginv22*((-(cdA212*chi) + 1.5*A12*dchi2)*qud11 +
|
|
(-(cdA222*chi) + 1.5*A22*dchi2)*qud21 +
|
|
(-(cdA223*chi) + 1.5*A23*dchi2)*qud31) +
|
|
ginv33*((-(cdA313*chi) + 1.5*A13*dchi3)*qud11 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud21 +
|
|
(-(cdA333*chi) + 1.5*A33*dchi3)*qud31) +
|
|
chi*((0.66666666666666666667*dK1 - dTheta1)*qud11 +
|
|
(0.66666666666666666667*dK2 - dTheta2)*qud21 +
|
|
(0.66666666666666666667*dK3 - dTheta3)*qud31) +
|
|
ginv12*((-(cdA212*chi) + 1.5*A12*dchi2)*qud21 +
|
|
(-(cdA213*chi) + 1.5*A13*dchi2)*qud31 -
|
|
chi*((cdA112 + cdA211)*qud11 + cdA122*qud21 + cdA123*qud31) +
|
|
1.5*((A12*dchi1 + A11*dchi2)*qud11 + dchi1*(A22*qud21 + A23*qud31))\
|
|
) + ginv13*((-(cdA312*chi) + 1.5*A12*dchi3)*qud21 +
|
|
(-(cdA313*chi) + 1.5*A13*dchi3)*qud31 -
|
|
chi*((cdA113 + cdA311)*qud11 + cdA123*qud21 + cdA133*qud31) +
|
|
1.5*((A13*dchi1 + A11*dchi3)*qud11 + dchi1*(A23*qud21 + A33*qud31))\
|
|
) + ginv23*((-(cdA322*chi) + 1.5*A22*dchi3)*qud21 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud31 -
|
|
chi*((cdA213 + cdA312)*qud11 + cdA223*qud21 + cdA233*qud31) +
|
|
1.5*((A13*dchi2 + A12*dchi3)*qud11 + dchi2*(A23*qud21 + A33*qud31))\
|
|
) + 0.5*(kappa1*((G1 - Gfromg1)*qdd11 + (G2 - Gfromg2)*qdd12 +
|
|
(G3 - Gfromg3)*qdd13) - dG13*qdd13*sup1 - dG21*qdd11*sup2 +
|
|
(dGfromgdu22*qdd12 - dG23*qdd13)*sup2 +
|
|
(dGfromgdu31*qdd11 + dGfromgdu32*qdd12 - dG33*qdd13)*sup3 +
|
|
qdd11*((-dG11 + dGfromgdu11)*sup1 + dGfromgdu21*sup2 -
|
|
dG31*sup3) + qdd12*
|
|
((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3))*pow2(chi) +
|
|
sup1*(-2.*AA11*qud11 + 0.5*dGfromgdu13*qdd13*pow2(chi))) +
|
|
sup2*(chi*(-(cdda12*qud11) - cdda22*qud21 - cdda23*qud31 +
|
|
alpha*qud21*Rf22) + alpha*
|
|
(chi*(qud11*Rf12 + qud31*Rf23) + 0.5*dGfromgdu23*qdd13*pow2(chi))) +
|
|
sup3*(chi*(-(cdda13*qud11) - cdda23*qud21 - cdda33*qud31 +
|
|
alpha*qud21*Rf23) + alpha*
|
|
(chi*(qud11*Rf13 + qud31*Rf33) + 0.5*dGfromgdu33*qdd13*pow2(chi)))
|
|
;
|
|
|
|
rACsA2
|
|
=
|
|
(qud12*(lieA11 + alpha*chi*Rf11) +
|
|
qud22*(lieA12 + alpha*(-2.*AA12 + chi*Rf12)) +
|
|
qud32*(lieA13 + alpha*(-2.*AA13 + chi*Rf13)))*sup1 +
|
|
qud12*((-(cdda11*chi) + A11*alpha*K)*sup1 + lieA12*sup2 +
|
|
(A13*alpha*K + lieA13)*sup3 +
|
|
alpha*((-2.*AA21 + A12*K)*sup2 - 2.*AA31*sup3)) +
|
|
qud22*((-(cdda12*chi) + A12*alpha*K)*sup1 + lieA22*sup2 +
|
|
(A23*alpha*K + lieA23)*sup3 +
|
|
alpha*((-2.*AA22 + A22*K)*sup2 - 2.*AA32*sup3)) +
|
|
qud32*((-(cdda13*chi) + A13*alpha*K)*sup1 + lieA23*sup2 +
|
|
(A33*alpha*K + lieA33)*sup3 +
|
|
alpha*((-2.*AA23 + A23*K)*sup2 - 2.*AA33*sup3)) +
|
|
alpha*(ginv11*((-(cdA111*chi) + 1.5*A11*dchi1)*qud12 +
|
|
(-(cdA112*chi) + 1.5*A12*dchi1)*qud22 +
|
|
(-(cdA113*chi) + 1.5*A13*dchi1)*qud32) +
|
|
ginv22*((-(cdA212*chi) + 1.5*A12*dchi2)*qud12 +
|
|
(-(cdA222*chi) + 1.5*A22*dchi2)*qud22 +
|
|
(-(cdA223*chi) + 1.5*A23*dchi2)*qud32) +
|
|
ginv33*((-(cdA313*chi) + 1.5*A13*dchi3)*qud12 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud22 +
|
|
(-(cdA333*chi) + 1.5*A33*dchi3)*qud32) +
|
|
chi*((0.66666666666666666667*dK1 - dTheta1)*qud12 +
