Task: Implement cgauss.x for EinsteinInitialData/RotatingDBHIVP thorn

thorn_name: EinsteinInitialData/RotatingDBHIVP
src_filename: cgauss.x
interface: # Interface definition for thorn RotatingDBHIVP
# $Header$

implements: rotatingdbhivp
inherits: ADMBase grid StaticConformal

private:

real sph_to_car_coord TYPE=GF
{
eta,
abseta,
sign_eta,
q,
phi
} "coordinate"

real sph_to_car_psi TYPE=GF
{
psi3d,
detapsi3d,
dqpsi3d,
dphipsi3d,
detaetapsi3d,
detaqpsi3d,
detaphipsi3d,
dqqpsi3d,
dqphipsi3d,
dphiphipsi3d
}"psi"




schedule: # Schedule definitions for thorn RotatingDBHIVP
# $Header$

if (CCTK_Equals(initial_data,"rotatingdbh"))
{ 
  STORAGE: sph_to_car_coord, sph_to_car_psi

  schedule RotatingDBHIVP_ParamCheck at PARAMCHECK
  {
    LANG: C
  } "Check Parameters"

  schedule RotatingDBHIVP IN ADMBase_InitialData
  {
    LANG: Fortran
  } "Construct RotatingDBHIVP"
}


param: # Parameter definitions for thorn RotatingDBHIVP
# $Header$

shares: StaticConformal

USES KEYWORD conformal_storage

shares:ADMBase

USES KEYWORD metric_type

EXTENDS KEYWORD initial_lapse 
{
  "schwarz" :: "Set lapse to Schwarzschild"
}

EXTENDS KEYWORD initial_data 
{
  "rotatingdbh" :: "Non-Aix BH + Brill Wave IVP"
}

private:

BOOLEAN kerr_slice "initial slice for kerr"
{
} "no"

BOOLEAN kerr_shift "kerr shift"
{
} "no"

REAL amp "Brill wave amplitude"
{
  *:* :: "No restriction"
} 0.1

REAL eta0 "Brill wave center (in eta coords)"
{
  *:* :: "No restriction"
} 0.0

REAL sigma "Brill wave width (in eta)"
{
  *:* :: "No restriction"
} 1.0

REAL byJ "Bowen York Angular momenta"
{
  *:* :: "No restriction"
} 1.0

REAL mm "Azimuthal dependence factor"
{
  *:* :: "No restriction"
} 0.0

REAL etamax "Eta value for outer edge of grid"
{
  *:* :: "No restriction"
} 5.0


INT neta "Eta resolution for solve"
{
  *:* :: "No restriction"
} 202

INT ntheta "Theta resolution for solve"
{
  *:* :: "No restriction"
} 54

INT nphi "Eta resolution for solve"
{
  *:* :: "No restriction"
} 5

BOOLEAN verbose ""
{
} "yes"

INT interpolation_order "Order for interpolation" STEERABLE = ALWAYS
{
  1:3 :: "Choose between first, second, and third-order"
} 1



