new test case: Brill-Lindquist 2BH, Carpet, set an excision mask

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1461 f88db872-0e4f-0410-b76b-b9085cfa78c5

10 files changed, 10931 insertions, 0 deletions

diff --git a/test/bl-carpet-mask.par b/test/bl-carpet-mask.par
new file mode 100644
index 0000000..7e482ff
--- /dev/null
+++ b/test/bl-carpet-mask.par
@@ -0,0 +1,170 @@
+# This parameter file sets up Brill-Lindquist initial data and finds the
+# apparent horizons in it with AHFinderDirect.
+
+########################################
+
+#
+# ***** output setup (also see below for more output stuff) *****
+#
+ActiveThorns = "IOUtil"
+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 = "minmax"
+CoordBase::xmin = -3.0
+CoordBase::xmax = +3.0
+CoordBase::ymin = -3.0
+CoordBase::ymax = +3.0
+CoordBase::zmin = -3.0
+CoordBase::zmax = +3.0
+CoordBase::dx   = 0.15
+CoordBase::dy   = 0.15
+CoordBase::dz   = 0.15
+
+#
+# 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
+
+ActiveThorns = "CartGrid3D"
+CartGrid3D::type = "CoordBase"
+
+########################################
+########################################
+
+#
+# physics
+#
+
+ActiveThorns = "ADMBase ADMCoupling CoordGauge StaticConformal"
+ActiveThorns = "IDAnalyticBH"
+
+ADMBase::initial_data              = "bl_bh"
+IDAnalyticBH::bl_nbh = 2
+
+IDAnalyticBH::bl_m_1 = 1.0
+IDAnalyticBH::bl_x0_1 = 0.0
+IDAnalyticBH::bl_y0_1 = 0.0
+IDAnalyticBH::bl_z0_1 = 1.0
+
+IDAnalyticBH::bl_m_2 = 1.0
+IDAnalyticBH::bl_x0_2 = 0.0
+IDAnalyticBH::bl_y0_2 = 0.0
+IDAnalyticBH::bl_z0_2 = -1.0
+
+########################################
+
+#
+# numerical methods
+#
+
+Cactus::cctk_itlast = 0
+ADMBase::metric_type            = "static conformal"
+StaticConformal::conformal_storage = "factor+derivs+2nd derivs"
+ADMBase::evolution_method       = "none"
+ADMBase::initial_lapse          = "Cadez"
+ADMBase::lapse_evolution_method = "static"
+ADMBase::initial_shift          = "zero"
+ADMBase::shift_evolution_method = "static"
+
+########################################
+
+#
+# apparent horizons
+#
+
+ActiveThorns = "SpaceMask"
+SpaceMask::use_mask = true
+
+ActiveThorns = "SphericalSurface"
+ActiveThorns = "AEILocalInterp AHFinderDirect"
+
+AHFinderDirect::print_timing_stats = "true"
+AHFinderDirect::verbose_level      = "algorithm highlights"
+
+AHFinderDirect::h_base_file_name              = "bl.h"
+AHFinderDirect::BH_diagnostics_base_file_name = "bl.BH_diagnostics"
+
+AHFinderDirect::N_horizons = 2
+AHFinderDirect::set_mask_for_all_horizons = true
+
+AHFinderDirect::origin_x[1] = 0.0
+AHFinderDirect::origin_y[1] = 0.0
+AHFinderDirect::origin_z[1] = +1.0
+AHFinderDirect::initial_guess_method[1] = "coordinate sphere"
+AHFinderDirect::initial_guess__coord_sphere__x_center[1] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__y_center[1] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__z_center[1] = +1.0
+AHFinderDirect::initial_guess__coord_sphere__radius[1] = 0.5
+
+AHFinderDirect::origin_x[2] = 0.0
+AHFinderDirect::origin_y[2] = 0.0
+AHFinderDirect::origin_z[2] = -1.0
+AHFinderDirect::initial_guess_method[2] = "coordinate sphere"
+AHFinderDirect::initial_guess__coord_sphere__x_center[2] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__y_center[2] = 0.0
+AHFinderDirect::initial_guess__coord_sphere__z_center[2] = -1.0
+AHFinderDirect::initial_guess__coord_sphere__radius[2] = 0.5
+
+########################################
+
+#
+# ASCII output
+#
+
+########################################
+
+ActiveThorns = "CarpetIOASCII"
+CarpetIOASCII::out3D_ghosts = true
+CarpetIOASCII::out3D_outer_ghosts = true
+
+IOASCII::out2d_every = 1
+IOASCII::out2d_vars = "SpaceMask::emask"
+
+########################################
diff --git a/test/bl-carpet-mask/bl.BH_diagnostics.ah1.gp b/test/bl-carpet-mask/bl.BH_diagnostics.ah1.gp
new file mode 100644
index 0000000..ad1f037
--- /dev/null
+++ b/test/bl-carpet-mask/bl.BH_diagnostics.ah1.gp
@@ -0,0 +1,40 @@
+# apparent horizon 1/2
+#
+# 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	-0.000000	-0.000000	0.993568	0.3916242119	0.4223341017	0.4133767330	0.05722127784	2.039566003e-17	4.775307478e-17	0.05722127784	3.253714096e-17	0.05647005197	-0.4167524269	0.4167524269	-0.4167524269	0.4167524269	0.6083757881	1.422334102	15.60477905	15.66827224	15.66827224	1.004068830	1.004068830	78.63837679	1.250784073	2.501568146	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000
diff --git a/test/bl-carpet-mask/bl.BH_diagnostics.ah2.gp b/test/bl-carpet-mask/bl.BH_diagnostics.ah2.gp
new file mode 100644
index 0000000..2f0e335
--- /dev/null
+++ b/test/bl-carpet-mask/bl.BH_diagnostics.ah2.gp
@@ -0,0 +1,40 @@
+# apparent horizon 2/2
+#
+# 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	-0.000000	-0.000000	-0.993568	0.3916242119	0.4223341017	0.4133767330	0.05722127784	2.612622766e-17	1.131443665e-16	0.05722127784	1.685527145e-16	0.05647005197	-0.4167524269	0.4167524269	-0.4167524269	0.4167524269	-1.422334102	-0.6083757881	15.60477905	15.66827224	15.66827224	1.004068830	1.004068830	78.63837679	1.250784073	2.501568146	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000
diff --git a/test/bl-carpet-mask/bl.h.ah1.dx b/test/bl-carpet-mask/bl.h.ah1.dx
new file mode 100644
index 0000000..861b455
--- /dev/null
+++ b/test/bl-carpet-mask/bl.h.ah1.dx
@@ -0,0 +1,17 @@
+# 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 19 19
+object "+y 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 19 19
+object "-y patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "-z patch" class array type int rank 1 shape 2 items 1 data follows 19 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"
+member 5 value "-z patch"
diff --git a/test/bl-carpet-mask/bl.h.ah2.dx b/test/bl-carpet-mask/bl.h.ah2.dx
new file mode 100644
index 0000000..861b455
--- /dev/null
+++ b/test/bl-carpet-mask/bl.h.ah2.dx
@@ -0,0 +1,17 @@
+# 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 19 19
+object "+y 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 19 19
+object "-y patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "-z patch" class array type int rank 1 shape 2 items 1 data follows 19 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"
+member 5 value "-z patch"
diff --git a/test/bl-carpet-mask/bl.h.t0.ah1.gp b/test/bl-carpet-mask/bl.h.t0.ah1.gp
new file mode 100644
index 0000000..cc357b3
--- /dev/null
+++ b/test/bl-carpet-mask/bl.h.t0.ah1.gp
@@ -0,0 +1,2337 @@
+# N_patches = 6
+# origin = 0 0 1
+
+### +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	0.421318775179041	-0.2432485083	-0.2432485083	1.243248508
+-40	-45	0.421382732892571	-0.2150204864	-0.2562514371	1.256251437
+-35	-45	0.421529210075248	-0.1870378244	-0.2671176961	1.267117696
+-30	-45	0.421667159750387	-0.1593752058	-0.2760459539	1.276045954
+-25	-45	0.421775097419537	-0.1320770214	-0.2832400865	1.283240087
+-20	-45	0.421837517896121	-0.1051402887	-0.2888705689	1.288870569
+-15	-45	0.421862830104261	-0.07853262939	-0.2930877629	1.293087763
+-10	-45	0.421871715150912	-0.05219566883	-0.2960163477	1.296016348
+-5	-45	0.421874604338864	-0.02604897879	-0.2977411900	1.297741190
+0	-45	0.421875207760178	0.000000000	-0.2983108202	1.298310820
+5	-45	0.421874604338864	0.02604897879	-0.2977411900	1.297741190
+10	-45	0.421871715150912	0.05219566883	-0.2960163477	1.296016348
+15	-45	0.421862830104261	0.07853262939	-0.2930877629	1.293087763
+20	-45	0.421837517896121	0.1051402887	-0.2888705689	1.288870569
+25	-45	0.421775097419536	0.1320770214	-0.2832400865	1.283240087
+30	-45	0.421667159750387	0.1593752058	-0.2760459539	1.276045954
+35	-45	0.421529210075248	0.1870378244	-0.2671176961	1.267117696
+40	-45	0.421382732892571	0.2150204864	-0.2562514371	1.256251437
+45	-45	0.421318775179040	0.2432485083	-0.2432485083	1.243248508
+
+-45	-40	0.421382732892571	-0.2562514371	-0.2150204864	1.256251437
+-40	-40	0.421272221754933	-0.2277887162	-0.2277887162	1.271468021
+-35	-40	0.421330633409097	-0.1991562866	-0.2386606220	1.284424654
+-30	-40	0.421442926937622	-0.1704659712	-0.2477489683	1.295255723
+-25	-40	0.421538852330462	-0.1418033388	-0.2551687221	1.304098241
+-20	-40	0.421597735701028	-0.1132299405	-0.2610411302	1.311096705
+-15	-40	0.421620768314446	-0.08477485060	-0.2654777394	1.316384050
+-10	-40	0.421626555524844	-0.05643837964	-0.2685772951	1.320077956
+-5	-40	0.421628329185557	-0.02819436737	-0.2704108431	1.322263094
+0	-40	0.421628724074912	0.000000000	-0.2710177197	1.322986341
+5	-40	0.421628329185558	0.02819436737	-0.2704108431	1.322263094
+10	-40	0.421626555524844	0.05643837964	-0.2685772951	1.320077956
+15	-40	0.421620768314446	0.08477485060	-0.2654777394	1.316384050
+20	-40	0.421597735701028	0.1132299405	-0.2610411302	1.311096705
+25	-40	0.421538852330463	0.1418033388	-0.2551687221	1.304098241
+30	-40	0.421442926937622	0.1704659712	-0.2477489683	1.295255723
+35	-40	0.421330633409097	0.1991562866	-0.2386606220	1.284424654
+40	-40	0.421272221754933	0.2277887162	-0.2277887162	1.271468021
+45	-40	0.421382732892571	0.2562514371	-0.2150204864	1.256251437
+
+-45	-35	0.421529210075248	-0.2671176961	-0.1870378244	1.267117696
+-40	-35	0.421330633409097	-0.2386606220	-0.1991562866	1.284424654
+-35	-35	0.421282319496889	-0.2096059900	-0.2096059900	1.299348377
+-30	-35	0.421325856227415	-0.1801315738	-0.2184626778	1.311997038
+-25	-35	0.421372554121305	-0.1503587660	-0.2257787097	1.322445414
+-20	-35	0.421400697435995	-0.1204018921	-0.2316296898	1.330801480
+-15	-35	0.421401582376915	-0.09034330092	-0.2360860272	1.337165789
+-10	-35	0.421390485055737	-0.06023992018	-0.2392171977	1.341637564
+-5	-35	0.421383212896456	-0.03012181234	-0.2410771775	1.344293890
+0	-35	0.421380852538489	0.000000000	-0.2416941277	1.345174987
+5	-35	0.421383212896457	0.03012181234	-0.2410771775	1.344293890
+10	-35	0.421390485055737	0.06023992018	-0.2392171977	1.341637564
+15	-35	0.421401582376915	0.09034330092	-0.2360860272	1.337165789
+20	-35	0.421400697435995	0.1204018921	-0.2316296898	1.330801480
+25	-35	0.421372554121305	0.1503587660	-0.2257787097	1.322445414
+30	-35	0.421325856227415	0.1801315738	-0.2184626778	1.311997038
+35	-35	0.421282319496889	0.2096059900	-0.2096059900	1.299348377
+40	-35	0.421330633409097	0.2386606220	-0.1991562866	1.284424654
+45	-35	0.421529210075248	0.2671176961	-0.1870378244	1.267117696
+
+-45	-30	0.421667159750387	-0.2760459539	-0.1593752058	1.276045954
+-40	-30	0.421442926937622	-0.2477489683	-0.1704659712	1.295255723
+-35	-30	0.421325856227415	-0.2184626778	-0.1801315738	1.311997038
+-30	-30	0.421321930786916	-0.1884208955	-0.1884208955	1.326354564
+-25	-30	0.421328440031135	-0.1577679435	-0.1953374838	1.338334447
+-20	-30	0.421313496657360	-0.1266580350	-0.2009121728	1.347990091
+-15	-30	0.421278913148296	-0.09522783368	-0.2051874645	1.355395114
+-10	-30	0.421242857212014	-0.06358820422	-0.2082078799	1.360626627
+-5	-30	0.421222991887966	-0.03182375849	-0.2100095577	1.363747224
+0	-30	0.421216993526032	0.000000000	-0.2106084968	1.364784617
+5	-30	0.421222991887966	0.03182375849	-0.2100095577	1.363747224
+10	-30	0.421242857212014	0.06358820422	-0.2082078799	1.360626627
+15	-30	0.421278913148297	0.09522783368	-0.2051874645	1.355395114
+20	-30	0.421313496657360	0.1266580350	-0.2009121728	1.347990091
+25	-30	0.421328440031136	0.1577679435	-0.1953374838	1.338334447
+30	-30	0.421321930786916	0.1884208955	-0.1884208955	1.326354564
+35	-30	0.421325856227415	0.2184626778	-0.1801315738	1.311997038
+40	-30	0.421442926937622	0.2477489683	-0.1704659712	1.295255723
+45	-30	0.421667159750387	0.2760459539	-0.1593752058	1.276045954
+
+-45	-25	0.421775097419536	-0.2832400865	-0.1320770214	1.283240087
+-40	-25	0.421538852330462	-0.2551687221	-0.1418033388	1.304098241
+-35	-25	0.421372554121305	-0.2257787097	-0.1503587660	1.322445414
+-30	-25	0.421328440031135	-0.1953374838	-0.1577679435	1.338334447
+-25	-25	0.421305330993533	-0.1640064220	-0.1640064220	1.351712907
+-20	-25	0.421267406499696	-0.1319684657	-0.1690740077	1.362580380
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+0	30	0.421216993526032	0.000000000	0.2106084968	1.364784617
+5	30	0.421222991887965	0.03182375849	0.2100095577	1.363747224
+10	30	0.421242857212013	0.06358820422	0.2082078799	1.360626627
+15	30	0.421278913148296	0.09522783368	0.2051874645	1.355395114
+20	30	0.421313496657360	0.1266580350	0.2009121728	1.347990091
+25	30	0.421328440031135	0.1577679435	0.1953374838	1.338334447
+30	30	0.421321930786915	0.1884208955	0.1884208955	1.326354564
+35	30	0.421325856227415	0.2184626778	0.1801315738	1.311997038
+40	30	0.421442926937622	0.2477489683	0.1704659712	1.295255723
+45	30	0.421667159750387	0.2760459539	0.1593752058	1.276045954
+
+-45	35	0.421529210075248	-0.2671176961	0.1870378244	1.267117696
+-40	35	0.421330633409097	-0.2386606220	0.1991562866	1.284424654
+-35	35	0.421282319496889	-0.2096059900	0.2096059900	1.299348377
+-30	35	0.421325856227415	-0.1801315738	0.2184626778	1.311997038
+-25	35	0.421372554121305	-0.1503587660	0.2257787097	1.322445414
+-20	35	0.421400697435995	-0.1204018921	0.2316296898	1.330801480
+-15	35	0.421401582376914	-0.09034330092	0.2360860272	1.337165789
+-10	35	0.421390485055736	-0.06023992018	0.2392171977	1.341637564
+-5	35	0.421383212896456	-0.03012181234	0.2410771775	1.344293890
+0	35	0.421380852538488	0.000000000	0.2416941277	1.345174987
+5	35	0.421383212896456	0.03012181234	0.2410771775	1.344293890
+10	35	0.421390485055737	0.06023992018	0.2392171977	1.341637564
+15	35	0.421401582376914	0.09034330092	0.2360860272	1.337165789
+20	35	0.421400697435995	0.1204018921	0.2316296898	1.330801480
+25	35	0.421372554121305	0.1503587660	0.2257787097	1.322445414
+30	35	0.421325856227415	0.1801315738	0.2184626778	1.311997038
+35	35	0.421282319496889	0.2096059900	0.2096059900	1.299348377
+40	35	0.421330633409096	0.2386606220	0.1991562866	1.284424654
+45	35	0.421529210075248	0.2671176961	0.1870378244	1.267117696
+
+-45	40	0.421382732892571	-0.2562514371	0.2150204864	1.256251437
+-40	40	0.421272221754932	-0.2277887162	0.2277887162	1.271468021
+-35	40	0.421330633409097	-0.1991562866	0.2386606220	1.284424654
+-30	40	0.421442926937622	-0.1704659712	0.2477489683	1.295255723
+-25	40	0.421538852330462	-0.1418033388	0.2551687221	1.304098241
+-20	40	0.421597735701027	-0.1132299405	0.2610411302	1.311096705
+-15	40	0.421620768314446	-0.08477485060	0.2654777394	1.316384050
+-10	40	0.421626555524843	-0.05643837964	0.2685772951	1.320077956
+-5	40	0.421628329185557	-0.02819436737	0.2704108431	1.322263094
+0	40	0.421628724074912	0.000000000	0.2710177197	1.322986341
+5	40	0.421628329185557	0.02819436737	0.2704108431	1.322263094
+10	40	0.421626555524844	0.05643837964	0.2685772951	1.320077956
+15	40	0.421620768314446	0.08477485060	0.2654777394	1.316384050
+20	40	0.421597735701028	0.1132299405	0.2610411302	1.311096705
+25	40	0.421538852330462	0.1418033388	0.2551687221	1.304098241
+30	40	0.421442926937622	0.1704659712	0.2477489683	1.295255723
+35	40	0.421330633409097	0.1991562866	0.2386606220	1.284424654
+40	40	0.421272221754932	0.2277887162	0.2277887162	1.271468021
+45	40	0.421382732892571	0.2562514371	0.2150204864	1.256251437
+
+-45	45	0.421318775179040	-0.2432485083	0.2432485083	1.243248508
+-40	45	0.421382732892571	-0.2150204864	0.2562514371	1.256251437
+-35	45	0.421529210075248	-0.1870378244	0.2671176961	1.267117696
+-30	45	0.421667159750387	-0.1593752058	0.2760459539	1.276045954
+-25	45	0.421775097419536	-0.1320770214	0.2832400865	1.283240087
+-20	45	0.421837517896121	-0.1051402887	0.2888705689	1.288870569
+-15	45	0.421862830104260	-0.07853262939	0.2930877629	1.293087763
+-10	45	0.421871715150911	-0.05219566883	0.2960163477	1.296016348
+-5	45	0.421874604338863	-0.02604897879	0.2977411900	1.297741190
+0	45	0.421875207760178	0.000000000	0.2983108202	1.298310820
+5	45	0.421874604338863	0.02604897879	0.2977411900	1.297741190
+10	45	0.421871715150911	0.05219566883	0.2960163477	1.296016348
+15	45	0.421862830104260	0.07853262939	0.2930877629	1.293087763
+20	45	0.421837517896121	0.1051402887	0.2888705689	1.288870569
+25	45	0.421775097419536	0.1320770214	0.2832400865	1.283240087
+30	45	0.421667159750387	0.1593752058	0.2760459539	1.276045954
+35	45	0.421529210075248	0.1870378244	0.2671176961	1.267117696
+40	45	0.421382732892571	0.2150204864	0.2562514371	1.256251437
+45	45	0.421318775179040	0.2432485083	0.2432485083	1.243248508
+
+
+### +x patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	-45	0.421317295454029	0.2432476539	-0.2432476539	1.243247654
+45	-40	0.421383484215573	0.2562518940	-0.2150208697	1.256251894
+45	-35	0.421529869183829	0.2671181138	-0.1870381169	1.267118114
+45	-30	0.421667446949536	0.2760461420	-0.1593753144	1.276046142
+45	-25	0.421775248654315	0.2832401881	-0.1320770688	1.283240188
+45	-20	0.421837585830951	0.2888706155	-0.1051403056	1.288870615
+45	-15	0.421862858734393	0.2930877828	-0.07853263472	1.293087783
+45	-10	0.421871721447427	0.2960163521	-0.05219566961	1.296016352
+45	-5	0.421874605062139	0.2977411905	-0.02604897884	1.297741191
+45	0	0.421875207994685	0.2983108204	0.000000000	1.298310820
+45	5	0.421874605062139	0.2977411905	0.02604897884	1.297741191
+45	10	0.421871721447427	0.2960163521	0.05219566961	1.296016352
+45	15	0.421862858734392	0.2930877828	0.07853263472	1.293087783
+45	20	0.421837585830950	0.2888706155	0.1051403056	1.288870615
+45	25	0.421775248654314	0.2832401881	0.1320770688	1.283240188
+45	30	0.421667446949536	0.2760461420	0.1593753144	1.276046142
+45	35	0.421529869183828	0.2671181138	0.1870381169	1.267118114
+45	40	0.421383484215572	0.2562518940	0.2150208697	1.256251894
+45	45	0.421317295454029	0.2432476539	0.2432476539	1.243247654
+
+50	-45	0.421233930166748	0.2561609471	-0.2561609471	1.214944556
+50	-40	0.421357842549579	0.2715231950	-0.2278350128	1.227835013
+50	-35	0.421579106337178	0.2845923886	-0.1992737358	1.238801368
+50	-30	0.421800153288746	0.2955059898	-0.1706104627	1.247958967
+50	-25	0.421964049994406	0.3044049790	-0.1419463729	1.255426106
+50	-20	0.422057549538732	0.3114360010	-0.1133534343	1.261325834
+50	-15	0.422092443828016	0.3167379948	-0.08486968991	1.265774735
+50	-10	0.422097272783192	0.3204353016	-0.05650138924	1.268877143
+50	-5	0.422094460465481	0.3226193717	-0.02822553766	1.270709796
+50	0	0.422092640652910	0.3233417219	0.000000000	1.271315920
+50	5	0.422094460465481	0.3226193717	0.02822553766	1.270709796
+50	10	0.422097272783191	0.3204353016	0.05650138924	1.268877143
+50	15	0.422092443828015	0.3167379948	0.08486968991	1.265774735
+50	20	0.422057549538731	0.3114360010	0.1133534343	1.261325834
+50	25	0.421964049994405	0.3044049790	0.1419463729	1.255426106
+50	30	0.421800153288746	0.2955059898	0.1706104627	1.247958967
+50	35	0.421579106337177	0.2845923886	0.1992737358	1.238801368
+50	40	0.421357842549578	0.2715231950	0.2278350128	1.227835013
+50	45	0.421233930166748	0.2561609471	0.2561609471	1.214944556
+
+55	-45	0.420974391528746	0.2667661147	-0.2667661147	1.186791644
+55	-40	0.421160417370069	0.2843097472	-0.2385642040	1.199075828
+55	-35	0.421433896643666	0.2994560821	-0.2096814061	1.209681406
+55	-30	0.421740723023141	0.3123042519	-0.1803089439	1.218677791
+55	-25	0.421988055236152	0.3229164119	-0.1505783958	1.226108506
+55	-20	0.422146272101116	0.3313867593	-0.1206149164	1.232039507
+55	-15	0.422221936551192	0.3378221592	-0.09051917473	1.236545622
+55	-10	0.422245340255341	0.3423306283	-0.06036212609	1.239702486
+55	-5	0.422249870494668	0.3450019987	-0.03018376378	1.241573000
+55	0	0.422249842289697	0.3458868215	0.000000000	1.242192560
+55	5	0.422249870494667	0.3450019987	0.03018376378	1.241573000
+55	10	0.422245340255340	0.3423306283	0.06036212609	1.239702486
+55	15	0.422221936551191	0.3378221592	0.09051917473	1.236545622
+55	20	0.422146272101115	0.3313867593	0.1206149164	1.232039507
+55	25	0.421988055236151	0.3229164119	0.1505783958	1.226108506
+55	30	0.421740723023140	0.3123042519	0.1803089439	1.218677791
+55	35	0.421433896643665	0.2994560821	0.2096814061	1.209681406
+55	40	0.421160417370069	0.2843097472	0.2385642040	1.199075828
+55	45	0.420974391528746	0.2667661147	0.2667661147	1.186791644
+
+60	-45	0.420559993702196	0.2753211436	-0.2753211436	1.158956736
+60	-40	0.420779147405269	0.2947906905	-0.2473587596	1.170197484
+60	-35	0.421067389084512	0.3118056397	-0.2183286594	1.180021070
+60	-30	0.421429461477641	0.3264378572	-0.1884689847	1.188468985
+60	-25	0.421747854641817	0.3386712443	-0.1579249948	1.195531934
+60	-20	0.421972410989472	0.3485343311	-0.1268561221	1.201226390
+60	-15	0.422095920256010	0.3560843490	-0.09541251375	1.205585395
