init

2024-02-05 16:43:04 -05:00 · 2024-02-05 16:43:04 -05:00 · 1bf03503b0
commit 1bf03503b0
97 changed files with 631996 additions and 0 deletions
--- a/.gitignore
+++ b/.gitignore
@ -0,0 +1,4 @@
 .venv
 parfiles/
 *.csv
 *.log
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@ -0,0 +1,4 @@
 {
 	"editor.rulers": [80],
 	"editor.tabSize": 2
 }
--- a/Teuk_psi4.wl
+++ b/Teuk_psi4.wl
@ -0,0 +1,189 @@
 (*
  This script is used to get a analytical formula of \psi_4,
  and save to a file.
 *)
 (*
 	Usage: Please set the fowllowing variables from outside as
    command line arguments, like this:
 		  wolframscript -file Teuk_psi4.wl m a L n in|out [filename]
    for example:
      wolframscript -file Teuk_psi4.wl 0 1e-8 1 1 out
    if filename is not given, it's "./psi4_analytical.txt" by default.
 *)
 (* variable name : description *)
 (* Begin of variables *)
 (* m : the Teukolsky multiple order *)
 (* a : wave amplitude *)
 (* L : wave width *)
 (* n : the order N in F formula *)
 (* End of variables *)
 (* Parsing arguments *)
 argv = Rest@$ScriptCommandLine;
 Check[
  {m, a, L, n} = Interpreter["Number"]/@argv[[;;4]];
  type = argv[[5]];
  If[Length@argv >= 6,
    filename = argv[[6]],
    filename = "./psi4_analytical.txt"
  ],
  Print["Error: Check your command line arguments!"];Abort[]
 ];
 (* Set Assumptions *)
 $Assumptions = aa > 0 && r > 0 && Pi > theta > 0 &&
   2 Pi >= phi >= 0 && t ~Element~ Reals &&
   x ~Element~ Reals && y ~Element~ Reals && z ~Element~ Reals;
 (* Global Simplify time limit *)
 tc = 60
 (* Help functions *)
 pSimplify[list_] :=
  ArrayReshape[
    ParallelMap[
      Simplify[#, TimeConstraint->tc]&, Flatten@list, Method->"FinestGrained"
    ],
    Dimensions@list
 ];
 psi4analytical[g_, coordinates_, vecn_, vecmb_] :=
  Module[
    {dim = Length[coordinates], t1, t2,
      t3, t4, ig, dg, gamma, dgamma, RiemR, psi4},
    dg = D[g, {coordinates}];
    ig = Inverse[g] // pSimplify;
    t1 =
      AbsoluteTiming[
        gamma = pSimplify[
          ParallelTable[
            1/2 Plus @@ ((ig[[i, #]] (dg[[#, j, k]] + dg[[#, k, j]] -
                    dg[[k, j, #]])) &) /@ Range[dim],
            {i, 1, dim}, {j,1, dim}, {k, 1, dim}
          ]
        ];
      ][[1]];
    Print["Finish computing gamma, time cost:", t1, "s"];
    t2 =
      AbsoluteTiming[
        dgamma = pSimplify[
          D[gamma, {coordinates}]
        ];
      ][[1]];
    Print["Finish computing dgamma, time cost:", t2, "s"];
    t3 =
      AbsoluteTiming[
        RiemR = ParallelTable[
            dgamma[[l, i, k, j]] - dgamma[[l, j, k, i]] +
              Plus @@ ((gamma[[#, k, i]] gamma[[l, j, #]] -\
                gamma[[#, k, j]] gamma[[l, i, #]]) &) /@ Range[dim],
            {i, 1, dim}, {j, 1, dim}, {k, 1, dim}, {l, 1, dim}
        ];
      ][[1]];
    Print["Finish computing RiemR, time cost:" , t3, "s"];
    t4 =
      AbsoluteTiming[
        psi4 = ((((RiemR . g) . vecmb) . vecn) . vecmb) . vecn;
      ][[1]];
    Print["Finish computing psi4, time cost:" , t4, "s"];
    psi4
  ];
 (* set metric *)
 Switch[m,
  0,
    frr = 2 - 3 Sin[theta]^2;
    frtheta = -3 Cos[theta] Sin[theta];
    frphi = 0;
    fthetatheta1 = 3 Sin[theta]^2;
    fthetatheta2 = -1; fthetaphi = 0;
    fphiphi1 = -fthetatheta1;
    fphiphi2 = 3 Sin[theta]^2 - 1;,
  1,
    frr = Sin[2 theta] Cos[phi];
    frtheta = Cos[2 theta] Cos[phi];
    frphi = -Cos[theta] Sin[phi];
    fthetatheta1 = -frr;
    fthetatheta2 = 0;
    fthetaphi = -Sin[theta] Sin[phi];
    fphiphi1 = -fthetatheta1;
    fphiphi2 = -frr;,
  -1,
    frr = Sin[2 theta] Sin[phi];
    frtheta = Cos[2 theta] Sin[phi];
    frphi = Cos[theta] Cos[phi];
    fthetatheta1 = -frr;
    fthetatheta2 = 0;
    fthetaphi = Sin[theta] Cos[phi];
