path: root/ML_BSSN/src/ML_BSSN_constraints.c

/*  File produced by user diener */
/*  Produced with Mathematica Version 6.0 for Linux x86 (32-bit) (April 20, 2007) */

/*  Mathematica script written by Ian Hinder and Sascha Husa */

#define KRANC_C

#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "GenericFD.h"
#include "Differencing.h"
#include "loopcontrol.h"

/* Define macros used in calculations */
#define INITVALUE  (42)
#define INV(x) ((1.0) / (x))
#define SQR(x) ((x) * (x))
#define CUB(x) ((x) * (x) * (x))
#define QAD(x) ((x) * (x) * (x) * (x))

void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[3], CCTK_REAL tangentA[3], CCTK_REAL tangentB[3], CCTK_INT min[3], CCTK_INT max[3], CCTK_INT n_subblock_gfs, CCTK_REAL *subblock_gfs[])
{
  DECLARE_CCTK_ARGUMENTS
  DECLARE_CCTK_PARAMETERS
  
  
  /* Declare finite differencing variables */
  CCTK_REAL dx = INITVALUE, dy = INITVALUE, dz = INITVALUE;
  CCTK_REAL dxi = INITVALUE, dyi = INITVALUE, dzi = INITVALUE;
  CCTK_REAL khalf = INITVALUE, kthird = INITVALUE, ktwothird = INITVALUE, kfourthird = INITVALUE, keightthird = INITVALUE;
  CCTK_REAL hdxi = INITVALUE, hdyi = INITVALUE, hdzi = INITVALUE;
  
  
  /* Declare predefined quantities */
  CCTK_REAL p1o12dx = INITVALUE;
  CCTK_REAL p1o12dy = INITVALUE;
  CCTK_REAL p1o12dz = INITVALUE;
  CCTK_REAL p1o144dxdy = INITVALUE;
  CCTK_REAL p1o144dxdz = INITVALUE;
  CCTK_REAL p1o144dydz = INITVALUE;
  CCTK_REAL pm1o12dx2 = INITVALUE;
  CCTK_REAL pm1o12dy2 = INITVALUE;
  CCTK_REAL pm1o12dz2 = INITVALUE;
  
  if (verbose > 1)
  {
    CCTK_VInfo(CCTK_THORNSTRING,"Entering ML_BSSN_constraints_Body");
  }
  
  if (cctk_iteration % ML_BSSN_constraints_calc_every != ML_BSSN_constraints_calc_offset)
  {
    return;
  }
  
  /* Include user-supplied include files */
  
  /* Initialise finite differencing variables */
  dx = CCTK_DELTA_SPACE(0);
  dy = CCTK_DELTA_SPACE(1);
  dz = CCTK_DELTA_SPACE(2);
  dxi = 1.0 / dx;
  dyi = 1.0 / dy;
  dzi = 1.0 / dz;
  khalf = 0.5;
  kthird = 1/3.0;
  ktwothird = 2.0/3.0;
  kfourthird = 4.0/3.0;
  keightthird = 8.0/3.0;
  hdxi = 0.5 * dxi;
  hdyi = 0.5 * dyi;
  hdzi = 0.5 * dzi;
  
  /* Initialize predefined quantities */
  p1o12dx = INV(dx)/12.;
  p1o12dy = INV(dy)/12.;
  p1o12dz = INV(dz)/12.;
  p1o144dxdy = (INV(dx)*INV(dy))/144.;
  p1o144dxdz = (INV(dx)*INV(dz))/144.;
  p1o144dydz = (INV(dy)*INV(dz))/144.;
  pm1o12dx2 = -pow(dx,-2)/12.;
  pm1o12dy2 = -pow(dy,-2)/12.;
  pm1o12dz2 = -pow(dz,-2)/12.;
  
  /* Loop over the grid points */
  LC_LOOP3 (somename,
            i,j,k, min[0],min[1],min[2], max[0],max[1],max[2],
            cctk_lsh[0],cctk_lsh[1],cctk_lsh[2])
  {
    int index = INITVALUE;
    int subblock_index = INITVALUE;
    index = CCTK_GFINDEX3D(cctkGH,i,j,k);
    subblock_index = i - min[0] + (max[0] - min[0]) * (j - min[1] + (max[1]-min[1]) * (k - min[2]));
    
    /* Declare shorthands */
    CCTK_REAL Atm11 = INITVALUE, Atm12 = INITVALUE, Atm13 = INITVALUE, Atm21 = INITVALUE, Atm22 = INITVALUE, Atm23 = INITVALUE;
    CCTK_REAL Atm31 = INITVALUE, Atm32 = INITVALUE, Atm33 = INITVALUE;
    CCTK_REAL detgt = INITVALUE;
    CCTK_REAL e4phi = INITVALUE;
    CCTK_REAL em4phi = INITVALUE;
    CCTK_REAL Gt111 = INITVALUE, Gt112 = INITVALUE, Gt113 = INITVALUE, Gt122 = INITVALUE, Gt123 = INITVALUE, Gt133 = INITVALUE;
    CCTK_REAL Gt211 = INITVALUE, Gt212 = INITVALUE, Gt213 = INITVALUE, Gt222 = INITVALUE, Gt223 = INITVALUE, Gt233 = INITVALUE;
    CCTK_REAL Gt311 = INITVALUE, Gt312 = INITVALUE, Gt313 = INITVALUE, Gt322 = INITVALUE, Gt323 = INITVALUE, Gt333 = INITVALUE;
    CCTK_REAL gtu11 = INITVALUE, gtu21 = INITVALUE, gtu22 = INITVALUE, gtu31 = INITVALUE, gtu32 = INITVALUE, gtu33 = INITVALUE;
    CCTK_REAL gu11 = INITVALUE, gu21 = INITVALUE, gu22 = INITVALUE, gu31 = INITVALUE, gu32 = INITVALUE, gu33 = INITVALUE;
    CCTK_REAL R11 = INITVALUE, R12 = INITVALUE, R13 = INITVALUE, R22 = INITVALUE, R23 = INITVALUE, R33 = INITVALUE;
    CCTK_REAL Rphi11 = INITVALUE, Rphi12 = INITVALUE, Rphi13 = INITVALUE, Rphi22 = INITVALUE, Rphi23 = INITVALUE, Rphi33 = INITVALUE;
    CCTK_REAL Rt11 = INITVALUE, Rt12 = INITVALUE, Rt13 = INITVALUE, Rt22 = INITVALUE, Rt23 = INITVALUE, Rt33 = INITVALUE;
    CCTK_REAL trR = INITVALUE;
    
    /* Declare local copies of grid functions */
    CCTK_REAL At11L = INITVALUE, At12L = INITVALUE, At13L = INITVALUE, At22L = INITVALUE, At23L = INITVALUE, At33L = INITVALUE;
    CCTK_REAL cAL = INITVALUE;
    CCTK_REAL cSL = INITVALUE;
    CCTK_REAL cXt1L = INITVALUE, cXt2L = INITVALUE, cXt3L = INITVALUE;
    CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE;
    CCTK_REAL HL = INITVALUE;
    CCTK_REAL M1L = INITVALUE, M2L = INITVALUE, M3L = INITVALUE;
    CCTK_REAL phiL = INITVALUE;
    CCTK_REAL trKL = INITVALUE;
    CCTK_REAL Xt1L = INITVALUE, Xt2L = INITVALUE, Xt3L = INITVALUE;
    /* Declare precomputed derivatives*/
    
