Carpet test case for AHFinderDirect

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1410 f88db872-0e4f-0410-b76b-b9085cfa78c5
author: jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5> 2005-05-26 10:04:34 +0000
committer: jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5> 2005-05-26 10:04:34 +0000
commit: 2927bf635a6df5d6a12de1c4f04bf5998eca9ef4 (patch)
tree: d6c1d937ef81a70b30163289906ac0560cc26db7 /test
parent: 34439126cceb680bbae74cf5972a9e15f7e845a1 (diff)
5 files changed, 2646 insertions, 0 deletions
diff --git a/test/Kerr-carpet.par b/test/Kerr-carpet.par
new file mode 100644
index 0000000..cfb3d54
--- /dev/null
+++ b/test/Kerr-carpet.par
@@ -0,0 +1,135 @@
+# This parameter file sets up Kerr/Kerr-Schild initial data, then
+# finds the apparent horizon in it.  The local coordinate system origin
+# and the initial guess are both deliberately de-centered with respect
+# to the black hole, to make this a non-trivial test for the apparent
+# horizon finder.
+
+# flesh
+cactus::cctk_itlast = 0
+
+########################################
+
+#
+# ***** output setup (also see below for more output stuff) *****
+#
+ActiveThorns = "IOUtil IOBasic"
+IOUtil::parfile_write = "no"
+IO::out_dir = $parfile
+
+########################################
+
+#
+# basic grid setup
+#
+
+ActiveThorns = "Carpet CarpetLib CarpetInterp CarpetReduce"
+Carpet::domain_from_coordbase    = true
+
+ActiveThorns = "SymBase Boundary"
+ActiveThorns = "CoordBase"
+CoordBase::domainsize = "spacing"
+CoordBase::zero_origin_x = true
+CoordBase::zero_origin_y = true
+CoordBase::zero_origin_z = true
+CoordBase::dx   = 0.04
+CoordBase::dy   = 0.04
+CoordBase::dz   = 0.04
+CoordBase::ncells_x = 80
+CoordBase::ncells_y = 80
+CoordBase::ncells_z = 80
+
+#
+# ghost zones
+#
+
+driver::ghost_size_x = 2
+driver::ghost_size_y = 2
+driver::ghost_size_z = 2
+
+# ghost zones are outside the nominal grid
+CoordBase::boundary_internal_x_lower = false
+CoordBase::boundary_internal_x_upper = false
+CoordBase::boundary_internal_y_lower = false
+CoordBase::boundary_internal_y_upper = false
+CoordBase::boundary_internal_z_lower = false
+CoordBase::boundary_internal_z_upper = false
+
+# ghost zone widths
+CoordBase::boundary_size_x_lower     = 2
+CoordBase::boundary_size_x_upper     = 2
+CoordBase::boundary_size_y_lower     = 2
+CoordBase::boundary_size_y_upper     = 2
+CoordBase::boundary_size_z_lower     = 2
+CoordBase::boundary_size_z_upper     = 2
+
+# ghost zones start 0.5 point outside nominal grid boundary
+CoordBase::boundary_shiftout_x_lower = 0
+CoordBase::boundary_shiftout_x_upper = 0
+CoordBase::boundary_shiftout_y_lower = 0
+CoordBase::boundary_shiftout_y_upper = 0
+CoordBase::boundary_shiftout_z_lower = 0
+CoordBase::boundary_shiftout_z_upper = 0
+
+# staggered grids everywhere
+CoordBase::boundary_staggered_x_lower = true
+CoordBase::boundary_staggered_x_upper = true
+CoordBase::boundary_staggered_y_lower = true
+CoordBase::boundary_staggered_y_upper = true
+CoordBase::boundary_staggered_z_lower = true
+CoordBase::boundary_staggered_z_upper = true
+
+# octant symmetry
+ActiveThorns = "ReflectionSymmetry"
+ReflectionSymmetry::avoid_origin_x = true
+ReflectionSymmetry::avoid_origin_y = true
+ReflectionSymmetry::avoid_origin_z = true
+ReflectionSymmetry::reflection_x = true
+ReflectionSymmetry::reflection_y = true
+ReflectionSymmetry::reflection_z = true
+
+ActiveThorns = "CartGrid3D"
+CartGrid3D::type = "CoordBase"
+
+########################################
+
+#
+# Kerr initial data
+#
+ActiveThorns = "ADMBase ADMCoupling StaticConformal CoordGauge SpaceMask Exact"
+ADMBase::initial_lapse = "exact"
+ADMBase::initial_shift = "exact"
+ADMBase::initial_data = "exact"
+ADMBase::lapse_evolution_method = "static"
+ADMBase::shift_evolution_method = "static"
+ADMBase::metric_type = "physical"
+Exact::exact_model = "Kerr/Kerr-Schild"
+Exact::Kerr_KerrSchild__mass = 1.0
+Exact::Kerr_KerrSchild__spin = 0.6
+
+########################################
+
+ActiveThorns = "IOUtil"
+IOUtil::parfile_write = "no"
+
+########################################
+
+ActiveThorns = "SphericalSurface"
+ActiveThorns = "AEILocalInterp AHFinderDirect"
+
+AHFinderDirect::print_timing_stats = "true"
+
+AHFinderDirect::output_Theta_every = 1
+AHFinderDirect::h_base_file_name     = "Kerr.h"
+AHFinderDirect::Theta_base_file_name = "Kerr.Theta"
+
+AHFinderDirect::N_horizons = 1
+AHFinderDirect::patch_system_type[1] = "+z hemisphere"
+AHFinderDirect::origin_x[1] = 0.5
+AHFinderDirect::origin_y[1] = 0.7
+AHFinderDirect::origin_z[1] = 0.0
+
+AHFinderDirect::initial_guess_method[1] = "coordinate sphere"
+AHFinderDirect::initial_guess__coord_sphere__x_center[1] = -0.2
+AHFinderDirect::initial_guess__coord_sphere__y_center[1] =  0.3
+AHFinderDirect::initial_guess__coord_sphere__z_center[1] =  0.0
+AHFinderDirect::initial_guess__coord_sphere__radius[1] = 2.0
diff --git a/test/Kerr-carpet/BH_diagnostics.ah1.gp b/test/Kerr-carpet/BH_diagnostics.ah1.gp
new file mode 100644
index 0000000..4bfb6ae
--- /dev/null
+++ b/test/Kerr-carpet/BH_diagnostics.ah1.gp
@@ -0,0 +1,40 @@
+# apparent horizon 1/1
+#
+# column  1 = cctk_iteration
+# column  2 = cctk_time
+# column  3 = centroid_x
+# column  4 = centroid_y
+# column  5 = centroid_z
+# column  6 = min radius
+# column  7 = max radius
+# column  8 = mean radius
+# column  9 = quadrupole_xx
+# column 10 = quadrupole_xy
+# column 11 = quadrupole_xz
+# column 12 = quadrupole_yy
+# column 13 = quadrupole_yz
+# column 14 = quadrupole_zz
+# column 15 = min x
+# column 16 = max x
+# column 17 = min y
+# column 18 = max y
+# column 19 = min z
+# column 20 = max z
+# column 21 = xy-plane circumference
+# column 22 = xz-plane circumference
+# column 23 = yz-plane circumference
+# column 24 = ratio of xz/xy-plane circumferences
+# column 25 = ratio of yz/xy-plane circumferences
+# column 26 = area
+# column 27 = irreducible mass
+# column 28 = areal radius
+# column 29 = [not implemented yet] (outer) expansion Theta_(l)
+# column 30 = [not implemented yet] inner expansion Theta_(n)
+# column 31 = [not implemented yet] product of inner and outer expansions
+# column 32 = [not implemented yet] mean curvature
+# column 33 = [not implemented yet] d/d(coordinate radius) of area
+# column 34 = [not implemented yet] d/d(coordinate radius) of (outer) expansion Theta_(l)
+# column 35 = [not implemented yet] d/d(coordinate radius) of inner expansion Theta_(n)
+# column 36 = [not implemented yet] d/d(coordinate radius) of product of inner and outer expansions
+# column 37 = [not implemented yet] d/d(coordinate radius) of mean curvature
+0	0.000000	0.000012	-0.000005	0.000000	1.037147702	2.757533954	1.996589100	1.199992441	6.349956123e-06	0.000000000	1.199980324	0.000000000	1.079986242	-1.896474015	1.896754066	-1.896898084	1.896467010	-1.799394038	1.799394038	12.56635368	10.83747889	11.22776372	0.8624203304	0.8934782524	45.23842102	0.9486779171	1.897355834	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000
diff --git a/test/Kerr-carpet/Kerr.Theta.t0.ah1.gp b/test/Kerr-carpet/Kerr.Theta.t0.ah1.gp
new file mode 100644
index 0000000..521fc85
--- /dev/null
+++ b/test/Kerr-carpet/Kerr.Theta.t0.ah1.gp
@@ -0,0 +1,1228 @@
+# N_patches = 5
+# origin = 0.5 0.7 0
+
+### +z patch
+# N_rho = 19
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn
+-45	-45	-1.39126991177685e-14
+-40	-45	-2.56170139354556e-14
+-35	-45	5.32863683733176e-15
+-30	-45	-7.55085555713408e-14
+-25	-45	-3.61030107719207e-14
+-20	-45	3.98292510084275e-15
+-15	-45	8.57468393164473e-16
+-10	-45	-4.21375174336491e-15
+-5	-45	-1.39104765033149e-14
+0	-45	-4.17996800367026e-14
+5	-45	1.75544528999844e-14
+10	-45	-1.04988880002960e-13
+15	-45	2.65084720667275e-14
+20	-45	3.86978860414389e-15
+25	-45	5.52910581902433e-15
+30	-45	-6.15306416928973e-15
+35	-45	2.50176940795599e-14
+40	-45	4.64006003758621e-15
+45	-45	1.83393881678096e-14
+
+-45	-40	2.49482238253579e-14
+-40	-40	-2.82331666726088e-15
+-35	-40	-3.70095664184444e-14
+-30	-40	2.92251032402158e-14
+-25	-40	7.48514206345974e-15
+-20	-40	-4.44375981324685e-14
+-15	-40	-1.62682367577105e-14
+-10	-40	3.04031973208385e-15
+-5	-40	4.16001326268567e-14
+0	-40	-4.13707425522131e-14
+5	-40	3.13992538567009e-14
+10	-40	1.32004867106628e-14
+15	-40	1.03432887255117e-16
+20	-40	-9.18953498366126e-15
+25	-40	-1.57709674313000e-14
+30	-40	4.21094908074904e-14
+35	-40	-3.08451723364522e-14
+40	-40	-1.68076381805438e-13
+45	-40	-1.70931628226678e-13
+
+-45	-35	-4.50330419655975e-14
+-40	-35	1.87963793835122e-14
+-35	-35	-3.74576129662241e-14
+-30	-35	3.36972203612840e-14
+-25	-35	-6.24897269346780e-14
+-20	-35	2.29010061782164e-14
+-15	-35	-4.27391683242156e-14
+-10	-35	4.58049125972443e-14
+-5	-35	3.91689718853838e-15
+0	-35	-2.58844595063534e-14
+5	-35	4.99122770024341e-14
+10	-35	2.13232751768155e-15
+15	-35	-5.82691989277351e-14
+20	-35	-2.11308835013080e-14
+25	-35	1.66710991799518e-14
+30	-35	2.35393302072673e-14
+35	-35	3.88456627975486e-14
+40	-35	-1.90028114771534e-14
+45	-35	4.26084948573768e-14
+
+-45	-30	-3.53059595448180e-14
+-40	-30	-3.37339748149312e-14
+-35	-30	4.46178738486985e-14
+-30	-30	-8.34147204434310e-15
+-25	-30	4.29972897564301e-15
+-20	-30	1.46558112867901e-14
+-15	-30	1.40254290386527e-14
+-10	-30	-1.21644773247442e-14
+-5	-30	3.89057818080130e-15
+0	-30	2.03050467065258e-14
+5	-30	1.59963188528511e-15
+10	-30	-4.82984962787980e-15
+15	-30	2.64767591531823e-15
+20	-30	9.61551259621996e-14
+25	-30	-1.74673914655338e-14
+30	-30	-1.42905706799340e-14
+35	-30	3.93610925103483e-14
+40	-30	-6.00057113372965e-15
+45	-30	1.07506234817145e-14
+
+-45	-25	4.75201746442250e-14
+-40	-25	5.22475129566963e-14
+-35	-25	-2.30948615266569e-15
+-30	-25	-4.13436103928466e-14
+-25	-25	2.19305910237333e-14
+-20	-25	1.89425840464719e-14
+-15	-25	-1.69390326418273e-15
+-10	-25	1.12643726811468e-14
+-5	-25	9.87166078048052e-16
+0	-25	-1.17269746430920e-14
+5	-25	-7.28310369912250e-14
+10	-25	5.08206215825424e-15
+15	-25	2.60698038677398e-14
+20	-25	1.48957994376697e-14
+25	-25	-3.37272798665161e-14
+30	-25	4.39151482106021e-14
+35	-25	5.05028961358955e-14
+40	-25	-1.60940054685921e-14
+45	-25	-1.16102873842783e-14
+
+-45	-20	-2.10310284812221e-14
+-40	-20	-1.70627401097079e-14
+-35	-20	3.80962080458180e-14
+-30	-20	7.62627808126304e-15
+-25	-20	4.93852192213345e-14
+-20	-20	-4.87413928662583e-15
+-15	-20	-7.80092136720700e-14
+-10	-20	-1.23932439831387e-15
+-5	-20	3.70605239205513e-14
+0	-20	-2.85463926802398e-14
+5	-20	6.34202434492137e-14
+10	-20	-1.61189692236136e-14
+15	-20	7.92012126455549e-14
+20	-20	-7.66142791569502e-14
+25	-20	5.71289706079864e-14
+30	-20	-3.71320541588810e-14
+35	-20	1.40972303275255e-14
+40	-20	-1.88361153931338e-14
+45	-20	-1.82570972229179e-14
+
+-45	-15	-3.23174104664703e-14
+-40	-15	1.07000725554224e-14
+-35	-15	1.08637057683048e-14
+-30	-15	-3.82481589802919e-14
+-25	-15	6.63379941256981e-15
+-20	-15	-6.41484478383636e-15
+-15	-15	-6.50876379702792e-15
+-10	-15	-2.85826592429095e-14
+-5	-15	1.45498305244296e-14
+0	-15	3.14859629254455e-14
+5	-15	9.05731652872666e-15
+10	-15	2.99492418712188e-14
+15	-15	-1.50817401102510e-14
+20	-15	4.06125870780483e-15
+25	-15	-3.01339357113017e-14
+30	-15	-1.24407320382935e-14
+35	-15	6.21974260289759e-15
+40	-15	2.03207676380268e-14
+45	-15	-2.10931532657055e-15
+
+-45	-10	-2.46823232425558e-14
+-40	-10	6.82950603621973e-14
+-35	-10	-1.84867583481046e-14
+-30	-10	3.00886431655462e-14
+-25	-10	-4.06245675120542e-14
+-20	-10	6.37828006556929e-15
+-15	-10	2.74595884225404e-15
+-10	-10	-6.47398801234544e-15
+-5	-10	-1.41834786103467e-14
+0	-10	-3.69538926368873e-14
+5	-10	2.99136258298527e-14
+10	-10	-8.43596026367521e-15
+15	-10	2.99148726623510e-14
+20	-10	-1.42395860727729e-14
+25	-10	7.97764090031128e-15
+30	-10	-4.55668489052208e-15
+35	-10	6.39597424502425e-14
+40	-10	3.06519675093153e-14
+45	-10	1.35164774338337e-14
+
+-45	-5	-3.85402430455595e-14
+-40	-5	-5.98577448458065e-14
+-35	-5	4.64819697489072e-14
+-30	-5	-1.17916744077351e-14
+-25	-5	6.36101414597245e-16
+-20	-5	-2.30530926379618e-14
+-15	-5	2.14999459208221e-14
+-10	-5	-2.72158055640570e-14
+-5	-5	3.43007415005980e-14
+0	-5	-3.14027775137615e-14
+5	-5	2.27308948573535e-14
+10	-5	-3.46955808267629e-14
+15	-5	1.18037253148823e-13
+20	-5	1.61409188965955e-13
+25	-5	-4.88246324880509e-14
+30	-5	2.73493792717072e-14
+35	-5	3.95485510659710e-14
+40	-5	-2.20306086741451e-14
+45	-5	-2.67900393709219e-14
+
+-45	0	-2.65308608415893e-14
+-40	0	1.61307599222393e-15
+-35	0	-5.77381024935431e-15
+-30	0	-5.68121938382404e-17
+-25	0	1.08796977503489e-15
+-20	0	1.51751170223563e-14
+-15	0	2.56138426441010e-14
+-10	0	9.40783909109122e-15
+-5	0	-1.72105710759263e-14
+0	0	-9.94205260652914e-15
+5	0	-1.16268214674087e-14
+10	0	-9.95834274417073e-15
+15	0	3.66966114613565e-14
+20	0	-2.38160457067399e-14
+25	0	2.16131908377382e-14
+30	0	-2.03537273840704e-14
+35	0	1.91705375532369e-14
+40	0	-7.53022318979168e-14
+45	0	3.23958524936496e-14
+
+-45	5	3.38444550163075e-15
+-40	5	1.53235171947153e-14
+-35	5	-1.63018199200032e-14
+-30	5	-6.52399683755134e-15
+-25	5	7.39268672320104e-15
+-20	5	-6.15980790680259e-14
+-15	5	-3.69521579134113e-14
+-10	5	-6.08380533451136e-14
+-5	5	-3.13801718984652e-14
+0	5	4.20762329058494e-14
+5	5	4.98976944832141e-15
+10	5	1.86112247575060e-14
+15	5	-2.31299354669368e-14
+20	5	7.10017981908617e-14
+25	5	8.55628502077765e-14
+30	5	-7.67859083608546e-15
+35	5	-1.25672042217140e-14
+40	5	6.58647398774082e-15
+45	5	4.33990950815533e-14
+
+-45	10	2.70793587206497e-14
+-40	10	-9.25821919128822e-15
+-35	10	5.03086613166948e-14