+60	-10	0.422143074517670	0.3613973039	-0.06372409543	1.208652831
+60	-5	0.422156306298631	0.3645531879	-0.03189427119	1.210474881
+60	0	0.422158185633100	0.3655997132	0.000000000	1.211079093
+60	5	0.422156306298631	0.3645531879	0.03189427119	1.210474881
+60	10	0.422143074517670	0.3613973039	0.06372409543	1.208652831
+60	15	0.422095920256010	0.3560843490	0.09541251375	1.205585395
+60	20	0.421972410989471	0.3485343311	0.1268561221	1.201226390
+60	25	0.421747854641816	0.3386712443	0.1579249948	1.195531934
+60	30	0.421429461477640	0.3264378572	0.1884689847	1.188468985
+60	35	0.421067389084511	0.3118056397	0.2183286594	1.180021070
+60	40	0.420779147405269	0.2947906905	0.2473587596	1.170197484
+60	45	0.420559993702195	0.2753211436	0.2753211436	1.158956736
+
+65	-45	0.420040278579633	0.2820750812	-0.2820750812	1.131533771
+65	-40	0.420256526120293	0.3031731709	-0.2543924958	1.141371971
+65	-35	0.420521269749207	0.3217939889	-0.2253225768	1.150055001
+65	-30	0.420895133174356	0.3379864933	-0.1951365929	1.157605690
+65	-25	0.421254844396123	0.3516707600	-0.1639867685	1.163986769
+65	-20	0.421528520292079	0.3628051176	-0.1320502636	1.169178805
+65	-15	0.421685230990907	0.3713826168	-0.09951167225	1.173178558
+65	-10	0.421738283850168	0.3774355762	-0.06655207557	1.176001100
+65	-5	0.421741831447011	0.3810319770	-0.03333597842	1.177678129
+65	0	0.421738502012694	0.3822248885	0.000000000	1.178234393
+65	5	0.421741831447011	0.3810319770	0.03333597842	1.177678129
+65	10	0.421738283850168	0.3774355762	0.06655207557	1.176001100
+65	15	0.421685230990907	0.3713826168	0.09951167225	1.173178558
+65	20	0.421528520292079	0.3628051176	0.1320502636	1.169178805
+65	25	0.421254844396123	0.3516707600	0.1639867685	1.163986769
+65	30	0.420895133174355	0.3379864933	0.1951365929	1.157605690
+65	35	0.420521269749207	0.3217939889	0.2253225768	1.150055001
+65	40	0.420256526120293	0.3031731709	0.2543924958	1.141371971
+65	45	0.420040278579632	0.2820750812	0.2820750812	1.131533771
+
+70	-45	0.419465656408432	0.2872463394	-0.2872463394	1.104549117
+70	-40	0.419651515881371	0.3096605903	-0.2598360871	1.112707238
+70	-35	0.419869695852162	0.3295996365	-0.2307881501	1.119964457
+70	-30	0.420207519358542	0.3470765928	-0.2003847643	1.126325549
+70	-25	0.420572650126287	0.3619824103	-0.1687951700	1.131750823
+70	-20	0.420862034392392	0.3741995837	-0.1361975101	1.136197510
+70	-15	0.420995778515202	0.3836326914	-0.1027940699	1.139630881
+70	-10	0.421011860991740	0.3903003194	-0.06882047688	1.142057699
+70	-5	0.420989416240125	0.3942704769	-0.03449419709	1.143502718
+70	0	0.420976478579508	0.3955884904	0.000000000	1.143982436
+70	5	0.420989416240125	0.3942704769	0.03449419709	1.143502718
+70	10	0.421011860991740	0.3903003194	0.06882047688	1.142057699
+70	15	0.420995778515201	0.3836326914	0.1027940699	1.139630881
+70	20	0.420862034392392	0.3741995837	0.1361975101	1.136197510
+70	25	0.420572650126286	0.3619824103	0.1687951700	1.131750823
+70	30	0.420207519358541	0.3470765928	0.2003847643	1.126325549
+70	35	0.419869695852162	0.3295996365	0.2307881501	1.119964457
+70	40	0.419651515881370	0.3096605903	0.2598360871	1.112707238
+70	45	0.419465656408432	0.2872463394	0.2872463394	1.104549117
+
+75	-45	0.418844673013456	0.2909909086	-0.2909909086	1.077970779
+75	-40	0.418992791401501	0.3144120169	-0.2638230074	1.084246446
+75	-35	0.419158621920595	0.3353711838	-0.2348294310	1.089862438
+75	-30	0.419444724877337	0.3538477740	-0.2042941076	1.094813225
+75	-25	0.419789601277831	0.3697131158	-0.1724000572	1.099064331
+75	-20	0.420040729651619	0.3827624025	-0.1393141213	1.102560877
+75	-15	0.420124716342017	0.3928641370	-0.1052676283	1.105267628
+75	-10	0.420090594508189	0.4000159031	-0.07053359643	1.107183938
+75	-5	0.420031937688743	0.4042786810	-0.03536980149	1.108326146
+75	0	0.420005891847984	0.4056945381	0.000000000	1.108705524
+75	5	0.420031937688742	0.4042786810	0.03536980149	1.108326146
+75	10	0.420090594508189	0.4000159031	0.07053359643	1.107183938
+75	15	0.420124716342017	0.3928641370	0.1052676283	1.105267628
+75	20	0.420040729651618	0.3827624025	0.1393141213	1.102560877
+75	25	0.419789601277831	0.3697131158	0.1724000572	1.099064331
+75	30	0.419444724877337	0.3538477740	0.2042941076	1.094813225
+75	35	0.419158621920594	0.3353711838	0.2348294310	1.089862438
+75	40	0.418992791401500	0.3144120169	0.2638230074	1.084246446
+75	45	0.418844673013456	0.2909909086	0.2909909086	1.077970779
+
+80	-45	0.418165123766224	0.2934155295	-0.2934155295	1.051737074
+80	-40	0.418267944942893	0.3175282659	-0.2664378508	1.055988800
+80	-35	0.418378784564103	0.3391958621	-0.2375074995	1.059809382
+80	-30	0.418613636256461	0.3583757466	-0.2069083338	1.063191313
+80	-25	0.418939283148840	0.3749306046	-0.1748330122	1.066110381
+80	-20	0.419138631315848	0.3885637361	-0.1414256341	1.068514270
+80	-15	0.419171014284574	0.3991402665	-0.1069493121	1.070379198
+80	-10	0.419088046488126	0.4066359035	-0.07170088111	1.071700881
+80	-5	0.418993791653686	0.4111052439	-0.03596704835	1.072488946
+80	0	0.418954765638670	0.4125899014	0.000000000	1.072750732
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+135	30	0.404312156366899	0.2646844373	0.1528156311	0.7353155627
+135	35	0.404600376776806	0.2563901099	0.1795262877	0.7436098901
+135	40	0.404953884308432	0.2462607191	0.2066372786	0.7537392809
+135	45	0.405481246888699	0.2341047070	0.2341047070	0.7658952930
+
+
+### +y patch
+# N_rho = 19
+# 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	0.421317295454029	0.2432476539	0.2432476539	1.243247654
+40	45	0.421383484215572	0.2150208697	0.2562518940	1.256251894
+35	45	0.421529869183828	0.1870381169	0.2671181138	1.267118114
+30	45	0.421667446949536	0.1593753144	0.2760461420	1.276046142
+25	45	0.421775248654314	0.1320770688	0.2832401881	1.283240188
+20	45	0.421837585830950	0.1051403056	0.2888706155	1.288870615
+15	45	0.421862858734392	0.07853263472	0.2930877828	1.293087783
+10	45	0.421871721447427	0.05219566961	0.2960163521	1.296016352
+5	45	0.421874605062139	0.02604897884	0.2977411905	1.297741191
+0	45	0.421875207994685	0.000000000	0.2983108204	1.298310820
+-5	45	0.421874605062139	-0.02604897884	0.2977411905	1.297741191
+-10	45	0.421871721447427	-0.05219566961	0.2960163521	1.296016352
+-15	45	0.421862858734392	-0.07853263472	0.2930877828	1.293087783
+-20	45	0.421837585830950	-0.1051403056	0.2888706155	1.288870615
+-25	45	0.421775248654314	-0.1320770688	0.2832401881	1.283240188
+-30	45	0.421667446949536	-0.1593753144	0.2760461420	1.276046142
+-35	45	0.421529869183828	-0.1870381169	0.2671181138	1.267118114
+-40	45	0.421383484215572	-0.2150208697	0.2562518940	1.256251894
+-45	45	0.421317295454029	-0.2432476539	0.2432476539	1.243247654
+
+45	50	0.421233930166748	0.2561609471	0.2561609471	1.214944556
+40	50	0.421357842549578	0.2278350128	0.2715231950	1.227835013
+35	50	0.421579106337177	0.1992737358	0.2845923886	1.238801368
+30	50	0.421800153288746	0.1706104627	0.2955059898	1.247958967
+25	50	0.421964049994405	0.1419463729	0.3044049790	1.255426106
+20	50	0.422057549538731	0.1133534343	0.3114360010	1.261325834
+15	50	0.422092443828015	0.08486968991	0.3167379948	1.265774735
+10	50	0.422097272783191	0.05650138924	0.3204353016	1.268877143
+5	50	0.422094460465481	0.02822553766	0.3226193717	1.270709796
+0	50	0.422092640652910	0.000000000	0.3233417219	1.271315920
+-5	50	0.422094460465481	-0.02822553766	0.3226193717	1.270709796
+-10	50	0.422097272783191	-0.05650138924	0.3204353016	1.268877143
+-15	50	0.422092443828015	-0.08486968991	0.3167379948	1.265774735
+-20	50	0.422057549538731	-0.1133534343	0.3114360010	1.261325834
+-25	50	0.421964049994405	-0.1419463729	0.3044049790	1.255426106
+-30	50	0.421800153288746	-0.1706104627	0.2955059898	1.247958967
+-35	50	0.421579106337177	-0.1992737358	0.2845923886	1.238801368
+-40	50	0.421357842549578	-0.2278350128	0.2715231950	1.227835013
+-45	50	0.421233930166747	-0.2561609471	0.2561609471	1.214944556
+
+45	55	0.420974391528746	0.2667661147	0.2667661147	1.186791644
+40	55	0.421160417370069	0.2385642040	0.2843097472	1.199075828
+35	55	0.421433896643665	0.2096814061	0.2994560821	1.209681406
+30	55	0.421740723023140	0.1803089439	0.3123042519	1.218677791
+25	55	0.421988055236151	0.1505783958	0.3229164119	1.226108506
+20	55	0.422146272101115	0.1206149164	0.3313867593	1.232039507
+15	55	0.422221936551191	0.09051917473	0.3378221592	1.236545622
+10	55	0.422245340255340	0.06036212609	0.3423306283	1.239702486
+5	55	0.422249870494667	0.03018376378	0.3450019987	1.241573000
+0	55	0.422249842289696	0.000000000	0.3458868215	1.242192560
+-5	55	0.422249870494667	-0.03018376378	0.3450019987	1.241573000
+-10	55	0.422245340255340	-0.06036212609	0.3423306283	1.239702486
+-15	55	0.422221936551191	-0.09051917473	0.3378221592	1.236545622
+-20	55	0.422146272101115	-0.1206149164	0.3313867593	1.232039507
+-25	55	0.421988055236151	-0.1505783958	0.3229164119	1.226108506
+-30	55	0.421740723023140	-0.1803089439	0.3123042519	1.218677791
+-35	55	0.421433896643665	-0.2096814061	0.2994560821	1.209681406
+-40	55	0.421160417370069	-0.2385642040	0.2843097472	1.199075828
+-45	55	0.420974391528746	-0.2667661147	0.2667661147	1.186791644
+
+45	60	0.420559993702195	0.2753211436	0.2753211436	1.158956736
+40	60	0.420779147405269	0.2473587596	0.2947906905	1.170197484
+35	60	0.421067389084512	0.2183286594	0.3118056397	1.180021070
+30	60	0.421429461477641	0.1884689847	0.3264378572	1.188468985
+25	60	0.421747854641816	0.1579249948	0.3386712443	1.195531934
+20	60	0.421972410989471	0.1268561221	0.3485343311	1.201226390
+15	60	0.422095920256010	0.09541251375	0.3560843490	1.205585395
+10	60	0.422143074517669	0.06372409543	0.3613973039	1.208652831
+5	60	0.422156306298630	0.03189427119	0.3645531879	1.210474881
+0	60	0.422158185633099	0.000000000	0.3655997132	1.211079093
+-5	60	0.422156306298630	-0.03189427119	0.3645531879	1.210474881
+-10	60	0.422143074517669	-0.06372409543	0.3613973039	1.208652831
+-15	60	0.422095920256010	-0.09541251375	0.3560843490	1.205585395
+-20	60	0.421972410989471	-0.1268561221	0.3485343311	1.201226390
+-25	60	0.421747854641816	-0.1579249948	0.3386712443	1.195531934
+-30	60	0.421429461477640	-0.1884689847	0.3264378572	1.188468985
+-35	60	0.421067389084511	-0.2183286594	0.3118056397	1.180021070
+-40	60	0.420779147405269	-0.2473587596	0.2947906905	1.170197484
+-45	60	0.420559993702195	-0.2753211436	0.2753211436	1.158956736
+
+45	65	0.420040278579632	0.2820750812	0.2820750812	1.131533771
+40	65	0.420256526120293	0.2543924958	0.3031731709	1.141371971
+35	65	0.420521269749207	0.2253225768	0.3217939889	1.150055001
+30	65	0.420895133174355	0.1951365929	0.3379864933	1.157605690
+25	65	0.421254844396123	0.1639867685	0.3516707600	1.163986769
+20	65	0.421528520292079	0.1320502636	0.3628051176	1.169178805
+15	65	0.421685230990907	0.09951167225	0.3713826168	1.173178558
+10	65	0.421738283850168	0.06655207557	0.3774355762	1.176001100
+5	65	0.421741831447010	0.03333597842	0.3810319770	1.177678129
+0	65	0.421738502012693	0.000000000	0.3822248885	1.178234393
+-5	65	0.421741831447010	-0.03333597842	0.3810319770	1.177678129
+-10	65	0.421738283850168	-0.06655207557	0.3774355762	1.176001100
+-15	65	0.421685230990906	-0.09951167225	0.3713826168	1.173178558
+-20	65	0.421528520292079	-0.1320502636	0.3628051176	1.169178805
+-25	65	0.421254844396122	-0.1639867685	0.3516707600	1.163986769
+-30	65	0.420895133174355	-0.1951365929	0.3379864933	1.157605690
+-35	65	0.420521269749206	-0.2253225768	0.3217939889	1.150055001
+-40	65	0.420256526120293	-0.2543924958	0.3031731709	1.141371971
+-45	65	0.420040278579632	-0.2820750812	0.2820750812	1.131533771
+
+45	70	0.419465656408432	0.2872463394	0.2872463394	1.104549117
+40	70	0.419651515881370	0.2598360871	0.3096605903	1.112707238
+35	70	0.419869695852162	0.2307881501	0.3295996365	1.119964457
+30	70	0.420207519358541	0.2003847643	0.3470765928	1.126325549
+25	70	0.420572650126286	0.1687951700	0.3619824103	1.131750823
+20	70	0.420862034392391	0.1361975101	0.3741995837	1.136197510
+15	70	0.420995778515201	0.1027940699	0.3836326914	1.139630881
+10	70	0.421011860991739	0.06882047688	0.3903003194	1.142057699
+5	70	0.420989416240124	0.03449419709	0.3942704769	1.143502718
+0	70	0.420976478579507	0.000000000	0.3955884904	1.143982436
+-5	70	0.420989416240124	-0.03449419709	0.3942704769	1.143502718
+-10	70	0.421011860991739	-0.06882047688	0.3903003194	1.142057699
+-15	70	0.420995778515201	-0.1027940699	0.3836326914	1.139630881
+-20	70	0.420862034392391	-0.1361975101	0.3741995837	1.136197510
+-25	70	0.420572650126286	-0.1687951700	0.3619824103	1.131750823
+-30	70	0.420207519358541	-0.2003847643	0.3470765928	1.126325549
+-35	70	0.419869695852161	-0.2307881501	0.3295996365	1.119964457
+-40	70	0.419651515881370	-0.2598360871	0.3096605903	1.112707238
+-45	70	0.419465656408431	-0.2872463394	0.2872463394	1.104549117
+
+45	75	0.418844673013456	0.2909909086	0.2909909086	1.077970779
+40	75	0.418992791401500	0.2638230074	0.3144120169	1.084246446
+35	75	0.419158621920594	0.2348294310	0.3353711838	1.089862438
+30	75	0.419444724877337	0.2042941076	0.3538477740	1.094813225
+25	75	0.419789601277830	0.1724000572	0.3697131158	1.099064331
+20	75	0.420040729651618	0.1393141213	0.3827624025	1.102560877
+15	75	0.420124716342016	0.1052676283	0.3928641370	1.105267628
+10	75	0.420090594508189	0.07053359643	0.4000159031	1.107183938
+5	75	0.420031937688742	0.03536980149	0.4042786810	1.108326146
+0	75	0.420005891847984	0.000000000	0.4056945381	1.108705524
+-5	75	0.420031937688742	-0.03536980149	0.4042786810	1.108326146
+-10	75	0.420090594508189	-0.07053359643	0.4000159031	1.107183938
+-15	75	0.420124716342016	-0.1052676283	0.3928641370	1.105267628
+-20	75	0.420040729651618	-0.1393141213	0.3827624025	1.102560877
+-25	75	0.419789601277830	-0.1724000572	0.3697131158	1.099064331
+-30	75	0.419444724877337	-0.2042941076	0.3538477740	1.094813225
+-35	75	0.419158621920594	-0.2348294310	0.3353711838	1.089862438
+-40	75	0.418992791401500	-0.2638230074	0.3144120169	1.084246446
+-45	75	0.418844673013455	-0.2909909086	0.2909909086	1.077970779
+
+45	80	0.418165123766223	0.2934155295	0.2934155295	1.051737074
+40	80	0.418267944942893	0.2664378508	0.3175282659	1.055988800
+35	80	0.418378784564102	0.2375074995	0.3391958621	1.059809382
+30	80	0.418613636256460	0.2069083338	0.3583757466	1.063191313
+25	80	0.418939283148839	0.1748330122	0.3749306046	1.066110381
+20	80	0.419138631315848	0.1414256341	0.3885637361	1.068514270
+15	80	0.419171014284574	0.1069493121	0.3991402665	1.070379198
+10	80	0.419088046488126	0.07170088111	0.4066359035	1.071700881
+5	80	0.418993791653686	0.03596704835	0.4111052439	1.072488946
+0	80	0.418954765638670	0.000000000	0.4125899014	1.072750732
+-5	80	0.418993791653686	-0.03596704835	0.4111052439	1.072488946
+-10	80	0.419088046488126	-0.07170088111	0.4066359035	1.071700881
+-15	80	0.419171014284574	-0.1069493121	0.3991402665	1.070379198
+-20	80	0.419138631315848	-0.1414256341	0.3885637361	1.068514270
+-25	80	0.418939283148839	-0.1748330122	0.3749306046	1.066110381
+-30	80	0.418613636256460	-0.2069083338	0.3583757466	1.063191313
+-35	80	0.418378784564102	-0.2375074995	0.3391958621	1.059809382
+-40	80	0.418267944942893	-0.2664378508	0.3175282659	1.055988800
+-45	80	0.418165123766223	-0.2934155295	0.2934155295	1.051737074
+
+45	85	0.417413105836212	0.2945924538	0.2945924538	1.025773500
+40	85	0.417460944315203	0.2677380956	0.3190778373	1.027915694
+35	85	0.417514185569646	0.2388636717	0.3411326766	1.029845242
+30	85	0.417699839258210	0.2082530161	0.3607048046	1.031557581
+25	85	0.417999772834335	0.1761016147	0.3776511314	1.033040193
+20	85	0.418164746481572	0.1425398723	0.3916250805	1.034262755
+15	85	0.418158635230793	0.1078430218	0.4024756365	1.035212056
+10	85	0.418038313237822	0.07232364175	0.4101677546	1.035885029
+5	85	0.417916487369995	0.03628626512	0.4147539082	1.036286265
+0	85	0.417867347085979	0.000000000	0.4162772357	1.036419539
+-5	85	0.417916487369995	-0.03628626512	0.4147539082	1.036286265
+-10	85	0.418038313237822	-0.07232364175	0.4101677546	1.035885029
+-15	85	0.418158635230793	-0.1078430218	0.4024756365	1.035212056
+-20	85	0.418164746481572	-0.1425398723	0.3916250805	1.034262755
+-25	85	0.417999772834335	-0.1761016147	0.3776511314	1.033040193
+-30	85	0.417699839258210	-0.2082530161	0.3607048046	1.031557581
+-35	85	0.417514185569646	-0.2388636717	0.3411326766	1.029845242
+-40	85	0.417460944315203	-0.2677380956	0.3190778373	1.027915694
+-45	85	0.417413105836212	-0.2945924538	0.2945924538	1.025773500
+
+45	90	0.416575066505252	0.2945630544	0.2945630544	1.000000000
+40	90	0.416555918685633	0.2677569833	0.3191003468	1.000000000
+35	90	0.416547633196943	0.2389219070	0.3412158453	1.000000000
+30	90	0.416686399350284	0.2083431997	0.3608610072	1.000000000
+25	90	0.416964026317032	0.1762166120	0.3778977440	1.000000000
+20	90	0.417109159696414	0.1426597346	0.3919543994	1.000000000
+15	90	0.417082752909536	0.1079489598	0.4028710027	1.000000000
+10	90	0.416942990231221	0.07240139044	0.4106086893	1.000000000
+5	90	0.416806825517986	0.03632710846	0.4152207497	1.000000000
+0	90	0.416752426852034	0.000000000	0.4167524269	1.000000000
+-5	90	0.416806825517986	-0.03632710846	0.4152207497	1.000000000
+-10	90	0.416942990231221	-0.07240139044	0.4106086893	1.000000000
+-15	90	0.417082752909536	-0.1079489598	0.4028710027	1.000000000
+-20	90	0.417109159696414	-0.1426597346	0.3919543994	1.000000000
+-25	90	0.416964026317032	-0.1762166120	0.3778977440	1.000000000
+-30	90	0.416686399350284	-0.2083431997	0.3608610072	1.000000000
+-35	90	0.416547633196943	-0.2389219070	0.3412158453	1.000000000
+-40	90	0.416555918685633	-0.2677569833	0.3191003468	1.000000000
+-45	90	0.416575066505252	-0.2945630544	0.2945630544	1.000000000
+
+45	95	0.415639245817503	0.2933405386	0.2933405386	0.9743360283
+40	95	0.415539863863006	0.2665060129	0.3176094983	0.9722127695
+35	95	0.415464568999817	0.2376910674	0.3394580241	0.9703012712
+30	95	0.415554437496206	0.2071833810	0.3588521424	0.9686045057
+25	95	0.415806686263465	0.1751776762	0.3756697389	0.9671331566
+20	95	0.415945201094532	0.1417832955	0.3895464030	0.9659191058
+15	95	0.415917052169241	0.1072649180	0.4003181238	0.9649767024
+10	95	0.415777307102880	0.07193247139	0.4079493172	0.9643090594
+5	95	0.415641844713099	0.03608876564	0.4124964789	0.9639112344
+0	95	0.415587819109994	0.000000000	0.4140063820	0.9637791349
+-5	95	0.415641844713099	-0.03608876564	0.4124964789	0.9639112344
+-10	95	0.415777307102880	-0.07193247139	0.4079493172	0.9643090594
+-15	95	0.415917052169241	-0.1072649180	0.4003181238	0.9649767024
+-20	95	0.415945201094532	-0.1417832955	0.3895464030	0.9659191058
+-25	95	0.415806686263465	-0.1751776762	0.3756697389	0.9671331566
+-30	95	0.415554437496206	-0.2071833810	0.3588521424	0.9686045057
+-35	95	0.415464568999817	-0.2376910674	0.3394580241	0.9703012712
+-40	95	0.415539863863006	-0.2665060129	0.3176094983	0.9722127695
+-45	95	0.415639245817503	-0.2933405386	0.2933405386	0.9743360283
+
+45	100	0.414597002169521	0.2909118719	0.2909118719	0.9487043880
+40	100	0.414405029193084	0.2639771627	0.3145957320	0.9445282844
+35	100	0.414257567334615	0.2351679450	0.3358546319	0.9407797668
+30	100	0.414291008610012	0.2047717869	0.3546751388	0.9374612036
+25	100	0.414487472870191	0.1729751692	0.3709464475	0.9345921329
+20	100	0.414638373852076	0.1399071585	0.3843917588	0.9322213618
+15	100	0.414623343886616	0.1057889975	0.3948099137	0.9303843600
+10	100	0.414499125027480	0.07091577231	0.4021833302	0.9290842277
+5	100	0.414376977444354	0.03557073418	0.4065753521	0.9283097957
+0	100	0.414328157157069	0.000000000	0.4080335815	0.9280526706
+-5	100	0.414376977444354	-0.03557073418	0.4065753521	0.9283097957
+-10	100	0.414499125027480	-0.07091577231	0.4021833302	0.9290842277
+-15	100	0.414623343886616	-0.1057889975	0.3948099137	0.9303843600
+-20	100	0.414638373852076	-0.1399071585	0.3843917588	0.9322213618
+-25	100	0.414487472870191	-0.1729751692	0.3709464475	0.9345921329
+-30	100	0.414291008610013	-0.2047717869	0.3546751388	0.9374612036
+-35	100	0.414257567334616	-0.2351679450	0.3358546319	0.9407797668
+-40	100	0.414405029193084	-0.2639771627	0.3145957320	0.9445282844
+-45	100	0.414597002169521	-0.2909118719	0.2909118719	0.9487043880
+
+45	105	0.413445284369719	0.2872397017	0.2872397017	0.9230343539
+40	105	0.413153891777358	0.2601464858	0.3100305090	0.9169275755
+35	105	0.412935799970452	0.2313431572	0.3303922688	0.9114716584
+30	105	0.412913020786160	0.2011127857	0.3483375629	0.9066632313
+25	105	0.413036046994869	0.1696264936	0.3637651895	0.9025294112
