Task: Implement psi_2nd_deriv.x for EinsteinInitialData/DistortedBHIVP thorn

thorn_name: EinsteinInitialData/DistortedBHIVP
src_filename: psi_2nd_deriv.x
interface: # Interface definition for thorn DistortedBHIVP
# $Header$

implements: distortedbhivp
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 DistortedBHIVP
# $Header$

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

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

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





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

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 
{
"distortedbh" :: "Non-Aix BH + Brill Wave IVP"
}

private:

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

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

REAL c "Azimuthal dependence of Brill wave"
{
  *:* :: "No restriction"
} 0.0

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

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


INT n "sin^n theta in brill wave"
{
  *:* :: "No restriction"
} 2

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

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

REAL tolerance "Tolerance"
{
 0:* :: "Tolerance"
} 1.e-9

context: ParamCheck.c:
```
 /*@@
   @file      ParamCheck.c
   @date      Fri Apr 26 18:03:09 2002
   @author    Tom Goodale
   @desc 
              Check the parameters for DistortedBHIVP
   @enddesc 
   @version $Header: /arrangements/PerturbedBH2/DistortedBHIVP/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(DistortedBHIVP_ParamCheck_c)

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

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

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

void DistortedBHIVP_ParamCheck(CCTK_ARGUMENTS);
void DistortedBHIVP_ConformalCheck(CCTK_ARGUMENTS);

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

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

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

void DistortedBHIVP_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    DistortedBHIVP_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 DistortedBHIVP_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, "DistortedBHIVP needs second derivatives of the conformal factor when running with a static conformal metric");
    }
  }

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