+-30	10	2.67620669548718e-14
+-25	10	-5.24457322188809e-14
+-20	10	-9.41992794531443e-15
+-15	10	5.12507787944760e-14
+-10	10	-3.60594800546954e-15
+-5	10	1.45026135198179e-14
+0	10	-2.09634013707133e-14
+5	10	-1.54022302724377e-14
+10	10	-6.46200757833948e-15
+15	10	-2.07221690978407e-13
+20	10	-7.08363489393404e-16
+25	10	1.15407900250220e-14
+30	10	2.85110476894168e-14
+35	10	-5.60452292214242e-14
+40	10	-1.21166640089376e-14
+45	10	5.03699187394402e-14
+
+-45	15	-2.80620795697906e-14
+-40	15	1.76542808150160e-14
+-35	15	-1.04727695699608e-14
+-30	15	-1.98037658320771e-14
+-25	15	5.15985366413008e-15
+-20	15	-2.96637714392034e-16
+-15	15	-1.48295817899852e-14
+-10	15	1.35739401489754e-15
+-5	15	1.10923369014276e-14
+0	15	3.38968761913472e-14
+5	15	-2.37759031213036e-14
+10	15	-9.04657479570276e-14
+15	15	6.42567596353949e-14
+20	15	-1.40149935927425e-14
+25	15	4.67478703317092e-14
+30	15	3.86996207649148e-14
+35	15	5.57951037802318e-14
+40	15	-1.28719734523997e-14
+45	15	-4.05069857864482e-14
+
+-45	20	5.97166630381119e-14
+-40	20	-3.42230042048308e-14
+-35	20	7.00985493609640e-15
+-30	20	-3.52058063691346e-14
+-25	20	-2.35792559522691e-14
+-20	20	3.99436343376247e-15
+-15	20	-2.55050158510378e-14
+-10	20	-6.65772775451656e-14
+-5	20	3.58664920679930e-14
+0	20	-2.34472543377690e-14
+5	20	-6.52769938797038e-14
+10	20	-3.77220498760933e-14
+15	20	-1.93665070959137e-14
+20	20	8.54459190034740e-14
+25	20	-5.58164083529211e-14
+30	20	2.06951426481861e-14
+35	20	5.67112546159820e-14
+40	20	-5.08707659330199e-15
+45	20	-9.75909891093307e-14
+
+-45	25	8.75748041792579e-15
+-40	25	-1.51545984962420e-14
+-35	25	-1.27593248466784e-14
+-30	25	1.63912937042876e-14
+-25	25	3.47241224489536e-14
+-20	25	2.14507773522998e-14
+-15	25	1.16245446428465e-14
+-10	25	-1.23358354781056e-14
+-5	25	-7.83563752076999e-15
+0	25	2.30543123654059e-14
+5	25	-2.72795566517992e-14
+10	25	-1.64685973191858e-14
+15	25	-2.10094528579896e-14
+20	25	1.08115773278517e-13
+25	25	3.10653195875754e-14
+30	25	-1.63747054110486e-14
+35	25	-3.50894443709726e-14
+40	25	-1.02279838244679e-14
+45	25	1.56636531002674e-13
+
+-45	30	-2.18649967922979e-14
+-40	30	4.77445231787665e-14
+-35	30	-1.25561453595546e-15
+-30	30	-4.46165999111459e-14
+-25	30	-3.42838821568159e-14
+-20	30	1.20842138379151e-13
+-15	30	2.80290114035298e-14
+-10	30	4.28734738683323e-14
+-5	30	-2.56084216332386e-14
+0	30	-2.82338171939123e-14
+5	30	3.34333255525010e-14
+10	30	1.59508582557588e-13
+15	30	-3.99070425143033e-14
+20	30	3.78785544596916e-14
+25	30	-2.38544535687002e-14
+30	30	6.34399217186443e-15
+35	30	1.54370873722831e-14
+40	30	2.34222363726388e-14
+45	30	-1.38309611159848e-13
+
+-45	35	5.68940511022631e-15
+-40	35	-6.75093119427428e-14
+-35	35	-1.74296341248770e-15
+-30	35	3.86236181926236e-14
+-25	35	-5.60561796633663e-14
+-20	35	-2.28088489935552e-14
+-15	35	-4.09329688200177e-15
+-10	35	-5.98282274416606e-14
+-5	35	-1.63346983508839e-14
+0	35	-1.00861701803068e-14
+5	35	-6.37804696210220e-14
+10	35	-2.49854390649284e-15
+15	35	2.08223195630186e-14
+20	35	4.55625120965308e-15
+25	35	6.73769850675909e-14
+30	35	4.06913543658793e-14
+35	35	-3.43687751869215e-14
+40	35	4.37814931877889e-14
+45	35	1.35115009458620e-13
+
+-45	40	1.58454521205498e-14
+-40	40	8.84363112255149e-14
+-35	40	-1.52895816667165e-14
+-30	40	-1.14323698077734e-14
+-25	40	4.89456565555546e-14
+-20	40	-1.35834269179846e-14
+-15	40	1.00277858933184e-14
+-10	40	7.36969079512262e-14
+-5	40	9.88803223328505e-15
+0	40	5.72149749453188e-15
+5	40	4.41959294682215e-14
+10	40	-6.60583783854141e-14
+15	40	-6.49676709998936e-14
+20	40	8.71317449614717e-14
+25	40	-1.79614461325028e-13
+30	40	-5.34703032718797e-14
+35	40	-2.96302695920736e-14
+40	40	9.06023303257064e-14
+45	40	-7.26871362578818e-14
+
+-45	45	-5.81928168846835e-14
+-40	45	-3.26088440104344e-14
+-35	45	1.59860189322125e-14
+-30	45	3.22858601832510e-14
+-25	45	-7.19526977062401e-14
+-20	45	6.55978093025422e-14
+-15	45	-1.32883992438187e-13
+-10	45	-3.19058473217948e-14
+-5	45	6.40695721303153e-14
+0	45	-3.12178668332441e-14
+5	45	-2.05743625261712e-15
+10	45	6.74078306193981e-14
+15	45	5.92881863395456e-14
+20	45	-3.01275931285927e-14
+25	45	6.21575273890285e-14
+30	45	-2.39418944739112e-14
+35	45	1.94832268807926e-13
+40	45	-1.16532326323304e-13
+45	45	-4.62269653979386e-14
+
+
+### +x patch
+# N_rho = 10
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn
+45	-45	-1.08297160301973e-14
+45	-40	1.01255321401789e-13
+45	-35	2.26362982178041e-14
+45	-30	-2.01932654625425e-16
+45	-25	-9.14547300737145e-14
+45	-20	5.16692808330554e-14
+45	-15	-5.31240633080965e-14
+45	-10	5.79500640182640e-14
+45	-5	-3.18217674433185e-14
+45	0	1.94840346114111e-14
+45	5	-1.75978480919381e-14
+45	10	-4.38049661648232e-14
+45	15	5.78225618427797e-14
+45	20	4.59120588769402e-14
+45	25	-5.99518264893240e-14
+45	30	5.03358205811155e-14
+45	35	-2.40738418783026e-14
+45	40	4.28924474063508e-14
+45	45	2.98987722600896e-14
+
+50	-45	3.19687852579076e-14
+50	-40	-5.06181468268307e-14
+50	-35	-2.48205861246020e-14
+50	-30	4.53025204155688e-14
+50	-25	1.06895828994036e-14
+50	-20	1.15476313407303e-13
+50	-15	4.69121811709494e-14
+50	-10	-5.29231606455349e-15
+50	-5	-1.50926363420845e-14
+50	0	1.31459513413867e-15
+50	5	-4.67877689716567e-14
+50	10	1.04075168622098e-13
+50	15	-1.74448129552918e-15
+50	20	-4.90451321048802e-14
+50	25	9.89150168023700e-15
+50	30	6.00583493527707e-14
+50	35	-4.15027170616589e-15
+50	40	1.38105672731204e-15
+50	45	-1.32719573178730e-13
+
+55	-45	-8.15737993646592e-14
+55	-40	2.72782013990835e-14
+55	-35	-3.79562917554588e-15
+55	-30	-7.21308863332881e-15
+55	-25	-3.51720605765160e-15
+55	-20	-2.81079955317953e-14
+55	-15	-1.32966554433622e-14
+55	-10	-3.81959546456867e-14
+55	-5	-3.92655742989523e-14
+55	0	3.53769747871158e-14
+55	5	-3.64909925193446e-14
+55	10	-3.86357070468468e-14
+55	15	8.35595698536751e-14
+55	20	1.41479709891978e-14
+55	25	-6.49196950537612e-14
+55	30	5.83010202614975e-14
+55	35	-3.77909509241547e-15
+55	40	1.39410510045790e-14
+55	45	5.68755112451136e-14
+
+60	-45	4.95501534768239e-14
+60	-40	-5.84157288513465e-15
+60	-35	1.83808046907985e-14
+60	-30	-2.76359881160038e-14
+60	-25	4.65000217150791e-14
+60	-20	6.33454877094208e-14
+60	-15	-1.11733810138209e-13
+60	-10	-1.40731610392963e-14
+60	-5	1.09818295949971e-14
+60	0	6.27612111586684e-15
+60	5	-4.41293594548309e-14
+60	10	2.43764969147520e-14
+60	15	-6.63851027100926e-14
+60	20	2.35714225915729e-14
+60	25	1.23459619263966e-13
+60	30	-8.08230435703217e-14
+60	35	-2.68117776244803e-15
+60	40	3.10473218315122e-14
+60	45	9.24271510022168e-15
+
+65	-45	-3.82859976361116e-14
+65	-40	-1.79448469972421e-14
+65	-35	-6.80738018038474e-15
+65	-30	4.35949019939041e-14
+65	-25	-3.68064411414293e-14
+65	-20	-2.66298484999372e-14
+65	-15	3.16512224415866e-14
+65	-10	3.22771323557625e-14
+65	-5	-4.84529950883772e-14
+65	0	4.90524504695444e-14
+65	5	-2.53453941861936e-15
+65	10	2.40602893511466e-14
+65	15	6.94898240512221e-14
+65	20	1.53312150301399e-14
+65	25	-3.81639164714898e-15
+65	30	6.53979908421531e-14
+65	35	-1.47507602920455e-13
+65	40	1.10408644032889e-13
+65	45	3.25519233963789e-14
+
+70	-45	-8.69123566518692e-15
+70	-40	2.57077887623469e-14
+70	-35	-9.10843666115935e-15
+70	-30	-6.48211952863909e-15
+70	-25	6.47653588745079e-15
+70	-20	-1.22127785315285e-14
+70	-15	2.03808324383825e-14
+70	-10	-1.83393881678096e-14
+70	-5	2.14989701388668e-14
+70	0	-3.06111472975212e-14
+70	5	1.71873691494351e-14
+70	10	-9.09107316336699e-14
+70	15	-2.70812560744516e-14
+70	20	2.72858992345082e-14
+70	25	-2.27150112955266e-14
+70	30	-5.05573772950629e-14
+70	35	1.16098320193658e-13
+70	40	-4.16422538812578e-14
+70	45	-1.18549972356191e-13
+
+75	-45	1.84273169639981e-14
+75	-40	-1.87369651044600e-14
+75	-35	-1.40747331324464e-14
+75	-30	2.13005611413020e-14
+75	-25	-2.41288109284477e-14
+75	-20	-4.01431275373620e-14
+75	-15	-8.77152083605948e-15
+75	-10	5.51507082190150e-14
+75	-5	-9.55407628011606e-14
+75	0	-2.31955296983721e-14
+75	5	2.13065242532506e-14
+75	10	-3.09016050595301e-14
+75	15	-7.73410740832758e-14
+75	20	-1.70254435549744e-14
+75	25	-3.49565211846259e-14
+75	30	1.10873224663799e-14
+75	35	-2.50938592821770e-16
+75	40	-1.37621088570211e-13
+75	45	-7.08081596828558e-15
+
+80	-45	2.94184164875699e-14
+80	-40	7.07496127655416e-14
+80	-35	-3.56482421706716e-14
+80	-30	-8.23012448122884e-15
+80	-25	-8.83342878010840e-15
+80	-20	4.56555366429301e-14
+80	-15	-6.51455885763985e-14
+80	-10	-1.27754794590484e-14
+80	-5	3.71910076520099e-14
+80	0	1.04371806336490e-14
+80	5	-9.57773357151970e-15
+80	10	4.68205660873744e-14
+80	15	3.24876844176591e-14
+80	20	-1.35950278812302e-14
+80	25	1.01665637713966e-13
+80	30	-7.35690805150901e-15
+80	35	2.60690449262191e-14
+80	40	-3.33867048590841e-14
+80	45	4.66996775451423e-14
+
+85	-45	-1.86996143396179e-14
+85	-40	-1.46331514613851e-14
+85	-35	2.83280885728099e-14
+85	-30	-3.15928923647069e-14
+85	-25	-4.99392736365289e-14
+85	-20	-3.01076438086190e-14
+85	-15	2.93798731003381e-14
+85	-10	-3.57108548461327e-14
+85	-5	3.62002637067926e-14
+85	0	-6.49078772500811e-14
+85	5	5.05194844291346e-14
+85	10	-6.90657925815630e-14
+85	15	-1.30515010691307e-13
+85	20	3.26288475405168e-14
+85	25	1.01614788632076e-13
+85	30	-7.89797914568791e-15
+85	35	-5.69404007451368e-14
+85	40	-2.23368415777636e-14
+85	45	6.41743060601774e-14
+
+90	-45	-3.47535585379366e-15
+90	-40	2.05913302901706e-14
+90	-35	-2.65327039852825e-14
+90	-30	1.64679467978823e-14
+90	-25	-9.61307856234273e-15
+90	-20	-1.96674274088871e-16
+90	-15	-3.26995375221628e-14
+90	-10	6.41302332418658e-14
+90	-5	-7.50866382959181e-14
+90	0	7.92468304519622e-14
+90	5	-1.03337043783069e-13
+90	10	5.16349116241877e-14
+90	15	3.96152294995789e-14
+90	20	-1.18257400399946e-13
+90	25	-4.32303932235145e-14
+90	30	3.75199545911420e-14
+90	35	-1.02498847083521e-14
+90	40	4.15958500282754e-14
+90	45	-8.99308839202861e-14
+
+
+### +y patch
+# N_rho = 10
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn
+45	45	-2.72623178372566e-14
+40	45	5.58000911102252e-15
+35	45	5.78053230282372e-15
+30	45	-1.24617113503311e-14
+25	45	3.88588900640530e-15
+20	45	-5.32460360525011e-14
+15	45	3.48527630367190e-14
+10	45	1.49185134731833e-14
+5	45	-2.29615588695498e-14
+0	45	8.86259381854826e-14
+-5	45	-9.35597628017037e-14
+-10	45	7.30886163223532e-14
+-15	45	-6.41771791959345e-15
+-20	45	-2.83703182474282e-14
+-25	45	8.43329312633090e-14
+-30	45	-7.09727957827477e-14
+-35	45	-1.10070372955073e-14
+-40	45	1.28868270221627e-15
+-45	45	-2.26827020707865e-14
+
+45	50	-9.07777542372146e-14
+40	50	1.28586919757867e-13
+35	50	-7.88985847141599e-14
+30	50	1.01571854226046e-14
+25	50	-7.28387077215953e-14
+20	50	7.74017351948264e-14
+15	50	-6.14149573210931e-14
+10	50	-5.81879921850159e-14
+5	50	6.31687627553057e-14
+0	50	-4.04686050295422e-14
+-5	50	8.82323727968704e-14
+-10	50	1.16199367836134e-15
+-15	50	-4.01819419751370e-14
+-20	50	6.27886414736323e-14
+-25	50	-7.37312771600940e-14
+-30	50	3.72950368504599e-14
+-35	50	1.33394814291754e-14
+-40	50	-6.47995112429411e-15
+-45	50	1.46731585215498e-14
+
+45	55	-1.79364444304053e-14
+40	55	-2.06223926824123e-14
+35	55	3.65333848242888e-14
+30	55	1.80174885427986e-14
+25	55	-8.01471519359942e-14
+20	55	3.77038894897042e-14
+15	55	1.20103579859254e-14
+10	55	9.41185606014028e-14
+5	55	-2.16419764054177e-14
+0	55	-3.35282474527021e-14
+-5	55	-5.48214360192312e-14
+-10	55	3.95648683086669e-14
+-15	55	-1.51249997769332e-14
+-20	55	-1.82444174785107e-13
+-25	55	-1.50498699873908e-13
+-30	55	2.13407362528034e-13
+-35	55	-4.64875533900955e-14
+-40	55	2.61381086046064e-14
+-45	55	8.26216265542579e-14
+
+45	60	4.43605655681134e-14
+40	60	-9.42293660634308e-14
+35	60	1.29432055351320e-15
+30	60	-7.63317902809091e-14
+25	60	9.58176138259048e-14
+20	60	4.90505531157426e-14
+15	60	5.55771791435622e-14
+10	60	-1.19669465309391e-13
+5	60	2.48647131530222e-14
+0	60	1.50508945584438e-14
+-5	60	1.68224809082851e-14
+-10	60	-3.60716231190272e-14
+-15	60	1.81993417731896e-13
+-20	60	4.14235703030674e-14
+-25	60	9.38057682746407e-14
+-30	60	5.81761201712272e-15
+-35	60	-6.64656589315082e-14
+-40	60	1.90920413159490e-14
+-45	60	-1.92014373151528e-14
+
+45	65	1.74430890738375e-13
+40	65	-9.04063607830297e-14
+35	65	6.87735458859695e-14
+30	65	4.39701443658014e-14
+25	65	-1.06585205071619e-13
+20	65	-1.09231905204982e-13
+15	65	4.44442659758293e-14
+10	65	5.89306706731685e-14
+5	65	4.24782821764613e-14
+0	65	-4.50839994677044e-14
+-5	65	9.85836846184585e-14
+-10	65	2.81394373947974e-14
+-15	65	5.89344653807722e-14
+-20	65	4.04310916343742e-14
+-25	65	-2.01936449333029e-14
+-30	65	3.33609008473790e-16
+-35	65	2.97537602195197e-14
+-40	65	-2.66290895584165e-15
+-45	65	2.13766179237018e-14
+
+45	70	3.60009331373812e-16
+40	70	-7.50093346810199e-14
+35	70	-7.11416602711124e-14
+30	70	-1.83200351590307e-14
+25	70	-1.31402213329052e-13
+20	70	3.88469096300470e-14
+15	70	8.54297101809953e-16
+10	70	-1.02960391948348e-13
+5	70	-9.14811846067232e-15
+0	70	-5.21436192835179e-15
+-5	70	-5.77691106756761e-14
+-10	70	-2.83399605865986e-14
+-15	70	-1.69796902232955e-14
+-20	70	-5.62237431091239e-14
+-25	70	2.92265127030400e-14
+-30	70	-1.66172956471422e-14
+-35	70	-4.13120601096273e-14
+-40	70	-4.70371354713284e-14
+-45	70	2.51939311426974e-14
+
+45	75	-1.94982918699793e-14
+40	75	1.05039729084849e-13
+35	75	1.03201843772160e-13
+30	75	2.72160766146001e-14
+25	75	-7.14532599754847e-15
+20	75	-4.08224886186415e-14
+15	75	3.39447437172624e-14
+10	75	9.33469339152448e-14
+5	75	-2.01729366718084e-14
+0	75	2.59940723459917e-14
+-5	75	1.47505705566653e-14