    fphiphi1 = -fthetatheta1;
    fphiphi2 = -frr;,
  2,
    frr = Sin[theta]^2 Cos[2 phi];
    frtheta = Sin[theta] Cos[theta] Cos[2 phi];
    frphi = -Sin[theta] Sin[2 phi];
    fthetatheta1 = (1 + Cos[theta]^2) Cos[2 phi];
    fthetatheta2 = -Cos[2 phi];
    fthetaphi = Cos[theta] Sin[2 phi];
    fphiphi1 = -fthetatheta1;
    fphiphi2 = Cos[theta]^2 Cos[2 phi];,
  -2,
    frr = Sin[theta]^2 Sin[2 phi];
    frtheta = Sin[theta] Cos[theta] Sin[2 phi];
    frphi = Sin[theta] Cos[2 phi];
    fthetatheta1 = (1 + Cos[theta]^2) Sin[2 phi];
    fthetatheta2 = -Sin[2 phi];
    fthetaphi = -Cos[theta] Cos[2 phi];
    fphiphi1 = -fthetatheta1; fphiphi2 = Cos[theta]^2 Sin[2 phi];,
  _,
    Print["Error: m must be one of {0,1,2,-1,-2}."];Abort[]
 ]
 h = aa {
     {0, 0, 0, 0},
     {0, AA[t, r] frr, BB[t, r] frtheta r, BB[t, r] frphi r Sin[theta]},
     {0, BB[t, r] frtheta r,
        (CC[t, r] fthetatheta1 + AA[t, r] fthetatheta2) r^2,
        (AA[t, r] - 2 CC[t, r]) fthetaphi r^2 Sin[theta]},
     {0, BB[t, r] frphi r Sin[theta],
        (AA[t, r] - 2 CC[t, r]) fthetaphi r^2 Sin[theta],
        (CC[t, r] fphiphi1 + AA [t, r] fphiphi2) r^2 Sin[theta]^2}
    } // Simplify;
 g = DiagonalMatrix[{-1, 1, r^2, r^2 Sin[theta]^2}] + h // Simplify;
 rule1 = Switch[type,
  "in",
    {
      AA -> Function[{t, r},3 (F''[t + r]/r^3 - (3 F'[t + r])/r^4 + (3 F[t + r])/r^5)],
      BB -> Function[{t, r}, -(-(F'''[t + r]/r^2) + (3 F''[t + r])/r^3 - (6 F'[t + r])/r^4 + (6 F[t + r])/r^5)],
      CC -> Function[{t, r}, 1/4 (F''''[t + r]/r - (2 F'''[t + r])/r^2 + (9 F''[t + r])/r^3 - (21 F'[t + r])/r^4 + (21 F[t + r])/r^5)]
    },
  "out",
    {
      AA -> Function[{t, r}, 3 (F''[t - r]/r^3 + (3 F'[t - r])/r^4 + (3 F[t - r])/r^5)],
      BB -> Function[{t, r}, -(F'''[t - r]/r^2 + (3 F''[t - r])/r^3 + (6 F'[t - r])/r^4 + (6 F[t - r])/r^5)],
      CC -> Function[{t, r}, 1/4 (F''''[t - r]/r + (2 F'''[t - r])/r^2 + (9 F''[t - r])/r^3 + (21 F'[t - r])/r^4 + (21 F[t - r])/r^5)]
    },
  _,
    Print["Error: check wave type, can only be in or out"];Abort[]
 ]
 rule2 = F -> Function[L^5 (#/L)^n E^(-(#^2/L^2))]
 (* set tetrad *)
 vecn = 1/2 {1, -1, 0, 0};
 vecmb = 1/(Sqrt[2] r) {0, 0, 1, -(I/Sin[theta])};
 (* Calculate psi4 *)
 psi4 = psi4analytical[g, {t, r, theta, phi}, vecn, vecmb];
 psi4 = psi4 /. {aa->a};
 psi4 = psi4 /. rule1;
 psi4 = psi4 /. rule2;
 psi4 = psi4 /. {t->0};
 (* psi4 = Simplify[psi4, TimeConstraint->tc]; *)
 Put[psi4, filename]
--- a/calculate_modes.wl
+++ b/calculate_modes.wl
@ -0,0 +1,61 @@
 (*
  Usage: Please set the fowllowing variables from outside as
  command line arguments, like this:
    wolframscript -file calculate_modes.wl psi4_file r rfilename ifilename
  for example:
    wolframscript -file calculate_modes.wl psi4.txt 2.5 rmodes.txt imodes.txt
 *)
 (* Parsing arguments *)
 argv = Rest@$ScriptCommandLine;
 (* Print[argv] *)
 Check[
  psi4file = argv[[1]];
  (* {l, m, r} = Interpreter["Number"]/@argv[[2;;4]]; *)
 	r = Interpreter["Number"]@argv[[2]];
 	rfilename = argv[[3]];
 	ifilename = argv[[4]];
 ,
  Print["Error: Check your command line arguments!"];Abort[]
 ];
 (* Set Assumptions *)
 $Assumptions = Pi > theta > 0 && 2 Pi >= phi >= 0 &&\
                Element[l, Reals] && Element[m, Reals] && -l<=m<=l;
 Y[s_, l_, m_, theta_, phi_] :=
    (-1)^m*
      (Sqrt[(((l + m)!*(l - m)!)*(2*l + 1))/((((l + s)!*(l - s)!)*4)*Pi)]*
        Sin[theta/2]^(2*l))*
        Sum[
          (((Binomial[l - s, r]*Binomial[l + s, r + s - m])*(-1)^(l - r - s))*
          E^((I*m)*phi))*Cot[theta/2]^(2*r + s - m),
          {r, 0, l - s}
        ]
 (* Y[l_, m_, theta_, phi_] := ((-1)^(l + m) E^(I m phi)
  Binomial[-2 + l, -2 - m] Cot[theta/2]^(-2 -m)
  Sqrt[((1 + 2 l) (l - m)! (l + m)!)/((-2 + l)! (2 + l)!)]