context: RotatingDBHIVP.F:
```
/*@@
c  @file      RotatingDBH.F
c  @date      8 June 1999
c  @author    Ryoji Takahashi
c  @desc 
c  
c  @enddesc 
c@@*/

#include "cctk.h" 
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"

c/*@@
c  @routine    RotatingDBHIVP
c  @date       
c  @author     
c  @desc 
c  
c  @enddesc 
c  @calls     
c  @calledby   
c  @history 
c
c  @endhistory 
c@@*/

      subroutine RotatingDBHIVP(CCTK_ARGUMENTS)
      
      implicit none
      
      DECLARE_CCTK_ARGUMENTS
      DECLARE_CCTK_PARAMETERS
      DECLARE_CCTK_FUNCTIONS

      real*8 deta,dq,dphi
      real*8, allocatable :: ac(:,:,:),ae(:,:,:),aw(:,:,:),an(:,:,:),
     $     as(:,:,:),aq(:,:,:),ab(:,:,:),rhs(:,:,:),Ksq(:,:,:),
     $     psisph(:,:,:),psip(:,:,:),psipp(:,:,:),detapsisph(:,:,:),
     $     dqpsisph(:,:,:),dphipsisph(:,:,:),detaetapsisph(:,:,:),
     $     detaqpsisph(:,:,:),detaphipsisph(:,:,:),dqqpsisph(:,:,:),
     $     dqphipsisph(:,:,:),dphiphipsisph(:,:,:)
      real*8, allocatable :: etagrd(:),qgrd(:),phigrd(:)
      real*8 o1,o2,o3,o4,o5,o6,o7,o8,o9,o10,o11,o12,o13,o14,o15,o16,o17,
     $     o18,o19,o20,o21,o22,o23,o24,o25,o26,o27,o28,o29,o30,o31,o32,
     $     o33,o34,o35,o36,o37,o38,o39,o40,o41,o42,o43,o44,o45,o46,o47,
     $     o48,o49,o50,o51,o52,o53,o54,o55,o56,o57,o58,o59,o60,o61,o62,
     $     o63,o64,o65,o66,o67,o68,o69,o70,o71,o72,o73,o74,o75,o76,o77,
     $     o78,o79,o80,o81,o82,o83,o84,o85,o86,o87,o88,o89,o90,o91,o92,
     $     o93,o94,o95,o96,o97,o98,o99,o100,o101,o102,o103,o104,o105,
     $     o106,o107,o108,o109,o110,o111,o112,o113,o114,o115,o116,o117,
     $     o118,o119,o120,o121,o122,o123,o124
      real*8 t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,
     $     t11,t12,t13,t14,t15,t16
      real*8 gtil,dngtil,dnngtil,dnnngtil,dnnnngtil,dnnnnngtil,
     $     dnnnnnngtil,dnnnnnnngtil
      real*8 rhsmax,rmax,adm
      real*8,parameter :: rbh_tol = 1.0d-7,rbh_eps = 1.0d-10
      integer,parameter :: itmax = 30 
      real*8 pi
      integer :: ne,nq,np
      integer :: nx,ny,nz
      integer i,j,k,it,ier,nquads,nocts,ntries
      integer npoints,ierror
      integer make_conformal_derivs

      integer       param_table_handle, interp_handle
      character(30) options_string
      CCTK_REAL,    dimension(3)  :: coord_origin, coord_delta
      CCTK_POINTER, dimension(3)  :: interp_coords
      CCTK_INT,     dimension(3 ) :: in_array_dims
      CCTK_POINTER, dimension(10) :: in_arrays, out_arrays
      CCTK_INT,     dimension(10), parameter :: type_codes = CCTK_VARIABLE_REAL


c Check if we should create and store conformal factor stuff 

      if (CCTK_EQUALS(metric_type, "static conformal")) then
    
         conformal_state = 1

         if(CCTK_EQUALS(conformal_storage,"factor+derivs")) then

            conformal_state = 2
            make_conformal_derivs = 1

          else if (CCTK_EQUALS(conformal_storage,"factor+derivs+2nd derivs")) then

            conformal_state = 3
            make_conformal_derivs = 1

          endif

       else

         make_conformal_derivs = 0

       endif

      pi = 4.0d0*atan(1.0d0)

c     DO NOT use integer*4
      ne = neta
      nq = ntheta
      np = nphi

c     Set up the grid spacings
      nx = cctk_lsh(1)
      ny = cctk_lsh(2)
      nz = cctk_lsh(3)      
       
c     Distorted Rotating BH parameters (for Extrinsic curveture!)
c     
      print *,"Brill wave + Rotating Distorted BH solve"
      write(*,123)amp,eta0,sigma,byJ,mm
      print*,'etamax=',etamax
 123  format(1x, 'Pars: amp',f8.5,' eta0',f8.5,' sigma',f8.5,' byJ',f9.5
     $     ,' mm',f8.5)
      
c     Sovle on this sized cartesian grid
c     3D grid size NE x NT
c     Add 2 zones for eta coordinate and 4 for theta
c     and phi coordenate.
      ne = ne+2
      nq = nq+2
      np = np+2
c     
      allocate(ac(ne,nq,np),ae(ne,nq,np),aw(ne,nq,np),an(ne,nq,np),
     $     as(ne,nq,np),aq(ne,nq,np),ab(ne,nq,np),rhs(ne,nq,np),
     $     Ksq(ne,nq,np),psisph(ne,nq,np),psip(ne,nq,np),
     $     psipp(ne,nq,np),detapsisph(ne,nq,np),dqpsisph(ne,nq,np),
     $     dphipsisph(ne,nq,np),detaetapsisph(ne,nq,np),
     $     detaqpsisph(ne,nq,np),detaphipsisph(ne,nq,np),
     $     dqqpsisph(ne,nq,np),dqphipsisph(ne,nq,np),
     $     dphiphipsisph(ne,nq,np))
      allocate(etagrd(ne),qgrd(nq),phigrd(np))
c     
c     Initialize some array
c     
      nocts = 4
      nquads = 2      
      dphi = nocts*0.5*pi/(np-2)
      dq = nquads*0.5*pi/(nq-2)
      deta = etamax/(ne-3)
      
      do k = 1,np
         phigrd(k) = (k-1.5)*dphi
      enddo
      do j = 1,nq
         qgrd(j) = (j-1.5)*dq
      enddo
      do i=1,ne
         etagrd(i) = (i-2)*deta
      enddo
      
c     
c     Specify the initial guess for the conformal factor:
c     
      psip = 0.
      psipp = 0.
      do k = 1,np
         do j = 1,nq
            do i = 1,ne
               psisph(i,j,k) = 2.*cosh(0.5*etagrd(i))
            enddo
         enddo
      enddo
c     
c     Compute K^2:
c     
      do k = 1,np
         do j = 1,nq
            do i = 1,ne
#include "gauss.x"
#include "ksq_odd.x"
            enddo
         enddo
      enddo
c     
c     Solve the Hamiltonian constraint for the conformal factor:
c     
       ntries = 0
       
      do it = 1,itmax+1
         
         ac = 0.
         ae = 0.
         aw = 0.
         an = 0.
         as = 0.
         aq = 0.
         ab = 0.
         rhs = 0.
                  
c     
         do k = 2,np-1
            do j = 2,nq-1
               do i = 2,ne-1
                  rhs(i,j,k) =
     $                 (psip(i+1,j,k)-2.*psip(i,j,k)+psip(i-1,j,k))/
     $                 deta**2+(psip(i,j+1,k)-2.*psip(i,j,k)+
     $                 psip(i,j-1,k))/dq**2+0.5*(psip(i,j+1,k)-
     $                 psip(i,j-1,k))/(dq*tan(qgrd(j)))+
     $                 (psip(i,j,k+1)-2.*psip(i,j,k)+psip(i,j,k-1))/
     $                 (dphi**2*sin(qgrd(j))**2)-0.25*psip(i,j,k)+0.125*
     $                 Ksq(i,j,k)/(psisph(i,j,k)+psip(i,j,k))**7
               enddo
            enddo
         enddo
c     
         rhs = -rhs
         
c     
c     See if the residual is small enough:
c     
         rhsmax = 0.
c     
         do k = 2,np-1
            do j = 2,nq-1
               do i = 2,ne-1
                  rhsmax = max(rhsmax,abs(rhs(i,j,k)))
               enddo
            enddo
         enddo
         
         if (verbose == 1) then
            ntries = ntries+1
            print*,'-----------Retry', ntries
            print*,'residual =', rhsmax
            print*,'--------------------------------------------------'
         endif
         
         if (rhsmax.lt.rbh_tol) goto 110
c     
c     Compute stencil coefficients:
c     
         do k = 2,np-1
            do j = 2,nq-1
               do i = 2,ne-1
                  ac(i,j,k) = -2./deta**2-2./dq**2-2./(dphi**2*
     $                 sin(qgrd(j))**2)-0.25-0.875*Ksq(i,j,k)/(psisph(i,j,k)+
     $                 psip(i,j,k))**8
c     
                  ae(i,j,k) = 1./deta**2
c     
                  aw(i,j,k) = 1./deta**2
c         
                  an(i,j,k) = 1./dq**2 + 0.5/(tan(qgrd(j))*dq)
c     
                  as(i,j,k) = 1./dq**2 - 0.5/(tan(qgrd(j))*dq)
c     
                  aq(i,j,k) = 1./(sin(qgrd(j))**2*dphi**2)
c     
                  ab(i,j,k) = 1./(sin(qgrd(j))**2*dphi**2)
               enddo
            enddo
         enddo
c     
c     Apply boundary conditions:
c     
c     i=2:
c     
         do k = 3,np-2
            do j = 3,nq-2
               ae(2,j,k) = ae(2,j,k) + aw(2,j,k)
               aw(2,j,k) = 0.
c     
c     i=ne-1:
c     
               ac(ne-1,j,k) = ac(ne-1,j,k) + 4.*
     &              ae(ne-1,j,k)/(3.+deta)
               aw(ne-1,j,k) = aw(ne-1,j,k) -
     &              ae(ne-1,j,k)/(3.+deta)
               ae(ne-1,j,k) = 0.
            enddo
c     
c     j=2:
c     
            do i = 3,ne-2
               ac(i,2,k) = ac(i,2,k) + as(i,2,k)
               as(i,2,k) = 0.
c     
c     j=nq-1:
c     
               ac(i,nq-1,k) = ac(i,nq-1,k) +
     &              an(i,nq-1,k)
               an(i,nq-1,k) = 0.
            enddo
         enddo
c     
c     k=2:
c
         do j = 3,nq-2
            do i = 3,ne-2
               ac(i,j,2) = ac(i,j,2) + ab(i,j,2)
               ab(i,j,2) = 0.
c
c     k=np-1:
c
               ac(i,j,np-1) = ac(i,j,np-1) +
     &              aq(i,j,np-1)
               aq(i,j,np-1) = 0.
            enddo
         enddo
c     
c     i=2, j=2:
c
         do k = 3,np-2
            ae(2,2,k) = ae(2,2,k) + aw(2,2,k)
            ac(2,2,k) = ac(2,2,k) + as(2,2,k)
            aw(2,2,k) = 0.
            as(2,2,k) = 0.
c     
c     i=2, j=nq-1:
c
            ae(2,nq-1,k) = ae(2,nq-1,k) + aw(2,nq-1,k)
            ac(2,nq-1,k) = ac(2,nq-1,k) + an(2,nq-1,k)
            aw(2,nq-1,k) = 0.
            an(2,nq-1,k) = 0.
c     
c     i=ne-1, j=2:
c     
            ac(ne-1,2,k) = ac(ne-1,2,k) + 4.*ae(ne-1,2,k)/(3.+deta) +
     &           as(ne-1,2,k)
            aw(ne-1,2,k) = aw(ne-1,2,k) - ae(ne-1,2,k)/(3.+deta)
            ae(ne-1,2,k) = 0.
            as(ne-1,2,k) = 0.
c     
c     i=ne-1, j=nq-1:
c
            ac(ne-1,nq-1,k) = ac(ne-1,nq-1,k) + 4.*
     &           ae(ne-1,nq-1,k)/(3.+deta) + an(ne-1,nq-1,k)
            aw(ne-1,nq-1,k) = aw(ne-1,nq-1,k) -
     &           ae(ne-1,nq-1,k)/(3.+deta)
            ae(ne-1,nq-1,k) = 0.
            an(ne-1,nq-1,k) = 0.
         enddo
c     
c     i=2, k=2:
c     
         do j = 3,nq-2
            ae(2,j,2) = ae(2,j,2) + aw(2,j,2)
            ac(2,j,2) = ac(2,j,2) + ab(2,j,2)
            aw(2,j,2) = 0.
            ab(2,j,2) = 0.
c     
c     i=2, k=np-1:
c     
            ae(2,j,np-1) = ae(2,j,np-1) + aw(2,j,np-1)
            ac(2,j,np-1) = ac(2,j,np-1) + aq(2,j,np-1)
            aw(2,j,np-1) = 0.
            aq(2,j,np-1) = 0.
c
c     i=ne-1, k=2:
c     
            ac(ne-1,j,2) = ac(ne-1,j,2) + 4.*ae(ne-1,j,2)/(3.+deta) +
     &           ab(ne-1,j,2)
            aw(ne-1,j,2) = aw(ne-1,j,2) - ae(ne-1,j,2)/(3.+deta)
            ae(ne-1,j,2) = 0.
            ab(ne-1,j,2) = 0.
c     
c     i=ne-1, k=np-1:
c
            ac(ne-1,j,np-1) = ac(ne-1,j,np-1) + 4.*
     &           ae(ne-1,j,np-1)/(3.+deta) + aq(ne-1,j,np-1)
            aw(ne-1,j,np-1) = aw(ne-1,j,np-1) -
     &           ae(ne-1,j,np-1)/(3.+deta)
            ae(ne-1,j,np-1) = 0.
            aq(ne-1,j,np-1) = 0.
         enddo
c     
c     j=2, k=2:
c
         do i = 3,ne-2
            ac(i,2,2) = ac(i,2,2) + as(i,2,2) + ab(i,2,2)
            as(i,2,2) = 0.
            ab(i,2,2) = 0.
c
c     j=2, k=np-1:
c     
            ac(i,2,np-1) = ac(i,2,np-1) + as(i,2,np-1) +
     &           aq(i,2,np-1)
            as(i,2,np-1) = 0.
            aq(i,2,np-1) = 0.
c     
c  j=nq-1, k=2:
c     
            ac(i,nq-1,2) = ac(i,nq-1,2) + an(i,nq-1,2) +
     &           ab(i,nq-1,2)
            an(i,nq-1,2) = 0.
            ab(i,nq-1,2) = 0.
c
c  j=nq-1, k=np-1:
c
            ac(i,nq-1,np-1) = ac(i,nq-1,np-1) + an(i,nq-1,np-1) +
     &           aq(i,nq-1,np-1)
            an(i,nq-1,np-1) = 0.
            aq(i,nq-1,np-1) = 0.
         enddo
c
c  i=2, j=2, k=2:
c
         ae(2,2,2) = ae(2,2,2) + aw(2,2,2)
         ac(2,2,2) = ac(2,2,2) + as(2,2,2) + ab(2,2,2)
         aw(2,2,2) = 0.
         as(2,2,2) = 0.
         ab(2,2,2) = 0.
c
c  i=2, j=2, k=np-1:
c
         ae(2,2,np-1) = ae(2,2,np-1) + aw(2,2,np-1)
         ac(2,2,np-1) = ac(2,2,np-1) + as(2,2,np-1) + aq(2,2,np-1)
         aw(2,2,np-1) = 0.
         as(2,2,np-1) = 0.
         aq(2,2,np-1) = 0.
c
c  i=2, j=nq-1, k=2:
c
         ae(2,nq-1,2) = ae(2,nq-1,2) + aw(2,nq-1,2)
         ac(2,nq-1,2) = ac(2,nq-1,2) + an(2,nq-1,2) + ab(2,nq-1,2)
         aw(2,nq-1,2) = 0.
         an(2,nq-1,2) = 0.
         ab(2,nq-1,2) = 0.
c
c  i=2, j=nq-1, k=np-1:
c
         ae(2,nq-1,np-1) = ae(2,nq-1,np-1) + aw(2,nq-1,np-1)
         ac(2,nq-1,np-1) = ac(2,nq-1,np-1) + an(2,nq-1,np-1) + aq(2,nq-1,np-1)
         aw(2,nq-1,np-1) = 0.
         an(2,nq-1,np-1) = 0.
         aq(2,nq-1,np-1) = 0.
c
c  i=ne-1, j=2, k=2:
c
         ac(ne-1,2,2) = ac(ne-1,2,2) + 4.*ae(ne-1,2,2)/(3.+deta) +
     &        as(ne-1,2,2) + ab(ne-1,2,2)
         aw(ne-1,2,2) = aw(ne-1,2,2) - ae(ne-1,2,2)/(3.+deta)
         ae(ne-1,2,2) = 0.
         as(ne-1,2,2) = 0.
         ab(ne-1,2,2) = 0.
c
c  i=ne-1, j=2, k=np-1:
         ac(ne-1,2,np-1) = ac(ne-1,2,np-1) + 4.*ae(ne-1,2,np-1)/(3.+deta) +
     &        as(ne-1,2,np-1) + aq(ne-1,2,np-1)
         aw(ne-1,2,np-1) = aw(ne-1,2,np-1) - ae(ne-1,2,np-1)/(3.+deta)
         ae(ne-1,2,np-1) = 0.
         as(ne-1,2,np-1) = 0.
         aq(ne-1,2,np-1) = 0.
c
c  i=ne-1, j=nq-1, k=2:
c
         ac(ne-1,nq-1,2) = ac(ne-1,nq-1,2) + 4.*ae(ne-1,nq-1,2)/(3.+deta) +
     &        an(ne-1,nq-1,2) + ab(ne-1,nq-1,2)
         aw(ne-1,nq-1,2) = aw(ne-1,nq-1,2) - ae(ne-1,nq-1,2)/(3.+deta)
         ae(ne-1,nq-1,2) = 0.
         an(ne-1,nq-1,2) = 0.
         ab(ne-1,nq-1,2) = 0.
c
c  i=ne-1, j=nq-1, k=np-1:
c
         ac(ne-1,nq-1,np-1) = ac(ne-1,nq-1,np-1) +
     &        4.*ae(ne-1,nq-1,np-1)/(3.+deta) + an(ne-1,nq-1,np-1) +
     &        aq(ne-1,nq-1,np-1)
         aw(ne-1,nq-1,np-1) = aw(ne-1,nq-1,np-1) - ae(ne-1,nq-1,np-1)/
     $        (3.+deta)
         ae(ne-1,nq-1,np-1) = 0.
         an(ne-1,nq-1,np-1) = 0.
         aq(ne-1,nq-1,np-1) = 0.
c     
c     Call stab routine:
c     
         call rbicgst3d(ac,ae,aw,an,as,aq,ab,psipp,rhs,rbh_eps,rmax,ier,
     $        ne,nq,np)
         if (rmax.gt.1.0e-10) then
            write(*,*) '***WARNING: bicgst3d did not converge.'
         endif
         if (ier.eq.-1) then
            write(*,*) '***WARNING: ier=-1'
         endif
c     
c     Now, apply boundary conditions to psipp:
c     
         do k = 1,np
            do j = 1,nq
               psipp(1,j,k) = psipp(3,j,k)
               psipp(ne,j,k) = (4.*psipp(ne-1,j,k)-psipp(ne-2,j,k))/(3.+
     $              deta)
            enddo
            do i = 1,ne
               psipp(i,1,k) = psipp(i,2,k)
               psipp(i,nq,k) = psipp(i,nq-1,k)
            enddo
         enddo
         do j = 1,nq
            do i = 1,ne
               psipp(i,j,1) = psipp(i,j,2)
               psipp(i,j,np) = psipp(i,j,np-1)
            enddo
         enddo
c     
c     Update psip:
c     
         do k = 1,np
            do j = 1,nq
               do i = 1,ne
                  psip(i,j,k) = psip(i,j,k) + psipp(i,j,k)
               enddo
            enddo
         enddo
c     
      enddo
c     
      write(*,*) 'It did not converge.'
      stop
c     
 110  continue
      
      write(*,*) '--------------------------------------------------'
      print*,'Converge at Residual = ',rhsmax

c     
c     Here, compute the derivatives of the spherical conformal factor
c     
      do k = 1,np
         do j = 1,nq
            do i = 2,ne-1
               detapsisph(i,j,k)=0.5*(psip(i+1,j,k)-psip(i-1,j,k))/
     $              deta + sinh(0.5*etagrd(i))
            enddo
            detapsisph(1,j,k) = -detapsisph(3,j,k)
         enddo
      enddo
c     
      do k = 1,np
         do j = 2,nq-1
            do i = 1,ne
               dqpsisph(i,j,k)=0.5*(psip(i,j+1,k)-psip(i,j-1,k))/dq
            enddo
         enddo
         do i = 1,ne
            dqpsisph(i,1,k) = -dqpsisph(i,2,k)
            dqpsisph(i,nq,k) = -dqpsisph(i,nq-1,k)
         enddo
      enddo
c     
      do k = 2,np-1
         do j = 1,nq
            do i = 1,ne
               dphipsisph(i,j,k)=0.5*(psip(i,j,k+1)-psip(i,j,k-1))/
     $              dphi
            enddo
         enddo
      enddo
      do j = 1,nq
         do i = 1,ne
            dphipsisph(i,j,1) = -dphipsisph(i,j,2)
            dphipsisph(i,j,np) = -dphipsisph(i,j,np-1)
         enddo
      enddo
c     
      do k = 1,np
         do j = 1,nq
            do i = 2,ne-1
               detaetapsisph(i,j,k)=(psip(i+1,j,k)-2.*psip(i,j,k)+
     &              psip(i-1,j,k))/deta**2 + sqrt(0.25)*
     &              cosh(0.5*etagrd(i))
            enddo
            detaetapsisph(1,j,k) = detaetapsisph(3,j,k)
         enddo
      enddo
c     
      do k = 1,np
         do j = 2,nq-1
            do i = 1,ne
               detaqpsisph(i,j,k)=0.5*(detapsisph(i,j+1,k)-
     $              detapsisph(i,j-1,k))/dq
            enddo
         enddo
         do i = 1,ne
            detaqpsisph(i,1,k) = -detaqpsisph(i,2,k)
            detaqpsisph(i,nq,k) = -detaqpsisph(i,nq-1,k)
         enddo
      enddo
c     
      do k = 2,np-1
         do j = 1,nq
            do i = 1,ne
               detaphipsisph(i,j,k)=0.5*(detapsisph(i,j,k+1)-
     $              detapsisph(i,j,k-1))/dphi
            enddo
         enddo
      enddo
      do j = 1,nq
         do i = 1,ne
            detaphipsisph(i,j,1) = -detaphipsisph(i,j,2)
            detaphipsisph(i,j,np) = -detaphipsisph(i,j,np-1)
         enddo
      enddo
c     
      do k = 1,np
         do j = 2,nq-1
            do i = 1,ne
               dqqpsisph(i,j,k)=0.5*(dqpsisph(i,j+1,k)-
     $              dqpsisph(i,j-1,k))/dq
            enddo
         enddo
         do i = 1,ne
            dqqpsisph(i,1,k) = dqqpsisph(i,2,k)
            dqqpsisph(i,nq,k) = dqqpsisph(i,nq-1,k)
         enddo
      enddo
c     
      do k = 2,np-1
         do j = 1,nq
            do i = 1,ne
               dqphipsisph(i,j,k)=0.5*(dqpsisph(i,j,k+1)-
     $              dqpsisph(i,j,k-1))/dphi
            enddo
         enddo
      enddo
      do j = 1,nq
         do i = 1,ne
            dqphipsisph(i,j,1) = -dqphipsisph(i,j,2)
            dqphipsisph(i,j,np) = -dqphipsisph(i,j,np-1)
         enddo
      enddo
c     
      do k = 2,np-1
         do j = 1,nq
            do i = 1,ne
               dphiphipsisph(i,j,k)=0.5*(dphipsisph(i,j,k+1)-
     $              dphipsisph(i,j,k-1))/dphi
            enddo
         enddo
      enddo
      do j = 1,nq
         do i = 1,ne
            dphiphipsisph(i,j,1) = dphiphipsisph(i,j,2)
            dphiphipsisph(i,j,np) = dphiphipsisph(i,j,np-1)
         enddo
      enddo
c     
      do k = 1,np
         do j = 1,nq
            psisph(:,j,k)=psip(:,j,k)+2.0*cosh(0.5*etagrd)
         enddo
      enddo
c     
c     Now compute on the Cartesian coordinate.
c     
c     Compute eta,q,phi at the each points of cartesian grid
c     

      eta = 0.5d0 * log (x**2 + y**2 + z**2)
      abseta = abs (eta)
      q = atan2 (sqrt (x**2 + y**2), z)
      phi = atan2 (y, x)

      do k = 1,nz
         do j = 1,ny
            do i = 1,nx

               if(eta(i,j,k) .lt. 0)then
                  sign_eta(i,j,k) = -1.0d0
               else
                  sign_eta(i,j,k) = 1.0d0
               endif

            enddo
         enddo
      enddo
      
      npoints = nx*ny*nz

!     Parameter table and interpolator handles.
      options_string = "order = " // char(ichar('0') + interpolation_order)
      call Util_TableCreateFromString (param_table_handle, options_string)
      if (param_table_handle .lt. 0) then
        call CCTK_WARN(0,"Cannot create parameter table for interpolator")
      endif

      call CCTK_InterpHandle (interp_handle, "uniform cartesian")
      if (interp_handle .lt. 0) then
        call CCTK_WARN(0,"Cannot get handle for interpolation ! Forgot to activate an implementation providing interpolation operators ??")
      endif

!     fill in the input/output arrays for the interpolator
      coord_origin(1) = etagrd(1)
      coord_origin(2) = qgrd(1)
      coord_origin(3) = phigrd(1)-pi
      coord_delta(1)  = etagrd(2) - etagrd(1)
      coord_delta(2)  = qgrd(2) - qgrd(1)
      coord_delta(3)  = phigrd(2) - phigrd(1)

      interp_coords(1) = CCTK_PointerTo(abseta)
      interp_coords(2) = CCTK_PointerTo(q)
      interp_coords(3) = CCTK_PointerTo(phi)

      in_array_dims(1) = ne
      in_array_dims(2) = nq
      in_array_dims(3) = np

      in_arrays(1) = CCTK_PointerTo(psisph)
      in_arrays(2) = CCTK_PointerTo(detapsisph)
      in_arrays(3) = CCTK_PointerTo(dqpsisph)
      in_arrays(4) = CCTK_PointerTo(dphipsisph)
      in_arrays(5) = CCTK_PointerTo(detaetapsisph)
      in_arrays(6) = CCTK_PointerTo(detaqpsisph)
      in_arrays(7) = CCTK_PointerTo(detaphipsisph)
      in_arrays(8) = CCTK_PointerTo(dqqpsisph)
      in_arrays(9) = CCTK_PointerTo(dqphipsisph)
      in_arrays(10) = CCTK_PointerTo(dphiphipsisph)

      out_arrays(1) = CCTK_PointerTo(psi3d)
      out_arrays(2) = CCTK_PointerTo(detapsi3d)
      out_arrays(3) = CCTK_PointerTo(dqpsi3d)
      out_arrays(4) = CCTK_PointerTo(dphipsi3d)
      out_arrays(5) = CCTK_PointerTo(detaetapsi3d)
      out_arrays(6) = CCTK_PointerTo(detaqpsi3d)
      out_arrays(7) = CCTK_PointerTo(detaphipsi3d)
      out_arrays(8) = CCTK_PointerTo(dqqpsi3d)
      out_arrays(9) = CCTK_PointerTo(dqphipsi3d)
      out_arrays(10) = CCTK_PointerTo(dphiphipsi3d)

      call CCTK_InterpLocalUniform (ierror, 3,
     $                              interp_handle, param_table_handle,
     $                              coord_origin, coord_delta,
     $                              npoints, type_codes(1), interp_coords,
     $                              10, in_array_dims, type_codes, in_arrays,
     $                              10, type_codes, out_arrays)

      psi = psi3d*exp(-0.5*eta)
      detapsi3d = sign_eta*detapsi3d
      detaqpsi3d = sign_eta*detaqpsi3d
      detaphipsi3d = sign_eta*detaphipsi3d

      do k=1,nz
         do j=1,ny
            do i=1,nx
c     psix = \partial psi / \partial x / psi
#include "psi_1st_deriv.x"
               
c     psixx = \partial^2\psi / \partial x^2 / psi
#include "psi_2nd_deriv.x"
            enddo
         enddo
      enddo
      
c     Conformal metric (here, we define conformally flat)
c     gxx = 1...
      
c     Derivatives of the metric
c     dxgxx = 1/2 \partial gxx / \partial x = 0...
c     
      do k= 1,nz
         do j= 1,ny
            do i= 1,nx
#include "gij.x"
            enddo
         enddo
      enddo
c     Extrinsic Curvture:Cactus only needs physical extrinsic curvature
      do k= 1,nz
         do j= 1,ny
            do i= 1,nx 
#include "cgauss.x"
#include "kij_odd.x"
            enddo
         enddo
      enddo
      
      kxx = kxx/psi**2
      kxy = kxy/psi**2
      kxz = kxz/psi**2
      kyy = kyy/psi**2
      kyz = kyz/psi**2
      kzz = kzz/psi**2

c     Set ADM mass
      i = ne-15
      adm = 0.0
      do k=2,np-1
         do j=2,nq-1
            adm=adm+(psisph(i,j,k)-(psisph(i+1,j,k)-psisph(i-1,j,k))/
     $           deta)*exp(0.5*etagrd(i))
         enddo
      enddo
      adm=adm/(nq-2)/(np-2)
      print *,'ADM mass: ',adm
      if (CCTK_Equals(initial_lapse,"schwarz")==1) then 
         write (*,*)"Initial with schwarzschild-like lapse"
         write (*,*)"using alp = (2.*r - adm)/(2.*r+adm)."
         alp = (2.*r - adm)/(2.*r+adm)
      endif
c
      print*,'Angular momentum parameter: a/m = ', byJ/adm**2
c
c     kerr functions
c     
c     isotropic coordinate for schwarzschild
c

      deallocate(ac,ae,aw,an,as,aq,ab,rhs,Ksq,psisph,psip,psipp,
     $     detapsisph,dqpsisph,dphipsisph,detaetapsisph,detaqpsisph,
     $     detaphipsisph,dqqpsisph,dqphipsisph,dphiphipsisph)
      deallocate(etagrd,qgrd,phigrd)
      
      return
      end

      
      