```

bhbrill3d.m:
```
$Path = Union[$Path,{"~/SetTensor"}];
Needs["SetTensor`"];

Dimension = 3;
x[1] = eta; x[2] = q; x[3] = phi
qf[eta_,q_,phi_] := amp (Exp[-(eta-eta0)^2/sigma^2]+Exp[-(eta+eta0)^2/sigma^2]) Sin[q]^n (1+c Cos[phi]^2)

md = {
{Exp[2 qf[eta,q,phi]],0,0},
{0,Exp[2 qf[eta,q,phi]],0},
{0,0,Sin[q]^2}} psisph[eta,q,phi]^4;
InitializeMetric[md];

Clear[exc];
DefineTensor[exc];
SetTensor[exc[la,lb],{{0,0,0},{0,0,0},{0,0,0}}];

tmp = RicciR[la,lb] Metricg[ua,ub]+exc[la,lb] Metricg[ua,ub] exc[lc,ld] Metricg[uc,ud]-
  exc[la,lb] exc[lc,ld] Metricg[ua,uc] Metricg[ub,ud];
tmp = RicciToAffine[tmp];
tmp = EvalMT[tmp];
tmp = ExpandAll[-Exp[2 qf[eta,q,phi]] psisph[eta,q,phi]^5/8 tmp]
sav=tmp
tmp = SubFun[sav,psisph[eta,q,phi],2 Cosh[eta/2]+psisph[eta,q,phi]]

(* Make the stencil... *)

stencil = ExpandAll[tmp /. {
 D[psisph[eta,q,phi],eta]->(psisph[i+1,j,k]-psisph[i-1,j,k])/(2 deta),
 D[psisph[eta,q,phi],eta,eta]->(psisph[i+1,j,k]+psisph[i-1,j,k]-2 psisph[i,j,k])/(deta deta),
 D[psisph[eta,q,phi],q]->(psisph[i,j+1,k]-psisph[i,j-1,k])/(2 dq),
 D[psisph[eta,q,phi],q,q]->(psisph[i,j+1,k]+psisph[i,j-1,k]-2 psisph[i,j,k])/(dq dq),
 D[psisph[eta,q,phi],phi]->(psisph[i,j,k+1]-psisph[i,j,k-1])/(2 dphi),
 D[psisph[eta,q,phi],phi,phi]->(psisph[i,j,k+1]+psisph[i,j,k-1]-2 psisph[i,j,k])/(dphi dphi),
 psisph[eta,q,phi]->psisph[i,j,k]
 }];

ac = Coefficient[stencil,psisph[i,j,k]]
an = Coefficient[stencil,psisph[i+1,j,k]]
as = Coefficient[stencil,psisph[i-1,j,k]]
ae = Coefficient[stencil,psisph[i,j,k+1]]
aw = Coefficient[stencil,psisph[i,j,k-1]]
aq = Coefficient[stencil,psisph[i,j+1,k]]
ab = Coefficient[stencil,psisph[i,j-1,k]]
rhs = -SubFun[tmp,psisph[eta,q,phi],0]

FortranOutputOfDepList = "(i,j,k)";
$FortranReplace = Union[{
      "UND"->"_",
      "(eta,q,phi)"->"(i,j,k)"
}];
fd = FortranOpen["bhbrill3d.x"];
FortranWrite[fd,An[i,j,k],an ];
FortranWrite[fd,As[i,j,k],as ];
FortranWrite[fd,Ae[i,j,k],ae ];
FortranWrite[fd,Aw[i,j,k],aw ];
FortranWrite[fd,Aq[i,j,k],aq ];
FortranWrite[fd,Ab[i,j,k],ab ];
FortranWrite[fd,Ac[i,j,k],ac ];
FortranWrite[fd,Rhs[i,j,k],rhs ];
FortranClose[fd];

(* Next part, write out conformal g's and d's *)


xv = Exp[eta] Sin[q] Cos[phi];
yv = Exp[eta] Sin[q] Sin[phi];
zv = Exp[eta] Cos[q];

mc = Table[ D[ {xv,yv,zv}[[i]], {eta,q,phi}[[j]] ],{i,1,3},{j,1,3}];
mci = Simplify[Inverse[mc]];

Clear[mct];
DefineTensor[mct,{{1,2},1}];
Iter[mct[ua,lb],
  mct[ua,lb]=mc[[ua,-lb]];
];

Clear[mcti];
DefineTensor[mcti,{{1,2},1}];
Iter[mcti[ua,lb],
  mcti[ua,lb]=mci[[ua,-lb]];
];

gijtmp = Exp[2 eta]/psisph[eta,q,phi]^4 Metricg[lc,ld] mcti[uc,la] mcti[ud,lb]

Clear[i2];
DefineTensor[i2,{{2,1},1}];

fd = FortranOpen["gij.x"];
Iter[i2[ua,ub],
  v1 = {x,y,z}[[ua]];
  v2 = {x,y,z}[[ub]];
  metv = ToExpression["g"<>ToString[v1]<>ToString[v2]<>"[i,j,k]"];
  gg[v1,v2]=Simplify[EvalMT[gijtmp,{la->-ua,lb->-ub}]];
  FortranWrite[fd,metv,gg[v1,v2]];
  For[ii=1,ii<=3,ii++,
    v3 = {x,y,z}[[ii]];
    dmetv = ToExpression["d"<>ToString[v3]<>ToString[metv]];
    res = OD[gg[v1,v2],lc] mcti[uc,ld]/2;
    res = EvalMT[res,ld-> -ii];
    res = Simplify[res];
    FortranWrite[fd,dmetv,res];
  ];
];
FortranClose[fd];

$FortranReplace = {
  "UND"->"_",
  "(eta,q,phi)"->""
};

fd = FortranOpen["psi_1st_deriv.x"];
For[ii=1,ii<=3,ii++,
  v1 = {x,y,z}[[ii]];
  psv =ToExpression["psi"<>ToString[v1]<>"[i,j,k]"];
  rhs = CD[Exp[-eta/2] psi3d[eta,q,phi],lc] mcti[uc,la];
  rhs = EvalMT[rhs,{la->-ii}]/(Exp[-eta/2] psi3d[eta,q,phi]);
  FortranWrite[fd,psv,rhs];
];
FortranClose[fd];

fd = FortranOpen["psi_2nd_deriv.x"];
Iter[i2[ua,ub],
  v1 = {x,y,z}[[ua]];
  v2 = {x,y,z}[[ub]];
  psv = ToExpression["psi"<>ToString[v1]<>ToString[v2]<>"[i,j,k]"];
  rhs = OD[OD[Exp[-eta/2] psi3d[eta,q,phi],lc] mcti[uc,la],ld] mcti[ud,lb];
  rhs = EvalMT[rhs,{la->-ua,lb->-ub}]/(Exp[-eta/2] psi3d[eta,q,phi]);
  FortranWrite[fd,psv,rhs];
];
FortranClose[fd];