  Hypergeometric2F1[-2 - l, -l - m, -1 - m,
          -Cot[theta/2]^2] Sin[theta/2]^(2 l))/(2 Sqrt[Pi]) *)
 psi4[theta_, phi_] = ToExpression[Import[psi4file, "Text"] ]/.{t->0};
 mode[l_, m_] := Module[{f},
  (* f = Simplify[Conjugate[Y[-2, l,m,theta,phi] ]*psi4[r,theta,phi]*Sin[theta] ]; *)
  f = Conjugate[Y[-2, l,m,theta,phi] ]*psi4[theta,phi]*Sin[theta];
  Quiet[NIntegrate[f,{theta, 0, Pi}, {phi, 0, 2 Pi}] ]
 ]
 (* mode[0,0,2.2]//Print *)
 (* result = ParallelTable[mode[l,m],{l,1,8},{m,-l,l}]//Flatten; *)
 lmlist = Flatten[Table[{l, m}, {l, 1, 8}, {m, -l, l}], 1]
 result = ParallelMap[mode@@#&, lmlist]
 rmodes = Re/@result;
 imodes = Im/@result;
 Export[rfilename, rmodes, "Table"]
 Export[ifilename, imodes, "Table"]
 (* result = mode[l,m]
 Print[Re@result, " ", Im@result] *)
--- a/modes_wolfram/imode_a1e-06-m0-N1-l0.5-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N1-l0.5-r0.4.txt
@ -0,0 +1,80 @@
 0
 0
 0
 -1.3069104711516916e-20
 -2.783462761240938e-22
 0
 1.3772040211125065e-21
 -1.737079286361358e-22
 -2.107594162239173e-20
 3.3067372167419834e-20
 -1.7766598786720205e-19
 0
 1.5757790669135177e-22
 -8.094375884137652e-21
 -1.3565762045869654e-22
 5.920545234348296e-22
 8.7305811727675e-21
 -7.330557306506187e-20
 1.6353360710173357e-21
 0
 6.712239798622798e-20
 -2.997371667647151e-20
 9.101571677497533e-23
 5.107840282514946e-22
 1.315217173959314e-22
 -2.8144820342116767e-22
 -1.234298230536314e-20
 7.230840683662919e-20
 2.5347489380918494e-20
 0.
 -6.026010762448807e-22
 4.5432895144475045e-22
 1.6724558010056528e-21
 3.241658782049374e-20
 5.790264287871194e-24
 -2.2333876538931747e-23
 -1.972825760938971e-22
 -6.394312930188042e-21
 -4.453747213138639e-20
 -8.529783079070252e-21
 1.3834595744949388e-21
 0.
 6.3953469059537335e-21
 -8.871512069631222e-23
 -1.2674474935843767e-20
 1.611451230829867e-22
 9.48745143325352e-20
 -3.3190622078690235e-23
 1.613228376677149e-22
 -1.9802083479060068e-19
 -3.8308802118862094e-22
 -3.861899484856948e-23
 -2.0300935426975485e-19
 1.9838893016318677e-20
 -9.156351713563857e-20
 0.
 -3.5078248236536245e-20
 -7.837536303939937e-23
 3.695222591427513e-21
 3.0894549644002027e-22
 -3.405993720369518e-21
 -3.3504444063335197e-19
 -1.694173169494291e-20
 -4.446095792472524e-24
 2.3636686003702766e-22
 -3.701633241174799e-23
 -1.238702967298159e-22
 1.5450829113695577e-21
 1.0463291911518812e-20
 4.841162422906678e-20
 -1.3413324230618977e-20
 0
 1.877100284551272e-20
 -1.1067263005653234e-20
 -1.013218702195032e-21
 9.98130410834182e-20
 -4.272387863836388e-22
 -3.556876633978019e-23
 1.2449068218923067e-22
 -2.0886310466963949e-22
--- a/modes_wolfram/imode_a1e-06-m0-N1-l0.5-r1.3.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N1-l0.5-r1.3.txt
@ -0,0 +1,80 @@
 0
 0
 0
 -3.2415031202290234e-21
 1.1577834988093405e-20
 0.
 2.544850154308443e-20
 -1.015106212838398e-25
 -1.5117358297743696e-21
 9.797589103625165e-21
 -5.1013766478205555e-20
 0
 -1.5422425072397827e-20
 5.190881461197027e-24
 2.447005996953357e-20
 1.756464908231908e-20
 -8.356905471344161e-20
 -9.553828550090644e-21
 8.059686461680011e-20
 0.
 3.726495663039566e-21
 -2.918154260593567e-26
 1.5251245184216548e-20
 -8.449374575353496e-21
 -7.740419322353816e-23
 8.666248695044287e-22
 -3.458766217765848e-21
 -5.066345744516439e-21
 -2.0318512368757383e-22
 0
 1.0545745016484157e-24
 -2.2163835993089548e-26
 9.031693747424331e-24
 9.006898271451424e-25
 -1.5660895830779967e-23
 2.0646799674364366e-23
 3.842677027189502e-21
 -1.407515717405698e-21
 5.185611699956195e-21
 -4.389693626144415e-22
 1.775269494287173e-22
 0.
 -1.734130839842004e-24
 3.981538760831491e-25
 -5.432411737713976e-26
 -2.805345888969514e-22
 -2.820256142628209e-21
 1.873519891027076e-20
 -2.7847673478515564e-24
 8.087002647381154e-20
 -4.613618041869768e-22
 -5.286570263756787e-21
 -4.834106810580703e-21
 -4.070822202167473e-21
 -2.0026791606006653e-22
 0
 -2.9157793475067447e-22
 -8.436520282540424e-25
 6.194419817721264e-24
 -2.315552628990609e-22
 2.39818763896981e-24
 -3.32663875743108e-20
 -2.0416477533588798e-23
 -4.114799455828666e-24
 -3.687682810356704e-20
 1.1537604243130386e-20
 4.548401333113337e-22
 -2.8368886121716336e-21
 5.510194710389765e-21
 -7.003131997414492e-22
 4.19348410283001e-21
 0.
