add another test case, this one to test setting an excision mask

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1025 f88db872-0e4f-0410-b76b-b9085cfa78c5

13 files changed, 12949 insertions, 1 deletions

diff --git a/test/config b/test/config
index e5cdcaf..001a062 100644
--- a/test/config
+++ b/test/config
@@ -1 +1 @@
-EXTENSIONS gp
+EXTENSIONS gp xg asc
diff --git a/test/misner1.2-025-init-mask.par b/test/misner1.2-025-init-mask.par
new file mode 100644
index 0000000..2b475b1
--- /dev/null
+++ b/test/misner1.2-025-init-mask.par
@@ -0,0 +1,116 @@
+# This parameter file sets up Misner initial data and finds the
+# apparent horizons in it with AHFinderDirect.
+#
+# Note that the grid is very high-resolution, but small (the outer
+# boundaries are very close in).  This isn't a problem for the purposes
+# of this test.  This run takes about 185 megabytes of memory, and
+# 36 cpu seconds on a 1.07GHz PIII laptop.
+
+########################################
+ 
+#
+# ***** grid *****
+#
+
+ActiveThorns = "CartGrid3D PUGH"
+
+Driver::global_nx   = 44
+Driver::global_ny   = 44
+Driver::global_nz   = 100
+PUGH::ghost_size    = 3
+
+Grid::domain        = "octant"
+Grid::type          = "byspacing"
+Grid::dxyz          = 0.025
+Grid::avoid_origin  = "true"
+
+########################################
+
+#
+# physics
+#
+
+ActiveThorns = "ADMBase ADMCoupling CoordGauge StaticConformal SpaceMask"
+ActiveThorns = "IDAnalyticBH"
+
+ADMBase::initial_data              = "misner_bh"
+IDAnalyticBH::mu                   = 1.2
+
+########################################
+
+#
+# numerical methods
+#
+
+Cactus::cctk_itlast = 0
+ADMBase::metric_type            = "static conformal"
+StaticConformal::conformal_storage = "factor+derivs+2nd derivs"
+SpaceMask::use_mask                = "true"
+
+ADMBase::evolution_method       = "none"
+ADMBase::initial_lapse          = "Cadez"
+ADMBase::lapse_evolution_method = "static"
+ADMBase::initial_shift          = "zero"
+ADMBase::shift_evolution_method = "static"
+
+########################################
+
+# automagically create output directory
+ActiveThorns = "PUGHSlab IOUtil IOASCII"
+IO::out_dir = "misner1.2-025-init-mask"
+IO::parfile_write = "no"
+IOASCII::out1d_every = 1
+IOASCII::out2d_every = 1
+IOASCII::out1d_vars = "SpaceMask::emask"
+IOASCII::out2d_vars = "SpaceMask::emask"
+
+########################################
+
+#
+# AHFinderDirect
+#
+
+ActiveThorns = "LocalInterp PUGHInterp PUGHReduce AHFinderDirect"
+
+AHFinderDirect::find_AHs_at_postinitial = "true"
+AHFinderDirect::find_AHs_at_poststep    = "false"
+AHFinderDirect::print_timing_stats = "true"
+##AHFinderDirect::verbose_level = "algorithm details"
+
+AHFinderDirect::h_base_file_name              = "misner1.2-025-init-mask/h"
+AHFinderDirect::BH_diagnostics_base_file_name = "misner1.2-025-init-mask/BH_diagnostics"
+AHFinderDirect::Theta_norm_for_convergence = 1.0e-12
+
+AHFinderDirect::set_horizon_mask = "true"
+# only test old-style mask for now,
+# since we don't have a thorn to set up the new-style bit fields yet
+AHFinderDirect::set_old_style_mask = "true"
+AHFinderDirect::set_new_style_mask = "false"
+# have mask directly show horizon position for testing (no buffer zone)
+AHFinderDirect::mask_radius_multiplier[1] = 1.0
+AHFinderDirect::mask_radius_multiplier[2] = 1.0
+AHFInderDirect::mask_radius_offset[1]     = 0.0
+AHFInderDirect::mask_radius_offset[2]     = 0.0
+
+AHFinderDirect::N_horizons = 2
+