+-10	75	8.15374243817724e-14
+-15	75	1.31674185444020e-14
+-20	75	4.28312984038226e-14
+-25	75	-3.16327910046543e-14
+-30	75	2.38533151564191e-14
+-35	75	-4.65111889974557e-15
+-40	75	2.16529214263489e-13
+-45	75	-4.05946977422023e-14
+
+45	80	8.34508243757748e-14
+40	80	3.18108712114851e-14
+35	80	5.29277685047680e-14
+30	80	-9.49468368510731e-15
+25	80	-1.73264831301867e-13
+20	80	-1.30713690739415e-13
+15	80	-1.02269972004909e-13
+10	80	6.39171875149724e-14
+5	80	-1.89147742607476e-14
+0	80	-3.03511556165592e-14
+-5	80	2.36951300594535e-14
+-10	80	-2.92555693212626e-15
+-15	80	-1.41767023467687e-14
+-20	80	-5.66825774685198e-14
+-25	80	-1.21884219297236e-13
+-30	80	1.63821864060387e-14
+-35	80	-3.81815889669013e-14
+-40	80	-4.16972771415114e-14
+-45	80	2.09297639983119e-14
+
+45	85	-1.01008882247983e-13
+40	85	-3.89991858251726e-14
+35	85	-1.40963087556789e-13
+30	85	1.32274182926273e-13
+25	85	3.63676103121158e-14
+20	85	1.67169934579131e-13
+15	85	3.11408342688890e-14
+10	85	-6.11108386117110e-14
+5	85	-3.61223095705909e-14
+0	85	8.10371734993875e-14
+-5	85	-3.70140116473516e-14
+-10	85	2.85329485733010e-15
+-15	85	1.40612890255076e-14
+-20	85	5.54851303791182e-15
+-25	85	2.76119188277746e-14
+-30	85	-5.97509238267624e-15
+-35	85	5.60990598592881e-14
+-40	85	3.12375993127834e-14
+-45	85	-3.92139662755420e-15
+
+45	90	-2.73110527249099e-14
+40	90	1.27187756854275e-13
+35	90	8.35779470804987e-14
+30	90	-6.70275467073989e-15
+25	90	4.15330205123798e-14
+20	90	-8.71407980496119e-14
+15	90	-3.70366172626480e-14
+10	90	7.89806588186170e-14
+5	90	3.70721790939055e-14
+0	90	-8.89431215310432e-14
+-5	90	8.66711216684912e-14
+-10	90	-4.60113717959398e-15
+-15	90	3.31689428527404e-14
+-20	90	-2.69695832506855e-14
+-25	90	4.55213124139764e-15
+-30	90	3.04846209039922e-14
+-35	90	-6.91423372549405e-14
+-40	90	-4.39491108436552e-14
+-45	90	5.59152333809432e-14
+
+
+### -x patch
+# N_rho = 10
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn
+-90	45	-4.55375754465637e-15
+-90	40	-3.02880550501206e-14
+-90	35	-2.54721916302658e-14
+-90	30	4.55122593258361e-14
+-90	25	-5.07829455570485e-15
+-90	20	5.11316249757199e-14
+-90	15	-3.64188930748743e-14
+-90	10	2.58262378496910e-15
+-90	5	2.29422600708795e-14
+-90	-2.84217e-14	-4.93984193827846e-15
+-90	-5	-1.96125667789593e-14
+-90	-10	1.01400008181707e-14
+-90	-15	-4.39864073983887e-14
+-90	-20	-7.38509730799364e-15
+-90	-25	3.75681473777090e-15
+-90	-30	9.49641840858328e-15
+-90	-35	-1.22881305825162e-14
+-90	-40	4.36813671171599e-14
+-90	-45	5.28190772369763e-15
+
+-85	45	7.62661418393651e-14
+-85	40	4.13026817608353e-16
+-85	35	3.90478665027172e-14
+-85	30	-1.86893686290879e-14
+-85	25	6.12368229041538e-15
+-85	20	-1.80461656902609e-14
+-85	15	5.87951454016078e-14
+-85	10	-2.65074420746636e-14
+-85	5	-1.52215479803930e-14
+-85	-2.84217e-14	3.66579054437988e-14
+-85	-5	-2.94654708618558e-14
+-85	-10	-3.91505404484516e-16
+-85	-15	-3.91771034016775e-14
+-85	-20	4.08457447552413e-14
+-85	-25	-1.32837534375096e-14
+-85	-30	-2.45957768041372e-14
+-85	-35	-1.49279460320839e-14
+-85	-40	2.43088969092975e-15
+-85	-45	-1.10258482032000e-14
+
+-80	45	9.12719335874335e-15
+-80	40	2.28551606893529e-13
+-80	35	6.12899488106056e-16
+-80	30	6.68177535870229e-15
+-80	25	1.08073272553355e-15
+-80	20	2.37358960611389e-14
+-80	15	-1.41457158486791e-13
+-80	10	6.27861478086356e-15
+-80	5	5.80145740475269e-15
+-80	-2.84217e-14	6.69695418911709e-15
+-80	-5	9.32755392021867e-15
+-80	-10	-1.15603056641267e-14
+-80	-15	2.79829328111991e-14
+-80	-20	-1.28115833913922e-14
+-80	-25	3.80675851084644e-14
+-80	-30	3.02687562514503e-14
+-80	-35	2.38498457094671e-14
+-80	-40	2.86887484254872e-14
+-80	-45	1.68005420773248e-13
+
+-75	45	-6.35771817136810e-14
+-75	40	-2.52741621034613e-14
+-75	35	5.93270007773206e-14
+-75	30	1.25894845763586e-14
+-75	25	2.60809169400078e-14
+-75	20	-2.62652855194390e-14
+-75	15	7.88925131819940e-15
+-75	10	-6.48880363503246e-14
+-75	5	-6.62298449589926e-14
+-75	-2.84217e-14	4.05523759103993e-13
+-75	-5	5.87545420302482e-15
+-75	-10	-6.94420649455241e-15
+-75	-15	-2.73267736564109e-14
+-75	-20	1.22355467771507e-14
+-75	-25	-9.60006813627290e-15
+-75	-30	-2.70198902314889e-14
+-75	-35	-2.90432825358899e-14
+-75	-40	2.15639680591073e-14
+-75	-45	-1.04893307581455e-14
+
+-70	45	5.75845794659191e-14
+-70	40	8.82789934902872e-15
+-70	35	1.12477843879077e-14
+-70	30	7.27076818890504e-15
+-70	25	-6.35662312717389e-14
+-70	20	-6.85524770629997e-15
+-70	15	5.55154880399478e-15
+-70	10	1.15448015730601e-14
+-70	5	-6.71511457550622e-15
+-70	-2.84217e-14	3.21817225645837e-14
+-70	-5	-2.77590450625809e-14
+-70	-10	-5.78627857433789e-15
+-70	-15	1.96576695893347e-15
+-70	-20	2.26549464951709e-15
+-70	-25	2.72877423782014e-14
+-70	-30	1.79002320778443e-14
+-70	-35	3.68711680111267e-14
+-70	-40	-4.14888934839597e-14
+-70	-45	-6.23806561961260e-15
+
+-65	45	3.66004969387657e-15
+-65	40	1.16038905914606e-14
+-65	35	-1.48244589347202e-14
+-65	30	-1.38872203667151e-14
+-65	25	1.02093355471011e-14
+-65	20	1.08741141091606e-14
+-65	15	-1.03324467037869e-14
+-65	10	-1.04635267464404e-14
+-65	5	-1.41386468505145e-14
+-65	-2.84217e-14	6.90474153547393e-15
+-65	-5	2.58847847670052e-14
+-65	-10	-1.39012933109139e-13
+-65	-15	5.71949172051278e-15
+-65	-20	1.32104071605410e-14
+-65	-25	9.87702758123432e-15
+-65	-30	-2.52516106982736e-15
+-65	-35	-3.38986651249318e-15
+-65	-40	4.29320207856465e-14
+-65	-45	-9.55333902263877e-15
+
+-60	45	-3.93214649209439e-14
+-60	40	9.23772777022824e-15
+-60	35	-1.38162593345259e-14
+-60	30	1.35944315700354e-14
+-60	25	2.76765372772547e-14
+-60	20	-3.79579722688261e-14
+-60	15	1.80367331313602e-14
+-60	10	-2.99104274334439e-15
+-60	5	1.03954171659648e-13
+-60	-2.84217e-14	6.47555468448469e-14
+-60	-5	1.11150238318869e-14
+-60	-10	-1.55374844934553e-14
+-60	-15	1.82948274585204e-15
+-60	-20	-1.37641092100294e-14
+-60	-25	3.79995297380975e-13
+-60	-30	-3.81921057279744e-15
+-60	-35	-3.76802538823440e-14
+-60	-40	-2.65923893148778e-14
+-60	-45	-3.07566472290688e-14
+
+-55	45	5.43557169760400e-14
+-55	40	6.15214259744312e-15
+-55	35	1.42487475811304e-14
+-55	30	-4.90243696332771e-15
+-55	25	-1.33175805452912e-14
+-55	20	4.32952285134292e-14
+-55	15	1.12301661026049e-15
+-55	10	-2.94113691734488e-14
+-55	5	9.99515140792662e-15
+-55	-2.84217e-14	-5.37286686495830e-14
+-55	-5	-2.73088301104563e-14
+-55	-10	3.12882315542384e-14
+-55	-15	4.04790133703981e-14
+-55	-20	1.16628169795352e-14
+-55	-25	-3.17246229286638e-14
+-55	-30	2.45991920409805e-14
+-55	-35	-2.03555705277636e-14
+-55	-40	-2.31157324184772e-14
+-55	-45	-3.90100278468974e-14
+
+-50	45	-2.31859887192543e-14
+-50	40	-4.68192650447674e-14
+-50	35	-7.55645546135497e-15
+-50	30	-1.41874901583849e-14
+-50	25	2.73053064533957e-14
+-50	20	-3.65613030302303e-14
+-50	15	-1.30015356120117e-14
+-50	10	2.62695139079117e-14
+-50	5	-6.33392535469290e-14
+-50	-2.84217e-14	6.70907556940548e-14
+-50	-5	-1.63660317936687e-16
+-50	-10	2.40963390733817e-14
+-50	-15	-3.88595405853565e-14
+-50	-20	6.43345240362164e-14
+-50	-25	6.38904077213120e-15
+-50	-30	2.33861595453494e-14
+-50	-35	-4.91179904908712e-14
+-50	-40	1.04391403290757e-13
+-50	-45	2.42234617781056e-14
+
+-45	45	6.29981635434651e-14
+-45	40	-3.40774500631746e-14
+-45	35	-2.89281402651720e-15
+-45	30	9.57003573609505e-15
+-45	25	-1.64885466391596e-14
+-45	20	-3.86073551600363e-15
+-45	15	3.95752766495228e-14
+-45	10	1.54674721381670e-14
+-45	5	2.20047775573856e-14
+-45	-2.84217e-14	-7.93312898011989e-14
+-45	-5	1.35682914556567e-13
+-45	-10	-8.27422711510012e-14
+-45	-15	6.11326310753779e-14
+-45	-20	-1.18221404887819e-14
+-45	-25	8.17922118923065e-16
+-45	-30	-2.91187972172036e-14
+-45	-35	-2.52732947417234e-14
+-45	-40	4.78798316098927e-14
+-45	-45	-4.23012319616944e-14
+
+
+### -y patch
+# N_rho = 10
+# N_sigma = 19
+# nominal_gfn=44
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn
+-45	-90	3.55087053510728e-15
+-40	-90	-7.60822611509115e-15
+-35	-90	-2.26239925231464e-14
+-30	-90	-4.61132868001535e-15
+-25	-90	-2.40221796447837e-14
+-20	-90	3.77238930197865e-14
+-15	-90	6.68735899989059e-16
+-10	-90	-2.78263198073836e-14
+-5	-90	-1.42692390021903e-14
+-2.84217e-14	-90	-1.63289520793697e-14
+5	-90	4.59701721133854e-17
+10	-90	3.36736389640324e-14
+15	-90	2.31856634586025e-15
+20	-90	-1.25604821682446e-15
+25	-90	1.34657909822700e-15
+30	-90	-2.69946283208700e-14
+35	-90	5.31888985980111e-14
+40	-90	-2.44041982802590e-14
+45	-90	-3.14824121633306e-14
+
+-45	-85	2.19328136381869e-14
+-40	-85	3.73480543366944e-15
+-35	-85	2.35737536262437e-14
+-30	-85	-1.53118078112524e-14
+-25	-85	2.47706802986025e-13
+-20	-85	-1.20714527783450e-14
+-15	-85	2.34551961186824e-14
+-10	-85	-6.72183662897563e-15
+-5	-85	2.30411393090102e-14
+-2.84217e-14	-85	-2.94585861780605e-14
+5	-85	1.20911310477756e-14
+10	-85	1.54704807991957e-15
+15	-85	5.61289296291401e-14
+20	-85	5.80536053257363e-16
+25	-85	-3.98466524532959e-14
+30	-85	-5.33974448858887e-14
+35	-85	5.13069404670108e-14
+40	-85	1.12062052345929e-14
+45	-85	1.54790459963583e-14
+
+-45	-80	1.41273657269098e-13
+-40	-80	7.04421330294247e-14
+-35	-80	2.14541925891432e-15
+-30	-80	-2.34852285188603e-14
+-25	-80	-1.64945097511082e-14
+-20	-80	-1.84418994832181e-14
+-15	-80	3.96194578880515e-14
+-10	-80	6.38016115633855e-14
+-5	-80	-9.27984902462931e-14
+-2.84217e-14	-80	1.10273660862414e-14
+5	-80	3.66324809028540e-15
+10	-80	-2.03921081409764e-14
+15	-80	-4.21912396512958e-14
+20	-80	1.60571859628145e-13
+25	-80	-7.97615012232411e-15
+30	-80	-6.84294201164226e-15
+35	-80	7.74147456208962e-15
+40	-80	-7.46331165271674e-14
+45	-80	-2.52321492692775e-14
+
+-45	-75	-7.82631338208661e-15
+-40	-75	-2.93189409382444e-14
+-35	-75	9.48129378827711e-15
+-30	-75	3.04904755957236e-15
+-25	-75	9.85973455658318e-16
+-20	-75	7.70520799941998e-15
+-15	-75	8.87809790961480e-15
+-10	-75	1.60277607158532e-15
+-5	-75	-3.47470533249017e-15
+-2.84217e-14	-75	3.42391046070922e-16
+5	-75	-1.61277241561564e-14
+10	-75	2.39706800415906e-14
+15	-75	4.86216969464159e-14
+20	-75	-3.90960050791755e-14
+25	-75	-5.13586569106383e-16
+30	-75	1.32821271342509e-14
+35	-75	2.54016642789456e-14
+40	-75	-2.16488068791043e-14
+45	-75	-9.49761103097302e-15
+
+-45	-70	2.96366663848913e-14
+-40	-70	-3.74162506533438e-14
+-35	-70	3.77637916597340e-14
+-30	-70	-4.56585181989044e-14
+-25	-70	2.59020777916563e-14
+-20	-70	-1.88573115456059e-14
+-15	-70	-1.20208205368899e-14
+-10	-70	-1.22731685925359e-16
+-5	-70	-2.65595108839972e-13
+-2.84217e-14	-70	-7.36982089938332e-14
+5	-70	2.51060023465088e-14
+10	-70	-3.48658818830061e-14
+15	-70	7.25951959136550e-14
+20	-70	-3.84507963663294e-14
+25	-70	4.25022430444733e-14
+30	-70	5.03658529812934e-14
+35	-70	4.74318392722217e-14
+40	-70	4.25077724755529e-15
+45	-70	-5.59527467761112e-14
+
+-45	-65	6.34968423326998e-15
+-40	-65	-3.29494461229207e-14
+-35	-65	2.45338688600882e-15
+-30	-65	1.22474187909394e-14
+-25	-65	-1.30880549453760e-14
+-20	-65	2.12263475025953e-14
+-15	-65	1.88626783463597e-14
+-10	-65	1.31366272027034e-14
+-5	-65	2.67910151528772e-14
+-2.84217e-14	-65	2.40299316903170e-14
+5	-65	-2.12282448563972e-14
+10	-65	3.12862799903280e-14
+15	-65	-1.98924535697864e-14
+20	-65	-1.96405934051180e-14
+25	-65	1.57088589098492e-13
+30	-65	-7.47502103617959e-14
+35	-65	-2.68822507656918e-14
+40	-65	-1.33657733318582e-14
+45	-65	5.73044216245489e-14
+
+-45	-60	-2.69036637585984e-14
+-40	-60	1.95264811264639e-16
+-35	-60	8.98982494348943e-15
+-30	-60	3.10181025829637e-14
+-25	-60	3.81048274530893e-15
+-20	-60	-6.00539041238635e-14
+-15	-60	3.86456274967251e-14
+-10	-60	-1.28388510760302e-14
+-5	-60	-6.27788836540799e-14
+-2.84217e-14	-60	1.32746461392608e-14
+5	-60	3.03591787126356e-14
+10	-60	-3.95748429686538e-14
+15	-60	1.19983233418108e-14
+20	-60	2.99756964042275e-14
+25	-60	8.48550830295780e-15
+30	-60	-4.29618363453899e-14
+35	-60	1.35979552270959e-14
+40	-60	-6.31146610668987e-15
+45	-60	-6.21161108660395e-15
+
+-45	-55	-3.79652906334904e-14
+-40	-55	1.47117561188903e-14
+-35	-55	-5.60112936934254e-14
+-30	-55	-3.69225049839939e-15
+-25	-55	7.31883900272762e-14
+-20	-55	1.52354528732551e-14
+-15	-55	-2.41257480573104e-14
+-10	-55	1.21238468483303e-14
+-5	-55	5.76680088230919e-14
+-2.84217e-14	-55	-3.64779820932748e-15
+5	-55	-4.12809977173856e-14
+10	-55	6.30450552874251e-14
+15	-55	2.37196330285516e-15
+20	-55	-2.04928305228003e-14
+25	-55	3.03055649152062e-14
+30	-55	-2.09148020083316e-15
+35	-55	-4.76777905350501e-16
+40	-55	2.70144150105178e-14
+45	-55	-7.50896740620011e-15
+
+-45	-50	-4.43929832130707e-14
+-40	-50	1.23110072483557e-14
+-35	-50	1.05808103164490e-14
+-30	-50	-5.43904385506139e-14
+-25	-50	-3.58496327242108e-14
+-20	-50	3.55494171426496e-14
+-15	-50	2.84078045375419e-14
+-10	-50	7.52024310879396e-15
+-5	-50	3.19549616802084e-15
+-2.84217e-14	-50	1.84162689438605e-13
+5	-50	3.03298510438699e-14
+10	-50	2.91433001863017e-14
+15	-50	7.21669360555233e-14
+20	-50	4.39213552680395e-14
+25	-50	-1.61633401975225e-13
+30	-50	2.63631347655058e-14
+35	-50	-1.80267042612647e-14
+40	-50	-1.30363385017485e-14
+45	-50	-7.18359833423721e-15
+
+-45	-45	2.14102824011575e-16
+-40	-45	-1.15132512898408e-14
+-35	-45	-5.02884409461779e-14
+-30	-45	-2.11775584048335e-14
+-25	-45	9.36416742758350e-14
+-20	-45	-1.97382529158047e-14
+-15	-45	-1.55838612413833e-14
+-10	-45	-2.93232506418800e-14
+-5	-45	1.37942771354788e-14
+-2.84217e-14	-45	1.36182298077214e-14
+5	-45	1.29870073029004e-14
+10	-45	1.12897430119829e-14
+15	-45	6.23392938832457e-14
+20	-45	-8.84510834801150e-14
+25	-45	6.78258447669999e-14
+30	-45	-7.29716851180506e-15
+35	-45	-1.25423217818554e-14