|
|
(0.66666666666666666667*dK2 - dTheta2)*qud22 +
|
|
(0.66666666666666666667*dK3 - dTheta3)*qud32) +
|
|
ginv12*((-(cdA212*chi) + 1.5*A12*dchi2)*qud22 +
|
|
(-(cdA213*chi) + 1.5*A13*dchi2)*qud32 -
|
|
chi*((cdA112 + cdA211)*qud12 + cdA122*qud22 + cdA123*qud32) +
|
|
1.5*((A12*dchi1 + A11*dchi2)*qud12 + dchi1*(A22*qud22 + A23*qud32))\
|
|
) + ginv13*((-(cdA312*chi) + 1.5*A12*dchi3)*qud22 +
|
|
(-(cdA313*chi) + 1.5*A13*dchi3)*qud32 -
|
|
chi*((cdA113 + cdA311)*qud12 + cdA123*qud22 + cdA133*qud32) +
|
|
1.5*((A13*dchi1 + A11*dchi3)*qud12 + dchi1*(A23*qud22 + A33*qud32))\
|
|
) + ginv23*((-(cdA322*chi) + 1.5*A22*dchi3)*qud22 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud32 -
|
|
chi*((cdA213 + cdA312)*qud12 + cdA223*qud22 + cdA233*qud32) +
|
|
1.5*((A13*dchi2 + A12*dchi3)*qud12 + dchi2*(A23*qud22 + A33*qud32))\
|
|
) + 0.5*(kappa1*((G1 - Gfromg1)*qdd12 + (G2 - Gfromg2)*qdd22 +
|
|
(G3 - Gfromg3)*qdd23) - dG13*qdd23*sup1 - dG21*qdd12*sup2 +
|
|
(dGfromgdu22*qdd22 - dG23*qdd23)*sup2 +
|
|
(dGfromgdu31*qdd12 + dGfromgdu32*qdd22 - dG33*qdd23)*sup3 +
|
|
qdd12*((-dG11 + dGfromgdu11)*sup1 + dGfromgdu21*sup2 -
|
|
dG31*sup3) + qdd22*
|
|
((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3))*pow2(chi) +
|
|
sup1*(-2.*AA11*qud12 + 0.5*dGfromgdu13*qdd23*pow2(chi))) +
|
|
sup2*(chi*(-(cdda12*qud12) - cdda22*qud22 - cdda23*qud32 +
|
|
alpha*qud22*Rf22) + alpha*
|
|
(chi*(qud12*Rf12 + qud32*Rf23) + 0.5*dGfromgdu23*qdd23*pow2(chi))) +
|
|
sup3*(chi*(-(cdda13*qud12) - cdda23*qud22 - cdda33*qud32 +
|
|
alpha*qud22*Rf23) + alpha*
|
|
(chi*(qud12*Rf13 + qud32*Rf33) + 0.5*dGfromgdu33*qdd23*pow2(chi)))
|
|
;
|
|
|
|
rACsA3
|
|
=
|
|
(qud13*(lieA11 + alpha*chi*Rf11) +
|
|
qud23*(lieA12 + alpha*(-2.*AA12 + chi*Rf12)) +
|
|
qud33*(lieA13 + alpha*(-2.*AA13 + chi*Rf13)))*sup1 +
|
|
qud13*((-(cdda11*chi) + A11*alpha*K)*sup1 + lieA12*sup2 +
|
|
(A13*alpha*K + lieA13)*sup3 +
|
|
alpha*((-2.*AA21 + A12*K)*sup2 - 2.*AA31*sup3)) +
|
|
qud23*((-(cdda12*chi) + A12*alpha*K)*sup1 + lieA22*sup2 +
|
|
(A23*alpha*K + lieA23)*sup3 +
|
|
alpha*((-2.*AA22 + A22*K)*sup2 - 2.*AA32*sup3)) +
|
|
qud33*((-(cdda13*chi) + A13*alpha*K)*sup1 + lieA23*sup2 +
|
|
(A33*alpha*K + lieA33)*sup3 +
|
|
alpha*((-2.*AA23 + A23*K)*sup2 - 2.*AA33*sup3)) +
|
|
alpha*(ginv11*((-(cdA111*chi) + 1.5*A11*dchi1)*qud13 +
|
|
(-(cdA112*chi) + 1.5*A12*dchi1)*qud23 +
|
|
(-(cdA113*chi) + 1.5*A13*dchi1)*qud33) +
|
|
ginv22*((-(cdA212*chi) + 1.5*A12*dchi2)*qud13 +
|
|
(-(cdA222*chi) + 1.5*A22*dchi2)*qud23 +
|
|
(-(cdA223*chi) + 1.5*A23*dchi2)*qud33) +
|
|
ginv33*((-(cdA313*chi) + 1.5*A13*dchi3)*qud13 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud23 +
|
|
(-(cdA333*chi) + 1.5*A33*dchi3)*qud33) +
|
|
chi*((0.66666666666666666667*dK1 - dTheta1)*qud13 +
|
|
(0.66666666666666666667*dK2 - dTheta2)*qud23 +
|
|
(0.66666666666666666667*dK3 - dTheta3)*qud33) +
|
|
ginv12*((-(cdA212*chi) + 1.5*A12*dchi2)*qud23 +
|
|
(-(cdA213*chi) + 1.5*A13*dchi2)*qud33 -
|
|
chi*((cdA112 + cdA211)*qud13 + cdA122*qud23 + cdA123*qud33) +
|
|
1.5*((A12*dchi1 + A11*dchi2)*qud13 + dchi1*(A22*qud23 + A23*qud33))\
|
|