+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] = 1.1
+AHFinderDirect::initial_guess__coord_sphere__radius[1] = 0.60
+
+AHFinderDirect::N_zones_per_right_angle[2] = 30
+AHFinderDirect::origin_x[2] = 0.0
+AHFinderDirect::origin_y[2] = 0.0
+AHFinderDirect::origin_z[2] = 0.0
+AHFinderDirect::initial_guess_method[2] = "coordinate ellipsoid"
+AHFinderDirect::initial_guess__coord_ellipsoid__x_center[2] = 0.0
+AHFinderDirect::initial_guess__coord_ellipsoid__y_center[2] = 0.0
+AHFinderDirect::initial_guess__coord_ellipsoid__z_center[2] = 0.0
+AHFinderDirect::initial_guess__coord_ellipsoid__x_radius[2] = 0.6
+AHFinderDirect::initial_guess__coord_ellipsoid__y_radius[2] = 0.6
+AHFinderDirect::initial_guess__coord_ellipsoid__z_radius[2] = 1.8
diff --git a/test/misner1.2-025-init-mask/BH_diagnostics.ah1.gp b/test/misner1.2-025-init-mask/BH_diagnostics.ah1.gp
new file mode 100644
index 0000000..86c8b7d
--- /dev/null
+++ b/test/misner1.2-025-init-mask/BH_diagnostics.ah1.gp
@@ -0,0 +1,22 @@
+# 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 = min x
+# column 10 = max x
+# column 11 = min y
+# column 12 = max y
+# column 13 = min z
+# column 14 = max z
+# column 15 = xy-plane circumference
+# column 16 = xz-plane circumference
+# column 17 = yz-plane circumference
+# column 18 = area
+# column 19 = m_irreducible
+0	0.000	0.000000	0.000000	1.127434	0.4629495868	0.8620251245	0.6607155931	-0.6621179725	0.6621179725	-0.6621179725	0.6621179725	0.5370504132	1.862025124	31.71501646	32.86874998	32.86874998	338.0473838	2.593306580
diff --git a/test/misner1.2-025-init-mask/BH_diagnostics.ah2.gp b/test/misner1.2-025-init-mask/BH_diagnostics.ah2.gp
new file mode 100644
index 0000000..5130bc9
--- /dev/null
+++ b/test/misner1.2-025-init-mask/BH_diagnostics.ah2.gp
@@ -0,0 +1,22 @@
+# 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 = min x
+# column 10 = max x
+# column 11 = min y
+# column 12 = max y
+# column 13 = min z
+# column 14 = max z
+# column 15 = xy-plane circumference
+# column 16 = xz-plane circumference
+# column 17 = yz-plane circumference
+# column 18 = area
+# column 19 = m_irreducible
+0	0.000	0.000000	0.000000	0.000000	0.3564208319	1.936847298	1.237030207	-0.7790848177	0.7790848177	-0.7790848177	0.7790848177	-1.936847298	1.936847298	14.51364495	64.12906004	64.12906004	719.7154614	3.783950867
diff --git a/test/misner1.2-025-init-mask/emask_3D_diagonal.xg b/test/misner1.2-025-init-mask/emask_3D_diagonal.xg
new file mode 100644
index 0000000..791e8bc
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_3D_diagonal.xg
@@ -0,0 +1,51 @@
+"Parameter file misner1.2-025-init-mask.par
+"Created Mar 26 2003 13:13:51
+"x-label diagonal
+"y-label SPACEMASK::emask
+
+
+"Time = 0.0000000000000
+-0.1082531754731		0.0000000000000
+-0.0649519052838		0.0000000000000
+-0.0216506350946		0.0000000000000
+0.0216506350946		0.0000000000000
+0.0649519052838		0.0000000000000
+0.1082531754731		0.0000000000000
+0.1515544456623		0.0000000000000
+0.1948557158515		0.0000000000000
+0.2381569860407		0.0000000000000
+0.2814582562299		0.0000000000000
+0.3247595264192		0.0000000000000
+0.3680607966084		0.0000000000000
+0.4113620667976		0.0000000000000
+0.4546633369868		0.0000000000000
+0.4979646071761		0.0000000000000
+0.5412658773653		0.0000000000000
+0.5845671475545		1.0000000000000
+0.6278684177437		1.0000000000000
+0.6711696879329		1.0000000000000
+0.7144709581222		1.0000000000000
+0.7577722283114		1.0000000000000
+0.8010734985006		1.0000000000000
+0.8443747686898		1.0000000000000