 1.6554719412606065e-25
 -3.578146848337674e-24
 -2.5233861502720774e-21
 1.722320796919053e-21
 2.953130025675852e-20
 -5.082056521599978e-24
 -1.2673133958132957e-19
 1.7688287605404054e-19
--- a/modes_wolfram/imode_a1e-06-m0-N1-l0.5-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N1-l0.5-r1.8.txt
@ -0,0 +1,80 @@
 0
 0
 0
 2.8489774482118965e-20
 4.380337070207105e-22
 0.
 -5.709225019257662e-22
 1.4431778980900765e-21
 6.907856906448373e-22
 4.061149282537417e-22
 2.306717101481701e-21
 0
 2.2978226705178614e-22
 2.161626459664164e-22
 -1.1073376161852272e-20
 5.480106445557063e-20
 -1.56860214190093e-20
 9.77066075888344e-21
 6.573290856723281e-22
 0
 -1.3598225531859083e-21
 -3.7757815139583854e-21
 6.016315619127936e-21
 1.878259113805749e-21
 0
 -2.5843966037724943e-21
 -5.925195639395979e-22
 1.2846126722196271e-23
 -1.5242747744548853e-18
 0.
 2.122453004782504e-22
 1.5713985551037176e-20
 6.357421746614603e-21
 7.089211908831214e-21
 -6.3456659104659695e-21
 -3.1715506810600325e-21
 -4.898139715219715e-24
 9.118464475774238e-21
 -5.592399531245952e-22
 7.694839096153348e-21
 4.2690588562224285e-21
 0
 -6.841142372463398e-20
 -1.3526463813284089e-21
 8.32601005896243e-22
 -1.218161594150612e-21
 3.970143489534022e-22
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 1.8361609751385232e-21
 -9.517565681557135e-21
 -1.4737082439199435e-20
 3.6639204341194534e-24
 5.653032388881299e-21
 1.214285830297295e-21
 -1.6678168409491978e-21
 0.
 1.103558854524374e-20
 -5.44385022083968e-25
 -2.3488347185199746e-20
 -4.366253413305285e-21
 -2.2141531567292006e-23
 2.6408333166270613e-20
 -2.0804323575638146e-20
 -5.280069787379648e-21
 7.651950780643815e-29
 -9.567266746257974e-22
 -1.7190210769494913e-23
 -5.117171670880455e-21
 -1.824367878407209e-20
 7.572762950825466e-25
 -1.975240210649679e-21
 0
 1.112492376506761e-22
 -2.2368828649842295e-21
 2.2239959591329178e-24
 -1.734084939299702e-20
 1.6527583215538982e-20
 -1.2961558913427557e-20
 -4.2304789219694925e-21
 1.4370043919610288e-22
--- a/modes_wolfram/imode_a1e-06-m0-N1-l1-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N1-l1-r0.4.txt
@ -0,0 +1,80 @@
 0
 0
 0
 1.1066022234734404e-20
 -5.171533189681529e-21
 0
 3.2549102154624735e-19
 -6.281940443972713e-20
 5.232744555010453e-21
 -1.0458044484507929e-20
 -1.4942190585157892e-20
 0.
 -3.4288290751548103e-19
 6.193928426797071e-21
 -5.795227371546512e-21
 -1.2177215310607514e-19
 -9.034466650304168e-21
 9.118839072784577e-21
 4.0813091423366385e-21
 0
 -5.366086069754001e-20
 -2.2290449556772713e-21
 1.941662956724081e-17
 -2.2762025223989194e-19
 3.6473495134760064e-20
 -3.6627557523848065e-20
 1.1276126110322873e-20
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 -6.1757304533209046e-21
 0.
 -1.9071476203022606e-20
 8.602678370551488e-22
 -2.4649982254080225e-21
 8.919736699343063e-20
 -7.112098906730932e-21
 1.0401666955883612e-21
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 5.293955920339377e-21
 -2.283183926768867e-20
 1.015777792215118e-20
 1.8112773873073647e-20
 0.
 -2.161307135315304e-19
 4.1044701994881233e-20
 1.5405411728187587e-20
 3.1745640946136665e-21
 -1.31371306233766e-21
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 5.885886366682324e-20
 1.3253584082692141e-19
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 -3.0357528480696116e-21
 0.
 9.974888288715705e-20
 -3.4936800351789677e-20
 7.940106699896513e-20
 1.009491219559715e-20
 7.867562798616899e-21
 -1.854538933343888e-21
 -1.9951596374779028e-21
 2.2208846250639796e-21
 4.8079549987217955e-21
 2.8863546590371582e-21
 -2.632588733361674e-21
 -2.4560646747924498e-20
 -1.2571400476701417e-20
 2.777445022284615e-20
 5.2582217178770863e-20
 0.