    /* Declare derivatives */
    CCTK_REAL PDstandard4th1At11 = INITVALUE;
    CCTK_REAL PDstandard4th2At11 = INITVALUE;
    CCTK_REAL PDstandard4th3At11 = INITVALUE;
    CCTK_REAL PDstandard4th1At12 = INITVALUE;
    CCTK_REAL PDstandard4th2At12 = INITVALUE;
    CCTK_REAL PDstandard4th3At12 = INITVALUE;
    CCTK_REAL PDstandard4th1At13 = INITVALUE;
    CCTK_REAL PDstandard4th2At13 = INITVALUE;
    CCTK_REAL PDstandard4th3At13 = INITVALUE;
    CCTK_REAL PDstandard4th1At22 = INITVALUE;
    CCTK_REAL PDstandard4th2At22 = INITVALUE;
    CCTK_REAL PDstandard4th3At22 = INITVALUE;
    CCTK_REAL PDstandard4th1At23 = INITVALUE;
    CCTK_REAL PDstandard4th2At23 = INITVALUE;
    CCTK_REAL PDstandard4th3At23 = INITVALUE;
    CCTK_REAL PDstandard4th1At33 = INITVALUE;
    CCTK_REAL PDstandard4th2At33 = INITVALUE;
    CCTK_REAL PDstandard4th3At33 = INITVALUE;
    CCTK_REAL PDstandard4th1gt11 = INITVALUE;
    CCTK_REAL PDstandard4th2gt11 = INITVALUE;
    CCTK_REAL PDstandard4th3gt11 = INITVALUE;
    CCTK_REAL PDstandard4th11gt11 = INITVALUE;
    CCTK_REAL PDstandard4th22gt11 = INITVALUE;
    CCTK_REAL PDstandard4th33gt11 = INITVALUE;
    CCTK_REAL PDstandard4th12gt11 = INITVALUE;
    CCTK_REAL PDstandard4th13gt11 = INITVALUE;
    CCTK_REAL PDstandard4th21gt11 = INITVALUE;
    CCTK_REAL PDstandard4th23gt11 = INITVALUE;
    CCTK_REAL PDstandard4th31gt11 = INITVALUE;
    CCTK_REAL PDstandard4th32gt11 = INITVALUE;
    CCTK_REAL PDstandard4th1gt12 = INITVALUE;
    CCTK_REAL PDstandard4th2gt12 = INITVALUE;
    CCTK_REAL PDstandard4th3gt12 = INITVALUE;
    CCTK_REAL PDstandard4th11gt12 = INITVALUE;
    CCTK_REAL PDstandard4th22gt12 = INITVALUE;
    CCTK_REAL PDstandard4th33gt12 = INITVALUE;
    CCTK_REAL PDstandard4th12gt12 = INITVALUE;
    CCTK_REAL PDstandard4th13gt12 = INITVALUE;
    CCTK_REAL PDstandard4th21gt12 = INITVALUE;
    CCTK_REAL PDstandard4th23gt12 = INITVALUE;
    CCTK_REAL PDstandard4th31gt12 = INITVALUE;
    CCTK_REAL PDstandard4th32gt12 = INITVALUE;
    CCTK_REAL PDstandard4th1gt13 = INITVALUE;
    CCTK_REAL PDstandard4th2gt13 = INITVALUE;
    CCTK_REAL PDstandard4th3gt13 = INITVALUE;
    CCTK_REAL PDstandard4th11gt13 = INITVALUE;
    CCTK_REAL PDstandard4th22gt13 = INITVALUE;
    CCTK_REAL PDstandard4th33gt13 = INITVALUE;
    CCTK_REAL PDstandard4th12gt13 = INITVALUE;
    CCTK_REAL PDstandard4th13gt13 = INITVALUE;
    CCTK_REAL PDstandard4th21gt13 = INITVALUE;
    CCTK_REAL PDstandard4th23gt13 = INITVALUE;
    CCTK_REAL PDstandard4th31gt13 = INITVALUE;
    CCTK_REAL PDstandard4th32gt13 = INITVALUE;
    CCTK_REAL PDstandard4th1gt22 = INITVALUE;
    CCTK_REAL PDstandard4th2gt22 = INITVALUE;
    CCTK_REAL PDstandard4th3gt22 = INITVALUE;
    CCTK_REAL PDstandard4th11gt22 = INITVALUE;
    CCTK_REAL PDstandard4th22gt22 = INITVALUE;
    CCTK_REAL PDstandard4th33gt22 = INITVALUE;
    CCTK_REAL PDstandard4th12gt22 = INITVALUE;
    CCTK_REAL PDstandard4th13gt22 = INITVALUE;
    CCTK_REAL PDstandard4th21gt22 = INITVALUE;
    CCTK_REAL PDstandard4th23gt22 = INITVALUE;
    CCTK_REAL PDstandard4th31gt22 = INITVALUE;
    CCTK_REAL PDstandard4th32gt22 = INITVALUE;
    CCTK_REAL PDstandard4th1gt23 = INITVALUE;
    CCTK_REAL PDstandard4th2gt23 = INITVALUE;
    CCTK_REAL PDstandard4th3gt23 = INITVALUE;
    CCTK_REAL PDstandard4th11gt23 = INITVALUE;
    CCTK_REAL PDstandard4th22gt23 = INITVALUE;
    CCTK_REAL PDstandard4th33gt23 = INITVALUE;
    CCTK_REAL PDstandard4th12gt23 = INITVALUE;
    CCTK_REAL PDstandard4th13gt23 = INITVALUE;
    CCTK_REAL PDstandard4th21gt23 = INITVALUE;
    CCTK_REAL PDstandard4th23gt23 = INITVALUE;
    CCTK_REAL PDstandard4th31gt23 = INITVALUE;
    CCTK_REAL PDstandard4th32gt23 = INITVALUE;
    CCTK_REAL PDstandard4th1gt33 = INITVALUE;
    CCTK_REAL PDstandard4th2gt33 = INITVALUE;
    CCTK_REAL PDstandard4th3gt33 = INITVALUE;
    CCTK_REAL PDstandard4th11gt33 = INITVALUE;
    CCTK_REAL PDstandard4th22gt33 = INITVALUE;
    CCTK_REAL PDstandard4th33gt33 = INITVALUE;
    CCTK_REAL PDstandard4th12gt33 = INITVALUE;
    CCTK_REAL PDstandard4th13gt33 = INITVALUE;
    CCTK_REAL PDstandard4th21gt33 = INITVALUE;
    CCTK_REAL PDstandard4th23gt33 = INITVALUE;
    CCTK_REAL PDstandard4th31gt33 = INITVALUE;
    CCTK_REAL PDstandard4th32gt33 = INITVALUE;
    CCTK_REAL PDstandard4th1phi = INITVALUE;
    CCTK_REAL PDstandard4th2phi = INITVALUE;
    CCTK_REAL PDstandard4th3phi = INITVALUE;
    CCTK_REAL PDstandard4th11phi = INITVALUE;
    CCTK_REAL PDstandard4th22phi = INITVALUE;
    CCTK_REAL PDstandard4th33phi = INITVALUE;
    CCTK_REAL PDstandard4th12phi = INITVALUE;
    CCTK_REAL PDstandard4th13phi = INITVALUE;
    CCTK_REAL PDstandard4th21phi = INITVALUE;
    CCTK_REAL PDstandard4th23phi = INITVALUE;
    CCTK_REAL PDstandard4th31phi = INITVALUE;
    CCTK_REAL PDstandard4th32phi = INITVALUE;
    CCTK_REAL PDstandard4th1trK = INITVALUE;
    CCTK_REAL PDstandard4th2trK = INITVALUE;
    CCTK_REAL PDstandard4th3trK = INITVALUE;
    CCTK_REAL PDstandard4th1Xt1 = INITVALUE;
    CCTK_REAL PDstandard4th2Xt1 = INITVALUE;
    CCTK_REAL PDstandard4th3Xt1 = INITVALUE;
    CCTK_REAL PDstandard4th1Xt2 = INITVALUE;
    CCTK_REAL PDstandard4th2Xt2 = INITVALUE;
    CCTK_REAL PDstandard4th3Xt2 = INITVALUE;
    CCTK_REAL PDstandard4th1Xt3 = INITVALUE;
    CCTK_REAL PDstandard4th2Xt3 = INITVALUE;
    CCTK_REAL PDstandard4th3Xt3 = INITVALUE;
    
    /* Assign local copies of grid functions */
    At11L = At11[index];
    At12L = At12[index];
    At13L = At13[index];
    At22L = At22[index];
    At23L = At23[index];
    At33L = At33[index];
    gt11L = gt11[index];
    gt12L = gt12[index];
    gt13L = gt13[index];
    gt22L = gt22[index];
    gt23L = gt23[index];
    gt33L = gt33[index];
    phiL = phi[index];
    trKL = trK[index];
    Xt1L = Xt1[index];
    Xt2L = Xt2[index];
    Xt3L = Xt3[index];
    
    /* Assign local copies of subblock grid functions */
    
    /* Include user supplied include files */
    
    /* Precompute derivatives (new style) */
    PDstandard4th1At11 = PDstandard4th1(At11, i, j, k);
    PDstandard4th2At11 = PDstandard4th2(At11, i, j, k);
    PDstandard4th3At11 = PDstandard4th3(At11, i, j, k);
    PDstandard4th1At12 = PDstandard4th1(At12, i, j, k);
    PDstandard4th2At12 = PDstandard4th2(At12, i, j, k);
    PDstandard4th3At12 = PDstandard4th3(At12, i, j, k);
    PDstandard4th1At13 = PDstandard4th1(At13, i, j, k);
    PDstandard4th2At13 = PDstandard4th2(At13, i, j, k);
    PDstandard4th3At13 = PDstandard4th3(At13, i, j, k);
    PDstandard4th1At22 = PDstandard4th1(At22, i, j, k);
    PDstandard4th2At22 = PDstandard4th2(At22, i, j, k);
    PDstandard4th3At22 = PDstandard4th3(At22, i, j, k);
    PDstandard4th1At23 = PDstandard4th1(At23, i, j, k);
    PDstandard4th2At23 = PDstandard4th2(At23, i, j, k);
    PDstandard4th3At23 = PDstandard4th3(At23, i, j, k);
    PDstandard4th1At33 = PDstandard4th1(At33, i, j, k);
    PDstandard4th2At33 = PDstandard4th2(At33, i, j, k);
    PDstandard4th3At33 = PDstandard4th3(At33, i, j, k);
    PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k);
    PDstandard4th2gt11 = PDstandard4th2(gt11, i, j, k);
    PDstandard4th3gt11 = PDstandard4th3(gt11, i, j, k);
    PDstandard4th11gt11 = PDstandard4th11(gt11, i, j, k);
    PDstandard4th22gt11 = PDstandard4th22(gt11, i, j, k);
    PDstandard4th33gt11 = PDstandard4th33(gt11, i, j, k);
    PDstandard4th12gt11 = PDstandard4th12(gt11, i, j, k);
    PDstandard4th13gt11 = PDstandard4th13(gt11, i, j, k);
    PDstandard4th23gt11 = PDstandard4th23(gt11, i, j, k);
    PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k);
    PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k);
    PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k);
    PDstandard4th11gt12 = PDstandard4th11(gt12, i, j, k);
    PDstandard4th22gt12 = PDstandard4th22(gt12, i, j, k);
    PDstandard4th33gt12 = PDstandard4th33(gt12, i, j, k);
    PDstandard4th12gt12 = PDstandard4th12(gt12, i, j, k);
    PDstandard4th13gt12 = PDstandard4th13(gt12, i, j, k);
    PDstandard4th23gt12 = PDstandard4th23(gt12, i, j, k);
    PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k);
    PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k);
    PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k);
    PDstandard4th11gt13 = PDstandard4th11(gt13, i, j, k);
    PDstandard4th22gt13 = PDstandard4th22(gt13, i, j, k);
    PDstandard4th33gt13 = PDstandard4th33(gt13, i, j, k);
    PDstandard4th12gt13 = PDstandard4th12(gt13, i, j, k);
    PDstandard4th13gt13 = PDstandard4th13(gt13, i, j, k);
    PDstandard4th23gt13 = PDstandard4th23(gt13, i, j, k);
    PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k);
    PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k);
    PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k);
    PDstandard4th11gt22 = PDstandard4th11(gt22, i, j, k);
    PDstandard4th22gt22 = PDstandard4th22(gt22, i, j, k);
    PDstandard4th33gt22 = PDstandard4th33(gt22, i, j, k);
    PDstandard4th12gt22 = PDstandard4th12(gt22, i, j, k);
    PDstandard4th13gt22 = PDstandard4th13(gt22, i, j, k);
    PDstandard4th23gt22 = PDstandard4th23(gt22, i, j, k);
    PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k);
    PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k);
    PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k);
    PDstandard4th11gt23 = PDstandard4th11(gt23, i, j, k);
    PDstandard4th22gt23 = PDstandard4th22(gt23, i, j, k);
    PDstandard4th33gt23 = PDstandard4th33(gt23, i, j, k);
    PDstandard4th12gt23 = PDstandard4th12(gt23, i, j, k);
    PDstandard4th13gt23 = PDstandard4th13(gt23, i, j, k);
    PDstandard4th23gt23 = PDstandard4th23(gt23, i, j, k);
    PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k);
    PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k);
    PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k);
    PDstandard4th11gt33 = PDstandard4th11(gt33, i, j, k);
    PDstandard4th22gt33 = PDstandard4th22(gt33, i, j, k);
    PDstandard4th33gt33 = PDstandard4th33(gt33, i, j, k);
    PDstandard4th12gt33 = PDstandard4th12(gt33, i, j, k);
    PDstandard4th13gt33 = PDstandard4th13(gt33, i, j, k);
    PDstandard4th23gt33 = PDstandard4th23(gt33, i, j, k);
    PDstandard4th1phi = PDstandard4th1(phi, i, j, k);
    PDstandard4th2phi = PDstandard4th2(phi, i, j, k);
    PDstandard4th3phi = PDstandard4th3(phi, i, j, k);
    PDstandard4th11phi = PDstandard4th11(phi, i, j, k);
    PDstandard4th22phi = PDstandard4th22(phi, i, j, k);
    PDstandard4th33phi = PDstandard4th33(phi, i, j, k);
    PDstandard4th12phi = PDstandard4th12(phi, i, j, k);
    PDstandard4th13phi = PDstandard4th13(phi, i, j, k);
    PDstandard4th23phi = PDstandard4th23(phi, i, j, k);
    PDstandard4th1trK = PDstandard4th1(trK, i, j, k);
    PDstandard4th2trK = PDstandard4th2(trK, i, j, k);
    PDstandard4th3trK = PDstandard4th3(trK, i, j, k);
    PDstandard4th1Xt1 = PDstandard4th1(Xt1, i, j, k);
    PDstandard4th2Xt1 = PDstandard4th2(Xt1, i, j, k);
    PDstandard4th3Xt1 = PDstandard4th3(Xt1, i, j, k);
    PDstandard4th1Xt2 = PDstandard4th1(Xt2, i, j, k);
    PDstandard4th2Xt2 = PDstandard4th2(Xt2, i, j, k);
    PDstandard4th3Xt2 = PDstandard4th3(Xt2, i, j, k);
    PDstandard4th1Xt3 = PDstandard4th1(Xt3, i, j, k);
    PDstandard4th2Xt3 = PDstandard4th2(Xt3, i, j, k);
    PDstandard4th3Xt3 = PDstandard4th3(Xt3, i, j, k);
    