) + ginv13*((-(cdA312*chi) + 1.5*A12*dchi3)*qud23 +
|
|
(-(cdA313*chi) + 1.5*A13*dchi3)*qud33 -
|
|
chi*((cdA113 + cdA311)*qud13 + cdA123*qud23 + cdA133*qud33) +
|
|
1.5*((A13*dchi1 + A11*dchi3)*qud13 + dchi1*(A23*qud23 + A33*qud33))\
|
|
) + ginv23*((-(cdA322*chi) + 1.5*A22*dchi3)*qud23 +
|
|
(-(cdA323*chi) + 1.5*A23*dchi3)*qud33 -
|
|
chi*((cdA213 + cdA312)*qud13 + cdA223*qud23 + cdA233*qud33) +
|
|
1.5*((A13*dchi2 + A12*dchi3)*qud13 + dchi2*(A23*qud23 + A33*qud33))\
|
|
) + 0.5*(kappa1*((G1 - Gfromg1)*qdd13 + (G2 - Gfromg2)*qdd23 +
|
|
(G3 - Gfromg3)*qdd33) - dG13*qdd33*sup1 - dG21*qdd13*sup2 +
|
|
(dGfromgdu22*qdd23 - dG23*qdd33)*sup2 +
|
|
(dGfromgdu31*qdd13 + dGfromgdu32*qdd23 - dG33*qdd33)*sup3 +
|
|
qdd13*((-dG11 + dGfromgdu11)*sup1 + dGfromgdu21*sup2 -
|
|
dG31*sup3) + qdd23*
|
|
((-dG12 + dGfromgdu12)*sup1 - dG22*sup2 - dG32*sup3))*pow2(chi) +
|
|
sup1*(-2.*AA11*qud13 + 0.5*dGfromgdu13*qdd33*pow2(chi))) +
|
|
sup2*(chi*(-(cdda12*qud13) - cdda22*qud23 - cdda23*qud33 +
|
|
alpha*qud23*Rf22) + alpha*
|
|
(chi*(qud13*Rf12 + qud33*Rf23) + 0.5*dGfromgdu23*qdd33*pow2(chi))) +
|
|
sup3*(chi*(-(cdda13*qud13) - cdda23*qud23 - cdda33*qud33 +
|
|
alpha*qud23*Rf23) + alpha*
|
|
(chi*(qud13*Rf13 + qud33*Rf33) + 0.5*dGfromgdu33*qdd33*pow2(chi)))
|
|
;
|
|
|
|
rACABTF11
|
|
=
|
|
-(qPhysuudd1211*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3311*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1111*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1211*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1311*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2211*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2311*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1311 + AA22*qPhysuudd2211 + AA23*qPhysuudd2311 +
|
|
AA33*qPhysuudd3311 + qPhysuudd1111*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1311 +
|
|
(0.5*(A12*dchi1*qPhysuudd1111 + A23*dchi3*qPhysuudd3311))/chi)*
|
|
sup2) - qPhysuudd3311*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1211*sup3 +
|
|
qPhysuudd1211*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1311*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2211*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2311*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2311*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1211 + A13*dchi2*qPhysuudd1311)*sup2 +
|
|
(A12*dchi3*qPhysuudd1211 -
|
|
0.5*dchi1*(A13*qPhysuudd1111 + A23*qPhysuudd1211))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1211 -
|
|
dchi3*(A11*qPhysuudd1311 + A12*qPhysuudd2311) +
|
|
dchi1*(A22*qPhysuudd2211 + A33*qPhysuudd3311))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1311) -
|
|
A22*dchi3*qPhysuudd2311 +
|
|
dchi2*(A11*qPhysuudd1111 + A33*qPhysuudd3311))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1311) +
|
|
A13*(-(dchi2*qPhysuudd1211) + dchi3*qPhysuudd1311) +
|
|
dchi3*(A11*qPhysuudd1111 + A22*qPhysuudd2211) +
|
|
A23*(-(dchi2*qPhysuudd2211) + dchi3*qPhysuudd2311))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF12
|
|
=
|
|