 9.861647262857196e-21
 -7.454551680327885e-21
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l0.5-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l0.5-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l1-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N2-l1-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l1-r1.3.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N2-l1-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l1-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N2-l1-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l2-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N2-l2-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l2-r1.3.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N2-l2-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N2-l2-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N2-l2-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l0.5-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l0.5-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l0.5-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l0.5-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l1-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l1-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l1-r1.3.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l1-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l1-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l1-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l2-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l2-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l2-r1.3.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l2-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N3-l2-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N3-l2-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l0.5-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l0.5-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l0.5-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l1-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l1-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l1-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N4-l1-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l2-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N4-l2-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l2-r1.3.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N4-l2-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m0-N4-l2-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m0-N4-l2-r1.8.txt
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--- a/modes_wolfram/imode_a1e-06-m1-N1-l0.5-r0.4.txt
+++ b/modes_wolfram/imode_a1e-06-m1-N1-l0.5-r0.4.txt
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--- a/modes_wolfram/imode_a1e-06-m1-N1-l0.5-r1.3.txt
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--- a/modes_wolfram/imode_a1e-06-m1-N1-l0.5-r1.8.txt
+++ b/modes_wolfram/imode_a1e-06-m1-N1-l0.5-r1.8.txt
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--- a/modes_wolfram/rmode_a1e-06-m0-N1-l0.5-r0.4.txt
+++ b/modes_wolfram/rmode_a1e-06-m0-N1-l0.5-r0.4.txt
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--- a/modes_wolfram/rmode_a1e-06-m0-N1-l0.5-r1.3.txt
+++ b/modes_wolfram/rmode_a1e-06-m0-N1-l0.5-r1.3.txt
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 1.0328999620903535e-15
 -1.7689789896965828e-19
 -7.933972251959613e-16
 -5.340232849901386e-18
 2.314003544132584e-16
 2.913841211541396e-10
 8.948360022990027e-17
 -3.685749528706404e-10
 -8.798822663404451e-17
 2.9138412006755877e-10
 -2.312206267867665e-16
 -3.763029067780322e-18
 5.237047238364224e-18
 9.485753593347467e-18
 7.645424744047839e-18
 8.304486670046677e-18
 6.005587673124872e-18
 -1.0559601584214127e-19
 4.636202576752523e-18
 -8.238567630373635e-18
 7.95311711355863e-18
 -5.680011865565838e-18
 4.563135955486913e-18
 -3.9663493385628204e-18
 -2.4171159450722013e-18
 -5.079681400102416e-18
 -5.182958721154091e-16
 1.004652119272226e-17
 8.406433852359605e-16
 1.485879782886608e-17
 -8.404614131526195e-16
 5.9700110679563185e-18
 5.191036928759181e-16
 -7.644048212110974e-18
 2.860968498962603e-18
 -2.998379070235664e-18
 -3.390285663934713e-18
 7.617278372742073e-18
 -7.08810958329234e-18
 -5.439306779258094e-18
 -2.6053054280898796e-18
 2.693076787406057e-18
 7.000755226402466e-19
 -6.535421670883463e-19
 1.414981669880533e-18
 -1.125952924831988e-18
 -2.9569511768220177e-18
 7.03210402744973e-18
 -7.057713022226489e-18
 -4.220662088784339e-18
 -4.059879432368364e-18
 5.899794374706637e-19
 6.4409127703816764e-18
 -6.833900489141332e-18
 -1.9214126601584673e-18
 -6.205480521039257e-19
 -1.4643845149773797e-18
 -4.8588543686431155e-18
 -7.208562641815335e-19
 2.181136004582809e-17
 -7.35945175927843e-20
 -7.30483462609399e-18
 1.8094718588253146e-18
 -1.4886865126875166e-18
 2.798933106647211e-18
 -6.311826359748858e-18
 -7.10699065285811e-18
 7.825315227377349e-19
--- a/modes_wolfram/rmode_a1e-06-m1-N1-l0.5-r1.3.txt
+++ b/modes_wolfram/rmode_a1e-06-m1-N1-l0.5-r1.3.txt
@ -0,0 +1,80 @@
 0.
 0.
 0.
 -2.6057079908403694e-15
 -1.269208099590147e-9
 -2.1213096170837854e-15
 1.2692080991356608e-9
 -2.6055722255041474e-15
 -3.4539689084134877e-19
 -3.3293652497937057e-19
 -9.968942733168899e-17
 -2.2120553202082214e-20
 -2.612850968526872e-18
 -9.739480083042728e-17
 -4.980776999200916e-19
 6.338697960962842e-19
 4.229237001358863e-19
 -7.812328952622021e-16
 -1.3849491481547943e-18
 9.936602371698712e-16
 1.6274039719245812e-18
 -7.813017552588481e-16
 -5.365174290278023e-19
 6.205856274294858e-19
 3.915208087075756e-20
 9.96231520992165e-19
 -5.831807063641204e-19
 -8.137931627581516e-19
 -6.271756895794946e-19
 3.1891931119128034e-19
 -5.856294065086564e-19
 1.2088467691366262e-18
 -4.808911401818817e-19
 -1.0578561250857027e-18
 1.7255287531802404e-19
 7.415925481980183e-19
 -2.840869632177534e-19
 -1.5035468625004764e-19
 -3.1170576366142183e-19
 -1.2107826702875885e-18
 3.97955457976492e-19
 1.0913432543122871e-18
 -4.069884506054849e-19
 -1.4167862081086442e-18
 2.934222596897224e-19
 -9.622664483576015e-20
 2.836552249896474e-19
 8.349456114937672e-19
 2.787972980696497e-20
 3.599455355267846e-20
 6.079372980451008e-19
 3.546799327441265e-19
 1.2285743871754592e-18
 5.467190462981066e-19
 -6.312350812250107e-19
 1.936802557580113e-19
 -5.722484523333134e-19
 -8.848281997374168e-19
 1.0832631603256982e-18
 -3.0626069237540873e-19
 5.027567954365786e-19
 -1.0442834003010481e-19
 1.3092012081098702e-19
 -1.102969496033268e-19
 -4.329507282189492e-19
 4.84939181785046e-19
 -2.23921526364516e-20
 3.5261244152885935e-19
 5.735904254477455e-19
 7.194420561468611e-19
 -5.1577517134318e-19
 4.0108285432946673e-19
 8.88933445254646e-19
 6.652995426154171e-19
 -7.038961215080482e-19
 5.871770752177208e-20
 -1.9542933558773788e-19
 3.466194795449876e-19
 5.07686073064716e-19
 -1.5190805766615037e-19
--- a/modes_wolfram/rmode_a1e-06-m1-N1-l0.5-r1.8.txt
+++ b/modes_wolfram/rmode_a1e-06-m1-N1-l0.5-r1.8.txt
@ -0,0 +1,80 @@
 0.
 0.
 0.