    /* Precompute derivatives (old style) */
    
    /* Calculate temporaries and grid functions */
    detgt  =  1;
    
    gtu11  =  INV(detgt)*(gt22L*gt33L - SQR(gt23L));
    
    gtu21  =  (gt13L*gt23L - gt12L*gt33L)*INV(detgt);
    
    gtu31  =  (-(gt13L*gt22L) + gt12L*gt23L)*INV(detgt);
    
    gtu22  =  INV(detgt)*(gt11L*gt33L - SQR(gt13L));
    
    gtu32  =  (gt12L*gt13L - gt11L*gt23L)*INV(detgt);
    
    gtu33  =  INV(detgt)*(gt11L*gt22L - SQR(gt12L));
    
    Gt111  =  khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - 
          gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11);
    
    Gt211  =  khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - 
          gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11);
    
    Gt311  =  khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - 
          gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11);
    
    Gt112  =  khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + 
          gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12));
    
    Gt212  =  khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + 
          gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12));
    
    Gt312  =  khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + 
          gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12));
    
    Gt113  =  khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + 
          gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12));
    
    Gt213  =  khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + 
          gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12));
    
    Gt313  =  khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + 
          gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12));
    
    Gt122  =  khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + 
          gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22));
    
    Gt222  =  khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + 
          gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22));
    
    Gt322  =  khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + 
          gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22));
    
    Gt123  =  khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + 
          gtu21*PDstandard4th3gt22);
    
    Gt223  =  khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + 
          gtu22*PDstandard4th3gt22);
    
    Gt323  =  khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + 
          gtu32*PDstandard4th3gt22);
    
    Gt133  =  khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + 
          2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33);
    
    Gt233  =  khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + 
          2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33);
    
    Gt333  =  khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + 
          2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33);
    
    Rt11  =  -(gtu11*khalf*PDstandard4th11gt11) + gtu21*
         (2*Gt211*Gt212*gt22L + 4*Gt112*gt13L*Gt311 + 2*Gt113*gt11L*Gt312 + 2*gt13L*Gt312*Gt313 + 2*gt13L*Gt211*Gt322 + 
           2*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandard4th12gt11) - gtu31*PDstandard4th13gt11 + 
        gt11L*PDstandard4th1Xt1 + gt12L*(4*Gt111*Gt212*gtu21 + 2*Gt211*Gt222*gtu21 + 2*Gt212*Gt222*gtu22 + 
           4*Gt113*Gt211*gtu31 + 4*Gt113*Gt212*gtu32 + 4*Gt113*Gt213*gtu33 + PDstandard4th1Xt2) + 
        gt13L*(4*Gt111*Gt312*gtu21 + 2*Gt212*Gt312*gtu21 + 4*Gt112*Gt312*gtu22 + 4*Gt113*Gt311*gtu31 + 
           4*Gt113*Gt312*gtu32 + 4*Gt113*Gt313*gtu33 + PDstandard4th1Xt3) - gtu22*khalf*PDstandard4th22gt11 - 
        gtu32*PDstandard4th23gt11 - gtu33*khalf*PDstandard4th33gt11 + 
        Gt111*(6*Gt113*gt11L*gtu31 + 4*gt12L*Gt213*gtu31 + gt11L*Xt1L) + 
        Gt211*(2*Gt112*gt11L*gtu11 + 4*Gt111*gt12L*gtu11 + 2*gt11L*Gt122*gtu21 + 2*gt11L*Gt123*gtu31 + gt12L*Xt1L) + 
        Gt311*(4*Gt111*gt13L*gtu11 + 2*gt12L*Gt213*gtu11 + 2*gt13L*Gt313*gtu11 + 2*gt11L*Gt123*gtu21 + 
           2*gt11L*Gt133*gtu31 + gt13L*Xt1L) + gt12L*Gt212*Xt2L + gt13L*Gt312*Xt2L + 
        Gt112*(6*Gt111*gt11L*gtu21 + 4*gt12L*Gt211*gtu21 + 4*gt12L*Gt212*gtu22 + 2*gt11L*Gt213*gtu31 + 
           6*Gt113*gt11L*gtu32 + gt11L*Xt2L) + Gt113*gt11L*Xt3L + 
        Gt213*(2*gt11L*Gt122*gtu32 + 4*Gt112*gt12L*gtu32 + 2*gt11L*Gt123*gtu33 + gt12L*Xt3L) + 
        Gt313*(4*Gt111*gt13L*gtu31 + 2*gt12L*Gt213*gtu31 + 2*gt11L*Gt123*gtu32 + 4*Gt112*gt13L*gtu32 + 
           2*gt12L*Gt223*gtu32 + 2*gt11L*Gt133*gtu33 + gt13L*Xt3L) + 3*gt11L*gtu11*SQR(Gt111) + 3*gt11L*gtu22*SQR(Gt112) + 
        3*gt11L*gtu33*SQR(Gt113) + gt22L*gtu11*SQR(Gt211) + gt22L*gtu22*SQR(Gt212) + 
        2*(gt12L*Gt211*Gt212*gtu11 + Gt113*gt11L*Gt311*gtu11 + Gt211*gt23L*Gt311*gtu11 + gt13L*Gt211*Gt312*gtu11 + 
           Gt112*gt11L*Gt212*gtu21 + gt12L*Gt223*Gt311*gtu21 + Gt212*gt23L*Gt311*gtu21 + gt12L*Gt213*Gt312*gtu21 + 
           Gt211*gt23L*Gt312*gtu21 + gt11L*Gt122*Gt212*gtu22 + gt11L*Gt123*Gt312*gtu22 + gt12L*Gt223*Gt312*gtu22 + 
           Gt212*gt23L*Gt312*gtu22 + gt13L*Gt212*Gt322*gtu22 + gt13L*Gt312*Gt323*gtu22 + gt12L*Gt212*Gt213*gtu31 + 
           gt12L*Gt211*Gt223*gtu31 + Gt211*Gt213*gt22L*gtu31 + gt12L*Gt233*Gt311*gtu31 + Gt213*gt23L*Gt311*gtu31 + 
           gt13L*Gt213*Gt312*gtu31 + Gt113*gt11L*Gt313*gtu31 + Gt211*gt23L*Gt313*gtu31 + gt13L*Gt211*Gt323*gtu31 + 
           gt13L*Gt311*Gt333*gtu31 + Gt311*Gt313*gt33L*gtu31 + gt11L*Gt123*Gt212*gtu32 + gt12L*Gt213*Gt222*gtu32 + 
           gt12L*Gt212*Gt223*gtu32 + Gt212*Gt213*gt22L*gtu32 + gt11L*Gt133*Gt312*gtu32 + gt12L*Gt233*Gt312*gtu32 + 
           Gt213*gt23L*Gt312*gtu32 + Gt212*gt23L*Gt313*gtu32 + gt13L*Gt213*Gt322*gtu32 + gt13L*Gt212*Gt323*gtu32 + 
           gt13L*Gt313*Gt323*gtu32 + gt13L*Gt312*Gt333*gtu32 + Gt312*Gt313*gt33L*gtu32 + gt12L*Gt213*Gt223*gtu33 + 
           gt12L*Gt233*Gt313*gtu33 + Gt213*gt23L*Gt313*gtu33 + gt13L*Gt213*Gt323*gtu33 + gt13L*Gt313*Gt333*gtu33 + 
           gt12L*gtu21*SQR(Gt212)) + gt22L*gtu33*SQR(Gt213) + gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt312) + 
        2*gt13L*gtu31*SQR(Gt313) + gt33L*gtu33*SQR(Gt313);
    