+40	-45	-1.74549502456045e-14
+45	-45	4.32388500004599e-14
+
+
diff --git a/test/Kerr-carpet/Kerr.h.ah1.dx b/test/Kerr-carpet/Kerr.h.ah1.dx
new file mode 100644
index 0000000..42d895a
--- /dev/null
+++ b/test/Kerr-carpet/Kerr.h.ah1.dx
@@ -0,0 +1,15 @@
+# list the size of each patch (N_rho x N_sigma)
+object "+z patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "+x patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "+y patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "-x patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "-y patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+
+# collect all patch sizes into a single OpenDX group
+# for the ImportAHFinderDirectGnuplot macro to read
+object "patchsizes" class group
+member 0 value "+z patch"
+member 1 value "+x patch"
+member 2 value "+y patch"
+member 3 value "-x patch"
+member 4 value "-y patch"
diff --git a/test/Kerr-carpet/Kerr.h.t0.ah1.gp b/test/Kerr-carpet/Kerr.h.t0.ah1.gp
new file mode 100644
index 0000000..41b64ea
--- /dev/null
+++ b/test/Kerr-carpet/Kerr.h.t0.ah1.gp
@@ -0,0 +1,1228 @@
+# N_patches = 5
+# origin = 0.5 0.7 0
+
+### +z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-45	2.45808719009766	-0.9191773009	-0.7191773009	1.419177301
+-40	-45	2.43572361103085	-0.7428854687	-0.7812132225	1.481213223
+-35	-45	2.41002824343574	-0.5693599131	-0.8272042284	1.527204228
+-30	-45	2.38180547531377	-0.4002378513	-0.8592576973	1.559257697
+-25	-45	2.35162732871967	-0.2364017814	-0.8792187166	1.579218717
+-20	-45	2.31987658213283	-0.07821431981	-0.8886307873	1.588630787
+-15	-45	2.28679576275045	0.07429744623	-0.8887435596	1.588743560
+-10	-45	2.25251364180676	0.2213099341	-0.8805299038	1.580529904
+-5	-45	2.21707285291688	0.3631050954	-0.8647159199	1.564715920
+0	-45	2.18044949659022	0.5000000000	-0.8418106251	1.541810625
+5	-45	2.14256643086129	0.6322944471	-0.8121324495	1.512132450
+10	-45	2.10330579100567	0.7602294692	-0.7758346577	1.475834658
+15	-45	2.06251753166515	0.8839516387	-0.7329270232	1.432927023
+20	-45	2.02002689962312	1.003478715	-0.6832963997	1.383296400
+25	-45	1.97564410287152	1.118664284	-0.6267298379	1.326729838
+30	-45	1.92918059445153	1.229161727	-0.5629451576	1.262945158
+35	-45	1.88045730152240	1.334382610	-0.4916218617	1.191621862
+40	-45	1.82933851112300	1.433463158	-0.4124580715	1.112458072
+45	-45	1.77575876697900	1.525234802	-0.3252348021	1.025234802
+
+-45	-40	2.41011600943906	-0.9656407175	-0.5298185855	1.465640718
+-40	-40	2.38617388659333	-0.7902428838	-0.5902428838	1.537651592
+-35	-40	2.35875469559438	-0.6149458143	-0.6361047554	1.592307642
+-30	-40	2.32864795907838	-0.4418955938	-0.6689163885	1.631411024
+-25	-40	2.29644245238255	-0.2725105414	-0.6900979300	1.656654202
+-20	-40	2.26255929973794	-0.1076632609	-0.7009113112	1.669541088
+-15	-40	2.22728756355472	0.05216159962	-0.7024339211	1.671355664
+-10	-40	2.19080749844878	0.2067413717	-0.6955505041	1.663152327
+-5	-40	2.15321535730112	0.3560140754	-0.6809621882	1.645766649
+0	-40	2.11454434674188	0.5000000000	-0.6592029062	1.619834947
+5	-40	2.07478204855438	0.6387410742	-0.6306590760	1.585817734
+10	-40	2.03387563450366	0.7722519341	-0.5955844679	1.544017444
+15	-40	1.99175042493586	0.9004791922	-0.5541256028	1.494608693
+20	-40	1.94831876129731	1.023266609	-0.5063426540	1.437663192
+25	-40	1.90349336692387	1.140324642	-0.4522353571	1.373180626
+30	-40	1.85719648166034	1.251202077	-0.3917694495	1.301120164
+35	-40	1.80937935284367	1.355264831	-0.3249138506	1.221444764
+40	-40	1.76004452140040	1.451684591	-0.2516845908	1.134173530
+45	-40	1.70926811194135	1.539440812	-0.1721944020	1.039440812
+
+-45	-35	2.36091551119854	-0.9960821150	-0.3475679747	1.496082115
+-40	-35	2.33486541611382	-0.8225727930	-0.4036537320	1.576180877
+-35	-35	2.30534453031574	-0.6470076006	-0.4470076006	1.638096619
+-30	-35	2.27311518252433	-0.4718364283	-0.4786383922	1.683270070
+-25	-35	2.23877148248618	-0.2988629399	-0.4995725199	1.713167103
+-20	-35	2.20276751393073	-0.1293709956	-0.5107866906	1.729182599
+-15	-35	2.16542764375796	0.03575902555	-0.5131592072	1.732570904
+-10	-35	2.12697989777064	0.1959373697	-0.5074552911	1.724424867
+-5	-35	2.08757497743409	0.3507735007	-0.4943206752	1.705666692
+0	-35	2.04730316385289	0.5000000000	-0.4742848529	1.677052572
+5	-35	2.00621085920435	0.6434103333	-0.4477715214	1.639187611
+10	-35	1.96431017655901	0.7808081635	-0.4151100762	1.592542233
+15	-35	1.92159803611955	0.9119669144	-0.3765561051	1.537481456
+20	-35	1.87806209662261	1.036596715	-0.3323071211	1.474287357
+25	-35	1.83369606987806	1.154319498	-0.2825261008	1.403192692
+30	-35	1.78850893798274	1.264650270	-0.2273640488	1.324413118
+35	-35	1.74254230276439	1.366989398	-0.1669893976	1.238189180
+40	-35	1.69588331700471	1.460624591	-0.1016170606	1.144827807
+45	-35	1.64867835173504	1.544746491	-0.03153936837	1.044746491
+
+-45	-30	2.31118065938454	-1.013022902	-0.1735441800	1.513022902
+-40	-30	2.28258773352078	-0.8418394757	-0.2232650733	1.599142016
+-35	-30	2.25064909753884	-0.6669894487	-0.2622313894	1.666633655
+-30	-30	2.21610068951998	-0.4910703574	-0.2910703574	1.716584213
+-25	-30	2.17954047260677	-0.3161367367	-0.3104847226	1.750210880
+-20	-30	2.14144126366793	-0.1437741601	-0.3211911570	1.768754968
+-15	-30	2.10216823588457	0.02481617074	-0.3238788527	1.773410194
+-10	-30	2.06199409872194	0.1887341836	-0.3191826694	1.765276166
+-5	-30	2.02111670359118	0.3473028987	-0.3076701252	1.745335854
+0	-30	1.97967885410205	0.5000000000	-0.2898394271	1.714452179
+5	-30	1.93778122686131	0.6464010345	-0.2661214753	1.673371482
+10	-30	1.89549262466688	0.7861317885	-0.2368859175	1.622734010
+15	-30	1.85286537659101	0.9188302581	-0.2024537826	1.563095803
+20	-30	1.80994675940819	1.044118102	-0.1631110536	1.494952197
+25	-30	1.76678681309413	1.161579650	-0.1191227028	1.418762139
+30	-30	1.72344999559069	1.270750269	-0.07075026919	1.334978626
+35	-30	1.68002684119306	1.371114737	-0.01827037070	1.244080776
+40	-30	1.63664221269677	1.462114663	0.03800809916	1.146603606
+45	-30	1.59345713235010	1.543162561	0.09772981471	1.043162561
+
+-45	-25	2.26134045732750	-1.018587206	-0.008128843745	1.518587206
+-40	-25	2.22988498578380	-0.8498089184	-0.05012097769	1.608639628
+-35	-25	2.19530081343698	-0.6762801828	-0.08335126009	1.679902198
+-30	-25	2.15830325218548	-0.5006386624	-0.1081843834	1.733157003
+-25	-25	2.11949859817111	-0.3250818492	-0.1250818492	1.769393736
+-20	-25	2.07937741019046	-0.1513968142	-0.1345499009	1.789698038
+-15	-25	2.03833821827093	0.01898138751	-0.1371089335	1.795185901
+-10	-25	1.99669622404794	0.1849129351	-0.1332673238	1.786947543
+-5	-25	1.95469092678290	0.3454942581	-0.1235033863	1.766008711
+0	-25	1.91250762711104	0.5000000000	-0.1082606489	1.733320555
+5	-25	1.87029198389490	0.6478345485	-0.08794645286	1.689756621
+10	-25	1.82815403117182	0.7884903977	-0.06293078472	1.636110348
+15	-25	1.78618978648276	0.9215151956	-0.03355609676	1.573116126
+20	-25	1.74448075544008	1.046485309	-0.0001404528492	1.501456046
+25	-25	1.70310871380933	1.162988920	0.03701107977	1.421784328
+30	-25	1.66216384364775	1.270617106	0.07759679518	1.334747980
+35	-25	1.62175051285489	1.368962002	0.1213092347	1.241006351
+40	-25	1.58199200492661	1.457621999	0.1678266381	1.141249457
+45	-25	1.54303178547341	1.536212093	0.2168063656	1.036212093
+
+-45	-20	2.21162740281997	-1.014502715	0.1487660920	1.514502715
+-40	-20	2.17710176983291	-0.8479984791	0.1152883591	1.606482030
+-35	-20	2.13974221019473	-0.6761438160	0.08863648723	1.679707446
+-30	-20	2.10025353776330	-0.5015499265	0.06860796499	1.734735359
+-25	-20	2.05924726664259	-0.3264707474	0.05490926154	1.772372237
+-20	-20	2.01723538632549	-0.1528087937	0.04719120627	1.793577420
+-15	-20	1.97464217902768	0.01785382075	0.04507413059	1.799394038
+-10	-20	1.93181520930288	0.1842168683	0.04816747857	1.790895134
+-5	-20	1.88902874089238	0.3452205039	0.05608652399	1.769137735
+0	-20	1.84650258350688	0.5000000000	0.06845892174	1.735144852
+5	-20	1.80441122227920	0.6478462734	0.08493010871	1.689890638
+10	-20	1.76289195714194	0.7881701834	0.1051655128	1.634294322
+15	-20	1.72206287340349	0.9204741718	0.1288466353	1.569230972
+20	-20	1.68202154192376	1.044328372	0.1556716280	1.495529911
+25	-20	1.64285817753298	1.159354633	0.1853495197	1.413990574
+30	-20	1.60466291919016	1.265217151	0.2175956770	1.325394985
+35	-20	1.56752818410000	1.361617148	0.2521285076	1.230516812
+40	-20	1.53155177722515	1.448292586	0.2886659204	1.130131096
+45	-20	1.49684063715823	1.525023115	0.3269220968	1.025023115
+
+-45	-15	2.16213790248307	-1.002137936	0.2975033531	1.502137936
+-40	-15	2.12444032773786	-0.8376751290	0.2728409867	1.594179141
+-35	-15	2.08427536787888	-0.6676944552	0.2531570724	1.667640509
+-30	-15	2.04234296921469	-0.4947404497	0.2383393507	1.722940999
+-25	-15	1.99925757008812	-0.3210592125	0.2282038605	1.760767163
+-20	-15	1.95554703379459	-0.1485926184	0.2225162611	1.781993573
+-15	-15	1.91165782787456	0.02100964846	0.2210096485	1.787616328
+-10	-15	1.86795894092421	0.1863679791	0.2233999563	1.778695578
+-5	-15	1.82474579010566	0.3463428835	0.2293984545	1.756308878
+0	-15	1.78225678204337	0.5000000000	0.2387180015	1.721527855
+5	-15	1.74068249951780	0.6465783645	0.2510783590	1.675398373
+10	-15	1.70017234898149	0.7854604980	0.2662098358	1.618926933
+15	-15	1.66084734110982	0.9161465719	0.2838534281	1.553080150
+20	-15	1.62280307804538	1.038232054	0.3037619818	1.478780416
+25	-15	1.58612193362639	1.151391819	0.3256979510	1.396914264
+30	-15	1.55087363626517	1.255366146	0.3494333514	1.308332544
+35	-15	1.51712261643092	1.349952791	0.3747476260	1.213858385
+40	-15	1.48493148028531	1.435001978	0.4014263673	1.114291967
+45	-15	1.45436173979344	1.510412860	0.4292606901	1.010412860
+
+-45	-10	2.11287197465898	-0.9825469986	0.4385869640	1.482546999
+-40	-10	2.07199863835873	-0.8198689279	0.4226449705	1.572958537
+-35	-10	2.02909389036546	-0.6518868404	0.4099306740	1.645064895
+-30	-10	1.98485239311417	-0.4810538069	0.4003790161	1.699235039
+-25	-10	1.93988957896159	-0.3095606024	0.3938772627	1.736108314
+-20	-10	1.89474115311279	-0.1393230043	0.3902771589	1.756525518
+-15	-10	1.84986300086275	0.02801704165	0.3894063041	1.761464381
+-10	-10	1.80562922526052	0.1910787423	0.3910787423	1.751979512
+-5	-10	1.76234345154056	0.3487178249	0.3951018785	1.729163173
+0	-10	1.72024831998023	0.5000000000	0.4012820141	1.694113883
+5	-10	1.67953451244436	0.6441737329	0.4094284219	1.647913308
+10	-10	1.64034621963296	0.7806433404	0.4193566596	1.591607474
+15	-10	1.60279562085625	0.9089449967	0.4308891440	1.526203505
+20	-10	1.56696160258770	1.028723724	0.4438574664	1.452656494
+25	-10	1.53290270906196	1.139715608	0.4581015031	1.371874548
+30	-10	1.50066299346972	1.241733314	0.4734692393	1.284719785
+35	-10	1.47027265197671	1.334652220	0.4898170217	1.192006904
+40	-10	1.44175492856068	1.418401922	0.5070085697	1.094508790
+45	-10	1.41512823327030	1.492958466	0.5249146317	0.9929584660
+
+-45	-5	2.06376268793440	-0.9565161125	0.5725713519	1.456516112
+-40	-5	2.01980232361008	-0.7953978928	0.5649354306	1.543795093
+-35	-5	1.97431123086306	-0.6295214533	0.5588699536	1.613123812
+-30	-5	1.92797900167298	-0.4612343703	0.5543395320	1.664906767
+-25	-5	1.88141699110491	-0.2926333734	0.5512860913	1.699807755
+-20	-5	1.83515303423664	-0.1255488568	0.5496348649	1.718681359
+-15	-5	1.78963376371327	0.03845383855	0.5492995763	1.722513725
+-10	-5	1.74522529457181	0.1980634430	0.5501872729	1.712367306
+-5	-5	1.70222121909556	0.3522019295	0.5522019295	1.689339676
+0	-5	1.66085173903213	0.5000000000	0.5552472331	1.654531697
+5	-5	1.62129242645411	0.6407712990	0.5592287010	1.609023311
+10	-5	1.58366911878733	0.7739861739	0.5640554946	1.553852807
+15	-5	1.54807089965712	0.8992471509	0.5696409594	1.490010652
+20	-5	1.51455421257072	1.016266294	0.5759034563	1.418429986
+25	-5	1.48315028703548	1.124845221	0.5827665119	1.339984900
+30	-5	1.45387239082756	1.224858575	0.5901586933	1.255491881
+35	-5	1.42671815851836	1.316238465	0.5980136481	1.165709336
+40	-5	1.40167710451757	1.398963996	0.6062695827	1.071343572
+45	-5	1.37873202890089	1.473050548	0.6148691080	0.9730505482
+
+-45	0	2.01470070864697	-0.9246085331	0.7000000000	1.424608533
+-40	0	1.96782284559925	-0.7648921432	0.7000000000	1.507439756
+-35	0	1.91998557243646	-0.6012584825	0.7000000000	1.572760107
+-30	0	1.87186412845347	-0.4359320642	0.7000000000	1.621081888
+-25	0	1.82404877236225	-0.2708763215	0.7000000000	1.653149606
+-20	0	1.77704434922271	-0.1077849630	0.7000000000	1.669875462
+-15	0	1.73127000472248	0.05191435056	0.7000000000	1.672278410
+-10	0	1.68706396608023	0.2070444167	0.7000000000	1.661433674
+-5	0	1.64469041910992	0.3566557849	0.7000000000	1.638431876
+0	0	1.60435045192532	0.5000000000	0.7000000000	1.604350452
+5	0	1.56619088407603	0.6365025298	0.7000000000	1.560231055
+10	0	1.53030887215719	0.7657353469	0.7000000000	1.507060042
+15	0	1.49676431933696	0.8873911119	0.7000000000	1.445763312
+20	0	1.46558728051050	1.001260372	0.7000000000	1.377201553
+25	0	1.43678169784984	1.107210184	0.7000000000	1.302166441
+30	0	1.41033364287096	1.205166821	0.7000000000	1.221384763
+35	0	1.38621631094989	1.295101012	0.7000000000	1.135521925
+40	0	1.36439396218848	1.377015534	0.7000000000	1.045186413
+45	0	1.34482574782655	1.450935406	0.7000000000	0.9509354058
+
+-45	5	1.96555135296479	-0.8872027206	0.8213645121	1.387202721
+-40	5	1.91600799796225	-0.7288295216	0.8281238229	1.464461997
+-35	5	1.86614466780635	-0.5676383765	0.8333979564	1.524745619
+-30	5	1.81660771728488	-0.4057078805	0.8372462719	1.568732066