+20	105	0.413182152731024	0.1370393500	0.3765125196	0.8991137744
+15	105	0.413182779355283	0.1035282370	0.3863726406	0.8964717630
+10	105	0.413082016309701	0.06935684972	0.3933422409	0.8946042642
+5	105	0.412980525279281	0.03477602032	0.3974917311	0.8934924117
+0	105	0.412939855060755	0.000000000	0.3988692707	0.8931233010
+-5	105	0.412980525279281	-0.03477602032	0.3974917311	0.8934924117
+-10	105	0.413082016309701	-0.06935684972	0.3933422409	0.8946042642
+-15	105	0.413182779355283	-0.1035282370	0.3863726406	0.8964717630
+-20	105	0.413182152731024	-0.1370393500	0.3765125196	0.8991137744
+-25	105	0.413036046994869	-0.1696264936	0.3637651895	0.9025294112
+-30	105	0.412913020786160	-0.2011127857	0.3483375629	0.9066632313
+-35	105	0.412935799970453	-0.2313431572	0.3303922688	0.9114716584
+-40	105	0.413153891777358	-0.2601464858	0.3100305090	0.9169275755
+-45	105	0.413445284369719	-0.2872397017	0.2872397017	0.9230343539
+
+45	110	0.412193089113133	0.2822661502	0.2822661502	0.8972635232
+40	110	0.411806057146319	0.2549784059	0.3038714312	0.8893998440
+35	110	0.411532116427935	0.2262052651	0.3230545984	0.8824177421
+30	110	0.411465751513899	0.1962160690	0.3398562009	0.8763024590
+25	110	0.411513913770974	0.1651594820	0.3541856522	0.8710869652
+20	110	0.411590774157013	0.1331971859	0.3659562606	0.8668028141
+15	110	0.411611809340913	0.1005027966	0.3750815431	0.8634814829
+10	110	0.411535676999638	0.06727145758	0.3815153943	0.8611397525
+5	110	0.411457589774367	0.03371319717	0.3853436069	0.8597463971
+0	110	0.411426467355646	0.000000000	0.3866144154	0.8592838607
+-5	110	0.411457589774367	-0.03371319717	0.3853436069	0.8597463971
+-10	110	0.411535676999638	-0.06727145758	0.3815153943	0.8611397525
+-15	110	0.411611809340914	-0.1005027966	0.3750815431	0.8634814829
+-20	110	0.411590774157014	-0.1331971859	0.3659562606	0.8668028141
+-25	110	0.411513913770974	-0.1651594820	0.3541856522	0.8710869652
+-30	110	0.411465751513899	-0.1962160690	0.3398562009	0.8763024590
+-35	110	0.411532116427936	-0.2262052651	0.3230545984	0.8824177421
+-40	110	0.411806057146319	-0.2549784059	0.3038714312	0.8893998440
+-45	110	0.412193089113134	-0.2822661502	0.2822661502	0.8972635232
+
+45	115	0.410861221174009	0.2759109500	0.2759109500	0.8713406110
+40	115	0.410396669893040	0.2484240616	0.2960602679	0.8619448298
+35	115	0.410099864329442	0.2197386073	0.3138192540	0.8536636786
+30	115	0.410006859569762	0.1900885407	0.3292430104	0.8464714629
+25	115	0.410000497984177	0.1596056583	0.3422754388	0.8403943417
+20	115	0.410006254414508	0.1284407374	0.3528880258	0.8354456111
+15	115	0.409979437386298	0.09674927269	0.3610732013	0.8316288011
+10	115	0.409916722310054	0.06468658342	0.3668558445	0.8289323102
+5	115	0.409863121137783	0.03239704280	0.3702998936	0.8273263238
+0	115	0.409842510270318	0.000000000	0.3714434585	0.8267930707
+-5	115	0.409863121137783	-0.03239704280	0.3702998936	0.8273263238
+-10	115	0.409916722310054	-0.06468658342	0.3668558445	0.8289323102
+-15	115	0.409979437386299	-0.09674927269	0.3610732013	0.8316288011
+-20	115	0.410006254414508	-0.1284407374	0.3528880258	0.8354456111
+-25	115	0.410000497984177	-0.1596056583	0.3422754388	0.8403943417
+-30	115	0.410006859569762	-0.1900885407	0.3292430104	0.8464714629
+-35	115	0.410099864329443	-0.2197386073	0.3138192540	0.8536636786
+-40	115	0.410396669893041	-0.2484240616	0.2960602679	0.8619448298
+-45	115	0.410861221174010	-0.2759109500	0.2759109500	0.8713406110
+
+45	120	0.409483464825415	0.2680698533	0.2680698533	0.8452297980
+40	120	0.408973597448124	0.2404187622	0.2865199236	0.8345776450
+35	120	0.408687783070896	0.2119096803	0.3026383875	0.8252716455
+30	120	0.408591532607701	0.1827276884	0.3164936402	0.8172723116
+25	120	0.408557298593188	0.1529857438	0.3280789864	0.8105835089
+20	120	0.408521160772016	0.1228123188	0.3374240727	0.8051881208
+15	120	0.408460567065285	0.09233031546	0.3445814284	0.8010558196
+10	120	0.408388640859697	0.06164781160	0.3496221131	0.7981455789
+5	120	0.408336282868854	0.03085015656	0.3526189031	0.7964153814
+0	120	0.408317245024597	0.000000000	0.3536131070	0.7958413775
+-5	120	0.408336282868854	-0.03085015656	0.3526189031	0.7964153814
+-10	120	0.408388640859697	-0.06164781160	0.3496221131	0.7981455789
+-15	120	0.408460567065286	-0.09233031546	0.3445814284	0.8010558196
+-20	120	0.408521160772016	-0.1228123188	0.3374240727	0.8051881208
+-25	120	0.408557298593189	-0.1529857438	0.3280789864	0.8105835089
+-30	120	0.408591532607702	-0.1827276884	0.3164936402	0.8172723116
+-35	120	0.408687783070896	-0.2119096803	0.3026383875	0.8252716455
+-40	120	0.408973597448124	-0.2404187622	0.2865199236	0.8345776450
+-45	120	0.409483464825416	-0.2680698533	0.2680698533	0.8452297980
+
+45	125	0.408114012981202	0.2586166565	0.2586166565	0.8189146676
+40	125	0.407605109056096	0.2308858677	0.2751590623	0.8073315504
+35	125	0.407349729987815	0.2026739302	0.2894483694	0.7973260698
+30	125	0.407232900944229	0.1741063414	0.3015610292	0.7888446941
+25	125	0.407151873444531	0.1452843871	0.3115633735	0.7818409772
+20	125	0.407063084704379	0.1163053737	0.3195463880	0.7762512103
+15	125	0.406959866536060	0.08724717519	0.3256108906	0.7720047999
+10	125	0.406863708905255	0.05816324340	0.3298601449	0.7690294400
+5	125	0.406799430555320	0.02907931719	0.3323781164	0.7672663373
+0	125	0.406776919224707	0.000000000	0.3332121450	0.7666823443
+-5	125	0.406799430555320	-0.02907931719	0.3323781164	0.7672663373
+-10	125	0.406863708905255	-0.05816324340	0.3298601449	0.7690294400
+-15	125	0.406959866536061	-0.08724717519	0.3256108906	0.7720047999
+-20	125	0.407063084704380	-0.1163053737	0.3195463880	0.7762512103
+-25	125	0.407151873444532	-0.1452843871	0.3115633735	0.7818409772
+-30	125	0.407232900944229	-0.1741063414	0.3015610292	0.7888446941
+-35	125	0.407349729987815	-0.2026739302	0.2894483694	0.7973260698
+-40	125	0.407605109056096	-0.2308858677	0.2751590623	0.8073315504
+-45	125	0.408114012981202	-0.2586166565	0.2586166565	0.8189146676
+
+45	130	0.406795594720916	0.2473807008	0.2473807008	0.7924229452
+40	130	0.406289306919104	0.2196872114	0.2618130234	0.7803127886
+35	130	0.406013998432556	0.1919163569	0.2740849626	0.7700154089
+30	130	0.405832116775405	0.1641516834	0.2843190559	0.7614279851
+25	130	0.405671576403576	0.1364656749	0.2926515842	0.7544361636
+20	130	0.405508438276746	0.1089087831	0.2992244222	0.7489208977
+15	130	0.405347985375320	0.08150289901	0.3041729601	0.7447685814
+10	130	0.405216174033674	0.05424170742	0.3076200092	0.7418761638
+5	130	0.405131857886018	0.02709124517	0.3096543492	0.7401691498
+0	130	0.405102909412565	0.000000000	0.3103268326	0.7396048692
+-5	130	0.405131857886018	-0.02709124517	0.3096543492	0.7401691498
+-10	130	0.405216174033674	-0.05424170742	0.3076200092	0.7418761638
+-15	130	0.405347985375321	-0.08150289901	0.3041729601	0.7447685814
+-20	130	0.405508438276746	-0.1089087831	0.2992244222	0.7489208977
+-25	130	0.405671576403576	-0.1364656749	0.2926515842	0.7544361636
+-30	130	0.405832116775405	-0.1641516834	0.2843190559	0.7614279851
+-35	130	0.406013998432556	-0.1919163569	0.2740849626	0.7700154089
+-40	130	0.406289306919104	-0.2196872114	0.2618130234	0.7803127886
+-45	130	0.406795594720916	-0.2473807008	0.2473807008	0.7924229452
+
+45	135	0.405481246888699	0.2341047070	0.2341047070	0.7658952930
+40	135	0.404953884308432	0.2066372786	0.2462607191	0.7537392809
+35	135	0.404600376776805	0.1795262877	0.2563901099	0.7436098901
+30	135	0.404312156366899	0.1528156311	0.2646844373	0.7353155627
+25	135	0.404045335367779	0.1265250242	0.2713337901	0.7286662099
+20	135	0.403792076974580	0.1006425785	0.2765132120	0.7234867880
+15	135	0.403565989481414	0.07512654831	0.2803760953	0.7196239047
+10	135	0.403393035592475	0.04990941212	0.2830503416	0.7169496584
+5	135	0.403285294975797	0.02490116729	0.2846216445	0.7153783555
+0	135	0.403248758763943	0.000000000	0.2851399318	0.7148600682
+-5	135	0.403285294975797	-0.02490116729	0.2846216445	0.7153783555
+-10	135	0.403393035592475	-0.04990941212	0.2830503416	0.7169496584
+-15	135	0.403565989481415	-0.07512654831	0.2803760953	0.7196239047
+-20	135	0.403792076974581	-0.1006425785	0.2765132120	0.7234867880
+-25	135	0.404045335367779	-0.1265250242	0.2713337901	0.7286662099
+-30	135	0.404312156366899	-0.1528156311	0.2646844373	0.7353155627
+-35	135	0.404600376776806	-0.1795262877	0.2563901099	0.7436098901
+-40	135	0.404953884308432	-0.2066372786	0.2462607191	0.7537392809
+-45	135	0.405481246888700	-0.2341047070	0.2341047070	0.7658952930
+
+
+### -x patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-135	45	0.405481246888700	-0.2341047070	0.2341047070	0.7658952930
+-135	40	0.404953884308432	-0.2462607191	0.2066372786	0.7537392809
+-135	35	0.404600376776806	-0.2563901099	0.1795262877	0.7436098901
+-135	30	0.404312156366899	-0.2646844373	0.1528156311	0.7353155627
+-135	25	0.404045335367779	-0.2713337901	0.1265250242	0.7286662099
+-135	20	0.403792076974580	-0.2765132120	0.1006425785	0.7234867880
+-135	15	0.403565989481414	-0.2803760953	0.07512654831	0.7196239047
+-135	10	0.403393035592475	-0.2830503416	0.04990941212	0.7169496584
+-135	5	0.403285294975798	-0.2846216445	0.02490116729	0.7153783555
+-135	-2.84217e-14	0.403248758763943	-0.2851399318	-9.170914980e-17	0.7148600682
+-135	-5	0.403285294975798	-0.2846216445	-0.02490116729	0.7153783555
+-135	-10	0.403393035592475	-0.2830503416	-0.04990941212	0.7169496584
+-135	-15	0.403565989481415	-0.2803760953	-0.07512654831	0.7196239047
+-135	-20	0.403792076974581	-0.2765132120	-0.1006425785	0.7234867880
+-135	-25	0.404045335367780	-0.2713337901	-0.1265250242	0.7286662099
+-135	-30	0.404312156366900	-0.2646844373	-0.1528156311	0.7353155627
+-135	-35	0.404600376776806	-0.2563901099	-0.1795262877	0.7436098901
+-135	-40	0.404953884308433	-0.2462607191	-0.2066372786	0.7537392809
+-135	-45	0.405481246888700	-0.2341047070	-0.2341047070	0.7658952930
+
+-130	45	0.406795594720916	-0.2473807008	0.2473807008	0.7924229452
+-130	40	0.406289306919104	-0.2618130234	0.2196872114	0.7803127886
+-130	35	0.406013998432556	-0.2740849626	0.1919163569	0.7700154089
+-130	30	0.405832116775405	-0.2843190559	0.1641516834	0.7614279851
+-130	25	0.405671576403576	-0.2926515842	0.1364656749	0.7544361636
+-130	20	0.405508438276746	-0.2992244222	0.1089087831	0.7489208977
+-130	15	0.405347985375320	-0.3041729601	0.08150289901	0.7447685814
+-130	10	0.405216174033674	-0.3076200092	0.05424170742	0.7418761638
+-130	5	0.405131857886018	-0.3096543492	0.02709124517	0.7401691498
+-130	-2.84217e-14	0.405102909412565	-0.3103268326	-9.980997680e-17	0.7396048692
+-130	-5	0.405131857886018	-0.3096543492	-0.02709124517	0.7401691498
+-130	-10	0.405216174033674	-0.3076200092	-0.05424170742	0.7418761638
+-130	-15	0.405347985375321	-0.3041729601	-0.08150289901	0.7447685814
+-130	-20	0.405508438276747	-0.2992244222	-0.1089087831	0.7489208977
+-130	-25	0.405671576403577	-0.2926515842	-0.1364656749	0.7544361636
+-130	-30	0.405832116775406	-0.2843190559	-0.1641516834	0.7614279851
+-130	-35	0.406013998432557	-0.2740849626	-0.1919163569	0.7700154089
+-130	-40	0.406289306919105	-0.2618130234	-0.2196872114	0.7803127886
+-130	-45	0.406795594720917	-0.2473807008	-0.2473807008	0.7924229452
+
+-125	45	0.408114012981202	-0.2586166565	0.2586166565	0.8189146676
+-125	40	0.407605109056096	-0.2751590623	0.2308858677	0.8073315504
+-125	35	0.407349729987815	-0.2894483694	0.2026739302	0.7973260698
+-125	30	0.407232900944229	-0.3015610292	0.1741063414	0.7888446941
+-125	25	0.407151873444531	-0.3115633735	0.1452843871	0.7818409772
+-125	20	0.407063084704379	-0.3195463880	0.1163053737	0.7762512103
+-125	15	0.406959866536060	-0.3256108906	0.08724717519	0.7720047999
+-125	10	0.406863708905255	-0.3298601449	0.05816324340	0.7690294400
+-125	5	0.406799430555320	-0.3323781164	0.02907931719	0.7672663373
+-125	-2.84217e-14	0.406776919224708	-0.3332121450	-1.071705472e-16	0.7666823443
+-125	-5	0.406799430555320	-0.3323781164	-0.02907931719	0.7672663373
+-125	-10	0.406863708905255	-0.3298601449	-0.05816324340	0.7690294400
+-125	-15	0.406959866536061	-0.3256108906	-0.08724717519	0.7720047999
+-125	-20	0.407063084704380	-0.3195463880	-0.1163053737	0.7762512103
+-125	-25	0.407151873444532	-0.3115633735	-0.1452843871	0.7818409772
+-125	-30	0.407232900944230	-0.3015610292	-0.1741063414	0.7888446941
+-125	-35	0.407349729987816	-0.2894483694	-0.2026739302	0.7973260698
+-125	-40	0.407605109056097	-0.2751590623	-0.2308858677	0.8073315504
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+-70	-30	0.420207519358542	-0.3470765928	-0.2003847643	1.126325549
+-70	-35	0.419869695852162	-0.3295996365	-0.2307881501	1.119964457
+-70	-40	0.419651515881371	-0.3096605903	-0.2598360871	1.112707238
+-70	-45	0.419465656408432	-0.2872463394	-0.2872463394	1.104549117
+
+-65	45	0.420040278579632	-0.2820750812	0.2820750812	1.131533771
+-65	40	0.420256526120293	-0.3031731709	0.2543924958	1.141371971
+-65	35	0.420521269749207	-0.3217939889	0.2253225768	1.150055001
+-65	30	0.420895133174355	-0.3379864933	0.1951365929	1.157605690
+-65	25	0.421254844396123	-0.3516707600	0.1639867685	1.163986769
+-65	20	0.421528520292079	-0.3628051176	0.1320502636	1.169178805
+-65	15	0.421685230990907	-0.3713826168	0.09951167225	1.173178558
+-65	10	0.421738283850168	-0.3774355762	0.06655207557	1.176001100
+-65	5	0.421741831447011	-0.3810319770	0.03333597842	1.177678129
+-65	-2.84217e-14	0.421738502012694	-0.3822248885	-1.229344460e-16	1.178234393
+-65	-5	0.421741831447011	-0.3810319770	-0.03333597842	1.177678129
+-65	-10	0.421738283850168	-0.3774355762	-0.06655207557	1.176001100
+-65	-15	0.421685230990907	-0.3713826168	-0.09951167225	1.173178558
+-65	-20	0.421528520292079	-0.3628051176	-0.1320502636	1.169178805
+-65	-25	0.421254844396123	-0.3516707600	-0.1639867685	1.163986769
+-65	-30	0.420895133174356	-0.3379864933	-0.1951365929	1.157605690
+-65	-35	0.420521269749207	-0.3217939889	-0.2253225768	1.150055001
+-65	-40	0.420256526120294	-0.3031731709	-0.2543924958	1.141371971
+-65	-45	0.420040278579633	-0.2820750812	-0.2820750812	1.131533771
+
+-60	45	0.420559993702195	-0.2753211436	0.2753211436	1.158956736
+-60	40	0.420779147405269	-0.2947906905	0.2473587596	1.170197484
+-60	35	0.421067389084511	-0.3118056397	0.2183286594	1.180021070
+-60	30	0.421429461477640	-0.3264378572	0.1884689847	1.188468985
+-60	25	0.421747854641816	-0.3386712443	0.1579249948	1.195531934
+-60	20	0.421972410989471	-0.3485343311	0.1268561221	1.201226390
+-60	15	0.422095920256010	-0.3560843490	0.09541251375	1.205585395
+-60	10	0.422143074517670	-0.3613973039	0.06372409543	1.208652831
+-60	5	0.422156306298631	-0.3645531879	0.03189427119	1.210474881
+-60	-2.84217e-14	0.422158185633100	-0.3655997132	-1.175873146e-16	1.211079093
+-60	-5	0.422156306298631	-0.3645531879	-0.03189427119	1.210474881
+-60	-10	0.422143074517670	-0.3613973039	-0.06372409543	1.208652831
+-60	-15	0.422095920256010	-0.3560843490	-0.09541251375	1.205585395
+-60	-20	0.421972410989471	-0.3485343311	-0.1268561221	1.201226390
+-60	-25	0.421747854641816	-0.3386712443	-0.1579249948	1.195531934
+-60	-30	0.421429461477641	-0.3264378572	-0.1884689847	1.188468985
+-60	-35	0.421067389084512	-0.3118056397	-0.2183286594	1.180021070
+-60	-40	0.420779147405269	-0.2947906905	-0.2473587596	1.170197484
+-60	-45	0.420559993702196	-0.2753211436	-0.2753211436	1.158956736
+
+-55	45	0.420974391528745	-0.2667661147	0.2667661147	1.186791644
+-55	40	0.421160417370069	-0.2843097472	0.2385642040	1.199075828
+-55	35	0.421433896643665	-0.2994560821	0.2096814061	1.209681406
+-55	30	0.421740723023140	-0.3123042519	0.1803089439	1.218677791
+-55	25	0.421988055236151	-0.3229164119	0.1505783958	1.226108506
+-55	20	0.422146272101115	-0.3313867593	0.1206149164	1.232039507
+-55	15	0.422221936551192	-0.3378221592	0.09051917473	1.236545622
+-55	10	0.422245340255340	-0.3423306283	0.06036212609	1.239702486
+-55	5	0.422249870494667	-0.3450019987	0.03018376378	1.241573000
+-55	-2.84217e-14	0.422249842289697	-0.3458868215	-1.112470853e-16	1.242192560
+-55	-5	0.422249870494667	-0.3450019987	-0.03018376378	1.241573000
+-55	-10	0.422245340255340	-0.3423306283	-0.06036212609	1.239702486
+-55	-15	0.422221936551192	-0.3378221592	-0.09051917473	1.236545622
+-55	-20	0.422146272101116	-0.3313867593	-0.1206149164	1.232039507
+-55	-25	0.421988055236152	-0.3229164119	-0.1505783958	1.226108506
+-55	-30	0.421740723023141	-0.3123042519	-0.1803089439	1.218677791
+-55	-35	0.421433896643665	-0.2994560821	-0.2096814061	1.209681406
+-55	-40	0.421160417370069	-0.2843097472	-0.2385642040	1.199075828
+-55	-45	0.420974391528746	-0.2667661147	-0.2667661147	1.186791644
+
+-50	45	0.421233930166747	-0.2561609471	0.2561609471	1.214944556
+-50	40	0.421357842549578	-0.2715231950	0.2278350128	1.227835013
+-50	35	0.421579106337177	-0.2845923886	0.1992737358	1.238801368
+-50	30	0.421800153288746	-0.2955059898	0.1706104627	1.247958967
+-50	25	0.421964049994405	-0.3044049790	0.1419463729	1.255426106
+-50	20	0.422057549538731	-0.3114360010	0.1133534343	1.261325834
+-50	15	0.422092443828015	-0.3167379948	0.08486968991	1.265774735
+-50	10	0.422097272783192	-0.3204353016	0.05650138924	1.268877143
+-50	5	0.422094460465481	-0.3226193717	0.02822553766	1.270709796
+-50	-2.84217e-14	0.422092640652910	-0.3233417219	-1.039959371e-16	1.271315920
+-50	-5	0.422094460465481	-0.3226193717	-0.02822553766	1.270709796
+-50	-10	0.422097272783192	-0.3204353016	-0.05650138924	1.268877143
+-50	-15	0.422092443828015	-0.3167379948	-0.08486968991	1.265774735
+-50	-20	0.422057549538732	-0.3114360010	-0.1133534343	1.261325834
+-50	-25	0.421964049994405	-0.3044049790	-0.1419463729	1.255426106
+-50	-30	0.421800153288746	-0.2955059898	-0.1706104627	1.247958967
+-50	-35	0.421579106337178	-0.2845923886	-0.1992737358	1.238801368
+-50	-40	0.421357842549579	-0.2715231950	-0.2278350128	1.227835013
+-50	-45	0.421233930166748	-0.2561609471	-0.2561609471	1.214944556
+
+-45	45	0.421317295454029	-0.2432476539	0.2432476539	1.243247654
+-45	40	0.421383484215572	-0.2562518940	0.2150208697	1.256251894
+-45	35	0.421529869183828	-0.2671181138	0.1870381169	1.267118114
+-45	30	0.421667446949536	-0.2760461420	0.1593753144	1.276046142
+-45	25	0.421775248654314	-0.2832401881	0.1320770688	1.283240188
+-45	20	0.421837585830950	-0.2888706155	0.1051403056	1.288870615
+-45	15	0.421862858734393	-0.2930877828	0.07853263472	1.293087783
+-45	10	0.421871721447427	-0.2960163521	0.05219566961	1.296016352
+-45	5	0.421874605062139	-0.2977411905	0.02604897884	1.297741191
+-45	-2.84217e-14	0.421875207994685	-0.2983108204	-9.594528391e-17	1.298310820
+-45	-5	0.421874605062139	-0.2977411905	-0.02604897884	1.297741191
+-45	-10	0.421871721447427	-0.2960163521	-0.05219566961	1.296016352
+-45	-15	0.421862858734393	-0.2930877828	-0.07853263472	1.293087783
+-45	-20	0.421837585830951	-0.2888706155	-0.1051403056	1.288870615
+-45	-25	0.421775248654315	-0.2832401881	-0.1320770688	1.283240188
+-45	-30	0.421667446949536	-0.2760461420	-0.1593753144	1.276046142
+-45	-35	0.421529869183829	-0.2671181138	-0.1870381169	1.267118114
+-45	-40	0.421383484215573	-0.2562518940	-0.2150208697	1.256251894
+-45	-45	0.421317295454029	-0.2432476539	-0.2432476539	1.243247654
+
+
+### -y patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-135	0.405481246888700	-0.2341047070	-0.2341047070	0.7658952930
+-40	-135	0.404953884308433	-0.2066372786	-0.2462607191	0.7537392809
+-35	-135	0.404600376776806	-0.1795262877	-0.2563901099	0.7436098901
+-30	-135	0.404312156366900	-0.1528156311	-0.2646844373	0.7353155627
+-25	-135	0.404045335367780	-0.1265250242	-0.2713337901	0.7286662099
+-20	-135	0.403792076974581	-0.1006425785	-0.2765132120	0.7234867880
+-15	-135	0.403565989481415	-0.07512654831	-0.2803760953	0.7196239047
+-10	-135	0.403393035592475	-0.04990941212	-0.2830503416	0.7169496584
+-5	-135	0.403285294975798	-0.02490116729	-0.2846216445	0.7153783555
+-2.84217e-14	-135	0.403248758763943	-9.170914980e-17	-0.2851399318	0.7148600682
+5	-135	0.403285294975798	0.02490116729	-0.2846216445	0.7153783555
+10	-135	0.403393035592475	0.04990941212	-0.2830503416	0.7169496584
+15	-135	0.403565989481415	0.07512654831	-0.2803760953	0.7196239047
+20	-135	0.403792076974581	0.1006425785	-0.2765132120	0.7234867880
+25	-135	0.404045335367779	0.1265250242	-0.2713337901	0.7286662099
+30	-135	0.404312156366899	0.1528156311	-0.2646844373	0.7353155627
+35	-135	0.404600376776806	0.1795262877	-0.2563901099	0.7436098901
+40	-135	0.404953884308433	0.2066372786	-0.2462607191	0.7537392809
+45	-135	0.405481246888700	0.2341047070	-0.2341047070	0.7658952930
+