+0.8876760388790		1.0000000000000
+0.9309773090683		1.0000000000000
+0.9742785792575		1.0000000000000
+1.0175798494467		1.0000000000000
+1.0608811196359		1.0000000000000
+1.1041823898252		1.0000000000000
+1.1474836600144		1.0000000000000
+1.1907849302036		1.0000000000000
+1.2340862003928		1.0000000000000
+1.2773874705820		1.0000000000000
+1.3206887407713		1.0000000000000
+1.3639900109605		1.0000000000000
+1.4072912811497		1.0000000000000
+1.4505925513389		1.0000000000000
+1.4938938215282		1.0000000000000
+1.5371950917174		1.0000000000000
+1.5804963619066		1.0000000000000
+1.6237976320958		1.0000000000000
+1.6670989022850		1.0000000000000
+1.7104001724743		1.0000000000000
+1.7537014426635		1.0000000000000
diff --git a/test/misner1.2-025-init-mask/emask_x_[3][3].xg b/test/misner1.2-025-init-mask/emask_x_[3][3].xg
new file mode 100644
index 0000000..8a57f0d
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_x_[3][3].xg
@@ -0,0 +1,52 @@
+"Parameter file misner1.2-025-init-mask.par
+"Created Mar 26 2003 13:13:51
+"x-label x
+"y-label SPACEMASK::emask (y = 0.0125000000000, z = 0.0125000000000), (yi = 3, zi = 3) 
+
+
+
+"Time = 0.0000000000000
+-0.0625000000000		0.0000000000000
+-0.0375000000000		0.0000000000000
+-0.0125000000000		0.0000000000000
+0.0125000000000		0.0000000000000
+0.0375000000000		0.0000000000000
+0.0625000000000		0.0000000000000
+0.0875000000000		0.0000000000000
+0.1125000000000		0.0000000000000
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+0.1625000000000		0.0000000000000
+0.1875000000000		0.0000000000000
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+0.3625000000000		1.0000000000000
+0.3875000000000		1.0000000000000
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+0.6875000000000		1.0000000000000
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+0.7875000000000		1.0000000000000
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+0.8375000000000		1.0000000000000
+0.8625000000000		1.0000000000000
+0.8875000000000		1.0000000000000
+0.9125000000000		1.0000000000000
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+0.9625000000000		1.0000000000000
+0.9875000000000		1.0000000000000
+1.0125000000000		1.0000000000000
diff --git a/test/misner1.2-025-init-mask/emask_xy_[3].asc b/test/misner1.2-025-init-mask/emask_xy_[3].asc
new file mode 100644
index 0000000..70ccb97
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_xy_[3].asc
@@ -0,0 +1,1988 @@
+#Parameter file misner1.2-025-init-mask.par
+#Created Mar 26 2003 13:13:52
+#x-label x
+#y-label y
+#z-label SPACEMASK::emask (z = 0.0125000000000), (zi = 3)
+
+
+#Time = 0.0000000000000
+-0.0625000000000		-0.0625000000000		0.0000000000000
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+-0.0125000000000		-0.0625000000000		0.0000000000000
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diff --git a/test/misner1.2-025-init-mask/emask_xz_[3].asc b/test/misner1.2-025-init-mask/emask_xz_[3].asc
new file mode 100644
index 0000000..68e28e5
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_xz_[3].asc
@@ -0,0 +1,4508 @@
+#Parameter file misner1.2-025-init-mask.par
+#Created Mar 26 2003 13:13:52
+#x-label x
+#y-label z
+#z-label SPACEMASK::emask (y = 0.0125000000000), (yi = 3)
+
+
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diff --git a/test/misner1.2-025-init-mask/emask_y_[3][3].xg b/test/misner1.2-025-init-mask/emask_y_[3][3].xg
new file mode 100644
index 0000000..ff12c51
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_y_[3][3].xg