    Rt12  =  khalf*(-(gtu11*PDstandard4th11gt12) - 2*gtu21*PDstandard4th12gt12 - 2*gtu31*PDstandard4th13gt12 + 
          gt12L*PDstandard4th1Xt1 + gt22L*PDstandard4th1Xt2 + gt23L*PDstandard4th1Xt3 - gtu22*PDstandard4th22gt12 - 
          2*gtu32*PDstandard4th23gt12 + gt11L*PDstandard4th2Xt1 + gt12L*PDstandard4th2Xt2 + gt13L*PDstandard4th2Xt3 - 
          gtu33*PDstandard4th33gt12 + (Gt111*gt12L + Gt211*gt22L + gt23L*Gt311)*Xt1L + 
          (Gt112*gt11L + gt12L*Gt212 + gt13L*Gt312)*Xt1L + (Gt112*gt12L + Gt212*gt22L + gt23L*Gt312)*Xt2L + 
          (gt11L*Gt122 + gt12L*Gt222 + gt13L*Gt322)*Xt2L + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt3L + 
          (gt11L*Gt123 + gt12L*Gt223 + gt13L*Gt323)*Xt3L + 
          2*gtu21*(Gt112*gt11L*Gt222 + Gt112*Gt211*gt22L + Gt211*Gt222*gt22L + 2*Gt122*gt13L*Gt311 + Gt112*gt23L*Gt311 + 
             Gt222*gt23L*Gt311 + gt13L*Gt222*Gt312 + Gt213*gt22L*Gt312 + Gt212*gt23L*Gt312 + gt23L*Gt312*Gt313 + 
             Gt113*gt11L*Gt322 + Gt211*gt23L*Gt322 + gt13L*Gt313*Gt322 + 
             Gt111*(2*gt11L*Gt122 + Gt112*gt12L + gt12L*Gt222 + gt13L*Gt322) + 
             gt12L*(2*Gt122*Gt211 + Gt112*Gt212 + Gt212*Gt222 + Gt113*Gt312 + Gt213*Gt322) + Gt311*Gt322*gt33L + 
             gt22L*SQR(Gt212)) + 2*((Gt123*gt12L*Gt211 + Gt113*gt12L*Gt212 + 2*Gt112*gt12L*Gt213 + gt12L*Gt212*Gt223 + 
                Gt212*Gt213*gt22L + Gt211*Gt223*gt22L + gt12L*Gt133*Gt311 + gt22L*Gt233*Gt311 + Gt113*gt13L*Gt312 + 
                gt12L*Gt233*Gt312 + Gt213*gt23L*Gt312 + gt11L*(2*Gt112*Gt113 + Gt123*Gt212 + Gt133*Gt312) + 
                2*Gt112*gt13L*Gt313 + Gt212*gt23L*Gt313 + Gt111*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + 
                gt13L*Gt212*Gt323 + Gt211*gt23L*Gt323 + gt23L*Gt311*Gt333 + gt13L*Gt312*Gt333 + Gt312*Gt313*gt33L)*gtu31 + 
             (Gt123*gt12L*Gt212 + 2*Gt122*gt12L*Gt213 + Gt113*gt12L*Gt222 + gt12L*Gt222*Gt223 + Gt213*Gt222*gt22L + 
                Gt212*Gt223*gt22L + gt12L*Gt133*Gt312 + gt22L*Gt233*Gt312 + 2*Gt122*gt13L*Gt313 + Gt222*gt23L*Gt313 + 
                Gt112*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + Gt113*gt13L*Gt322 + gt12L*Gt233*Gt322 + 
                Gt213*gt23L*Gt322 + gt11L*(2*Gt113*Gt122 + Gt123*Gt222 + Gt133*Gt322) + gt13L*Gt222*Gt323 + 
                Gt212*gt23L*Gt323 + gt23L*Gt312*Gt333 + gt13L*Gt322*Gt333 + Gt313*Gt322*gt33L)*gtu32 + 
             gtu11*(3*Gt112*gt12L*Gt211 + 2*Gt211*Gt212*gt22L + Gt113*gt12L*Gt311 + 2*Gt112*gt13L*Gt311 + 
                Gt213*gt22L*Gt311 + Gt212*gt23L*Gt311 + gt13L*Gt212*Gt312 + gt12L*Gt213*Gt312 + 2*Gt211*gt23L*Gt312 + 
                gt11L*(2*Gt111*Gt112 + Gt112*Gt212 + Gt113*Gt312) + 
                Gt111*(gt12L*Gt212 + Gt211*gt22L + gt23L*Gt311 + gt13L*Gt312) + gt23L*Gt311*Gt313 + gt13L*Gt312*Gt313 + 
                Gt311*Gt312*gt33L + gt12L*SQR(Gt111) + gt12L*SQR(Gt212))) + 
          2*gtu22*(gt11L*Gt122*Gt222 + 2*Gt212*Gt222*gt22L + 2*Gt122*gt13L*Gt312 + Gt223*gt22L*Gt312 + Gt222*gt23L*Gt312 + 
             gt11L*Gt123*Gt322 + gt13L*Gt222*Gt322 + 2*Gt212*gt23L*Gt322 + 
             Gt112*(2*gt11L*Gt122 + gt12L*Gt222 + Gt212*gt22L + gt23L*Gt312 + gt13L*Gt322) + gt23L*Gt312*Gt323 + 
             gt13L*Gt322*Gt323 + Gt312*Gt322*gt33L + gt12L*SQR(Gt112) + 
             gt12L*(3*Gt122*Gt212 + Gt123*Gt312 + Gt223*Gt322 + SQR(Gt222))) + 
          2*gtu33*(gt11L*Gt123*Gt223 + 2*Gt213*Gt223*gt22L + 2*Gt123*gt13L*Gt313 + gt22L*Gt233*Gt313 + Gt223*gt23L*Gt313 + 
             gt11L*Gt133*Gt323 + gt13L*Gt223*Gt323 + 2*Gt213*gt23L*Gt323 + 
             Gt113*(2*gt11L*Gt123 + gt12L*Gt223 + Gt213*gt22L + gt23L*Gt313 + gt13L*Gt323) + gt23L*Gt313*Gt333 + 
             gt13L*Gt323*Gt333 + Gt313*Gt323*gt33L + gt12L*SQR(Gt113) + 
             gt12L*(3*Gt123*Gt213 + Gt133*Gt313 + Gt233*Gt323 + SQR(Gt223))) + 
          2*gtu21*(Gt122*gt12L*Gt211 + 3*Gt112*gt12L*Gt212 + gt12L*Gt212*Gt222 + Gt211*Gt222*gt22L + Gt123*gt12L*Gt311 + 
             Gt223*gt22L*Gt311 + 3*Gt112*gt13L*Gt312 + gt12L*Gt223*Gt312 + 2*Gt212*gt23L*Gt312 + 
             Gt111*(Gt112*gt12L + Gt212*gt22L + gt23L*Gt312) + gt13L*Gt212*Gt322 + Gt211*gt23L*Gt322 + gt23L*Gt311*Gt323 + 
             gt13L*Gt312*Gt323 + gt11L*(Gt122*Gt212 + Gt123*Gt312 + 2*SQR(Gt112)) + gt22L*SQR(Gt212) + gt33L*SQR(Gt312)) + 
          2*gtu31*(Gt112*gt11L*Gt223 + Gt113*Gt211*gt22L + Gt212*Gt213*gt22L + Gt211*Gt223*gt22L + 2*Gt123*gt13L*Gt311 + 
             Gt113*gt23L*Gt311 + Gt223*gt23L*Gt311 + gt13L*Gt223*Gt312 + Gt213*gt23L*Gt312 + Gt213*gt22L*Gt313 + 
             Gt113*gt11L*Gt323 + Gt211*gt23L*Gt323 + gt13L*Gt313*Gt323 + 
             Gt111*(2*gt11L*Gt123 + Gt113*gt12L + gt12L*Gt223 + gt13L*Gt323) + 
             gt12L*(2*Gt123*Gt211 + Gt112*Gt213 + Gt212*Gt223 + Gt113*Gt313 + Gt213*Gt323) + Gt311*Gt323*gt33L + 
             gt23L*SQR(Gt313)) + 2*gtu32*(gt11L*Gt122*Gt223 + Gt113*Gt212*gt22L + Gt213*Gt222*gt22L + Gt212*Gt223*gt22L + 
             2*Gt123*gt13L*Gt312 + Gt113*gt23L*Gt312 + Gt223*gt23L*Gt312 + Gt223*gt22L*Gt313 + gt13L*Gt223*Gt322 + 
             Gt213*gt23L*Gt322 + gt11L*Gt123*Gt323 + Gt212*gt23L*Gt323 + gt23L*Gt313*Gt323 + 
             Gt112*(2*gt11L*Gt123 + Gt113*gt12L + gt12L*Gt223 + gt13L*Gt323) + 
             gt12L*(Gt122*Gt213 + Gt123*(2*Gt212 + Gt313) + Gt223*(Gt222 + Gt323)) + Gt312*Gt323*gt33L + gt13L*SQR(Gt323)));
    