+-45	-130	0.406795594720917	-0.2473807008	-0.2473807008	0.7924229452
+-40	-130	0.406289306919105	-0.2196872114	-0.2618130234	0.7803127886
+-35	-130	0.406013998432557	-0.1919163569	-0.2740849626	0.7700154089
+-30	-130	0.405832116775406	-0.1641516834	-0.2843190559	0.7614279851
+-25	-130	0.405671576403577	-0.1364656749	-0.2926515842	0.7544361636
+-20	-130	0.405508438276747	-0.1089087831	-0.2992244222	0.7489208977
+-15	-130	0.405347985375321	-0.08150289901	-0.3041729601	0.7447685814
+-10	-130	0.405216174033674	-0.05424170742	-0.3076200092	0.7418761638
+-5	-130	0.405131857886019	-0.02709124517	-0.3096543492	0.7401691498
+-2.84217e-14	-130	0.405102909412565	-9.980997680e-17	-0.3103268326	0.7396048692
+5	-130	0.405131857886019	0.02709124517	-0.3096543492	0.7401691498
+10	-130	0.405216174033674	0.05424170742	-0.3076200092	0.7418761638
+15	-130	0.405347985375321	0.08150289901	-0.3041729601	0.7447685814
+20	-130	0.405508438276747	0.1089087831	-0.2992244222	0.7489208977
+25	-130	0.405671576403576	0.1364656749	-0.2926515842	0.7544361636
+30	-130	0.405832116775406	0.1641516834	-0.2843190559	0.7614279851
+35	-130	0.406013998432557	0.1919163569	-0.2740849626	0.7700154089
+40	-130	0.406289306919104	0.2196872114	-0.2618130234	0.7803127886
+45	-130	0.406795594720916	0.2473807008	-0.2473807008	0.7924229452
+
+-45	-125	0.408114012981203	-0.2586166565	-0.2586166565	0.8189146676
+-40	-125	0.407605109056097	-0.2308858677	-0.2751590623	0.8073315504
+-35	-125	0.407349729987816	-0.2026739302	-0.2894483694	0.7973260698
+-30	-125	0.407232900944230	-0.1741063414	-0.3015610292	0.7888446941
+-25	-125	0.407151873444532	-0.1452843871	-0.3115633735	0.7818409772
+-20	-125	0.407063084704380	-0.1163053737	-0.3195463880	0.7762512103
+-15	-125	0.406959866536061	-0.08724717519	-0.3256108906	0.7720047999
+-10	-125	0.406863708905256	-0.05816324340	-0.3298601449	0.7690294400
+-5	-125	0.406799430555321	-0.02907931719	-0.3323781164	0.7672663373
+-2.84217e-14	-125	0.406776919224708	-1.071705472e-16	-0.3332121450	0.7666823443
+5	-125	0.406799430555321	0.02907931719	-0.3323781164	0.7672663373
+10	-125	0.406863708905256	0.05816324340	-0.3298601449	0.7690294400
+15	-125	0.406959866536061	0.08724717519	-0.3256108906	0.7720047999
+20	-125	0.407063084704380	0.1163053737	-0.3195463880	0.7762512103
+25	-125	0.407151873444532	0.1452843871	-0.3115633735	0.7818409772
+30	-125	0.407232900944229	0.1741063414	-0.3015610292	0.7888446941
+35	-125	0.407349729987816	0.2026739302	-0.2894483694	0.7973260698
+40	-125	0.407605109056096	0.2308858677	-0.2751590623	0.8073315504
+45	-125	0.408114012981202	0.2586166565	-0.2586166565	0.8189146676
+
+-45	-120	0.409483464825416	-0.2680698533	-0.2680698533	0.8452297980
+-40	-120	0.408973597448125	-0.2404187622	-0.2865199236	0.8345776450
+-35	-120	0.408687783070896	-0.2119096803	-0.3026383875	0.8252716455
+-30	-120	0.408591532607702	-0.1827276884	-0.3164936402	0.8172723116
+-25	-120	0.408557298593189	-0.1529857438	-0.3280789864	0.8105835089
+-20	-120	0.408521160772016	-0.1228123188	-0.3374240727	0.8051881208
+-15	-120	0.408460567065286	-0.09233031546	-0.3445814284	0.8010558196
+-10	-120	0.408388640859697	-0.06164781160	-0.3496221131	0.7981455789
+-5	-120	0.408336282868854	-0.03085015656	-0.3526189031	0.7964153814
+-2.84217e-14	-120	0.408317245024598	-1.137320795e-16	-0.3536131070	0.7958413775
+5	-120	0.408336282868854	0.03085015656	-0.3526189031	0.7964153814
+10	-120	0.408388640859697	0.06164781160	-0.3496221131	0.7981455789
+15	-120	0.408460567065286	0.09233031546	-0.3445814284	0.8010558196
+20	-120	0.408521160772016	0.1228123188	-0.3374240727	0.8051881208
+25	-120	0.408557298593189	0.1529857438	-0.3280789864	0.8105835089
+30	-120	0.408591532607702	0.1827276884	-0.3164936402	0.8172723116
+35	-120	0.408687783070896	0.2119096803	-0.3026383875	0.8252716455
+40	-120	0.408973597448124	0.2404187622	-0.2865199236	0.8345776450
+45	-120	0.409483464825416	0.2680698533	-0.2680698533	0.8452297980
+
+-45	-115	0.410861221174010	-0.2759109500	-0.2759109500	0.8713406110
+-40	-115	0.410396669893041	-0.2484240616	-0.2960602679	0.8619448298
+-35	-115	0.410099864329443	-0.2197386073	-0.3138192540	0.8536636786
+-30	-115	0.410006859569762	-0.1900885407	-0.3292430104	0.8464714629
+-25	-115	0.410000497984177	-0.1596056583	-0.3422754388	0.8403943417
+-20	-115	0.410006254414508	-0.1284407374	-0.3528880258	0.8354456111
+-15	-115	0.409979437386299	-0.09674927269	-0.3610732013	0.8316288011
+-10	-115	0.409916722310055	-0.06468658342	-0.3668558445	0.8289323102
+-5	-115	0.409863121137784	-0.03239704280	-0.3702998936	0.8273263238
+-2.84217e-14	-115	0.409842510270319	-1.194668301e-16	-0.3714434585	0.8267930707
+5	-115	0.409863121137784	0.03239704280	-0.3702998936	0.8273263238
+10	-115	0.409916722310054	0.06468658342	-0.3668558445	0.8289323102
+15	-115	0.409979437386299	0.09674927269	-0.3610732013	0.8316288011
+20	-115	0.410006254414508	0.1284407374	-0.3528880258	0.8354456111
+25	-115	0.410000497984177	0.1596056583	-0.3422754388	0.8403943417
+30	-115	0.410006859569762	0.1900885407	-0.3292430104	0.8464714629
+35	-115	0.410099864329442	0.2197386073	-0.3138192540	0.8536636786
+40	-115	0.410396669893041	0.2484240616	-0.2960602679	0.8619448298
+45	-115	0.410861221174010	0.2759109500	-0.2759109500	0.8713406110
+
+-45	-110	0.412193089113134	-0.2822661502	-0.2822661502	0.8972635232
+-40	-110	0.411806057146319	-0.2549784059	-0.3038714312	0.8893998440
+-35	-110	0.411532116427936	-0.2262052651	-0.3230545984	0.8824177421
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+45	-60	0.420559993702196	0.2753211436	-0.2753211436	1.158956736
+
+-45	-55	0.420974391528746	-0.2667661147	-0.2667661147	1.186791644
+-40	-55	0.421160417370069	-0.2385642040	-0.2843097472	1.199075828
+-35	-55	0.421433896643665	-0.2096814061	-0.2994560821	1.209681406
+-30	-55	0.421740723023141	-0.1803089439	-0.3123042519	1.218677791
+-25	-55	0.421988055236152	-0.1505783958	-0.3229164119	1.226108506
+-20	-55	0.422146272101116	-0.1206149164	-0.3313867593	1.232039507
+-15	-55	0.422221936551192	-0.09051917473	-0.3378221592	1.236545622
+-10	-55	0.422245340255341	-0.06036212609	-0.3423306283	1.239702486
+-5	-55	0.422249870494668	-0.03018376378	-0.3450019987	1.241573000
+-2.84217e-14	-55	0.422249842289697	-1.112470853e-16	-0.3458868215	1.242192560
+5	-55	0.422249870494668	0.03018376378	-0.3450019987	1.241573000
+10	-55	0.422245340255341	0.06036212609	-0.3423306283	1.239702486
+15	-55	0.422221936551192	0.09051917473	-0.3378221592	1.236545622
+20	-55	0.422146272101116	0.1206149164	-0.3313867593	1.232039507
+25	-55	0.421988055236152	0.1505783958	-0.3229164119	1.226108506
+30	-55	0.421740723023140	0.1803089439	-0.3123042519	1.218677791
+35	-55	0.421433896643665	0.2096814061	-0.2994560821	1.209681406
+40	-55	0.421160417370069	0.2385642040	-0.2843097472	1.199075828
+45	-55	0.420974391528746	0.2667661147	-0.2667661147	1.186791644
+
+-45	-50	0.421233930166748	-0.2561609471	-0.2561609471	1.214944556
+-40	-50	0.421357842549579	-0.2278350128	-0.2715231950	1.227835013
+-35	-50	0.421579106337178	-0.1992737358	-0.2845923886	1.238801368
+-30	-50	0.421800153288746	-0.1706104627	-0.2955059898	1.247958967
+-25	-50	0.421964049994406	-0.1419463729	-0.3044049790	1.255426106
+-20	-50	0.422057549538732	-0.1133534343	-0.3114360010	1.261325834
+-15	-50	0.422092443828016	-0.08486968991	-0.3167379948	1.265774735
+-10	-50	0.422097272783192	-0.05650138924	-0.3204353016	1.268877143
+-5	-50	0.422094460465481	-0.02822553766	-0.3226193717	1.270709796
+-2.84217e-14	-50	0.422092640652910	-1.039959371e-16	-0.3233417219	1.271315920
+5	-50	0.422094460465481	0.02822553766	-0.3226193717	1.270709796
+10	-50	0.422097272783192	0.05650138924	-0.3204353016	1.268877143
+15	-50	0.422092443828016	0.08486968991	-0.3167379948	1.265774735
+20	-50	0.422057549538732	0.1133534343	-0.3114360010	1.261325834
+25	-50	0.421964049994406	0.1419463729	-0.3044049790	1.255426106
+30	-50	0.421800153288746	0.1706104627	-0.2955059898	1.247958967
+35	-50	0.421579106337178	0.1992737358	-0.2845923886	1.238801368
+40	-50	0.421357842549578	0.2278350128	-0.2715231950	1.227835013
+45	-50	0.421233930166748	0.2561609471	-0.2561609471	1.214944556
+
+-45	-45	0.421317295454029	-0.2432476539	-0.2432476539	1.243247654
+-40	-45	0.421383484215573	-0.2150208697	-0.2562518940	1.256251894
+-35	-45	0.421529869183829	-0.1870381169	-0.2671181138	1.267118114
+-30	-45	0.421667446949536	-0.1593753144	-0.2760461420	1.276046142
+-25	-45	0.421775248654315	-0.1320770688	-0.2832401881	1.283240188
+-20	-45	0.421837585830951	-0.1051403056	-0.2888706155	1.288870615
+-15	-45	0.421862858734393	-0.07853263472	-0.2930877828	1.293087783
+-10	-45	0.421871721447427	-0.05219566961	-0.2960163521	1.296016352
+-5	-45	0.421874605062139	-0.02604897884	-0.2977411905	1.297741191
+-2.84217e-14	-45	0.421875207994685	-9.594528391e-17	-0.2983108204	1.298310820
+5	-45	0.421874605062139	0.02604897884	-0.2977411905	1.297741191
+10	-45	0.421871721447427	0.05219566961	-0.2960163521	1.296016352
+15	-45	0.421862858734393	0.07853263472	-0.2930877828	1.293087783
+20	-45	0.421837585830951	0.1051403056	-0.2888706155	1.288870615
+25	-45	0.421775248654315	0.1320770688	-0.2832401881	1.283240188
+30	-45	0.421667446949536	0.1593753144	-0.2760461420	1.276046142
+35	-45	0.421529869183828	0.1870381169	-0.2671181138	1.267118114
+40	-45	0.421383484215573	0.2150208697	-0.2562518940	1.256251894
+45	-45	0.421317295454029	0.2432476539	-0.2432476539	1.243247654
+
+
+### -z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = 180 - drho = 180 - dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+135	45	0.405481674472939	0.2341049539	0.2341049539	0.7658950461
+140	45	0.404954325213094	0.2066375035	0.2462609872	0.7537390128
+145	45	0.404600138471220	0.1795261819	0.2563899589	0.7436100411
+150	45	0.404312090779579	0.1528156063	0.2646843943	0.7353156057
+155	45	0.404045349772517	0.1265250287	0.2713337998	0.7286662002
+160	45	0.403792100607266	0.1006425844	0.2765132282	0.7234867718
+165	45	0.403566000239541	0.07512655031	0.2803761028	0.7196238972
+170	45	0.403393040297300	0.04990941270	0.2830503449	0.7169496551
+175	45	0.403285295971307	0.02490116735	0.2846216452	0.7153783548
+180	45	0.403248759262706	-9.170914991e-17	0.2851399322	0.7148600678
+185	45	0.403285295971307	-0.02490116735	0.2846216452	0.7153783548
+190	45	0.403393040297301	-0.04990941270	0.2830503449	0.7169496551
+195	45	0.403566000239541	-0.07512655031	0.2803761028	0.7196238972
+200	45	0.403792100607267	-0.1006425844	0.2765132282	0.7234867718
+205	45	0.404045349772517	-0.1265250287	0.2713337998	0.7286662002
+210	45	0.404312090779579	-0.1528156063	0.2646843943	0.7353156057
+215	45	0.404600138471221	-0.1795261819	0.2563899589	0.7436100411
+220	45	0.404954325213094	-0.2066375035	0.2462609872	0.7537390128
+225	45	0.405481674472939	-0.2341049539	0.2341049539	0.7658950461
+
+135	40	0.404954325213094	0.2462609872	0.2066375035	0.7537390128
+140	40	0.404118281795431	0.2185133029	0.2185133029	0.7395859862
+145	40	0.403511417621326	0.1907334268	0.2285670167	0.7276044367
+150	40	0.403019661552551	0.1630140966	0.2369186881	0.7176513023
+155	40	0.402574254381548	0.1354237529	0.2436889447	0.7095828247
+160	40	0.402159570267887	0.1080093662	0.2490055801	0.7032467054
+165	40	0.401791822777130	0.08078786509	0.2529922452	0.6984955829
+170	40	0.401506832715866	0.05374517984	0.2557609754	0.6951959387
+175	40	0.401329098255662	0.02683695390	0.2573919547	0.6932522133
+180	40	0.401268851602535	-9.886533481e-17	0.2579306460	0.6926102260
+185	40	0.401329098255662	-0.02683695390	0.2573919547	0.6932522133
+190	40	0.401506832715867	-0.05374517984	0.2557609754	0.6951959387
+195	40	0.401791822777131	-0.08078786509	0.2529922452	0.6984955829
+200	40	0.402159570267888	-0.1080093662	0.2490055801	0.7032467054
+205	40	0.402574254381549	-0.1354237529	0.2436889447	0.7095828247
+210	40	0.403019661552552	-0.1630140966	0.2369186881	0.7176513023
+215	40	0.403511417621326	-0.1907334268	0.2285670167	0.7276044367
+220	40	0.404118281795432	-0.2185133029	0.2185133029	0.7395859862
+225	40	0.404954325213094	-0.2462609872	0.2066375035	0.7537390128
+
+135	35	0.404600138471220	0.2563899589	0.1795261819	0.7436100411
+140	35	0.403511417621326	0.2285670167	0.1907334268	0.7276044367
+145	35	0.402650861803492	0.2003360421	0.2003360421	0.7138904808
+150	35	0.401926117385888	0.1718375054	0.2084036728	0.7023687101
+155	35	0.401266409047524	0.1431842713	0.2150054890	0.6929403394
+160	35	0.400654498385723	0.1144743233	0.2202262069	0.6854843816
+165	35	0.400112560668404	0.08577919728	0.2241590654	0.6798676775
+170	35	0.399691399322722	0.05713792514	0.2268989450	0.6759547239
+175	35	0.399430785110637	0.02855258298	0.2285179934	0.6736424832
+180	35	0.399343064959331	-1.052120038e-16	0.2290537721	0.6728773120
+185	35	0.399430785110638	-0.02855258298	0.2285179934	0.6736424832
+190	35	0.399691399322722	-0.05713792514	0.2268989450	0.6759547239
+195	35	0.400112560668404	-0.08577919728	0.2241590654	0.6798676775
+200	35	0.400654498385724	-0.1144743233	0.2202262069	0.6854843816
+205	35	0.401266409047525	-0.1431842713	0.2150054890	0.6929403394
+210	35	0.401926117385889	-0.1718375054	0.2084036728	0.7023687101
+215	35	0.402650861803492	-0.2003360421	0.2003360421	0.7138904808
+220	35	0.403511417621326	-0.2285670167	0.1907334268	0.7276044367
+225	35	0.404600138471221	-0.2563899589	0.1795261819	0.7436100411
+
+135	30	0.404312090779579	0.2646843943	0.1528156063	0.7353156057
+140	30	0.403019661552551	0.2369186881	0.1630140966	0.7176513023
+145	30	0.401926117385888	0.2084036728	0.1718375054	0.7023687101
+150	30	0.401000097620797	0.1793326955	0.1793326955	0.6893866600
+155	30	0.400163068931276	0.1498424945	0.1855247346	0.6786617336
+160	30	0.399391927888277	0.1200678288	0.1904584132	0.6701163517
+165	30	0.398708704640039	0.09012595938	0.1941944532	0.6636453405
+170	30	0.398168473869742	0.06010503869	0.1968028950	0.6591273868
+175	30	0.397827508487727	0.03005620964	0.1983452487	0.6564559518
+180	30	0.397711338186444	-1.107779260e-16	0.1988556691	0.6555718778
+185	30	0.397827508487727	-0.03005620964	0.1983452487	0.6564559518
+190	30	0.398168473869742	-0.06010503869	0.1968028950	0.6591273868
+195	30	0.398708704640040	-0.09012595938	0.1941944532	0.6636453405
+200	30	0.399391927888277	-0.1200678288	0.1904584132	0.6701163517
+205	30	0.400163068931277	-0.1498424945	0.1855247346	0.6786617336
+210	30	0.401000097620797	-0.1793326955	0.1793326955	0.6893866600
+215	30	0.401926117385889	-0.2084036728	0.1718375054	0.7023687101
+220	30	0.403019661552552	-0.2369186881	0.1630140966	0.7176513023
+225	30	0.404312090779579	-0.2646843943	0.1528156063	0.7353156057
+
+135	25	0.404045349772517	0.2713337998	0.1265250287	0.7286662002
+140	25	0.402574254381548	0.2436889447	0.1354237529	0.7095828247
+145	25	0.401266409047525	0.2150054890	0.1431842713	0.6929403394
+150	25	0.400163068931276	0.1855247346	0.1498424945	0.6786617336
+155	25	0.399177112164364	0.1553923131	0.1553923131	0.6667601091
+160	25	0.398265161285882	0.1247626602	0.1598421476	0.6572174083
+165	25	0.397449595261696	0.09379240949	0.1632254176	0.6499619624
+170	25	0.396795800496520	0.06261604676	0.1655920269	0.6448867524
+175	25	0.396378089204662	0.03133113778	0.1669924868	0.6418834564
+180	25	0.396234791397780	-1.155002551e-16	0.1674560588	0.6408893231
+185	25	0.396378089204662	-0.03133113778	0.1669924868	0.6418834564
+190	25	0.396795800496520	-0.06261604676	0.1655920269	0.6448867524
+195	25	0.397449595261697	-0.09379240949	0.1632254176	0.6499619624
+200	25	0.398265161285883	-0.1247626602	0.1598421476	0.6572174083
+205	25	0.399177112164365	-0.1553923131	0.1553923131	0.6667601091
+210	25	0.400163068931277	-0.1855247346	0.1498424945	0.6786617336
+215	25	0.401266409047525	-0.2150054890	0.1431842713	0.6929403394
+220	25	0.402574254381549	-0.2436889447	0.1354237529	0.7095828247
+225	25	0.404045349772517	-0.2713337998	0.1265250287	0.7286662002
+
+135	20	0.403792100607267	0.2765132282	0.1006425844	0.7234867718
+140	20	0.402159570267888	0.2490055801	0.1080093662	0.7032467054
+145	20	0.400654498385723	0.2202262069	0.1144743233	0.6854843816
+150	20	0.399391927888277	0.1904584132	0.1200678288	0.6701163517
+155	20	0.398265161285882	0.1598421476	0.1247626602	0.6572174083
+160	20	0.397216665961989	0.1285455006	0.1285455006	0.6468241397
+165	20	0.396270985869463	0.09675704480	0.1314304549	0.6388977928
+170	20	0.395505410021133	0.06465107863	0.1334513195	0.6333455132
+175	20	0.395012222203306	0.03236572921	0.1346478683	0.6300580223
+180	20	0.394842300222227	-1.193339773e-16	0.1350440201	0.6289696041
+185	20	0.395012222203306	-0.03236572921	0.1346478683	0.6300580223
+190	20	0.395505410021133	-0.06465107863	0.1334513195	0.6333455132
+195	20	0.396270985869464	-0.09675704480	0.1314304549	0.6388977928
+200	20	0.397216665961990	-0.1285455006	0.1285455006	0.6468241397
+205	20	0.398265161285883	-0.1598421476	0.1247626602	0.6572174083
+210	20	0.399391927888277	-0.1904584132	0.1200678288	0.6701163517
+215	20	0.400654498385724	-0.2202262069	0.1144743233	0.6854843816
+220	20	0.402159570267888	-0.2490055801	0.1080093662	0.7032467054
+225	20	0.403792100607267	-0.2765132282	0.1006425844	0.7234867718
+
+135	15	0.403566000239541	0.2803761028	0.07512655031	0.7196238972
+140	15	0.401791822777130	0.2529922452	0.08078786509	0.6984955829
+145	15	0.400112560668404	0.2241590654	0.08577919728	0.6798676775
+150	15	0.398708704640040	0.1941944532	0.09012595938	0.6636453405
+155	15	0.397449595261697	0.1632254176	0.09379240949	0.6499619624
+160	15	0.396270985869464	0.1314304549	0.09675704480	0.6388977928
+165	15	0.395201356554911	0.09902276126	0.09902276126	0.6304420239
+170	15	0.394330304155799	0.06620842004	0.1006113336	0.6245133911
+175	15	0.393766298533229	0.03315804005	0.1015522434	0.6210018679
+180	15	0.393571465787465	-1.222705901e-16	0.1018637910	0.6198391567
+185	15	0.393766298533229	-0.03315804005	0.1015522434	0.6210018679
+190	15	0.394330304155800	-0.06620842004	0.1006113336	0.6245133911
+195	15	0.395201356554911	-0.09902276126	0.09902276126	0.6304420239
+200	15	0.396270985869464	-0.1314304549	0.09675704480	0.6388977928
+205	15	0.397449595261697	-0.1632254176	0.09379240949	0.6499619624
+210	15	0.398708704640040	-0.1941944532	0.09012595938	0.6636453405
+215	15	0.400112560668404	-0.2241590654	0.08577919728	0.6798676775
+220	15	0.401791822777131	-0.2529922452	0.08078786509	0.6984955829
+225	15	0.403566000239541	-0.2803761028	0.07512655031	0.7196238972
+
+135	10	0.403393040297301	0.2830503449	0.04990941270	0.7169496551
+140	10	0.401506832715867	0.2557609754	0.05374517984	0.6951959387
+145	10	0.399691399322722	0.2268989450	0.05713792514	0.6759547239
+150	10	0.398168473869742	0.1968028950	0.06010503869	0.6591273868
+155	10	0.396795800496520	0.1655920269	0.06261604676	0.6448867524
+160	10	0.395505410021133	0.1334513195	0.06465107863	0.6333455132
+165	10	0.394330304155799	0.1006113336	0.06620842004	0.6245133911
+170	10	0.393370857589972	0.06730098205	0.06730098205	0.6183171641
+175	10	0.392748115755232	0.03371408062	0.06794825527	0.6146462952
+180	10	0.392532718012423	-1.243317213e-16	0.06816259116	0.6134307360
+185	10	0.392748115755232	-0.03371408062	0.06794825527	0.6146462952
+190	10	0.393370857589972	-0.06730098205	0.06730098205	0.6183171641
+195	10	0.394330304155800	-0.1006113336	0.06620842004	0.6245133911
+200	10	0.395505410021134	-0.1334513195	0.06465107863	0.6333455132
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+160	-45	0.403792100607267	0.1006425844	-0.2765132282	0.7234867718
+165	-45	0.403566000239542	0.07512655031	-0.2803761028	0.7196238972
+170	-45	0.403393040297301	0.04990941270	-0.2830503449	0.7169496551
+175	-45	0.403285295971307	0.02490116735	-0.2846216452	0.7153783548
+180	-45	0.403248759262706	-9.170914991e-17	-0.2851399322	0.7148600678
+185	-45	0.403285295971307	-0.02490116735	-0.2846216452	0.7153783548
+190	-45	0.403393040297301	-0.04990941270	-0.2830503449	0.7169496551
+195	-45	0.403566000239542	-0.07512655031	-0.2803761028	0.7196238972
+200	-45	0.403792100607267	-0.1006425844	-0.2765132282	0.7234867718
+205	-45	0.404045349772518	-0.1265250287	-0.2713337998	0.7286662002
+210	-45	0.404312090779580	-0.1528156063	-0.2646843943	0.7353156057
+215	-45	0.404600138471221	-0.1795261819	-0.2563899589	0.7436100411
+220	-45	0.404954325213095	-0.2066375035	-0.2462609872	0.7537390128
+225	-45	0.405481674472940	-0.2341049539	-0.2341049539	0.7658950461
+
+
diff --git a/test/bl-carpet-mask/bl.h.t0.ah2.gp b/test/bl-carpet-mask/bl.h.t0.ah2.gp
new file mode 100644
index 0000000..19a14df
--- /dev/null
+++ b/test/bl-carpet-mask/bl.h.t0.ah2.gp