-(qPhysuudd1212*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3312*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1112*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1212*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1312*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2212*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2312*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1312 + AA22*qPhysuudd2212 + AA23*qPhysuudd2312 +
|
|
AA33*qPhysuudd3312 + qPhysuudd1112*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1312 +
|
|
(0.5*(A12*dchi1*qPhysuudd1112 + A23*dchi3*qPhysuudd3312))/chi)*
|
|
sup2) - qPhysuudd3312*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1212*sup3 +
|
|
qPhysuudd1212*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1312*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2212*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2312*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2312*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1212 + A13*dchi2*qPhysuudd1312)*sup2 +
|
|
(A12*dchi3*qPhysuudd1212 -
|
|
0.5*dchi1*(A13*qPhysuudd1112 + A23*qPhysuudd1212))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1212 -
|
|
dchi3*(A11*qPhysuudd1312 + A12*qPhysuudd2312) +
|
|
dchi1*(A22*qPhysuudd2212 + A33*qPhysuudd3312))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1312) -
|
|
A22*dchi3*qPhysuudd2312 +
|
|
dchi2*(A11*qPhysuudd1112 + A33*qPhysuudd3312))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1312) +
|
|
A13*(-(dchi2*qPhysuudd1212) + dchi3*qPhysuudd1312) +
|
|
dchi3*(A11*qPhysuudd1112 + A22*qPhysuudd2212) +
|
|
A23*(-(dchi2*qPhysuudd2212) + dchi3*qPhysuudd2312))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF13
|
|
=
|
|
-(qPhysuudd1213*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3313*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1113*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1213*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1313*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2213*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2313*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1313 + AA22*qPhysuudd2213 + AA23*qPhysuudd2313 +
|
|
AA33*qPhysuudd3313 + qPhysuudd1113*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1313 +
|
|
(0.5*(A12*dchi1*qPhysuudd1113 + A23*dchi3*qPhysuudd3313))/chi)*
|
|
sup2) - qPhysuudd3313*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1213*sup3 +
|
|
qPhysuudd1213*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1313*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2213*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2313*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2313*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1213 + A13*dchi2*qPhysuudd1313)*sup2 +
|
|
(A12*dchi3*qPhysuudd1213 -
|
|
0.5*dchi1*(A13*qPhysuudd1113 + A23*qPhysuudd1213))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1213 -
|
|
dchi3*(A11*qPhysuudd1313 + A12*qPhysuudd2313) +
|
|
dchi1*(A22*qPhysuudd2213 + A33*qPhysuudd3313))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1313) -
|
|
A22*dchi3*qPhysuudd2313 +