    Rt13  =  khalf*(-(gtu11*PDstandard4th11gt13) - 2*gtu21*PDstandard4th12gt13 - 2*gtu31*PDstandard4th13gt13 + 
          gt13L*PDstandard4th1Xt1 + gt23L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 - gtu22*PDstandard4th22gt13 - 
          2*gtu32*PDstandard4th23gt13 - gtu33*PDstandard4th33gt13 + gt11L*PDstandard4th3Xt1 + gt12L*PDstandard4th3Xt2 + 
          gt13L*PDstandard4th3Xt3 + (Gt113*gt11L + gt12L*Gt213 + gt13L*Gt313)*Xt1L + 
          (Gt111*gt13L + Gt211*gt23L + Gt311*gt33L)*Xt1L + (gt11L*Gt123 + gt12L*Gt223 + gt13L*Gt323)*Xt2L + 
          (Gt112*gt13L + Gt212*gt23L + Gt312*gt33L)*Xt2L + (gt11L*Gt133 + gt12L*Gt233 + gt13L*Gt333)*Xt3L + 
          (Gt113*gt13L + Gt213*gt23L + Gt313*gt33L)*Xt3L + 
          2*((Gt122*gt13L*Gt211 + 2*Gt113*gt12L*Gt212 + Gt112*gt12L*Gt213 + gt12L*Gt213*Gt222 + Gt212*Gt213*gt22L + 
                Gt211*Gt222*gt23L + Gt123*gt13L*Gt311 + Gt223*gt23L*Gt311 + 2*Gt113*gt13L*Gt312 + Gt213*gt23L*Gt312 + 
                Gt112*gt13L*Gt313 + gt12L*Gt223*Gt313 + Gt212*gt23L*Gt313 + 
                gt11L*(2*Gt112*Gt113 + Gt122*Gt213 + Gt123*Gt313) + gt13L*Gt213*Gt322 + gt13L*Gt313*Gt323 + 
                Gt312*Gt313*gt33L + Gt211*Gt322*gt33L + Gt311*Gt323*gt33L + Gt111*(Gt112*gt13L + Gt212*gt23L + Gt312*gt33L))
               *gtu21 + (Gt122*gt13L*Gt213 + gt11L*Gt122*Gt233 + Gt212*gt22L*Gt233 + Gt113*Gt212*gt23L + 
                Gt213*Gt222*gt23L + 2*Gt133*gt13L*Gt312 + Gt233*gt23L*Gt312 + Gt123*gt13L*Gt313 + Gt223*gt23L*Gt313 + 
                gt13L*Gt233*Gt322 + gt11L*Gt123*Gt333 + Gt212*gt23L*Gt333 + gt13L*Gt323*Gt333 + 
                Gt112*(2*gt11L*Gt133 + Gt113*gt13L + gt12L*Gt233 + gt13L*Gt333) + 
                gt12L*(2*Gt133*Gt212 + Gt222*Gt233 + Gt223*Gt333) + Gt113*Gt312*gt33L + Gt213*Gt322*gt33L + 
                Gt313*Gt323*gt33L + Gt312*Gt333*gt33L)*gtu32 + 
             gtu21*(2*Gt123*gt12L*Gt211 + Gt112*gt13L*Gt212 + gt12L*Gt212*Gt223 + Gt211*Gt223*gt22L + Gt112*Gt211*gt23L + 
                2*Gt123*gt13L*Gt311 + Gt223*gt23L*Gt311 + Gt113*gt13L*Gt312 + gt13L*Gt223*Gt312 + Gt213*gt23L*Gt312 + 
                gt12L*Gt213*Gt323 + Gt211*gt23L*Gt323 + gt13L*Gt313*Gt323 + 
                gt11L*(2*Gt111*Gt123 + Gt112*Gt223 + Gt113*Gt323) + Gt111*(Gt112*gt13L + gt12L*Gt223 + gt13L*Gt323) + 
                Gt112*Gt311*gt33L + Gt212*Gt312*gt33L + Gt312*Gt313*gt33L + Gt311*Gt323*gt33L + gt23L*SQR(Gt212))) + 
          2*gtu32*(Gt123*gt13L*Gt212 + 2*Gt123*gt12L*Gt213 + Gt113*gt12L*Gt223 + Gt213*Gt223*gt22L + Gt212*Gt223*gt23L + 
             Gt133*gt13L*Gt312 + Gt233*gt23L*Gt312 + 2*Gt123*gt13L*Gt313 + Gt223*gt23L*Gt313 + Gt113*gt13L*Gt323 + 
             gt13L*Gt223*Gt323 + gt12L*Gt233*Gt323 + Gt213*gt23L*Gt323 + 
             gt11L*(2*Gt113*Gt123 + Gt123*Gt223 + Gt133*Gt323) + gt13L*Gt323*Gt333 + Gt212*Gt323*gt33L + 
             Gt313*Gt323*gt33L + Gt312*Gt333*gt33L + Gt112*(Gt113*gt13L + Gt213*gt23L + Gt313*gt33L) + gt12L*SQR(Gt223)) + 
          2*gtu11*(2*Gt113*gt12L*Gt211 + Gt112*gt13L*Gt211 + gt12L*Gt212*Gt213 + Gt211*Gt213*gt22L + Gt211*Gt212*gt23L + 
             3*Gt113*gt13L*Gt311 + 2*Gt213*gt23L*Gt311 + gt13L*Gt213*Gt312 + gt12L*Gt213*Gt313 + Gt211*gt23L*Gt313 + 
             gt11L*(2*Gt111*Gt113 + Gt112*Gt213 + Gt113*Gt313) + Gt211*Gt312*gt33L + 2*Gt311*Gt313*gt33L + 
             Gt111*(gt12L*Gt213 + Gt211*gt23L + gt13L*Gt313 + Gt311*gt33L) + gt13L*SQR(Gt111) + gt13L*SQR(Gt313)) + 
          2*gtu31*(Gt112*gt13L*Gt213 + Gt112*gt11L*Gt233 + Gt211*gt22L*Gt233 + Gt113*Gt211*gt23L + Gt212*Gt213*gt23L + 
             2*Gt133*gt13L*Gt311 + Gt233*gt23L*Gt311 + gt13L*Gt233*Gt312 + Gt113*gt13L*Gt313 + Gt213*gt23L*Gt313 + 
             Gt113*gt11L*Gt333 + Gt211*gt23L*Gt333 + gt13L*Gt313*Gt333 + 
             Gt111*(2*gt11L*Gt133 + Gt113*gt13L + gt12L*Gt233 + gt13L*Gt333) + 
             gt12L*(2*Gt133*Gt211 + Gt212*Gt233 + Gt213*Gt333) + Gt113*Gt311*gt33L + Gt213*Gt312*gt33L + 
             Gt311*Gt333*gt33L + gt33L*SQR(Gt313)) + 
          2*gtu31*(Gt123*gt13L*Gt211 + 3*Gt113*gt12L*Gt213 + gt12L*Gt213*Gt223 + Gt211*Gt223*gt23L + Gt133*gt13L*Gt311 + 
             Gt233*gt23L*Gt311 + 3*Gt113*gt13L*Gt313 + gt12L*Gt233*Gt313 + 2*Gt213*gt23L*Gt313 + gt13L*Gt213*Gt323 + 
             gt13L*Gt313*Gt333 + Gt211*Gt323*gt33L + Gt311*Gt333*gt33L + Gt111*(Gt113*gt13L + Gt213*gt23L + Gt313*gt33L) + 
             gt11L*(Gt123*Gt213 + Gt133*Gt313 + 2*SQR(Gt113)) + gt22L*SQR(Gt213) + gt33L*SQR(Gt313)) + 
          2*gtu22*(2*Gt123*gt12L*Gt212 + Gt122*gt13L*Gt212 + gt12L*Gt222*Gt223 + Gt212*Gt223*gt22L + Gt212*Gt222*gt23L + 
             3*Gt123*gt13L*Gt312 + 2*Gt223*gt23L*Gt312 + gt13L*Gt223*Gt322 + gt12L*Gt223*Gt323 + Gt212*gt23L*Gt323 + 
             gt11L*(2*Gt112*Gt123 + Gt122*Gt223 + Gt123*Gt323) + Gt212*Gt322*gt33L + 2*Gt312*Gt323*gt33L + 
             Gt112*(gt12L*Gt223 + Gt212*gt23L + gt13L*Gt323 + Gt312*gt33L) + gt13L*SQR(Gt112) + gt13L*SQR(Gt323)) + 
          2*gtu33*(2*gt12L*Gt133*Gt213 + Gt123*gt13L*Gt213 + gt11L*Gt123*Gt233 + gt12L*Gt223*Gt233 + Gt213*gt22L*Gt233 + 
             Gt213*Gt223*gt23L + 3*Gt133*gt13L*Gt313 + 2*Gt233*gt23L*Gt313 + gt13L*Gt233*Gt323 + gt11L*Gt133*Gt333 + 
             gt12L*Gt233*Gt333 + Gt213*gt23L*Gt333 + Gt213*Gt323*gt33L + 2*Gt313*Gt333*gt33L + 
             Gt113*(2*gt11L*Gt133 + gt12L*Gt233 + Gt213*gt23L + gt13L*Gt333 + Gt313*gt33L) + gt13L*SQR(Gt113) + 
             gt13L*SQR(Gt333)));
    
    Rt22  =  4*(Gt122*gt12L*Gt212*gtu21 + Gt112*gt12L*Gt222*gtu21 + Gt122*gt12L*Gt222*gtu22 + Gt123*gt12L*Gt212*gtu31 + 
           Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandard4th11gt22 + 
        gtu21*(6*Gt212*Gt222*gt22L + 2*Gt122*gt23L*Gt311 + 2*Gt122*gt13L*Gt312 + 4*Gt222*gt23L*Gt312 + 
           2*Gt113*gt12L*Gt322 + 2*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandard4th12gt22) + 
        gtu31*(6*Gt212*Gt223*gt22L + 2*Gt123*gt13L*Gt312 + 2*Gt112*gt23L*Gt313 + 2*Gt113*gt12L*Gt323 + 
           2*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandard4th13gt22) - gtu22*khalf*PDstandard4th22gt22 + 
        gtu32*(4*Gt122*gt12L*Gt223 + 2*Gt123*Gt212*gt22L + 2*gt12L*Gt133*Gt322 + 4*Gt223*gt23L*Gt322 + 
           2*Gt123*gt12L*Gt323 + 4*Gt222*gt23L*Gt323 + 2*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - PDstandard4th23gt22) + 
        gt12L*(2*Gt111*Gt123*gtu31 + 4*Gt112*Gt223*gtu31 + 2*Gt113*Gt122*gtu32 + 2*Gt113*Gt123*gtu33 + PDstandard4th2Xt1) + 
        gt22L*(2*Gt122*Gt213*gtu32 + 6*Gt222*Gt223*gtu32 + 2*Gt123*Gt213*gtu33 + PDstandard4th2Xt2) + 
        gt23L*(4*Gt212*Gt322*gtu21 + 2*Gt313*Gt322*gtu21 + 4*Gt222*Gt322*gtu22 + 2*Gt123*Gt311*gtu31 + 
           4*Gt212*Gt323*gtu31 + 2*Gt313*Gt323*gtu31 + 2*Gt122*Gt313*gtu32 + 2*Gt123*Gt313*gtu33 + 4*Gt223*Gt323*gtu33 + 
           2*Gt323*Gt333*gtu33 + PDstandard4th2Xt3) - gtu33*khalf*PDstandard4th33gt22 + Gt212*gt22L*Xt1L + 
        Gt112*(2*Gt111*gt12L*gtu11 + 4*gt12L*Gt212*gtu11 + 2*gt11L*Gt122*gtu21 + 2*Gt122*gt12L*gtu22 + 
           2*gt11L*Gt123*gtu31 + 2*Gt123*gt12L*gtu32 + gt12L*Xt1L) + 
        Gt312*(2*Gt213*gt22L*gtu11 + 4*Gt212*gt23L*gtu11 + 2*gt23L*Gt313*gtu11 + 2*Gt123*gt12L*gtu21 + 
           2*Gt122*gt23L*gtu22 + 2*gt12L*Gt133*gtu31 + 2*gt22L*Gt233*gtu31 + 4*Gt223*gt23L*gtu31 + 2*Gt123*gt23L*gtu32 + 
           gt23L*Xt1L) + Gt122*gt12L*Xt2L + Gt222*gt22L*Xt2L + gt23L*Gt322*Xt2L + Gt123*gt12L*Xt3L + Gt223*gt22L*Xt3L + 
        gt23L*Gt323*Xt3L + gt11L*gtu11*SQR(Gt112) + 2*
         (Gt112*Gt211*gt22L*gtu11 + Gt112*gt23L*Gt311*gtu11 + Gt113*gt12L*Gt312*gtu11 + Gt112*gt13L*Gt312*gtu11 + 
           Gt111*Gt122*gt12L*gtu21 + Gt122*Gt211*gt22L*gtu21 + Gt112*Gt212*gt22L*gtu21 + Gt223*gt22L*Gt312*gtu21 + 
           Gt112*gt23L*Gt312*gtu21 + Gt112*gt13L*Gt322*gtu21 + Gt213*gt22L*Gt322*gtu21 + Gt122*Gt212*gt22L*gtu22 + 
           Gt123*gt12L*Gt322*gtu22 + Gt122*gt13L*Gt322*gtu22 + Gt223*gt22L*Gt322*gtu22 + gt23L*Gt322*Gt323*gtu22 + 
           Gt112*Gt113*gt12L*gtu31 + Gt123*Gt211*gt22L*gtu31 + Gt112*Gt213*gt22L*gtu31 + Gt112*gt13L*Gt323*gtu31 + 
           Gt213*gt22L*Gt323*gtu31 + gt11L*Gt122*Gt123*gtu32 + Gt123*gt13L*Gt322*gtu32 + gt22L*Gt233*Gt322*gtu32 + 
           Gt122*gt13L*Gt323*gtu32 + Gt223*gt22L*Gt323*gtu32 + gt12L*Gt133*Gt323*gtu33 + Gt123*gt13L*Gt323*gtu33 + 
           gt22L*Gt233*Gt323*gtu33 + gt12L*gtu21*SQR(Gt112)) + gt11L*gtu22*SQR(Gt122) + gt11L*gtu33*SQR(Gt123) + 
        3*gt22L*gtu11*SQR(Gt212) + 3*gt22L*gtu22*SQR(Gt222) + 3*gt22L*gtu33*SQR(Gt223) + gt33L*gtu11*SQR(Gt312) + 
        gt33L*gtu22*SQR(Gt322) + 2*gt23L*gtu32*SQR(Gt323) + gt33L*gtu33*SQR(Gt323);
    