@@ -0,0 +1,2337 @@
+# N_patches = 6
+# origin = 0 0 -1
+
+### +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	0.405481674472941	-0.2341049539	-0.2341049539	-0.7658950461
+-40	-45	0.404954325213096	-0.2066375035	-0.2462609872	-0.7537390128
+-35	-45	0.404600138471222	-0.1795261819	-0.2563899589	-0.7436100411
+-30	-45	0.404312090779581	-0.1528156063	-0.2646843943	-0.7353156057
+-25	-45	0.404045349772519	-0.1265250287	-0.2713337998	-0.7286662002
+-20	-45	0.403792100607268	-0.1006425844	-0.2765132282	-0.7234867718
+-15	-45	0.403566000239542	-0.07512655031	-0.2803761028	-0.7196238972
+-10	-45	0.403393040297302	-0.04990941270	-0.2830503449	-0.7169496551
+-5	-45	0.403285295971308	-0.02490116735	-0.2846216452	-0.7153783548
+0	-45	0.403248759262706	0.000000000	-0.2851399322	-0.7148600678
+5	-45	0.403285295971307	0.02490116735	-0.2846216452	-0.7153783548
+10	-45	0.403393040297301	0.04990941270	-0.2830503449	-0.7169496551
+15	-45	0.403566000239542	0.07512655031	-0.2803761028	-0.7196238972
+20	-45	0.403792100607268	0.1006425844	-0.2765132282	-0.7234867718
+25	-45	0.404045349772518	0.1265250287	-0.2713337998	-0.7286662002
+30	-45	0.404312090779580	0.1528156063	-0.2646843943	-0.7353156057
+35	-45	0.404600138471221	0.1795261819	-0.2563899589	-0.7436100411
+40	-45	0.404954325213095	0.2066375035	-0.2462609872	-0.7537390128
+45	-45	0.405481674472940	0.2341049539	-0.2341049539	-0.7658950461
+
+-45	-40	0.404954325213096	-0.2462609872	-0.2066375035	-0.7537390128
+-40	-40	0.404118281795434	-0.2185133029	-0.2185133029	-0.7395859862
+-35	-40	0.403511417621328	-0.1907334268	-0.2285670167	-0.7276044367
+-30	-40	0.403019661552553	-0.1630140966	-0.2369186881	-0.7176513023
+-25	-40	0.402574254381550	-0.1354237529	-0.2436889447	-0.7095828247
+-20	-40	0.402159570267889	-0.1080093662	-0.2490055801	-0.7032467054
+-15	-40	0.401791822777132	-0.08078786509	-0.2529922452	-0.6984955829
+-10	-40	0.401506832715868	-0.05374517984	-0.2557609754	-0.6951959387
+-5	-40	0.401329098255663	-0.02683695390	-0.2573919547	-0.6932522133
+0	-40	0.401268851602536	0.000000000	-0.2579306460	-0.6926102260
+5	-40	0.401329098255663	0.02683695390	-0.2573919547	-0.6932522133
+10	-40	0.401506832715867	0.05374517984	-0.2557609754	-0.6951959387
+15	-40	0.401791822777131	0.08078786509	-0.2529922452	-0.6984955829
+20	-40	0.402159570267888	0.1080093662	-0.2490055801	-0.7032467054
+25	-40	0.402574254381549	0.1354237529	-0.2436889447	-0.7095828247
+30	-40	0.403019661552552	0.1630140966	-0.2369186881	-0.7176513023
+35	-40	0.403511417621327	0.1907334268	-0.2285670167	-0.7276044367
+40	-40	0.404118281795432	0.2185133029	-0.2185133029	-0.7395859862
+45	-40	0.404954325213095	0.2462609872	-0.2066375035	-0.7537390128
+
+-45	-35	0.404600138471223	-0.2563899589	-0.1795261819	-0.7436100411
+-40	-35	0.403511417621328	-0.2285670167	-0.1907334268	-0.7276044367
+-35	-35	0.402650861803494	-0.2003360421	-0.2003360421	-0.7138904808
+-30	-35	0.401926117385890	-0.1718375054	-0.2084036728	-0.7023687101
+-25	-35	0.401266409047527	-0.1431842713	-0.2150054890	-0.6929403394
+-20	-35	0.400654498385725	-0.1144743233	-0.2202262069	-0.6854843816
+-15	-35	0.400112560668405	-0.08577919728	-0.2241590654	-0.6798676775
+-10	-35	0.399691399322723	-0.05713792514	-0.2268989450	-0.6759547239
+-5	-35	0.399430785110639	-0.02855258298	-0.2285179934	-0.6736424832
+0	-35	0.399343064959332	0.000000000	-0.2290537721	-0.6728773120
+5	-35	0.399430785110639	0.02855258298	-0.2285179934	-0.6736424832
+10	-35	0.399691399322723	0.05713792514	-0.2268989450	-0.6759547239
+15	-35	0.400112560668405	0.08577919728	-0.2241590654	-0.6798676775
+20	-35	0.400654498385724	0.1144743233	-0.2202262069	-0.6854843816
+25	-35	0.401266409047526	0.1431842713	-0.2150054890	-0.6929403394
+30	-35	0.401926117385889	0.1718375054	-0.2084036728	-0.7023687101
+35	-35	0.402650861803493	0.2003360421	-0.2003360421	-0.7138904808
+40	-35	0.403511417621327	0.2285670167	-0.1907334268	-0.7276044367
+45	-35	0.404600138471221	0.2563899589	-0.1795261819	-0.7436100411
+
+-45	-30	0.404312090779581	-0.2646843943	-0.1528156063	-0.7353156057
+-40	-30	0.403019661552554	-0.2369186881	-0.1630140966	-0.7176513023
+-35	-30	0.401926117385890	-0.2084036728	-0.1718375054	-0.7023687101
+-30	-30	0.401000097620799	-0.1793326955	-0.1793326955	-0.6893866600
+-25	-30	0.400163068931278	-0.1498424945	-0.1855247346	-0.6786617336
+-20	-30	0.399391927888278	-0.1200678288	-0.1904584132	-0.6701163517
+-15	-30	0.398708704640041	-0.09012595938	-0.1941944532	-0.6636453405
+-10	-30	0.398168473869743	-0.06010503869	-0.1968028950	-0.6591273868
+-5	-30	0.397827508487728	-0.03005620964	-0.1983452487	-0.6564559518
+0	-30	0.397711338186445	0.000000000	-0.1988556691	-0.6555718778
+5	-30	0.397827508487728	0.03005620964	-0.1983452487	-0.6564559518
+10	-30	0.398168473869743	0.06010503869	-0.1968028950	-0.6591273868
+15	-30	0.398708704640040	0.09012595938	-0.1941944532	-0.6636453405
+20	-30	0.399391927888278	0.1200678288	-0.1904584132	-0.6701163517
+25	-30	0.400163068931277	0.1498424945	-0.1855247346	-0.6786617336
+30	-30	0.401000097620798	0.1793326955	-0.1793326955	-0.6893866600
+35	-30	0.401926117385889	0.2084036728	-0.1718375054	-0.7023687101
+40	-30	0.403019661552552	0.2369186881	-0.1630140966	-0.7176513023
+45	-30	0.404312090779580	0.2646843943	-0.1528156063	-0.7353156057
+
+-45	-25	0.404045349772519	-0.2713337998	-0.1265250287	-0.7286662002
+-40	-25	0.402574254381551	-0.2436889447	-0.1354237529	-0.7095828247
+-35	-25	0.401266409047527	-0.2150054890	-0.1431842713	-0.6929403394
+-30	-25	0.400163068931278	-0.1855247346	-0.1498424945	-0.6786617336
+-25	-25	0.399177112164366	-0.1553923131	-0.1553923131	-0.6667601091
+-20	-25	0.398265161285884	-0.1247626602	-0.1598421476	-0.6572174083
+-15	-25	0.397449595261698	-0.09379240949	-0.1632254176	-0.6499619624
+-10	-25	0.396795800496522	-0.06261604676	-0.1655920269	-0.6448867524
+-5	-25	0.396378089204663	-0.03133113778	-0.1669924868	-0.6418834564
+0	-25	0.396234791397781	0.000000000	-0.1674560588	-0.6408893231
+5	-25	0.396378089204663	0.03133113778	-0.1669924868	-0.6418834564
+10	-25	0.396795800496521	0.06261604676	-0.1655920269	-0.6448867524
+15	-25	0.397449595261698	0.09379240949	-0.1632254176	-0.6499619624
+20	-25	0.398265161285884	0.1247626602	-0.1598421476	-0.6572174083
+25	-25	0.399177112164365	0.1553923131	-0.1553923131	-0.6667601091
+30	-25	0.400163068931277	0.1855247346	-0.1498424945	-0.6786617336
+35	-25	0.401266409047526	0.2150054890	-0.1431842713	-0.6929403394
+40	-25	0.402574254381549	0.2436889447	-0.1354237529	-0.7095828247
+45	-25	0.404045349772518	0.2713337998	-0.1265250287	-0.7286662002
+
+-45	-20	0.403792100607269	-0.2765132282	-0.1006425844	-0.7234867718
+-40	-20	0.402159570267890	-0.2490055801	-0.1080093662	-0.7032467054
+-35	-20	0.400654498385725	-0.2202262069	-0.1144743233	-0.6854843816
+-30	-20	0.399391927888279	-0.1904584132	-0.1200678288	-0.6701163517
+-25	-20	0.398265161285884	-0.1598421476	-0.1247626602	-0.6572174083
+-20	-20	0.397216665961991	-0.1285455006	-0.1285455006	-0.6468241397
+-15	-20	0.396270985869465	-0.09675704480	-0.1314304549	-0.6388977928
+-10	-20	0.395505410021134	-0.06465107863	-0.1334513195	-0.6333455132
+-5	-20	0.395012222203307	-0.03236572921	-0.1346478683	-0.6300580223
+0	-20	0.394842300222228	0.000000000	-0.1350440201	-0.6289696041
+5	-20	0.395012222203307	0.03236572921	-0.1346478683	-0.6300580223
+10	-20	0.395505410021134	0.06465107863	-0.1334513195	-0.6333455132
+15	-20	0.396270985869465	0.09675704480	-0.1314304549	-0.6388977928
+20	-20	0.397216665961990	0.1285455006	-0.1285455006	-0.6468241397
+25	-20	0.398265161285883	0.1598421476	-0.1247626602	-0.6572174083
+30	-20	0.399391927888278	0.1904584132	-0.1200678288	-0.6701163517
+35	-20	0.400654498385724	0.2202262069	-0.1144743233	-0.6854843816
+40	-20	0.402159570267888	0.2490055801	-0.1080093662	-0.7032467054
+45	-20	0.403792100607267	0.2765132282	-0.1006425844	-0.7234867718
+
+-45	-15	0.403566000239543	-0.2803761028	-0.07512655031	-0.7196238972
+-40	-15	0.401791822777133	-0.2529922452	-0.08078786509	-0.6984955829
+-35	-15	0.400112560668406	-0.2241590654	-0.08577919728	-0.6798676775
+-30	-15	0.398708704640041	-0.1941944532	-0.09012595938	-0.6636453405
+-25	-15	0.397449595261698	-0.1632254176	-0.09379240949	-0.6499619624
+-20	-15	0.396270985869465	-0.1314304549	-0.09675704480	-0.6388977928
+-15	-15	0.395201356554912	-0.09902276126	-0.09902276126	-0.6304420239
+-10	-15	0.394330304155801	-0.06620842004	-0.1006113336	-0.6245133911
+-5	-15	0.393766298533230	-0.03315804005	-0.1015522434	-0.6210018679
+0	-15	0.393571465787466	0.000000000	-0.1018637910	-0.6198391567
+5	-15	0.393766298533230	0.03315804005	-0.1015522434	-0.6210018679
+10	-15	0.394330304155800	0.06620842004	-0.1006113336	-0.6245133911
+15	-15	0.395201356554912	0.09902276126	-0.09902276126	-0.6304420239
+20	-15	0.396270985869465	0.1314304549	-0.09675704480	-0.6388977928
+25	-15	0.397449595261697	0.1632254176	-0.09379240949	-0.6499619624
+30	-15	0.398708704640040	0.1941944532	-0.09012595938	-0.6636453405
+35	-15	0.400112560668405	0.2241590654	-0.08577919728	-0.6798676775
+40	-15	0.401791822777131	0.2529922452	-0.08078786509	-0.6984955829
+45	-15	0.403566000239542	0.2803761028	-0.07512655031	-0.7196238972
+
+-45	-10	0.403393040297303	-0.2830503449	-0.04990941270	-0.7169496551
+-40	-10	0.401506832715869	-0.2557609754	-0.05374517984	-0.6951959387
+-35	-10	0.399691399322724	-0.2268989450	-0.05713792514	-0.6759547239
+-30	-10	0.398168473869744	-0.1968028950	-0.06010503869	-0.6591273868
+-25	-10	0.396795800496522	-0.1655920269	-0.06261604676	-0.6448867524
+-20	-10	0.395505410021134	-0.1334513195	-0.06465107863	-0.6333455132
+-15	-10	0.394330304155801	-0.1006113336	-0.06620842004	-0.6245133911
+-10	-10	0.393370857589973	-0.06730098205	-0.06730098205	-0.6183171641
+-5	-10	0.392748115755233	-0.03371408062	-0.06794825527	-0.6146462952
+0	-10	0.392532718012424	0.000000000	-0.06816259116	-0.6134307360
+5	-10	0.392748115755233	0.03371408062	-0.06794825527	-0.6146462952
+10	-10	0.393370857589973	0.06730098205	-0.06730098205	-0.6183171641
+15	-10	0.394330304155800	0.1006113336	-0.06620842004	-0.6245133911
+20	-10	0.395505410021134	0.1334513195	-0.06465107863	-0.6333455132
+25	-10	0.396795800496521	0.1655920269	-0.06261604676	-0.6448867524
+30	-10	0.398168473869743	0.1968028950	-0.06010503869	-0.6591273868
+35	-10	0.399691399322722	0.2268989450	-0.05713792514	-0.6759547239
+40	-10	0.401506832715867	0.2557609754	-0.05374517984	-0.6951959387
+45	-10	0.403393040297301	0.2830503449	-0.04990941270	-0.7169496551
+
+-45	-5	0.403285295971309	-0.2846216452	-0.02490116735	-0.7153783548
+-40	-5	0.401329098255664	-0.2573919547	-0.02683695390	-0.6932522133
+-35	-5	0.399430785110639	-0.2285179934	-0.02855258298	-0.6736424832
+-30	-5	0.397827508487729	-0.1983452487	-0.03005620964	-0.6564559518
+-25	-5	0.396378089204663	-0.1669924868	-0.03133113778	-0.6418834564
+-20	-5	0.395012222203307	-0.1346478683	-0.03236572921	-0.6300580223
+-15	-5	0.393766298533231	-0.1015522434	-0.03315804005	-0.6210018679
+-10	-5	0.392748115755233	-0.06794825527	-0.03371408062	-0.6146462952
+-5	-5	0.392086680478515	-0.03404355097	-0.03404355097	-0.6108804319
+0	-5	0.391857792622263	0.000000000	-0.03415265697	-0.6096333446
+5	-5	0.392086680478515	0.03404355097	-0.03404355097	-0.6108804319
+10	-5	0.392748115755233	0.06794825527	-0.03371408062	-0.6146462952
+15	-5	0.393766298533230	0.1015522434	-0.03315804005	-0.6210018679
+20	-5	0.395012222203307	0.1346478683	-0.03236572921	-0.6300580223
+25	-5	0.396378089204662	0.1669924868	-0.03133113778	-0.6418834564
+30	-5	0.397827508487728	0.1983452487	-0.03005620964	-0.6564559518
+35	-5	0.399430785110639	0.2285179934	-0.02855258298	-0.6736424832
+40	-5	0.401329098255663	0.2573919547	-0.02683695390	-0.6932522133
+45	-5	0.403285295971308	0.2846216452	-0.02490116735	-0.7153783548
+
+-45	0	0.403248759262707	-0.2851399322	0.000000000	-0.7148600678
+-40	0	0.401268851602537	-0.2579306460	0.000000000	-0.6926102260
+-35	0	0.399343064959333	-0.2290537721	0.000000000	-0.6728773120
+-30	0	0.397711338186446	-0.1988556691	0.000000000	-0.6555718778
+-25	0	0.396234791397782	-0.1674560588	0.000000000	-0.6408893231
+-20	0	0.394842300222228	-0.1350440201	0.000000000	-0.6289696041
+-15	0	0.393571465787466	-0.1018637910	0.000000000	-0.6198391567
+-10	0	0.392532718012424	-0.06816259116	0.000000000	-0.6134307360
+-5	0	0.391857792622263	-0.03415265697	0.000000000	-0.6096333446
+0	0	0.391624211908763	0.000000000	0.000000000	-0.6083757881
+5	0	0.391857792622263	0.03415265697	0.000000000	-0.6096333446
+10	0	0.392532718012423	0.06816259116	0.000000000	-0.6134307360
+15	0	0.393571465787466	0.1018637910	0.000000000	-0.6198391567
+20	0	0.394842300222228	0.1350440201	0.000000000	-0.6289696041
+25	0	0.396234791397781	0.1674560588	0.000000000	-0.6408893231
+30	0	0.397711338186445	0.1988556691	0.000000000	-0.6555718778
+35	0	0.399343064959332	0.2290537721	0.000000000	-0.6728773120
+40	0	0.401268851602536	0.2579306460	0.000000000	-0.6926102260
+45	0	0.403248759262707	0.2851399322	0.000000000	-0.7148600678
+
+-45	5	0.403285295971308	-0.2846216452	0.02490116735	-0.7153783548
+-40	5	0.401329098255664	-0.2573919547	0.02683695390	-0.6932522133
+-35	5	0.399430785110639	-0.2285179934	0.02855258298	-0.6736424832
+-30	5	0.397827508487729	-0.1983452487	0.03005620964	-0.6564559518
+-25	5	0.396378089204663	-0.1669924868	0.03133113778	-0.6418834564
+-20	5	0.395012222203307	-0.1346478683	0.03236572921	-0.6300580223
+-15	5	0.393766298533231	-0.1015522434	0.03315804005	-0.6210018679
+-10	5	0.392748115755233	-0.06794825527	0.03371408062	-0.6146462952
+-5	5	0.392086680478515	-0.03404355097	0.03404355097	-0.6108804319
+0	5	0.391857792622263	0.000000000	0.03415265697	-0.6096333446
+5	5	0.392086680478515	0.03404355097	0.03404355097	-0.6108804319
+10	5	0.392748115755233	0.06794825527	0.03371408062	-0.6146462952
+15	5	0.393766298533230	0.1015522434	0.03315804005	-0.6210018679
+20	5	0.395012222203307	0.1346478683	0.03236572921	-0.6300580223
+25	5	0.396378089204662	0.1669924868	0.03133113778	-0.6418834564
+30	5	0.397827508487728	0.1983452487	0.03005620964	-0.6564559518
+35	5	0.399430785110639	0.2285179934	0.02855258298	-0.6736424832
+40	5	0.401329098255663	0.2573919547	0.02683695390	-0.6932522133
+45	5	0.403285295971308	0.2846216452	0.02490116735	-0.7153783548
+
+-45	10	0.403393040297302	-0.2830503449	0.04990941270	-0.7169496551
+-40	10	0.401506832715868	-0.2557609754	0.05374517984	-0.6951959387
+-35	10	0.399691399322724	-0.2268989450	0.05713792514	-0.6759547239
+-30	10	0.398168473869744	-0.1968028950	0.06010503869	-0.6591273868
+-25	10	0.396795800496522	-0.1655920269	0.06261604676	-0.6448867524
+-20	10	0.395505410021134	-0.1334513195	0.06465107863	-0.6333455132
+-15	10	0.394330304155801	-0.1006113336	0.06620842004	-0.6245133911
+-10	10	0.393370857589973	-0.06730098205	0.06730098205	-0.6183171641
+-5	10	0.392748115755233	-0.03371408062	0.06794825527	-0.6146462952
+0	10	0.392532718012423	0.000000000	0.06816259116	-0.6134307360
+5	10	0.392748115755233	0.03371408062	0.06794825527	-0.6146462952
+10	10	0.393370857589973	0.06730098205	0.06730098205	-0.6183171641
+15	10	0.394330304155801	0.1006113336	0.06620842004	-0.6245133911
+20	10	0.395505410021134	0.1334513195	0.06465107863	-0.6333455132
+25	10	0.396795800496521	0.1655920269	0.06261604676	-0.6448867524
+30	10	0.398168473869743	0.1968028950	0.06010503869	-0.6591273868
+35	10	0.399691399322723	0.2268989450	0.05713792514	-0.6759547239
+40	10	0.401506832715868	0.2557609754	0.05374517984	-0.6951959387
+45	10	0.403393040297302	0.2830503449	0.04990941270	-0.7169496551
+
+-45	15	0.403566000239543	-0.2803761028	0.07512655031	-0.7196238972
+-40	15	0.401791822777132	-0.2529922452	0.08078786509	-0.6984955829
+-35	15	0.400112560668406	-0.2241590654	0.08577919728	-0.6798676775
+-30	15	0.398708704640041	-0.1941944532	0.09012595938	-0.6636453405
+-25	15	0.397449595261698	-0.1632254176	0.09379240949	-0.6499619624
+-20	15	0.396270985869465	-0.1314304549	0.09675704480	-0.6388977928
+-15	15	0.395201356554912	-0.09902276126	0.09902276126	-0.6304420239
+-10	15	0.394330304155801	-0.06620842004	0.1006113336	-0.6245133911
+-5	15	0.393766298533230	-0.03315804005	0.1015522434	-0.6210018679
+0	15	0.393571465787466	0.000000000	0.1018637910	-0.6198391567
+5	15	0.393766298533230	0.03315804005	0.1015522434	-0.6210018679
+10	15	0.394330304155801	0.06620842004	0.1006113336	-0.6245133911
+15	15	0.395201356554912	0.09902276126	0.09902276126	-0.6304420239
+20	15	0.396270985869465	0.1314304549	0.09675704480	-0.6388977928
+25	15	0.397449595261698	0.1632254176	0.09379240949	-0.6499619624
+30	15	0.398708704640040	0.1941944532	0.09012595938	-0.6636453405
+35	15	0.400112560668405	0.2241590654	0.08577919728	-0.6798676775
+40	15	0.401791822777131	0.2529922452	0.08078786509	-0.6984955829
+45	15	0.403566000239542	0.2803761028	0.07512655031	-0.7196238972
+
+-45	20	0.403792100607269	-0.2765132282	0.1006425844	-0.7234867718
+-40	20	0.402159570267890	-0.2490055801	0.1080093662	-0.7032467054
+-35	20	0.400654498385725	-0.2202262069	0.1144743233	-0.6854843816
+-30	20	0.399391927888279	-0.1904584132	0.1200678288	-0.6701163517
+-25	20	0.398265161285884	-0.1598421476	0.1247626602	-0.6572174083
+-20	20	0.397216665961991	-0.1285455006	0.1285455006	-0.6468241397
+-15	20	0.396270985869465	-0.09675704480	0.1314304549	-0.6388977928
+-10	20	0.395505410021134	-0.06465107863	0.1334513195	-0.6333455132
+-5	20	0.395012222203307	-0.03236572921	0.1346478683	-0.6300580223
+0	20	0.394842300222228	0.000000000	0.1350440201	-0.6289696041
+5	20	0.395012222203307	0.03236572921	0.1346478683	-0.6300580223
+10	20	0.395505410021134	0.06465107863	0.1334513195	-0.6333455132
+15	20	0.396270985869465	0.09675704480	0.1314304549	-0.6388977928
+20	20	0.397216665961990	0.1285455006	0.1285455006	-0.6468241397
+25	20	0.398265161285884	0.1598421476	0.1247626602	-0.6572174083
+30	20	0.399391927888278	0.1904584132	0.1200678288	-0.6701163517
+35	20	0.400654498385724	0.2202262069	0.1144743233	-0.6854843816
+40	20	0.402159570267889	0.2490055801	0.1080093662	-0.7032467054
+45	20	0.403792100607268	0.2765132282	0.1006425844	-0.7234867718
+
+-45	25	0.404045349772519	-0.2713337998	0.1265250287	-0.7286662002
+-40	25	0.402574254381550	-0.2436889447	0.1354237529	-0.7095828247
+-35	25	0.401266409047527	-0.2150054890	0.1431842713	-0.6929403394
+-30	25	0.400163068931278	-0.1855247346	0.1498424945	-0.6786617336
+-25	25	0.399177112164366	-0.1553923131	0.1553923131	-0.6667601091
+-20	25	0.398265161285884	-0.1247626602	0.1598421476	-0.6572174083
+-15	25	0.397449595261698	-0.09379240949	0.1632254176	-0.6499619624
+-10	25	0.396795800496521	-0.06261604676	0.1655920269	-0.6448867524
+-5	25	0.396378089204663	-0.03133113778	0.1669924868	-0.6418834564
+0	25	0.396234791397781	0.000000000	0.1674560588	-0.6408893231
+5	25	0.396378089204663	0.03133113778	0.1669924868	-0.6418834564
+10	25	0.396795800496521	0.06261604676	0.1655920269	-0.6448867524
+15	25	0.397449595261698	0.09379240949	0.1632254176	-0.6499619624
+20	25	0.398265161285884	0.1247626602	0.1598421476	-0.6572174083
+25	25	0.399177112164365	0.1553923131	0.1553923131	-0.6667601091
+30	25	0.400163068931277	0.1855247346	0.1498424945	-0.6786617336
+35	25	0.401266409047526	0.2150054890	0.1431842713	-0.6929403394
+40	25	0.402574254381549	0.2436889447	0.1354237529	-0.7095828247
+45	25	0.404045349772518	0.2713337998	0.1265250287	-0.7286662002
+
+-45	30	0.404312090779581	-0.2646843943	0.1528156063	-0.7353156057
+-40	30	0.403019661552553	-0.2369186881	0.1630140966	-0.7176513023
+-35	30	0.401926117385890	-0.2084036728	0.1718375054	-0.7023687101
+-30	30	0.401000097620799	-0.1793326955	0.1793326955	-0.6893866600
+-25	30	0.400163068931278	-0.1498424945	0.1855247346	-0.6786617336
+-20	30	0.399391927888278	-0.1200678288	0.1904584132	-0.6701163517
+-15	30	0.398708704640041	-0.09012595938	0.1941944532	-0.6636453405
+-10	30	0.398168473869743	-0.06010503869	0.1968028950	-0.6591273868
+-5	30	0.397827508487728	-0.03005620964	0.1983452487	-0.6564559518
+0	30	0.397711338186445	0.000000000	0.1988556691	-0.6555718778
+5	30	0.397827508487728	0.03005620964	0.1983452487	-0.6564559518
+10	30	0.398168473869743	0.06010503869	0.1968028950	-0.6591273868
+15	30	0.398708704640041	0.09012595938	0.1941944532	-0.6636453405
+20	30	0.399391927888278	0.1200678288	0.1904584132	-0.6701163517
+25	30	0.400163068931278	0.1498424945	0.1855247346	-0.6786617336
+30	30	0.401000097620798	0.1793326955	0.1793326955	-0.6893866600
+35	30	0.401926117385889	0.2084036728	0.1718375054	-0.7023687101