```

ParamCheck.c:
```
 /*@@
   @file      ParamCheck.c
   @date      Fri Apr 26 18:03:09 2002
   @author    Tom Goodale
   @desc 
              Check the parameters for RotatingDBHIVP
   @enddesc 
   @version $Header: /arrangements/PerturbedBH2/RotatingDBHIVP/src/ParamCheck.c,v 1.1 2002/04/30 guzman
 @@*/

#include "cctk.h"

#include "cctk_Arguments.h"
#include "cctk_Parameters.h"

static const char *rcsid = "$Header$";

CCTK_FILEVERSION(RotatingDBHIVP_ParamCheck_c)

/********************************************************************
 *********************     Local Data Types   ***********************
 ********************************************************************/

/********************************************************************
 ********************* Local Routine Prototypes *********************
 ********************************************************************/

/********************************************************************
 ***************** Scheduled Routine Prototypes *********************
 ********************************************************************/

void RotatingDBHIVP_ParamCheck(CCTK_ARGUMENTS);
void RotatingDBHIVP_ConformalCheck(CCTK_ARGUMENTS);

/********************************************************************
 ********************* Other Routine Prototypes *********************
 ********************************************************************/

/********************************************************************
 *********************     Local Data   *****************************
 ********************************************************************/

/********************************************************************
 *********************     External Routines   **********************
 ********************************************************************/

void RotatingDBHIVP_ParamCheck(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS
  DECLARE_CCTK_PARAMETERS

  /* Do we know how to deal with this type of metric ? */
  if(! CCTK_EQUALS(metric_type, "physical") &&
     ! CCTK_EQUALS(metric_type, "static conformal"))
  {
    CCTK_PARAMWARN("Unknown ADMBase::metric_type - known types are \"physical\" and \"static conformal\"");
  }

  if(CCTK_EQUALS(metric_type, "static conformal") &&
     ! CCTK_EQUALS(conformal_storage, "factor+derivs+2nd derivs"))
  {
    CCTK_PARAMWARN("ADMConstraints can currently only work with a physical metric or a static conf");
  }
   
}

/********************************************************************
 *********************     Local Routines   *************************
 ********************************************************************/

 /*@@
   @routine    RotatingDBHIVP_ConformalCheck
   @date       Tu Apr 30 2002
   @author     Goodale-Guzman
   @desc
   Check that the initial data has setup enough derivatives.
   @enddesc
   @calls
   @calledby
   @history

   @endhistory

 @@*/
void RotatingDBHIVP_ConformalCheck(CCTK_ARGUMENTS)
{
  DECLARE_CCTK_ARGUMENTS;
  DECLARE_CCTK_PARAMETERS;

  if(CCTK_EQUALS(metric_type, "physical"))
  {
    /* Use this internally so we don't need to check the parameter again. */
    *conformal_state = 0;
  }
  else if(CCTK_EQUALS(metric_type, "static conformal"))
  {
    if(*conformal_state < 3)
    {
      CCTK_WARN(0, "RotatingDBHIVP needs second derivatives of the conformal factor when running with a static conformal metric");
    }
  }

}
/********************************************************************
 *********************     Local Routines   *************************
 ********************************************************************/


```

gauss.x:
```
        gtil = amp*(exp(-((-eta0 + etagrd(i))**2/sigma**2)) + exp(-((eta0 +
     &   etagrd(i))**2/sigma**2)))
        dngtil = amp*((-2.00000000000000d0*(-eta0 + etagrd(i))*exp(-((-eta0
     &   + etagrd(i))**2/sigma**2)))/sigma**2 - (2.00000000000000d0*(eta0 +
     &   etagrd(i))*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**2)
        dnngtil = amp*((4.0000000000000d0*(-eta0 + etagrd(i))**2*exp(-((-et
     &  a0 + etagrd(i))**2/sigma**2)))/sigma**4 - (2.00000000000000d0*exp(-
     &  ((-eta0 + etagrd(i))**2/sigma**2)))/sigma**2 + (4.0000000000000d0*(
     &  eta0 + etagrd(i))**2*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**4 
     &  - (2.00000000000000d0*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma
     &  **2)
        dnnngtil = amp*((-8.0000000000000d0*(-eta0 + etagrd(i))**3*exp(-((-
     &  eta0 + etagrd(i))**2/sigma**2)))/sigma**6 + (1.20000000000000d1*(-e
     &  ta0 + etagrd(i))*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sigma**4 - (
     &  8.0000000000000d0*(eta0 + etagrd(i))**3*exp(-((eta0 + etagrd(i))**2/si
     &  gma**2)))/sigma**6 + (1.20000000000000d1*(eta0 + etagrd(i))*exp(-((
     &  eta0 + etagrd(i))**2/sigma**2)))/sigma**4)
        dnnnngtil = amp*((1.60000000000000d1*(-eta0 + etagrd(i))**4*exp(-((
     &  -eta0 + etagrd(i))**2/sigma**2)))/sigma**8 - (4.8000000000000d1*(-e
     &  ta0 + etagrd(i))**2*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sigma**6 
     &  + (1.20000000000000d1*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sigm
     &  a**4 + (1.60000000000000d1*(eta0 + etagrd(i))**4*exp(-((eta0 + etag
     &  rd(i))**2/sigma**2)))/sigma**8 - (4.8000000000000d1*(eta0 + etagrd(i))
     &  **2*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**6 + (1.200000000
     &  00000d1*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**4)
        dnnnnngtil = amp*((-3.2000000000000d1*(-eta0 + etagrd(i))**5*exp(-(
     &  (-eta0 + etagrd(i))**2/sigma**2)))/sigma**10 + (1.60000000000000d2*
     &  (-eta0 + etagrd(i))**3*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sigma*
     &  *8 - (1.20000000000000d2*(-eta0 + etagrd(i))*exp(-((-eta0 + etagrd(i))
     &  **2/sigma**2)))/sigma**6 - (3.2000000000000d1*(eta0 + etagrd(i))**5
     &  *exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**10 + (1.60000000000
     &  000d2*(eta0 + etagrd(i))**3*exp(-((eta0 + etagrd(i))**2/sigma**2)))/si
     &  gma**8 - (1.20000000000000d2*(eta0 + etagrd(i))*exp(-((eta0 + etagr
     &  d(i))**2/sigma**2)))/sigma**6)
        dnnnnnngtil = amp*((6.4000000000000d1*(-eta0 + etagrd(i))**6*exp(-(
     &  (-eta0 + etagrd(i))**2/sigma**2)))/sigma**12 - (4.8000000000000d2*(
     &  -eta0 + etagrd(i))**4*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sigma**
     &  10 + (7.2000000000000d2*(-eta0 + etagrd(i))**2*exp(-((-eta0 + etagr
     &  d(i))**2/sigma**2)))/sigma**8 - (1.20000000000000d2*exp(-((-eta0 + 
     &  etagrd(i))**2/sigma**2)))/sigma**6 + (6.4000000000000d1*(eta0 + eta
     &  grd(i))**6*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**12 - (4.8000
     &  000000000d2*(eta0 + etagrd(i))**4*exp(-((eta0 + etagrd(i))**2/sigma**2
     &  )))/sigma**10 + (7.2000000000000d2*(eta0 + etagrd(i))**2*exp(-((eta
     &  0 + etagrd(i))**2/sigma**2)))/sigma**8 - (1.20000000000000d2*exp(-(
     &  (eta0 + etagrd(i))**2/sigma**2)))/sigma**6)
        dnnnnnnngtil = amp*((-1.28000000000000d2*(-eta0 + etagrd(i))**7*exp
     &  (-((-eta0 + etagrd(i))**2/sigma**2)))/sigma**14 + (1.34400000000000
     &  d3*(-eta0 + etagrd(i))**5*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sig
     &  ma**12 - (3.3600000000000d3*(-eta0 + etagrd(i))**3*exp(-((-eta0 + e
     &  tagrd(i))**2/sigma**2)))/sigma**10 + (1.68000000000000d3*(-eta0 + e
     &  tagrd(i))*exp(-((-eta0 + etagrd(i))**2/sigma**2)))/sigma**8 - (1.28000
     &  000000000d2*(eta0 + etagrd(i))**7*exp(-((eta0 + etagrd(i))**2/sigma**2
     &  )))/sigma**14 + (1.34400000000000d3*(eta0 + etagrd(i))**5*exp(-((et
     &  a0 + etagrd(i))**2/sigma**2)))/sigma**12 - (3.3600000000000d3*(eta0
     &   + etagrd(i))**3*exp(-((eta0 + etagrd(i))**2/sigma**2)))/sigma**10 + (
     &  1.68000000000000d3*(eta0 + etagrd(i))*exp(-((eta0 + etagrd(i))**2/sigm
     &  a**2)))/sigma**8)

```

psi_2nd_deriv.x:
```
        o1 = 5.0000000000000d-1*eta(i,j,k)
        o2 = exp(o1)
        o3 = psi3d(i,j,k)
        o4 = 1/o3
        o5 = cos(phi(i,j,k))
        o6 = o5**2
        o7 = cos(q(i,j,k))
        o8 = o7**2
        o9 = detapsi3d(i,j,k)
        o10 = -2.50000000000000d0*eta(i,j,k)
        o11 = exp(o10)
        o12 = dqqpsi3d(i,j,k)
        o13 = detaphipsi3d(i,j,k)
        o14 = sin(phi(i,j,k))
        o15 = dphipsi3d(i,j,k)
        o16 = o14**2
        o17 = sin(q(i,j,k))
        o18 = o17**2
        o19 = 1/o18
        o20 = dphiphipsi3d(i,j,k)
        o21 = detaqpsi3d(i,j,k)
        o22 = dqpsi3d(i,j,k)
        o23 = detaetapsi3d(i,j,k)
        o24 = tan(q(i,j,k))
        o25 = o24**2
        o26 = 1/o25
        o27 = dqphipsi3d(i,j,k)
        o28 = 1/o24
        psixx(i,j,k) = o2*o4*(1.00000000000000d0*o11*o16*o19*o20 + 1.000
     &  00000000000d0*o11*o16*o22*o28 - 5.0000000000000d-1*o11*o16*o3 - 
     &  2.00000000000000d0*o11*o13*o14*o5 + 2.00000000000000d0*o11*o14*o
     &  15*o5 + 1.00000000000000d0*o11*o14*o15*o19*o5 + 1.00000000000000
     &  d0*o11*o14*o15*o26*o5 - 2.00000000000000d0*o11*o14*o27*o28*o5 + 
     &  o11*o18*o23*o6 + 7.5000000000000d-1*o11*o18*o3*o6 + 2.0000000000
     &  0000d0*o11*o17*o21*o6*o7 - 3.00000000000000d0*o11*o17*o22*o6*o7 
     &  + o11*o12*o6*o8 - 5.0000000000000d-1*o11*o3*o6*o8 + o11*o16*o9 -
     &   2.00000000000000d0*o11*o18*o6*o9 + o11*o6*o8*o9)
        psixy(i,j,k) = o2*o4*(-(o11*o13*o16) + 1.50000000000000d0*o11*o1
     &  5*o16 + 1.00000000000000d0*o11*o15*o16*o26 - o11*o16*o27*o28 - o
     &  11*o14*o19*o20*o5 + o11*o14*o18*o23*o5 - o11*o14*o22*o28*o5 + 5.
     &  0000000000000d-1*o11*o14*o3*o5 + 7.5000000000000d-1*o11*o14*o18*
     &  o3*o5 + o11*o13*o6 - 5.0000000000000d-1*o11*o15*o6 - o11*o15*o19
     &  *o6 + 1.00000000000000d0*o11*o27*o28*o6 + 2.00000000000000d0*o11
     &  *o14*o17*o21*o5*o7 - 3.00000000000000d0*o11*o14*o17*o22*o5*o7 + 
     &  o11*o12*o14*o5*o8 - 5.0000000000000d-1*o11*o14*o3*o5*o8 - o11*o1
     &  4*o5*o9 - 2.00000000000000d0*o11*o14*o18*o5*o9 + o11*o14*o5*o8*o
     &  9)
        psixz(i,j,k) = o2*o4*(o11*o14*o27 - o11*o13*o14*o28 + 5.00000000
     &  00000d-1*o11*o14*o15*o28 - o11*o18*o21*o5 + 1.50000000000000d0*o
     &  11*o18*o22*o5 - o11*o12*o17*o5*o7 + o11*o17*o23*o5*o7 + 1.250000
     &  00000000d0*o11*o17*o3*o5*o7 + o11*o21*o5*o8 - 1.50000000000000d0
     &  *o11*o22*o5*o8 - 3.00000000000000d0*o11*o17*o5*o7*o9)
        psiyy(i,j,k) = o2*o4*(o11*o16*o18*o23 + 7.5000000000000d-1*o11*o
     &  16*o18*o3 + 2.00000000000000d0*o11*o13*o14*o5 - 2.00000000000000
     &  d0*o11*o14*o15*o5 - o11*o14*o15*o19*o5 - o11*o14*o15*o26*o5 + 2.
     &  00000000000000d0*o11*o14*o27*o28*o5 + 1.00000000000000d0*o11*o19
     &  *o20*o6 + 1.00000000000000d0*o11*o22*o28*o6 - 5.0000000000000d-1
     &  *o11*o3*o6 + 2.00000000000000d0*o11*o16*o17*o21*o7 - 3.000000000
     &  00000d0*o11*o16*o17*o22*o7 + o11*o12*o16*o8 - 5.0000000000000d-1
     &  *o11*o16*o3*o8 - 2.00000000000000d0*o11*o16*o18*o9 + o11*o6*o9 +
     &   o11*o16*o8*o9)
        psiyz(i,j,k) = o2*o4*(-(o11*o14*o18*o21) + 1.50000000000000d0*o1
     &  1*o14*o18*o22 - o11*o27*o5 + 1.00000000000000d0*o11*o13*o28*o5 -
     &   5.0000000000000d-1*o11*o15*o28*o5 - o11*o12*o14*o17*o7 + o11*o1
     &  4*o17*o23*o7 + 1.25000000000000d0*o11*o14*o17*o3*o7 + o11*o14*o2
     &  1*o8 - 1.50000000000000d0*o11*o14*o22*o8 - 3.00000000000000d0*o1
     &  1*o14*o17*o7*o9)
        psizz(i,j,k) = o2*o4*(o11*o12*o18 - 5.0000000000000d-1*o11*o18*o
     &  3 - 2.00000000000000d0*o11*o17*o21*o7 + 3.00000000000000d0*o11*o
     &  17*o22*o7 + o11*o23*o8 + 7.5000000000000d-1*o11*o3*o8 + o11*o18*
     &  o9 - 2.00000000000000d0*o11*o8*o9)