    Rt23  =  khalf*(-(gtu11*PDstandard4th11gt23) - 2*gtu21*PDstandard4th12gt23 - 2*gtu31*PDstandard4th13gt23 - 
          gtu22*PDstandard4th22gt23 - 2*gtu32*PDstandard4th23gt23 + gt13L*PDstandard4th2Xt1 + gt23L*PDstandard4th2Xt2 + 
          gt33L*PDstandard4th2Xt3 - gtu33*PDstandard4th33gt23 + gt12L*PDstandard4th3Xt1 + gt22L*PDstandard4th3Xt2 + 
          gt23L*PDstandard4th3Xt3 + (Gt113*gt12L + Gt213*gt22L + gt23L*Gt313)*Xt1L + 
          (Gt112*gt13L + Gt212*gt23L + Gt312*gt33L)*Xt1L + (Gt123*gt12L + Gt223*gt22L + gt23L*Gt323)*Xt2L + 
          (Gt122*gt13L + Gt222*gt23L + Gt322*gt33L)*Xt2L + (gt12L*Gt133 + gt22L*Gt233 + gt23L*Gt333)*Xt3L + 
          (Gt123*gt13L + Gt223*gt23L + Gt323*gt33L)*Xt3L + 
          2*((Gt112*gt11L*Gt123 + Gt111*Gt123*gt12L + Gt111*Gt122*gt13L + Gt123*gt12L*Gt212 + Gt112*gt13L*Gt222 + 
                2*Gt112*gt12L*Gt223 + Gt123*Gt211*gt22L + 2*Gt212*Gt223*gt22L + Gt122*Gt211*gt23L + Gt212*Gt222*gt23L + 
                Gt123*gt23L*Gt311 + Gt123*gt13L*Gt312 + 2*Gt223*gt23L*Gt312 + Gt113*gt13L*Gt322 + Gt213*gt23L*Gt322 + 
                Gt113*gt12L*Gt323 + Gt112*gt13L*Gt323 + Gt213*gt22L*Gt323 + Gt212*gt23L*Gt323 + gt23L*Gt313*Gt323 + 
                Gt122*Gt311*gt33L + Gt222*Gt312*gt33L + Gt313*Gt322*gt33L + Gt312*Gt323*gt33L)*gtu21 + 
             (Gt112*gt11L*Gt133 + Gt111*gt12L*Gt133 + Gt111*Gt123*gt13L + gt12L*Gt133*Gt212 + Gt112*gt13L*Gt223 + 
                Gt133*Gt211*gt22L + 2*Gt112*gt12L*Gt233 + 2*Gt212*gt22L*Gt233 + Gt123*Gt211*gt23L + Gt212*Gt223*gt23L + 
                Gt133*gt23L*Gt311 + Gt133*gt13L*Gt312 + 2*Gt233*gt23L*Gt312 + Gt113*gt13L*Gt323 + Gt213*gt23L*Gt323 + 
                Gt113*gt12L*Gt333 + Gt112*gt13L*Gt333 + Gt213*gt22L*Gt333 + Gt212*gt23L*Gt333 + gt23L*Gt313*Gt333 + 
                Gt123*Gt311*gt33L + Gt223*Gt312*gt33L + Gt313*Gt323*gt33L + Gt312*Gt333*gt33L)*gtu31 + 
             gtu21*(Gt113*gt11L*Gt122 + Gt122*gt13L*Gt212 + 2*Gt122*gt12L*Gt213 + Gt113*gt12L*Gt222 + Gt113*Gt212*gt22L + 
                2*Gt213*Gt222*gt22L + Gt212*Gt222*gt23L + Gt123*gt13L*Gt312 + Gt113*gt23L*Gt312 + Gt223*gt23L*Gt312 + 
                Gt123*gt12L*Gt313 + Gt122*gt13L*Gt313 + Gt223*gt22L*Gt313 + Gt222*gt23L*Gt313 + Gt113*gt13L*Gt322 + 
                2*Gt213*gt23L*Gt322 + gt23L*Gt313*Gt323 + Gt212*Gt322*gt33L + Gt313*Gt322*gt33L + Gt312*Gt323*gt33L + 
                Gt112*(Gt113*gt12L + Gt212*gt23L + Gt312*gt33L) + gt13L*SQR(Gt112))) + 
          2*gtu31*(2*Gt213*Gt223*gt22L + Gt112*Gt213*gt23L + Gt212*Gt223*gt23L + Gt133*gt13L*Gt312 + Gt233*gt23L*Gt312 + 
             gt12L*Gt133*Gt313 + gt22L*Gt233*Gt313 + Gt223*gt23L*Gt313 + Gt123*(2*gt12L*Gt213 + gt13L*(Gt212 + Gt313)) + 
             2*Gt213*gt23L*Gt323 + Gt113*(gt11L*Gt123 + Gt112*gt13L + gt12L*Gt223 + Gt213*gt22L + gt23L*Gt313 + 
                gt13L*Gt323) + gt23L*Gt313*Gt333 + Gt112*Gt313*gt33L + Gt212*Gt323*gt33L + Gt313*Gt323*gt33L + 
             Gt312*Gt333*gt33L + gt12L*SQR(Gt113)) + 
          2*gtu11*(Gt112*Gt113*gt11L + Gt111*Gt113*gt12L + Gt111*Gt112*gt13L + Gt113*gt12L*Gt212 + Gt112*gt13L*Gt212 + 
             2*Gt112*gt12L*Gt213 + Gt113*Gt211*gt22L + 2*Gt212*Gt213*gt22L + Gt112*Gt211*gt23L + Gt113*gt23L*Gt311 + 
             2*Gt113*gt13L*Gt312 + 3*Gt213*gt23L*Gt312 + Gt113*gt12L*Gt313 + Gt112*gt13L*Gt313 + Gt213*gt22L*Gt313 + 
             Gt212*gt23L*Gt313 + Gt112*Gt311*gt33L + Gt212*Gt312*gt33L + 2*Gt312*Gt313*gt33L + gt23L*SQR(Gt212) + 
             gt23L*SQR(Gt313)) + 2*gtu22*(gt11L*Gt122*Gt123 + Gt112*Gt123*gt12L + Gt112*Gt122*gt13L + Gt123*gt12L*Gt222 + 
             Gt122*gt13L*Gt222 + 2*Gt122*gt12L*Gt223 + Gt123*Gt212*gt22L + 2*Gt222*Gt223*gt22L + Gt122*Gt212*gt23L + 
             Gt123*gt23L*Gt312 + 2*Gt123*gt13L*Gt322 + 3*Gt223*gt23L*Gt322 + Gt123*gt12L*Gt323 + Gt122*gt13L*Gt323 + 
             Gt223*gt22L*Gt323 + Gt222*gt23L*Gt323 + Gt122*Gt312*gt33L + Gt222*Gt322*gt33L + 2*Gt322*Gt323*gt33L + 
             gt23L*SQR(Gt222) + gt23L*SQR(Gt323)) + 2*gtu32*
           (gt11L*Gt122*Gt133 + Gt112*gt12L*Gt133 + Gt112*Gt123*gt13L + gt12L*Gt133*Gt222 + Gt122*gt13L*Gt223 + 
             Gt133*Gt212*gt22L + 2*Gt122*gt12L*Gt233 + 2*Gt222*gt22L*Gt233 + Gt123*Gt212*gt23L + Gt222*Gt223*gt23L + 
             Gt133*gt23L*Gt312 + Gt133*gt13L*Gt322 + 2*Gt233*gt23L*Gt322 + Gt123*gt13L*Gt323 + Gt223*gt23L*Gt323 + 
             Gt123*gt12L*Gt333 + Gt122*gt13L*Gt333 + Gt223*gt22L*Gt333 + Gt222*gt23L*Gt333 + gt23L*Gt323*Gt333 + 
             Gt123*Gt312*gt33L + Gt223*Gt322*gt33L + Gt322*Gt333*gt33L + gt33L*SQR(Gt323)) + 
          2*gtu32*(Gt113*Gt123*gt12L + Gt113*Gt122*gt13L + Gt123*gt13L*Gt222 + 3*Gt123*gt12L*Gt223 + Gt123*Gt213*gt22L + 
             Gt122*Gt213*gt23L + Gt222*Gt223*gt23L + Gt123*gt23L*Gt313 + Gt133*gt13L*Gt322 + Gt233*gt23L*Gt322 + 
             gt12L*Gt133*Gt323 + 2*Gt123*gt13L*Gt323 + gt22L*Gt233*Gt323 + 3*Gt223*gt23L*Gt323 + gt23L*Gt323*Gt333 + 
             Gt122*Gt313*gt33L + Gt222*Gt323*gt33L + Gt322*Gt333*gt33L + gt11L*SQR(Gt123) + 2*gt22L*SQR(Gt223) + 
             gt33L*SQR(Gt323)) + 2*gtu33*(gt11L*Gt123*Gt133 + Gt113*gt12L*Gt133 + Gt113*Gt123*gt13L + gt12L*Gt133*Gt223 + 
             Gt123*gt13L*Gt223 + Gt133*Gt213*gt22L + 2*Gt123*gt12L*Gt233 + 2*Gt223*gt22L*Gt233 + Gt123*Gt213*gt23L + 
             Gt133*gt23L*Gt313 + 2*Gt133*gt13L*Gt323 + 3*Gt233*gt23L*Gt323 + gt12L*Gt133*Gt333 + Gt123*gt13L*Gt333 + 
             gt22L*Gt233*Gt333 + Gt223*gt23L*Gt333 + Gt123*Gt313*gt33L + Gt223*Gt323*gt33L + 2*Gt323*Gt333*gt33L + 
             gt23L*SQR(Gt223) + gt23L*SQR(Gt333)));
    
