2187 lines
68 KiB
C
2187 lines
68 KiB
C
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// Z4c rhs without advection term
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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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#include "macrodef.fh"
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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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{
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#ifdef fortran1
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void z4c_rhs_point
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#endif
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#ifdef fortran2
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void Z4C_RHS_POINT
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#endif
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#ifdef fortran3
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void
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z4c_rhs_point_
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#endif
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(double &A11,
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double &A12,
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double &A13,
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double &A22,
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double &A23,
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double &A33,
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double &alpha,
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double &B1,
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double &B2,
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double &B3,
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double &beta1,
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double &beta2,
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double &beta3,
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double &chi,
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double &chiDivFloor,
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double &da1,
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double &dA111,
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double &dA112,
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double &dA113,
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double &dA122,
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double &dA123,
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double &dA133,
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double &da2,
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double &dA211,
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double &dA212,
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double &dA213,
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double &dA222,
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double &dA223,
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double &dA233,
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double &da3,
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double &dA311,
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double &dA312,
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double &dA313,
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double &dA322,
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double &dA323,
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double &dA333,
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double &db11,
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double &dB11,
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double &db12,
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double &dB12,
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double &db13,
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double &dB13,
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double &db21,
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double &dB21,
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double &db22,
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double &dB22,
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double &db23,
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double &dB23,
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double &db31,
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double &dB31,
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double &db32,
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double &dB32,
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double &db33,
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double &dB33,
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double &dchi1,
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double &dchi2,
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double &dchi3,
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double &dda11,
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double &dda12,
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double &dda13,
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double &dda22,
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double &dda23,
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double &dda33,
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double &ddb111,
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double &ddb112,
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double &ddb113,
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double &ddb121,
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double &ddb122,
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double &ddb123,
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double &ddb131,
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double &ddb132,
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double &ddb133,
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double &ddb221,
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double &ddb222,
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double &ddb223,
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double &ddb231,
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double &ddb232,
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double &ddb233,
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double &ddb331,
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double &ddb332,
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double &ddb333,
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double &ddchi11,
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double &ddchi12,
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double &ddchi13,
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double &ddchi22,
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double &ddchi23,
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double &ddchi33,
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double &deldelg1111,
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double &deldelg1112,
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double &deldelg1113,
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double &deldelg1122,
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double &deldelg1123,
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double &deldelg1133,
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double &deldelg1211,
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double &deldelg1212,
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double &deldelg1213,
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double &deldelg1222,
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double &deldelg1223,
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double &deldelg1233,
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double &deldelg1311,
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double &deldelg1312,
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double &deldelg1313,
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double &deldelg1322,
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double &deldelg1323,
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double &deldelg1333,
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double &deldelg2211,
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double &deldelg2212,
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double &deldelg2213,
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double &deldelg2222,
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double &deldelg2223,
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double &deldelg2233,
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double &deldelg2311,
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double &deldelg2312,
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double &deldelg2313,
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double &deldelg2322,