+40	30	0.403019661552553	0.2369186881	0.1630140966	-0.7176513023
+45	30	0.404312090779580	0.2646843943	0.1528156063	-0.7353156057
+
+-45	35	0.404600138471223	-0.2563899589	0.1795261819	-0.7436100411
+-40	35	0.403511417621328	-0.2285670167	0.1907334268	-0.7276044367
+-35	35	0.402650861803494	-0.2003360421	0.2003360421	-0.7138904808
+-30	35	0.401926117385890	-0.1718375054	0.2084036728	-0.7023687101
+-25	35	0.401266409047526	-0.1431842713	0.2150054890	-0.6929403394
+-20	35	0.400654498385725	-0.1144743233	0.2202262069	-0.6854843816
+-15	35	0.400112560668406	-0.08577919728	0.2241590654	-0.6798676775
+-10	35	0.399691399322723	-0.05713792514	0.2268989450	-0.6759547239
+-5	35	0.399430785110639	-0.02855258298	0.2285179934	-0.6736424832
+0	35	0.399343064959333	0.000000000	0.2290537721	-0.6728773120
+5	35	0.399430785110639	0.02855258298	0.2285179934	-0.6736424832
+10	35	0.399691399322723	0.05713792514	0.2268989450	-0.6759547239
+15	35	0.400112560668405	0.08577919728	0.2241590654	-0.6798676775
+20	35	0.400654498385724	0.1144743233	0.2202262069	-0.6854843816
+25	35	0.401266409047526	0.1431842713	0.2150054890	-0.6929403394
+30	35	0.401926117385890	0.1718375054	0.2084036728	-0.7023687101
+35	35	0.402650861803493	0.2003360421	0.2003360421	-0.7138904808
+40	35	0.403511417621327	0.2285670167	0.1907334268	-0.7276044367
+45	35	0.404600138471222	0.2563899589	0.1795261819	-0.7436100411
+
+-45	40	0.404954325213096	-0.2462609872	0.2066375035	-0.7537390128
+-40	40	0.404118281795434	-0.2185133029	0.2185133029	-0.7395859862
+-35	40	0.403511417621328	-0.1907334268	0.2285670167	-0.7276044367
+-30	40	0.403019661552553	-0.1630140966	0.2369186881	-0.7176513023
+-25	40	0.402574254381550	-0.1354237529	0.2436889447	-0.7095828247
+-20	40	0.402159570267889	-0.1080093662	0.2490055801	-0.7032467054
+-15	40	0.401791822777132	-0.08078786509	0.2529922452	-0.6984955829
+-10	40	0.401506832715868	-0.05374517984	0.2557609754	-0.6951959387
+-5	40	0.401329098255663	-0.02683695390	0.2573919547	-0.6932522133
+0	40	0.401268851602536	0.000000000	0.2579306460	-0.6926102260
+5	40	0.401329098255663	0.02683695390	0.2573919547	-0.6932522133
+10	40	0.401506832715868	0.05374517984	0.2557609754	-0.6951959387
+15	40	0.401791822777132	0.08078786509	0.2529922452	-0.6984955829
+20	40	0.402159570267889	0.1080093662	0.2490055801	-0.7032467054
+25	40	0.402574254381550	0.1354237529	0.2436889447	-0.7095828247
+30	40	0.403019661552553	0.1630140966	0.2369186881	-0.7176513023
+35	40	0.403511417621327	0.1907334268	0.2285670167	-0.7276044367
+40	40	0.404118281795433	0.2185133029	0.2185133029	-0.7395859862
+45	40	0.404954325213095	0.2462609872	0.2066375035	-0.7537390128
+
+-45	45	0.405481674472941	-0.2341049539	0.2341049539	-0.7658950461
+-40	45	0.404954325213096	-0.2066375035	0.2462609872	-0.7537390128
+-35	45	0.404600138471222	-0.1795261819	0.2563899589	-0.7436100411
+-30	45	0.404312090779581	-0.1528156063	0.2646843943	-0.7353156057
+-25	45	0.404045349772519	-0.1265250287	0.2713337998	-0.7286662002
+-20	45	0.403792100607268	-0.1006425844	0.2765132282	-0.7234867718
+-15	45	0.403566000239543	-0.07512655031	0.2803761028	-0.7196238972
+-10	45	0.403393040297302	-0.04990941270	0.2830503449	-0.7169496551
+-5	45	0.403285295971308	-0.02490116735	0.2846216452	-0.7153783548
+0	45	0.403248759262707	0.000000000	0.2851399322	-0.7148600678
+5	45	0.403285295971308	0.02490116735	0.2846216452	-0.7153783548
+10	45	0.403393040297302	0.04990941270	0.2830503449	-0.7169496551
+15	45	0.403566000239543	0.07512655031	0.2803761028	-0.7196238972
+20	45	0.403792100607268	0.1006425844	0.2765132282	-0.7234867718
+25	45	0.404045349772519	0.1265250287	0.2713337998	-0.7286662002
+30	45	0.404312090779581	0.1528156063	0.2646843943	-0.7353156057
+35	45	0.404600138471222	0.1795261819	0.2563899589	-0.7436100411
+40	45	0.404954325213095	0.2066375035	0.2462609872	-0.7537390128
+45	45	0.405481674472941	0.2341049539	0.2341049539	-0.7658950461
+
+
+### +x patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	-45	0.405481246888700	0.2341047070	-0.2341047070	-0.7658952930
+45	-40	0.404953884308433	0.2462607191	-0.2066372786	-0.7537392809
+45	-35	0.404600376776807	0.2563901099	-0.1795262877	-0.7436098901
+45	-30	0.404312156366900	0.2646844373	-0.1528156311	-0.7353155627
+45	-25	0.404045335367780	0.2713337901	-0.1265250242	-0.7286662099
+45	-20	0.403792076974581	0.2765132120	-0.1006425785	-0.7234867880
+45	-15	0.403565989481415	0.2803760953	-0.07512654831	-0.7196239047
+45	-10	0.403393035592475	0.2830503416	-0.04990941212	-0.7169496584
+45	-5	0.403285294975798	0.2846216445	-0.02490116729	-0.7153783555
+45	0	0.403248758763944	0.2851399318	0.000000000	-0.7148600682
+45	5	0.403285294975798	0.2846216445	0.02490116729	-0.7153783555
+45	10	0.403393035592476	0.2830503416	0.04990941212	-0.7169496584
+45	15	0.403565989481415	0.2803760953	0.07512654831	-0.7196239047
+45	20	0.403792076974581	0.2765132120	0.1006425785	-0.7234867880
+45	25	0.404045335367780	0.2713337901	0.1265250242	-0.7286662099
+45	30	0.404312156366900	0.2646844373	0.1528156311	-0.7353155627
+45	35	0.404600376776807	0.2563901099	0.1795262877	-0.7436098901
+45	40	0.404953884308433	0.2462607191	0.2066372786	-0.7537392809
+45	45	0.405481246888701	0.2341047070	0.2341047070	-0.7658952930
+
+50	-45	0.406795594720917	0.2473807008	-0.2473807008	-0.7924229452
+50	-40	0.406289306919105	0.2618130234	-0.2196872114	-0.7803127886
+50	-35	0.406013998432557	0.2740849626	-0.1919163569	-0.7700154089
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+105	-30	0.419444724877339	0.3538477740	-0.2042941076	-1.094813225
+105	-25	0.419789601277833	0.3697131158	-0.1724000572	-1.099064331
+105	-20	0.420040729651620	0.3827624025	-0.1393141213	-1.102560877
+105	-15	0.420124716342019	0.3928641370	-0.1052676283	-1.105267628
+105	-10	0.420090594508191	0.4000159031	-0.07053359643	-1.107183938
+105	-5	0.420031937688745	0.4042786810	-0.03536980149	-1.108326146
+105	0	0.420005891847987	0.4056945381	0.000000000	-1.108705524
+105	5	0.420031937688745	0.4042786810	0.03536980149	-1.108326146
+105	10	0.420090594508192	0.4000159031	0.07053359643	-1.107183938
+105	15	0.420124716342019	0.3928641370	0.1052676283	-1.105267628
+105	20	0.420040729651621	0.3827624025	0.1393141213	-1.102560877
+105	25	0.419789601277833	0.3697131158	0.1724000572	-1.099064331
+105	30	0.419444724877340	0.3538477740	0.2042941076	-1.094813225
+105	35	0.419158621920597	0.3353711838	0.2348294310	-1.089862438
+105	40	0.418992791401503	0.3144120169	0.2638230074	-1.084246446
+105	45	0.418844673013459	0.2909909086	0.2909909086	-1.077970779
+
+110	-45	0.419465656408434	0.2872463394	-0.2872463394	-1.104549117
+110	-40	0.419651515881373	0.3096605903	-0.2598360871	-1.112707238
+110	-35	0.419869695852164	0.3295996365	-0.2307881501	-1.119964457
+110	-30	0.420207519358544	0.3470765928	-0.2003847643	-1.126325549
+110	-25	0.420572650126289	0.3619824103	-0.1687951700	-1.131750823
+110	-20	0.420862034392394	0.3741995837	-0.1361975101	-1.136197510
+110	-15	0.420995778515204	0.3836326914	-0.1027940699	-1.139630881
+110	-10	0.421011860991742	0.3903003194	-0.06882047688	-1.142057699
+110	-5	0.420989416240127	0.3942704769	-0.03449419709	-1.143502718
+110	0	0.420976478579511	0.3955884904	0.000000000	-1.143982436
+110	5	0.420989416240128	0.3942704769	0.03449419709	-1.143502718
+110	10	0.421011860991743	0.3903003194	0.06882047688	-1.142057699
+110	15	0.420995778515205	0.3836326914	0.1027940699	-1.139630881
+110	20	0.420862034392395	0.3741995837	0.1361975101	-1.136197510
+110	25	0.420572650126290	0.3619824103	0.1687951700	-1.131750823
+110	30	0.420207519358544	0.3470765928	0.2003847643	-1.126325549
+110	35	0.419869695852165	0.3295996365	0.2307881501	-1.119964457
+110	40	0.419651515881373	0.3096605903	0.2598360871	-1.112707238
+110	45	0.419465656408435	0.2872463394	0.2872463394	-1.104549117
+
+115	-45	0.420040278579634	0.2820750812	-0.2820750812	-1.131533771
+115	-40	0.420256526120296	0.3031731709	-0.2543924958	-1.141371971
+115	-35	0.420521269749209	0.3217939889	-0.2253225768	-1.150055001
+115	-30	0.420895133174358	0.3379864933	-0.1951365929	-1.157605690
+115	-25	0.421254844396126	0.3516707600	-0.1639867685	-1.163986769
+115	-20	0.421528520292082	0.3628051176	-0.1320502636	-1.169178805
+115	-15	0.421685230990910	0.3713826168	-0.09951167225	-1.173178558
+115	-10	0.421738283850171	0.3774355762	-0.06655207557	-1.176001100
+115	-5	0.421741831447014	0.3810319770	-0.03333597842	-1.177678129
+115	0	0.421738502012697	0.3822248885	0.000000000	-1.178234393
+115	5	0.421741831447014	0.3810319770	0.03333597842	-1.177678129
+115	10	0.421738283850172	0.3774355762	0.06655207557	-1.176001100
+115	15	0.421685230990910	0.3713826168	0.09951167225	-1.173178558
+115	20	0.421528520292082	0.3628051176	0.1320502636	-1.169178805
+115	25	0.421254844396126	0.3516707600	0.1639867685	-1.163986769
+115	30	0.420895133174359	0.3379864933	0.1951365929	-1.157605690
+115	35	0.420521269749210	0.3217939889	0.2253225768	-1.150055001
+115	40	0.420256526120296	0.3031731709	0.2543924958	-1.141371971
+115	45	0.420040278579635	0.2820750812	0.2820750812	-1.131533771
+
+120	-45	0.420559993702198	0.2753211436	-0.2753211436	-1.158956736
+120	-40	0.420779147405272	0.2947906905	-0.2473587596	-1.170197484
+120	-35	0.421067389084515	0.3118056397	-0.2183286594	-1.180021070
+120	-30	0.421429461477643	0.3264378572	-0.1884689847	-1.188468985
+120	-25	0.421747854641819	0.3386712443	-0.1579249948	-1.195531934
+120	-20	0.421972410989474	0.3485343311	-0.1268561221	-1.201226390
+120	-15	0.422095920256013	0.3560843490	-0.09541251375	-1.205585395
+120	-10	0.422143074517673	0.3613973039	-0.06372409543	-1.208652831
+120	-5	0.422156306298634	0.3645531879	-0.03189427119	-1.210474881
+120	0	0.422158185633103	0.3655997132	0.000000000	-1.211079093
+120	5	0.422156306298634	0.3645531879	0.03189427119	-1.210474881
+120	10	0.422143074517673	0.3613973039	0.06372409543	-1.208652831
+120	15	0.422095920256014	0.3560843490	0.09541251375	-1.205585395
+120	20	0.421972410989475	0.3485343311	0.1268561221	-1.201226390
+120	25	0.421747854641820	0.3386712443	0.1579249948	-1.195531934
+120	30	0.421429461477644	0.3264378572	0.1884689847	-1.188468985
+120	35	0.421067389084515	0.3118056397	0.2183286594	-1.180021070
+120	40	0.420779147405272	0.2947906905	0.2473587596	-1.170197484
+120	45	0.420559993702199	0.2753211436	0.2753211436	-1.158956736
+
+125	-45	0.420974391528749	0.2667661147	-0.2667661147	-1.186791644
+125	-40	0.421160417370072	0.2843097472	-0.2385642040	-1.199075828
+125	-35	0.421433896643668	0.2994560821	-0.2096814061	-1.209681406
+125	-30	0.421740723023143	0.3123042519	-0.1803089439	-1.218677791
+125	-25	0.421988055236155	0.3229164119	-0.1505783958	-1.226108506
+125	-20	0.422146272101119	0.3313867593	-0.1206149164	-1.232039507
+125	-15	0.422221936551195	0.3378221592	-0.09051917473	-1.236545622
+125	-10	0.422245340255344	0.3423306283	-0.06036212609	-1.239702486
+125	-5	0.422249870494671	0.3450019987	-0.03018376378	-1.241573000
+125	0	0.422249842289700	0.3458868215	0.000000000	-1.242192560
+125	5	0.422249870494671	0.3450019987	0.03018376378	-1.241573000
+125	10	0.422245340255344	0.3423306283	0.06036212609	-1.239702486
+125	15	0.422221936551195	0.3378221592	0.09051917473	-1.236545622
+125	20	0.422146272101119	0.3313867593	0.1206149164	-1.232039507
+125	25	0.421988055236155	0.3229164119	0.1505783958	-1.226108506
+125	30	0.421740723023144	0.3123042519	0.1803089439	-1.218677791
+125	35	0.421433896643669	0.2994560821	0.2096814061	-1.209681406
+125	40	0.421160417370072	0.2843097472	0.2385642040	-1.199075828
+125	45	0.420974391528749	0.2667661147	0.2667661147	-1.186791644
+
+130	-45	0.421233930166751	0.2561609471	-0.2561609471	-1.214944556
+130	-40	0.421357842549581	0.2715231950	-0.2278350128	-1.227835013
+130	-35	0.421579106337181	0.2845923886	-0.1992737358	-1.238801368
+130	-30	0.421800153288749	0.2955059898	-0.1706104627	-1.247958967
+130	-25	0.421964049994409	0.3044049790	-0.1419463729	-1.255426106
+130	-20	0.422057549538735	0.3114360010	-0.1133534343	-1.261325834
+130	-15	0.422092443828019	0.3167379948	-0.08486968991	-1.265774735
+130	-10	0.422097272783196	0.3204353016	-0.05650138924	-1.268877143
+130	-5	0.422094460465485	0.3226193717	-0.02822553766	-1.270709796
+130	0	0.422092640652914	0.3233417219	0.000000000	-1.271315920
+130	5	0.422094460465485	0.3226193717	0.02822553766	-1.270709796
+130	10	0.422097272783196	0.3204353016	0.05650138924	-1.268877143
+130	15	0.422092443828019	0.3167379948	0.08486968991	-1.265774735
+130	20	0.422057549538736	0.3114360010	0.1133534343	-1.261325834
+130	25	0.421964049994409	0.3044049790	0.1419463729	-1.255426106
+130	30	0.421800153288750	0.2955059898	0.1706104627	-1.247958967
+130	35	0.421579106337181	0.2845923886	0.1992737358	-1.238801368
+130	40	0.421357842549582	0.2715231950	0.2278350128	-1.227835013
+130	45	0.421233930166751	0.2561609471	0.2561609471	-1.214944556
+
+135	-45	0.421317295454033	0.2432476539	-0.2432476539	-1.243247654
+135	-40	0.421383484215576	0.2562518940	-0.2150208697	-1.256251894
+135	-35	0.421529869183832	0.2671181138	-0.1870381169	-1.267118114
+135	-30	0.421667446949540	0.2760461420	-0.1593753144	-1.276046142
+135	-25	0.421775248654318	0.2832401881	-0.1320770688	-1.283240188
+135	-20	0.421837585830954	0.2888706155	-0.1051403056	-1.288870615
+135	-15	0.421862858734397	0.2930877828	-0.07853263472	-1.293087783
+135	-10	0.421871721447431	0.2960163521	-0.05219566961	-1.296016352
+135	-5	0.421874605062143	0.2977411905	-0.02604897884	-1.297741191
+135	0	0.421875207994689	0.2983108204	0.000000000	-1.298310820
+135	5	0.421874605062143	0.2977411905	0.02604897884	-1.297741191
+135	10	0.421871721447431	0.2960163521	0.05219566961	-1.296016352
+135	15	0.421862858734397	0.2930877828	0.07853263472	-1.293087783
+135	20	0.421837585830955	0.2888706155	0.1051403056	-1.288870615
+135	25	0.421775248654318	0.2832401881	0.1320770688	-1.283240188
+135	30	0.421667446949540	0.2760461420	0.1593753144	-1.276046142
+135	35	0.421529869183832	0.2671181138	0.1870381169	-1.267118114
+135	40	0.421383484215576	0.2562518940	0.2150208697	-1.256251894
+135	45	0.421317295454032	0.2432476539	0.2432476539	-1.243247654
+
+
+### +y patch
+# N_rho = 19
+# 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	0.405481246888701	0.2341047070	0.2341047070	-0.7658952930
+40	45	0.404953884308434	0.2066372786	0.2462607191	-0.7537392809
+35	45	0.404600376776807	0.1795262877	0.2563901099	-0.7436098901
+30	45	0.404312156366901	0.1528156311	0.2646844373	-0.7353155627
+25	45	0.404045335367780	0.1265250242	0.2713337901	-0.7286662099
+20	45	0.403792076974582	0.1006425785	0.2765132120	-0.7234867880
+15	45	0.403565989481416	0.07512654831	0.2803760953	-0.7196239047
+10	45	0.403393035592476	0.04990941212	0.2830503416	-0.7169496584
+5	45	0.403285294975799	0.02490116729	0.2846216445	-0.7153783555
+0	45	0.403248758763944	0.000000000	0.2851399318	-0.7148600682
+-5	45	0.403285294975799	-0.02490116729	0.2846216445	-0.7153783555
+-10	45	0.403393035592476	-0.04990941212	0.2830503416	-0.7169496584
+-15	45	0.403565989481416	-0.07512654831	0.2803760953	-0.7196239047
+-20	45	0.403792076974582	-0.1006425785	0.2765132120	-0.7234867880
+-25	45	0.404045335367781	-0.1265250242	0.2713337901	-0.7286662099
+-30	45	0.404312156366901	-0.1528156311	0.2646844373	-0.7353155627
+-35	45	0.404600376776808	-0.1795262877	0.2563901099	-0.7436098901
+-40	45	0.404953884308434	-0.2066372786	0.2462607191	-0.7537392809
+-45	45	0.405481246888702	-0.2341047070	0.2341047070	-0.7658952930
+
+45	50	0.406795594720918	0.2473807008	0.2473807008	-0.7924229452
+40	50	0.406289306919106	0.2196872114	0.2618130234	-0.7803127886
+35	50	0.406013998432558	0.1919163569	0.2740849626	-0.7700154089
+30	50	0.405832116775407	0.1641516834	0.2843190559	-0.7614279851
+25	50	0.405671576403578	0.1364656749	0.2926515842	-0.7544361636
+20	50	0.405508438276748	0.1089087831	0.2992244222	-0.7489208977
+15	50	0.405347985375322	0.08150289901	0.3041729601	-0.7447685814
+10	50	0.405216174033675	0.05424170742	0.3076200092	-0.7418761638
+5	50	0.405131857886020	0.02709124517	0.3096543492	-0.7401691498
+0	50	0.405102909412566	0.000000000	0.3103268326	-0.7396048692
+-5	50	0.405131857886020	-0.02709124517	0.3096543492	-0.7401691498
+-10	50	0.405216174033675	-0.05424170742	0.3076200092	-0.7418761638
+-15	50	0.405347985375322	-0.08150289901	0.3041729601	-0.7447685814
+-20	50	0.405508438276748	-0.1089087831	0.2992244222	-0.7489208977
+-25	50	0.405671576403578	-0.1364656749	0.2926515842	-0.7544361636
+-30	50	0.405832116775407	-0.1641516834	0.2843190559	-0.7614279851
+-35	50	0.406013998432558	-0.1919163569	0.2740849626	-0.7700154089
+-40	50	0.406289306919106	-0.2196872114	0.2618130234	-0.7803127886
+-45	50	0.406795594720918	-0.2473807008	0.2473807008	-0.7924229452
+
+45	55	0.408114012981204	0.2586166565	0.2586166565	-0.8189146676
+40	55	0.407605109056098	0.2308858677	0.2751590623	-0.8073315504
+35	55	0.407349729987817	0.2026739302	0.2894483694	-0.7973260698
+30	55	0.407232900944231	0.1741063414	0.3015610292	-0.7888446941
+25	55	0.407151873444534	0.1452843871	0.3115633735	-0.7818409772
+20	55	0.407063084704381	0.1163053737	0.3195463880	-0.7762512103
+15	55	0.406959866536062	0.08724717519	0.3256108906	-0.7720047999
+10	55	0.406863708905257	0.05816324340	0.3298601449	-0.7690294400
+5	55	0.406799430555321	0.02907931719	0.3323781164	-0.7672663373
+0	55	0.406776919224709	0.000000000	0.3332121450	-0.7666823443
+-5	55	0.406799430555321	-0.02907931719	0.3323781164	-0.7672663373
+-10	55	0.406863708905257	-0.05816324340	0.3298601449	-0.7690294400
+-15	55	0.406959866536062	-0.08724717519	0.3256108906	-0.7720047999
+-20	55	0.407063084704381	-0.1163053737	0.3195463880	-0.7762512103
+-25	55	0.407151873444533	-0.1452843871	0.3115633735	-0.7818409772
+-30	55	0.407232900944231	-0.1741063414	0.3015610292	-0.7888446941
+-35	55	0.407349729987817	-0.2026739302	0.2894483694	-0.7973260698
+-40	55	0.407605109056098	-0.2308858677	0.2751590623	-0.8073315504
+-45	55	0.408114012981205	-0.2586166565	0.2586166565	-0.8189146676
+
+45	60	0.409483464825417	0.2680698533	0.2680698533	-0.8452297980
+40	60	0.408973597448126	0.2404187622	0.2865199236	-0.8345776450
+35	60	0.408687783070898	0.2119096803	0.3026383875	-0.8252716455
+30	60	0.408591532607703	0.1827276884	0.3164936402	-0.8172723116
+25	60	0.408557298593191	0.1529857438	0.3280789864	-0.8105835089
+20	60	0.408521160772018	0.1228123188	0.3374240727	-0.8051881208
+15	60	0.408460567065287	0.09233031546	0.3445814284	-0.8010558196
+10	60	0.408388640859699	0.06164781160	0.3496221131	-0.7981455789
+5	60	0.408336282868856	0.03085015656	0.3526189031	-0.7964153814
+0	60	0.408317245024599	0.000000000	0.3536131070	-0.7958413775
+-5	60	0.408336282868855	-0.03085015656	0.3526189031	-0.7964153814
+-10	60	0.408388640859698	-0.06164781160	0.3496221131	-0.7981455789
+-15	60	0.408460567065287	-0.09233031546	0.3445814284	-0.8010558196
+-20	60	0.408521160772017	-0.1228123188	0.3374240727	-0.8051881208
+-25	60	0.408557298593191	-0.1529857438	0.3280789864	-0.8105835089
+-30	60	0.408591532607703	-0.1827276884	0.3164936402	-0.8172723116
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+40	120	0.420779147405272	0.2473587596	0.2947906905	-1.170197484
+35	120	0.421067389084515	0.2183286594	0.3118056397	-1.180021070
+30	120	0.421429461477644	0.1884689847	0.3264378572	-1.188468985
+25	120	0.421747854641819	0.1579249948	0.3386712443	-1.195531934
+20	120	0.421972410989475	0.1268561221	0.3485343311	-1.201226390
+15	120	0.422095920256013	0.09541251375	0.3560843490	-1.205585395
+10	120	0.422143074517673	0.06372409543	0.3613973039	-1.208652831
+5	120	0.422156306298634	0.03189427119	0.3645531879	-1.210474881
+0	120	0.422158185633103	0.000000000	0.3655997132	-1.211079093
+-5	120	0.422156306298634	-0.03189427119	0.3645531879	-1.210474881
+-10	120	0.422143074517673	-0.06372409543	0.3613973039	-1.208652831
+-15	120	0.422095920256013	-0.09541251375	0.3560843490	-1.205585395
+-20	120	0.421972410989474	-0.1268561221	0.3485343311	-1.201226390
+-25	120	0.421747854641819	-0.1579249948	0.3386712443	-1.195531934
+-30	120	0.421429461477644	-0.1884689847	0.3264378572	-1.188468985
+-35	120	0.421067389084515	-0.2183286594	0.3118056397	-1.180021070
+-40	120	0.420779147405272	-0.2473587596	0.2947906905	-1.170197484
+-45	120	0.420559993702199	-0.2753211436	0.2753211436	-1.158956736
+
+45	125	0.420974391528749	0.2667661147	0.2667661147	-1.186791644
+40	125	0.421160417370072	0.2385642040	0.2843097472	-1.199075828
+35	125	0.421433896643668	0.2096814061	0.2994560821	-1.209681406
+30	125	0.421740723023144	0.1803089439	0.3123042519	-1.218677791