    Rt33  =  4*(Gt123*gt13L*Gt323*gtu22 + Gt223*gt23L*Gt323*gtu22 + Gt133*gt13L*Gt313*gtu31 + Gt233*gt23L*Gt313*gtu31 + 
           Gt113*gt13L*Gt333*gtu31 + Gt133*gt13L*Gt323*gtu32 + Gt233*gt23L*Gt323*gtu32 + Gt123*gt13L*Gt333*gtu32 + 
           Gt133*gt13L*Gt333*gtu33) + gtu21*(2*Gt212*Gt223*gt23L + 4*Gt123*gt13L*Gt313 + 4*Gt223*gt23L*Gt313 + 
           4*Gt113*gt13L*Gt323 + 4*Gt213*gt23L*Gt323 + 2*Gt123*Gt311*gt33L - PDstandard4th12gt33) + 
        gtu31*(4*Gt213*gt23L*Gt333 + 2*Gt233*Gt312*gt33L + 6*Gt313*Gt333*gt33L - PDstandard4th13gt33) - 
        gtu22*khalf*PDstandard4th22gt33 + gtu32*(4*Gt223*gt23L*Gt333 + 2*Gt123*Gt313*gt33L + 6*Gt323*Gt333*gt33L - 
           PDstandard4th23gt33) - gtu33*khalf*PDstandard4th33gt33 + gt13L*PDstandard4th3Xt1 + gt23L*PDstandard4th3Xt2 + 
        gt33L*(2*Gt213*Gt322*gtu21 + 6*Gt313*Gt323*gtu21 + 2*Gt123*Gt312*gtu22 + 2*Gt133*Gt311*gtu31 + 
           2*Gt133*Gt312*gtu32 + 2*Gt133*Gt313*gtu33 + PDstandard4th3Xt3) + Gt113*gt13L*Xt1L + Gt213*gt23L*Xt1L + 
        Gt313*gt33L*Xt1L + Gt123*gt13L*Xt2L + Gt223*gt23L*Xt2L + Gt323*gt33L*Xt2L + Gt133*gt13L*Xt3L + Gt333*gt33L*Xt3L + 
        Gt233*(4*gt23L*Gt333*gtu33 + 2*Gt323*gt33L*gtu33 + gt23L*Xt3L) + 
        gtu11*(2*Gt212*Gt213*gt23L + 4*Gt113*gt13L*Gt313 + 4*Gt213*gt23L*Gt313 + 2*Gt113*Gt311*gt33L + 
           2*Gt213*Gt312*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt113)) + 
        2*(Gt111*Gt113*gt13L*gtu11 + Gt113*gt12L*Gt213*gtu11 + Gt112*gt13L*Gt213*gtu11 + Gt113*Gt211*gt23L*gtu11 + 
           Gt113*gt11L*Gt123*gtu21 + Gt112*Gt113*gt13L*gtu21 + Gt111*Gt123*gt13L*gtu21 + Gt123*gt12L*Gt213*gtu21 + 
           Gt122*gt13L*Gt213*gtu21 + Gt113*gt12L*Gt223*gtu21 + Gt112*gt13L*Gt223*gtu21 + Gt213*Gt223*gt22L*gtu21 + 
           Gt123*Gt211*gt23L*gtu21 + Gt113*Gt212*gt23L*gtu21 + Gt213*Gt222*gt23L*gtu21 + Gt113*Gt312*gt33L*gtu21 + 
           Gt223*Gt312*gt33L*gtu21 + Gt112*Gt123*gt13L*gtu22 + Gt123*gt12L*Gt223*gtu22 + Gt122*gt13L*Gt223*gtu22 + 
           Gt123*Gt212*gt23L*gtu22 + Gt222*Gt223*gt23L*gtu22 + Gt223*Gt322*gt33L*gtu22 + Gt113*gt11L*Gt133*gtu31 + 
           Gt111*Gt133*gt13L*gtu31 + gt12L*Gt133*Gt213*gtu31 + Gt123*gt13L*Gt213*gtu31 + Gt113*gt12L*Gt233*gtu31 + 
           Gt112*gt13L*Gt233*gtu31 + Gt213*gt22L*Gt233*gtu31 + Gt133*Gt211*gt23L*gtu31 + Gt113*Gt213*gt23L*gtu31 + 
           Gt213*Gt223*gt23L*gtu31 + Gt212*Gt233*gt23L*gtu31 + Gt113*Gt313*gt33L*gtu31 + Gt213*Gt323*gt33L*gtu31 + 
           gt11L*Gt123*Gt133*gtu32 + Gt113*Gt123*gt13L*gtu32 + Gt112*Gt133*gt13L*gtu32 + gt12L*Gt133*Gt223*gtu32 + 
           Gt123*gt13L*Gt223*gtu32 + Gt123*gt12L*Gt233*gtu32 + Gt122*gt13L*Gt233*gtu32 + Gt223*gt22L*Gt233*gtu32 + 
           Gt133*Gt212*gt23L*gtu32 + Gt123*Gt213*gt23L*gtu32 + Gt222*Gt233*gt23L*gtu32 + Gt233*Gt322*gt33L*gtu32 + 
           Gt223*Gt323*gt33L*gtu32 + Gt113*Gt133*gt13L*gtu33 + gt12L*Gt133*Gt233*gtu33 + Gt123*gt13L*Gt233*gtu33 + 
           Gt133*Gt213*gt23L*gtu33 + Gt223*Gt233*gt23L*gtu33 + gt13L*gtu31*SQR(Gt113)) + gt11L*gtu22*SQR(Gt123) + 
        gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt213) + gt22L*gtu22*SQR(Gt223) + 2*gt23L*gtu32*SQR(Gt223) + 
        gt22L*gtu33*SQR(Gt233) + 3*gt33L*gtu11*SQR(Gt313) + 3*gt33L*gtu22*SQR(Gt323) + 3*gt33L*gtu33*SQR(Gt333);
    
    Rphi11  =  2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu21*PDstandard4th12phi - 
          2*gt11L*gtu31*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu32*PDstandard4th23phi - 
          gt11L*gtu33*PDstandard4th33phi + Gt311*PDstandard4th3phi + gt11L*Gt311*gtu11*PDstandard4th3phi + 
          2*gt11L*Gt312*gtu21*PDstandard4th3phi + gt11L*Gt322*gtu22*PDstandard4th3phi + 
          2*gt11L*Gt313*gtu31*PDstandard4th3phi + 2*gt11L*Gt323*gtu32*PDstandard4th3phi + 
          gt11L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi*
           (Gt111 + Gt111*gt11L*gtu11 + 2*Gt112*gt11L*gtu21 + gt11L*Gt122*gtu22 + 2*Gt113*gt11L*gtu31 + 
             2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandard4th2phi - 4*gt11L*gtu31*PDstandard4th3phi) + 
          PDstandard4th2phi*(Gt211 + gt11L*Gt211*gtu11 + 
             gt11L*(2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - 
             4*gt11L*gtu32*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - 
          2*gt11L*gtu22*SQR(PDstandard4th2phi) - 2*gt11L*gtu33*SQR(PDstandard4th3phi));
    
    Rphi12  =  2*(-(gt12L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt12L*gtu21*PDstandard4th12phi - 
          2*gt12L*gtu31*PDstandard4th13phi - gt12L*gtu22*PDstandard4th22phi - 2*gt12L*gtu32*PDstandard4th23phi - 
          gt12L*gtu33*PDstandard4th33phi + Gt312*PDstandard4th3phi + gt12L*Gt311*gtu11*PDstandard4th3phi + 
          2*gt12L*Gt312*gtu21*PDstandard4th3phi + gt12L*Gt322*gtu22*PDstandard4th3phi + 
          2*gt12L*Gt313*gtu31*PDstandard4th3phi + 2*gt12L*Gt323*gtu32*PDstandard4th3phi + 
          gt12L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi*
           (Gt112 + Gt111*gt12L*gtu11 + 2*Gt112*gt12L*gtu21 + Gt122*gt12L*gtu22 + 2*Gt113*gt12L*gtu31 + 
             2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandard4th2phi - 
             4*gt12L*gtu31*PDstandard4th3phi) + PDstandard4th2phi*
           (Gt212 + 2*gt12L*Gt212*gtu21 + gt12L*(Gt211*gtu11 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - 
             4*gt12L*gtu32*PDstandard4th3phi) - 2*gt12L*gtu11*SQR(PDstandard4th1phi) - 
          2*gt12L*gtu22*SQR(PDstandard4th2phi) - 2*gt12L*gtu33*SQR(PDstandard4th3phi));
    
    Rphi13  =  2*(-PDstandard4th13phi + gt13L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 
             2*gtu31*PDstandard4th13phi) - gt13L*gtu22*PDstandard4th22phi - 2*gt13L*gtu32*PDstandard4th23phi - 
          gt13L*gtu33*PDstandard4th33phi + Gt313*PDstandard4th3phi + gt13L*Gt311*gtu11*PDstandard4th3phi + 
          2*gt13L*Gt312*gtu21*PDstandard4th3phi + gt13L*Gt322*gtu22*PDstandard4th3phi + 
          2*gt13L*Gt313*gtu31*PDstandard4th3phi + 2*gt13L*Gt323*gtu32*PDstandard4th3phi + 
          gt13L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi*
           (Gt113 + Gt111*gt13L*gtu11 + 2*Gt112*gt13L*gtu21 + Gt122*gt13L*gtu22 + 2*Gt113*gt13L*gtu31 + 
             2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandard4th2phi + 
             (2 - 4*gt13L*gtu31)*PDstandard4th3phi) + 
          PDstandard4th2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + 
             gt13L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt223*gtu32 + Gt233*gtu33) - 
             4*gt13L*gtu32*PDstandard4th3phi) - 2*gt13L*gtu11*SQR(PDstandard4th1phi) - 
          2*gt13L*gtu22*SQR(PDstandard4th2phi) - 2*gt13L*gtu33*SQR(PDstandard4th3phi));
    
    Rphi22  =  2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 
             2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu32*PDstandard4th23phi - 
          gt22L*gtu33*PDstandard4th33phi + Gt322*PDstandard4th3phi + gt22L*Gt311*gtu11*PDstandard4th3phi + 
          2*gt22L*Gt312*gtu21*PDstandard4th3phi + gt22L*Gt322*gtu22*PDstandard4th3phi + 
          2*gt22L*Gt313*gtu31*PDstandard4th3phi + 2*gt22L*Gt323*gtu32*PDstandard4th3phi + 
          gt22L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi*
           (Gt122 + Gt111*gt22L*gtu11 + 2*Gt112*gt22L*gtu21 + Gt122*gt22L*gtu22 + 2*Gt113*gt22L*gtu31 + 
             2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandard4th2phi - 4*gt22L*gtu31*PDstandard4th3phi) + 
          PDstandard4th2phi*(Gt222 + Gt222*gt22L*gtu22 + 
             gt22L*(Gt211*gtu11 + 2*Gt212*gtu21 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - 
             4*gt22L*gtu32*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + 
          (2 - 2*gt22L*gtu22)*SQR(PDstandard4th2phi) - 2*gt22L*gtu33*SQR(PDstandard4th3phi));
    
    Rphi23  =  2*(-PDstandard4th23phi + gt23L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 
             2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi) - 
          gt23L*gtu33*PDstandard4th33phi + Gt323*PDstandard4th3phi + gt23L*Gt311*gtu11*PDstandard4th3phi + 
          2*gt23L*Gt312*gtu21*PDstandard4th3phi + gt23L*Gt322*gtu22*PDstandard4th3phi + 
          2*gt23L*Gt313*gtu31*PDstandard4th3phi + 2*gt23L*Gt323*gtu32*PDstandard4th3phi + 
          gt23L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi*
           (Gt123 + Gt111*gt23L*gtu11 + 2*Gt112*gt23L*gtu21 + Gt122*gt23L*gtu22 + 2*Gt113*gt23L*gtu31 + 
             2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandard4th2phi - 4*gt23L*gtu31*PDstandard4th3phi) + 
          PDstandard4th2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + 
             gt23L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + Gt233*gtu33) + 
             (2 - 4*gt23L*gtu32)*PDstandard4th3phi) - 2*gt23L*gtu11*SQR(PDstandard4th1phi) - 
          2*gt23L*gtu22*SQR(PDstandard4th2phi) - 2*gt23L*gtu33*SQR(PDstandard4th3phi));
    