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double &deldelg2323,
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double &deldelg2333,
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double &deldelg3311,
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double &deldelg3312,
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double &deldelg3313,
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double &deldelg3322,
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double &deldelg3323,
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double &deldelg3333,
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double &delG11,
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double &delg111,
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double &delg112,
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double &delg113,
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double &delG12,
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double &delg122,
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double &delg123,
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double &delG13,
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double &delg133,
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double &delG21,
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double &delg211,
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double &delg212,
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double &delg213,
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double &delG22,
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double &delg222,
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double &delg223,
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double &delG23,
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double &delg233,
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double &delG31,
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double &delg311,
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double &delg312,
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double &delg313,
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double &delG32,
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double &delg322,
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double &delg323,
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double &delG33,
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double &delg333,
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double &dKhat1,
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double &dKhat2,
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double &dKhat3,
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double &dTheta1,
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double &dTheta2,
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double &dTheta3,
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double &G1,
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double &g11,
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double &g12,
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double &g13,
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double &G2,
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double &g22,
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double &g23,
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double &G3,
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double &g33,
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double &kappa1,
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double &kappa2,
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double &Khat,
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double &rA11,
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double &rA12,
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double &rA13,
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double &rA22,
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double &rA23,
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double &rA33,
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double &rchi,
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double &rG1,
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double &rg11,
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double &rg12,
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double &rg13,
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double &rG2,
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double &rg22,
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double &rg23,
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double &rG3,
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double &rg33,
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double &rKhat,
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double &rTheta,
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double &Theta)
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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 AA22;
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double AA23;
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double AA33;
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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 cAA;
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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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double chiguard;
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double chiguarded;
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double chipsipower;
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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 dGd11;
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double dGd12;
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double dGd13;
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double dGd21;
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double dGd22;
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double dGd23;
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double dGd31;
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double dGd32;
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double dGd33;
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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 divAinv1;
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double divAinv2;
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double divAinv3;
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double divbeta;
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double dK1;
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double dK2;
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double dK3;
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double dphi1;
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double dphi2;
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double dphi3;
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double dZ11;
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double DZ11;
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double dZ12;
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double DZ12;
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double dZ13;
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double DZ13;
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double dZ21;
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double DZ21;
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double dZ22;
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double DZ22;
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double dZ23;
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double DZ23;
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double dZ31;
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double DZ31;
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double dZ32;
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double DZ32;
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double dZ33;
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double DZ33;
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double dZinv11;
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double DZinv11;
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double dZinv12;
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double DZinv12;
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double dZinv13;
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double DZinv13;
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double dZinv21;
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double DZinv21;
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double dZinv22;
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double DZinv22;
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double dZinv23;
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double DZinv23;
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double dZinv31;