+-25	5	1.76794848795957	-0.2448295517	0.8397449536	1.597292128
+-20	5	1.72062619711773	-0.08651007871	0.8409812619	1.611423198
+-15	5	1.67501079508509	0.06801507742	0.8410483204	1.612189679
+-10	5	1.63139151029817	0.2177575083	0.8400410662	1.600676712
+-5	5	1.58998718192872	0.3619468287	0.8380531713	1.577954968
+0	5	1.55095205572713	0.5000000000	0.8351743784	1.545050215
+5	5	1.51439310352279	0.6314895950	0.8314895950	1.502932948
+10	5	1.48037164738034	0.7561149667	0.8270772973	1.452500154
+15	5	1.44891705040763	0.8736753946	0.8220095518	1.394575558
+20	5	1.42003270566768	0.9840467356	0.8163518277	1.329907476
+25	5	1.39370049644602	1.087160386	0.8101630576	1.259169510
+30	5	1.36988757355111	1.182986183	0.8034961817	1.182966770
+35	5	1.34855206071221	1.271518928	0.7963987906	1.101843218
+40	5	1.32964624821794	1.352767089	0.7889137001	1.016288242
+45	5	1.31311930178498	1.426743870	0.7810795826	0.9267438702
+
+-45	10	1.91616187580460	-0.8445206675	0.9370752698	1.344520668
+-40	10	1.86428471110870	-0.6875545753	0.9495507147	1.415272432
+-35	10	1.81279375256372	-0.5290964247	0.9591481175	1.469702008
+-30	10	1.76228360918290	-0.3710446428	0.9660233832	1.508693577
+-25	10	1.71324304173639	-0.2149757821	0.9703569601	1.533270513
+-20	10	1.66606142003677	-0.06216195579	0.9723418318	1.544527280
+-15	10	1.62103771331275	0.08640062796	0.9721737201	1.543573870
+-10	10	1.57839061616525	0.2299565119	0.9700434881	1.531492725
+-5	10	1.53827488920263	0.3679522026	0.9661326450	1.509313231
+0	10	1.50078952530282	0.5000000000	0.9606093661	1.477989160
+5	10	1.46599229898751	0.6258429527	0.9536272358	1.438391531
+10	10	1.43390555008840	0.7453238460	0.9453238460	1.391300668
+15	10	1.40452765321934	0.8583579522	0.9358214822	1.337410085
+20	10	1.37783799290767	0.9649096915	0.9252275447	1.277328880
+25	10	1.35380457266741	1.064973830	0.9136360574	1.211590289
+30	10	1.33238656661071	1.158559255	0.9011287970	1.140658090
+35	10	1.31354026190951	1.245677541	0.8877772834	1.064937893
+40	10	1.29721879388786	1.326332000	0.8736440122	0.9847841297
+45	10	1.28337603052614	1.400511392	0.8587844548	0.9005113916
+
+-45	15	1.86637533139647	-0.7966578983	1.047438437	1.296657898
+-40	15	1.81257999272445	-0.6413091457	1.064453579	1.360159275
+-35	15	1.75993621709942	-0.4859866858	1.077308615	1.408134920
+-30	15	1.70895798126468	-0.3323624662	1.086300765	1.441694082
+-25	15	1.66004387853328	-0.1817502357	1.091746569	1.462018099
+-20	15	1.61348719362171	-0.03514227250	1.093963369	1.470291310
+-15	15	1.56949253828494	0.1067435439	1.093256456	1.467653075
+-10	15	1.52819338195025	0.2434149284	1.089910622	1.455166252
+-5	15	1.48966589657162	0.3745590934	1.084184513	1.433796123
+0	15	1.45394544209326	0.5000000000	1.076308771	1.404403453
+5	15	1.42103602329257	0.6196617627	1.066484884	1.367740206
+10	15	1.39091995377512	0.7335367370	1.054886018	1.324452651
+15	15	1.36356718916197	0.8416592226	1.041659223	1.275089577
+20	15	1.33894076701743	0.9440839739	1.026927674	1.220110691
+25	15	1.31700101702241	1.040868688	1.010793369	1.159896643
+30	15	1.29771126010326	1.132061266	0.9933406543	1.094762226
+35	15	1.28103614537221	1.217687704	0.9746383469	1.024964264
+40	15	1.26694560505338	1.297744989	0.9547434388	0.9507154565
+45	15	1.25541344162006	1.372194208	0.9337037338	0.8721942084
+
+-45	20	1.81604152440699	-0.7436090346	1.152636672	1.243609035
+-40	20	1.76083328789807	-0.5902570688	1.172912996	1.299317779
+-35	20	1.70758574641657	-0.4386020458	1.187888501	1.340462641
+-30	20	1.65669989185382	-0.2900320724	1.198048020	1.368375689
+-25	20	1.60845309156894	-0.1455462879	1.203872560	1.384378482
+-20	20	1.56301788093835	-0.005816933586	1.205816934	1.389720603
+-15	20	1.52048675539013	0.1287444442	1.204296992	1.385544597
+-10	20	1.48089246426217	0.2579267117	1.199682301	1.372865839
+-5	20	1.44422739755045	0.3816657556	1.192293983	1.352566603
+0	20	1.41045678718268	0.5000000000	1.182404633	1.325395835
+5	20	1.37953116980407	0.6130332931	1.170240972	1.291976452
+10	20	1.35139425167886	0.7209049328	1.155987052	1.252814129
+15	20	1.32599186246616	0.8237659547	1.139789235	1.208310993
+20	20	1.30327682164864	0.9217606808	1.121760681	1.158777947
+25	20	1.28321096601390	1.015011647	1.101985484	1.104446041
+30	20	1.26576835446301	1.103608174	1.080523610	1.045480025
+35	20	1.25093485390524	1.187596518	1.057414983	0.9819895963
+40	20	1.23870968186813	1.266973226	1.032684480	0.9140430972
+45	20	1.22910189736436	1.341678014	1.006345744	0.8416780142
+
+-45	25	1.76502895138219	-0.6852927210	1.252711073	1.185292721
+-40	25	1.70900413225587	-0.5345058306	1.274899539	1.232876040
+-35	25	1.65577468099989	-0.3871927403	1.290831641	1.267042544
+-30	25	1.60558941195662	-0.2443879075	1.301218706	1.289317676
+-25	25	1.55857281613223	-0.1067237517	1.306723752	1.301123284
+-20	25	1.51475608770868	0.02547946085	1.307941366	1.303734466
+-15	25	1.47410673583327	0.1521319326	1.305389187	1.298261302
+-10	25	1.43654997344140	0.2733063702	1.299505392	1.285643461
+-5	25	1.40199072585590	0.3891816531	1.290653026	1.266659501
+0	25	1.37032509842175	0.5000000000	1.279124411	1.241936307
+5	25	1.34145358121831	0.6060332751	1.265148971	1.211965880
+10	25	1.31528592686406	0.7075576531	1.248899112	1.177117944
+15	25	1.29174835919611	0.8048341035	1.230497874	1.137656362
+20	25	1.27078793290576	0.8980937789	1.210025712	1.093753668
+25	25	1.25237342805944	0.9875259577	1.187525958	1.045502790
+30	25	1.23649766007979	1.073268545	1.163010978	0.9929302460
+35	25	1.22317592218162	1.155398836	1.136467018	0.9360065410
+40	25	1.21244645994006	1.233926214	1.107860284	0.8746592020
+45	25	1.20436702291296	1.308784164	1.077142250	0.8087841645
+
+-45	30	1.71323644184469	-0.6215765254	1.347542509	1.121576525
+-40	30	1.65709142513421	-0.4741359145	1.370263234	1.160929976
+-35	30	1.60456958532088	-0.3319892149	1.386009749	1.188203739
+-30	30	1.55572741143749	-0.1957424493	1.395742449	1.205061271
+-25	30	1.51051166461132	-0.06561650319	1.400307693	1.212968505
+-20	30	1.46879764913839	0.05844038826	1.400426949	1.213175063
+-15	30	1.43042100189540	0.1766610219	1.396698670	1.206717494
+-10	30	1.39520095531478	0.2893891332	1.389606549	1.194433580
+-5	30	1.36295783292345	0.3970273662	1.379531215	1.176982590
+0	30	1.33352468403424	0.5000000000	1.366762342	1.154866253
+5	30	1.30675786570632	0.5987266781	1.351511543	1.128451094
+10	30	1.28253881164339	0.6936040896	1.333920985	1.097983354
+15	30	1.26077878637921	0.7849922672	1.314072992	1.063605621
+20	30	1.24142267063178	0.8732046499	1.291998424	1.025371349
+25	30	1.22444967797788	0.9584995677	1.267682825	0.9832554959
+30	30	1.20987403343919	1.041072117	1.241072117	0.9371643965
+35	30	1.19774488202889	1.121045565	1.212077926	0.8869449852
+40	30	1.18814617501930	1.198462283	1.180583440	0.8323949356
+45	30	1.18119430222797	1.273273186	1.146449482	0.7732731858
+
+-45	35	1.66061276194621	-0.5523091747	1.436834817	1.052309175
+-40	35	1.60514380030721	-0.4092256472	1.458725935	1.083572932
+-35	35	1.55407771854717	-0.2732201984	1.473220198	1.104272885
+-30	35	1.50724347782039	-0.1443994257	1.481524422	1.116132546
+-25	35	1.46439211565315	-0.02254041999	1.484646648	1.120591547
+-20	35	1.42523783227795	0.09278346545	1.483404961	1.118818234
+-15	35	1.38948771485329	0.2021109744	1.478446613	1.111736978
+-10	35	1.35686275245650	0.3060295455	1.470271083	1.100061112
+-5	35	1.32711000759981	0.4051339556	1.459251733	1.084323850
+0	35	1.30001063292067	0.5000000000	1.445655466	1.064906368
+5	35	1.27538395401395	0.5911685016	1.429658787	1.042060742
+10	35	1.25308926317442	0.6791355046	1.411360395	1.015927931
+15	35	1.23302734502725	0.7643458523	1.390791253	0.9865521517
+20	35	1.21514269540367	0.8471885086	1.367922781	0.9538925877
+25	35	1.19942444176699	0.9279917550	1.342672381	0.9178312805
+30	35	1.18590768672075	1.007017110	1.314907832	0.8781793948
+35	35	1.17467496959158	1.084451088	1.284451088	0.8346826560
+40	35	1.16585735036202	1.160394043	1.251082219	0.7870269733
+45	35	1.15963445039665	1.234845594	1.214544424	0.7348455940
+
+-45	40	1.60717626245419	-0.4773566755	1.520099626	0.9773566755
+-40	40	1.55327561131564	-0.3398812909	1.539881291	1.000931546
+-35	40	1.50445802614582	-0.2111333714	1.552192696	1.015603707
+-30	40	1.46029978108711	-0.09066460609	1.558450198	1.023061108
+-25	40	1.42035002980178	0.02220210468	1.559775796	1.024640893
+-20	40	1.38416983032804	0.1282487920	1.557037945	1.021378050
+-15	40	1.35135224312224	0.2282850060	1.550892474	1.014054163
+-10	40	1.32153706566699	0.3231007757	1.541822807	1.003245355
+-5	40	1.29441389744734	0.4134422940	1.530170862	0.9893591067
+0	40	1.26972478690338	0.5000000000	1.516163361	0.9726656173
+5	40	1.24726270212903	0.5834046965	1.499930497	0.9533200434
+10	40	1.22687078527352	0.6642273197	1.481520122	0.9313794128
+15	40	1.20844288165720	0.7429803569	1.460908163	0.9068150371
+20	40	1.19192275383617	0.8201187555	1.438004112	0.8795190524
+25	40	1.17730661255054	0.8960394338	1.412655126	0.8493093066
+30	40	1.16464545779825	0.9710778290	1.384647178	0.8159307341
+35	40	1.15404919307560	1.045500691	1.353705372	0.7790557251
+40	40	1.14569102326752	1.119493700	1.319493700	0.7382838425
+45	40	1.13981172833133	1.193142767	1.281615840	0.6931427669
+
+-45	45	1.55304344397497	-0.3966500504	1.596650050	0.8966500504
+-40	45	1.50168513961242	-0.2662702903	1.613205371	0.9132053714
+-35	45	1.45592882855803	-0.1460139751	1.622603571	0.9226035708
+-30	45	1.41509160197145	-0.03485435160	1.626394912	0.9263949116
+-25	45	1.37853446132199	0.06831798105	1.625745077	0.9257450771
+-20	45	1.34568691233422	0.1645961907	1.621514392	0.9215143924
+-15	45	1.31605357573901	0.2550076936	1.614323735	0.9143237348
+-10	45	1.28921574348377	0.3404930324	1.604608965	0.9046089654
+-5	45	1.26482572608393	0.4219023421	1.592660314	0.8926603142
+0	45	1.24260122947985	0.5000000000	1.578651756	0.8786517557
+5	45	1.22231992120308	0.5754731036	1.562661521	0.8626615212
+10	45	1.20381648190974	0.6489410268	1.544686537	0.8446865373
+15	45	1.18697912157190	0.7209642206	1.524649698	0.8246496978
+20	45	1.17175032176340	0.7920512326	1.502404167	0.8024041669
+25	45	1.15812767051044	0.8626625993	1.477732454	0.7777324541
+30	45	1.14616954553420	0.9332113683	1.450344100	0.7503441002
+35	45	1.13600171000499	1.004058279	1.419869827	0.7198698271
+40	45	1.12782678117149	1.075500238	1.385854476	0.6858544760
+45	45	1.12193546245908	1.147749741	1.347749741	0.6477497413
+
+
+### +x patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	-45	1.77575907784335	1.525234982	-0.3252349816	1.025234982
+45	-40	1.70926821207757	1.539440873	-0.1721944531	1.039440873
+45	-35	1.64867855495667	1.544746620	-0.03153945854	1.044746620
+45	-30	1.59345725926693	1.543162644	0.09772976674	1.043162644
+45	-25	1.54303184901825	1.536212136	0.2168063457	1.036212136
+45	-20	1.49684067295646	1.525023139	0.3269220879	1.025023139
+45	-15	1.45436178628674	1.510412893	0.4292606814	1.010412893
+45	-10	1.41512825250643	1.492958480	0.5249146293	0.9929584795
+45	-5	1.37873204642448	1.473050561	0.6148691069	0.9730505606
+45	0	1.34482575966260	1.450935414	0.7000000000	0.9509354142
+45	5	1.31311931152921	1.426743877	0.7810795832	0.9267438771
+45	10	1.28337604348171	1.400511401	0.8587844564	0.9005114006
+45	15	1.25541344483032	1.372194211	0.9337037344	0.8721942106
+45	20	1.22910191066901	1.341678023	1.006345747	0.8416780233
+45	25	1.20436704733656	1.308784181	1.077142257	0.8087841809
+45	30	1.18119433842065	1.273273209	1.146449496	0.7732732095
+45	35	1.15963446671224	1.234845604	1.214544432	0.7348456043
+45	40	1.13981176072931	1.193142787	1.281615857	0.6931427866
+45	45	1.12193544754802	1.147749733	1.347749733	0.6477497327
+
+50	-45	1.78960340508716	1.588294343	-0.3882943429	0.9131873817
+50	-40	1.71976462305894	1.608217144	-0.2299045971	0.9299045971
+50	-35	1.65538478342473	1.617488752	-0.08247404818	0.9376843999
+50	-30	1.59618244480158	1.618258183	0.05437333675	0.9383300293
+50	-25	1.54177922940029	1.612239950	0.1813539935	0.9332801321
+50	-20	1.49175613595787	1.600765917	0.2993539713	0.9236522749
+50	-15	1.44569263034674	1.584847150	0.4093160822	0.9102948436
+50	-10	1.40318930951217	1.565231686	0.5121709131	0.8938355148
+50	-5	1.36388659792467	1.542459162	0.6087966412	0.8747270980
+50	0	1.32746841945494	1.516899806	0.7000000000	0.8532802523
+50	5	1.29366960316203	1.488790220	0.7865079349	0.8296935093
+50	10	1.26227118409841	1.458253639	0.8689659709	0.8040702748
+50	15	1.23310560704446	1.425321936	0.9479392655	0.7764372952
+50	20	1.20605832349399	1.389949680	1.023915194	0.7467564485
+50	25	1.18106888404290	1.352023410	1.097305041	0.7149325293
+50	30	1.15813356988872	1.311368617	1.168443889	0.6808191069
+50	35	1.13730913267387	1.267755132	1.237587931	0.6442230484
+50	40	1.11871825791133	1.220902580	1.304909089	0.6049090887
+50	45	1.10255447387232	1.170485870	1.370485870	0.5626044465
+
+55	-45	1.80157578690699	1.641635650	-0.4416356497	0.7993818878
+55	-40	1.72909481195744	1.667247653	-0.2794370755	0.8173156059
+55	-35	1.66157064716575	1.680653574	-0.1267025324	0.8267025324
+55	-30	1.59895232137458	1.684044085	0.01639182872	0.8290765940
+55	-25	1.54105424304125	1.679255433	0.1501041608	0.8257235435
+55	-20	1.48760921162711	1.667780052	0.2749628208	0.8176883956
+55	-15	1.43831278290104	1.650802191	0.3916434821	0.8058003695
+55	-10	1.39285298414098	1.629239785	0.5008845582	0.7907022098
+55	-5	1.35093243011716	1.603788115	0.6034310530	0.7728807585
+55	0	1.31227726129462	1.574954601	0.7000000000	0.7526913150
+55	5	1.27665268679201	1.543097368	0.7912591947	0.7303846402
+55	10	1.24385967883407	1.508445150	0.8778160885	0.7061208957
+55	15	1.21374495485366	1.471124202	0.9602119458	0.6799884870