```

bhbrill3d.x:
```
        o1 = deta**2
        o2 = 1/o1
        o3 = dq**2
        o4 = 1/o3
        o5 = 1/dq
        o6 = tan(q)
        o7 = 1/o6
        o8 = dphi**2
        o9 = 1/o8
        o10 = eta**2
        o11 = sigma**2
        o12 = 1/o11
        o13 = -(o10*o12)
        o14 = -2.00000000000000d0*eta*eta0*o12
        o15 = eta0**2
        o16 = -(o12*o15)
        o17 = o13 + o14 + o16
        o18 = exp(o17)
        o19 = sin(q)
        o20 = o19**n
        o21 = 2.00000000000000d0*amp*o18*o20
        o22 = cos(phi)
        o23 = o22**2
        o24 = 2.00000000000000d0*amp*c*o18*o20*o23
        o25 = 2.00000000000000d0*eta*eta0*o12
        o26 = o13 + o16 + o25
        o27 = exp(o26)
        o28 = 2.00000000000000d0*amp*o20*o27
        o29 = 2.00000000000000d0*amp*c*o20*o23*o27
        o30 = o21 + o24 + o28 + o29
        o31 = exp(o30)
        o32 = o19**2
        o33 = 1/o32
        o34 = 1.00000000000000d0*o31*o33*o9
        o35 = 1/dphi
        o36 = o13 + o14 + o16 + o21 + o24 + o28 + o29
        o37 = exp(o36)
        o38 = sin(phi)
        o39 = -2.00000000000000d0 + n
        o40 = o19**o39
        o41 = o13 + o16 + o21 + o24 + o25 + o28 + o29
        o42 = exp(o41)
        o43 = cos(q)
        o44 = o43**2
        o45 = n**2
        o46 = o38**2
        o47 = o11**2
        o48 = 1/o47
        o49 = amp**2
        o50 = c**2
        o51 = -2.00000000000000d0*o10*o12
        o52 = -2.00000000000000d0*o12*o15
        o53 = o21 + o24 + o28 + o29 + o51 + o52
        o54 = exp(o53)
        o55 = 2.00000000000000d0*n
        o56 = -2.00000000000000d0 + o55
        o57 = o19**o56
        o58 = -4.0000000000000d0*eta*eta0*o12
        o59 = o21 + o24 + o28 + o29 + o51 + o52 + o58
        o60 = exp(o59)
        o61 = 4.0000000000000d0*eta*eta0*o12
        o62 = o21 + o24 + o28 + o29 + o51 + o52 + o61
        o63 = exp(o62)
        o64 = o6**2
        o65 = 1/o64
        o66 = 5.0000000000000d-1*eta
        o67 = cosh(o66)
        Ae(i,j,k) = o2
        Aw(i,j,k) = o2
        An(i,j,k) = o4 + 5.0000000000000d-1*o5*o7
        As(i,j,k) = o4 - 5.0000000000000d-1*o5*o7
        Ab(i,j,k) = o34 - 2.00000000000000d0*amp*c*o22*o35*o37*o38*o40 -
     &   2.00000000000000d0*amp*c*o22*o35*o38*o40*o42
        Aq(i,j,k) = o34 + 2.00000000000000d0*amp*c*o22*o35*o37*o38*o40 +
     &   2.00000000000000d0*amp*c*o22*o35*o38*o40*o42
        Ac(i,j,k) = -1.25000000000000d-1 - 2.00000000000000d0*o2 - 2.500
     &  00000000000d-1*amp*n*o18*o20 - 5.0000000000000d-1*amp*o12*o18*o2
     &  0 - 2.50000000000000d-1*amp*c*n*o18*o20*o23 - 5.0000000000000d-1
     &  *amp*c*o12*o18*o20*o23 - 2.50000000000000d-1*amp*n*o20*o27 - 5.0
     &  000000000000d-1*amp*o12*o20*o27 - 2.50000000000000d-1*amp*c*n*o2
     &  0*o23*o27 - 5.0000000000000d-1*amp*c*o12*o20*o23*o27 - 1.2500000
     &  0000000d-1*o33 - 2.00000000000000d0*o4 - amp*c*o23*o37*o40 - amp
     &  *c*o23*o40*o42 - 2.50000000000000d-1*amp*n*o18*o40*o44 - 2.50000