@@ -0,0 +1,52 @@
+"Parameter file misner1.2-025-init-mask.par
+"Created Mar 26 2003 13:13:51
+"x-label y
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+
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diff --git a/test/misner1.2-025-init-mask/emask_yz_[3].asc b/test/misner1.2-025-init-mask/emask_yz_[3].asc
new file mode 100644
index 0000000..2b14f13
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_yz_[3].asc
@@ -0,0 +1,4508 @@
+#Parameter file misner1.2-025-init-mask.par
+#Created Mar 26 2003 13:13:52
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+0.4625000000000		2.4125000000000		1.0000000000000
+0.4875000000000		2.4125000000000		1.0000000000000
+0.5125000000000		2.4125000000000		1.0000000000000
+0.5375000000000		2.4125000000000		1.0000000000000
+0.5625000000000		2.4125000000000		1.0000000000000
+0.5875000000000		2.4125000000000		1.0000000000000
+0.6125000000000		2.4125000000000		1.0000000000000
+0.6375000000000		2.4125000000000		1.0000000000000
+0.6625000000000		2.4125000000000		1.0000000000000
+0.6875000000000		2.4125000000000		1.0000000000000
+0.7125000000000		2.4125000000000		1.0000000000000
+0.7375000000000		2.4125000000000		1.0000000000000
+0.7625000000000		2.4125000000000		1.0000000000000
+0.7875000000000		2.4125000000000		1.0000000000000
+0.8125000000000		2.4125000000000		1.0000000000000
+0.8375000000000		2.4125000000000		1.0000000000000
+0.8625000000000		2.4125000000000		1.0000000000000
+0.8875000000000		2.4125000000000		1.0000000000000
+0.9125000000000		2.4125000000000		1.0000000000000
+0.9375000000000		2.4125000000000		1.0000000000000
+0.9625000000000		2.4125000000000		1.0000000000000
+0.9875000000000		2.4125000000000		1.0000000000000
+1.0125000000000		2.4125000000000		1.0000000000000
+
diff --git a/test/misner1.2-025-init-mask/emask_z_[3][3].xg b/test/misner1.2-025-init-mask/emask_z_[3][3].xg
new file mode 100644
index 0000000..2e5b40a
--- /dev/null
+++ b/test/misner1.2-025-init-mask/emask_z_[3][3].xg
@@ -0,0 +1,108 @@
+"Parameter file misner1.2-025-init-mask.par
+"Created Mar 26 2003 13:13:51
+"x-label z
+"y-label SPACEMASK::emask (x = 0.0125000000000, y = 0.0125000000000), (xi = 3, yi = 3) 
+
+
+
+"Time = 0.0000000000000
+-0.0625000000000		0.0000000000000
+-0.0375000000000		0.0000000000000
+-0.0125000000000		0.0000000000000
+0.0125000000000		0.0000000000000
+0.0375000000000		0.0000000000000
+0.0625000000000		0.0000000000000
+0.0875000000000		0.0000000000000
+0.1125000000000		0.0000000000000
+0.1375000000000		0.0000000000000
+0.1625000000000		0.0000000000000
+0.1875000000000		0.0000000000000
+0.2125000000000		0.0000000000000
+0.2375000000000		0.0000000000000
+0.2625000000000		0.0000000000000
+0.2875000000000		0.0000000000000
+0.3125000000000		0.0000000000000
+0.3375000000000		0.0000000000000
+0.3625000000000		0.0000000000000
+0.3875000000000		0.0000000000000
+0.4125000000000		0.0000000000000
+0.4375000000000		0.0000000000000
+0.4625000000000		0.0000000000000
+0.4875000000000		0.0000000000000
+0.5125000000000		0.0000000000000
+0.5375000000000		0.0000000000000
+0.5625000000000		0.0000000000000
+0.5875000000000		0.0000000000000
+0.6125000000000		0.0000000000000
+0.6375000000000		0.0000000000000
+0.6625000000000		0.0000000000000
+0.6875000000000		0.0000000000000
+0.7125000000000		0.0000000000000
+0.7375000000000		0.0000000000000
+0.7625000000000		0.0000000000000
+0.7875000000000		0.0000000000000
+0.8125000000000		0.0000000000000
+0.8375000000000		0.0000000000000