    Rphi33  =  2*(-PDstandard4th33phi + (Gt333 + gt33L*
              (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandard4th3phi + 
          PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + 
                Gt233*gtu33 - 4*gtu32*PDstandard4th3phi)) + 
          PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + 
                Gt133*gtu33 - 4*(gtu21*PDstandard4th2phi + gtu31*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + 
          gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 2*gtu31*PDstandard4th13phi - 
             gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi - gtu33*PDstandard4th33phi + 
             Gt311*gtu11*PDstandard4th3phi - 2*gtu11*SQR(PDstandard4th1phi) - 2*gtu22*SQR(PDstandard4th2phi) - 
             2*gtu33*SQR(PDstandard4th3phi)));
    
    e4phi  =  exp(4*phiL);
    
    em4phi  =  INV(e4phi);
    
    gu11  =  em4phi*gtu11;
    
    gu21  =  em4phi*gtu21;
    
    gu31  =  em4phi*gtu31;
    
    gu22  =  em4phi*gtu22;
    
    gu32  =  em4phi*gtu32;
    
    gu33  =  em4phi*gtu33;
    
    R11  =  Rphi11 + Rt11;
    
    R12  =  Rphi12 + Rt12;
    
    R13  =  Rphi13 + Rt13;
    
    R22  =  Rphi22 + Rt22;
    
    R23  =  Rphi23 + Rt23;
    
    R33  =  Rphi33 + Rt33;
    
    trR  =  gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33;
    
    Atm11  =  At11L*gtu11 + At12L*gtu21 + At13L*gtu31;
    
    Atm21  =  At11L*gtu21 + At12L*gtu22 + At13L*gtu32;
    
    Atm31  =  At11L*gtu31 + At12L*gtu32 + At13L*gtu33;
    
    Atm12  =  At12L*gtu11 + At22L*gtu21 + At23L*gtu31;
    
    Atm22  =  At12L*gtu21 + At22L*gtu22 + At23L*gtu32;
    
    Atm32  =  At12L*gtu31 + At22L*gtu32 + At23L*gtu33;
    
    Atm13  =  At13L*gtu11 + At23L*gtu21 + At33L*gtu31;
    
    Atm23  =  At13L*gtu21 + At23L*gtu22 + At33L*gtu32;
    
    Atm33  =  At13L*gtu31 + At23L*gtu32 + At33L*gtu33;
    
    HL  =  -2*(Atm12*Atm21 + Atm13*Atm31 + Atm23*Atm32) + trR - SQR(Atm11) - SQR(Atm22) - SQR(Atm33) + ktwothird*SQR(trKL);
    
    M1L  =  -(At12L*Gt112*gtu22) - At11L*Gt122*gtu22 - At22L*Gt212*gtu22 - At12L*Gt222*gtu22 - At23L*Gt312*gtu22 - 
        At13L*Gt322*gtu22 - At13L*Gt111*gtu31 - 3*At11L*Gt113*gtu31 - At23L*Gt211*gtu31 - 3*At12L*Gt213*gtu31 - 
        At33L*Gt311*gtu31 - 3*At13L*Gt313*gtu31 - At13L*Gt112*gtu32 - At12L*Gt113*gtu32 - At23L*Gt212*gtu32 - 
        At22L*Gt213*gtu32 - 2*At12L*Gt223*gtu32 - At33L*Gt312*gtu32 - At23L*Gt313*gtu32 - 2*At13L*Gt323*gtu32 - 
        2*(At11L*Gt111*gtu11 + At12L*Gt211*gtu11 + At13L*Gt311*gtu11 + At11L*Gt123*gtu32) - At13L*Gt113*gtu33 - 
        At11L*Gt133*gtu33 - At23L*Gt213*gtu33 - At12L*Gt233*gtu33 - At33L*Gt313*gtu33 - At13L*Gt333*gtu33 + 
        gtu11*PDstandard4th1At11 + gtu21*(-(At12L*Gt111) - 3*At11L*Gt112 - At22L*Gt211 - 3*At12L*Gt212 - At23L*Gt311 - 
           3*At13L*Gt312 + PDstandard4th1At12) + gtu31*PDstandard4th1At13 + 6*At11L*gtu11*PDstandard4th1phi + 
        6*At12L*gtu21*PDstandard4th1phi + 6*At13L*gtu31*PDstandard4th1phi - ktwothird*PDstandard4th1trK + 
        gtu21*PDstandard4th2At11 + gtu22*PDstandard4th2At12 + gtu32*PDstandard4th2At13 + 6*At11L*gtu21*PDstandard4th2phi + 
        6*At12L*gtu22*PDstandard4th2phi + 6*At13L*gtu32*PDstandard4th2phi + gtu31*PDstandard4th3At11 + 
        gtu32*PDstandard4th3At12 + gtu33*PDstandard4th3At13 + 6*At11L*gtu31*PDstandard4th3phi + 
        6*At12L*gtu32*PDstandard4th3phi + 6*At13L*gtu33*PDstandard4th3phi;
    
    M2L  =  -(At12L*Gt111*gtu11) - At11L*Gt112*gtu11 - At22L*Gt211*gtu11 - At12L*Gt212*gtu11 - At23L*Gt311*gtu11 - 
        At13L*Gt312*gtu11 - 3*At12L*Gt112*gtu21 - At11L*Gt122*gtu21 - 3*At22L*Gt212*gtu21 - At12L*Gt222*gtu21 - 
        3*At23L*Gt312*gtu21 - At13L*Gt322*gtu21 - 2*At12L*Gt122*gtu22 - 2*At22L*Gt222*gtu22 - 2*At23L*Gt322*gtu22 - 
        At13L*Gt112*gtu31 - 2*At12L*Gt113*gtu31 - At11L*Gt123*gtu31 - At23L*Gt212*gtu31 - 2*At22L*Gt213*gtu31 - 
        At12L*Gt223*gtu31 - At33L*Gt312*gtu31 - 2*At23L*Gt313*gtu31 - At13L*Gt323*gtu31 - At13L*Gt122*gtu32 - 
        3*At12L*Gt123*gtu32 - At23L*Gt222*gtu32 - 3*At22L*Gt223*gtu32 - At33L*Gt322*gtu32 - 3*At23L*Gt323*gtu32 - 
        At13L*Gt123*gtu33 - At12L*Gt133*gtu33 - At23L*Gt223*gtu33 - At22L*Gt233*gtu33 - At33L*Gt323*gtu33 - 
        At23L*Gt333*gtu33 + gtu11*PDstandard4th1At12 + gtu21*PDstandard4th1At22 + gtu31*PDstandard4th1At23 + 
        6*At12L*gtu11*PDstandard4th1phi + 6*At22L*gtu21*PDstandard4th1phi + 6*At23L*gtu31*PDstandard4th1phi + 
        gtu21*PDstandard4th2At12 + gtu22*PDstandard4th2At22 + gtu32*PDstandard4th2At23 + 6*At12L*gtu21*PDstandard4th2phi + 
        6*At22L*gtu22*PDstandard4th2phi + 6*At23L*gtu32*PDstandard4th2phi - ktwothird*PDstandard4th2trK + 
        gtu31*PDstandard4th3At12 + gtu32*PDstandard4th3At22 + gtu33*PDstandard4th3At23 + 6*At12L*gtu31*PDstandard4th3phi + 
        6*At22L*gtu32*PDstandard4th3phi + 6*At23L*gtu33*PDstandard4th3phi;
    
    M3L  =  -(At13L*Gt111*gtu11) - At11L*Gt113*gtu11 - At23L*Gt211*gtu11 - At12L*Gt213*gtu11 - At33L*Gt311*gtu11 - 
        At13L*Gt313*gtu11 - 2*At13L*Gt112*gtu21 - At12L*Gt113*gtu21 - At11L*Gt123*gtu21 - 2*At23L*Gt212*gtu21 - 
        At22L*Gt213*gtu21 - At12L*Gt223*gtu21 - 2*At33L*Gt312*gtu21 - At23L*Gt313*gtu21 - At13L*Gt323*gtu21 - 
        At13L*Gt122*gtu22 - At12L*Gt123*gtu22 - At23L*Gt222*gtu22 - At22L*Gt223*gtu22 - At33L*Gt322*gtu22 - 
        At23L*Gt323*gtu22 - 3*At13L*Gt113*gtu31 - At11L*Gt133*gtu31 - 3*At23L*Gt213*gtu31 - At12L*Gt233*gtu31 - 
        3*At33L*Gt313*gtu31 - At13L*Gt333*gtu31 - 3*At13L*Gt123*gtu32 - At12L*Gt133*gtu32 - 3*At23L*Gt223*gtu32 - 
        At22L*Gt233*gtu32 - 3*At33L*Gt323*gtu32 - At23L*Gt333*gtu32 - 2*At13L*Gt133*gtu33 - 2*At23L*Gt233*gtu33 - 
        2*At33L*Gt333*gtu33 + gtu11*PDstandard4th1At13 + gtu21*PDstandard4th1At23 + gtu31*PDstandard4th1At33 + 
        6*At13L*gtu11*PDstandard4th1phi + 6*At23L*gtu21*PDstandard4th1phi + 6*At33L*gtu31*PDstandard4th1phi + 
        gtu21*PDstandard4th2At13 + gtu22*PDstandard4th2At23 + gtu32*PDstandard4th2At33 + 6*At13L*gtu21*PDstandard4th2phi + 
        6*At23L*gtu22*PDstandard4th2phi + 6*At33L*gtu32*PDstandard4th2phi + gtu31*PDstandard4th3At13 + 
        gtu32*PDstandard4th3At23 + gtu33*PDstandard4th3At33 + 6*At13L*gtu31*PDstandard4th3phi + 
        6*At23L*gtu32*PDstandard4th3phi + 6*At33L*gtu33*PDstandard4th3phi - ktwothird*PDstandard4th3trK;
    
    cSL  =  trR;
    
    cXt1L  =  Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + Gt133*gtu33 - Xt1L;
    
    cXt2L  =  Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + Gt233*gtu33 - Xt2L;
    
    cXt3L  =  Gt311*gtu11 + Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33 - Xt3L;
    
    cAL  =  At11L*gtu11 + At22L*gtu22 + 2*(At12L*gtu21 + At13L*gtu31 + At23L*gtu32) + At33L*gtu33;
    
    
    /* Copy local copies back to grid functions */
    cA[index] = cAL;
    cS[index] = cSL;
    cXt1[index] = cXt1L;
    cXt2[index] = cXt2L;
    cXt3[index] = cXt3L;
    H[index] = HL;
    M1[index] = M1L;
    M2[index] = M2L;
    M3[index] = M3L;
    
    /* Copy local copies back to subblock grid functions */
  }
  LC_ENDLOOP3 (somename);
}

void ML_BSSN_constraints(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS
  DECLARE_CCTK_PARAMETERS
  
  GenericFD_LoopOverInterior(cctkGH, &ML_BSSN_constraints_Body);
}