     &  000000000d-1*amp*c*n*o18*o23*o40*o44 - 2.50000000000000d-1*amp*n
     &  *o27*o40*o44 - 2.50000000000000d-1*amp*c*n*o23*o27*o40*o44 + 2.5
     &  0000000000000d-1*amp*o18*o40*o44*o45 + 2.50000000000000d-1*amp*c
     &  *o18*o23*o40*o44*o45 + 2.50000000000000d-1*amp*o27*o40*o44*o45 +
     &   2.50000000000000d-1*amp*c*o23*o27*o40*o44*o45 + amp*c*o37*o40*o
     &  46 + amp*c*o40*o42*o46 + 2.00000000000000d0*amp*eta*eta0*o18*o20
     &  *o48 + amp*o10*o18*o20*o48 + amp*o15*o18*o20*o48 + 2.00000000000
     &  000d0*amp*c*eta*eta0*o18*o20*o23*o48 + amp*c*o10*o18*o20*o23*o48
     &   + amp*c*o15*o18*o20*o23*o48 - 2.00000000000000d0*amp*eta*eta0*o
     &  20*o27*o48 + amp*o10*o20*o27*o48 + amp*o15*o20*o27*o48 - 2.00000
     &  000000000d0*amp*c*eta*eta0*o20*o23*o27*o48 + amp*c*o10*o20*o23*o
     &  27*o48 + amp*c*o15*o20*o23*o27*o48 + 6.0000000000000d0*o23*o46*o
     &  49*o50*o54*o57 + 3.00000000000000d0*o23*o46*o49*o50*o57*o60 + 3.
     &  00000000000000d0*o23*o46*o49*o50*o57*o63 + 1.25000000000000d-1*o
     &  65 - 2.00000000000000d0*o31*o33*o9
        t1 = -2.50000000000000d-1*o67 + 5.0000000000000d-1*amp*n*o18*o20
     &  *o67 + amp*o12*o18*o20*o67 + 5.0000000000000d-1*amp*c*n*o18*o20*
     &  o23*o67 + amp*c*o12*o18*o20*o23*o67 + 5.0000000000000d-1*amp*n*o
     &  20*o27*o67 + amp*o12*o20*o27*o67 + 5.0000000000000d-1*amp*c*n*o2
     &  0*o23*o27*o67 + amp*c*o12*o20*o23*o27*o67 + 2.50000000000000d-1*
     &  o33*o67 + 2.00000000000000d0*amp*c*o23*o37*o40*o67 + 2.000000000
     &  00000d0*amp*c*o23*o40*o42*o67 + 5.0000000000000d-1*amp*n*o18*o40
     &  *o44*o67 + 5.0000000000000d-1*amp*c*n*o18*o23*o40*o44*o67 + 5.00
     &  00000000000d-1*amp*n*o27*o40*o44*o67 + 5.0000000000000d-1*amp*c*
     &  n*o23*o27*o40*o44*o67 - 5.0000000000000d-1*amp*o18*o40*o44*o45*o
     &  67 - 5.0000000000000d-1*amp*c*o18*o23*o40*o44*o45*o67 - 5.000000
     &  0000000d-1*amp*o27*o40*o44*o45*o67
        t2 = -5.0000000000000d-1*amp*c*o23*o27*o40*o44*o45*o67 - 2.00000
     &  000000000d0*amp*c*o37*o40*o46*o67 - 2.00000000000000d0*amp*c*o40
     &  *o42*o46*o67 - 4.0000000000000d0*amp*eta*eta0*o18*o20*o48*o67 - 
     &  2.00000000000000d0*amp*o10*o18*o20*o48*o67 - 2.00000000000000d0*
     &  amp*o15*o18*o20*o48*o67 - 4.0000000000000d0*amp*c*eta*eta0*o18*o
     &  20*o23*o48*o67 - 2.00000000000000d0*amp*c*o10*o18*o20*o23*o48*o6
     &  7 - 2.00000000000000d0*amp*c*o15*o18*o20*o23*o48*o67 + 4.0000000
     &  000000d0*amp*eta*eta0*o20*o27*o48*o67 - 2.00000000000000d0*amp*o
     &  10*o20*o27*o48*o67 - 2.00000000000000d0*amp*o15*o20*o27*o48*o67 
     &  + 4.0000000000000d0*amp*c*eta*eta0*o20*o23*o27*o48*o67 - 2.00000
     &  000000000d0*amp*c*o10*o20*o23*o27*o48*o67 - 2.00000000000000d0*a
     &  mp*c*o15*o20*o23*o27*o48*o67 - 1.20000000000000d1*o23*o46*o49*o5
     &  0*o54*o57*o67 - 6.0000000000000d0*o23*o46*o49*o50*o57*o60*o67 - 
     &  6.0000000000000d0*o23*o46*o49*o50*o57*o63*o67 - 2.50000000000000
     &  d-1*o65*o67
        Rhs(i,j,k) = t1 + t2