```

gij.x:
```
        gxx(i,j,k) = 1.00000000000000d0
c        dxgxx(i,j,k) = 0
c        dygxx(i,j,k) = 0
c        dzgxx(i,j,k) = 0
        gxy(i,j,k) = 0
c        dxgxy(i,j,k) = 0
c        dygxy(i,j,k) = 0
c        dzgxy(i,j,k) = 0
        gxz(i,j,k) = 0
c        dxgxz(i,j,k) = 0
c        dygxz(i,j,k) = 0
c        dzgxz(i,j,k) = 0
        gyy(i,j,k) = 1.00000000000000d0
c        dxgyy(i,j,k) = 0
c        dygyy(i,j,k) = 0
c        dzgyy(i,j,k) = 0
        gyz(i,j,k) = 0
c        dxgyz(i,j,k) = 0
c        dygyz(i,j,k) = 0
c        dzgyz(i,j,k) = 0
        gzz(i,j,k) = 1.00000000000000d0
c        dxgzz(i,j,k) = 0
c        dygzz(i,j,k) = 0
c        dzgzz(i,j,k) = 0

```

ksq_odd.x:
```
        o1 = mm**2
        o2 = 5.0000000000000d1*o1
        o3 = -8.0000000000000d1 + o2
        o4 = 1/o3
        o5 = 2.00000000000000d0*qgrd(j)
        o6 = cos(o5)
        o7 = 5.0000000000000d0*o6
        o8 = 3.00000000000000d0 + o7
        o9 = dnnnnngtil
        o10 = mm*phigrd(k)
        o11 = sin(o10)
        o12 = sin(qgrd(j))
        o13 = o12**2
        o14 = o13**2
        o15 = 2.50000000000000d1*o1
        o16 = -4.0000000000000d1 + o15
        o17 = 1/o16
        o18 = dnnngtil
        o19 = 2.00000000000000d1*o1
        o20 = -3.2000000000000d1 + o19
        o21 = 1/o20
        o22 = dngtil
        o23 = 5.0000000000000d0*o1
        o24 = -8.0000000000000d0 + o23
        o25 = 1/o24
        o26 = cos(o10)
        o27 = cos(qgrd(j))
        o28 = 1.03000000000000d2*o1
        o29 = -9.2800000000000d2 + o28
        o30 = o12*o13
        o31 = 3.5000000000000d1*o1
        o32 = -8.3000000000000d1 + o31
        o33 = -1.60000000000000d1 + o1
        o34 = dnnnnnnngtil
        o35 = 4.0000000000000d0*qgrd(j)
        o36 = cos(o35)
        o37 = dnnnngtil
        o38 = 1.00000000000000d1*o1
        o39 = -1.60000000000000d1 + o38
        o40 = 1/o39
        o41 = dnngtil
        o42 = dnnnnnngtil
        o43 = o27**2
        o44 = gtil
        o45 = o13*o14
        o46 = 1.07000000000000d2*o1
        o47 = 5.3000000000000d1*o1
        o48 = sin(o5)
        o49 = byJ**2
        o50 = o24**2
        o51 = 1/o50
        o52 = o26**2
        o53 = o37**2
        o54 = o1**2
        o55 = o6**2
        o56 = o36**2
        o57 = o39**2
        o58 = 1/o57
        o59 = o41**2
        o60 = o9**2
        o61 = o16**2
        o62 = 1/o61
        o63 = o18**2
        o64 = o20**2
        o65 = 1/o64
        o66 = o22**2
        o67 = o11**2
        o68 = o1*o54
        o69 = o3**2
        o70 = 1/o69
        o71 = o42**2
        o72 = o34**2
        o73 = o14**2
        o74 = o48**2
        o75 = o43**2
        o76 = o44**2
        t1 = -1.00800000000000d2*byJ*o13*o25*o26*o37 - 1.39500000000000d1*
     &  byJ*o1*o13*o25*o26*o37 - 9.7440000000000d2*byJ*o13*o25*o26*o36*o37 +
     &   1.08150000000000d2*byJ*o1*o13*o25*o26*o36*o37 + 1.33200000000000d
     &  3*byJ*o13*o26*o40*o41 - 4.6800000000000d2*byJ*o1*o13*o26*o40*o41 + 6
     &  .9720000000000d3*byJ*o13*o26*o36*o40*o41 - 2.94000000000000d3*byJ*o1
     &  *o13*o26*o36*o40*o41 - 9.6000000000000d2*byJ*o14*o26*o4*o42 + 6.00
     &  00000000000d1*byJ*o1*o14*o26*o4*o42 - 1.80000000000000d2*byJ*o14*o26
     &  *o44 + 7.2000000000000d2*byJ*o13*o26*o43*o44 - 2.70000000000000d3*
     &  byJ*o14*o26*o43*o44 + 4.5000000000000d2*byJ*o26*o44*o45 + 1.80000000
     &  000000d1*o13*o49 - 3.7296000000000d3*o13*o25*o37*o40*o41*o52 + 7
     &  .9425000000000d2*o1*o13*o25*o37*o40*o41*o52 - 5.5574400000000d4*
     &  o13*o25*o36*o37*o40*o41*o52 + 2.21991000000000d4*o1*o13*o25*o36*
     &  o37*o40*o41*o52 + 2.68800000000000d3*o14*o25*o37*o4*o42*o52 + 2.
     &  04000000000000d2*o1*o14*o25*o37*o4*o42*o52 + 2.59840000000000d4*
     &  o14*o25*o36*o37*o4*o42*o52 - 4.5080000000000d3*o1*o14*o25*o36*o3
     &  7*o4*o42*o52 - 3.5520000000000d4*o14*o4*o40*o41*o42*o52 + 1.4700
     &  0000000000d4*o1*o14*o4*o40*o41*o42*o52 - 1.85920000000000d5*o14*
     &  o36*o4*o40*o41*o42*o52 + 9.0020000000000d4*o1*o14*o36*o4*o40*o41
     &  *o42*o52
        t2 = -1.10400000000000d5*o14*o17*o18*o21*o22*o43*o52 + 2.9160000
     &  0000000d4*o1*o14*o17*o18*o21*o22*o43*o52 + 5.0400000000000d2*o14
     &  *o25*o37*o44*o52 + 6.9750000000000d1*o1*o14*o25*o37*o44*o52 + 4.
     &  8720000000000d3*o14*o25*o36*o37*o44*o52 - 5.4075000000000d2*o1*o
     &  14*o25*o36*o37*o44*o52 - 6.6600000000000d3*o14*o40*o41*o44*o52 +
     &   2.34000000000000d3*o1*o14*o40*o41*o44*o52 - 3.4860000000000d4*o
     &  14*o36*o40*o41*o44*o52 + 1.47000000000000d4*o1*o14*o36*o40*o41*o
     &  44*o52 - 2.01600000000000d3*o13*o25*o37*o43*o44*o52 - 2.79000000
     &  000000d2*o1*o13*o25*o37*o43*o44*o52 + 7.5600000000000d3*o14*o25*
     &  o37*o43*o44*o52 + 1.04625000000000d3*o1*o14*o25*o37*o43*o44*o52 
     &  - 1.94880000000000d4*o13*o25*o36*o37*o43*o44*o52 + 2.16300000000
     &  000d3*o1*o13*o25*o36*o37*o43*o44*o52 + 7.3080000000000d4*o14*o25
     &  *o36*o37*o43*o44*o52 - 8.1112500000000d3*o1*o14*o25*o36*o37*o43*
     &  o44*o52 + 2.66400000000000d4*o13*o40*o41*o43*o44*o52 - 9.3600000
     &  000000d3*o1*o13*o40*o41*o43*o44*o52 - 9.9900000000000d4*o14*o40*
     &  o41*o43*o44*o52 + 3.5100000000000d4*o1*o14*o40*o41*o43*o44*o52 +
     &   1.39440000000000d5*o13*o36*o40*o41*o43*o44*o52 - 5.880000000000
     &  0d4*o1*o13*o36*o40*o41*o43*o44*o52 - 5.2290000000000d5*o14*o36*o
     &  40*o41*o43*o44*o52 + 2.20500000000000d5*o1*o14*o36*o40*o41*o43*o
     &  44*o52 - 1.92000000000000d4*o14*o4*o42*o43*o44*o52
        t3 = 1.20000000000000d3*o1*o14*o4*o42*o43*o44*o52 - 7.6800000000
     &  000d3*o17*o21*o22*o34*o43*o45*o52 + 1.44000000000000d3*o1*o17*o2
     &  1*o22*o34*o43*o45*o52 - 1.26000000000000d3*o25*o37*o44*o45*o52 -
     &   1.74375000000000d2*o1*o25*o37*o44*o45*o52 - 1.21800000000000d4*
     &  o25*o36*o37*o44*o45*o52 + 1.35187500000000d3*o1*o25*o36*o37*o44*
     &  o45*o52 + 1.66500000000000d4*o40*o41*o44*o45*o52 - 5.85000000000
     &  00d3*o1*o40*o41*o44*o45*o52 + 8.7150000000000d4*o36*o40*o41*o44*
     &  o45*o52 - 3.6750000000000d4*o1*o36*o40*o41*o44*o45*o52 + 4.80000
     &  00000000d3*o4*o42*o44*o45*o52 - 3.00000000000000d2*o1*o4*o42*o44
     &  *o45*o52 + 7.2000000000000d4*o4*o42*o43*o44*o45*o52 - 4.50000000
     &  00000d3*o1*o4*o42*o43*o44*o45*o52 + 1.41120000000000d2*o13*o51*o
     &  52*o53 + 3.9060000000000d1*o1*o13*o51*o52*o53 + 2.72832000000000
     &  d3*o13*o36*o51*o52*o53 + 7.4760000000000d1*o1*o13*o36*o51*o52*o5
     &  3 + 1.81350000000000d2*o13*o25*o37*o40*o41*o52*o54 - 2.667000000
     &  00000d2*o13*o25*o36*o37*o40*o41*o52*o54 - 2.32500000000000d1*o14
     &  *o25*o37*o4*o42*o52*o54 + 1.80250000000000d2*o14*o25*o36*o37*o4*
     &  o42*o52*o54 - 7.8000000000000d2*o14*o4*o40*o41*o42*o52*o54 - 4.9
     &  000000000000d3*o14*o36*o4*o40*o41*o42*o52*o54 - 1.92000000000000
     &  d3*o14*o17*o18*o21*o22*o43*o52*o54 - 6.0000000000000d1*o17*o21*o
     &  22*o34*o43*o45*o52*o54
        t4 = 2.70281250000000d0*o13*o51*o52*o53*o54 - 4.1908125000000d1*
     &  o13*o36*o51*o52*o53*o54 - 2.74432000000000d4*o13*o25*o37*o40*o41
     &  *o52*o55 + 9.5432000000000d3*o1*o13*o25*o37*o40*o41*o52*o55 + 1.
     &  14688000000000d4*o14*o25*o37*o4*o42*o52*o55 - 4.2560000000000d2*
     &  o1*o14*o25*o37*o4*o42*o52*o55 - 1.20064000000000d5*o14*o4*o40*o4
     &  1*o42*o52*o55 + 5.2304000000000d4*o1*o14*o4*o40*o41*o42*o52*o55 
     &  - 1.99200000000000d6*o14*o17*o18*o21*o22*o43*o52*o55 + 2.0850000
     &  0000000d6*o1*o14*o17*o18*o21*o22*o43*o52*o55 + 1.31072000000000d
     &  3*o13*o51*o52*o53*o55 + 6.6560000000000d1*o1*o13*o51*o52*o53*o55
     &   + 2.60000000000000d2*o13*o25*o37*o40*o41*o52*o54*o55 - 1.820000
     &  00000000d1*o14*o25*o37*o4*o42*o52*o54*o55 - 2.80000000000000d3*o
     &  14*o4*o40*o41*o42*o52*o54*o55 - 5.2500000000000d5*o14*o17*o18*o2
     &  1*o22*o43*o52*o54*o55 + 8.4500000000000d-1*o13*o51*o52*o53*o54*o
     &  55 - 1.88708800000000d5*o13*o25*o37*o40*o41*o52*o56 + 1.00521050
     &  000000d5*o1*o13*o25*o37*o40*o41*o52*o56 + 1.31868800000000d4*o13
     &  *o51*o52*o53*o56 - 2.92726000000000d3*o1*o13*o51*o52*o53*o56 - 8
     &  .8322500000000d3*o13*o25*o37*o40*o41*o52*o54*o56 + 1.62450312500
     &  000d2*o13*o51*o52*o53*o54*o56 + 2.46420000000000d4*o13*o52*o58*o
     &  59 - 1.73160000000000d4*o1*o13*o52*o58*o59 + 2.57964000000000d5*
     &  o13*o36*o52*o58*o59 - 1.99416000000000d5*o1*o13*o36*o52*o58*o59
        t5 = 3.04200000000000d3*o13*o52*o54*o58*o59 + 3.8220000000000d4*
     &  o13*o36*o52*o54*o58*o59 + 1.43648000000000d5*o13*o52*o55*o58*o59
     &   - 1.07200000000000d5*o1*o13*o52*o55*o58*o59 + 2.00000000000000d
     &  4*o13*o52*o54*o55*o58*o59 + 6.7512200000000d5*o13*o52*o56*o58*o5
     &  9 - 5.6938000000000d5*o1*o13*o52*o56*o58*o59 + 1.20050000000000d
     &  5*o13*o52*o54*o56*o58*o59 - 3.07200000000000d2*byJ*o13*o25*o26*o37
     &  *o6 - 7.8000000000000d0*byJ*o1*o13*o25*o26*o37*o6 + 3.216000000000
     &  0d3*byJ*o13*o26*o40*o41*o6 - 1.20000000000000d3*byJ*o1*o13*o26*o40*o
     &  41*o6 - 1.34400000000000d3*byJ*o14*o26*o4*o42*o6 + 8.4000000000000
     &  d1*byJ*o1*o14*o26*o4*o42*o6 - 2.03712000000000d4*o13*o25*o37*o40*o
     &  41*o52*o6 + 5.8188000000000d3*o1*o13*o25*o37*o40*o41*o52*o6 - 1.
     &  46540800000000d5*o13*o25*o36*o37*o40*o41*o52*o6 + 6.571880000000
     &  0d4*o1*o13*o25*o36*o37*o40*o41*o52*o6 + 1.19552000000000d4*o14*o
     &  25*o37*o4*o42*o52*o6 - 1.84000000000000d1*o1*o14*o25*o37*o4*o42*
     &  o52*o6 + 3.6377600000000d4*o14*o25*o36*o37*o4*o42*o52*o6 - 6.311
     &  2000000000d3*o1*o14*o25*o36*o37*o4*o42*o52*o6 - 1.35488000000000
     &  d5*o14*o4*o40*o41*o42*o52*o6 + 5.7940000000000d4*o1*o14*o4*o40*o
     &  41*o42*o52*o6 - 2.60288000000000d5*o14*o36*o4*o40*o41*o42*o52*o6
     &   + 1.26028000000000d5*o1*o14*o36*o4*o40*o41*o42*o52*o6 + 9.50400
     &  00000000d5*o14*o17*o18*o21*o22*o43*o52*o6
        t6 = -6.3960000000000d5*o1*o14*o17*o18*o21*o22*o43*o52*o6 + 1.53
     &  600000000000d3*o14*o25*o37*o44*o52*o6 + 3.9000000000000d1*o1*o14
     &  *o25*o37*o44*o52*o6 - 1.60800000000000d4*o14*o40*o41*o44*o52*o6 
     &  + 6.0000000000000d3*o1*o14*o40*o41*o44*o52*o6 - 6.1440000000000d
     &  3*o13*o25*o37*o43*o44*o52*o6 - 1.56000000000000d2*o1*o13*o25*o37
     &  *o43*o44*o52*o6 + 2.30400000000000d4*o14*o25*o37*o43*o44*o52*o6 
     &  + 5.8500000000000d2*o1*o14*o25*o37*o43*o44*o52*o6 + 6.4320000000
     &  000d4*o13*o40*o41*o43*o44*o52*o6 - 2.40000000000000d4*o1*o13*o40
     &  *o41*o43*o44*o52*o6 - 2.41200000000000d5*o14*o40*o41*o43*o44*o52
     &  *o6 + 9.0000000000000d4*o1*o14*o40*o41*o43*o44*o52*o6 - 2.688000
     &  00000000d4*o14*o4*o42*o43*o44*o52*o6 + 1.68000000000000d3*o1*o14
     &  *o4*o42*o43*o44*o52*o6 + 3.8400000000000d4*o17*o21*o22*o34*o43*o
     &  45*o52*o6 - 2.64000000000000d4*o1*o17*o21*o22*o34*o43*o45*o52*o6
     &   - 3.8400000000000d3*o25*o37*o44*o45*o52*o6 - 9.7500000000000d1*
     &  o1*o25*o37*o44*o45*o52*o6 + 4.0200000000000d4*o40*o41*o44*o45*o5
     &  2*o6 - 1.50000000000000d4*o1*o40*o41*o44*o45*o52*o6 + 6.72000000
     &  00000d3*o4*o42*o44*o45*o52*o6 - 4.2000000000000d2*o1*o4*o42*o44*
     &  o45*o52*o6 + 1.00800000000000d5*o4*o42*o43*o44*o45*o52*o6 - 6.30
     &  00000000000d3*o1*o4*o42*o43*o44*o45*o52*o6 + 8.6016000000000d2*o
     &  13*o51*o52*o53*o6 + 1.40880000000000d2*o1*o13*o51*o52*o53*o6
        t7 = 8.3148800000000d3*o13*o36*o51*o52*o53*o6 - 7.1176000000000d
     &  2*o1*o13*o36*o51*o52*o53*o6 + 5.6640000000000d2*o13*o25*o37*o40*
     &  o41*o52*o54*o6 - 2.96800000000000d3*o13*o25*o36*o37*o40*o41*o52*
     &  o54*o6 - 4.5550000000000d1*o14*o25*o37*o4*o42*o52*o54*o6 + 2.523
     &  50000000000d2*o14*o25*o36*o37*o4*o42*o52*o54*o6 - 3.092000000000
     &  00d3*o14*o4*o40*o41*o42*o52*o54*o6 - 6.8600000000000d3*o14*o36*o
     &  4*o40*o41*o42*o52*o54*o6 + 6.9000000000000d4*o14*o17*o18*o21*o22
     &  *o43*o52*o54*o6 + 1.50000000000000d3*o17*o21*o22*o34*o43*o45*o52
     &  *o54*o6 + 3.02250000000000d0*o13*o51*o52*o53*o54*o6 - 2.34325000
     &  000000d1*o13*o36*o51*o52*o53*o54*o6 + 1.18992000000000d5*o13*o52
     &  *o58*o59*o6 - 8.6208000000000d4*o1*o13*o52*o58*o59*o6 + 6.228320
     &  0000000d5*o13*o36*o52*o58*o59*o6 - 4.9504000000000d5*o1*o13*o36*
     &  o52*o58*o59*o6 + 1.56000000000000d4*o13*o52*o54*o58*o59*o6 + 9.8
     &  000000000000d4*o13*o36*o52*o54*o58*o59*o6 + 6.1952000000000d2*o1
     &  4*o43*o51*o52*o60 - 1.93600000000000d2*o1*o14*o43*o51*o52*o60 + 
     &  1.51250000000000d1*o14*o43*o51*o52*o54*o60 + 4.3059200000000d3*o
     &  14*o43*o51*o52*o55*o60 - 9.5584000000000d2*o1*o14*o43*o51*o52*o5
     &  5*o60 + 5.3045000000000d1*o14*o43*o51*o52*o54*o55*o60 - 3.266560
     &  0000000d3*o14*o43*o51*o52*o6*o60 + 8.7296000000000d2*o1*o14*o43*
     &  o51*o52*o6*o60 - 5.6650000000000d1*o14*o43*o51*o52*o54*o6*o60
        t8 = 1.47200000000000d4*o18*o34*o43*o45*o52*o62 - 2.968000000000
     &  00d3*o1*o18*o34*o43*o45*o52*o62 + 1.28000000000000d2*o18*o34*o43
     &  *o45*o52*o54*o62 - 5.3120000000000d4*o18*o34*o43*o45*o52*o6*o62 
     &  + 2.57200000000000d4*o1*o18*o34*o43*o45*o52*o6*o62 - 1.400000000