|
|
dchi2*(A11*qPhysuudd1113 + A33*qPhysuudd3313))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1313) +
|
|
A13*(-(dchi2*qPhysuudd1213) + dchi3*qPhysuudd1313) +
|
|
dchi3*(A11*qPhysuudd1113 + A22*qPhysuudd2213) +
|
|
A23*(-(dchi2*qPhysuudd2213) + dchi3*qPhysuudd2313))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF22
|
|
=
|
|
-(qPhysuudd1222*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3322*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1122*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1222*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1322*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2222*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2322*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1322 + AA22*qPhysuudd2222 + AA23*qPhysuudd2322 +
|
|
AA33*qPhysuudd3322 + qPhysuudd1122*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1322 +
|
|
(0.5*(A12*dchi1*qPhysuudd1122 + A23*dchi3*qPhysuudd3322))/chi)*
|
|
sup2) - qPhysuudd3322*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1222*sup3 +
|
|
qPhysuudd1222*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1322*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2222*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2322*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2322*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1222 + A13*dchi2*qPhysuudd1322)*sup2 +
|
|
(A12*dchi3*qPhysuudd1222 -
|
|
0.5*dchi1*(A13*qPhysuudd1122 + A23*qPhysuudd1222))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1222 -
|
|
dchi3*(A11*qPhysuudd1322 + A12*qPhysuudd2322) +
|
|
dchi1*(A22*qPhysuudd2222 + A33*qPhysuudd3322))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1322) -
|
|
A22*dchi3*qPhysuudd2322 +
|
|
dchi2*(A11*qPhysuudd1122 + A33*qPhysuudd3322))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1322) +
|
|
A13*(-(dchi2*qPhysuudd1222) + dchi3*qPhysuudd1322) +
|
|
dchi3*(A11*qPhysuudd1122 + A22*qPhysuudd2222) +
|
|
A23*(-(dchi2*qPhysuudd2222) + dchi3*qPhysuudd2322))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF23
|
|
=
|
|
-(qPhysuudd1223*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3323*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1123*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1223*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1323*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2223*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2323*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1323 + AA22*qPhysuudd2223 + AA23*qPhysuudd2323 +
|
|
AA33*qPhysuudd3323 + qPhysuudd1123*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1323 +
|
|
(0.5*(A12*dchi1*qPhysuudd1123 + A23*dchi3*qPhysuudd3323))/chi)*
|
|
sup2) - qPhysuudd3323*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1223*sup3 +
|
|
qPhysuudd1223*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1323*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2223*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2323*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2323*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1223 + A13*dchi2*qPhysuudd1323)*sup2 +