+55	20	1.18620170460083	1.431173777	1.038919538	0.6520148982
+55	25	1.16117174926163	1.388559309	1.114342011	0.6221759265
+55	30	1.13864758947445	1.343182705	1.186811762	0.5904028861
+55	35	1.11867413118565	1.294890433	1.256588273	0.5565882731
+55	40	1.10135134234879	1.243481364	1.323854939	0.5205912559
+55	45	1.08683554425295	1.188713854	1.388713854	0.4822426319
+
+60	-45	1.81172405631492	1.686051804	-0.4860518038	0.6847673282
+60	-40	1.73719235823748	1.717047323	-0.3212239595	0.7026625993
+60	-35	1.66710987181451	1.734515599	-0.1644171285	0.7127479135
+60	-30	1.60161956931277	1.740609184	-0.01626604622	0.7162660462
+60	-25	1.54071384528152	1.737221409	0.1230741821	0.7143101136
+60	-20	1.48427710547457	1.725960548	0.2537868523	0.7078086522
+60	-15	1.43212894065853	1.708158329	0.3762749515	0.6975305362
+60	-10	1.38405299906691	1.684889798	0.4910719594	0.6840964439
+60	-5	1.33982057359415	1.657002404	0.5987754060	0.6679956495
+60	0	1.29920894051823	1.625147947	0.7000000000	0.6496044703
+60	5	1.26201788426691	1.589815872	0.7953465341	0.6292054868
+60	10	1.22806890032986	1.551351583	0.8853816503	0.6069981194
+60	15	1.19721905236091	1.509985992	0.9706249310	0.5831156845
+60	20	1.16936357597347	1.465853077	1.051541771	0.5576355342
+60	25	1.14443645321592	1.419003412	1.128538329	0.5305868675
+60	30	1.12241407306304	1.369418203	1.201958833	0.5019588333
+60	35	1.10331722747488	1.317020132	1.272083656	0.4717067933
+60	40	1.08720962341765	1.261680510	1.339125835	0.4397564475
+60	45	1.07419878814401	1.203228180	1.403228180	0.4060089789
+
+65	-45	1.82012248940126	1.722290397	-0.5222903972	0.5699633727
+65	-40	1.74402853070134	1.758142651	-0.3557070341	0.5866815530
+65	-35	1.67190774503210	1.779387991	-0.1958371153	0.5965884178
+65	-30	1.60406015230070	1.788089653	-0.04367890777	0.6006460695
+65	-25	1.54063254102219	1.786146435	0.1002600676	0.5997399324
+65	-20	1.48165223425361	1.775242332	0.2358497498	0.5946552652
+65	-15	1.42705610735242	1.756823319	0.3632352067	0.5860663385
+65	-10	1.37672495763367	1.732102936	0.4827470094	0.5745390347
+65	-5	1.33050405224603	1.702073286	0.5948322147	0.5605359791
+65	0	1.28822363254321	1.667527110	0.7000000000	0.5444268323
+65	5	1.24971937295252	1.629086583	0.7987822761	0.5265017203
+65	10	1.21483154497106	1.587216081	0.8917055290	0.5069771847
+65	15	1.18342521391873	1.542255029	0.9792713934	0.4860115019
+65	20	1.15539073093013	1.494432523	1.061943838	0.4637115010
+65	25	1.13064865621122	1.443884866	1.140140741	0.4401407413
+65	30	1.10915165496300	1.390669074	1.214228029	0.4153258100
+65	35	1.09088778738264	1.334776164	1.284516563	0.3892625182
+65	40	1.07587894031738	1.276139357	1.351258248	0.3619197258
+65	45	1.06418208432046	1.214643959	1.414643959	0.3332439512
+
+70	-45	1.82685344042650	1.751012938	-0.5510129382	0.4553314722
+70	-40	1.74959772315220	1.791027062	-0.3833003319	0.4698954223
+70	-35	1.67589775495007	1.815587422	-0.2211842302	0.4788346622
+70	-30	1.60617646636478	1.826645121	-0.06593891780	0.4828593355
+70	-25	1.54070720453212	1.826070317	0.08164325601	0.4826501239
+70	-20	1.47963767248843	1.815585051	0.2211662007	0.4788337993
+70	-15	1.42301600433719	1.796724308	0.3525437688	0.4719690503
+70	-10	1.37081146326342	1.770814914	0.4759210432	0.4625388020
+70	-5	1.32294097591241	1.738977868	0.5916034822	0.4509510649
+70	0	1.27928659753532	1.702136176	0.7000000000	0.4375417854
+70	5	1.23971596112831	1.661034896	0.8015773914	0.4225821432
+70	10	1.20408808783206	1.616253504	0.8968256101	0.4062830495
+70	15	1.17227196741968	1.568233633	0.9862323393	0.3888052456
+70	20	1.14415005588390	1.517294124	1.070264781	0.3702647806
+70	25	1.11962453811080	1.463648941	1.149356881	0.3507395308
+70	30	1.09862206028638	1.407423080	1.223900960	0.3302749910
+70	35	1.08109596292958	1.348665288	1.294241832	0.3088889037
+70	40	1.06702711318935	1.287358637	1.360672342	0.2865751077
+70	45	1.05642471712231	1.223430222	1.423430222	0.2633070673
+
+75	-45	1.83199679864056	1.772773530	-0.5727735299	0.3410386395
+75	-40	1.75390954577191	1.816132996	-0.4043667112	0.3526567733
+75	-35	1.67903790632022	1.843407724	-0.2406642153	0.3599650148
+75	-30	1.60789444876948	1.856435873	-0.08313861633	0.3634558967
+75	-25	1.54085142955424	1.857044055	0.06719996447	0.3636188588
+75	-20	1.47815551877574	1.846970229	0.2097429304	0.3609195850
+75	-15	1.41994374102076	1.827808031	0.3442149103	0.3557850897
+75	-10	1.36626483889888	1.800975720	0.4706028794	0.3485953934
+75	-5	1.31709624865472	1.767698683	0.5890907365	0.3396788383
+75	0	1.27236726366714	1.729012401	0.7000000000	0.3293128802
+75	5	1.23197346963575	1.685768425	0.8037412948	0.3177256920
+75	10	1.19578722644083	1.638644649	0.9007737730	0.3050989140
+75	15	1.16368140233218	1.588173754	0.9915752787	0.2915752787
+75	20	1.13552769263373	1.534750387	1.076618341	0.2772605307
+75	25	1.11121014865510	1.478654462	1.156354070	0.2622296727
+75	30	1.09063128147093	1.420067480	1.231201207	0.2465313384
+75	35	1.07371114072187	1.359082356	1.301535941	0.2301904234
+75	40	1.06039521519570	1.295720130	1.367688467	0.2132125661
+75	45	1.05065248244170	1.229937230	1.429937230	0.1955860913
+
+80	-45	1.83562105714528	1.788007282	-0.5880072818	0.2271104351
+80	-40	1.75697500605898	1.833808229	-0.4191979931	0.2351863779
+80	-35	1.68129699405014	1.863092500	-0.2544476436	0.2403499849
+80	-30	1.60915771981026	1.877602279	-0.09535904658	0.2429084505
+80	-25	1.54100002855850	1.879121261	0.05690519453	0.2431762880
+80	-20	1.47714230706211	1.869389244	0.2015830759	0.2414602709
+80	-15	1.41778771357502	1.850036492	0.3382588121	0.2380478585
+80	-10	1.36304636118476	1.822546881	0.4667993017	0.2332006983
+80	-5	1.31294323086005	1.788223973	0.5872950062	0.2271486437
+80	0	1.26744219540518	1.748186901	0.7000000000	0.2200890275
+80	5	1.22646334149392	1.703372272	0.8052814318	0.2121869994
+80	10	1.18988881510929	1.654534274	0.9035755426	0.2035755426
+80	15	1.15759089471851	1.602273589	0.9953533179	0.1943605738
+80	20	1.12943348559830	1.547044730	1.081093116	0.1846222358
+80	25	1.10528620231632	1.489178243	1.161261390	0.1744188130
+80	30	1.08502935254478	1.428895217	1.236297903	0.1637892889
+80	35	1.06855837593025	1.366321603	1.306604917	0.1527558727
+80	40	1.05579034550583	1.301503633	1.372541403	0.1413267157
+80	45	1.04666453713710	1.234417128	1.434417128	0.1294975548
+
+85	-45	1.83777597360071	1.797024281	-0.5970242811	0.1134749209
+85	-40	1.75880960652584	1.844310583	-0.4280105144	0.1176119363
+85	-35	1.68265865959350	1.874827185	-0.2626643585	0.1202817930
+85	-30	1.60993051492774	1.890255914	-0.1026646263	0.1216316319
+85	-25	1.54110827658622	1.892348327	0.05073731243	0.1218146943
+85	-20	1.47655267452938	1.882840292	0.1966872951	0.1209828490
+85	-15	1.41651008554116	1.863384013	0.3346823546	0.1192806452
+85	-10	1.36112715522662	1.835500722	0.4645151900	0.1168411733
+85	-5	1.31046052859593	1.800543631	0.5862171759	0.1137828241
+85	0	1.26449549411229	1.759683707	0.7000000000	0.1102080440
+85	5	1.22316579445653	1.713909498	0.8062033197	0.1062033197
+85	10	1.18636143577947	1.664025380	0.9052490806	0.1018390248
+85	15	1.15395462760305	1.610675672	0.9976046494	0.09717153018
+85	20	1.12580340951619	1.554352034	1.083752757	0.09224385030
+85	25	1.10176660572669	1.495415386	1.164169818	0.08708756177
+85	30	1.08171041342041	1.434111308	1.239309415	0.08172414995
+85	35	1.06551512067366	1.370586049	1.309590914	0.07616640988
+85	40	1.05307969854704	1.304900188	1.375391451	0.07041964175
+85	45	1.04432456852316	1.237039956	1.437039956	0.06448264072
+
+90	-45	1.83849088478710	1.800009372	-0.6000093718	0.000000000
+90	-40	1.75942030405196	1.847794147	-0.4309335717	0.000000000
+90	-35	1.68311384487191	1.878726147	-0.2653944411	0.000000000
+90	-30	1.61019079288464	1.894466132	-0.1050953964	0.000000000
+90	-25	1.54114759480442	1.896754066	0.04868288240	0.000000000
+90	-20	1.47635923198370	1.887323876	0.1950554039	0.000000000
+90	-15	1.41608684065960	1.867834852	0.3334897561	0.000000000
+90	-10	1.36048943706430	1.839820546	0.4637534885	0.000000000
+90	-5	1.30963451605055	1.804650961	0.5858578310	0.000000000
+90	0	1.26351473398103	1.763514734	0.7000000000	0.000000000
+90	5	1.22206852937733	1.717418190	0.8065102904	0.000000000
+90	10	1.18518840759856	1.667182733	0.9058058072	0.000000000
+90	15	1.15274621806895	1.613467343	0.9983526754	0.000000000
+90	20	1.12459803972155	1.556776479	1.084635183	0.000000000
+90	25	1.10059922878479	1.497481651	1.165133333	0.000000000
+90	30	1.08061112714332	1.435836688	1.240305564	0.000000000
+90	35	1.06450872756046	1.371994500	1.310577122	0.000000000
+90	40	1.05218480076486	1.306020320	1.376331353	0.000000000
+90	45	1.04355344679962	1.237903719	1.437903719	0.000000000
+
+
+### +y patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	45	1.12193548966302	1.147749757	1.347749757	0.6477497570
+40	45	1.12782684500838	1.075500270	1.385854515	0.6858545148
+35	45	1.13600177625133	1.004058309	1.419869869	0.7198698691
+30	45	1.14616957726518	0.9332113803	1.450344121	0.7503441210
+25	45	1.15812769058036	0.8626626056	1.477732468	0.7777324676
+20	45	1.17175033899469	0.7920512369	1.502404179	0.8024041787
+15	45	1.18697912978009	0.7209642221	1.524649704	0.8246497035
+10	45	1.20381648826125	0.6489410276	1.544686542	0.8446865418
+5	45	1.22231992939774	0.5754731041	1.562661527	0.8626615270
+0	45	1.24260124074671	0.5000000000	1.578651764	0.8786517636
+-5	45	1.26482574316408	0.4219023411	1.592660326	0.8926603263
+-10	45	1.28921576586600	0.3404930296	1.604608981	0.9046089811
+-15	45	1.31605361199212	0.2550076869	1.614323760	0.9143237600
+-20	45	1.34568696893454	0.1645961766	1.621514431	0.9215144311
+-25	45	1.37853458326604	0.06831794286	1.625745159	0.9257451590
+-30	45	1.41509170316778	-0.03485438985	1.626394978	0.9263949779
+-35	45	1.45592900618914	-0.1460140539	1.622603683	0.9226036834
+-40	45	1.50168540811818	-0.2662704273	1.613205535	0.9132055347
+-45	45	1.55304362635081	-0.3966501557	1.596650156	0.8966501557
+
+45	50	1.10255452673073	1.170485902	1.370485902	0.5626044735
+40	50	1.10631218814650	1.098200926	1.412908102	0.5982009258
+35	50	1.11274329244940	1.025976049	1.451171647	0.6303078516
+30	50	1.12157721428140	0.9536575106	1.485757858	0.6593291286
+25	50	1.13261755476023	0.8810062819	1.517070608	0.6856036461
+20	50	1.14573601073046	0.8077142246	1.545437884	0.7094066163
+15	50	1.16086794708974	0.7334145141	1.571114826	0.7309521292
+10	50	1.17800806542658	0.6576866199	1.594285261	0.7503944325
+5	50	1.19720708477937	0.5800574678	1.615061044	0.7678273843
+0	50	1.21856973033369	0.5000000000	1.633478570	0.7832815242
+-5	50	1.24225619751098	0.4169300894	1.649493423	0.7967195808
+-10	50	1.26848156549593	0.3302027156	1.662968252	0.8080263051
+-15	50	1.29751785922165	0.2391094298	1.673656863	0.8169951149
+-20	50	1.32969692969801	0.1428787646	1.681182530	0.8233098993
+-25	50	1.36541016142195	0.04068357258	1.685007257	0.8265192263
+-30	50	1.40510515847389	-0.06833938873	1.684392697	0.8260035492
+-35	50	1.44927940017345	-0.1850513129	1.678354667	0.8209370402
+-40	50	1.49846065908236	-0.3102419580	1.665608764	0.8102419580
+-45	50	1.55317078084930	-0.4445148403	1.644514840	0.7925420541
+
+45	55	1.08683558023942	1.188713876	1.388713876	0.4822426479
+40	55	1.08860985294701	1.116637586	1.434880058	0.5145685565
+35	55	1.09335557905925	1.043991210	1.476899962	0.5439912095
+30	55	1.10083997066100	0.9706476792	1.515185693	0.5707991672
+25	55	1.11088960147655	0.8963997844	1.550082081	0.5952338812
+20	55	1.12339003957160	0.8209730955	1.581866332	0.6174894535
+15	55	1.13828367134969	0.7440339775	1.610747203	0.6377120567
+10	55	1.15556779194145	0.6651943127	1.636863502	0.6559988865
+5	55	1.17529298031708	0.5840136805	1.660280762	0.6723958282
+0	55	1.19756046328321	0.5000000000	1.680984102	0.6868924628
+-5	55	1.22252495695157	0.4126100276	1.698871955	0.6994176726
+-10	55	1.25039121322647	0.3212501954	1.713740517	0.7098287520
+-15	55	1.28141588914299	0.2252802407	1.725268100	0.7179004520
+-20	55	1.31590490404099	0.1240218841	1.732991384	0.7233083536
+-25	55	1.35420843728661	0.01677652590	1.736276084	0.7256083259
+-30	55	1.39671463564497	-0.09714447086	1.734284563	0.7242138477
+-35	55	1.44383402071854	-0.2183692390	1.725937597	0.7183692390
+-40	55	1.49597486001449	-0.3473874490	1.709877037	0.7071235138
+-45	55	1.55350258502493	-0.4844348186	1.684434819	0.6893086809
+
+45	60	1.07419879494666	1.203228184	1.403228184	0.4060089814
+40	60	1.07420295700192	1.131479751	1.452568261	0.4344954883
+35	60	1.07739731263216	1.058643858	1.497826113	0.4606251211
+30	60	1.08359546209544	0.9845986227	1.539349436	0.4845986227
+25	60	1.09265764478755	0.9091495688	1.577424082	0.5065810298
+20	60	1.10449489115954	0.8320405201	1.612273831	0.5267015421
+15	60	1.11906628649111	0.7529589184	1.644055536	0.5450507176
+10	60	1.13638047734427	0.6715409357	1.672856990	0.5616792449
+5	60	1.15649276068262	0.5873740205	1.698689624	0.5765937231
+0	60	1.17950566445550	0.5000000000	1.721481869	0.5897528322
+-5	60	1.20556880618125	0.4089182422	1.741069256	0.6010616149
+-10	60	1.23487478043949	0.3135909764	1.757178107	0.6103620645
+-15	60	1.26766033524282	0.2134521957	1.769410965	0.6174247082
+-20	60	1.30419879644622	0.1079231782	1.777222215	0.6219345356
+-25	60	1.34479252033113	-0.003562376036	1.779893000	0.6234765144
+-30	60	1.38976133123629	-0.1215201618	1.776504498	0.6215201618
+-35	60	1.43942477972499	-0.2463595867	1.765911956	0.6154045547
+-40	60	1.49407357782599	-0.3783044248	1.746722454	0.6043254904
+-45	60	1.55392965967871	-0.5172857557	1.717285756	0.5873302049
+
+45	65	1.06418210411211	1.214643973	1.414643973	0.3332439574
+40	65	1.06266523579572	1.143259640	1.466606987	0.3574747087