     &  00000d3*o18*o34*o43*o45*o52*o54*o6*o62 + 1.05800000000000d5*o14*
     &  o43*o52*o62*o63 - 2.94400000000000d4*o1*o14*o43*o52*o62*o63 + 2.
     &  04800000000000d3*o14*o43*o52*o54*o62*o63 + 1.37780000000000d6*o1
     &  4*o43*o52*o55*o62*o63 - 1.16200000000000d6*o1*o14*o43*o52*o55*o6
     &  2*o63 + 2.45000000000000d5*o14*o43*o52*o54*o55*o62*o63 - 7.63600
     &  00000000d5*o14*o43*o52*o6*o62*o63 + 4.2824000000000d5*o1*o14*o43
     &  *o52*o6*o62*o63 - 4.4800000000000d4*o14*o43*o52*o54*o6*o62*o63 +
     &   2.88000000000000d4*o14*o43*o52*o65*o66 - 7.2000000000000d3*o1*o
     &  14*o43*o52*o65*o66 + 4.5000000000000d2*o14*o43*o52*o54*o65*o66 +
     &   7.2000000000000d5*o14*o43*o52*o55*o65*o66 - 9.0000000000000d5*o
     &  1*o14*o43*o52*o55*o65*o66 + 2.81250000000000d5*o14*o43*o52*o54*o
     &  55*o65*o66 - 2.88000000000000d5*o14*o43*o52*o6*o65*o66 + 2.16000
     &  000000000d5*o1*o14*o43*o52*o6*o65*o66 - 2.25000000000000d4*o14*o
     &  43*o52*o54*o6*o65*o66 - 2.10600000000000d4*o1*o14*o17*o18*o21*o2
     &  2*o67 - 6.7562000000000d4*o1*o14*o17*o18*o22*o25*o67 - 7.0180000
     &  000000d4*o1*o14*o17*o18*o22*o40*o67 + 1.92000000000000d3*o1*o14*
     &  o17*o42*o43*o44*o67
        t9 = -3.3600000000000d3*o1*o17*o42*o43*o44*o45*o67 - 5.440000000
     &  0000d2*o1*o17*o25*o27*o30*o37*o42*o48*o67 + 1.98400000000000d3*o
     &  1*o17*o27*o30*o40*o41*o42*o48*o67 - 1.02000000000000d3*o1*o12*o2
     &  5*o27*o37*o44*o48*o67 + 1.78500000000000d3*o1*o25*o27*o30*o37*o4
     &  4*o48*o67 + 3.7200000000000d3*o1*o12*o27*o40*o41*o44*o48*o67 - 6
     &  .5100000000000d3*o1*o27*o30*o40*o41*o44*o48*o67 + 4.625200000000
     &  0d4*o14*o17*o18*o22*o25*o54*o67 + 6.6494000000000d4*o14*o17*o18*
     &  o22*o40*o54*o67 - 1.20000000000000d2*o14*o17*o42*o43*o44*o54*o67
     &   + 2.10000000000000d2*o17*o42*o43*o44*o45*o54*o67 + 1.2200000000
     &  0000d2*o17*o25*o27*o30*o37*o42*o48*o54*o67 - 5.7200000000000d2*o
     &  17*o27*o30*o40*o41*o42*o48*o54*o67 + 1.65000000000000d2*o12*o25*
     &  o27*o37*o44*o48*o54*o67 - 2.88750000000000d2*o25*o27*o30*o37*o44
     &  *o48*o54*o67 - 8.4000000000000d2*o12*o27*o40*o41*o44*o48*o54*o67
     &   + 1.47000000000000d3*o27*o30*o40*o41*o44*o48*o54*o67 - 5.850000
     &  0000000d4*o1*o14*o17*o18*o21*o22*o55*o67 - 1.42506000000000d5*o1
     &  *o14*o17*o18*o22*o25*o55*o67 - 1.31652000000000d5*o1*o14*o17*o18
     &  *o22*o40*o55*o67 + 9.2016000000000d4*o14*o17*o18*o22*o25*o54*o55
     &  *o67 + 1.25082000000000d5*o14*o17*o18*o22*o40*o54*o55*o67 - 7.02
     &  00000000000d4*o1*o14*o17*o18*o21*o22*o6*o67 - 1.96332000000000d5
     &  *o1*o14*o17*o18*o22*o25*o6*o67 - 1.92408000000000d5*o1*o14*o17*o
     &  18*o22*o40*o6*o67 - 1.29920000000000d3*o1*o17*o25*o27*o30*o37*o4
     &  2*o48*o6*o67 + 1.33760000000000d4*o1*o17*o27*o30*o40*o41*o42*o48
     &  *o6*o67
        t10 = -2.43600000000000d3*o1*o12*o25*o27*o37*o44*o48*o6*o67 + 4.
     &  2630000000000d3*o1*o25*o27*o30*o37*o44*o48*o6*o67 + 2.5080000000
     &  0000d4*o1*o12*o27*o40*o41*o44*o48*o6*o67 - 4.3890000000000d4*o1*
     &  o27*o30*o40*o41*o44*o48*o6*o67 + 1.30692000000000d5*o14*o17*o18*
     &  o22*o25*o54*o6*o67 + 1.82664000000000d5*o14*o17*o18*o22*o40*o54*
     &  o6*o67 + 1.08400000000000d2*o17*o25*o27*o30*o37*o42*o48*o54*o6*o
     &  67 - 6.5320000000000d3*o17*o27*o30*o40*o41*o42*o48*o54*o6*o67 + 
     &  5.1000000000000d1*o12*o25*o27*o37*o44*o48*o54*o6*o67 - 8.9250000
     &  000000d1*o25*o27*o30*o37*o44*o48*o54*o6*o67 - 1.06800000000000d4
     &  *o12*o27*o40*o41*o44*o48*o54*o6*o67 + 1.86900000000000d4*o27*o30
     &  *o40*o41*o44*o48*o54*o6*o67 + 4.0960000000000d3*o1*o14*o60*o62*o
     &  67 - 5.1200000000000d2*o14*o54*o60*o62*o67 + 9.2160000000000d3*o
     &  1*o14*o55*o60*o62*o67 - 1.15200000000000d3*o14*o54*o55*o60*o62*o
     &  67 + 1.22880000000000d4*o1*o14*o6*o60*o62*o67 - 1.53600000000000
     &  d3*o14*o54*o6*o60*o62*o67 + 2.63438000000000d5*o1*o14*o62*o63*o6
     &  7 - 1.49158000000000d5*o14*o54*o62*o63*o67 + 5.8030200000000d5*o
     &  1*o14*o55*o62*o63*o67 - 3.2531400000000d5*o14*o54*o55*o62*o63*o6
     &  7 + 7.8147600000000d5*o1*o14*o6*o62*o63*o67 - 4.4056800000000d5*
     &  o14*o54*o6*o62*o63*o67 + 6.8890000000000d3*o1*o14*o51*o66*o67 - 
     &  5.8100000000000d3*o14*o51*o54*o66*o67 + 1.36890000000000d4*o1*o1
     &  4*o51*o55*o66*o67
        t11 = -1.05300000000000d4*o14*o51*o54*o55*o66*o67 + 1.4641000000
     &  0000d4*o1*o14*o58*o66*o67 - 1.69400000000000d4*o14*o54*o58*o66*o
     &  67 + 2.52810000000000d4*o1*o14*o55*o58*o66*o67 - 2.8620000000000
     &  0d4*o14*o54*o55*o58*o66*o67 + 1.94220000000000d4*o1*o14*o51*o6*o
     &  66*o67 - 1.56600000000000d4*o14*o51*o54*o6*o66*o67 + 3.847800000
     &  0000d4*o1*o14*o58*o6*o66*o67 - 4.4040000000000d4*o14*o54*o58*o6*
     &  o66*o67 + 8.1000000000000d3*o1*o14*o65*o66*o67 + 2.2500000000000
     &  0d4*o1*o14*o55*o65*o66*o67 + 2.70000000000000d4*o1*o14*o6*o65*o6
     &  6*o67 - 7.4900000000000d3*o14*o17*o18*o22*o25*o67*o68 - 1.498000
     &  00000000d4*o14*o17*o18*o22*o40*o67*o68 - 5.5000000000000d0*o17*o
     &  25*o27*o30*o37*o42*o48*o67*o68 + 2.80000000000000d1*o17*o27*o30*
     &  o40*o41*o42*o48*o67*o68 - 1.43100000000000d4*o14*o17*o18*o22*o25
     &  *o55*o67*o68 - 2.86200000000000d4*o14*o17*o18*o22*o40*o55*o67*o6
     &  8 - 2.07600000000000d4*o14*o17*o18*o22*o25*o6*o67*o68 - 4.152000
     &  0000000d4*o14*o17*o18*o22*o40*o6*o67*o68 - 1.70000000000000d0*o1
     &  7*o25*o27*o30*o37*o42*o48*o6*o67*o68 + 3.5600000000000d2*o17*o27
     &  *o30*o40*o41*o42*o48*o6*o67*o68 + 1.60000000000000d1*o14*o60*o62
     &  *o67*o68 + 3.6000000000000d1*o14*o55*o60*o62*o67*o68 + 4.8000000
     &  000000d1*o14*o6*o60*o62*o67*o68 + 2.28980000000000d4*o14*o62*o63
     &  *o67*o68 + 5.0562000000000d4*o14*o55*o62*o63*o67*o68
        t12 = 6.8052000000000d4*o14*o6*o62*o63*o67*o68 + 1.2250000000000
     &  0d3*o14*o51*o66*o67*o68 + 2.02500000000000d3*o14*o51*o55*o66*o67
     &  *o68 + 4.9000000000000d3*o14*o58*o66*o67*o68 + 8.1000000000000d3
     &  *o14*o55*o58*o66*o67*o68 + 3.15000000000000d3*o14*o51*o6*o66*o67
     &  *o68 + 1.26000000000000d4*o14*o58*o6*o66*o67*o68 + 1.42420000000
     &  000d4*o1*o14*o60*o67*o70 - 1.90400000000000d3*o14*o54*o60*o67*o7
     &  0 + 3.15540000000000d4*o1*o14*o55*o60*o67*o70 - 4.2480000000000d
     &  3*o14*o54*o55*o60*o67*o70 + 4.2396000000000d4*o1*o14*o6*o60*o67*
     &  o70 - 5.6880000000000d3*o14*o54*o6*o60*o67*o70 + 6.4000000000000
     &  d1*o14*o60*o67*o68*o70 + 1.44000000000000d2*o14*o55*o60*o67*o68*
     &  o70 + 1.92000000000000d2*o14*o6*o60*o67*o68*o70 + 5.120000000000
     &  0d2*o1*o43*o45*o62*o67*o71 - 6.4000000000000d1*o43*o45*o54*o62*o
     &  67*o71 + 2.00000000000000d0*o43*o45*o62*o67*o68*o71 + 1.28000000
     &  000000d4*o45*o52*o70*o71 - 1.60000000000000d3*o1*o45*o52*o70*o71
     &   + 5.0000000000000d1*o45*o52*o54*o70*o71 + 2.50880000000000d4*o4
     &  5*o52*o55*o70*o71 - 3.13600000000000d3*o1*o45*o52*o55*o70*o71 + 
     &  9.8000000000000d1*o45*o52*o54*o55*o70*o71 + 3.5840000000000d4*o4
     &  5*o52*o6*o70*o71 - 4.4800000000000d3*o1*o45*o52*o6*o70*o71 + 1.4
     &  0000000000000d2*o45*o52*o54*o6*o70*o71
        t13 = -1.20000000000000d4*o4*o42*o44*o52*o73 + 7.5000000000000d2
     &  *o1*o4*o42*o44*o52*o73 - 1.68000000000000d4*o4*o42*o44*o52*o6*o7
     &  3 + 1.05000000000000d3*o1*o4*o42*o44*o52*o6*o73 + 5.120000000000
     &  0d2*o43*o52*o62*o72*o73 - 6.4000000000000d1*o1*o43*o52*o62*o72*o
     &  73 + 2.00000000000000d0*o43*o52*o54*o62*o72*o73 - 1.054000000000
     &  00d3*o1*o25*o37*o40*o41*o67*o74 + 1.44500000000000d2*o1*o51*o53*
     &  o67*o74 + 4.0850000000000d2*o25*o37*o40*o41*o54*o67*o74 - 4.6750
     &  000000000d1*o51*o53*o54*o67*o74 - 1.69708000000000d4*o1*o25*o37*
     &  o40*o41*o55*o67*o74 + 8.2418000000000d2*o1*o51*o53*o55*o67*o74 +
     &   7.5821000000000d3*o25*o37*o40*o41*o54*o55*o67*o74 - 3.451000000
     &  0000d1*o51*o53*o54*o55*o67*o74 + 1.92200000000000d3*o1*o58*o59*o
     &  67*o74 - 8.6800000000000d2*o54*o58*o59*o67*o74 + 8.7362000000000
     &  d4*o1*o55*o58*o59*o67*o74 - 7.4404000000000d4*o54*o55*o58*o59*o6
     &  7*o74 - 9.6232000000000d3*o1*o25*o37*o40*o41*o6*o67*o74 + 6.9020
     &  000000000d2*o1*o51*o53*o6*o67*o74 + 4.7966000000000d3*o25*o37*o4
     &  0*o41*o54*o6*o67*o74 - 1.26100000000000d2*o51*o53*o54*o6*o67*o74
     &   + 2.59160000000000d4*o1*o58*o59*o6*o67*o74 - 1.68880000000000d4
     &  *o54*o58*o59*o6*o67*o74 - 3.8500000000000d1*o25*o37*o40*o41*o67*
     &  o68*o74 + 3.7812500000000d0*o51*o53*o67*o68*o74
        t14 = -1.51300000000000d2*o25*o37*o40*o41*o55*o67*o68*o74 + 3.61
     &  25000000000d-1*o51*o53*o55*o67*o68*o74 + 9.8000000000000d1*o58*o
     &  59*o67*o68*o74 + 1.58420000000000d4*o55*o58*o59*o67*o68*o74 - 5.
     &  0140000000000d2*o25*o37*o40*o41*o6*o67*o68*o74 + 2.3375000000000
     &  0d0*o51*o53*o6*o67*o68*o74 + 2.49200000000000d3*o58*o59*o6*o67*o
     &  68*o74 - 3.6000000000000d3*o14*o43*o52*o76 + 4.5000000000000d2*o
     &  45*o52*o76 + 2.25000000000000d4*o43*o45*o52*o76 + 1.800000000000
     &  00d3*o1*o13*o43*o67*o76 - 6.3000000000000d3*o1*o14*o43*o67*o76 +
     &   5.5125000000000d3*o1*o43*o45*o67*o76 - 2.25000000000000d3*o52*o
     &  73*o76 + 2.81250000000000d3*o13*o52*o73*o76 - 3.3750000000000d4*
     &  o43*o52*o73*o76 + 7.2000000000000d3*o13*o52*o75*o76 - 5.40000000
     &  00000d4*o14*o52*o75*o76 + 1.01250000000000d5*o45*o52*o75*o76 - 1
     &  .61920000000000d4*o14*o17*o18*o25*o43*o52*o9 + 4.7828000000000d3
     &  *o1*o14*o17*o18*o25*o43*o52*o9 + 8.4480000000000d3*o14*o21*o22*o
     &  25*o43*o52*o9 - 2.37600000000000d3*o1*o14*o21*o22*o25*o43*o52*o9
     &   - 1.12640000000000d3*o17*o25*o34*o43*o45*o52*o9 + 2.46400000000
     &  000d2*o1*o17*o25*o34*o43*o45*o52*o9 - 3.5200000000000d2*o14*o17*
     &  o18*o25*o43*o52*o54*o9 + 1.65000000000000d2*o14*o21*o22*o25*o43*
     &  o52*o54*o9
        t15 = -1.10000000000000d1*o17*o25*o34*o43*o45*o52*o54*o9 - 1.540
     &  48000000000d5*o14*o17*o18*o25*o43*o52*o55*o9 + 8.2058000000000d4
     &  *o1*o14*o17*o18*o25*o43*o52*o55*o9 + 1.11360000000000d5*o14*o21*
     &  o22*o25*o43*o52*o55*o9 - 8.1960000000000d4*o1*o14*o21*o22*o25*o4
     &  3*o52*o55*o9 - 7.2100000000000d3*o14*o17*o18*o25*o43*o52*o54*o55
     &  *o9 + 7.7250000000000d3*o14*o21*o22*o25*o43*o52*o54*o55*o9 + 1.0
     &  1120000000000d5*o14*o17*o18*o25*o43*o52*o6*o9 - 4.4447200000000d
     &  4*o1*o14*o17*o18*o25*o43*o52*o6*o9 - 6.4512000000000d4*o14*o21*o
     &  22*o25*o43*o52*o6*o9 + 3.8256000000000d4*o1*o14*o21*o22*o25*o43*
     &  o52*o6*o9 + 2.96960000000000d3*o17*o25*o34*o43*o45*o52*o6*o9 - 5
     &  .1520000000000d2*o1*o17*o25*o34*o43*o45*o52*o6*o9 + 4.5092000000
     &  000d3*o14*o17*o18*o25*o43*o52*o54*o6*o9 - 4.4340000000000d3*o14*
     &  o21*o22*o25*o43*o52*o54*o6*o9 + 2.06000000000000d1*o17*o25*o34*o
     &  43*o45*o52*o54*o6*o9 + 1.06240000000000d4*o1*o14*o17*o22*o25*o67
     &  *o9 - 7.1126000000000d4*o1*o14*o17*o18*o4*o67*o9 + 1.62000000000
     &  000d3*o1*o14*o21*o22*o4*o67*o9 + 2.87980000000000d4*o1*o14*o22*o
     &  4*o40*o67*o9 - 5.1440000000000d3*o14*o17*o22*o25*o54*o67*o9 + 3.
     &  01060000000000d4*o14*o17*o18*o4*o54*o67*o9 - 1.85960000000000d4*
     &  o14*o22*o4*o40*o54*o67*o9 + 2.24640000000000d4*o1*o14*o17*o22*o2
     &  5*o55*o67*o9 - 1.52406000000000d5*o1*o14*o17*o18*o4*o55*o67*o9 +
     &   4.5000000000000d3*o1*o14*o21*o22*o4*o55*o67*o9 + 5.628600000000
     &  0d4*o1*o14*o22*o4*o40*o55*o67*o9
        t16 = -1.00440000000000d4*o14*o17*o22*o25*o54*o55*o67*o9 + 6.622
     &  2000000000d4*o14*o17*o18*o4*o54*o55*o67*o9 - 3.5676000000000d4*o
     &  14*o22*o4*o40*o54*o55*o67*o9 + 3.09120000000000d4*o1*o14*o17*o22
     &  *o25*o6*o67*o9 - 2.08212000000000d5*o1*o14*o17*o18*o4*o6*o67*o9 
     &  + 5.4000000000000d3*o1*o14*o21*o22*o4*o6*o67*o9 + 8.067600000000
     &  0d4*o1*o14*o22*o4*o40*o6*o67*o9 - 1.44120000000000d4*o14*o17*o22
     &  *o25*o54*o6*o67*o9 + 8.9304000000000d4*o14*o17*o18*o4*o54*o6*o67
     &  *o9 - 5.1648000000000d4*o14*o22*o4*o40*o54*o6*o67*o9 - 5.2096000
     &  000000d4*o1*o14*o18*o62*o67*o9 + 1.69520000000000d4*o14*o18*o54*
     &  o62*o67*o9 - 1.16928000000000d5*o1*o14*o18*o55*o62*o67*o9 + 3.78
     &  36000000000d4*o14*o18*o54*o55*o62*o67*o9 - 1.56096000000000d5*o1
     &  *o14*o18*o6*o62*o67*o9 + 5.0652000000000d4*o14*o18*o54*o6*o62*o6
     &  7*o9 + 2.80000000000000d2*o14*o17*o22*o25*o67*o68*o9 - 1.7120000
     &  0000000d3*o14*o17*o18*o4*o67*o68*o9 + 1.12000000000000d3*o14*o22
     &  *o4*o40*o67*o68*o9 + 5.4000000000000d2*o14*o17*o22*o25*o55*o67*o
     &  68*o9 - 3.8160000000000d3*o14*o17*o18*o4*o55*o67*o68*o9 + 2.1600
     &  0000000000d3*o14*o22*o4*o40*o55*o67*o68*o9 + 7.8000000000000d2*o
     &  14*o17*o22*o25*o6*o67*o68*o9 - 5.1120000000000d3*o14*o17*o18*o4*
     &  o6*o67*o68*o9 + 3.12000000000000d3*o14*o22*o4*o40*o6*o67*o68*o9 
     &  - 8.5600000000000d2*o14*o18*o62*o67*o68*o9 - 1.90800000000000d3*
     &  o14*o18*o55*o62*o67*o68*o9 - 2.55600000000000d3*o14*o18*o6*o62*o
     &  67*o68*o9
        ksq(i,j,k) = t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + 
     &  t11 + t12 + t13 + t14 + t15 + t16