 -1.2531757219225479e-18
 -1.526825540098167e-12
 -1.5278948174896158e-18
 1.5268255658246428e-12
 -1.3310795385214837e-18
 4.1008364325047995e-19
 -1.4970740539525037e-18
 9.001098860682261e-19
 -6.15920622738822e-20
 9.22905693148503e-19
 1.491354451718304e-18
 2.8066030303150574e-19
 7.763881105588602e-20
 -3.9972734304731364e-19
 -4.421949967270777e-19
 6.382858501515121e-19
 -2.4584747355271442e-18
 -4.829785418811541e-19
 -3.2895485597693803e-19
 1.4676546896740814e-19
 1.2103335748990722e-19
 -6.691609125173394e-20
 2.140332322101621e-19
 -6.521271239691065e-19
 -4.340700695518899e-19
 2.654759614955498e-19
 -5.344037431454167e-20
 2.4444326981530704e-20
 5.162132581703684e-19
 -5.769305440934513e-19
 -2.0820638386662396e-19
 -1.0378570445076747e-19
 2.4463848729446135e-19
 -4.503411262973411e-19
 -4.8671685182496366e-20
 9.12472975590007e-20
 -2.2634846389077213e-19
 -9.006973887786464e-19
 -1.1742710788081754e-18
 9.72767709158865e-19
 -3.1675359049268585e-19
 3.249722325436031e-20
 -1.269917832320213e-19
 3.5768438950931424e-19
 2.973140932679077e-19
 2.896233063857655e-19
 4.677201724070813e-19
 2.0104119699079363e-18
 1.157673487811456e-19
 -6.226576088128237e-19
 1.6210561227833816e-20
 8.313300938516327e-19
 5.444841115575204e-20
 8.440014558144011e-19
 -1.4245355886527933e-19
 -5.310610883700667e-19
 3.9134843345984515e-20
 2.0243045113381847e-18
 -3.836922650967532e-19
 3.251461186704697e-19
 -1.3964612645891238e-19
 -5.178829688208674e-19
 -7.451677688978282e-21
 -6.948892260456319e-19
 8.6072271351018e-20
 3.235666439158413e-20
 1.1378847347754145e-19
 -1.3583697464309015e-19
 -6.449553920711095e-20
 2.421574826209614e-19
 7.808185952615417e-20
 9.591861257262731e-20
 1.4571276753632887e-19
 6.564154822512305e-19
 -9.90503761450908e-20
 4.738888740811404e-19
 -1.1093047771231868e-19
--- a/psi4_analytical/psi4-m0-a1e-06-L0.5-N1.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L0.5-N1.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L0.5-N2.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L0.5-N2.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L0.5-N3.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L0.5-N3.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L0.5-N4.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L0.5-N4.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L1-N1.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L1-N1.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L1-N2.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L1-N2.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L1-N3.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L1-N3.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L1-N4.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L1-N4.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L2-N1.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L2-N1.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L2-N2.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L2-N2.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L2-N3.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L2-N3.txt
--- a/psi4_analytical/psi4-m0-a1e-06-L2-N4.txt
+++ b/psi4_analytical/psi4-m0-a1e-06-L2-N4.txt
--- a/psi4_analytical/psi4-m1-a1e-06-L0.5-N1.txt
+++ b/psi4_analytical/psi4-m1-a1e-06-L0.5-N1.txt
--- a/psi4_value.wl
+++ b/psi4_value.wl
@ -0,0 +1,22 @@
 (*
  Usage: Please set the fowllowing variables from outside as
  command line arguments, like this:
    wolframscript -file psi4_value.wl psi4_file x y z
  for example:
    wolframscript -file psi4_value.wl psi4.txt 1.2 2.1 3.4
 *)
 (* Parsing arguments *)
 argv = Rest@$ScriptCommandLine;
 (* Print[argv] *)
 Check[
  psi4file = argv[[1]];
 	{x, y, z} = ToExpression[argv[[2]]];
 ,
  Print["Error: Check your command line arguments!"];Abort[]
 ];
 psi4[r_, theta_, phi_] = ToExpression[Import[psi4file, "Text"] ]/.{t->0};
 result = psi4@@ToSphericalCoordinates[{x,y,z}]
 Print[Re@result, " ", Im@result]
--- a/test_Inv_modes.py
+++ b/test_Inv_modes.py
@ -0,0 +1,304 @@
 import os
 import subprocess
 import csv
 import itertools
 import numpy as np
 from datetime import datetime
 # from wolframclient.evaluation import WolframLanguageSession
 # from wolframclient.language import wl, wlexpr
 nmesh_exe = "/home/wyj/Code/NR/nmesh/exe/nmesh"
 def timestr():
  now = datetime.now()
  return now.strftime('%y-%m-%d %H:%M:%S')
 class nmesh_tester:
  def __init__(self, a=1e-8, m=0, N=1, l=1, type="out", ntheta=16, nphi=32,
               interp="yes", n=20, luni=0, rlist="", rmodes=[], imodes=[],
               rpsi4s=[], ipsi4s=[], mode_file="mode.csv", psi4_file="psi4.csv",
               l2_file="l2.csv",
               outlist="0.05 0.08 0.1 -0.4 0.42 0.33 1.4 0.2 0.35"):
    self.a = a
    self.m = m
    self.N = N
    self.l = l
    self.type = type
    self.ntheta = ntheta
    self.nphi = nphi
    self.interp = interp
    self.n = n
    self.luni = luni
    self.rlist = rlist
    self.rarray = list(map(float, rlist.split()))
    self.outlist = outlist
    self.outarray = list(map(float, outlist.split()))
    self.rmodes = rmodes
    self.imodes = imodes
    self.rpsi4s = rpsi4s
    self.ipsi4s = ipsi4s
    self.mode_file = mode_file
    self.psi4_file = psi4_file
    self.l2_file = l2_file
    if max(max(self.rarray),max(self.outarray)) < 2.0:
      self.mesh_type = "CubedSpheres"
    else:
      self.mesh_type = "Shell"
    print(f"[{timestr()}]Start a now tester.")