```

gij.x:
```
        o1 = 2.00000000000000d0*phi(i,j,k)
        o2 = cos(o1)
        o3 = cos(phi(i,j,k))
        o4 = o3**2
        o5 = c*o4
        o6 = 1.00000000000000d0 + o5
        o7 = -eta0
        o8 = eta(i,j,k) + o7
        o9 = o8**2
        o10 = sigma**2
        o11 = 1/o10
        o12 = -(o11*o9)
        o13 = exp(o12)
        o14 = eta(i,j,k) + eta0
        o15 = o14**2
        o16 = -(o11*o15)
        o17 = exp(o16)
        o18 = o13 + o17
        o19 = sin(q(i,j,k))
        o20 = o19**n
        o21 = 2.00000000000000d0*amp*o18*o20*o6
        o22 = exp(o21)
        o23 = -1.00000000000000d0 + o22
        o24 = -eta(i,j,k)
        o25 = exp(o24)
        o26 = sin(phi(i,j,k))
        o27 = o26**2
        o28 = 1/o19
        o29 = sin(o1)
        o30 = cos(q(i,j,k))
        o31 = o30**2
        o32 = -1.00000000000000d0 + n
        o33 = o19**o32
        o34 = amp*n*o18*o22*o3*o31*o33*o6
        o35 = 2.00000000000000d0*amp*c*o18*o22*o27*o3*o33
        o36 = 4.0000000000000d0*eta(i,j,k)*eta0*o11
        o37 = exp(o36)
        o38 = eta(i,j,k)*o37
        o39 = -(eta0*o37)
        o40 = eta(i,j,k) + eta0 + o38 + o39
        o41 = o16 + o21
        o42 = exp(o41)
        o43 = 1.00000000000000d0 + n
        o44 = o19**o43
        o45 = -2.00000000000000d0*amp*o11*o3*o40*o42*o44*o6
        o46 = -2.00000000000000d0*amp*c*o18*o22*o26*o33*o4
        o47 = amp*n*o18*o22*o26*o31*o33*o6
        o48 = -2.00000000000000d0*amp*o11*o26*o40*o42*o44*o6
        o49 = c*o2
        o50 = 2.00000000000000d0 + c + o49
        o51 = -1.00000000000000d0 + o37
        o52 = -2.00000000000000d0*eta0*o51
        o53 = 1.00000000000000d0 + o37
        o54 = 2.00000000000000d0*eta(i,j,k)*o53
        o55 = n*o10*o53
        o56 = o52 + o54 + o55
        o57 = o16 + o21 + o24
        o58 = exp(o57)
        o59 = o11*o9
        o60 = exp(o59)
        o61 = o11*o15
        o62 = exp(o61)
        o63 = o60 + o62
        o64 = o19**2
        gxx(i,j,k) = 5.0000000000000d-1*(1.00000000000000d0 + o22 + o2*o
     &  23)
c        dxgxx(i,j,k) = 5.0000000000000d-1*o25*(1.00000000000000d0*o22*o2
c     &  6*o28*o29 - 2.00000000000000d0*o27*o28*o3 + 2.00000000000000d0*a
c     &  mp*c*o18*o2*o22*o27*o3*o33 + o34 + o35 + o45 + amp*n*o18*o2*o22*
c     &  o3*o31*o33*o6 - 2.00000000000000d0*amp*o11*o2*o3*o40*o42*o44*o6)
c        dygxx(i,j,k) = 5.0000000000000d-1*o25*(1.00000000000000d0*o28*o2
c     &  9*o3 - 2.00000000000000d0*o22*o26*o28*o4 - 2.00000000000000d0*am
c     &  p*c*o18*o2*o22*o26*o33*o4 + o46 + o47 + o48 + amp*n*o18*o2*o22*o
c     &  26*o31*o33*o6 - 2.00000000000000d0*amp*o11*o2*o26*o40*o42*o44*o6
c     &  )
c        dzgxx(i,j,k) = -5.0000000000000d-1*amp*o11*o20*o30*o4*o50*o56*o5
c     &  8
        gxy(i,j,k) = 5.0000000000000d-1*o23*o29
c        dxgxy(i,j,k) = 5.0000000000000d-1*o25*(1.00000000000000d0*o2*o26
c     &  *o28 - o2*o22*o26*o28 + 2.00000000000000d0*amp*c*o18*o22*o27*o29
c     &  *o3*o33 + amp*n*o18*o22*o29*o3*o31*o33*o6 - 2.00000000000000d0*a
c     &  mp*o11*o29*o3*o40*o42*o44*o6)
c        dygxy(i,j,k) = 5.0000000000000d-1*o25*(-(o2*o28*o3) + 1.00000000
c     &  000000d0*o2*o22*o28*o3 - 2.00000000000000d0*amp*c*o18*o22*o26*o2
c     &  9*o33*o4 + amp*n*o18*o22*o26*o29*o31*o33*o6 - 2.00000000000000d0
c     &  *amp*o11*o26*o29*o40*o42*o44*o6)
c        dzgxy(i,j,k) = -5.0000000000000d-1*amp*o11*o20*o29*o30*o56*o58*o
c     &  6
        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) = 5.0000000000000d-1*(1.00000000000000d0 + o22 - o2*o
     &  23)
c        dxgyy(i,j,k) = 5.0000000000000d-1*o25*(1.00000000000000d0*o26*o2
c     &  8*o29 - 2.00000000000000d0*o22*o27*o28*o3 - 2.00000000000000d0*a
c     &  mp*c*o18*o2*o22*o27*o3*o33 + o34 + o35 + o45 - amp*n*o18*o2*o22*
c     &  o3*o31*o33*o6 + 2.00000000000000d0*amp*o11*o2*o3*o40*o42*o44*o6)
c        dygyy(i,j,k) = 5.0000000000000d-1*o25*(1.00000000000000d0*o22*o2
c     &  8*o29*o3 - 2.00000000000000d0*o26*o28*o4 + 2.00000000000000d0*am
c     &  p*c*o18*o2*o22*o26*o33*o4 + o46 + o47 + o48 - amp*n*o18*o2*o22*o
c     &  26*o31*o33*o6 + 2.00000000000000d0*amp*o11*o2*o26*o40*o42*o44*o6
c     &  )
c        dzgyy(i,j,k) = -5.0000000000000d-1*amp*o11*o20*o27*o30*o50*o56*o
c     &  58
        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) = o22
c        dxgzz(i,j,k) = amp*o11*o3*o33*(n*o10*o31*o6*o63 + 2.000000000000
c     &  00d0*(c*o10*o27*o63 - o40*o6*o60*o64))*exp(o12 + o16 + o21 + o24
c     &  )
c        dygzz(i,j,k) = amp*o26*o33*(-2.00000000000000d0*c*o18*o4 + n*o18
c     &  *o31*o6 - 2.00000000000000d0*o11*o17*o40*o6*o64)*exp(o21 + o24)
c        dzgzz(i,j,k) = -(amp*o11*o20*o30*o56*o58*o6)