```

kij_odd.x:
```
        o1 = mm**2
        o2 = 5.0000000000000d1*o1
        o3 = -8.0000000000000d1 + o2
        o4 = 1/o3
        o5 = 2.00000000000000d0*q(i,j,k)
        o6 = cos(o5)
        o7 = 5.0000000000000d0*o6
        o8 = 3.00000000000000d0 + o7
        o9 = dnnnnngtil
        o10 = dnnngtil
        o11 = -2.60000000000000d1*o10
        o12 = dngtil
        o13 = 2.50000000000000d1*o12
        o14 = o11 + o13 + o9
        o15 = -3.00000000000000d0*eta(i,j,k)
        o16 = exp(o15)
        o17 = sin(phi(i,j,k))
        o18 = o17**2
        o19 = mm*phi(i,j,k)
        o20 = sin(o19)
        o21 = sin(q(i,j,k))
        o22 = o21**2
        o23 = 2.50000000000000d1*o1
        o24 = -4.0000000000000d1 + o23
        o25 = 1/o24
        o26 = cos(phi(i,j,k))
        o27 = o26**2
        o28 = -1.60000000000000d1 + o1
        o29 = 3.00000000000000d0*o6
        o30 = 2.00000000000000d0 + o29
        o31 = 2.00000000000000d0*o28*o30*o9
        o32 = -1.07000000000000d2*o1
        o33 = 6.0900000000000d2*o6
        o34 = -1.59000000000000d2*o1*o6
        o35 = 4.0700000000000d2 + o32 + o33 + o34
        o36 = o10*o35
        o37 = 3.5000000000000d1*o1
        o38 = 5.0000000000000d0*o1
        o39 = -1.30000000000000d1 + o38
        o40 = 9.0000000000000d0*o39*o6
        o41 = -8.3000000000000d1 + o37 + o40
        o42 = 5.0000000000000d0*o12*o41
        o43 = o31 + o36 + o42
        o44 = o22**2
        o45 = cos(q(i,j,k))
        o46 = o45**2
        o47 = -3.00000000000000d0*mm*o14*o20*o22*o4*o8
        o48 = -(mm*o20*o22*o25*o43)
        o49 = o47 + o48
        o50 = -8.0000000000000d0 + o38
        o51 = 1/o50
        o52 = cos(o19)
        o53 = -9.0000000000000d0*o1
        o54 = 5.0000000000000d0*o50*o6
        o55 = 8.0000000000000d0 + o53 + o54
        o56 = -7.5000000000000d1*o12*o55
        o57 = 2.88000000000000d2*o9
        o58 = -1.20000000000000d1*o1*o9
        o59 = -9.4000000000000d1*o1
        o60 = -4.1500000000000d2*o6
        o61 = 1.75000000000000d2*o1*o6
        o62 = 1.15000000000000d2 + o59 + o60 + o61
        o63 = 4.0000000000000d0*o10*o62
        o64 = dnnnnnnngtil
        o65 = 3.2000000000000d1*o22*o64
        o66 = -2.00000000000000d0*o1*o22*o64
        o67 = -9.2800000000000d2*o22*o9
        o68 = 1.03000000000000d2*o1*o22*o9
        o69 = o57 + o58 + o63 + o65 + o66 + o67 + o68
        o70 = 2.00000000000000d0*o69
        o71 = o56 + o70
        o72 = sin(o5)
        o73 = dnnnnnngtil
        o74 = 3.2000000000000d1*o73
        o75 = -2.00000000000000d0*o1*o73
        o76 = -3.2000000000000d1*o6*o73
        o77 = 2.00000000000000d0*o1*o6*o73
        o78 = dnnnngtil
        o79 = -3.4000000000000d2*o78
        o80 = 5.5000000000000d1*o1*o78
        o81 = -8.1200000000000d2*o6*o78
        o82 = 1.70000000000000d1*o1*o6*o78
        o83 = 7.0000000000000d0*o1
        o84 = -2.09000000000000d2*o6
        o85 = 8.9000000000000d1*o1*o6
        o86 = -3.10000000000000d1 + o83 + o84 + o85
        o87 = dnngtil
        o88 = -2.00000000000000d1*o86*o87
        o89 = 7.0000000000000d0*o6
        o90 = 1.00000000000000d0 + o89
        o91 = gtil
        o92 = 7.5000000000000d1*o50*o90*o91
        o93 = o74 + o75 + o76 + o77 + o79 + o80 + o81 + o82 + o88 + o92
        o94 = -2.40000000000000d2*byJ
        o95 = 1.50000000000000d2*byJ*o1
        o96 = -1.15200000000000d3*o46*o52*o78
        o97 = 7.2000000000000d1*o1*o46*o52*o78
        o98 = 3.9000000000000d1*o1
        o99 = -2.68000000000000d2*o6
        o100 = 1.00000000000000d2*o1*o6
        o101 = 4.0000000000000d0*q(i,j,k)
        o102 = cos(o101)
        o103 = -5.8100000000000d2*o102
        o104 = 2.45000000000000d2*o1*o102
        o105 = -1.11000000000000d2 + o100 + o103 + o104 + o98 + o99
        o106 = -5.0000000000000d0*o105*o52*o87
        o107 = -1.92000000000000d2*o22*o46*o52*o73
        o108 = 1.20000000000000d1*o1*o22*o46*o52*o73
        o109 = 2.88000000000000d2*o22*o52*o78
        o110 = -1.80000000000000d1*o1*o22*o52*o78
        o111 = 5.5680000000000d3*o22*o46*o52*o78
        o112 = -6.1800000000000d2*o1*o22*o46*o52*o78
        o113 = 3.2000000000000d1*o44*o52*o73
        o114 = -2.00000000000000d0*o1*o44*o52*o73
        o115 = -9.2800000000000d2*o44*o52*o78
        o116 = 1.03000000000000d2*o1*o44*o52*o78
        o117 = o106 + o107 + o108 + o109 + o110 + o111 + o112 + o113 + o
     &  114 + o115 + o116 + o94 + o95 + o96 + o97
        o118 = 2.00000000000000d0*o117
        o119 = 2.00000000000000d1*o6
        o120 = 3.5000000000000d1*o102
        o121 = 9.0000000000000d0 + o119 + o120
        o122 = 1.87500000000000d1*o121*o50*o52*o91
        o123 = o118 + o122
        o124 = o21*o22
        kxx(i,j,k) = mm*o16*o20*o25*o27*o43*o44 + o16*o27*o46*o49 - 1.00
     &  000000000000d-1*o123*o16*o17*o22*o26*o51 - 1.00000000000000d-1*o
     &  16*o17*o22*o26*o46*o51*o52*o71 + 3.00000000000000d0*mm*o14*o16*o
     &  18*o20*o22*o4*o8 + 5.0000000000000d-2*mm*o16*o20*o21*o27*o45*o51
     &  *o72*o93
        kxy(i,j,k) = mm*o16*o17*o20*o25*o26*o43*o44 + o16*o17*o26*o46*o4
     &  9 - 5.0000000000000d-2*o123*o16*o18*o22*o51 + 5.0000000000000d-2
     &  *o123*o16*o22*o27*o51 - 5.0000000000000d-2*o16*o18*o22*o46*o51*o
     &  52*o71 + 5.0000000000000d-2*o16*o22*o27*o46*o51*o52*o71 - 3.0000
     &  0000000000d0*mm*o14*o16*o17*o20*o22*o26*o4*o8 + 5.0000000000000d
     &  -2*mm*o16*o17*o20*o21*o26*o45*o51*o72*o93
        kxz(i,j,k) = mm*o124*o16*o20*o25*o26*o43*o45 - o16*o21*o26*o45*o
     &  49 - 5.0000000000000d-2*o123*o16*o17*o21*o45*o51 + 5.00000000000
     &  00d-2*o124*o16*o17*o45*o51*o52*o71 - 2.50000000000000d-2*mm*o16*
     &  o20*o22*o26*o51*o72*o93 + 2.50000000000000d-2*mm*o16*o20*o26*o46
     &  *o51*o72*o93
        kyy(i,j,k) = mm*o16*o18*o20*o25*o43*o44 + o16*o18*o46*o49 + 1.00
     &  000000000000d-1*o123*o16*o17*o22*o26*o51 + 1.00000000000000d-1*o
     &  16*o17*o22*o26*o46*o51*o52*o71 + 3.00000000000000d0*mm*o14*o16*o
     &  20*o22*o27*o4*o8 + 5.0000000000000d-2*mm*o16*o18*o20*o21*o45*o51
     &  *o72*o93
        kyz(i,j,k) = mm*o124*o16*o17*o20*o25*o43*o45 - o16*o17*o21*o45*o
     &  49 + 5.0000000000000d-2*o123*o16*o21*o26*o45*o51 - 5.00000000000
     &  00d-2*o124*o16*o26*o45*o51*o52*o71 - 2.50000000000000d-2*mm*o16*
     &  o17*o20*o22*o51*o72*o93 + 2.50000000000000d-2*mm*o16*o17*o20*o46
     &  *o51*o72*o93
        kzz(i,j,k) = mm*o16*o20*o22*o25*o43*o46 + o16*o22*o49 - 5.000000
     &  0000000d-2*mm*o16*o20*o21*o45*o51*o72*o93