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double DZinv31;
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double dZinv32;
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double DZinv32;
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double dZinv33;
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double DZinv33;
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double DZsym11;
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double DZsym12;
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double DZsym13;
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double DZsym21;
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double DZsym22;
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double DZsym23;
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double DZsym31;
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double DZsym32;
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double DZsym33;
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double f;
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double ff;
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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 gammaF111;
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double gammaF112;
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double gammaF113;
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double gammaF121;
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double gammaF122;
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double gammaF123;
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double gammaF131;
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double gammaF132;
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double gammaF133;
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double gammaF211;
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double gammaF212;
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double gammaF213;
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double gammaF221;
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double gammaF222;
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double gammaF223;
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double gammaF231;
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double gammaF232;
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double gammaF233;
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double gammaF311;
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double gammaF312;
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double gammaF313;
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double gammaF321;
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double gammaF322;
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double gammaF323;
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double gammaF331;
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double gammaF332;
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double gammaF333;
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double Gd1;
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double Gd2;
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double Gd3;
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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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double Hhat;
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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 liechi;
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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 oochipsipower;
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double ootddivbeta1;
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double ootddivbeta2;
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double ootddivbeta3;
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double pseudolieG1;
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double pseudolieG2;
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double pseudolieG3;
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double psim4;
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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 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 totdivbeta;
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double trcdda;
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double trcddf;
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double trDZsym;
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double Z1;
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double Z2;
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double Z3;
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double Zinv1;
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double Zinv2;
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double Zinv3;
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chipsipower =
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-4.;
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K =
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Khat + 2. * Theta;
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dK1 =
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dKhat1 + 2. * dTheta1;
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dK2 =
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dKhat2 + 2. * dTheta2;
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dK3 =
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dKhat3 + 2. * dTheta3;
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detginv =
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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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ginv11 =
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detginv * (g22 * g33 - pow2(g23));
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ginv12 =
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detginv * (g13 * g23 - g12 * g33);
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ginv13 =
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detginv * (-(g13 * g22) + g12 * g23);
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ginv22 =
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detginv * (g11 * g33 - pow2(g13));
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ginv23 =
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detginv * (g12 * g13 - g11 * g23);
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ginv33 =
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detginv * (g11 * g22 - pow2(g12));
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dginv111 =
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-2. * (delg123 * ginv12 * ginv13 + ginv11 * (delg112 * ginv12 + delg113 * ginv13)) -
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delg111 * pow2(ginv11) - delg122 * pow2(ginv12) - delg133 * pow2(ginv13);
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dginv112 =
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-(ginv11 * (delg111 * ginv12 + delg112 * ginv22 + delg113 * ginv23)) -
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ginv12 * (delg113 * ginv13 + delg122 * ginv22 + delg123 * ginv23) -
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ginv13 * (delg123 * ginv22 + delg133 * ginv23) - delg112 * pow2(ginv12);
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dginv113 =
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-(ginv11 * (delg111 * ginv13 + delg112 * ginv23 + delg113 * ginv33)) -
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ginv12 * (delg112 * ginv13 + delg122 * ginv23 + delg123 * ginv33) -
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ginv13 * (delg123 * ginv23 + delg133 * ginv33) - delg113 * pow2(ginv13);
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dginv122 =
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-2. * (delg123 * ginv22 * ginv23 + ginv12 * (delg112 * ginv22 + delg113 * ginv23)) -
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delg111 * pow2(ginv12) - delg122 * pow2(ginv22) - delg133 * pow2(ginv23);
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dginv123 =
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-(ginv13 * (delg112 * ginv22 + delg113 * ginv23)) - delg133 * ginv23 * ginv33 -
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ginv12 * (delg111 * ginv13 + delg112 * ginv23 + delg113 * ginv33) -
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ginv22 * (delg122 * ginv23 + delg123 * ginv33) - delg123 * pow2(ginv23);
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dginv133 =
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-2. * (delg123 * ginv23 * ginv33 + ginv13 * (delg112 * ginv23 + delg113 * ginv33)) -
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delg111 * pow2(ginv13) - delg122 * pow2(ginv23) - delg133 * pow2(ginv33);
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dginv211 =