+25	125	0.421988055236155	0.1505783958	0.3229164119	-1.226108506
+20	125	0.422146272101119	0.1206149164	0.3313867593	-1.232039507
+15	125	0.422221936551195	0.09051917473	0.3378221592	-1.236545622
+10	125	0.422245340255344	0.06036212609	0.3423306283	-1.239702486
+5	125	0.422249870494671	0.03018376378	0.3450019987	-1.241573000
+0	125	0.422249842289700	0.000000000	0.3458868215	-1.242192560
+-5	125	0.422249870494671	-0.03018376378	0.3450019987	-1.241573000
+-10	125	0.422245340255344	-0.06036212609	0.3423306283	-1.239702486
+-15	125	0.422221936551195	-0.09051917473	0.3378221592	-1.236545622
+-20	125	0.422146272101119	-0.1206149164	0.3313867593	-1.232039507
+-25	125	0.421988055236155	-0.1505783958	0.3229164119	-1.226108506
+-30	125	0.421740723023144	-0.1803089439	0.3123042519	-1.218677791
+-35	125	0.421433896643669	-0.2096814061	0.2994560821	-1.209681406
+-40	125	0.421160417370073	-0.2385642040	0.2843097472	-1.199075828
+-45	125	0.420974391528749	-0.2667661147	0.2667661147	-1.186791644
+
+45	130	0.421233930166751	0.2561609471	0.2561609471	-1.214944556
+40	130	0.421357842549582	0.2278350128	0.2715231950	-1.227835013
+35	130	0.421579106337181	0.1992737358	0.2845923886	-1.238801368
+30	130	0.421800153288750	0.1706104627	0.2955059898	-1.247958967
+25	130	0.421964049994409	0.1419463729	0.3044049790	-1.255426106
+20	130	0.422057549538735	0.1133534343	0.3114360010	-1.261325834
+15	130	0.422092443828019	0.08486968991	0.3167379948	-1.265774735
+10	130	0.422097272783196	0.05650138924	0.3204353016	-1.268877143
+5	130	0.422094460465485	0.02822553766	0.3226193717	-1.270709796
+0	130	0.422092640652914	0.000000000	0.3233417219	-1.271315920
+-5	130	0.422094460465485	-0.02822553766	0.3226193717	-1.270709796
+-10	130	0.422097272783196	-0.05650138924	0.3204353016	-1.268877143
+-15	130	0.422092443828019	-0.08486968991	0.3167379948	-1.265774735
+-20	130	0.422057549538735	-0.1133534343	0.3114360010	-1.261325834
+-25	130	0.421964049994409	-0.1419463729	0.3044049790	-1.255426106
+-30	130	0.421800153288750	-0.1706104627	0.2955059898	-1.247958967
+-35	130	0.421579106337181	-0.1992737358	0.2845923886	-1.238801368
+-40	130	0.421357842549582	-0.2278350128	0.2715231950	-1.227835013
+-45	130	0.421233930166751	-0.2561609471	0.2561609471	-1.214944556
+
+45	135	0.421317295454032	0.2432476539	0.2432476539	-1.243247654
+40	135	0.421383484215576	0.2150208697	0.2562518940	-1.256251894
+35	135	0.421529869183832	0.1870381169	0.2671181138	-1.267118114
+30	135	0.421667446949540	0.1593753144	0.2760461420	-1.276046142
+25	135	0.421775248654318	0.1320770688	0.2832401881	-1.283240188
+20	135	0.421837585830955	0.1051403056	0.2888706155	-1.288870615
+15	135	0.421862858734397	0.07853263472	0.2930877828	-1.293087783
+10	135	0.421871721447431	0.05219566961	0.2960163521	-1.296016352
+5	135	0.421874605062143	0.02604897884	0.2977411905	-1.297741191
+0	135	0.421875207994689	0.000000000	0.2983108204	-1.298310820
+-5	135	0.421874605062143	-0.02604897884	0.2977411905	-1.297741191
+-10	135	0.421871721447431	-0.05219566961	0.2960163521	-1.296016352
+-15	135	0.421862858734397	-0.07853263472	0.2930877828	-1.293087783
+-20	135	0.421837585830955	-0.1051403056	0.2888706155	-1.288870615
+-25	135	0.421775248654319	-0.1320770688	0.2832401881	-1.283240188
+-30	135	0.421667446949540	-0.1593753144	0.2760461420	-1.276046142
+-35	135	0.421529869183832	-0.1870381169	0.2671181138	-1.267118114
+-40	135	0.421383484215576	-0.2150208697	0.2562518940	-1.256251894
+-45	135	0.421317295454033	-0.2432476539	0.2432476539	-1.243247654
+
+
+### -x patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-135	45	0.421317295454033	-0.2432476539	0.2432476539	-1.243247654
+-135	40	0.421383484215577	-0.2562518940	0.2150208697	-1.256251894
+-135	35	0.421529869183833	-0.2671181138	0.1870381169	-1.267118114
+-135	30	0.421667446949541	-0.2760461420	0.1593753144	-1.276046142
+-135	25	0.421775248654319	-0.2832401881	0.1320770688	-1.283240188
+-135	20	0.421837585830955	-0.2888706155	0.1051403056	-1.288870615
+-135	15	0.421862858734398	-0.2930877828	0.07853263472	-1.293087783
+-135	10	0.421871721447432	-0.2960163521	0.05219566961	-1.296016352
+-135	5	0.421874605062143	-0.2977411905	0.02604897884	-1.297741191
+-135	-2.84217e-14	0.421875207994690	-0.2983108204	-9.594528391e-17	-1.298310820
+-135	-5	0.421874605062144	-0.2977411905	-0.02604897884	-1.297741191
+-135	-10	0.421871721447432	-0.2960163521	-0.05219566961	-1.296016352
+-135	-15	0.421862858734398	-0.2930877828	-0.07853263472	-1.293087783
+-135	-20	0.421837585830955	-0.2888706155	-0.1051403056	-1.288870615
+-135	-25	0.421775248654319	-0.2832401881	-0.1320770688	-1.283240188
+-135	-30	0.421667446949541	-0.2760461420	-0.1593753144	-1.276046142
+-135	-35	0.421529869183833	-0.2671181138	-0.1870381169	-1.267118114
+-135	-40	0.421383484215577	-0.2562518940	-0.2150208697	-1.256251894
+-135	-45	0.421317295454034	-0.2432476539	-0.2432476539	-1.243247654
+
+-130	45	0.421233930166751	-0.2561609471	0.2561609471	-1.214944556
+-130	40	0.421357842549582	-0.2715231950	0.2278350128	-1.227835013
+-130	35	0.421579106337182	-0.2845923886	0.1992737358	-1.238801368
+-130	30	0.421800153288750	-0.2955059898	0.1706104627	-1.247958967
+-130	25	0.421964049994410	-0.3044049790	0.1419463729	-1.255426106
+-130	20	0.422057549538736	-0.3114360010	0.1133534343	-1.261325834
+-130	15	0.422092443828020	-0.3167379948	0.08486968991	-1.265774735
+-130	10	0.422097272783196	-0.3204353016	0.05650138924	-1.268877143
+-130	5	0.422094460465485	-0.3226193717	0.02822553766	-1.270709796
+-130	-2.84217e-14	0.422092640652914	-0.3233417219	-1.039959371e-16	-1.271315920
+-130	-5	0.422094460465485	-0.3226193717	-0.02822553766	-1.270709796
+-130	-10	0.422097272783196	-0.3204353016	-0.05650138924	-1.268877143
+-130	-15	0.422092443828020	-0.3167379948	-0.08486968991	-1.265774735
+-130	-20	0.422057549538736	-0.3114360010	-0.1133534343	-1.261325834
+-130	-25	0.421964049994409	-0.3044049790	-0.1419463729	-1.255426106
+-130	-30	0.421800153288750	-0.2955059898	-0.1706104627	-1.247958967
+-130	-35	0.421579106337182	-0.2845923886	-0.1992737358	-1.238801368
+-130	-40	0.421357842549583	-0.2715231950	-0.2278350128	-1.227835013
+-130	-45	0.421233930166752	-0.2561609471	-0.2561609471	-1.214944556
+
+-125	45	0.420974391528749	-0.2667661147	0.2667661147	-1.186791644
+-125	40	0.421160417370073	-0.2843097472	0.2385642040	-1.199075828
+-125	35	0.421433896643669	-0.2994560821	0.2096814061	-1.209681406
+-125	30	0.421740723023144	-0.3123042519	0.1803089439	-1.218677791
+-125	25	0.421988055236155	-0.3229164119	0.1505783958	-1.226108506
+-125	20	0.422146272101120	-0.3313867593	0.1206149164	-1.232039507
+-125	15	0.422221936551196	-0.3378221592	0.09051917473	-1.236545622
+-125	10	0.422245340255345	-0.3423306283	0.06036212609	-1.239702486
+-125	5	0.422249870494671	-0.3450019987	0.03018376378	-1.241573000
+-125	-2.84217e-14	0.422249842289701	-0.3458868215	-1.112470853e-16	-1.242192560
+-125	-5	0.422249870494672	-0.3450019987	-0.03018376378	-1.241573000
+-125	-10	0.422245340255345	-0.3423306283	-0.06036212609	-1.239702486
+-125	-15	0.422221936551196	-0.3378221592	-0.09051917473	-1.236545622
+-125	-20	0.422146272101120	-0.3313867593	-0.1206149164	-1.232039507
+-125	-25	0.421988055236155	-0.3229164119	-0.1505783958	-1.226108506
+-125	-30	0.421740723023144	-0.3123042519	-0.1803089439	-1.218677791
+-125	-35	0.421433896643669	-0.2994560821	-0.2096814061	-1.209681406
+-125	-40	0.421160417370073	-0.2843097472	-0.2385642040	-1.199075828
+-125	-45	0.420974391528750	-0.2667661147	-0.2667661147	-1.186791644
+
+-120	45	0.420559993702199	-0.2753211436	0.2753211436	-1.158956736
+-120	40	0.420779147405273	-0.2947906905	0.2473587596	-1.170197484
+-120	35	0.421067389084515	-0.3118056397	0.2183286594	-1.180021070
+-120	30	0.421429461477644	-0.3264378572	0.1884689847	-1.188468985
+-120	25	0.421747854641820	-0.3386712443	0.1579249948	-1.195531934
+-120	20	0.421972410989475	-0.3485343311	0.1268561221	-1.201226390
+-120	15	0.422095920256014	-0.3560843490	0.09541251375	-1.205585395
+-120	10	0.422143074517674	-0.3613973039	0.06372409543	-1.208652831
+-120	5	0.422156306298635	-0.3645531879	0.03189427119	-1.210474881
+-120	-2.84217e-14	0.422158185633104	-0.3655997132	-1.175873146e-16	-1.211079093
+-120	-5	0.422156306298635	-0.3645531879	-0.03189427119	-1.210474881
+-120	-10	0.422143074517674	-0.3613973039	-0.06372409543	-1.208652831
+-120	-15	0.422095920256014	-0.3560843490	-0.09541251375	-1.205585395
+-120	-20	0.421972410989475	-0.3485343311	-0.1268561221	-1.201226390
+-120	-25	0.421747854641820	-0.3386712443	-0.1579249948	-1.195531934
+-120	-30	0.421429461477645	-0.3264378572	-0.1884689847	-1.188468985
+-120	-35	0.421067389084516	-0.3118056397	-0.2183286594	-1.180021070
+-120	-40	0.420779147405273	-0.2947906905	-0.2473587596	-1.170197484
+-120	-45	0.420559993702199	-0.2753211436	-0.2753211436	-1.158956736
+
+-115	45	0.420040278579635	-0.2820750812	0.2820750812	-1.131533771
+-115	40	0.420256526120296	-0.3031731709	0.2543924958	-1.141371971
+-115	35	0.420521269749211	-0.3217939889	0.2253225768	-1.150055001
+-115	30	0.420895133174359	-0.3379864933	0.1951365929	-1.157605690
+-115	25	0.421254844396127	-0.3516707600	0.1639867685	-1.163986769
+-115	20	0.421528520292083	-0.3628051176	0.1320502636	-1.169178805
+-115	15	0.421685230990911	-0.3713826168	0.09951167225	-1.173178558
+-115	10	0.421738283850172	-0.3774355762	0.06655207557	-1.176001100
+-115	5	0.421741831447015	-0.3810319770	0.03333597842	-1.177678129
+-115	-2.84217e-14	0.421738502012698	-0.3822248885	-1.229344460e-16	-1.178234393
+-115	-5	0.421741831447015	-0.3810319770	-0.03333597842	-1.177678129
+-115	-10	0.421738283850172	-0.3774355762	-0.06655207557	-1.176001100
+-115	-15	0.421685230990911	-0.3713826168	-0.09951167225	-1.173178558
+-115	-20	0.421528520292083	-0.3628051176	-0.1320502636	-1.169178805
+-115	-25	0.421254844396127	-0.3516707600	-0.1639867685	-1.163986769
+-115	-30	0.420895133174359	-0.3379864933	-0.1951365929	-1.157605690
+-115	-35	0.420521269749211	-0.3217939889	-0.2253225768	-1.150055001
+-115	-40	0.420256526120297	-0.3031731709	-0.2543924958	-1.141371971
+-115	-45	0.420040278579636	-0.2820750812	-0.2820750812	-1.131533771
+
+-110	45	0.419465656408435	-0.2872463394	0.2872463394	-1.104549117
+-110	40	0.419651515881374	-0.3096605903	0.2598360871	-1.112707238
+-110	35	0.419869695852165	-0.3295996365	0.2307881501	-1.119964457
+-110	30	0.420207519358545	-0.3470765928	0.2003847643	-1.126325549
+-110	25	0.420572650126290	-0.3619824103	0.1687951700	-1.131750823
+-110	20	0.420862034392395	-0.3741995837	0.1361975101	-1.136197510
+-110	15	0.420995778515205	-0.3836326914	0.1027940699	-1.139630881
+-110	10	0.421011860991744	-0.3903003194	0.06882047688	-1.142057699
+-110	5	0.420989416240128	-0.3942704769	0.03449419709	-1.143502718
+-110	-2.84217e-14	0.420976478579512	-0.3955884904	-1.272325623e-16	-1.143982436
+-110	-5	0.420989416240128	-0.3942704769	-0.03449419709	-1.143502718
+-110	-10	0.421011860991743	-0.3903003194	-0.06882047688	-1.142057699
+-110	-15	0.420995778515205	-0.3836326914	-0.1027940699	-1.139630881
+-110	-20	0.420862034392395	-0.3741995837	-0.1361975101	-1.136197510
+-110	-25	0.420572650126290	-0.3619824103	-0.1687951700	-1.131750823
+-110	-30	0.420207519358545	-0.3470765928	-0.2003847643	-1.126325549
+-110	-35	0.419869695852165	-0.3295996365	-0.2307881501	-1.119964457
+-110	-40	0.419651515881374	-0.3096605903	-0.2598360871	-1.112707238
+-110	-45	0.419465656408435	-0.2872463394	-0.2872463394	-1.104549117
+
+-105	45	0.418844673013459	-0.2909909086	0.2909909086	-1.077970779
+-105	40	0.418992791401503	-0.3144120169	0.2638230074	-1.084246446
+-105	35	0.419158621920597	-0.3353711838	0.2348294310	-1.089862438
+-105	30	0.419444724877340	-0.3538477740	0.2042941076	-1.094813225
+-105	25	0.419789601277834	-0.3697131158	0.1724000572	-1.099064331
+-105	20	0.420040729651622	-0.3827624025	0.1393141213	-1.102560877
+-105	15	0.420124716342020	-0.3928641370	0.1052676283	-1.105267628
+-105	10	0.420090594508193	-0.4000159031	0.07053359643	-1.107183938
+-105	5	0.420031937688746	-0.4042786810	0.03536980149	-1.108326146
+-105	-2.84217e-14	0.420005891847988	-0.4056945381	-1.304829560e-16	-1.108705524
+-105	-5	0.420031937688746	-0.4042786810	-0.03536980149	-1.108326146
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+-50	30	0.405832116775407	-0.2843190559	0.1641516834	-0.7614279851
+-50	25	0.405671576403578	-0.2926515842	0.1364656749	-0.7544361636
+-50	20	0.405508438276748	-0.2992244222	0.1089087831	-0.7489208977
+-50	15	0.405347985375323	-0.3041729601	0.08150289901	-0.7447685814
+-50	10	0.405216174033676	-0.3076200092	0.05424170742	-0.7418761638
+-50	5	0.405131857886020	-0.3096543492	0.02709124517	-0.7401691498
+-50	-2.84217e-14	0.405102909412567	-0.3103268326	-9.980997680e-17	-0.7396048692
+-50	-5	0.405131857886020	-0.3096543492	-0.02709124517	-0.7401691498
+-50	-10	0.405216174033676	-0.3076200092	-0.05424170742	-0.7418761638
+-50	-15	0.405347985375323	-0.3041729601	-0.08150289901	-0.7447685814
+-50	-20	0.405508438276748	-0.2992244222	-0.1089087831	-0.7489208977
+-50	-25	0.405671576403578	-0.2926515842	-0.1364656749	-0.7544361636
+-50	-30	0.405832116775407	-0.2843190559	-0.1641516834	-0.7614279851
+-50	-35	0.406013998432558	-0.2740849626	-0.1919163569	-0.7700154089
+-50	-40	0.406289306919106	-0.2618130234	-0.2196872114	-0.7803127886
+-50	-45	0.406795594720918	-0.2473807008	-0.2473807008	-0.7924229452
+
+-45	45	0.405481246888702	-0.2341047070	0.2341047070	-0.7658952930
+-45	40	0.404953884308434	-0.2462607191	0.2066372786	-0.7537392809
+-45	35	0.404600376776808	-0.2563901099	0.1795262877	-0.7436098901
+-45	30	0.404312156366901	-0.2646844373	0.1528156311	-0.7353155627
+-45	25	0.404045335367781	-0.2713337901	0.1265250242	-0.7286662099
+-45	20	0.403792076974582	-0.2765132120	0.1006425785	-0.7234867880
+-45	15	0.403565989481416	-0.2803760953	0.07512654831	-0.7196239047
+-45	10	0.403393035592477	-0.2830503416	0.04990941212	-0.7169496584
+-45	5	0.403285294975799	-0.2846216445	0.02490116729	-0.7153783555
+-45	-2.84217e-14	0.403248758763945	-0.2851399318	-9.170914980e-17	-0.7148600682
+-45	-5	0.403285294975799	-0.2846216445	-0.02490116729	-0.7153783555
+-45	-10	0.403393035592477	-0.2830503416	-0.04990941212	-0.7169496584
+-45	-15	0.403565989481417	-0.2803760953	-0.07512654831	-0.7196239047
+-45	-20	0.403792076974583	-0.2765132120	-0.1006425785	-0.7234867880
+-45	-25	0.404045335367781	-0.2713337901	-0.1265250242	-0.7286662099
+-45	-30	0.404312156366901	-0.2646844373	-0.1528156311	-0.7353155627
+-45	-35	0.404600376776808	-0.2563901099	-0.1795262877	-0.7436098901
+-45	-40	0.404953884308434	-0.2462607191	-0.2066372786	-0.7537392809
+-45	-45	0.405481246888701	-0.2341047070	-0.2341047070	-0.7658952930
+
+
+### -y patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-135	0.421317295454034	-0.2432476539	-0.2432476539	-1.243247654
+-40	-135	0.421383484215577	-0.2150208697	-0.2562518940	-1.256251894
+-35	-135	0.421529869183833	-0.1870381169	-0.2671181138	-1.267118114
+-30	-135	0.421667446949541	-0.1593753144	-0.2760461420	-1.276046142
+-25	-135	0.421775248654320	-0.1320770688	-0.2832401881	-1.283240188
+-20	-135	0.421837585830956	-0.1051403056	-0.2888706155	-1.288870615
+-15	-135	0.421862858734398	-0.07853263472	-0.2930877828	-1.293087783
+-10	-135	0.421871721447432	-0.05219566961	-0.2960163521	-1.296016352
+-5	-135	0.421874605062144	-0.02604897884	-0.2977411905	-1.297741191
+-2.84217e-14	-135	0.421875207994690	-9.594528391e-17	-0.2983108204	-1.298310820
+5	-135	0.421874605062144	0.02604897884	-0.2977411905	-1.297741191
+10	-135	0.421871721447432	0.05219566961	-0.2960163521	-1.296016352
+15	-135	0.421862858734397	0.07853263472	-0.2930877828	-1.293087783
+20	-135	0.421837585830955	0.1051403056	-0.2888706155	-1.288870615
+25	-135	0.421775248654319	0.1320770688	-0.2832401881	-1.283240188
+30	-135	0.421667446949540	0.1593753144	-0.2760461420	-1.276046142
+35	-135	0.421529869183832	0.1870381169	-0.2671181138	-1.267118114
+40	-135	0.421383484215576	0.2150208697	-0.2562518940	-1.256251894
+45	-135	0.421317295454032	0.2432476539	-0.2432476539	-1.243247654
+
+-45	-130	0.421233930166752	-0.2561609471	-0.2561609471	-1.214944556
+-40	-130	0.421357842549583	-0.2278350128	-0.2715231950	-1.227835013
+-35	-130	0.421579106337182	-0.1992737358	-0.2845923886	-1.238801368
+-30	-130	0.421800153288751	-0.1706104627	-0.2955059898	-1.247958967
+-25	-130	0.421964049994410	-0.1419463729	-0.3044049790	-1.255426106
+-20	-130	0.422057549538736	-0.1133534343	-0.3114360010	-1.261325834
+-15	-130	0.422092443828020	-0.08486968991	-0.3167379948	-1.265774735
+-10	-130	0.422097272783197	-0.05650138924	-0.3204353016	-1.268877143
+-5	-130	0.422094460465486	-0.02822553766	-0.3226193717	-1.270709796
+-2.84217e-14	-130	0.422092640652915	-1.039959371e-16	-0.3233417219	-1.271315920
+5	-130	0.422094460465485	0.02822553766	-0.3226193717	-1.270709796
+10	-130	0.422097272783196	0.05650138924	-0.3204353016	-1.268877143
+15	-130	0.422092443828020	0.08486968991	-0.3167379948	-1.265774735
+20	-130	0.422057549538736	0.1133534343	-0.3114360010	-1.261325834
+25	-130	0.421964049994409	0.1419463729	-0.3044049790	-1.255426106
+30	-130	0.421800153288750	0.1706104627	-0.2955059898	-1.247958967
+35	-130	0.421579106337181	0.1992737358	-0.2845923886	-1.238801368
+40	-130	0.421357842549582	0.2278350128	-0.2715231950	-1.227835013
+45	-130	0.421233930166751	0.2561609471	-0.2561609471	-1.214944556
+
+-45	-125	0.420974391528750	-0.2667661147	-0.2667661147	-1.186791644
+-40	-125	0.421160417370073	-0.2385642040	-0.2843097472	-1.199075828
+-35	-125	0.421433896643669	-0.2096814061	-0.2994560821	-1.209681406
+-30	-125	0.421740723023145	-0.1803089439	-0.3123042519	-1.218677791
+-25	-125	0.421988055236156	-0.1505783958	-0.3229164119	-1.226108506
+-20	-125	0.422146272101120	-0.1206149164	-0.3313867593	-1.232039507
+-15	-125	0.422221936551196	-0.09051917473	-0.3378221592	-1.236545622
+-10	-125	0.422245340255345	-0.06036212609	-0.3423306283	-1.239702486
+-5	-125	0.422249870494672	-0.03018376378	-0.3450019987	-1.241573000
+-2.84217e-14	-125	0.422249842289701	-1.112470853e-16	-0.3458868215	-1.242192560
+5	-125	0.422249870494672	0.03018376378	-0.3450019987	-1.241573000
+10	-125	0.422245340255345	0.06036212609	-0.3423306283	-1.239702486
+15	-125	0.422221936551196	0.09051917473	-0.3378221592	-1.236545622
+20	-125	0.422146272101119	0.1206149164	-0.3313867593	-1.232039507
+25	-125	0.421988055236155	0.1505783958	-0.3229164119	-1.226108506
+30	-125	0.421740723023144	0.1803089439	-0.3123042519	-1.218677791
+35	-125	0.421433896643668	0.2096814061	-0.2994560821	-1.209681406
+40	-125	0.421160417370072	0.2385642040	-0.2843097472	-1.199075828
+45	-125	0.420974391528749	0.2667661147	-0.2667661147	-1.186791644
+
+-45	-120	0.420559993702199	-0.2753211436	-0.2753211436	-1.158956736
+-40	-120	0.420779147405273	-0.2473587596	-0.2947906905	-1.170197484
+-35	-120	0.421067389084516	-0.2183286594	-0.3118056397	-1.180021070
+-30	-120	0.421429461477645	-0.1884689847	-0.3264378572	-1.188468985
+-25	-120	0.421747854641820	-0.1579249948	-0.3386712443	-1.195531934
+-20	-120	0.421972410989476	-0.1268561221	-0.3485343311	-1.201226390
+-15	-120	0.422095920256015	-0.09541251375	-0.3560843490	-1.205585395
+-10	-120	0.422143074517674	-0.06372409543	-0.3613973039	-1.208652831
+-5	-120	0.422156306298635	-0.03189427119	-0.3645531879	-1.210474881
+-2.84217e-14	-120	0.422158185633104	-1.175873146e-16	-0.3655997132	-1.211079093
+5	-120	0.422156306298635	0.03189427119	-0.3645531879	-1.210474881
+10	-120	0.422143074517674	0.06372409543	-0.3613973039	-1.208652831
+15	-120	0.422095920256014	0.09541251375	-0.3560843490	-1.205585395
+20	-120	0.421972410989475	0.1268561221	-0.3485343311	-1.201226390
+25	-120	0.421747854641820	0.1579249948	-0.3386712443	-1.195531934
+30	-120	0.421429461477644	0.1884689847	-0.3264378572	-1.188468985
+35	-120	0.421067389084515	0.2183286594	-0.3118056397	-1.180021070
+40	-120	0.420779147405272	0.2473587596	-0.2947906905	-1.170197484
+45	-120	0.420559993702198	0.2753211436	-0.2753211436	-1.158956736
+
+-45	-115	0.420040278579636	-0.2820750812	-0.2820750812	-1.131533771
+-40	-115	0.420256526120297	-0.2543924958	-0.3031731709	-1.141371971
+-35	-115	0.420521269749211	-0.2253225768	-0.3217939889	-1.150055001
+-30	-115	0.420895133174359	-0.1951365929	-0.3379864933	-1.157605690
+-25	-115	0.421254844396127	-0.1639867685	-0.3516707600	-1.163986769
+-20	-115	0.421528520292083	-0.1320502636	-0.3628051176	-1.169178805
+-15	-115	0.421685230990911	-0.09951167225	-0.3713826168	-1.173178558