```

Stab3d.F:
```
      subroutine rbicgst3d(cc,ce,cw,cn,cs,ct,cb,u,rhs,
     &             eps,rmax,ier,im,jm,km)
c
c This routine was lifted from stab.f. Minor modifications have
c been made.
c
      implicit none
c
      integer,intent(in) :: im,jm,km
      real*8,intent(inout) :: cc(im,jm,km),cn(im,jm,km),cs(im,jm,km),
     $     ce(im,jm,km),cw(im,jm,km),ct(im,jm,km),cb(im,jm,km)
      real*8,intent(in) :: eps
      real*8,intent(out) :: rmax
      real*8,intent(inout) :: u(im,jm,km),rhs(im,jm,km)
c     Local variable
      integer ncyc
      integer iscale,i,j,k,ier
c
c******************************************************************************
c

      ncyc = (im-2)*(jm-2)*(km-2)
      
      ier=0

*
*  Determine whether we can diagonally scale the problem to speed
*  convergence. Can only be done if there are no zeros on the main
*  diagonal (ie. central difference coefficient).
*
      iscale=1
      do k = 2,km-1
         do j = 2,jm-1
            do i = 2,im-1
               if (cc(i,j,k).eq.0.) iscale = 0
            enddo
         enddo
      enddo

*
*  Do the diagonal scaling if we can.
*
      if (iscale.eq.1) then


         do k = 2,km-1
            do j = 2,jm-1
               do i = 2,im-1
                  rhs(i,j,k)=rhs(i,j,k)/cc(i,j,k)
                  cb(i,j,k)=cb(i,j,k)/cc(i,j,k)
                  ct(i,j,k)=ct(i,j,k)/cc(i,j,k)
                  cw(i,j,k)=cw(i,j,k)/cc(i,j,k)
                  ce(i,j,k)=ce(i,j,k)/cc(i,j,k)
                  cs(i,j,k)=cs(i,j,k)/cc(i,j,k)
                  cn(i,j,k)=cn(i,j,k)/cc(i,j,k)
                  cc(i,j,k)=1.
               enddo
            enddo
         enddo

      endif

* 
*   Now call the bicgstab routine
*
      
      call rbicgstab (cc,cn,cs,ce,cw,ct,cb,u,rhs,eps,ncyc,rmax,ier,
     &     im,jm,km)
      if (rmax.gt.eps) then
        ier = -1
        print*,'Did not converge'
        print*,' maximum residual    = ',rmax
        print*,' tolerance           = ',eps
      endif

      return
      end
c
c******************************************************************
c
      subroutine rbicgstab (cc,cn,cs,ce,cw,ct,cb,x,r,tol,ncyc,rnorm,
     $     ier,im,jm,km)
c
c This routine was lifted from stab.f. Minor modifications have
c been made.
c
      implicit none
c
      integer,intent(in) :: im,jm,km
      integer,intent(in) :: ncyc
      real*8,intent(in)  :: cc(im*jm*km),cn(im*jm*km)
      real*8,intent(in)  :: cs(im*jm*km),ce(im*jm*km)
      real*8,intent(in)  :: cw(im*jm*km),ct(im*jm*km)
      real*8,intent(in)  :: cb(im*jm*km)
      real*8,intent(in)  :: tol
      real*8,intent(out) :: rnorm
      integer,intent(out) :: ier
      real*8,intent(inout) :: x(im*jm*km),r(im*jm*km)
c     Local variables
      integer :: i,kk
      real*8, allocatable :: p(:),Ap(:),w(:),As(:)
      real*8 :: omega, chi,chi1,chi2, delta, deltap, pp
*
***********************************************************************
*
      allocate(p(im*jm*km),Ap(im*jm*km),w(im*jm*km),As(im*jm*km))

      do i = 1,im*jm*km
         p(i) = 0.
         Ap(i) = 0.
         w(i) = 0.
         As(i) = 0.
      enddo

      kk = 0
  10  call rusermv(cc,cn,cs,ce,cw,ct,cb,x,Ap,im,jm,km)

      do i = 1,im*jm*km
         r(i) = r(i)-Ap(i)
         p(i) = r(i)
      enddo

c      delta = sum(r)
      delta = 0.

      do i = 1,im*jm*km
         delta = delta+r(i)
      enddo

      if (delta.eq.0.) then
        ier=-1
        return
      endif

      call rusermv(cc,cn,cs,ce,cw,ct,cb,p,Ap,im,jm,km)

c      phi = sum(Ap)
      pp = 0.

      do i = 1,im*jm*km
         pp = pp+Ap(i)
      enddo
      pp = pp/delta

      if (pp.eq.0.) then
        ier=-1
        return
      endif

c      rnorm = sum(r**2)
      rnorm = 0.

      do i = 1,im*jm*km
         rnorm = rnorm + r(i)**2
      enddo
      rnorm=sqrt(rnorm)

c     Test if initial guess is great (residual less than tolerance)
      if (rnorm .lt. tol)  return
      
 1    continue
      kk = kk + 1

      omega = 1./pp


      do i = 1,im*jm*km
         w(i) = r(i) - omega*Ap(i)
      enddo

      call rusermv(cc,cn,cs,ce,cw,ct,cb,w,As,im,jm,km)

c      chi1 = sum(As*w)
      chi1 = 0.

      do i = 1,im*jm*km
         chi1 = chi1+As(i)*w(i)
      enddo
c      chi2 = sum(As**2)
      chi2 = 0.

      do i = 1,im*jm*km
         chi2 = chi2+As(i)**2
      enddo

      chi = chi1/chi2


      do i = 1,im*jm*km
         r(i) = w(i) - chi*As(i)
         x(i) = x(i) + omega*p(i) + chi*w(i)
      enddo

      deltap = delta
c      delta = sum(r)
      delta = 0.

      do i = 1,im*jm*km
         delta = delta+r(i)
      enddo

      if (delta.eq.0.) then
        goto 10
      endif


      do i = 1,im*jm*km
         p(i) = r(i) + (p(i)-chi*Ap(i))*omega*
     &        delta/(deltap*chi)
      enddo
      
      call rusermv(cc,cn,cs,ce,cw,ct,cb,p,Ap,im,jm,km)

c      phi = sum(Ap)
      pp = 0.

      do i = 1,im*jm*km
         pp = pp+Ap(i)
      enddo
      pp=pp/delta

      if (pp.eq.0.) then
        goto 10
      endif

      if (kk.gt.ncyc) then
        print*,' BI-CGStab solver reached maximum nuber of iterations.'
        ier=-1
        return
      endif

c      rnorm = sum(r**2)
      rnorm = 0.

      do i = 1,im*jm*km
         rnorm = rnorm+r(i)**2
      enddo
      rnorm=sqrt(rnorm)

      if (rnorm .gt. tol) goto 1
c
      deallocate(p,Ap,w,As)
c
      return
      end
c
c******************************************************************
c
      subroutine rusermv(cc,cn,cs,ce,cw,ct,cb,x,y,im,jm,km)
c
c This routine was lifted from stab.f. Minor modifications have
c been made.
c
c Be careful that the cs are zero on their outer boundary!!
c
      implicit none
c
      integer,intent(in) :: im,jm,km
      real*8,intent(in)  :: cc(im*jm*km),cn(im*jm*km)
      real*8,intent(in)  :: cs(im*jm*km),ce(im*jm*km)
      real*8,intent(in)  :: cw(im*jm*km),ct(im*jm*km)
      real*8,intent(in)  :: cb(im*jm*km)
      real*8,intent(inout) :: x(im*jm*km), y(im*jm*km)
c     Local variables
      integer :: i
*
***********************************************************************
*
*
      do i = im*jm+im+1,im*(jm*km-jm-1)
         y(i) = cw(i)*x(i-1)
     &        +cc(i)*x(i)
     &        +ce(i)*x(i+1)
     &        +cn(i)*x(i+im)
     &        +cs(i)*x(i-im)
     &        +ct(i)*x(i+im*jm)
     &        +cb(i)*x(i-im*jm)
      enddo
c     
      return
      end
      

```

ksq2d_odd.x:
```
        o1 = cos(q)
        o2 = 1.
        o3 = o2**2
        o4 = 1/o3
        o5 = sin(q)
        o6 = 2.00000000000000d0 + 3.0d0
        o7 = o5**2
        o8 = -(o6*o7)
        o9 = 1.00000000000000d0 + 3.0d0 + o8
        o10 = o3**2
        o11 = o10**2
        o12 = dngtil**2
        o13 = o1**2
        o14 = gtil**2
        o15 = o9**2
c        exc33(i,j,k) = 0
c        exc32(i,j,k) = -(dngtil*o1*o4*o5**n)
c        exc31(i,j,k) = gtil*o4*o5**(-1.00000000000000d0 + n)*o9
c        exc22(i,j,k) = 0
c        exc21(i,j,k) = 0
c        exc11(i,j,k) = 0
        ksq(i,j,k) = (2.00000000000000d0*o5**(2.00000000000000d0*(-2.000
     &  00000000000d0 + 3.d0))*(o14*o15 + o12*o13*o7))/(o10*o11)

```

psi_1st_deriv.x:
```
        o1 = 5.0000000000000d-1*eta(i,j,k)
        o2 = exp(o1)
        o3 = psi3d(i,j,k)
        o4 = 1/o3
        o5 = cos(phi(i,j,k))
        o6 = cos(q(i,j,k))
        o7 = dqpsi3d(i,j,k)
        o8 = -1.50000000000000d0*eta(i,j,k)
        o9 = exp(o8)
        o10 = dphipsi3d(i,j,k)
        o11 = sin(phi(i,j,k))
        o12 = sin(q(i,j,K))
        o13 = 1/o12
        o14 = detapsi3d(i,j,k)
        psix(i,j,k) = o2*o4*(-(o10*o11*o13*o9) + o12*o14*o5*o9 - 5.00000
     &  00000000d-1*o12*o3*o5*o9 + o5*o6*o7*o9)
        psiy(i,j,k) = o2*o4*(o11*o12*o14*o9 - 5.0000000000000d-1*o11*o12
     &  *o3*o9 + 1.00000000000000d0*o10*o13*o5*o9 + o11*o6*o7*o9)
        psiz(i,j,k) = o2*o4*(o14*o6*o9 - 5.0000000000000d-1*o3*o6*o9 - o
     &  12*o7*o9)

```

make.code.defn:
```
# Main make.code.defn file for thorn RotatingDBHIVP
# $Header$

# Source files in this directory
SRCS = RotatingDBHIVP.F Stab3d.F ParamCheck.c

# Subdirectories containing source files
SUBDIRS = 


```

kij_axi.x:
```
        o1 = cos(phi)
        o2 = cos(q)
        o3 = o2**2
        o4 = -3.00000000000000d0*eta
        o5 = exp(o4)
        o6 = sin(phi)
        o7 = sin(q)
        o8 = o7**2
        o9 = dnnnnngtil
        o10 = -3.6000000000000d1*o9
        o11 = dnnnnnnngtil
        o12 = -4.0000000000000d0*o11*o8
        o13 = 1.16000000000000d2*o8*o9
        o14 = dnnngtil
        o15 = -4.1500000000000d2*o8
        o16 = 1.50000000000000d2 + o15
        o17 = o14*o16
        o18 = dngtil
        o19 = 5.0000000000000d0*o8
        o20 = -2.00000000000000d0 + o19
        o21 = 7.5000000000000d1*o18*o20
        o22 = o10 + o12 + o13 + o17 + o21
        o23 = dnnnnnngtil
        o24 = 3.00000000000000d0*o23
        o25 = 2.00000000000000d0*q
        o26 = cos(o25)
        o27 = 4.0000000000000d0*o23*o26
        o28 = 4.0000000000000d0*q
        o29 = cos(o28)
        o30 = -7.0000000000000d0*o23*o29
        o31 = dnnnngtil
        o32 = 2.10000000000000d1*o31
        o33 = 6.4000000000000d1*o26*o31
        o34 = 2.03000000000000d2*o29*o31
        o35 = o24 + o27 + o30 + o32 + o33 + o34
        o36 = -4.0000000000000d0*o35
        o37 = 2.68000000000000d2*o26
        o38 = 5.8100000000000d2*o29
        o39 = 1.11000000000000d2 + o37 + o38
        o40 = dnngtil
        o41 = 5.0000000000000d0*o39*o40
        o42 = 2.00000000000000d1*o26
        o43 = 3.5000000000000d1*o29
        o44 = 9.0000000000000d0 + o42 + o43
        o45 = gtil
        o46 = -7.5000000000000d1*o44*o45
        o47 = o36 + o41 + o46
        o48 = o1**2
        o49 = o6**2
        o50 = o7*o8
        hxx(i,j,k) = 6.6666666666667d-1*o1*o22*o3*o5*o6*o8 - 8.333333333
     &  3333d-2*o1*o47*o5*o6*o8
        hxy(i,j,k) = -3.3333333333333d-1*o22*o3*o48*o5*o8 + 4.1666666666
     &  667d-2*o47*o48*o5*o8 + 3.3333333333333d-1*o22*o3*o49*o5*o8 - 4.1
     &  666666666667d-2*o47*o49*o5*o8
        hxz(i,j,k) = -3.3333333333333d-1*o2*o22*o5*o50*o6 - 4.1666666666
     &  667d-2*o2*o47*o5*o6*o7
        hyy(i,j,k) = -6.6666666666667d-1*o1*o22*o3*o5*o6*o8 + 8.33333333
     &  33333d-2*o1*o47*o5*o6*o8
        hyz(i,j,k) = 3.3333333333333d-1*o1*o2*o22*o5*o50 + 4.16666666666
     &  67d-2*o1*o2*o47*o5*o7
        hzz(i,j,k) = 0