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-2. * (delg223 * ginv12 * ginv13 + ginv11 * (delg212 * ginv12 + delg213 * ginv13)) -
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delg211 * pow2(ginv11) - delg222 * pow2(ginv12) - delg233 * pow2(ginv13);
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dginv212 =
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-(ginv11 * (delg211 * ginv12 + delg212 * ginv22 + delg213 * ginv23)) -
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ginv12 * (delg213 * ginv13 + delg222 * ginv22 + delg223 * ginv23) -
|
|
ginv13 * (delg223 * ginv22 + delg233 * ginv23) - delg212 * pow2(ginv12);
|
|
|
|
dginv213 =
|
|
-(ginv11 * (delg211 * ginv13 + delg212 * ginv23 + delg213 * ginv33)) -
|
|
ginv12 * (delg212 * ginv13 + delg222 * ginv23 + delg223 * ginv33) -
|
|
ginv13 * (delg223 * ginv23 + delg233 * ginv33) - delg213 * pow2(ginv13);
|
|
|
|
dginv222 =
|
|
-2. * (delg223 * ginv22 * ginv23 + ginv12 * (delg212 * ginv22 + delg213 * ginv23)) -
|
|
delg211 * pow2(ginv12) - delg222 * pow2(ginv22) - delg233 * pow2(ginv23);
|
|
|
|
dginv223 =
|
|
-(ginv13 * (delg212 * ginv22 + delg213 * ginv23)) - delg233 * ginv23 * ginv33 -
|
|
ginv12 * (delg211 * ginv13 + delg212 * ginv23 + delg213 * ginv33) -
|
|
ginv22 * (delg222 * ginv23 + delg223 * ginv33) - delg223 * pow2(ginv23);
|
|
|
|
dginv233 =
|
|
-2. * (delg223 * ginv23 * ginv33 + ginv13 * (delg212 * ginv23 + delg213 * ginv33)) -
|
|
delg211 * pow2(ginv13) - delg222 * pow2(ginv23) - delg233 * pow2(ginv33);
|
|
|
|
dginv311 =
|
|
-2. * (delg323 * ginv12 * ginv13 + ginv11 * (delg312 * ginv12 + delg313 * ginv13)) -
|
|
delg311 * pow2(ginv11) - delg322 * pow2(ginv12) - delg333 * pow2(ginv13);
|
|
|
|
dginv312 =
|
|
-(ginv11 * (delg311 * ginv12 + delg312 * ginv22 + delg313 * ginv23)) -
|
|
ginv12 * (delg313 * ginv13 + delg322 * ginv22 + delg323 * ginv23) -
|
|
ginv13 * (delg323 * ginv22 + delg333 * ginv23) - delg312 * pow2(ginv12);
|
|
|
|
dginv313 =
|
|
-(ginv11 * (delg311 * ginv13 + delg312 * ginv23 + delg313 * ginv33)) -
|
|
ginv12 * (delg312 * ginv13 + delg322 * ginv23 + delg323 * ginv33) -
|
|
ginv13 * (delg323 * ginv23 + delg333 * ginv33) - delg313 * pow2(ginv13);
|
|
|
|
dginv322 =
|
|
-2. * (delg323 * ginv22 * ginv23 + ginv12 * (delg312 * ginv22 + delg313 * ginv23)) -
|
|
delg311 * pow2(ginv12) - delg322 * pow2(ginv22) - delg333 * pow2(ginv23);
|
|
|
|
dginv323 =
|
|
-(ginv13 * (delg312 * ginv22 + delg313 * ginv23)) - delg333 * ginv23 * ginv33 -
|
|
ginv12 * (delg311 * ginv13 + delg312 * ginv23 + delg313 * ginv33) -
|
|
ginv22 * (delg322 * ginv23 + delg323 * ginv33) - delg323 * pow2(ginv23);
|
|
|
|
dginv333 =
|
|
-2. * (delg323 * ginv23 * ginv33 + ginv13 * (delg312 * ginv23 + delg313 * ginv33)) -
|
|
delg311 * pow2(ginv13) - delg322 * pow2(ginv23) - delg333 * pow2(ginv33);
|
|
|
|
gammado111 =
|
|
0.5 * delg111;
|
|
|
|
gammado112 =
|
|
0.5 * delg211;
|
|
|
|
gammado113 =
|
|
0.5 * delg311;
|
|
|
|
gammado122 =
|
|
-0.5 * delg122 + delg212;
|
|
|
|
gammado123 =
|
|
0.5 * (-delg123 + delg213 + delg312);
|
|
|
|
gammado133 =
|
|
-0.5 * delg133 + delg313;
|
|
|
|
gammado211 =
|
|
delg112 - 0.5 * delg211;
|
|
|
|
gammado212 =
|
|
0.5 * delg122;
|
|
|
|
gammado213 =
|
|
0.5 * (delg123 - delg213 + delg312);
|
|
|
|
gammado222 =
|
|
0.5 * delg222;
|
|
|
|
gammado223 =
|
|
0.5 * delg322;
|
|
|
|
gammado233 =
|
|
-0.5 * delg233 + delg323;
|
|
|
|
gammado311 =
|
|
delg113 - 0.5 * delg311;
|
|
|
|
gammado312 =
|
|
0.5 * (delg123 + delg213 - delg312);
|
|
|
|
gammado313 =
|
|
0.5 * delg133;
|
|
|
|
gammado322 =
|
|
delg223 - 0.5 * delg322;
|
|
|
|
gammado323 =
|
|
0.5 * delg233;
|
|
|
|
gammado333 =
|
|
0.5 * delg333;
|
|
|
|
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;
|
|
|
|
R11 =
|
|
delG11 * g11 + delG12 * g12 + delG13 * g13 + gammado111 * Gfromg1 +
|
|
gammado112 * Gfromg2 + gammado113 * Gfromg3 +
|
|
(-0.5 * deldelg1111 + 3. * gamma111 * gammado111 +
|
|
2. * (gamma211 * gammado112 + gamma311 * gammado113) +
|
|
gamma211 * gammado211 + gamma311 * gammado311) *
|
|
ginv11 +
|
|
(-deldelg1211 + 3. * (gamma112 * gammado111 + gamma111 * gammado112) +
|
|
2. * (gamma212 * gammado112 + gamma312 * gammado113 +
|
|
gamma211 * gammado122 + gamma311 * gammado123) +
|
|
gamma212 * gammado211 +
|
|
gamma211 * gammado212 + gamma312 * gammado311 + gamma311 * gammado312) *
|
|
ginv12 +
|
|
(-deldelg1311 + 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 * deldelg2211 + 3. * gamma112 * gammado112 +
|
|
2. * (gamma212 * gammado122 + gamma312 * gammado123) +
|
|
gamma212 * gammado212 + gamma312 * gammado312) *
|
|
ginv22 +
|
|
(-deldelg2311 + 3. * (gamma113 * gammado112 + gamma112 * gammado113) +
|
|
2. * (gamma213 * gammado122 + (gamma212 + gamma313) * gammado123 +
|
|
gamma312 * gammado133) +
|
|
gamma213 * gammado212 + gamma212 * gammado213 +
|
|
gamma313 * gammado312 + gamma312 * gammado313) *
|
|
ginv23 +
|
|
(-0.5 * deldelg3311 + 3. * gamma113 * gammado113 +
|
|
2. * (gamma213 * gammado123 + gamma313 * gammado133) + gamma213 * gammado213 +
|
|
gamma313 * gammado313) *
|
|
ginv33;
|
|
|
|
R12 =
|
|
0.5 * (delG21 * g11 + (delG11 + delG22) * g12 + delG23 * g13 + delG12 * g22 +
|
|
delG13 * g23 + (gammado112 + gammado211) * Gfromg1 +
|
|
(gammado122 + gammado212) * Gfromg2 + (gammado123 + gammado213) * Gfromg3) +
|
|
(-0.5 * deldelg1112 + gamma112 * gammado111 +
|
|
(gamma111 + gamma212) * gammado112 + gamma312 * gammado113 +
|
|
gamma111 * gammado211 + 2. * gamma211 * gammado212 +
|
|
gamma311 * (gammado213 + gammado312)) *
|
|
ginv11 +
|
|
(-deldelg1212 + 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 +
|
|
(-deldelg1312 + 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 * deldelg2212 + gamma122 * gammado112 +
|
|
(gamma112 + gamma222) * gammado122 + gamma322 * gammado123 +
|
|
gamma112 * gammado212 + 2. * gamma212 * gammado222 +
|
|
gamma312 * (gammado223 + gammado322)) *
|
|
ginv22 +
|
|
(-deldelg2312 + 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 * deldelg3312 + gamma123 * gammado113 +
|
|
(gamma113 + gamma223) * gammado123 + gamma323 * gammado133 +
|
|
gamma113 * gammado213 + 2. * gamma213 * gammado223 +
|
|
gamma313 * (gammado233 + gammado323)) *
|
|
ginv33;
|
|
|
|
R13 =
|
|
0.5 * (delG31 * g11 + delG32 * g12 + (delG11 + delG33) * g13 + delG12 * g23 +
|
|
delG13 * g33 + (gammado113 + gammado311) * Gfromg1 +
|
|
(gammado123 + gammado312) * Gfromg2 + (gammado133 + gammado313) * Gfromg3) +
|
|
(-0.5 * deldelg1113 + gamma113 * gammado111 + gamma213 * gammado112 +
|
|
(gamma111 + gamma313) * gammado113 + gamma111 * gammado311 +
|
|
gamma211 * (gammado213 + gammado312) + 2. * gamma311 * gammado313) *
|
|
ginv11 +
|
|
(-deldelg1213 + 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 +
|
|
(-deldelg1313 + 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 * deldelg2213 + gamma123 * gammado112 + gamma223 * gammado122 +
|
|
(gamma112 + gamma323) * gammado123 + gamma112 * gammado312 +
|
|
gamma212 * (gammado223 + gammado322) + 2. * gamma312 * gammado323) *
|
|
ginv22 +
|
|
(-deldelg2313 + 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 * deldelg3313 + gamma133 * gammado113 + gamma233 * gammado123 +
|
|
(gamma113 + gamma333) * gammado133 + gamma113 * gammado313 +
|
|
gamma213 * (gammado233 + gammado323) + 2. * gamma313 * gammado333) *
|
|
ginv33;
|
|
|
|
R22 =
|
|
delG21 * g12 + delG22 * g22 + delG23 * g23 + gammado212 * Gfromg1 +
|
|
gammado222 * Gfromg2 + gammado223 * Gfromg3 +
|
|
(-0.5 * deldelg1122 + gamma112 * (gammado112 + 2. * gammado211) +
|
|
3. * gamma212 * gammado212 + gamma312 * (2. * gammado213 + gammado312)) *
|
|
ginv11 +
|
|
(-deldelg1222 + gamma122 * (gammado112 + 2. * gammado211) +
|
|
gamma112 * (gammado122 + 2. * gammado212) +
|
|
3. * (gamma222 * gammado212 + gamma212 * gammado222) +
|
|
2. * (gamma322 * gammado213 + gamma312 * gammado223) +
|
|
gamma322 * gammado312 + gamma312 * gammado322) *
|
|
ginv12 +
|
|
(-deldelg1322 + 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 * deldelg2222 + gamma122 * (gammado122 + 2. * gammado212) +
|
|
3. * gamma222 * gammado222 + gamma322 * (2. * gammado223 + gammado322)) *
|
|
ginv22 +
|
|
(-deldelg2322 + 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 * deldelg3322 + gamma123 * (gammado123 + 2. * gammado213) +
|
|
3. * gamma223 * gammado223 + gamma323 * (2. * gammado233 + gammado323)) *
|
|
ginv33;
|
|
|
|
R23 =
|
|
0.5 * (delG31 * g12 + delG21 * g13 + delG32 * g22 + (delG22 + delG33) * g23 +
|
|
delG23 * g33 + (gammado213 + gammado312) * Gfromg1 +
|
|
(gammado223 + gammado322) * Gfromg2 + (gammado233 + gammado323) * Gfromg3) +
|
|
(-0.5 * deldelg1123 + gamma113 * gammado211 + gamma213 * gammado212 +
|
|
(gamma212 + gamma313) * gammado213 +
|
|
gamma112 * (gammado113 + gammado311) + gamma212 * gammado312 +
|
|
2. * gamma312 * gammado313) *
|
|
ginv11 +
|
|
(-deldelg1223 + 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 +
|
|
(-deldelg1323 + 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 * deldelg2223 + gamma123 * gammado212 + gamma223 * gammado222 +
|
|
(gamma222 + gamma323) * gammado223 +
|
|
gamma122 * (gammado123 + gammado312) + gamma222 * gammado322 +
|
|
2. * gamma322 * gammado323) *