```

DistortedBHIVP.F:
```
c     /*@@
c     @file      DistortedBHIVP.F
c     @date      
c     @author    
c     @desc 
c     
c     @enddesc 
c@@   */
      
#include "cctk.h" 

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

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

      subroutine DistortedBHIVP(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(:,:,:),
     $     qf(:,:,:),qfetaeta(:,:,:),qfqq(:,:,:),qfphi(:,:,:),
     $     qfphiphi(:,:,:),
     $     psisph(:,:,:),psiprim(:,:,:),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
      real*8 rmax,adm
      real*8 dbh_eps
      real*8 pi
      integer :: ne, nq, np
      integer :: nx,ny,nz
      integer i,j,k,ier,nquads,nocts
      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

      dbh_eps = tolerance

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     DONT 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 Schwarzchild BH parameters
      
      print *,"Brill wave + Distorted BH solve"
      write(*,123)amp,eta0,c,sigma,n
      print*,'etamax=',etamax
 123  format(1x, 'Pars: amp',f8.5,' eta0',f8.5,' c',f8.5,' sigma',f8.5,' n',i3)
      
c     Sovle on this sized cartesian grid
c     3D grid size NE x NT x NP
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),
     $     qf(ne,nq,np),qfetaeta(ne,nq,np),qfqq(ne,nq,np),
     $     qfphi(ne,nq,np),qfphiphi(ne,nq,np),
     $     psisph(ne,nq,np),psiprim(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 Initialize q-function and its derivatives: should be generalized
c     
      do k = 1,np
         do j = 1,nq
            do i = 1,ne
#include "qfunc.x"
            enddo
         enddo
      enddo
      
c     
c     Initialize psi to the Schwarzschild solution:
c     
      psiprim = 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     Initialize stencil coefficients:
c     
      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
               ac(i,j,k) = -2./deta**2-2./dq**2-2.*exp(2.*
     &              qf(i,j,k))/(dphi**2*
     &              sin(qgrd(j))**2)+0.25*
     &              (qfetaeta(i,j,k)+qfqq(i,j,k)+2.*
     &              exp(2.*qf(i,j,k))*qfphiphi(i,j,k)/
     &              sin(qgrd(j))**2+3.*exp(2.*
     &              qf(i,j,k))*qfphi(i,j,k)**2/
     &              sin(qgrd(j))**2-1.)
               ae(i,j,k) = 1./deta**2
               aw(i,j,k) = 1./deta**2
               an(i,j,k) = 1./dq**2+0.5/(dq*tan(qgrd(j)))
               
               as(i,j,k) = 1./dq**2-0.5/(dq*tan(qgrd(j)))
               
               aq(i,j,k) = exp(2.*qf(i,j,k))/(dphi**2*
     &              sin(qgrd(j))**2)+exp(2.*
     &              qf(i,j,k))*qfphi(i,j,k)/(dphi*
     &              sin(qgrd(j))**2)
               
               ab(i,j,k) = exp(2.*qf(i,j,k))/(dphi**2*
     &              sin(qgrd(j))**2)-exp(2.*
     &              qf(i,j,k))*qfphi(i,j,k)/(dphi*
     &              sin(qgrd(j))**2)
               
               rhs(i,j,k) = -0.25*(qfetaeta(i,j,k)+
     &              qfqq(i,j,k)+2.*exp(2.*qf(i,j,k))*
     &              qfphiphi(i,j,k)/sin(qgrd(j))**2+3.*
     &              exp(2.*qf(i,j,k))*qfphi(i,j,k)**2/
     &              sin(qgrd(j))**2)*psisph(i,j,k)
            enddo
         enddo
      enddo
c
c Apply boundary conditions to the faces of the cube:
c
c    i=2:
      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:
            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
      enddo
c
c    j=2:
      do k = 3,np-2
         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:
            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:
      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:
            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 Apply boundary conditions to the edges of the cube:
c
c    i=2, j=2:
      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=ne-1, j=2:
         aw(ne-1,2,k) = aw(ne-1,2,k) - ae(ne-1,2,k)/(3.+deta)
         ac(ne-1,2,k) = ac(ne-1,2,k) + as(ne-1,2,k) +
     &        4.*ae(ne-1,2,k)/(3.+deta)
         ae(ne-1,2,k) = 0.
         as(ne-1,2,k) = 0.
c
c    i=2, j=nq-1:
         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=nq-1:
         aw(ne-1,nq-1,k) = aw(ne-1,nq-1,k) - ae(ne-1,nq-1,k)/
     &        (3.+deta)
         ac(ne-1,nq-1,k) = ac(ne-1,nq-1,k) + an(ne-1,nq-1,k) +
     &        4.*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:
      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=ne-1, k=2:
         aw(ne-1,j,2) = aw(ne-1,j,2) - ae(ne-1,j,2)/(3.+deta)
         ac(ne-1,j,2) = ac(ne-1,j,2) + ab(ne-1,j,2) +
     &        4.*ae(ne-1,j,2)/(3.+deta)
         ae(ne-1,j,2) = 0.
         ab(ne-1,j,2) = 0.
c
c    i=2, k=np-1:
         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=np-1:
         aw(ne-1,j,np-1) = aw(ne-1,j,np-1) - ae(ne-1,j,np-1)/
     &        (3.+deta)
         ac(ne-1,j,np-1) = ac(ne-1,j,np-1) + aq(ne-1,j,np-1) +
     &        4.*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:
      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=nq-1, k=2:
         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=2, k=np-1:
         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=np-1:
         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 Apply boundary conditions to the corners of the cube:
c
c    i=2, j=2, k=2:
      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=ne-1, j=2, k=2:
      aw(ne-1,2,2) = aw(ne-1,2,2) - ae(ne-1,2,2)/(3.+deta)
      ac(ne-1,2,2) = ac(ne-1,2,2) + as(ne-1,2,2) + ab(ne-1,2,2) +
     &     4.*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=2, j=nq-1, k=2:
      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=2, k=np-1:
      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=ne-1, j=nq-1, k=2:
      aw(ne-1,nq-1,2) = aw(ne-1,nq-1,2) - ae(ne-1,nq-1,2)/(3.+deta)
      ac(ne-1,nq-1,2) = ac(ne-1,nq-1,2) + an(ne-1,nq-1,2) + ab(ne-1,nq-1,2) +
     &     4.*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=2, k=np-1:
      aw(ne-1,2,np-1) = aw(ne-1,2,np-1) - ae(ne-1,2,np-1)/(3.+deta)
      ac(ne-1,2,np-1) = ac(ne-1,2,np-1) + as(ne-1,2,np-1) + aq(ne-1,2,np-1) +
     &     4.*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=2, j=nq-1, k=np-1:
      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=nq-1, k=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)
      ac(ne-1,nq-1,np-1) = ac(ne-1,nq-1,np-1) + an(ne-1,nq-1,np-1) +
     &     aq(ne-1,nq-1,np-1) + 4.*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 Solve for psi:
c
      call bicgst3d(ac,ae,aw,an,as,aq,ab,psiprim,rhs,dbh_eps,rmax,ier,
     $     ne,nq,np)
c
      if (rmax.gt.dbh_eps) then
         write(*,*) '***WARNING: bicgst3d did not converge.'
      endif
      if (ier.eq.-1) then
         write(*,*) '***WARNING: ier=-1'
      endif
      print *,'psiprim = ',maxval(psiprim),' ',minval(psiprim)
c
c Now, apply boundary conditions to psiprim:
c
      do k = 1,np
         do j = 1,nq
            psiprim(1,j,k) = psiprim(3,j,k)
            psiprim(ne,j,k) = (4.*psiprim(ne-1,j,k)-psiprim(ne-2,j,k))/
     $           (3.+deta)
         enddo
      enddo
      do k = 1,np
         do i = 1,ne
            psiprim(i,1,k) = psiprim(i,2,k)
            psiprim(i,nq,k) = psiprim(i,nq-1,k)
         enddo
      enddo
      do j = 1,nq
         do i = 1,ne
            psiprim(i,j,1) = psiprim(i,j,2)
            psiprim(i,j,np) = psiprim(i,j,np-1)
         enddo
      enddo
c     
c     Here, compute the derivatives of the spherical conformal factor
c
c      goto 110 

      do k = 1,np
         do j = 1,nq
            do i = 2,ne-1
               detapsisph(i,j,k)=0.5*(psiprim(i+1,j,k)-psiprim(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*(psiprim(i,j+1,k)-psiprim(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*(psiprim(i,j,k+1)-psiprim(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)=(psiprim(i+1,j,k)-2.*psiprim(i,j,k)+
     &              psiprim(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)=psiprim(:,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

      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
c     gxx = ...
      
c     Derivatives of the metric
c     dxgxx = 1/2 \partial gxx / \partial x
c     
      do k=1,nz
         do j=1,ny
            do i=1,nx
#include "gij.x"
            enddo
         enddo
      enddo
      
c     Courvature
      kxx = 0.0d0
      kxy = 0.0d0
      kxz = 0.0d0
      kyy = 0.0d0
      kyz = 0.0d0
      kzz = 0.0d0
      
c 110  continue
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
      
      deallocate(ac,ae,aw,an,as,aq,ab,rhs,
     $     qf,qfetaeta,qfqq,qfphi,qfphiphi,
     $     psisph,psiprim,detapsisph,dqpsisph,dphipsisph,detaetapsisph,
     $     detaqpsisph,detaphipsisph,dqqpsisph,dqphipsisph,
     $     dphiphipsisph)
      deallocate(etagrd,qgrd,phigrd)
      
      return
      end