+-10	-115	0.421738283850172	-0.06655207557	-0.3774355762	-1.176001100
+-5	-115	0.421741831447015	-0.03333597842	-0.3810319770	-1.177678129
+-2.84217e-14	-115	0.421738502012698	-1.229344460e-16	-0.3822248885	-1.178234393
+5	-115	0.421741831447015	0.03333597842	-0.3810319770	-1.177678129
+10	-115	0.421738283850172	0.06655207557	-0.3774355762	-1.176001100
+15	-115	0.421685230990911	0.09951167225	-0.3713826168	-1.173178558
+20	-115	0.421528520292082	0.1320502636	-0.3628051176	-1.169178805
+25	-115	0.421254844396126	0.1639867685	-0.3516707600	-1.163986769
+30	-115	0.420895133174358	0.1951365929	-0.3379864933	-1.157605690
+35	-115	0.420521269749210	0.2253225768	-0.3217939889	-1.150055001
+40	-115	0.420256526120296	0.2543924958	-0.3031731709	-1.141371971
+45	-115	0.420040278579635	0.2820750812	-0.2820750812	-1.131533771
+
+-45	-110	0.419465656408435	-0.2872463394	-0.2872463394	-1.104549117
+-40	-110	0.419651515881374	-0.2598360871	-0.3096605903	-1.112707238
+-35	-110	0.419869695852165	-0.2307881501	-0.3295996365	-1.119964457
+-30	-110	0.420207519358545	-0.2003847643	-0.3470765928	-1.126325549
+-25	-110	0.420572650126290	-0.1687951700	-0.3619824103	-1.131750823
+-20	-110	0.420862034392395	-0.1361975101	-0.3741995837	-1.136197510
+-15	-110	0.420995778515205	-0.1027940699	-0.3836326914	-1.139630881
+-10	-110	0.421011860991744	-0.06882047688	-0.3903003194	-1.142057699
+-5	-110	0.420989416240128	-0.03449419709	-0.3942704769	-1.143502718
+-2.84217e-14	-110	0.420976478579512	-1.272325623e-16	-0.3955884904	-1.143982436
+5	-110	0.420989416240128	0.03449419709	-0.3942704769	-1.143502718
+10	-110	0.421011860991744	0.06882047688	-0.3903003194	-1.142057699
+15	-110	0.420995778515205	0.1027940699	-0.3836326914	-1.139630881
+20	-110	0.420862034392395	0.1361975101	-0.3741995837	-1.136197510
+25	-110	0.420572650126290	0.1687951700	-0.3619824103	-1.131750823
+30	-110	0.420207519358544	0.2003847643	-0.3470765928	-1.126325549
+35	-110	0.419869695852164	0.2307881501	-0.3295996365	-1.119964457
+40	-110	0.419651515881373	0.2598360871	-0.3096605903	-1.112707238
+45	-110	0.419465656408434	0.2872463394	-0.2872463394	-1.104549117
+
+-45	-105	0.418844673013459	-0.2909909086	-0.2909909086	-1.077970779
+-40	-105	0.418992791401504	-0.2638230074	-0.3144120169	-1.084246446
+-35	-105	0.419158621920598	-0.2348294310	-0.3353711838	-1.089862438
+-30	-105	0.419444724877340	-0.2042941076	-0.3538477740	-1.094813225
+-25	-105	0.419789601277834	-0.1724000572	-0.3697131158	-1.099064331
+-20	-105	0.420040729651622	-0.1393141213	-0.3827624025	-1.102560877
+-15	-105	0.420124716342020	-0.1052676283	-0.3928641370	-1.105267628
+-10	-105	0.420090594508193	-0.07053359643	-0.4000159031	-1.107183938
+-5	-105	0.420031937688746	-0.03536980149	-0.4042786810	-1.108326146
+-2.84217e-14	-105	0.420005891847987	-1.304829560e-16	-0.4056945381	-1.108705524
+5	-105	0.420031937688746	0.03536980149	-0.4042786810	-1.108326146
+10	-105	0.420090594508192	0.07053359643	-0.4000159031	-1.107183938
+15	-105	0.420124716342020	0.1052676283	-0.3928641370	-1.105267628
+20	-105	0.420040729651621	0.1393141213	-0.3827624025	-1.102560877
+25	-105	0.419789601277834	0.1724000572	-0.3697131158	-1.099064331
+30	-105	0.419444724877339	0.2042941076	-0.3538477740	-1.094813225
+35	-105	0.419158621920597	0.2348294310	-0.3353711838	-1.089862438
+40	-105	0.418992791401502	0.2638230074	-0.3144120169	-1.084246446
+45	-105	0.418844673013458	0.2909909086	-0.2909909086	-1.077970779
+
+-45	-100	0.418165123766226	-0.2934155295	-0.2934155295	-1.051737074
+-40	-100	0.418267944942896	-0.2664378508	-0.3175282659	-1.055988800
+-35	-100	0.418378784564106	-0.2375074995	-0.3391958621	-1.059809382
+-30	-100	0.418613636256464	-0.2069083338	-0.3583757466	-1.063191313
+-25	-100	0.418939283148843	-0.1748330122	-0.3749306046	-1.066110381
+-20	-100	0.419138631315851	-0.1414256341	-0.3885637361	-1.068514270
+-15	-100	0.419171014284577	-0.1069493121	-0.3991402665	-1.070379198
+-10	-100	0.419088046488129	-0.07170088111	-0.4066359035	-1.071700881
+-5	-100	0.418993791653689	-0.03596704835	-0.4111052439	-1.072488946
+-2.84217e-14	-100	0.418954765638673	-1.327007018e-16	-0.4125899014	-1.072750732
+5	-100	0.418993791653689	0.03596704835	-0.4111052439	-1.072488946
+10	-100	0.419088046488129	0.07170088111	-0.4066359035	-1.071700881
+15	-100	0.419171014284577	0.1069493121	-0.3991402665	-1.070379198
+20	-100	0.419138631315851	0.1414256341	-0.3885637361	-1.068514270
+25	-100	0.418939283148842	0.1748330122	-0.3749306046	-1.066110381
+30	-100	0.418613636256463	0.2069083338	-0.3583757466	-1.063191313
+35	-100	0.418378784564105	0.2375074995	-0.3391958621	-1.059809382
+40	-100	0.418267944942895	0.2664378508	-0.3175282659	-1.055988800
+45	-100	0.418165123766225	0.2934155295	-0.2934155295	-1.051737074
+
+-45	-95	0.417413105836215	-0.2945924538	-0.2945924538	-1.025773500
+-40	-95	0.417460944315206	-0.2677380956	-0.3190778373	-1.027915694
+-35	-95	0.417514185569649	-0.2388636717	-0.3411326766	-1.029845242
+-30	-95	0.417699839258214	-0.2082530161	-0.3607048046	-1.031557581
+-25	-95	0.417999772834338	-0.1761016147	-0.3776511314	-1.033040193
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+20	-45	0.403792076974581	0.1006425785	-0.2765132120	-0.7234867880
+25	-45	0.404045335367780	0.1265250242	-0.2713337901	-0.7286662099
+30	-45	0.404312156366900	0.1528156311	-0.2646844373	-0.7353155627
+35	-45	0.404600376776807	0.1795262877	-0.2563901099	-0.7436098901
+40	-45	0.404953884308433	0.2066372786	-0.2462607191	-0.7537392809
+45	-45	0.405481246888701	0.2341047070	-0.2341047070	-0.7658952930
+
+
+### -z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = 180 - drho = 180 - dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+135	45	0.421318775179044	0.2432485083	0.2432485083	-1.243248508
+140	45	0.421382732892575	0.2150204864	0.2562514371	-1.256251437
+145	45	0.421529210075252	0.1870378244	0.2671176961	-1.267117696
+150	45	0.421667159750391	0.1593752058	0.2760459539	-1.276045954
+155	45	0.421775097419540	0.1320770214	0.2832400865	-1.283240087
+160	45	0.421837517896125	0.1051402887	0.2888705689	-1.288870569
+165	45	0.421862830104264	0.07853262939	0.2930877629	-1.293087763
+170	45	0.421871715150916	0.05219566883	0.2960163477	-1.296016348
+175	45	0.421874604338868	0.02604897879	0.2977411900	-1.297741190
+180	45	0.421875207760182	-9.594528386e-17	0.2983108202	-1.298310820
+185	45	0.421874604338868	-0.02604897879	0.2977411900	-1.297741190
+190	45	0.421871715150916	-0.05219566883	0.2960163477	-1.296016348
+195	45	0.421862830104264	-0.07853262939	0.2930877629	-1.293087763
+200	45	0.421837517896125	-0.1051402887	0.2888705689	-1.288870569
+205	45	0.421775097419540	-0.1320770214	0.2832400865	-1.283240087
+210	45	0.421667159750391	-0.1593752058	0.2760459539	-1.276045954
+215	45	0.421529210075252	-0.1870378244	0.2671176961	-1.267117696
+220	45	0.421382732892575	-0.2150204864	0.2562514371	-1.256251437
+225	45	0.421318775179044	-0.2432485083	0.2432485083	-1.243248508
+
+135	40	0.421382732892574	0.2562514371	0.2150204864	-1.256251437
+140	40	0.421272221754936	0.2277887162	0.2277887162	-1.271468021
+145	40	0.421330633409101	0.1991562866	0.2386606220	-1.284424654
+150	40	0.421442926937626	0.1704659712	0.2477489683	-1.295255723
+155	40	0.421538852330466	0.1418033388	0.2551687221	-1.304098241
+160	40	0.421597735701032	0.1132299405	0.2610411302	-1.311096705
+165	40	0.421620768314450	0.08477485060	0.2654777394	-1.316384050
+170	40	0.421626555524848	0.05643837964	0.2685772951	-1.320077956
+175	40	0.421628329185561	0.02819436737	0.2704108431	-1.322263094
+180	40	0.421628724074916	-1.038816365e-16	0.2710177197	-1.322986341
+185	40	0.421628329185562	-0.02819436737	0.2704108431	-1.322263094
+190	40	0.421626555524848	-0.05643837964	0.2685772951	-1.320077956
+195	40	0.421620768314450	-0.08477485060	0.2654777394	-1.316384050
+200	40	0.421597735701032	-0.1132299405	0.2610411302	-1.311096705
+205	40	0.421538852330467	-0.1418033388	0.2551687221	-1.304098241
+210	40	0.421442926937626	-0.1704659712	0.2477489683	-1.295255723
+215	40	0.421330633409101	-0.1991562866	0.2386606220	-1.284424654
+220	40	0.421272221754937	-0.2277887162	0.2277887162	-1.271468021
+225	40	0.421382732892575	-0.2562514371	0.2150204864	-1.256251437
+
+135	35	0.421529210075252	0.2671176961	0.1870378244	-1.267117696
+140	35	0.421330633409101	0.2386606220	0.1991562866	-1.284424654
+145	35	0.421282319496893	0.2096059900	0.2096059900	-1.299348377
+150	35	0.421325856227419	0.1801315738	0.2184626778	-1.311997038
+155	35	0.421372554121309	0.1503587660	0.2257787097	-1.322445414
+160	35	0.421400697435999	0.1204018921	0.2316296898	-1.330801480
+165	35	0.421401582376919	0.09034330092	0.2360860272	-1.337165789
+170	35	0.421390485055741	0.06023992018	0.2392171977	-1.341637564
+175	35	0.421383212896461	0.03012181234	0.2410771775	-1.344293890
+180	35	0.421380852538493	-1.110181389e-16	0.2416941277	-1.345174987
+185	35	0.421383212896461	-0.03012181234	0.2410771775	-1.344293890
+190	35	0.421390485055742	-0.06023992018	0.2392171977	-1.341637564
+195	35	0.421401582376919	-0.09034330092	0.2360860272	-1.337165789
+200	35	0.421400697436000	-0.1204018921	0.2316296898	-1.330801480
+205	35	0.421372554121310	-0.1503587660	0.2257787097	-1.322445414
+210	35	0.421325856227420	-0.1801315738	0.2184626778	-1.311997038
+215	35	0.421282319496893	-0.2096059900	0.2096059900	-1.299348377
+220	35	0.421330633409101	-0.2386606220	0.1991562866	-1.284424654
+225	35	0.421529210075252	-0.2671176961	0.1870378244	-1.267117696
+
+135	30	0.421667159750391	0.2760459539	0.1593752058	-1.276045954
+140	30	0.421442926937626	0.2477489683	0.1704659712	-1.295255723
+145	30	0.421325856227419	0.2184626778	0.1801315738	-1.311997038
+150	30	0.421321930786920	0.1884208955	0.1884208955	-1.326354564
+155	30	0.421328440031140	0.1577679435	0.1953374838	-1.338334447
+160	30	0.421313496657365	0.1266580350	0.2009121728	-1.347990091
+165	30	0.421278913148301	0.09522783368	0.2051874645	-1.355395114
+170	30	0.421242857212019	0.06358820422	0.2082078799	-1.360626627
+175	30	0.421222991887971	0.03182375849	0.2100095577	-1.363747224
+180	30	0.421216993526037	-1.173251563e-16	0.2106084968	-1.364784617
+185	30	0.421222991887971	-0.03182375849	0.2100095577	-1.363747224
+190	30	0.421242857212019	-0.06358820422	0.2082078799	-1.360626627
+195	30	0.421278913148301	-0.09522783368	0.2051874645	-1.355395114
+200	30	0.421313496657365	-0.1266580350	0.2009121728	-1.347990091
+205	30	0.421328440031140	-0.1577679435	0.1953374838	-1.338334447
+210	30	0.421321930786920	-0.1884208955	0.1884208955	-1.326354564
+215	30	0.421325856227420	-0.2184626778	0.1801315738	-1.311997038
+220	30	0.421442926937627	-0.2477489683	0.1704659712	-1.295255723
+225	30	0.421667159750392	-0.2760459539	0.1593752058	-1.276045954
+
+135	25	0.421775097419540	0.2832400865	0.1320770214	-1.283240087
+140	25	0.421538852330466	0.2551687221	0.1418033388	-1.304098241
+145	25	0.421372554121309	0.2257787097	0.1503587660	-1.322445414
+150	25	0.421328440031140	0.1953374838	0.1577679435	-1.338334447
+155	25	0.421305330993538	0.1640064220	0.1640064220	-1.351712907
+160	25	0.421267406499701	0.1319684657	0.1690740077	-1.362580380
+165	25	0.421221759633631	0.09940229965	0.1729882189	-1.370974433
+170	25	0.421186793549213	0.06646504808	0.1757709501	-1.376942019
+175	25	0.421174919059817	0.03329116765	0.1774392910	-1.380519787
+180	25	0.421173127795214	-1.227696425e-16	0.1779954552	-1.381712485
+185	25	0.421174919059817	-0.03329116765	0.1774392910	-1.380519787
+190	25	0.421186793549213	-0.06646504808	0.1757709501	-1.376942019
+195	25	0.421221759633632	-0.09940229965	0.1729882189	-1.370974433
+200	25	0.421267406499702	-0.1319684657	0.1690740077	-1.362580380
+205	25	0.421305330993538	-0.1640064220	0.1640064220	-1.351712907
+210	25	0.421328440031140	-0.1953374838	0.1577679435	-1.338334447
+215	25	0.421372554121310	-0.2257787097	0.1503587660	-1.322445414
+220	25	0.421538852330467	-0.2551687221	0.1418033388	-1.304098241
+225	25	0.421775097419541	-0.2832400865	0.1320770214	-1.283240087
+
+135	20	0.421837517896125	0.2888705689	0.1051402887	-1.288870569
+140	20	0.421597735701032	0.2610411302	0.1132299405	-1.311096705
+145	20	0.421400697436000	0.2316296898	0.1204018921	-1.330801480
+150	20	0.421313496657365	0.2009121728	0.1266580350	-1.347990091
+155	20	0.421267406499701	0.1690740077	0.1319684657	-1.362580380
+160	20	0.421226978243287	0.1363156117	0.1363156117	-1.374524065
+165	20	0.421203919119877	0.1028448913	0.1396999142	-1.383822360
+170	20	0.421210165901621	0.06885289269	0.1421246107	-1.390484159
+175	20	0.421239497586365	0.03451468776	0.1435879631	-1.394504686
+180	20	0.421254805847485	-1.273166817e-16	0.1440776291	-1.395850033
+185	20	0.421239497586365	-0.03451468776	0.1435879631	-1.394504686
+190	20	0.421210165901621	-0.06885289269	0.1421246107	-1.390484159
+195	20	0.421203919119877	-0.1028448913	0.1396999142	-1.383822360
+200	20	0.421226978243288	-0.1363156117	0.1363156117	-1.374524065
+205	20	0.421267406499702	-0.1690740077	0.1319684657	-1.362580380
+210	20	0.421313496657366	-0.2009121728	0.1266580350	-1.347990091
+215	20	0.421400697436000	-0.2316296898	0.1204018921	-1.330801480
+220	20	0.421597735701033	-0.2610411302	0.1132299405	-1.311096705
+225	20	0.421837517896126	-0.2888705689	0.1051402887	-1.288870569
+
+135	15	0.421862830104264	0.2930877629	0.07853262939	-1.293087763
+140	15	0.421620768314450	0.2654777394	0.08477485060	-1.316384050
+145	15	0.421401582376919	0.2360860272	0.09034330092	-1.337165789
+150	15	0.421278913148301	0.2051874645	0.09522783368	-1.355395114
+155	15	0.421221759633631	0.1729882189	0.09940229965	-1.370974433
+160	15	0.421203919119877	0.1396999142	0.1028448913	-1.383822360
+165	15	0.421243800534086	0.1055480291	0.1055480291	-1.393910607
+170	15	0.421339166755552	0.07074323286	0.1075025049	-1.401204810
+175	15	0.421449205369422	0.03548914593	0.1086916591	-1.405642794
+180	15	0.421496998180878	-1.309461970e-16	0.1090914506	-1.407134836
+185	15	0.421449205369422	-0.03548914593	0.1086916591	-1.405642794
+190	15	0.421339166755553	-0.07074323286	0.1075025049	-1.401204810
+195	15	0.421243800534086	-0.1055480291	0.1055480291	-1.393910607
+200	15	0.421203919119878	-0.1396999142	0.1028448913	-1.383822360
+205	15	0.421221759633632	-0.1729882189	0.09940229965	-1.370974433
+210	15	0.421278913148302	-0.2051874645	0.09522783368	-1.355395114
+215	15	0.421401582376920	-0.2360860272	0.09034330092	-1.337165789
+220	15	0.421620768314451	-0.2654777394	0.08477485060	-1.316384050
+225	15	0.421862830104265	-0.2930877629	0.07853262939	-1.293087763
+
+135	10	0.421871715150916	0.2960163477	0.05219566883	-1.296016348
+140	10	0.421626555524848	0.2685772951	0.05643837964	-1.320077956
+145	10	0.421390485055741	0.2392171977	0.06023992018	-1.341637564
+150	10	0.421242857212019	0.2082078799	0.06358820422	-1.360626627
+155	10	0.421186793549213	0.1757709501	0.06646504808	-1.376942019
+160	10	0.421210165901620	0.1421246107	0.06885289269	-1.390484159
+165	10	0.421339166755552	0.1075025049	0.07074323286	-1.401204810
+170	10	0.421552851850315	0.07212257941	0.07212257941	-1.409027473
+175	10	0.421766733118938	0.03620508176	0.07296868527	-1.413825978
+180	10	0.421855970235807	-1.336196361e-16	0.07325452047	-1.415447030
+185	10	0.421766733118938	-0.03620508176	0.07296868527	-1.413825978
+190	10	0.421552851850316	-0.07212257941	0.07212257941	-1.409027473
+195	10	0.421339166755553	-0.1075025049	0.07074323286	-1.401204810
+200	10	0.421210165901621	-0.1421246107	0.06885289269	-1.390484159
+205	10	0.421186793549213	-0.1757709501	0.06646504808	-1.376942019
+210	10	0.421242857212019	-0.2082078799	0.06358820422	-1.360626627
+215	10	0.421390485055742	-0.2392171977	0.06023992018	-1.341637564
+220	10	0.421626555524849	-0.2685772951	0.05643837964	-1.320077956
+225	10	0.421871715150916	-0.2960163477	0.05219566883	-1.296016348
+
+135	5	0.421874604338868	0.2977411900	0.02604897879	-1.297741190
+140	5	0.421628329185562	0.2704108431	0.02819436737	-1.322263094
+145	5	0.421383212896461	0.2410771775	0.03012181234	-1.344293890
+150	5	0.421222991887971	0.2100095577	0.03182375849	-1.363747224
+155	5	0.421174919059817	0.1774392910	0.03329116765	-1.380519787
+160	5	0.421239497586365	0.1435879631	0.03451468776	-1.394504686
+165	5	0.421449205369422	0.1086916591	0.03548914593	-1.405642794
+170	5	0.421766733118938	0.07296868527	0.03620508176	-1.413825978
+175	5	0.422070244586029	0.03664692171	0.03664692171	-1.418876232
+180	5	0.422195099824641	-1.352732861e-16	0.03679672751	-1.420588520
+185	5	0.422070244586029	-0.03664692171	0.03664692171	-1.418876232
+190	5	0.421766733118938	-0.07296868527	0.03620508176	-1.413825978
+195	5	0.421449205369422	-0.1086916591	0.03548914593	-1.405642794
+200	5	0.421239497586366	-0.1435879631	0.03451468776	-1.394504686
+205	5	0.421174919059818	-0.1774392910	0.03329116765	-1.380519787
+210	5	0.421222991887971	-0.2100095577	0.03182375849	-1.363747224
+215	5	0.421383212896462	-0.2410771775	0.03012181234	-1.344293890
+220	5	0.421628329185562	-0.2704108431	0.02819436737	-1.322263094
+225	5	0.421874604338868	-0.2977411900	0.02604897879	-1.297741190
+
+135	-2.84217e-14	0.421875207760182	0.2983108202	-9.594528386e-17	-1.298310820
+140	-2.84217e-14	0.421628724074917	0.2710177197	-1.038816365e-16	-1.322986341
+145	-2.84217e-14	0.421380852538494	0.2416941277	-1.110181389e-16	-1.345174987
+150	-2.84217e-14	0.421216993526037	0.2106084968	-1.173251563e-16	-1.364784617
+155	-2.84217e-14	0.421173127795214	0.1779954552	-1.227696425e-16	-1.381712485
+160	-2.84217e-14	0.421254805847485	0.1440776291	-1.273166817e-16	-1.395850033
+165	-2.84217e-14	0.421496998180878	0.1090914506	-1.309461970e-16	-1.407134836
+170	-2.84217e-14	0.421855970235807	0.07325452047	-1.336196361e-16	-1.415447030
+175	-2.84217e-14	0.422195099824641	0.03679672751	-1.352732861e-16	-1.420588520
+180	-2.84217e-14	0.422334101719677	-1.358347151e-16	-1.358347151e-16	-1.422334102
+185	-2.84217e-14	0.422195099824641	-0.03679672751	-1.352732861e-16	-1.420588520
+190	-2.84217e-14	0.421855970235807	-0.07325452047	-1.336196361e-16	-1.415447030
+195	-2.84217e-14	0.421496998180878	-0.1090914506	-1.309461970e-16	-1.407134836
+200	-2.84217e-14	0.421254805847485	-0.1440776291	-1.273166817e-16	-1.395850033
+205	-2.84217e-14	0.421173127795214	-0.1779954552	-1.227696425e-16	-1.381712485
+210	-2.84217e-14	0.421216993526037	-0.2106084968	-1.173251563e-16	-1.364784617
+215	-2.84217e-14	0.421380852538494	-0.2416941277	-1.110181389e-16	-1.345174987
+220	-2.84217e-14	0.421628724074917	-0.2710177197	-1.038816365e-16	-1.322986341
+225	-2.84217e-14	0.421875207760183	-0.2983108202	-9.594528386e-17	-1.298310820
+
+135	-5	0.421874604338868	0.2977411900	-0.02604897879	-1.297741190
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+
diff --git a/test/bl-carpet-mask/emask.xy.asc b/test/bl-carpet-mask/emask.xy.asc
new file mode 100644
index 0000000..3a20e36
--- /dev/null
+++ b/test/bl-carpet-mask/emask.xy.asc
@@ -0,0 +1,1991 @@
+# 2D ASCII output created by CarpetIOASCII
+# created on carbon.aei.mpg.de by jonathan on Aug 14 2006 at 17:06:13+0200
+# parameter filename: "bl-carpet-mask.par"
+#
+# SPACEMASK::emask x y (emask)
+#
+# iteration 0
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it	2:tl 3:rl 4:c 5:ml	6:ix 7:iy 8:iz	9:time	10:x 11:y 12:z	13:data
+0	0 0 0 0	0 0 22	0	-3.225 -3.225 0.075	1
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+
+
+
diff --git a/test/bl-carpet-mask/emask.xz.asc b/test/bl-carpet-mask/emask.xz.asc
new file mode 100644
index 0000000..0d3d133
--- /dev/null
+++ b/test/bl-carpet-mask/emask.xz.asc
@@ -0,0 +1,1991 @@
+# 2D ASCII output created by CarpetIOASCII
+# created on carbon.aei.mpg.de by jonathan on Aug 14 2006 at 17:06:13+0200
+# parameter filename: "bl-carpet-mask.par"
+#
+# SPACEMASK::emask x z (emask)
+#
+# iteration 0
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it	2:tl 3:rl 4:c 5:ml	6:ix 7:iy 8:iz	9:time	10:x 11:y 12:z	13:data
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+
+
+
diff --git a/test/bl-carpet-mask/emask.yz.asc b/test/bl-carpet-mask/emask.yz.asc
new file mode 100644
index 0000000..8113a1a
--- /dev/null
+++ b/test/bl-carpet-mask/emask.yz.asc
@@ -0,0 +1,1991 @@
+# 2D ASCII output created by CarpetIOASCII
+# created on carbon.aei.mpg.de by jonathan on Aug 14 2006 at 17:06:13+0200
+# parameter filename: "bl-carpet-mask.par"
+#
+# SPACEMASK::emask y z (emask)
+#
+# iteration 0
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it	2:tl 3:rl 4:c 5:ml	6:ix 7:iy 8:iz	9:time	10:x 11:y 12:z	13:data
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