  def run_test(self):
    parfile = self.write_parfile()
    basename = parfile[:-4]
    print(f"[{timestr()}]Written to parfile {parfile}")
    print(f"[{timestr()}]Starting running nmesh")
    if os.path.exists(basename):
      print(f"[{timestr()}]\tHave already runed {parfile}, skipping.")
    else:
      print(f"[{timestr()}]running: {nmesh_exe} {parfile}")
      self.run_nmesh(parfile)
      print(f"[{timestr()}]Finished running nmesh")
    self.collect_result(basename)
    print(f"[{timestr()}]Finished result analysis.")
  def write_parfile(self):
    filename = f"parfiles/Inv-a{self.a}-m{self.m}-N{self.N}-l{self.l}-{self.type}-"+\
         f"nt{self.ntheta}-np{self.nphi}-{self.interp}-"+\
               f"n{self.n}-{self.luni}-{self.rlist}.par"
    preparfile =\
        '''###################################################################
 # modules we use
 physics = Invariants ADM Teukolsky
 ###################################################################
 # parameters for ADM
 ADM_Set1stDerivsInADMconstraints = yes
 '''
    if self.mesh_type == "Shell":
      mesh_parfile =\
        f'''###################################################################
 # initial mesh
 amr_mesh_type = Shell
 amr_Shell_rin = {np.floor(min(self.rarray+self.outarray))}
 amr_Shell_rout = {np.ceil(max(self.rarray+self.outarray))}
 amr_Shell_r1 = 0
 amr_n0 = {self.n}
 amr_n1 = {self.n}
 amr_n2 = {self.n}
 amr_luni = {self.luni}
 '''
    else:
      mesh_parfile =\
        f'''###################################################################
 # initial mesh
 amr_mesh_type = 7 CubedSpheres
 amr_n0 = {self.n}
 amr_n1 = {self.n}
 amr_n2 = {self.n}
 amr_luni = {self.luni}
 '''
    teukolsky_parfile =\
         f'''###################################################################
 # parameters for Teukolsky
 Teukolsky_waves_amplitude = {self.a}
 Teukolsky_wave_width = {self.l}
 Teukolsky_wave_mm = {self.m}
 Teukolsky_wave_N = {self.N}
 Teukolsky_wave_type = {self.type}
 '''
    invariants_parfile =\
         f'''###################################################################
 # parameters for Invariants
 Invariants_ntheta = {self.ntheta}
 Invariants_nphi = {self.nphi}
 Invariants_modes_lmin = 1
 Invariants_modes_lmax = 8
 Invariants_modes_test = no
 Invariants_compute_modes = yes
 Invariants_compute_modes_just_interp = {self.interp}
 Invariants_modes_r = {self.rlist}
 Invariants_psi4_test_0doutput = yes
 Invariants_psi4_test_0dout_coordinates = {self.outlist}
 '''
    output_parfile =\
         '''###################################################################
 # output
 logfile_creation = yes
 0douttime = 0.1
 0doutput = Invariants_rpsi4 Invariants_ipsi4
 1douttime = 0.1
 1doutput = Invariants_rpsi4 Invariants_ipsi4
 '''
    with open(filename, "w") as f:
      f.write(preparfile)
      f.write(mesh_parfile)
      f.write(teukolsky_parfile)
      f.write(invariants_parfile)
      f.write(output_parfile)
    return filename
  def run_nmesh(self, parfile):
    subprocess.run([nmesh_exe, parfile])
  def collect_result(self, basename):
    print(f"[{timestr()}]Starting collect and analysis result...")
    if not os.path.exists(self.mode_file):
      with open(self.mode_file, "w") as f:
        csv_writer = csv.writer(f)
        csv_writer.writerow(["a", "m", "N", "L", "type", "nt", "np", "interp",
                             "mesh", "n", "luni", "r", "l", "m", "re_mode",
                                "im_mode", "re_mode_err", "im_mode_err",
                                  "re_mode_rel_error", "im_mode_rel_err"])
    if not os.path.exists(self.psi4_file):
      with open(self.psi4_file, "w") as f:
        csv_writer = csv.writer(f)
        csv_writer.writerow(["a", "m", "N", "L", "type", "mesh", "n", "luni",
                             "x", "y", "z", "rpsi4", "ipsi4", "rpsi4_err",
                             "ipsi4_err", "rpsi4_rel_err", "ipsi4_rel_err"])
    if not os.path.exists(self.l2_file):
      with open(self.l2_file, "w") as f:
        csv_writer = csv.writer(f)
        csv_writer.writerow(["a", "m", "N", "L", "type", "nt", "np", "interp",
                             "mesh", "n", "luni", "r", "l2-norm",
                             "l2-distance", "l2-rel_err"])
    print(f"[{timestr()}]\tAnalysing modes...")