|
|
ginv22 +
|
|
(-deldelg2323 + 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 * deldelg3323 + gamma133 * gammado213 + gamma233 * gammado223 +
|
|
(gamma223 + gamma333) * gammado233 +
|
|
gamma123 * (gammado133 + gammado313) + gamma223 * gammado323 +
|
|
2. * gamma323 * gammado333) *
|
|
ginv33;
|
|
|
|
R33 =
|
|
delG31 * g13 + delG32 * g23 + delG33 * g33 + gammado313 * Gfromg1 +
|
|
gammado323 * Gfromg2 + gammado333 * Gfromg3 +
|
|
(-0.5 * deldelg1133 + gamma113 * (gammado113 + 2. * gammado311) +
|
|
gamma213 * (gammado213 + 2. * gammado312) + 3. * gamma313 * gammado313) *
|
|
ginv11 +
|
|
(-deldelg1233 + gamma123 * (gammado113 + 2. * gammado311) +
|
|
gamma113 * (gammado123 + 2. * gammado312) +
|
|
gamma223 * (gammado213 + 2. * gammado312) +
|
|
gamma213 * (gammado223 + 2. * gammado322) +
|
|
3. * (gamma323 * gammado313 + gamma313 * gammado323)) *
|
|
ginv12 +
|
|
(-deldelg1333 + gamma133 * (gammado113 + 2. * gammado311) +
|
|
gamma233 * (gammado213 + 2. * gammado312) +
|
|
gamma113 * (gammado133 + 2. * gammado313) +
|
|
gamma213 * (gammado233 + 2. * gammado323) +
|
|
3. * (gamma333 * gammado313 + gamma313 * gammado333)) *
|
|
ginv13 +
|
|
(-0.5 * deldelg2233 + gamma123 * (gammado123 + 2. * gammado312) +
|
|
gamma223 * (gammado223 + 2. * gammado322) + 3. * gamma323 * gammado323) *
|
|
ginv22 +
|
|
(-deldelg2333 + gamma133 * (gammado123 + 2. * gammado312) +
|
|
gamma123 * (gammado133 + 2. * gammado313) +
|
|
gamma233 * (gammado223 + 2. * gammado322) +
|
|
gamma223 * (gammado233 + 2. * gammado323) +
|
|
3. * (gamma333 * gammado323 + gamma323 * gammado333)) *
|
|
ginv23 +
|
|
(-0.5 * deldelg3333 + gamma133 * (gammado133 + 2. * gammado313) +
|
|
gamma233 * (gammado233 + 2. * gammado323) + 3. * gamma333 * gammado333) *
|
|
ginv33;
|
|
|
|
chiguard =
|
|
chiDivFloor;
|
|
|
|
chiguarded =
|
|
chi;
|
|
|
|
if (chiguarded < chiguard)
|
|
chiguarded = chiguard;
|
|
|
|
ff =
|
|
chiguarded;
|
|
|
|
oochipsipower =
|
|
1 / chipsipower;
|
|
|
|
f =
|
|
oochipsipower * log(ff);
|
|
|
|
psim4 =
|
|
exp(-4. * f);
|
|
|
|
df1 =
|
|
(dchi1 * oochipsipower) / chiguarded;
|
|
|
|
df2 =
|
|
(dchi2 * oochipsipower) / chiguarded;
|
|
|
|
df3 =
|
|
(dchi3 * oochipsipower) / chiguarded;
|
|
|
|
ddf11 =
|
|
(ddchi11 * oochipsipower) / chiguarded - chipsipower * pow2(df1);
|
|
|
|
ddf12 =
|
|
-(chipsipower * df1 * df2) + (ddchi12 * oochipsipower) / chiguarded;
|
|
|
|
ddf13 =
|
|
-(chipsipower * df1 * df3) + (ddchi13 * oochipsipower) / chiguarded;
|
|
|
|
ddf22 =
|
|
(ddchi22 * oochipsipower) / chiguarded - chipsipower * pow2(df2);
|
|
|
|
ddf23 =
|
|
-(chipsipower * df2 * df3) + (ddchi23 * oochipsipower) / chiguarded;
|
|
|
|
ddf33 =
|
|
(ddchi33 * oochipsipower) / chiguarded - 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);
|
|
|
|
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));
|
|
|
|
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));
|
|
|
|
AA33 =
|
|
2. * (A13 * (A23 * ginv12 + A33 * ginv13) + A23 * A33 * ginv23) + ginv11 * pow2(A13) +
|
|
ginv22 * pow2(A23) + ginv33 * pow2(A33);
|
|
|
|
cAA =
|
|
AA11 * ginv11 + AA22 * ginv22 + 2. * (AA12 * ginv12 + AA13 * ginv13 + AA23 * ginv23) +
|
|
AA33 * ginv33;
|
|
|
|
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);
|
|
|
|
divAinv1 =
|
|
(-1.5 * (Ainv11 * dchi1 + Ainv12 * dchi2 + Ainv13 * dchi3)) / chiguarded +
|
|
Ainv11 * gamma111 + Ainv22 * gamma122 +
|
|
2. * (Ainv12 * gamma112 + Ainv13 * gamma113 + Ainv23 * gamma123) +
|
|
Ainv33 * gamma133 - (0.66666666666666666667 * dKhat1 + 0.33333333333333333333 * dTheta1) * ginv11 -
|
|
(0.66666666666666666667 * dKhat2 + 0.33333333333333333333 * dTheta2) * ginv12 -
|
|
(0.66666666666666666667 * dKhat3 + 0.33333333333333333333 * dTheta3) * ginv13;
|
|
|
|
divAinv2 =
|
|
(-1.5 * (Ainv12 * dchi1 + Ainv22 * dchi2 + Ainv23 * dchi3)) / chiguarded +
|
|
Ainv11 * gamma211 + Ainv22 * gamma222 +
|
|
2. * (Ainv12 * gamma212 + Ainv13 * gamma213 + Ainv23 * gamma223) +
|
|
Ainv33 * gamma233 - (0.66666666666666666667 * dKhat1 + 0.33333333333333333333 * dTheta1) * ginv12 -
|
|
(0.66666666666666666667 * dKhat2 + 0.33333333333333333333 * dTheta2) * ginv22 -
|
|
(0.66666666666666666667 * dKhat3 + 0.33333333333333333333 * dTheta3) * ginv23;
|
|
|
|
divAinv3 =
|
|
(-1.5 * (Ainv13 * dchi1 + Ainv23 * dchi2 + Ainv33 * dchi3)) / chiguarded +
|
|
Ainv11 * gamma311 + Ainv22 * gamma322 +
|
|
2. * (Ainv12 * gamma312 + Ainv13 * gamma313 + Ainv23 * gamma323) +
|
|
Ainv33 * gamma333 - (0.66666666666666666667 * dKhat1 + 0.33333333333333333333 * dTheta1) * ginv13 -
|
|
(0.66666666666666666667 * dKhat2 + 0.33333333333333333333 * dTheta2) * ginv23 -
|
|
(0.66666666666666666667 * dKhat3 + 0.33333333333333333333 * dTheta3) * ginv33;
|
|
|
|
Rhat =
|
|
psim4 * (ginv11 * (R11 + Rphi11) + ginv22 * (R22 + Rphi22) +
|
|
2. * (ginv12 * (R12 + Rphi12) + ginv13 * (R13 + Rphi13) +
|
|
ginv23 * (R23 + Rphi23)) +
|
|
ginv33 * (R33 + Rphi33));
|
|
|
|
Hhat =
|
|
-cAA + Rhat + 0.66666666666666666667 * pow2(K);
|
|
|
|
divbeta =
|
|
db11 + db22 + db33;
|
|
|
|
totdivbeta =
|
|
0.66666666666666666667 * divbeta;
|
|
|
|
ootddivbeta1 =
|
|
0.33333333333333333333 * (ddb111 + ddb122 + ddb133);
|
|
|
|
ootddivbeta2 =
|
|
0.33333333333333333333 * (ddb121 + ddb222 + ddb233);
|
|
|
|
ootddivbeta3 =
|
|
0.33333333333333333333 * (ddb131 + ddb232 + ddb333);
|
|
|
|
lieg11 =
|
|
2. * (db11 * g11 + db12 * g12 + db13 * g13) - g11 * totdivbeta;
|
|
|
|
lieg12 =
|
|
db21 * g11 + db23 * g13 + db12 * g22 + db13 * g23 + g12 * (db11 + db22 - totdivbeta);
|
|
|
|
lieg13 =
|
|
db31 * g11 + db32 * g12 + db12 * g23 + db13 * g33 + g13 * (db11 + db33 - totdivbeta);
|
|
|
|
lieg22 =
|
|
2. * (db21 * g12 + db22 * g22 + db23 * g23) - g22 * totdivbeta;
|
|
|
|
lieg23 =
|
|
db31 * g12 + db21 * g13 + db32 * g22 + db23 * g33 + g23 * (db22 + db33 - totdivbeta);
|
|
|
|
lieg33 =
|
|
2. * (db31 * g13 + db32 * g23 + db33 * g33) - g33 * totdivbeta;
|
|
|
|
lieA11 =
|
|
2. * (A11 * db11 + A12 * db12 + A13 * db13) - A11 * totdivbeta;
|
|
|
|
lieA12 =
|
|
A22 * db12 + A23 * db13 + A11 * db21 + A13 * db23 + A12 * (db11 + db22 - totdivbeta);
|
|
|
|
lieA13 =
|
|
A23 * db12 + A33 * db13 + A11 * db31 + A12 * db32 + A13 * (db11 + db33 - totdivbeta);
|
|
|
|
lieA22 =
|
|
2. * (A12 * db21 + A22 * db22 + A23 * db23) - A22 * totdivbeta;
|
|
|
|
lieA23 =
|
|
A13 * db21 + A33 * db23 + A12 * db31 + A22 * db32 + A23 * (db22 + db33 - totdivbeta);
|
|
|
|
lieA33 =
|
|
2. * (A13 * db31 + A23 * db32 + A33 * db33) - A33 * totdivbeta;
|
|
|
|
liechi =
|
|
0.16666666666666666667 * chiguarded * chipsipower * divbeta;
|
|
|
|
pseudolieG1 =
|
|
-(db11 * Gfromg1) - db21 * Gfromg2 - db31 * Gfromg3 + ddb221 * ginv22 +
|
|
2. * ddb231 * ginv23 + ddb331 * ginv33 + ginv11 * (ddb111 + ootddivbeta1) +
|
|
ginv12 * (2. * ddb121 + ootddivbeta2) + ginv13 * (2. * ddb131 + ootddivbeta3) +
|
|
Gfromg1 * totdivbeta;
|
|
|
|
pseudolieG2 =
|
|
-(db12 * Gfromg1) - db22 * Gfromg2 - db32 * Gfromg3 + ddb112 * ginv11 +
|
|
2. * ddb132 * ginv13 + ddb332 * ginv33 + ginv12 * (2. * ddb122 + ootddivbeta1) +
|
|
ginv22 * (ddb222 + ootddivbeta2) + ginv23 * (2. * ddb232 + ootddivbeta3) +
|
|
Gfromg2 * totdivbeta;
|
|
|
|
pseudolieG3 =
|
|
-(db13 * Gfromg1) - db23 * Gfromg2 - db33 * Gfromg3 + ddb113 * ginv11 +
|
|
2. * ddb123 * ginv12 + ddb223 * ginv22 + ginv13 * (2. * ddb133 + ootddivbeta1) +
|
|
ginv23 * (2. * ddb233 + ootddivbeta2) + ginv33 * (ddb333 + ootddivbeta3) +
|
|
Gfromg3 * totdivbeta;
|
|
|
|
rg11 =
|
|
-2. * A11 * alpha + lieg11;
|
|
|
|
rg12 =
|
|
-2. * A12 * alpha + lieg12;
|
|
|
|
rg13 =
|
|
-2. * A13 * alpha + lieg13;
|
|
|
|
rg22 =
|
|
-2. * A22 * alpha + lieg22;
|
|
|
|
rg23 =
|
|
-2. * A23 * alpha + lieg23;
|
|
|
|
rg33 =
|
|
-2. * A33 * alpha + lieg33;
|
|
|
|
rA11 =
|
|
lieA11 + alpha * (-2. * AA11 + A11 * K + psim4 * R11 - 0.33333333333333333333 * g11 * Rhat) + psim4 * (-cdda11 + alpha * Rphi11) +
|
|
0.33333333333333333333 * g11 * trcdda;
|
|
|
|
rA12 =
|
|
lieA12 + alpha * (-2. * AA12 + A12 * K + psim4 * R12 - 0.33333333333333333333 * g12 * Rhat) + psim4 * (-cdda12 + alpha * Rphi12) +
|
|
0.33333333333333333333 * g12 * trcdda;
|
|
|
|
rA13 =
|
|
lieA13 + alpha * (-2. * AA13 + A13 * K + psim4 * R13 - 0.33333333333333333333 * g13 * Rhat) + psim4 * (-cdda13 + alpha * Rphi13) +
|
|
0.33333333333333333333 * g13 * trcdda;
|
|
|
|
rA22 =
|
|
lieA22 + alpha * (-2. * AA22 + A22 * K + psim4 * R22 - 0.33333333333333333333 * g22 * Rhat) + psim4 * (-cdda22 + alpha * Rphi22) +
|
|
0.33333333333333333333 * g22 * trcdda;
|
|
|
|
rA23 =
|
|
lieA23 + alpha * (-2. * AA23 + A23 * K + psim4 * R23 - 0.33333333333333333333 * g23 * Rhat) + psim4 * (-cdda23 + alpha * Rphi23) +
|
|
0.33333333333333333333 * g23 * trcdda;
|
|
|
|
rA33 =
|
|
lieA33 + alpha * (-2. * AA33 + A33 * K + psim4 * R33 - 0.33333333333333333333 * g33 * Rhat) + psim4 * (-cdda33 + alpha * Rphi33) +
|
|
0.33333333333333333333 * g33 * trcdda;
|
|
|
|
rG1 =
|
|
-2. * (Ainv11 * da1 + Ainv12 * da2 + Ainv13 * da3) +
|
|
alpha * (2. * divAinv1 + 2. * (-G1 + Gfromg1) * kappa1) + pseudolieG1;
|
|
|
|
rG2 =
|
|
-2. * (Ainv12 * da1 + Ainv22 * da2 + Ainv23 * da3) +
|
|