```

ksq_axi.x:
```
        o1 = cos(q)
        o2 = 2.00000000000000d0*q
        o3 = cos(o2)
        o4 = dnnnnngtil
        o5 = sin(q)
        o6 = o5**2
        o7 = o5*o6
        o8 = dnnngtil
        o9 = dngtil
        o10 = dnnnnnnngtil
        o11 = o6**2
        o12 = 4.0000000000000d0*q
        o13 = cos(o12)
        o14 = dnnnngtil
        o15 = dnngtil
        o16 = o1**2
        o17 = dnnnnnngtil
        o18 = o11*o6
        o19 = gtil
        o20 = byJ**2
        o21 = o14**2
        o22 = o3**2
        o23 = o13**2
        o24 = o15**2
        o25 = o4**2
        o26 = o8**2
        o27 = o9**2
        o28 = o16**2
        o29 = o17**2
        o30 = o10**2
        o31 = o11**2
        o32 = o31*o6
        o33 = o19**2
c        exc33(i,j,k) = 0
c        exc32(i,j,k) = 1.33333333333333d0*o1*o10*o11*o5 - 2.083333333333
c     &  33d-2*o1*(3.5200000000000d2 - 9.2800000000000d2*o3)*o4*o7 + 1.66
c     &  666666666667d-1*o1*(1.15000000000000d2 - 4.1500000000000d2*o3)*o
c     &  7*o8 - 1.56250000000000d0*o1*(8.0000000000000d0 - 4.000000000000
c     &  0d1*o3)*o7*o9
c        exc31(i,j,k) = -8.0000000000000d0*o11*o16*o17 + 1.33333333333333
c     &  d0*o17*o18 + 3.00000000000000d0*byJ*o6 - 2.08333333333333d-1*o15*(
c     &  -1.11000000000000d2 - 5.8100000000000d2*o13 - 2.68000000000000d2
c     &  *o3)*o6 - 5.2083333333333d-3*o14*(6.7200000000000d2 + 6.49600000
c     &  00000d3*o13 + 2.04800000000000d3*o3)*o6 + o19*(5.0000000000000d1
c     &  *o11 + 7.5000000000000d2*o11*o16 - 1.25000000000000d2*o18 - 2.00
c     &  000000000000d2*o16*o6)
c        exc22(i,j,k) = 0
c        exc21(i,j,k) = 0
c        exc11(i,j,k) = 0
        t1 = -9.6000000000000d1*byJ*o11*o16*o17 + 1.12000000000000d2*o11*o
     &  14*o16*o17 + 1.08266666666667d3*o11*o13*o14*o16*o17 - 7.40000000
     &  00000d2*o11*o15*o16*o17 - 3.8733333333333d3*o11*o13*o15*o16*o17 
     &  + 1.60000000000000d1*byJ*o17*o18 - 1.86666666666667d1*o14*o17*o18 
     &  - 1.80444444444444d2*o13*o14*o17*o18 + 1.23333333333333d2*o15*o1
     &  7*o18 + 6.4555555555556d2*o13*o15*o17*o18 + 6.0000000000000d2*byJ*
     &  o11*o19 - 7.0000000000000d2*o11*o14*o19 - 6.7666666666667d3*o11*
     &  o13*o14*o19 + 4.6250000000000d3*o11*o15*o19 + 2.42083333333333d4
     &  *o11*o13*o15*o19 + 9.0000000000000d3*byJ*o11*o16*o19 - 1.050000000
     &  00000d4*o11*o14*o16*o19 - 1.01500000000000d5*o11*o13*o14*o16*o19
     &   + 6.9375000000000d4*o11*o15*o16*o19 + 3.6312500000000d5*o11*o13
     &  *o15*o16*o19 - 1.50000000000000d3*byJ*o18*o19 + 1.75000000000000d3
     &  *o14*o18*o19 + 1.69166666666667d4*o13*o14*o18*o19 - 1.1562500000
     &  0000d4*o15*o18*o19 - 6.0520833333333d4*o13*o15*o18*o19 - 2.66666
     &  666666667d3*o16*o17*o18*o19 + 1.07555555555556d2*o11*o16*o25
        t2 = 7.4755555555556d2*o11*o16*o22*o25 + 7.3472222222222d2*o11*o
     &  16*o26 + 9.5680555555556d3*o11*o16*o22*o26 + 3.12500000000000d2*
     &  o11*o16*o27 + 7.8125000000000d3*o11*o16*o22*o27 + 6.400000000000
     &  0d3*o11*o17*o19*o28 - 2.40000000000000d4*o17*o18*o19*o28 + 1.280
     &  00000000000d2*o18*o28*o29 + 3.4133333333333d2*o11*o14*o16*o17*o3
     &   - 1.78666666666667d3*o11*o15*o16*o17*o3 - 5.6888888888889d1*o14
     &  *o17*o18*o3 + 2.97777777777778d2*o15*o17*o18*o3 - 2.133333333333
     &  33d3*o11*o14*o19*o3 + 1.11666666666667d4*o11*o15*o19*o3 - 3.2000
     &  000000000d4*o11*o14*o16*o19*o3 + 1.67500000000000d5*o11*o15*o16*
     &  o19*o3 + 5.3333333333333d3*o14*o18*o19*o3 - 2.79166666666667d4*o
     &  15*o18*o19*o3 - 5.6711111111111d2*o11*o16*o25*o3 - 5.30277777777
     &  78d3*o11*o16*o26*o3 - 3.12500000000000d3*o11*o16*o27*o3 + 2.6666
     &  6666666667d2*o17*o19*o31 + 8.0000000000000d3*o16*o17*o19*o31 - 4
     &  .2666666666667d1*o16*o29*o31 + 3.5555555555556d0*o16*o30*o31 - 6
     &  .6666666666667d2*o17*o19*o32 + 3.5555555555556d0*o29*o32 - 4.000
     &  0000000000d4*o11*o16*o33
        t3 = 5.0000000000000d3*o18*o33 + 2.50000000000000d5*o16*o18*o33 
     &  - 6.0000000000000d5*o11*o28*o33 + 1.12500000000000d6*o18*o28*o33
     &   - 2.50000000000000d4*o31*o33 - 3.7500000000000d5*o16*o31*o33 + 
     &  3.12500000000000d4*o32*o33 - 3.9111111111111d1*o10*o16*o18*o4 + 
     &  1.03111111111111d2*o10*o16*o18*o3*o4 - 4.2000000000000d1*byJ*o14*o
     &  6 - 4.0600000000000d2*byJ*o13*o14*o6 + 2.77500000000000d2*byJ*o15*o6
     &   + 1.45250000000000d3*byJ*o13*o15*o6 - 3.2375000000000d2*o14*o15*o
     &  6 - 4.8241666666667d3*o13*o14*o15*o6 - 2.40000000000000d3*byJ*o16*
     &  o19*o6 + 2.80000000000000d3*o14*o16*o19*o6 + 2.70666666666667d4*
     &  o13*o14*o16*o19*o6 - 1.85000000000000d4*o15*o16*o19*o6 - 9.68333
     &  33333333d4*o13*o15*o16*o19*o6 + 1.80000000000000d1*o20*o6 + 2.45
     &  000000000000d1*o21*o6 + 4.7366666666667d2*o13*o21*o6 - 2.3822222
     &  2222222d3*o14*o15*o22*o6 + 2.27555555555556d2*o21*o22*o6 - 1.638
     &  09722222222d4*o14*o15*o23*o6 + 2.28938888888889d3*o21*o23*o6
        t4 = 1.06953125000000d3*o24*o6 + 1.11963541666667d4*o13*o24*o6 +
     &   6.2347222222222d3*o22*o24*o6 + 2.93021701388889d4*o23*o24*o6 - 
     &  1.28000000000000d2*byJ*o14*o3*o6 + 6.7000000000000d2*byJ*o15*o3*o6 -
     &   1.76833333333333d3*o14*o15*o3*o6 - 1.27205555555556d4*o13*o14*o
     &  15*o3*o6 + 8.5333333333333d3*o14*o16*o19*o3*o6 - 4.4666666666667
     &  d4*o15*o16*o19*o3*o6 + 1.49333333333333d2*o21*o3*o6 + 1.44355555
     &  555556d3*o13*o21*o3*o6 + 5.1645833333333d3*o24*o3*o6 + 2.7032638
     &  8888889d4*o13*o24*o3*o6 + 8.0000000000000d4*o28*o33*o6 + 1.02222
     &  222222222d2*o10*o16*o18*o8 - 3.6888888888889d2*o10*o16*o18*o3*o8
     &   - 5.6222222222222d2*o11*o16*o4*o8 - 5.3488888888889d3*o11*o16*o
     &  22*o4*o8 + 3.5111111111111d3*o11*o16*o3*o4*o8 - 6.6666666666667d
     &  1*o10*o16*o18*o9 + 3.3333333333333d2*o10*o16*o18*o3*o9 + 3.66666
     &  66666667d2*o11*o16*o4*o9 + 4.8333333333333d3*o11*o16*o22*o4*o9 -
     &   2.80000000000000d3*o11*o16*o3*o4*o9 - 9.5833333333333d2*o11*o16
     &  *o8*o9 - 1.72916666666667d4*o11*o16*o22*o8*o9 + 8.2500000000000d
     &  3*o11*o16*o3*o8*o9
        ksq(i,j,k) = t1 + t2 + t3 + t4

```


combined_doc_context: ## README (README):
```
Cactus Code Thorn RotatingDBHIVP
Authors    : Ryoji Takahashi 
CVS info   : $Header$
--------------------------------------------------------------------------

This thorn does calculates initial data for a black hole distorted
by a non-axisymmetric odd parity perturbation 


```



Reference solution:
src_code:         gtil = amp*(exp(-((-eta0 + eta(i,j,k))**2/sigma**2)) + exp(-((eta0 +
     &   eta(i,j,k))**2/sigma**2)))
        dngtil = amp*((-2.00000000000000d0*(-eta0 + eta(i,j,k))*exp(-((-eta0
     &   + eta(i,j,k))**2/sigma**2)))/sigma**2 - (2.00000000000000d0*(eta0 +
     &   eta(i,j,k))*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**2)
        dnngtil = amp*((4.0000000000000d0*(-eta0 + eta(i,j,k))**2*exp(-((-et
     &  a0 + eta(i,j,k))**2/sigma**2)))/sigma**4 - (2.00000000000000d0*exp(-
     &  ((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**2 + (4.0000000000000d0*(
     &  eta0 + eta(i,j,k))**2*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**4 
     &  - (2.00000000000000d0*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma
     &  **2)
        dnnngtil = amp*((-8.0000000000000d0*(-eta0 + eta(i,j,k))**3*exp(-((-
     &  eta0 + eta(i,j,k))**2/sigma**2)))/sigma**6 + (1.20000000000000d1*(-e
     &  ta0 + eta(i,j,k))*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**4 - (
     &  8.0000000000000d0*(eta0 + eta(i,j,k))**3*exp(-((eta0 + eta(i,j,k))**2/si
     &  gma**2)))/sigma**6 + (1.20000000000000d1*(eta0 + eta(i,j,k))*exp(-((
     &  eta0 + eta(i,j,k))**2/sigma**2)))/sigma**4)
        dnnnngtil = amp*((1.60000000000000d1*(-eta0 + eta(i,j,k))**4*exp(-((
     &  -eta0 + eta(i,j,k))**2/sigma**2)))/sigma**8 - (4.8000000000000d1*(-e
     &  ta0 + eta(i,j,k))**2*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**6 
     &  + (1.20000000000000d1*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigm
     &  a**4 + (1.60000000000000d1*(eta0 + eta(i,j,k))**4*exp(-((eta0 + eta(i,j,k)
     &  )**2/sigma**2)))/sigma**8 - (4.8000000000000d1*(eta0 + eta(i,j,k))
     &  **2*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**6 + (1.200000000
     &  00000d1*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**4)
        dnnnnngtil = amp*((-3.2000000000000d1*(-eta0 + eta(i,j,k))**5*exp(-(
     &  (-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**10 + (1.60000000000000d2*
     &  (-eta0 + eta(i,j,k))**3*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma*
     &  *8 - (1.20000000000000d2*(-eta0 + eta(i,j,k))*exp(-((-eta0 + eta(i,j,k))
     &  **2/sigma**2)))/sigma**6 - (3.2000000000000d1*(eta0 + eta(i,j,k))**5
     &  *exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**10 + (1.60000000000
     &  000d2*(eta0 + eta(i,j,k))**3*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/si
     &  gma**8 - (1.20000000000000d2*(eta0 + eta(i,j,k))*exp(-((eta0 + eta(i,j,k)
     &  )**2/sigma**2)))/sigma**6)
        dnnnnnngtil = amp*((6.4000000000000d1*(-eta0 + eta(i,j,k))**6*exp(-(
     &  (-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**12 - (4.8000000000000d2*(
     &  -eta0 + eta(i,j,k))**4*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**
     &  10 + (7.2000000000000d2*(-eta0 + eta(i,j,k))**2*exp(-((-eta0 + eta(i,j,k)
     &  )**2/sigma**2)))/sigma**8 - (1.20000000000000d2*exp(-((-eta0 + 
     &  eta(i,j,k))**2/sigma**2)))/sigma**6 + (6.4000000000000d1*(eta0 + eta(i,j,k)
     &  )**6*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**12 - (4.8000
     &  000000000d2*(eta0 + eta(i,j,k))**4*exp(-((eta0 + eta(i,j,k))**2/sigma**2
     &  )))/sigma**10 + (7.2000000000000d2*(eta0 + eta(i,j,k))**2*exp(-((eta
     &  0 + eta(i,j,k))**2/sigma**2)))/sigma**8 - (1.20000000000000d2*exp(-(
     &  (eta0 + eta(i,j,k))**2/sigma**2)))/sigma**6)
        dnnnnnnngtil = amp*((-1.28000000000000d2*(-eta0 + eta(i,j,k))**7*exp
     &  (-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**14 + (1.34400000000000
     &  d3*(-eta0 + eta(i,j,k))**5*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sig
     &  ma**12 - (3.3600000000000d3*(-eta0 + eta(i,j,k))**3*exp(-((-eta0 + e
     &  ta(i,j,k))**2/sigma**2)))/sigma**10 + (1.68000000000000d3*(-eta0 + e
     &  ta(i,j,k))*exp(-((-eta0 + eta(i,j,k))**2/sigma**2)))/sigma**8 - (1.28000
     &  000000000d2*(eta0 + eta(i,j,k))**7*exp(-((eta0 + eta(i,j,k))**2/sigma**2
     &  )))/sigma**14 + (1.34400000000000d3*(eta0 + eta(i,j,k))**5*exp(-((et
     &  a0 + eta(i,j,k))**2/sigma**2)))/sigma**12 - (3.3600000000000d3*(eta0
     &   + eta(i,j,k))**3*exp(-((eta0 + eta(i,j,k))**2/sigma**2)))/sigma**10 + (
     &  1.68000000000000d3*(eta0 + eta(i,j,k))*exp(-((eta0 + eta(i,j,k))**2/sigm
     &  a**2)))/sigma**8)