+35	65	1.06449330267194	1.070373941	1.514578407	0.3798441493
+30	65	1.06952810406760	0.9958576467	1.558850637	0.4004886294
+25	65	1.07766788799877	0.9195163019	1.599655613	0.4195163019
+20	65	1.08885470993707	0.8411004110	1.637165677	0.4370075321
+15	65	1.10307035097531	0.7603087971	1.671485656	0.4530112014
+10	65	1.12033978296809	0.6767943314	1.702650477	0.4675435960
+5	65	1.14072859556949	0.5901672564	1.730616457	0.4805843463
+0	65	1.16434310854767	0.5000000000	1.755253226	0.4920726606
+-5	65	1.19132867524767	0.4058331328	1.776332217	0.5019019554
+-10	65	1.22186672806060	0.3071842895	1.793512233	0.5099131286
+-15	65	1.25617049383585	0.2035617629	1.806322562	0.5158866831
+-20	65	1.29447742946495	0.09448512356	1.814142966	0.5195333975
+-25	65	1.33703910851043	-0.02048475101	1.816183151	0.5204847510
+-30	65	1.38410707197013	-0.1417036381	1.811463305	0.5182838507
+-35	65	1.43591167755251	-0.2693863366	1.798797563	0.5123777184
+-40	65	1.49263500989291	-0.4035318239	1.776787297	0.5021141629
+-45	65	1.55437684486733	-0.5438307873	1.743830787	0.4867462899
+
+45	70	1.05642472863586	1.223430230	1.423430230	0.2633070701
+40	70	1.05365479447131	1.152392589	1.477491212	0.2829836585
+35	70	1.05433613515391	1.079532861	1.527658701	0.3012431311
+30	70	1.05837388426509	1.004707773	1.574179506	0.3181753196
+25	70	1.06570374495371	0.9277159838	1.617239887	0.3338480167
+20	70	1.07629877145054	0.8483070481	1.656965750	0.3483070481
+15	70	1.09016688504332	0.7661848329	1.693415320	0.3615736069
+10	70	1.10735121878520	0.6810125700	1.726573297	0.3736421235
+5	70	1.12793076913370	0.5924181577	1.756344376	0.3844779100
+0	70	1.15201766654817	0.5000000000	1.782542500	0.3940132474
+-5	70	1.17975336342128	0.4033357052	1.804877945	0.4021426846
+-10	70	1.21130869855503	0.3019940766	1.822947393	0.4087194259
+-15	70	1.24687349397701	0.1955522892	1.836214325	0.4135481941
+-20	70	1.28665064283392	0.08361980967	1.843995171	0.4163801903
+-25	70	1.33084258662054	-0.03412840948	1.845442071	0.4169068188
+-30	70	1.37963609353657	-0.1579083921	1.839530762	0.4147552784
+-35	70	1.43318141565288	-0.2877712797	1.825053983	0.4094861617
+-40	70	1.49156674529728	-0.4235350097	1.800626166	0.4005951634
+-45	70	1.55479135173773	-0.5647072470	1.764707247	0.3875217461
+
+45	75	1.05065249107689	1.229937236	1.429937236	0.1955860929
+40	75	1.04690601322926	1.159194856	1.485597838	0.2105003063
+35	75	1.04668098939625	1.086392569	1.537455379	0.2243954924
+30	75	1.04991768746108	1.011371307	1.585721084	0.2373282493
+25	75	1.05658485455831	0.9339204421	1.630545391	0.2493388860
+20	75	1.06668352800264	0.8537849259	1.672016095	0.2604509277
+15	75	1.08024655530365	0.7706696092	1.710152734	0.2706696092
+10	75	1.09733543641017	0.6842436271	1.744897533	0.2799794500
+5	75	1.11804105560217	0.5941473413	1.776109035	0.2883425470
+0	75	1.14248128990910	0.5000000000	1.803552184	0.2956959165
+-5	75	1.17079765239545	0.4014101623	1.826887001	0.3019484619
+-10	75	1.20315010770073	0.2979899925	1.845655683	0.3069775150
+-15	75	1.23970876372922	0.1893750922	1.859267938	0.3106249078
+-20	75	1.28064411053664	0.07525116884	1.866987823	0.3126934446
+-25	75	1.32611573849753	-0.04461194009	1.867924075	0.3129443126
+-30	75	1.37625477971388	-0.1703165526	1.861022326	0.3110949947
+-35	75	1.43114437593142	-0.3017843411	1.845066709	0.3068196998
+-40	75	1.49079942405676	-0.4386967880	1.818695269	0.2997534940
+-45	75	1.55514104608409	-0.5804289397	1.780428940	0.2895000619
+
+45	80	1.04666453847702	1.234417129	1.434417129	0.1294975550
+40	80	1.04222098223572	1.163897681	1.491202446	0.1395103385
+35	80	1.04134212347650	1.091154650	1.544256335	0.1488651705
+30	80	1.04399415843898	1.016015421	1.593764927	0.1575948710
+25	80	1.05017153550466	0.9382607702	1.639853255	0.1657214867
+20	80	1.05989739369889	0.8576302678	1.682581085	0.1732555561
+15	80	1.07322318268682	0.7738273334	1.721937521	0.1801951575
+10	80	1.09022718132528	0.6865246460	1.757833834	0.1865246460
+5	80	1.11101100138942	0.5953708318	1.790093595	0.1922129123
+0	80	1.13569780801254	0.5000000000	1.818444006	0.1972118547
+-5	80	1.16442712429837	0.4000438491	1.842504033	0.2014542866
+-10	80	1.19735214604442	0.2951475720	1.861775851	0.2048524280
+-15	80	1.23462606960994	0.1849915564	1.875627516	0.2072948504
+-20	80	1.27639626187695	0.06931874761	1.883287016	0.2086454268
+-25	80	1.32278781826127	-0.05202982407	1.883831778	0.2087414831
+-30	80	1.37388937052844	-0.1790728630	1.876188701	0.2073938024
+-35	80	1.42973543886021	-0.3116398384	1.859141817	0.2043879769
+-40	80	1.49028403384550	-0.4493150978	1.831349678	0.1994874729
+-45	80	1.55540230338722	-0.5913851119	1.791385112	0.1924406416
+
+45	85	1.04432456858508	1.237039956	1.437039956	0.06448264072
+40	85	1.03946368485659	1.166658836	1.494493063	0.06950913630
+35	85	1.03818994499799	1.093957932	1.548259836	0.07421311941
+30	85	1.04048649916532	1.018756368	1.598512386	0.07860964785
+25	85	1.04636367998888	0.9408287888	1.645360388	0.08270831694
+20	85	1.05585888657429	0.8599107579	1.688846680	0.08651287450
+15	85	1.06903544609803	0.7757040108	1.728941376	0.09002070586
+10	85	1.08598143832035	0.6878826175	1.765535273	0.09322225694
+5	85	1.10680645760065	0.5961002348	1.798430710	0.09610023478
+0	85	1.13163776111984	0.5000000000	1.827331538	0.09862872959
+-5	85	1.16061446924268	0.3992277988	1.851831530	0.1007722012
+-10	85	1.19388403712631	0.2934494551	1.871406350	0.1024847760
+-15	85	1.23159032681580	0.1823731205	1.885399652	0.1037090313
+-20	85	1.27386467653763	0.06577757972	1.893016295	0.1043754012
+-25	85	1.32081045427675	-0.05645210551	1.893315391	0.1044015687
+-30	85	1.37248988053281	-0.1842836177	1.885213993	0.1036927882
+-35	85	1.42890672876285	-0.3174905656	1.867497522	0.1021427979
+-40	85	1.48998625401226	-0.4556009671	1.838840886	0.09963566705
+-45	85	1.55556325256879	-0.5978505206	1.797850521	0.09604947480
+
+45	90	1.04355344678355	1.237903719	1.437903719	0.000000000
+40	90	1.03855348029636	1.167569309	1.495578122	0.000000000
+35	90	1.03714770211576	1.094883483	1.549581660	0.000000000
+30	90	1.03932500227902	1.019662501	1.600081855	0.000000000
+25	90	1.04510107021910	0.9416787976	1.647183238	0.000000000
+20	90	1.05451825146126	0.8606664835	1.690923019	0.000000000
+15	90	1.06764399271735	0.7763265987	1.731264906	0.000000000
+10	90	1.08456973780793	0.6883335585	1.768092686	0.000000000
+5	90	1.10540781176368	0.5963426389	1.801201401	0.000000000
+0	90	1.13028693400321	0.5000000000	1.830286934	0.000000000
+-5	90	1.15934615793793	0.3989563245	1.854934496	0.000000000
+-10	90	1.19273067394428	0.2928844920	1.874610415	0.000000000
+-15	90	1.23058151000019	0.1815020687	1.888650462	0.000000000
+-20	90	1.27302438997692	0.06460001568	1.896251625	0.000000000
+-25	90	1.32015527991691	-0.05792172963	1.896467010	0.000000000
+-30	90	1.37202744582303	-0.1860137229	1.888210623	0.000000000
+-35	90	1.42863414235674	-0.3194308802	1.870268578	0.000000000
+-40	90	1.48988989556769	-0.4576827647	1.841321875	0.000000000
+-45	90	1.55561819737237	-0.5999881763	1.799988176	0.000000000
+
+
+### -x patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-90	45	1.55561820456239	-0.5999881814	1.799988181	1.347052516e-16
+-90	40	1.62553444053442	-0.7452316253	1.744873397	1.524918560e-16
+-90	35	1.69923111046092	-0.8919286379	1.674638925	1.704564654e-16
+-90	30	1.77618663406097	-1.038222747	1.588093317	1.883717350e-16
+-90	25	1.85575921581176	-1.181889028	1.484277734	2.059651990e-16
+-90	20	1.93719251434708	-1.320365511	1.362558861	2.229231171e-16
+-90	15	2.01963531154335	-1.450817907	1.222720083	2.388984004e-16
+-90	10	2.10216069740700	-1.570224153	1.065036374	2.535209651e-16
+-90	5	2.18378678841473	-1.675476820	0.8903295595	2.664102737e-16
+-90	-2.84217e-14	2.26349236762395	-1.763492368	0.7000000000	2.771887135e-16
+-90	-5	2.34026429198193	-1.831358880	0.4960325274	2.854996897e-16
+-90	-10	2.41309509225887	-1.876434756	0.2809704347	2.910197101e-16
+-90	-15	2.48101246443958	-1.896474015	0.05786672307	2.934737305e-16
+-90	-20	2.54311733302008	-1.889748592	-0.1697973547	2.926501309e-16
+-90	-25	2.59857329475371	-1.855107212	-0.3982045288	2.884079256e-16
+-90	-30	2.64663449898639	-1.792052711	-0.6233172495	2.806862313e-16
+-90	-35	2.68666670323174	-1.700788522	-0.8410087133	2.695099608e-16
+-90	-40	2.71812927528388	-1.582207827	-1.047179820	2.549884935e-16
+-90	-45	2.74060720688101	-1.437901941	-1.237901941	2.373167029e-16
+
+-85	45	1.55556326098468	-0.5978505265	1.797850527	0.09604947532
+-85	40	1.62529011832943	-0.7422576603	1.742377945	0.1086834625
+-85	35	1.69872566603541	-0.8879548367	1.671856439	0.1214303137
+-85	30	1.77534674048762	-1.033101139	1.585136355	0.1341289697
+-85	25	1.85451709061869	-1.175504445	1.481300554	0.1465876446
+-85	20	1.93549374639148	-1.312653746	1.359752009	0.1585866537
+-85	15	2.01744040277046	-1.441776498	1.220297445	0.1698834307
+-85	10	2.09945414650518	-1.559926963	1.063220702	0.1802202570
+-85	5	2.18058167661013	-1.664080145	0.8893324796	0.1893324796
+-85	-2.84217e-14	2.25982724037898	-1.751227915	0.7000000000	0.1969569216
+-85	-5	2.33620543690528	-1.818526224	0.4971552393	0.2028447607
+-85	-10	2.40873387491552	-1.863383770	0.2832716755	0.2067692875
+-85	-15	2.47645973788165	-1.883580358	0.06132156803	0.2085362599
+-85	-20	2.53849797593518	-1.877387100	-0.1652981398	0.2079944201
+-85	-25	2.59401624134923	-1.843621294	-0.3928485571	0.2050402948
+-85	-30	2.64226741496346	-1.781730712	-0.6173578409	0.1996255705
+-85	-35	2.68260297562227	-1.691838182	-0.8347416173	0.1917609932
+-85	-40	2.71446723470988	-1.574748181	-1.040920433	0.1815169455
+-85	-45	2.73742166569675	-1.431956027	-1.231956027	0.1690242508
+
+-80	45	1.55540229129274	-0.5913851034	1.791385103	0.1924406401
+-80	40	1.62455856089568	-0.7332842355	1.734848347	0.2174612856
+-80	35	1.69721242092151	-0.8759957518	1.663482598	0.2426251764
+-80	30	1.77283674489138	-1.017728132	1.576260745	0.2676164190
+-80	25	1.85081125335339	-1.156387477	1.472386165	0.2920658027
+-80	20	1.93043028329798	-1.289611234	1.351365220	0.3155567455
+-80	15	2.01090931210955	-1.414814840	1.213073090	0.3376335194
+-80	10	2.09141306039560	-1.529272003	1.057815405	0.3578154053
+-80	5	2.17105879726136	-1.630183487	0.8863669064	0.3756088227
+-80	-2.84217e-14	2.24893742059317	-1.714771008	0.7000000000	0.3905238848
+-80	-5	2.32414298279151	-1.780385501	0.5004921202	0.4020934903
+-80	-10	2.39576399774578	-1.824579920	0.2901138412	0.4098861588
+-80	-15	2.46290862606389	-1.845214654	0.07160162729	0.4135246191
+-80	-20	2.52472582612578	-1.840554715	-0.1518922479	0.4127029461
+-80	-25	2.58040496456268	-1.809338924	-0.3768624257	0.4071987600
+-80	-30	2.62919622883976	-1.750858739	-0.5995338991	0.3968871255
+-80	-35	2.67041161306923	-1.665005977	-0.8159535052	0.3817489671
+-80	-40	2.70345703065198	-1.552330410	-1.022109690	0.3618812246
+-80	-45	2.72781606842944	-1.414037184	-1.214037184	0.3374963976
+
+-75	45	1.55514104970796	-0.5804289422	1.780428942	0.2895000625
+-75	40	1.62334508956990	-0.7181574818	1.722155494	0.3264043135
+-75	35	1.69469931839280	-0.8559385084	1.649438365	0.3633226283
+-75	30	1.76867912810251	-0.9920754399	1.561450157	0.3998004092
+-75	25	1.84469528830683	-1.124642537	1.457583257	0.4353216557
+-75	20	1.92209840199578	-1.251513485	1.337498773	0.4693166238
+-75	15	2.00019062723332	-1.370404511	1.201173378	0.5011733783
+-75	10	2.07823966893547	-1.478927710	1.048938348	0.5302520817
+-75	5	2.15548120948011	-1.574640098	0.8815074894	0.5558981388
+-75	-2.84217e-14	2.23113123354814	-1.655107280	0.7000000000	0.5774592554
+-75	-5	2.30441104332360	-1.717984333	0.5059515150	0.5943071108
+-75	-10	2.37451899013346	-1.761048857	0.3013160819	0.6058462151
+-75	-15	2.44066350462953	-1.782296481	0.08846050113	0.6115394989
+-75	-20	2.50205409840719	-1.779998510	-0.1298515919	0.6109237596
+-75	-25	2.55791846208335	-1.752785685	-0.3504912172	0.6036321050
+-75	-30	2.60750577422095	-1.699718006	-0.5700077829	0.5894126633
+-75	-35	2.65009403727897	-1.620355226	-0.7846887129	0.5681474705
+-75	-40	2.68501189348353	-1.514831811	-0.9906446296	0.5398725567
+-75	-45	2.71164147953627	-1.383903673	-1.183903673	0.5047904678
+
+-70	45	1.55479130698301	-0.5647072164	1.764707216	0.3875217350
+-70	40	1.62165746117735	-0.6966200233	1.704083420	0.4355340702
+-70	35	1.69120271845674	-0.8276018887	1.629596850	0.4832075704
+-70	30	1.76291728196399	-0.9561075075	1.540684061	0.5299797906
+-70	25	1.83625763113900	-1.080447428	1.436974739	0.5752358206
+-70	20	1.91065587131774	-1.198814750	1.318318002	0.6183180025
+-70	15	1.98552491161889	-1.309310935	1.184803404	0.6585353249
+-70	10	2.06026515302923	-1.409975043	1.036780133	0.6951740638
+-70	5	2.13426392694642	-1.498808578	0.8748730911	0.7275068262
+-70	-2.84217e-14	2.20689648801772	-1.573804345	0.7000000000	0.7548030531
+-70	-5	2.27753849801392	-1.632989940	0.5133875608	0.7763448482
+-70	-10	2.34553375862133	-1.674434167	0.3165885887	0.7914293130
+-70	-15	2.41021455584503	-1.696309664	0.1115005991	0.7993913430
+-70	-20	2.47088876188796	-1.696932654	-0.09961809267	0.7996180927
+-70	-25	2.52684628256504	-1.674829741	-0.3141397634	0.7915732903
+-70	-30	2.57734962950843	-1.628799906	-0.5290631991	0.7748198007
+-70	-35	2.62164900877872	-1.558006493	-0.7410316601	0.7490531054
+-70	-40	2.65899812928375	-1.462073052	-0.9463747740	0.7141361882
+-70	-45	2.68864981165244	-1.341163405	-1.141163405	0.6701286758
+
+-65	45	1.55437670909338	-0.5438306961	1.743830696	0.4867462474
+-65	40	1.61950971925917	-0.6683147466	1.680332473	0.5447941135
+-65	35	1.68675013993625	-0.7907457834	1.603789927	0.6018846435
+-65	30	1.75561462317604	-0.9097906660	1.513943020	0.6573961839
+-65	25	1.82562741686597	-1.024065040	1.410683200	0.7106831995