alpha * (2. * divAinv2 + 2. * (-G2 + Gfromg2) * kappa1) + pseudolieG2;
|
|
|
|
rG3 =
|
|
-2. * (Ainv13 * da1 + Ainv23 * da2 + Ainv33 * da3) +
|
|
alpha * (2. * divAinv3 + 2. * (-G3 + Gfromg3) * kappa1) + pseudolieG3;
|
|
|
|
rKhat =
|
|
-trcdda + alpha * (cAA + kappa1 * (Theta - kappa2 * Theta) +
|
|
0.33333333333333333333 * pow2(K));
|
|
|
|
rchi =
|
|
-0.16666666666666666667 * alpha * chiguarded * chipsipower * K + liechi;
|
|
|
|
rTheta =
|
|
alpha * (0.5 * Hhat - kappa1 * (2. + kappa2) * Theta);
|
|
|
|
#if 0
|
|
// this part is for CCZ4
|
|
dginv111
|
|
=
|
|
-2.*(delg123*ginv12*ginv13 + ginv11*(delg112*ginv12 + delg113*ginv13)) -
|
|
delg111*pow2(ginv11) - delg122*pow2(ginv12) - delg133*pow2(ginv13)
|
|
;
|
|
|
|
dginv112
|
|
=
|
|
-(ginv11*(delg111*ginv12 + delg112*ginv22 + delg113*ginv23)) -
|
|
ginv12*(delg113*ginv13 + delg122*ginv22 + delg123*ginv23) -
|
|
ginv13*(delg123*ginv22 + delg133*ginv23) - delg112*pow2(ginv12)
|
|
;
|
|
|
|
dginv113
|
|
=
|
|
-(ginv11*(delg111*ginv13 + delg112*ginv23 + delg113*ginv33)) -
|
|
ginv12*(delg112*ginv13 + delg122*ginv23 + delg123*ginv33) -
|
|
ginv13*(delg123*ginv23 + delg133*ginv33) - delg113*pow2(ginv13)
|
|
;
|
|
|
|
dginv122
|
|
=
|
|
-2.*(delg123*ginv22*ginv23 + ginv12*(delg112*ginv22 + delg113*ginv23)) -
|
|
delg111*pow2(ginv12) - delg122*pow2(ginv22) - delg133*pow2(ginv23)
|
|
;
|
|
|
|
dginv123
|
|
=
|
|
-(ginv13*(delg112*ginv22 + delg113*ginv23)) - delg133*ginv23*ginv33 -
|
|
ginv12*(delg111*ginv13 + delg112*ginv23 + delg113*ginv33) -
|
|
ginv22*(delg122*ginv23 + delg123*ginv33) - delg123*pow2(ginv23)
|
|
;
|
|
|
|
dginv133
|
|
=
|
|
-2.*(delg123*ginv23*ginv33 + ginv13*(delg112*ginv23 + delg113*ginv33)) -
|
|
delg111*pow2(ginv13) - delg122*pow2(ginv23) - delg133*pow2(ginv33)
|
|
;
|
|
|
|
dginv211
|
|
=
|
|
-2.*(delg223*ginv12*ginv13 + ginv11*(delg212*ginv12 + delg213*ginv13)) -
|
|
delg211*pow2(ginv11) - delg222*pow2(ginv12) - delg233*pow2(ginv13)
|
|
;
|
|
|
|
dginv212
|
|
=
|
|
-(ginv11*(delg211*ginv12 + delg212*ginv22 + delg213*ginv23)) -
|
|
ginv12*(delg213*ginv13 + delg222*ginv22 + delg223*ginv23) -
|
|
ginv13*(delg223*ginv22 + delg233*ginv23) - delg212*pow2(ginv12)
|
|
;
|
|
|
|
dginv213
|
|
=
|
|
-(ginv11*(delg211*ginv13 + delg212*ginv23 + delg213*ginv33)) -
|
|
ginv12*(delg212*ginv13 + delg222*ginv23 + delg223*ginv33) -
|
|
ginv13*(delg223*ginv23 + delg233*ginv33) - delg213*pow2(ginv13)
|
|
;
|
|
|
|
dginv222
|
|
=
|
|
-2.*(delg223*ginv22*ginv23 + ginv12*(delg212*ginv22 + delg213*ginv23)) -
|
|
delg211*pow2(ginv12) - delg222*pow2(ginv22) - delg233*pow2(ginv23)
|
|
;
|
|
|
|
dginv223
|
|
=
|
|
-(ginv13*(delg212*ginv22 + delg213*ginv23)) - delg233*ginv23*ginv33 -
|
|
ginv12*(delg211*ginv13 + delg212*ginv23 + delg213*ginv33) -
|
|
ginv22*(delg222*ginv23 + delg223*ginv33) - delg223*pow2(ginv23)
|
|
;
|
|
|
|
dginv233
|
|
=
|
|
-2.*(delg223*ginv23*ginv33 + ginv13*(delg212*ginv23 + delg213*ginv33)) -
|
|
delg211*pow2(ginv13) - delg222*pow2(ginv23) - delg233*pow2(ginv33)
|
|
;
|
|
|
|
dginv311
|
|
=
|
|
-2.*(delg323*ginv12*ginv13 + ginv11*(delg312*ginv12 + delg313*ginv13)) -
|
|
delg311*pow2(ginv11) - delg322*pow2(ginv12) - delg333*pow2(ginv13)
|
|
;
|
|
|
|
dginv312
|
|
=
|
|
-(ginv11*(delg311*ginv12 + delg312*ginv22 + delg313*ginv23)) -
|
|
ginv12*(delg313*ginv13 + delg322*ginv22 + delg323*ginv23) -
|
|
ginv13*(delg323*ginv22 + delg333*ginv23) - delg312*pow2(ginv12)
|
|
;
|
|
|
|
dginv313
|
|
=
|
|
-(ginv11*(delg311*ginv13 + delg312*ginv23 + delg313*ginv33)) -
|
|
ginv12*(delg312*ginv13 + delg322*ginv23 + delg323*ginv33) -
|
|
ginv13*(delg323*ginv23 + delg333*ginv33) - delg313*pow2(ginv13)
|
|
;
|
|
|
|
dginv322
|
|
=
|
|
-2.*(delg323*ginv22*ginv23 + ginv12*(delg312*ginv22 + delg313*ginv23)) -
|
|
delg311*pow2(ginv12) - delg322*pow2(ginv22) - delg333*pow2(ginv23)
|
|
;
|
|
|
|
dginv323
|
|
=
|
|
-(ginv13*(delg312*ginv22 + delg313*ginv23)) - delg333*ginv23*ginv33 -
|
|
ginv12*(delg311*ginv13 + delg312*ginv23 + delg313*ginv33) -
|
|
ginv22*(delg322*ginv23 + delg323*ginv33) - delg323*pow2(ginv23)
|
|
;
|
|
|
|
dginv333
|
|
=
|
|
-2.*(delg323*ginv23*ginv33 + ginv13*(delg312*ginv23 + delg313*ginv33)) -
|
|
delg311*pow2(ginv13) - delg322*pow2(ginv23) - delg333*pow2(ginv33)
|
|
;
|
|
|
|
dphi1
|
|
=
|
|
(-0.25*dchi1)/chiguarded
|
|
;
|
|
|
|
dphi2
|
|
=
|
|
(-0.25*dchi2)/chiguarded
|
|
;
|
|
|
|
dphi3
|
|
=
|
|
(-0.25*dchi3)/chiguarded
|
|
;
|
|
|
|
gammaF111
|
|
=
|
|
gamma111 + dphi1*(4. - 2.*g11*ginv11) - 2.*g11*(dphi2*ginv12 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF112
|
|
=
|
|
gamma112 + dphi2*(2. - 2.*g12*ginv12) - 2.*g12*(dphi1*ginv11 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF113
|
|
=
|
|
gamma113 - 2.*g13*(dphi1*ginv11 + dphi2*ginv12) + dphi3*(2. - 2.*g13*ginv13)
|
|
;
|
|
|
|
gammaF121
|
|
=
|
|
gamma112 + dphi2*(2. - 2.*g12*ginv12) - 2.*g12*(dphi1*ginv11 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF122
|
|
=
|
|
gamma122 - 2.*g22*(dphi1*ginv11 + dphi2*ginv12 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF123
|
|
=
|
|
gamma123 - 2.*g23*(dphi1*ginv11 + dphi2*ginv12 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF131
|
|
=
|
|
gamma113 - 2.*g13*(dphi1*ginv11 + dphi2*ginv12) + dphi3*(2. - 2.*g13*ginv13)
|
|
;
|
|
|
|
gammaF132
|
|
=
|
|
gamma123 - 2.*g23*(dphi1*ginv11 + dphi2*ginv12 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF133
|
|
=
|
|
gamma133 - 2.*g33*(dphi1*ginv11 + dphi2*ginv12 + dphi3*ginv13)
|
|
;
|
|
|
|
gammaF211
|
|
=
|
|
gamma211 - 2.*g11*(dphi1*ginv12 + dphi2*ginv22 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF212
|
|
=
|
|
gamma212 + dphi1*(2. - 2.*g12*ginv12) - 2.*g12*(dphi2*ginv22 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF213
|
|
=
|
|
gamma213 - 2.*g13*(dphi1*ginv12 + dphi2*ginv22 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF221
|
|
=
|
|
gamma212 + dphi1*(2. - 2.*g12*ginv12) - 2.*g12*(dphi2*ginv22 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF222
|
|
=
|
|
gamma222 + dphi2*(4. - 2.*g22*ginv22) - 2.*g22*(dphi1*ginv12 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF223
|
|
=
|
|
gamma223 - 2.*g23*(dphi1*ginv12 + dphi2*ginv22) + dphi3*(2. - 2.*g23*ginv23)
|
|
;
|
|
|
|
gammaF231
|
|
=
|
|
gamma213 - 2.*g13*(dphi1*ginv12 + dphi2*ginv22 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF232
|
|
=
|
|
gamma223 - 2.*g23*(dphi1*ginv12 + dphi2*ginv22) + dphi3*(2. - 2.*g23*ginv23)
|
|
;
|
|
|
|
gammaF233
|
|
=
|
|
gamma233 - 2.*g33*(dphi1*ginv12 + dphi2*ginv22 + dphi3*ginv23)
|
|
;
|
|
|
|
gammaF311
|
|
=
|
|
gamma311 - 2.*g11*(dphi1*ginv13 + dphi2*ginv23 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF312
|
|
=
|
|
gamma312 - 2.*g12*(dphi1*ginv13 + dphi2*ginv23 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF313
|
|
=
|
|
gamma313 + dphi1*(2. - 2.*g13*ginv13) - 2.*g13*(dphi2*ginv23 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF321
|
|
=
|
|
gamma312 - 2.*g12*(dphi1*ginv13 + dphi2*ginv23 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF322
|
|
=
|
|
gamma322 - 2.*g22*(dphi1*ginv13 + dphi2*ginv23 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF323
|
|
=
|
|
gamma323 + dphi2*(2. - 2.*g23*ginv23) - 2.*g23*(dphi1*ginv13 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF331
|
|
=
|
|
gamma313 + dphi1*(2. - 2.*g13*ginv13) - 2.*g13*(dphi2*ginv23 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF332
|
|
=
|
|
gamma323 + dphi2*(2. - 2.*g23*ginv23) - 2.*g23*(dphi1*ginv13 + dphi3*ginv33)
|
|
;
|
|
|
|
gammaF333
|
|
=
|
|
gamma333 - 2.*g33*(dphi1*ginv13 + dphi2*ginv23) + dphi3*(4. - 2.*g33*ginv33)
|
|
;
|
|
|
|
Gd1
|
|
=
|
|
ginv11*((2.*delg112 + delg211)*ginv12 + (2.*delg113 + delg311)*ginv13 +
|
|
delg212*ginv22 + (delg213 + delg312)*ginv23 + delg313*ginv33) +
|
|
ginv12*((2.*delg123 + delg213 + delg312)*ginv13 + delg222*ginv22 +
|
|
(delg223 + delg322)*ginv23 + delg323*ginv33) +
|
|
ginv13*(delg223*ginv22 + (delg233 + delg323)*ginv23 + delg333*ginv33) +
|
|
delg111*pow2(ginv11) + (delg122 + delg212)*pow2(ginv12) +
|
|
(delg133 + delg313)*pow2(ginv13)
|
|
;
|
|
|
|
Gd2
|
|
=
|
|
ginv11*(delg111*ginv12 + delg112*ginv22 + delg113*ginv23) +
|
|
ginv13*((delg123 + delg312)*ginv22 + (delg133 + delg313)*ginv23) +
|
|
delg333*ginv23*ginv33 + ginv12*
|
|
((delg113 + delg311)*ginv13 + (delg122 + 2.*delg212)*ginv22 +
|
|
(delg123 + 2.*delg213 + delg312)*ginv23 + delg313*ginv33) +
|
|
ginv22*((2.*delg223 + delg322)*ginv23 + delg323*ginv33) +
|
|
(delg112 + delg211)*pow2(ginv12) + delg222*pow2(ginv22) +
|
|
(delg233 + delg323)*pow2(ginv23)
|
|
;
|
|
|
|
Gd3
|
|
=
|
|
(delg233 + 2.*delg323)*ginv23*ginv33 +
|
|
ginv11*(delg111*ginv13 + delg112*ginv23 + delg113*ginv33) +
|
|
ginv12*((delg112 + delg211)*ginv13 + (delg122 + delg212)*ginv23 +
|
|
(delg123 + delg213)*ginv33) +
|
|
ginv22*(delg222*ginv23 + delg223*ginv33) +
|
|
ginv13*(delg212*ginv22 + (delg123 + delg213 + 2.*delg312)*ginv23 +
|
|
(delg133 + 2.*delg313)*ginv33) + (delg113 + delg311)*pow2(ginv13) +
|
|
(delg223 + delg322)*pow2(ginv23) + delg333*pow2(ginv33)
|
|
;
|
|
|
|
dGd11
|
|
=
|
|
(delg212*dginv111 + delg222*dginv112 + delg223*dginv113)*ginv22 +
|
|
((delg213 + delg312)*dginv111 + (delg223 + delg322)*dginv112 +