|
|
(A12*dchi3*qPhysuudd1223 -
|
|
0.5*dchi1*(A13*qPhysuudd1123 + A23*qPhysuudd1223))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1223 -
|
|
dchi3*(A11*qPhysuudd1323 + A12*qPhysuudd2323) +
|
|
dchi1*(A22*qPhysuudd2223 + A33*qPhysuudd3323))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1323) -
|
|
A22*dchi3*qPhysuudd2323 +
|
|
dchi2*(A11*qPhysuudd1123 + A33*qPhysuudd3323))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1323) +
|
|
A13*(-(dchi2*qPhysuudd1223) + dchi3*qPhysuudd1323) +
|
|
dchi3*(A11*qPhysuudd1123 + A22*qPhysuudd2223) +
|
|
A23*(-(dchi2*qPhysuudd2223) + dchi3*qPhysuudd2323))*sup3))/chi)
|
|
;
|
|
|
|
rACABTF33
|
|
=
|
|
-(qPhysuudd1233*(2.*cdda12*chi + alpha*(AA21 + cdA112*sup1))) +
|
|
qPhysuudd3333*(-(cdda33*chi) + lieA33 +
|
|
alpha*(0.66666666666666666667*A33*K + cdA313*sup1 + cdA323*sup2)) +
|
|
qPhysuudd1133*(-(cdda11*chi) + lieA11 +
|
|
alpha*(-AA11 + 0.66666666666666666667*A11*K + cdA112*sup2 +
|
|
cdA113*sup3)) + qPhysuudd1233*
|
|
(2.*lieA12 + alpha*(-AA12 + 1.3333333333333333333*A12*K + cdA211*sup1 +
|
|
cdA122*sup2 + cdA123*sup3)) +
|
|
qPhysuudd1333*(2.*(-(cdda13*chi) + lieA13) +
|
|
alpha*(-AA31 + 1.3333333333333333333*A13*K + cdA311*sup1 +
|
|
cdA123*sup2 + cdA133*sup3)) +
|
|
qPhysuudd2233*(-(cdda22*chi) + lieA22 +
|
|
alpha*(0.66666666666666666667*A22*K + cdA212*sup1 + cdA223*sup3)) +
|
|
qPhysuudd2333*(2.*(-(cdda23*chi) + lieA23) +
|
|
alpha*(-AA32 + 1.3333333333333333333*A23*K + cdA213*sup1 +
|
|
cdA322*sup2 + cdA233*sup3)) -
|
|
alpha*(AA13*qPhysuudd1333 + AA22*qPhysuudd2233 + AA23*qPhysuudd2333 +
|
|
AA33*qPhysuudd3333 + qPhysuudd1133*(cdA211*sup2 + cdA311*sup3)) +
|
|
alpha*(-((2.*cdA213*qPhysuudd1333 +
|
|
(0.5*(A12*dchi1*qPhysuudd1133 + A23*dchi3*qPhysuudd3333))/chi)*
|
|
sup2) - qPhysuudd3333*((cdA133 + (0.5*A13*dchi3)/chi)*sup1 +
|
|
cdA233*sup2) - 2.*cdA312*qPhysuudd1233*sup3 +
|
|
qPhysuudd1233*((-cdA212 + (0.5*A12*dchi2)/chi)*sup2 + cdA213*sup3) +
|
|
qPhysuudd1333*((-cdA113 + (0.5*A13*dchi1)/chi)*sup1 + cdA312*sup2 -
|
|
cdA313*sup3) - qPhysuudd2233*
|
|
((cdA122 + (0.5*A12*dchi2)/chi)*sup1 + cdA322*sup3) +
|
|
qPhysuudd2333*((cdA312 + (A23*dchi1)/chi)*sup1 +
|
|
(0.5*A23*dchi2*sup2)/chi - cdA323*sup3) -
|
|
qPhysuudd2333*((2.*cdA123 + (0.5*A13*dchi2)/chi)*sup1 + cdA223*sup2 +
|
|
(0.5*A33*dchi2*sup3)/chi) +
|
|
((-0.5*A22*dchi1*qPhysuudd1233 + A13*dchi2*qPhysuudd1333)*sup2 +
|
|
(A12*dchi3*qPhysuudd1233 -
|
|
0.5*dchi1*(A13*qPhysuudd1133 + A23*qPhysuudd1233))*sup3 +
|
|
0.5*(((A12*dchi1 - A11*dchi2)*qPhysuudd1233 -
|
|
dchi3*(A11*qPhysuudd1333 + A12*qPhysuudd2333) +
|
|
dchi1*(A22*qPhysuudd2233 + A33*qPhysuudd3333))*sup1 +
|
|
(-((A23*dchi1 + A12*dchi3)*qPhysuudd1333) -
|
|
A22*dchi3*qPhysuudd2333 +
|
|
dchi2*(A11*qPhysuudd1133 + A33*qPhysuudd3333))*sup2 +
|
|
(-(A33*dchi1*qPhysuudd1333) +
|
|
A13*(-(dchi2*qPhysuudd1233) + dchi3*qPhysuudd1333) +
|
|
dchi3*(A11*qPhysuudd1133 + A22*qPhysuudd2233) +
|
|
A23*(-(dchi2*qPhysuudd2233) + dchi3*qPhysuudd2333))*sup3))/chi)
|
|
;
|
|
|
|
} /* function */
|
|
|
|
}
|