+-65	20	1.89631980038364	-1.132142299	1.294051215	0.7610804531
+-65	15	1.96723592606812	-1.232565365	1.164239490	0.8079084979
+-65	10	2.03792820735798	-1.323848194	1.021593645	0.8504743801
+-65	5	2.10795509800083	-1.404478613	0.8666202886	0.8880729622
+-65	-2.84217e-14	2.17686917251083	-1.472913482	0.7000000000	0.9199846657
+-65	-5	2.24421656900514	-1.527587050	0.5226091188	0.9454793691
+-65	-10	2.30950562811447	-1.566896986	0.3355502951	0.9638098930
+-65	-15	2.37221992636337	-1.589239032	0.1401900885	0.9742281604
+-65	-20	2.43179285504018	-1.593018266	-0.06179634863	0.9759904461
+-65	-25	2.48760197358564	-1.576692739	-0.2683777278	0.9683777278
+-65	-30	2.53895822370934	-1.538829911	-0.4771189977	0.9507220009
+-65	-35	2.58510892633524	-1.478193668	-0.6851461184	0.9224468567
+-65	-40	2.62524608369546	-1.393853230	-0.8891315469	0.8831182646
+-65	-45	2.65850661574723	-1.285301333	-1.085301333	0.8324996839
+
+-60	45	1.55392945959679	-0.5172856247	1.717285625	0.5873301293
+-60	40	1.61693117209141	-0.6327943877	1.650527353	0.6540191447
+-60	35	1.68138598300718	-0.7450872370	1.571819469	0.7188514515
+-60	30	1.74686075397181	-0.8531125217	1.481219879	0.7812198786
+-60	25	1.81296713297849	-0.9558457808	1.378872037	0.8405329534
+-60	20	1.87935615836505	-1.052281913	1.264984412	0.8962103805
+-60	15	1.94571426466619	-1.141424055	1.139818250	0.9476766203
+-60	10	2.01175529790355	-1.222266655	1.003682079	0.9943511167
+-60	5	2.07720678384076	-1.293772457	0.8569347550	1.035635011
+-60	-2.84217e-14	2.14180240060973	-1.354855289	0.7000000000	1.070901200
+-60	-5	2.20526413834512	-1.404356419	0.5333904020	1.099480691
+-60	-10	2.26727597521348	-1.441018281	0.3577461071	1.120647427
+-60	-15	2.32748183415174	-1.463487004	0.1738852430	1.133619750
+-60	-20	2.38546260757264	-1.470307993	-0.01713346181	1.137557850
+-60	-25	2.44071843051372	-1.459941559	-0.2139357585	1.131572787
+-60	-30	2.49264866943097	-1.430797357	-0.4147463738	1.114746374
+-60	-35	2.54054630662294	-1.381306145	-0.6173047442	1.086172609
+-60	-40	2.58358235971237	-1.310013715	-0.8187818405	1.045011905
+-60	-45	2.62081032645389	-1.215723100	-1.015723100	0.9905731939
+
+-55	45	1.55350231050541	-0.4844346446	1.684434645	0.6893085591
+-55	40	1.61396542012268	-0.5895280792	1.614222609	0.7628957742
+-55	35	1.67517393933939	-0.6903195941	1.533470753	0.8334707526
+-55	30	1.73677277145210	-0.7861018429	1.442531245	0.9005382053
+-55	25	1.79848073811734	-0.8762449899	1.341753578	0.9636571164
+-55	20	1.86008078823340	-0.9601719478	1.231459126	1.022423405
+-55	15	1.92140497987324	-1.037326990	1.111925526	1.076447947
+-55	10	1.98232412678182	-1.107146839	0.9833833496	1.125336332
+-55	5	2.04272981815592	-1.169025663	0.8460208247	1.168664351
+-55	-2.84217e-14	2.10251867108700	-1.222282468	0.7000000000	1.205955167
+-55	-5	2.16158077205122	-1.266133607	0.5454833311	1.236660065
+-55	-10	2.21977143965919	-1.299654559	0.3826723453	1.260131688
+-55	-15	2.27689868041881	-1.321759510	0.2118610104	1.275609742
+-55	-20	2.33270815835181	-1.331186601	0.03350258402	1.282210662
+-55	-25	2.38684933754262	-1.326480191	-0.1517017006	1.278915198
+-55	-30	2.43885634130116	-1.306003460	-0.3426965840	1.264577237
+-55	-35	2.48812072143473	-1.267970942	-0.5379465807	1.237946581
+-55	-40	2.53386483045202	-1.210517987	-0.7352950122	1.197717589
+-55	-45	2.57512079519263	-1.131821278	-0.9318212775	1.142613560
+
+-50	45	1.55317037419733	-0.4445145930	1.644514593	0.7925418466
+-50	40	1.61067991304018	-0.5379229052	1.570920727	0.8709207269
+-50	35	1.66820675979272	-0.6261443920	1.488534792	0.9449473440
+-50	30	1.72550167386624	-0.7088570286	1.397933931	1.014351487
+-50	25	1.78240921105079	-0.7858304837	1.299592602	1.078939885
+-50	20	1.83884840510241	-0.8568850846	1.193865782	1.138561774
+-50	15	1.89479166805089	-0.9218508817	1.080983796	1.193074550
+-50	10	1.95025263212398	-0.9805350107	0.9610582683	1.242316381
+-50	5	2.00526440330850	-1.032683327	0.8340924159	1.286074014
+-50	-2.84217e-14	2.05986889428005	-1.077951120	0.7000000000	1.324058203
+-50	-5	2.11410294020603	-1.115871863	0.5586295302	1.355877485
+-50	-10	2.16797302329200	-1.145817527	0.4097979647	1.381004880
+-50	-15	2.22144688365599	-1.166972820	0.2533359791	1.398756278
+-50	-20	2.27443708011593	-1.178305695	0.08914668314	1.408265689
+-50	-25	2.32676469638392	-1.178528677	-0.08271077658	1.408452794
+-50	-30	2.37813498495595	-1.166080790	-0.2619121925	1.398007776
+-50	-35	2.42810451227759	-1.139123126	-0.4477263692	1.375387611
+-50	-40	2.47602328271318	-1.095550586	-0.6388259081	1.338825908
+-50	-45	2.52100109134941	-1.033072198	-0.8330721982	1.286400316
+
+-45	45	1.55304327917664	-0.3966499553	1.596649955	0.8966499553
+-45	40	1.60717602058326	-0.4773565284	1.520099502	0.9773565284
+-45	35	1.66061243160898	-0.5523089653	1.436834670	1.052308965
+-45	30	1.71323617425856	-0.6215763503	1.347542408	1.121576350
+-45	25	1.76502872788042	-0.6852925709	1.252711003	1.185292571
+-45	20	1.81604135785908	-0.7436089205	1.152636630	1.243608921
+-45	15	1.86637525422948	-0.7966578447	1.047438422	1.296657845
+-45	10	1.91616180840957	-0.8445206202	0.9370752615	1.344520620
+-45	5	1.96555130524201	-0.8872026870	0.8213645091	1.387202687
+-45	-2.84217e-14	2.01470068060574	-0.9246085133	0.7000000000	1.424608513
+-45	-5	2.06376267635611	-0.9565161043	0.5725713526	1.456516104
+-45	-10	2.11287199389406	-0.9825470121	0.4385869616	1.482547012
+-45	-15	2.16213786299112	-1.002137909	0.2975033604	1.502137909
+-45	-20	2.21162745239333	-1.014502749	0.1487660797	1.514502749
+-45	-25	2.26134044292005	-1.018587196	-0.008128839234	1.518587196
+-45	-30	2.31118043836460	-1.013022758	-0.1735440964	1.513022758
+-45	-35	2.36091523157666	-0.9960819378	-0.3475678506	1.496081938
+-45	-40	2.41011556670813	-0.9656404483	-0.5298183596	1.465640448
+-45	-45	2.45808669395284	-0.9191770144	-0.7191770144	1.419177014
+
+
+### -y patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-90	2.74060722654379	-1.437901954	-1.237901954	2.373167047e-16
+-40	-90	2.75380070677955	-1.270108974	-1.409533729	2.583348408e-16
+-35	-90	2.75753395387732	-1.081656498	-1.558839576	2.766189296e-16
+-30	-90	2.75175745895780	-0.8758787295	-1.683091865	2.918349439e-16
+-25	-90	2.73654965631959	-0.6565158589	-1.780156263	3.037215118e-16
+-20	-90	2.71210711213837	-0.4275952632	-1.848547040	3.120966898e-16
+-15	-90	2.67876306050315	-0.1933148974	-1.887486423	3.168652314e-16
+-10	-90	2.63695942328219	0.04209680157	-1.896898084	3.180177894e-16
+-5	-90	2.58725066763772	0.2745062464	-1.877405398	3.156307026e-16
+-2.84217e-14	-90	2.53030494336249	0.5000000000	-1.830304943	3.098627511e-16
+5	-90	2.46688400858862	0.7150031080	-1.757496770	3.009466159e-16
+10	-90	2.39783985907317	0.9163805219	-1.661411284	2.891799262e-16
+15	-90	2.32408844289387	1.101518352	-1.544897050	2.749115191e-16
+20	-90	2.24660098178585	1.268382790	-1.411114364	2.585284064e-16
+25	-90	2.16639353430592	1.415557470	-1.263419330	2.404415787e-16
+30	-90	2.08448850608500	1.542244253	-1.105220000	2.210683882e-16
+35	-90	2.00189493459953	1.648239763	-0.9398563281	2.008178479e-16
+40	-90	1.91959274550422	1.733890432	-0.7704933557	1.800775507e-16
+45	-90	1.83849087542906	1.800009365	-0.6000093652	1.591999729e-16
+
+-45	-85	2.73742169541042	-1.431956048	-1.231956048	0.1690242526
+-40	-85	2.75002064324413	-1.263722571	-1.401922710	0.1838944087
+-35	-85	2.75320144726993	-1.075131647	-1.549521121	0.1968075965
+-30	-85	2.74694191004528	-0.8695455059	-1.672122400	0.2075338185
+-25	-85	2.73134627376184	-0.6507051447	-1.767695146	0.2158953503
+-20	-85	2.70664017407187	-0.4226127931	-1.834857816	0.2217713225
+-15	-85	2.67316618388553	-0.1894089819	-1.872909348	0.2251004002
+-10	-85	2.63137295683303	0.04475350940	-1.881831146	0.2258809564
+-5	-85	2.58181650871725	0.2758296666	-1.862278636	0.2241703334
+-2.84217e-14	-85	2.52515041574287	0.5000000000	-1.815541456	0.2200813600
+5	-85	2.46212378745193	0.7137778221	-1.743491688	0.2137778221
+10	-85	2.39356097790169	0.9141033039	-1.648496539	0.2054668235
+15	-85	2.32035391712027	1.098418774	-1.533329271	0.1953909931
+20	-85	2.24344260431199	1.264722576	-1.401058011	0.1838187573
+25	-85	2.16381431533927	1.411606225	-1.254945858	0.1710356003
+30	-85	2.08246407425162	1.538256144	-1.098312392	0.1573319478
+35	-85	2.00037640131632	1.644433575	-0.9344205288	0.1429932677
+40	-85	1.91851409553092	1.730436804	-0.7663774821	0.1282914061
+45	-85	1.83777595922209	1.797024271	-0.5970242709	0.1134749200
+
+-45	-80	2.72781611576685	-1.414037217	-1.214037217	0.3374964035
+-40	-80	2.73865297486570	-1.244529605	-1.379049424	0.3665925077
+-35	-80	2.74020102205984	-1.055571929	-1.521586950	0.3917257192
+-30	-80	2.73252734602883	-0.8506074128	-1.639320660	0.4124853489
+-25	-80	2.71581496616267	-0.6333721382	-1.730524394	0.4285670279
+-20	-80	2.69034932561304	-0.4077768805	-1.794096481	0.4397765021
+-15	-80	2.65651003505677	-0.1777947689	-1.829564515	0.4460304734
+-10	-80	2.61476616582830	0.05264522680	-1.837074992	0.4473547732
+-5	-80	2.56566967719348	0.2797591106	-1.817364885	0.4438793496
+-2.84217e-14	-80	2.50984112393190	0.5000000000	-1.771710998	0.4358293374
+5	-80	2.44797732622435	0.7101380035	-1.701888371	0.4235177244
+10	-80	2.38083909984170	0.9073326898	-1.610098478	0.4073326898
+15	-80	2.30923666036005	1.089189767	-1.498886146	0.3877229550
+20	-80	2.23402978634260	1.253805675	-1.371064072	0.3651844746
+25	-80	2.15611227500734	1.399795314	-1.229617277	0.3402435884
+30	-80	2.07640548355835	1.526305791	-1.077613773	0.3134412695
+35	-80	1.99582245791508	1.632999136	-0.9180904580	0.2853130050
+40	-80	1.91527016015517	1.720032449	-0.7539780541	0.2563755603
+45	-80	1.83562101814777	1.788007254	-0.5880072544	0.2271104303
+
+-45	-75	2.71164155301276	-1.383903724	-1.183903724	0.5047904814
+-40	-75	2.71960669592889	-1.212427593	-1.340791737	0.5468284977
+-35	-75	2.71852788739267	-1.023028094	-1.475109536	0.5828188437
+-30	-75	2.70861113499115	-0.8192520057	-1.585011502	0.6122669866
+-25	-75	2.69015120203353	-0.6047968309	-1.669244450	0.6348371369
+-20	-75	2.66352347483269	-0.3834058373	-1.727137590	0.6503495572
+-15	-75	2.62916354669416	-0.1587705985	-1.758565344	0.6587705985
+-10	-75	2.58755960183861	0.06554636763	-1.763908987	0.6602024232
+-5	-75	2.53924855851471	0.2861764561	-1.744014290	0.6548716553
+-2.84217e-14	-75	2.48480185131356	0.5000000000	-1.700134281	0.6431140424
+5	-75	2.42483235229306	0.7041888515	-1.633889252	0.6253637404
+10	-75	2.35999918704315	0.8962460298	-1.547222905	0.6021415626
+15	-75	2.29098877088159	1.074036577	-1.442333672	0.5740365774
+20	-75	2.21853171266880	1.235816254	-1.321638542	0.5416964148
+25	-75	2.14339000785501	1.380251819	-1.187706117	0.5058093296
+30	-75	2.06635288005047	1.506434680	-1.043196001	0.4670879606
+35	-75	1.98822919449464	1.613885546	-0.8907934223	0.4262518128
+40	-75	1.90983875332179	1.702549098	-0.7331422083	0.3840092973
+45	-75	1.83199668760838	1.772773453	-0.5727734527	0.3410386188
+
+-45	-70	2.68864988003904	-1.341163452	-1.141163452	0.6701286929
+-40	-70	2.69274321850983	-1.167268758	-1.286973532	0.7231992218
+-35	-70	2.68818621757121	-0.9776049100	-1.410238507	0.7680640037
+-30	-70	2.67535566851750	-0.7757994332	-1.509749439	0.8042830209
+-25	-70	2.65468644871270	-0.5654479085	-1.584860413	0.8316211799
+-20	-70	2.62664896862447	-0.3500245219	-1.635423180	0.8500245219
+-15	-70	2.59173446136044	-0.1328209138	-1.661719802	0.8595957097
+-10	-70	2.55043862969820	0.08309392437	-1.664391847	0.8605682545
+-5	-70	2.50326357425578	0.2948925465	-1.644388921	0.8532877847
+-2.84217e-14	-70	2.45071725952949	0.5000000000	-1.602920924	0.8381946684
+5	-70	2.39330966141363	0.6960982675	-1.541413454	0.8158077799
+10	-70	2.33156180634601	0.8811274937	-1.461481426	0.7867149010
+15	-70	2.26601502664578	1.053290363	-1.364907745	0.7515649555
+20	-70	2.19723297510192	1.211058817	-1.253618044	0.7110588173
+25	-70	2.12581043589157	1.353185612	-1.129662450	0.6659426705
+30	-70	2.05237851325249	1.478719717	-0.9951922770	0.6169995302
+35	-70	1.97760344022178	1.587021626	-0.8524277685	0.5650374986
+40	-70	1.90218463878029	1.677777739	-0.7036208517	0.5108762102
+45	-70	1.82685329028241	1.751012835	-0.5510128354	0.4553314348
+
+-45	-65	2.65850672211308	-1.285301405	-1.085301405	0.8324997172
+-40	-65	2.65788882429462	-1.108891069	-1.217401712	0.8940991020
+-35	-65	2.64920351583818	-0.9194891091	-1.327240542	0.9453177896
+-30	-65	2.63301436997025	-0.7207255744	-1.414358717	0.9859416618
+-25	-65	2.60989084699586	-0.5159825386	-1.478781585	1.015982539
+-20	-65	2.58038649755577	-0.3083455825	-1.520911235	1.035627917
+-15	-65	2.54502670978039	-0.1005898362	-1.541431783	1.045196806
+-10	-65	2.50429695955838	0.1048114034	-1.541225903	1.045100802
+-5	-65	2.45864521475400	0.3056599139	-1.521317349	1.035817291
+-2.84217e-14	-65	2.40849047304962	0.5000000000	-1.482833671	1.017872057
+5	-65	2.35422192603647	0.6860860969	-1.426973821	0.9918241814
+10	-65	2.29621775297654	0.8623528223	-1.355004973	0.9582645566
+15	-65	2.23485274527994	1.027393225	-1.268258311	0.9178139238
+20	-65	2.17051387487831	1.179946707	-1.168138225	0.8711271606
+25	-65	2.10360894528741	1.318896299	-1.056128781	0.8188962994
+30	-65	2.03459169264599	1.443283159	-0.9338143574	0.7618601468
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author	jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>	2005-05-26 10:04:34 +0000
committer	jthorn <jthorn@f88db872-0e4f-0410-b76b-b9085cfa78c5>	2005-05-26 10:04:34 +0000
commit	2927bf635a6df5d6a12de1c4f04bf5998eca9ef4 (patch)
tree	d6c1d937ef81a70b30163289906ac0560cc26db7 /test
parent	34439126cceb680bbae74cf5972a9e15f7e845a1 (diff)