|
|
(delg233 + delg323)*dginv113)*ginv23 +
|
|
(delg313*dginv111 + delg323*dginv112 + delg333*dginv113)*ginv33 +
|
|
ginv11*(delg211*dginv112 + delg311*dginv113 +
|
|
2.*(delg111*dginv111 + delg112*dginv112 + delg113*dginv113) +
|
|
delg212*dginv122 + (delg213 + delg312)*dginv123 + delg313*dginv133 +
|
|
(2.*deldelg1112 + deldelg1211)*ginv12 +
|
|
(2.*deldelg1113 + deldelg1311)*ginv13 + deldelg1212*ginv22 +
|
|
(deldelg1213 + deldelg1312)*ginv23 + deldelg1313*ginv33) +
|
|
ginv12*((2.*delg112 + delg211)*dginv111 + (delg213 + delg312)*dginv113 +
|
|
2.*((delg122 + delg212)*dginv112 + delg123*dginv113) +
|
|
delg222*dginv122 + (delg223 + delg322)*dginv123 + delg323*dginv133 +
|
|
(2.*deldelg1123 + deldelg1213 + deldelg1312)*ginv13 +
|
|
deldelg1222*ginv22 + (deldelg1223 + deldelg1322)*ginv23 +
|
|
deldelg1323*ginv33) + ginv13*
|
|
((2.*delg113 + delg311)*dginv111 +
|
|
(2.*delg123 + delg213 + delg312)*dginv112 +
|
|
2.*(delg133 + delg313)*dginv113 + delg223*dginv122 +
|
|
(delg233 + delg323)*dginv123 + delg333*dginv133 + deldelg1223*ginv22 +
|
|
(deldelg1233 + deldelg1323)*ginv23 + deldelg1333*ginv33) +
|
|
deldelg1111*pow2(ginv11) + (deldelg1122 + deldelg1212)*pow2(ginv12) +
|
|
(deldelg1133 + deldelg1313)*pow2(ginv13)
|
|
;
|
|
|
|
dGd12
|
|
=
|
|
ginv11*(delg111*dginv112 + delg112*dginv122 + delg113*dginv123 +
|
|
deldelg1111*ginv12 + deldelg1112*ginv22 + deldelg1113*ginv23) +
|
|
ginv13*((delg113 + delg311)*dginv112 + (delg123 + delg312)*dginv122 +
|
|
(delg133 + delg313)*dginv123 + (deldelg1123 + deldelg1312)*ginv22 +
|
|
(deldelg1133 + deldelg1313)*ginv23) +
|
|
(delg313*dginv112 + delg323*dginv122 + delg333*dginv123)*ginv33 +
|
|
ginv12*(delg111*dginv111 + (delg113 + delg311)*dginv113 +
|
|
delg122*dginv122 + (delg123 + delg312)*dginv123 +
|
|
2.*((delg112 + delg211)*dginv112 + delg212*dginv122 +
|
|
delg213*dginv123) + delg313*dginv133 +
|
|
(deldelg1113 + deldelg1311)*ginv13 +
|
|
(deldelg1122 + 2.*deldelg1212)*ginv22 +
|
|
(deldelg1123 + 2.*deldelg1213 + deldelg1312)*ginv23 +
|
|
deldelg1313*ginv33) + ginv22*
|
|
(delg112*dginv111 + (delg122 + 2.*delg212)*dginv112 +
|
|
(delg123 + delg312)*dginv113 + delg322*dginv123 +
|
|
2.*(delg222*dginv122 + delg223*dginv123) + delg323*dginv133 +
|
|
(2.*deldelg1223 + deldelg1322)*ginv23 + deldelg1323*ginv33) +
|
|
ginv23*(delg113*dginv111 + (delg123 + 2.*delg213 + delg312)*dginv112 +
|
|
(delg133 + delg313)*dginv113 + (2.*delg223 + delg322)*dginv122 +
|
|
2.*(delg233 + delg323)*dginv123 + delg333*dginv133 + deldelg1333*ginv33\
|
|
) + (deldelg1112 + deldelg1211)*pow2(ginv12) + deldelg1222*pow2(ginv22) +
|
|
(deldelg1233 + deldelg1323)*pow2(ginv23)
|
|
;
|
|
|
|
dGd13
|
|
=
|
|
(delg113*dginv111 + (delg123 + delg213)*dginv112 +
|
|
(delg133 + 2.*delg313)*dginv113 + delg223*dginv122 +
|
|
(delg233 + 2.*delg323)*dginv123 + 2.*delg333*dginv133)*ginv33 +
|
|
ginv11*(delg111*dginv113 + delg112*dginv123 + delg113*dginv133 +
|
|
deldelg1111*ginv13 + deldelg1112*ginv23 + deldelg1113*ginv33) +
|
|
ginv12*((delg112 + delg211)*dginv113 + (delg122 + delg212)*dginv123 +
|
|
(delg123 + delg213)*dginv133 + (deldelg1112 + deldelg1211)*ginv13 +
|
|
(deldelg1122 + deldelg1212)*ginv23 + (deldelg1123 + deldelg1213)*ginv33\
|
|
) + ginv22*(delg212*dginv113 + delg222*dginv123 + delg223*dginv133 +
|
|
deldelg1222*ginv23 + deldelg1223*ginv33) +
|
|
ginv13*(delg111*dginv111 + (delg112 + delg211)*dginv112 +
|
|
delg212*dginv122 + (delg123 + delg213)*dginv123 + delg133*dginv133 +
|
|
2.*((delg113 + delg311)*dginv113 + delg312*dginv123 +
|
|
delg313*dginv133) + deldelg1212*ginv22 +
|
|
(deldelg1123 + deldelg1213 + 2.*deldelg1312)*ginv23 +
|
|
(deldelg1133 + 2.*deldelg1313)*ginv33) +
|
|
ginv23*(delg112*dginv111 + (delg122 + delg212)*dginv112 +
|
|
(delg123 + delg213 + 2.*delg312)*dginv113 + delg222*dginv122 +
|
|
delg233*dginv133 + 2.*((delg223 + delg322)*dginv123 +
|
|
delg323*dginv133) + (deldelg1233 + 2.*deldelg1323)*ginv33) +
|
|
(deldelg1113 + deldelg1311)*pow2(ginv13) +
|
|
(deldelg1223 + deldelg1322)*pow2(ginv23) + deldelg1333*pow2(ginv33)
|
|
;
|
|
|
|
dGd21
|
|
=
|
|
(delg212*dginv211 + delg222*dginv212 + delg223*dginv213)*ginv22 +
|
|
((delg213 + delg312)*dginv211 + (delg223 + delg322)*dginv212 +
|
|
(delg233 + delg323)*dginv213)*ginv23 +
|
|
(delg313*dginv211 + delg323*dginv212 + delg333*dginv213)*ginv33 +
|
|
ginv11*(delg211*dginv212 + delg311*dginv213 +
|
|
2.*(delg111*dginv211 + delg112*dginv212 + delg113*dginv213) +
|
|
delg212*dginv222 + (delg213 + delg312)*dginv223 + delg313*dginv233 +
|
|
(2.*deldelg1212 + deldelg2211)*ginv12 +
|
|
(2.*deldelg1213 + deldelg2311)*ginv13 + deldelg2212*ginv22 +
|
|
(deldelg2213 + deldelg2312)*ginv23 + deldelg2313*ginv33) +
|
|
ginv12*((2.*delg112 + delg211)*dginv211 + (delg213 + delg312)*dginv213 +
|
|
2.*((delg122 + delg212)*dginv212 + delg123*dginv213) +
|
|
delg222*dginv222 + (delg223 + delg322)*dginv223 + delg323*dginv233 +
|
|
(2.*deldelg1223 + deldelg2213 + deldelg2312)*ginv13 +
|
|
deldelg2222*ginv22 + (deldelg2223 + deldelg2322)*ginv23 +
|
|
deldelg2323*ginv33) + ginv13*
|
|
((2.*delg113 + delg311)*dginv211 +
|
|
(2.*delg123 + delg213 + delg312)*dginv212 +
|
|
2.*(delg133 + delg313)*dginv213 + delg223*dginv222 +
|
|
(delg233 + delg323)*dginv223 + delg333*dginv233 + deldelg2223*ginv22 +
|
|
(deldelg2233 + deldelg2323)*ginv23 + deldelg2333*ginv33) +
|
|
deldelg1211*pow2(ginv11) + (deldelg1222 + deldelg2212)*pow2(ginv12) +
|
|
(deldelg1233 + deldelg2313)*pow2(ginv13)
|
|
;
|
|
|
|
dGd22
|
|
=
|
|
ginv11*(delg111*dginv212 + delg112*dginv222 + delg113*dginv223 +
|
|
deldelg1211*ginv12 + deldelg1212*ginv22 + deldelg1213*ginv23) +
|
|
ginv13*((delg113 + delg311)*dginv212 + (delg123 + delg312)*dginv222 +
|
|
(delg133 + delg313)*dginv223 + (deldelg1223 + deldelg2312)*ginv22 +
|
|
(deldelg1233 + deldelg2313)*ginv23) +
|
|
(delg313*dginv212 + delg323*dginv222 + delg333*dginv223)*ginv33 +
|
|
ginv12*(delg111*dginv211 + (delg113 + delg311)*dginv213 +
|
|
delg122*dginv222 + (delg123 + delg312)*dginv223 +
|
|
2.*((delg112 + delg211)*dginv212 + delg212*dginv222 +
|
|
delg213*dginv223) + delg313*dginv233 +
|
|
(deldelg1213 + deldelg2311)*ginv13 +
|
|
(deldelg1222 + 2.*deldelg2212)*ginv22 +
|
|
(deldelg1223 + 2.*deldelg2213 + deldelg2312)*ginv23 +
|
|
deldelg2313*ginv33) + ginv22*
|
|
(delg112*dginv211 + (delg122 + 2.*delg212)*dginv212 +
|
|
(delg123 + delg312)*dginv213 + delg322*dginv223 +
|
|
2.*(delg222*dginv222 + delg223*dginv223) + delg323*dginv233 +
|
|
(2.*deldelg2223 + deldelg2322)*ginv23 + deldelg2323*ginv33) +
|
|
ginv23*(delg113*dginv211 + (delg123 + 2.*delg213 + delg312)*dginv212 +
|
|
(delg133 + delg313)*dginv213 + (2.*delg223 + delg322)*dginv222 +
|
|
2.*(delg233 + delg323)*dginv223 + delg333*dginv233 + deldelg2333*ginv33\
|
|
) + (deldelg1212 + deldelg2211)*pow2(ginv12) + deldelg2222*pow2(ginv22) +
|
|
(deldelg2233 + deldelg2323)*pow2(ginv23)
|
|
;
|
|
|
|
dGd23
|
|
=
|
|
(delg113*dginv211 + (delg123 + delg213)*dginv212 +
|
|
(delg133 + 2.*delg313)*dginv213 + delg223*dginv222 +
|
|
(delg233 + 2.*delg323)*dginv223 + 2.*delg333*dginv233)*ginv33 +
|
|
ginv11*(delg111*dginv213 + delg112*dginv223 + delg113*dginv233 +
|
|
deldelg1211*ginv13 + deldelg1212*ginv23 + deldelg1213*ginv33) +
|
|
ginv12*((delg112 + delg211)*dginv213 + (delg122 + delg212)*dginv223 +
|
|
(delg123 + delg213)*dginv233 + (deldelg1212 + deldelg2211)*ginv13 +
|
|
(deldelg1222 + deldelg2212)*ginv23 + (deldelg1223 + deldelg2213)*ginv33\
|
|
) + ginv22*(delg212*dginv213 + delg222*dginv223 + delg223*dginv233 +
|
|
deldelg2222*ginv23 + deldelg2223*ginv33) +
|
|
ginv13*(delg111*dginv211 + (delg112 + delg211)*dginv212 +
|
|
delg212*dginv222 + (delg123 + delg213)*dginv223 + delg133*dginv233 +
|
|
2.*((delg113 + delg311)*dginv213 + delg312*dginv223 +
|
|
delg313*dginv233) + deldelg2212*ginv22 +
|
|
(deldelg1223 + deldelg2213 + 2.*deldelg2312)*ginv23 +
|
|
(deldelg1233 + 2.*deldelg2313)*ginv33) +
|
|
ginv23*(delg112*dginv211 + (delg122 + delg212)*dginv212 +
|
|
(delg123 + delg213 + 2.*delg312)*dginv213 + delg222*dginv222 +
|
|
delg233*dginv233 + 2.*((delg223 + delg322)*dginv223 +
|
|
delg323*dginv233) + (deldelg2233 + 2.*deldelg2323)*ginv33) +
|
|
(deldelg1213 + deldelg2311)*pow2(ginv13) +
|
|
(deldelg2223 + deldelg2322)*pow2(ginv23) + deldelg2333*pow2(ginv33)
|
|
;
|
|
|
|
dGd31
|
|
=
|
|
(delg212*dginv311 + delg222*dginv312 + delg223*dginv313)*ginv22 +
|
|
((delg213 + delg312)*dginv311 + (delg223 + delg322)*dginv312 +
|
|
(delg233 + delg323)*dginv313)*ginv23 +
|
|
(delg313*dginv311 + delg323*dginv312 + delg333*dginv313)*ginv33 +
|
|
ginv11*(delg211*dginv312 + delg311*dginv313 +
|
|
2.*(delg111*dginv311 + delg112*dginv312 + delg113*dginv313) +
|
|
delg212*dginv322 + (delg213 + delg312)*dginv323 + delg313*dginv333 +
|
|
(2.*deldelg1312 + deldelg2311)*ginv12 +
|
|
(2.*deldelg1313 + deldelg3311)*ginv13 + deldelg2312*ginv22 +
|
|
(deldelg2313 + deldelg3312)*ginv23 + deldelg3313*ginv33) +
|
|
ginv12*((2.*delg112 + delg211)*dginv311 + (delg213 + delg312)*dginv313 +
|
|
2.*((delg122 + delg212)*dginv312 + delg123*dginv313) +
|
|
delg222*dginv322 + (delg223 + delg322)*dginv323 + delg323*dginv333 +