```

qfunc.x:
```
	qf(i,j,k) = amp*(1.00000000000000d0+c*cos(phigrd(k))**2)*
     $	(exp(-((etagrd(i)-eta0)**2/sigma**2))+exp(-((etagrd(i)+eta0)**2
     $	/sigma**2)))*sin(qgrd(j))**n

	qfetaeta(i,j,k) = amp*(1.00000000000000d0+c*cos(phigrd(k))
     $	**2)*((4.0000000000000d0*(etagrd(i)-eta0)**2*exp(-((etagrd(i)-eta0)
     $	**2/sigma**2)))/sigma**4-(2.00000000000000d0*exp(-((etagrd(i)
     $	-eta0)**2/sigma**2)))/sigma**2+(4.0000000000000d0*(etagrd(i)+
     $	eta0)**2*exp(-((etagrd(i)+eta0)**2/sigma**2)))/sigma**4-(2.00
     $	000000000000d0*exp(-((etagrd(i)+eta0)**2/sigma**2)))/sigma**2
     $	)*sin(qgrd(j))**n

	qfqq(i,j,k) = amp*(-1.00000000000000d0+n)*n*(1.00000000
     $	000000d0+c*cos(phigrd(k))**2)*cos(qgrd(j))**2*(exp(-((etagrd(i)-eta0)**2/
     $	sigma**2))+exp(-((etagrd(i)+eta0)**2/sigma**2)))*sin(qgrd(j))**(-2
     $	+n)-amp*n*(1.00000000000000d0+c*cos(phigrd(k))
     $	**2)*(exp(-((etagrd(i)-eta0)**2/sigma**2))+exp(-((etagrd(i)+eta0)**2
     $	/sigma**2)))*sin(qgrd(j))**n

	qfphi(i,j,k) = -2.00000000000000d0*amp*c*cos(phigrd(k))*(exp(-
     $	((etagrd(i)-eta0)**2/sigma**2))+exp(-((etagrd(i)+eta0)**2/sigma**2))
     $	)*sin(phigrd(k))*sin(qgrd(j))**n

	qfphiphi(i,j,k) = -2.00000000000000d0*amp*c*cos(phigrd(k))**2*
     $	(exp(-((etagrd(i)-eta0)**2/sigma**2))+exp(-((etagrd(i)+eta0)**2/
     $	sigma**2)))*sin(qgrd(j))**n+2.00000000000000d0*amp*c*(exp(-((
     $	etagrd(i)-eta0)**2/sigma**2))+exp(-((etagrd(i)+eta0)**2/sigma**2)))*
     $	sin(phigrd(k))**2*sin(qgrd(j))**n


```

Stab3d.F:
```
      subroutine bicgst3d(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 :: 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 bicgstab (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 bicgstab (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 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
*
***********************************************************************
*
c
      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 usermv(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 usermv(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 usermv(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 usermv(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 usermv(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(in) :: x(im*jm*km)
      real*8,intent(out) :: 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
      

```

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 DistortedBH
# $Header$

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

# Subdirectories containing source files
SUBDIRS = 


```


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

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


```



Reference solution:
src_code:         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)