    with open(self.mode_file, "a") as mode_fp:
      csv_writer = csv.writer(mode_fp)
      ind = 0
      for r in self.rarray:
        l2norm = np.dot(self.rmodes, self.rmodes)+\
          np.dot(self.imodes, self.imodes)
        l2distance = 0
        for l in range(1,9):
          for m in range(-l, l+1):
            output_line = [self.a, self.m, self.N, self.l, self.type,\
                           self.ntheta, self.nphi, self.interp, self.mesh_type,\
                                          self.n, self.luni, r, l, m]
            mode_file = f'{basename}/modes/psi4_r{r}_l{l}_m{m}.t'
            with open(mode_file, 'r') as f:
                lines = f.readlines()
                output_line.extend(map(float,lines[-1].split()[1:]))
            rmode = self.rmodes[ind]
            imode = self.imodes[ind]
            rmode_error = output_line[-2] - rmode
            imode_error = output_line[-1] - imode
            rmode_rel_error = 'nan' if rmode==0 else rmode_error/rmode
            imode_rel_error = 'nan' if imode==0 else imode_error/imode
            l2distance += rmode_error**2 + imode_error**2
            output_line.extend([rmode_error, imode_error,
                                rmode_rel_error, imode_rel_error])
            ind += 1
            csv_writer.writerow(output_line)
        with open(self.l2_file, "a") as l2_fp:
          l2_writer = csv.writer(l2_fp)
          l2_writer.writerow([self.a, self.m, self.N, self.l, self.type,
                              self.ntheta, self.nphi, self.interp,
                              self.mesh_type, self.n, self.luni, r, l2norm,
                              l2distance, l2distance/l2norm])
    print(f"[{timestr()}]\tAnalysing 0doutput...")
    with open(self.psi4_file, "a") as psi4_fp:
      csv_writer = csv.writer(psi4_fp)
      n_points = len(self.outarray)//3
      for i in range(n_points):
        output_line = [self.a, self.m, self.N, self.l, self.type,\
                        self.mesh_type, self.n, self.luni]
        psi4_files = [f"{basename}/Invariants_rpsi4_pt{i}.t",
                      f"{basename}/Invariants_ipsi4_pt{i}.t"]
        with open(psi4_files[0]) as f:
          line = f.readline()
          line_list = line.split()
          Nrpsi4 = float(line_list[1])
          output_line.extend(line_list[-3:])
          output_line.append(Nrpsi4)
        with open(psi4_files[1]) as f:
          line = f.readline()
          Nipsi4 = float(line.split()[1])
        output_line.append(Nipsi4)
        rpsi4 = self.rpsi4s[i]
        ipsi4 = self.ipsi4s[i]
        rpsi4_error = Nrpsi4 - rpsi4
        ipsi4_error = Nipsi4 - ipsi4
        rpsi4_rel_error = 'nan' if rpsi4==0 else rpsi4_error/rpsi4
        ipsi4_rel_error = 'nan' if ipsi4==0 else ipsi4_error/ipsi4
        output_line.extend([rpsi4_error, ipsi4_error,
                            rpsi4_rel_error, ipsi4_rel_error])
        csv_writer.writerow(output_line)
 rlist = [0.4, 1.3, 1.8]
 pointlist = [[0.05, 0.08, 0.1], [-0.4, 0.42, 0.33], [1.4, 0.2, 0.35]]#, [0.01, 0.02, 0.48]]
 rlist_str = ' '.join(str(r) for r in rlist)
 outlist = ' '.join(str(coord) for point in pointlist for coord in point)
 mode_file = "result_modes.csv"
 psi4_file = "result_psi4.csv"
 l2_file = "result_l2.csv"
 for a in [1e-6, 1e-8, 1e-10, 1e-12]:
  for m in [0, 1, -1, 2, -2]:
    for N in [1, 2, 3, 4]:
      for l in [0.5, 1, 2]:
        for type in ["in", "out"]:
          psi4_analytical = f"psi4_analytical/psi4-m{m}-a{a}-L{l}-N{N}.txt"
          if not os.path.exists(psi4_analytical):
            print(f"[{timestr()}]Staring calculate psi4 analytically...")
            subprocess.run(["wolframscript", "-file", "Teuk_psi4.wl", f"{m}",
                            f"{a}", f"{l}", f"{N}", f"{type}",
                            f"{psi4_analytical}"])
            print(f"[{timestr()}]Finished calculate psi4 and saved in {psi4_analytical}.")
          rmodes = []
          imodes = []
          for r in rlist:
            rmodes_file = f"modes_wolfram/rmode_a{a}-m{m}-N{N}-l{l}-r{r}.txt"
            imodes_file = f"modes_wolfram/imode_a{a}-m{m}-N{N}-l{l}-r{r}.txt"
            if (not os.path.exists(rmodes_file)) or \
              (not os.path.exists(imodes_file)):
              print(f"[{timestr()}]Starting calculate modes at r={r}...")
              subprocess.run(["wolframscript", "-file", "calculate_modes.wl",
                              f"{psi4_analytical}", f"{r}",
                              f"{rmodes_file}", f"{imodes_file}"])
              print(f"[{timestr()}]Finished calculate modes and saved in \
                    {rmodes_file} and {imodes_file}.")
            with open(rmodes_file) as f:
              rmodes.extend([float(line.strip()) for line in f.readlines()])
            with open(imodes_file) as f:
              imodes.extend([float(line.strip()) for line in f.readlines()])
          rpsi4s = []
          ipsi4s = []
          for point in pointlist:
            print(f"[{timestr()}]Starting calculate psi4 at {point}")
            result = subprocess.run(["wolframscript", "-file",
                                      "psi4_value.wl", f"{psi4_analytical}",
                                      "{"+
                                      f"{point[0]}, {point[1]}, {point[2]}"+
                                        "}"],
                                      capture_output=True, text=True)
            try:
              output = result.stdout.strip().split()
              rpsi4s.append(float(output[0].replace("*^", "e")))
              ipsi4s.append(float(output[1].replace("*^", "e")))
            except:
              print(result, output)
              raise SystemExit("wrong in wolframscript.")
          for ntheta in [16, 32, 64]:
            nphi = 2*ntheta
            for interp in ["yes"]:
              for n in [10, 20, 40]:
                for luni in [0, 1, 2]:
                  tester = nmesh_tester(a, m, N, l, type, ntheta, nphi,
                                        interp, n, luni, rlist_str, rmodes,
                                        imodes, rpsi4s, ipsi4s, mode_file,
                                        psi4_file, l2_file, outlist)
                  tester.run_test()