|
|
(2.*deldelg1323 + deldelg2313 + deldelg3312)*ginv13 +
|
|
deldelg2322*ginv22 + (deldelg2323 + deldelg3322)*ginv23 +
|
|
deldelg3323*ginv33) + ginv13*
|
|
((2.*delg113 + delg311)*dginv311 +
|
|
(2.*delg123 + delg213 + delg312)*dginv312 +
|
|
2.*(delg133 + delg313)*dginv313 + delg223*dginv322 +
|
|
(delg233 + delg323)*dginv323 + delg333*dginv333 + deldelg2323*ginv22 +
|
|
(deldelg2333 + deldelg3323)*ginv23 + deldelg3333*ginv33) +
|
|
deldelg1311*pow2(ginv11) + (deldelg1322 + deldelg2312)*pow2(ginv12) +
|
|
(deldelg1333 + deldelg3313)*pow2(ginv13)
|
|
;
|
|
|
|
dGd32
|
|
=
|
|
ginv11*(delg111*dginv312 + delg112*dginv322 + delg113*dginv323 +
|
|
deldelg1311*ginv12 + deldelg1312*ginv22 + deldelg1313*ginv23) +
|
|
ginv13*((delg113 + delg311)*dginv312 + (delg123 + delg312)*dginv322 +
|
|
(delg133 + delg313)*dginv323 + (deldelg1323 + deldelg3312)*ginv22 +
|
|
(deldelg1333 + deldelg3313)*ginv23) +
|
|
(delg313*dginv312 + delg323*dginv322 + delg333*dginv323)*ginv33 +
|
|
ginv12*(delg111*dginv311 + (delg113 + delg311)*dginv313 +
|
|
delg122*dginv322 + (delg123 + delg312)*dginv323 +
|
|
2.*((delg112 + delg211)*dginv312 + delg212*dginv322 +
|
|
delg213*dginv323) + delg313*dginv333 +
|
|
(deldelg1313 + deldelg3311)*ginv13 +
|
|
(deldelg1322 + 2.*deldelg2312)*ginv22 +
|
|
(deldelg1323 + 2.*deldelg2313 + deldelg3312)*ginv23 +
|
|
deldelg3313*ginv33) + ginv22*
|
|
(delg112*dginv311 + (delg122 + 2.*delg212)*dginv312 +
|
|
(delg123 + delg312)*dginv313 + delg322*dginv323 +
|
|
2.*(delg222*dginv322 + delg223*dginv323) + delg323*dginv333 +
|
|
(2.*deldelg2323 + deldelg3322)*ginv23 + deldelg3323*ginv33) +
|
|
ginv23*(delg113*dginv311 + (delg123 + 2.*delg213 + delg312)*dginv312 +
|
|
(delg133 + delg313)*dginv313 + (2.*delg223 + delg322)*dginv322 +
|
|
2.*(delg233 + delg323)*dginv323 + delg333*dginv333 + deldelg3333*ginv33\
|
|
) + (deldelg1312 + deldelg2311)*pow2(ginv12) + deldelg2322*pow2(ginv22) +
|
|
(deldelg2333 + deldelg3323)*pow2(ginv23)
|
|
;
|
|
|
|
dGd33
|
|
=
|
|
(delg113*dginv311 + (delg123 + delg213)*dginv312 +
|
|
(delg133 + 2.*delg313)*dginv313 + delg223*dginv322 +
|
|
(delg233 + 2.*delg323)*dginv323 + 2.*delg333*dginv333)*ginv33 +
|
|
ginv11*(delg111*dginv313 + delg112*dginv323 + delg113*dginv333 +
|
|
deldelg1311*ginv13 + deldelg1312*ginv23 + deldelg1313*ginv33) +
|
|
ginv12*((delg112 + delg211)*dginv313 + (delg122 + delg212)*dginv323 +
|
|
(delg123 + delg213)*dginv333 + (deldelg1312 + deldelg2311)*ginv13 +
|
|
(deldelg1322 + deldelg2312)*ginv23 + (deldelg1323 + deldelg2313)*ginv33\
|
|
) + ginv22*(delg212*dginv313 + delg222*dginv323 + delg223*dginv333 +
|
|
deldelg2322*ginv23 + deldelg2323*ginv33) +
|
|
ginv13*(delg111*dginv311 + (delg112 + delg211)*dginv312 +
|
|
delg212*dginv322 + (delg123 + delg213)*dginv323 + delg133*dginv333 +
|
|
2.*((delg113 + delg311)*dginv313 + delg312*dginv323 +
|
|
delg313*dginv333) + deldelg2312*ginv22 +
|
|
(deldelg1323 + deldelg2313 + 2.*deldelg3312)*ginv23 +
|
|
(deldelg1333 + 2.*deldelg3313)*ginv33) +
|
|
ginv23*(delg112*dginv311 + (delg122 + delg212)*dginv312 +
|
|
(delg123 + delg213 + 2.*delg312)*dginv313 + delg222*dginv322 +
|
|
delg233*dginv333 + 2.*((delg223 + delg322)*dginv323 +
|
|
delg323*dginv333) + (deldelg2333 + 2.*deldelg3323)*ginv33) +
|
|
(deldelg1313 + deldelg3311)*pow2(ginv13) +
|
|
(deldelg2323 + deldelg3322)*pow2(ginv23) + deldelg3333*pow2(ginv33)
|
|
;
|
|
|
|
Zinv1
|
|
=
|
|
0.5*(G1 - Gd1)
|
|
;
|
|
|
|
Zinv2
|
|
=
|
|
0.5*(G2 - Gd2)
|
|
;
|
|
|
|
Zinv3
|
|
=
|
|
0.5*(G3 - Gd3)
|
|
;
|
|
|
|
dZinv11
|
|
=
|
|
0.5*(delG11 - dGd11)
|
|
;
|
|
|
|
dZinv12
|
|
=
|
|
0.5*(delG12 - dGd12)
|
|
;
|
|
|
|
dZinv13
|
|
=
|
|
0.5*(delG13 - dGd13)
|
|
;
|
|
|
|
dZinv21
|
|
=
|
|
0.5*(delG21 - dGd21)
|
|
;
|
|
|
|
dZinv22
|
|
=
|
|
0.5*(delG22 - dGd22)
|
|
;
|
|
|
|
dZinv23
|
|
=
|
|
0.5*(delG23 - dGd23)
|
|
;
|
|
|
|
dZinv31
|
|
=
|
|
0.5*(delG31 - dGd31)
|
|
;
|
|
|
|
dZinv32
|
|
=
|
|
0.5*(delG32 - dGd32)
|
|
;
|
|
|
|
dZinv33
|
|
=
|
|
0.5*(delG33 - dGd33)
|
|
;
|
|
|
|
Z1
|
|
=
|
|
g11*Zinv1 + g12*Zinv2 + g13*Zinv3
|
|
;
|
|
|
|
Z2
|
|
=
|
|
g12*Zinv1 + g22*Zinv2 + g23*Zinv3
|
|
;
|
|
|
|
Z3
|
|
=
|
|
g13*Zinv1 + g23*Zinv2 + g33*Zinv3
|
|
;
|
|
|
|
dZ11
|
|
=
|
|
dZinv11*g11 + dZinv12*g12 + dZinv13*g13 + delg111*Zinv1 + delg112*Zinv2 +
|
|
delg113*Zinv3
|
|
;
|
|
|
|
dZ12
|
|
=
|
|
dZinv11*g12 + dZinv12*g22 + dZinv13*g23 + delg112*Zinv1 + delg122*Zinv2 +
|
|
delg123*Zinv3
|
|
;
|
|
|
|
dZ13
|
|
=
|
|
dZinv11*g13 + dZinv12*g23 + dZinv13*g33 + delg113*Zinv1 + delg123*Zinv2 +
|
|
delg133*Zinv3
|
|
;
|
|
|
|
dZ21
|
|
=
|
|
dZinv21*g11 + dZinv22*g12 + dZinv23*g13 + delg211*Zinv1 + delg212*Zinv2 +
|
|
delg213*Zinv3
|
|
;
|
|
|
|
dZ22
|
|
=
|
|
dZinv21*g12 + dZinv22*g22 + dZinv23*g23 + delg212*Zinv1 + delg222*Zinv2 +
|
|
delg223*Zinv3
|
|
;
|
|
|
|
dZ23
|
|
=
|
|
dZinv21*g13 + dZinv22*g23 + dZinv23*g33 + delg213*Zinv1 + delg223*Zinv2 +
|
|
delg233*Zinv3
|
|
;
|
|
|
|
dZ31
|
|
=
|
|
dZinv31*g11 + dZinv32*g12 + dZinv33*g13 + delg311*Zinv1 + delg312*Zinv2 +
|
|
delg313*Zinv3
|
|
;
|
|
|
|
dZ32
|
|
=
|
|
dZinv31*g12 + dZinv32*g22 + dZinv33*g23 + delg312*Zinv1 + delg322*Zinv2 +
|
|
delg323*Zinv3
|
|
;
|
|
|
|
dZ33
|
|
=
|
|
dZinv31*g13 + dZinv32*g23 + dZinv33*g33 + delg313*Zinv1 + delg323*Zinv2 +
|
|
delg333*Zinv3
|
|
;
|
|
|
|
DZinv11
|
|
=
|
|
dZinv11 + gammaF111*Zinv1 + gammaF112*Zinv2 + gammaF113*Zinv3
|
|
;
|
|
|
|
DZinv12
|
|
=
|
|
dZinv12 + gammaF211*Zinv1 + gammaF212*Zinv2 + gammaF213*Zinv3
|
|
;
|
|
|
|
DZinv13
|
|
=
|
|
dZinv13 + gammaF311*Zinv1 + gammaF312*Zinv2 + gammaF313*Zinv3
|
|
;
|
|
|
|
DZinv21
|
|
=
|
|
dZinv21 + gammaF121*Zinv1 + gammaF122*Zinv2 + gammaF123*Zinv3
|
|
;
|
|
|
|
DZinv22
|
|
=
|
|
dZinv22 + gammaF221*Zinv1 + gammaF222*Zinv2 + gammaF223*Zinv3
|
|
;
|
|
|
|
DZinv23
|
|
=
|
|
dZinv23 + gammaF321*Zinv1 + gammaF322*Zinv2 + gammaF323*Zinv3
|
|
;
|
|
|
|
DZinv31
|
|
=
|
|
dZinv31 + gammaF131*Zinv1 + gammaF132*Zinv2 + gammaF133*Zinv3
|
|
;
|
|
|
|
DZinv32
|
|
=
|
|
dZinv32 + gammaF231*Zinv1 + gammaF232*Zinv2 + gammaF233*Zinv3
|
|
;
|
|
|
|
DZinv33
|
|
=
|
|
dZinv33 + gammaF331*Zinv1 + gammaF332*Zinv2 + gammaF333*Zinv3
|
|
;
|
|
|
|
DZ11
|
|
=
|
|
dZ11 - gammaF111*Z1 - gammaF211*Z2 - gammaF311*Z3
|
|
;
|
|
|
|
DZ12
|
|
=
|
|
dZ12 - gammaF112*Z1 - gammaF212*Z2 - gammaF312*Z3
|
|
;
|
|
|
|
DZ13
|
|
=
|
|
dZ13 - gammaF113*Z1 - gammaF213*Z2 - gammaF313*Z3
|
|
;
|
|
|
|
DZ21
|
|
=
|
|
dZ21 - gammaF121*Z1 - gammaF221*Z2 - gammaF321*Z3
|
|
;
|
|
|
|
DZ22
|
|
=
|
|
dZ22 - gammaF122*Z1 - gammaF222*Z2 - gammaF322*Z3
|
|
;
|
|
|
|
DZ23
|
|
=
|
|
dZ23 - gammaF123*Z1 - gammaF223*Z2 - gammaF323*Z3
|
|
;
|
|
|
|
DZ31
|
|
=
|
|
dZ31 - gammaF131*Z1 - gammaF231*Z2 - gammaF331*Z3
|
|
;
|
|
|
|
DZ32
|
|
=
|
|
dZ32 - gammaF132*Z1 - gammaF232*Z2 - gammaF332*Z3
|
|
;
|
|
|
|
DZ33
|
|
=
|
|
dZ33 - gammaF133*Z1 - gammaF233*Z2 - gammaF333*Z3
|
|
;
|
|
|
|
DZsym11
|
|
=
|
|
2.*DZ11
|
|
;
|
|
|
|
DZsym12
|
|
=
|
|
DZ12 + DZ21
|
|
;
|
|
|
|
DZsym13
|
|
=
|
|
DZ13 + DZ31
|
|
;
|
|
|
|
DZsym21
|
|
=
|
|
DZ12 + DZ21
|
|
;
|
|
|
|
DZsym22
|
|
=
|
|
2.*DZ22
|
|
;
|
|
|
|
DZsym23
|
|
=
|
|
DZ23 + DZ32
|
|
;
|
|
|
|
DZsym31
|
|
=
|
|
DZ13 + DZ31
|
|
;
|
|
|
|
DZsym32
|
|
=
|
|
DZ23 + DZ32
|
|
;
|
|
|
|
DZsym33
|
|
=
|
|
2.*DZ33
|
|
;
|
|
|
|
trDZsym
|
|
=
|
|
(DZsym11*ginv11 + (DZsym12 + DZsym21)*ginv12 + (DZsym13 + DZsym31)*ginv13 +
|
|
DZsym22*ginv22 + (DZsym23 + DZsym32)*ginv23 + DZsym33*ginv33)*psim4
|
|
;
|
|
|
|
rA11
|
|
=
|
|
rA11 + alpha*(-2.*A11*Theta + chi*
|
|
(DZsym11 - 0.33333333333333333333*g11*trDZsym))
|
|
;
|
|
|
|
rA12
|
|
=
|
|
rA12 + alpha*(-2.*A12*Theta + chi*
|
|
(DZsym21 - 0.33333333333333333333*g12*trDZsym))
|
|
;
|
|
|
|
rA13
|
|
=
|
|
rA13 + alpha*(-2.*A13*Theta + chi*
|
|
(DZsym31 - 0.33333333333333333333*g13*trDZsym))
|
|
;
|
|
|
|
rA22
|
|
=
|
|
rA22 + alpha*(-2.*A22*Theta + chi*
|
|
(DZsym22 - 0.33333333333333333333*g22*trDZsym))
|
|
;
|
|
|
|
rA23
|
|
=
|
|
rA23 + alpha*(-2.*A23*Theta + chi*
|
|
(DZsym32 - 0.33333333333333333333*g23*trDZsym))
|
|
;
|
|
|
|
rA33
|
|
=
|
|
rA33 + alpha*(-2.*A33*Theta + chi*
|
|
(DZsym33 - 0.33333333333333333333*g33*trDZsym))
|
|
;
|
|
|
|
rTheta
|
|
=
|
|
alpha*(DZinv11 + DZinv22 + DZinv33) + rTheta - da1*Zinv1 - da2*Zinv2 -
|
|
da3*Zinv3
|
|
;
|
|
|
|
rG1
|
|
=
|
|
rG1 - ginv11*(1.3333333333333333333*alpha*K*Z1 +
|
|
2.*(da1*Theta + alpha*kappa1*Z1)) -
|
|
ginv12*(1.3333333333333333333*alpha*K*Z2 +
|
|
2.*(da2*Theta + alpha*kappa1*Z2)) -
|
|
ginv13*(1.3333333333333333333*alpha*K*Z3 +
|
|
2.*(da3*Theta + alpha*kappa1*Z3))
|
|
;
|
|
|
|
rG2
|
|
=
|
|
rG2 - ginv12*(1.3333333333333333333*alpha*K*Z1 +
|
|
2.*(da1*Theta + alpha*kappa1*Z1)) -
|
|
ginv22*(1.3333333333333333333*alpha*K*Z2 +
|
|
2.*(da2*Theta + alpha*kappa1*Z2)) -
|
|
ginv23*(1.3333333333333333333*alpha*K*Z3 +
|
|
2.*(da3*Theta + alpha*kappa1*Z3))
|
|
;
|
|
|
|
rG3
|
|
=
|
|
rG3 - ginv13*(1.3333333333333333333*alpha*K*Z1 +
|
|
2.*(da1*Theta + alpha*kappa1*Z1)) -
|
|
ginv23*(1.3333333333333333333*alpha*K*Z2 +
|
|
2.*(da2*Theta + alpha*kappa1*Z2)) -
|
|
ginv33*(1.3333333333333333333*alpha*K*Z3 +
|
|
2.*(da3*Theta + alpha*kappa1*Z3))
|
|
;
|
|
#endif
|
|
|
|
} /* function */
|
|
}
|