+0.8625000000000		0.0000000000000
+0.8875000000000		0.0000000000000
+0.9125000000000		0.0000000000000
+0.9375000000000		0.0000000000000
+0.9625000000000		0.0000000000000
+0.9875000000000		0.0000000000000
+1.0125000000000		0.0000000000000
+1.0375000000000		0.0000000000000
+1.0625000000000		0.0000000000000
+1.0875000000000		0.0000000000000
+1.1125000000000		0.0000000000000
+1.1375000000000		0.0000000000000
+1.1625000000000		0.0000000000000
+1.1875000000000		0.0000000000000
+1.2125000000000		0.0000000000000
+1.2375000000000		0.0000000000000
+1.2625000000000		0.0000000000000
+1.2875000000000		0.0000000000000
+1.3125000000000		0.0000000000000
+1.3375000000000		0.0000000000000
+1.3625000000000		0.0000000000000
+1.3875000000000		0.0000000000000
+1.4125000000000		0.0000000000000
+1.4375000000000		0.0000000000000
+1.4625000000000		0.0000000000000
+1.4875000000000		0.0000000000000
+1.5125000000000		0.0000000000000
+1.5375000000000		0.0000000000000
+1.5625000000000		0.0000000000000
+1.5875000000000		0.0000000000000
+1.6125000000000		0.0000000000000
+1.6375000000000		0.0000000000000
+1.6625000000000		0.0000000000000
+1.6875000000000		0.0000000000000
+1.7125000000000		0.0000000000000
+1.7375000000000		0.0000000000000
+1.7625000000000		0.0000000000000
+1.7875000000000		0.0000000000000
+1.8125000000000		0.0000000000000
+1.8375000000000		0.0000000000000
+1.8625000000000		0.0000000000000
+1.8875000000000		0.0000000000000
+1.9125000000000		0.0000000000000
+1.9375000000000		1.0000000000000
+1.9625000000000		1.0000000000000
+1.9875000000000		1.0000000000000
+2.0125000000000		1.0000000000000
+2.0375000000000		1.0000000000000
+2.0625000000000		1.0000000000000
+2.0875000000000		1.0000000000000
+2.1125000000000		1.0000000000000
+2.1375000000000		1.0000000000000
+2.1625000000000		1.0000000000000
+2.1875000000000		1.0000000000000
+2.2125000000000		1.0000000000000
+2.2375000000000		1.0000000000000
+2.2625000000000		1.0000000000000
+2.2875000000000		1.0000000000000
+2.3125000000000		1.0000000000000
+2.3375000000000		1.0000000000000
+2.3625000000000		1.0000000000000
+2.3875000000000		1.0000000000000
+2.4125000000000		1.0000000000000
diff --git a/test/misner1.2-025-init-mask/h.t0.ah1.gp b/test/misner1.2-025-init-mask/h.t0.ah1.gp
new file mode 100644
index 0000000..9e87ddb
--- /dev/null
+++ b/test/misner1.2-025-init-mask/h.t0.ah1.gp
@@ -0,0 +1,676 @@
+# N_patches = 4
+
+### +z patch
+# N_rho = 10
+# N_sigma = 10
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+0	0	0.862025124483768	0.000000000	0.000000000	1.862025124
+5	0	0.861037553933788	0.07504436755	0.000000000	1.857761046
+10	0	0.858087090090080	0.1490052595	0.000000000	1.845050819
+15	0	0.853210151696102	0.2208270367	0.000000000	1.824137721
+20	0	0.846467112354603	0.2895088031	0.000000000	1.795418899
+25	0	0.837941110551593	0.3541292156	0.000000000	1.759432554
+30	0	0.827736710560150	0.4138683553	0.000000000	1.716841019
+35	0	0.815978279654358	0.4680259138	0.000000000	1.668410276
+40	0	0.802807894979744	0.5160349679	0.000000000	1.614986527
+45	0	0.788382836575859	0.5574708499	0.000000000	1.557470850
+
+0	5	0.861037553933790	0.000000000	0.07504436755	1.857761046
+5	5	0.860061951410873	0.07467624975	0.07467624975	1.853553440
+10	5	0.857146658802097	0.1482925510	0.07357874016	1.841008848
+15	5	0.852326141932660	0.2198147281	0.07177217669	1.820359733
+20	5	0.845657521365349	0.2882593908	0.06928981130	1.791986167
+25	5	0.837219778702819	0.3527173086	0.06617683710	1.756404709
+30	5	0.827112694996973	0.4123743827	0.06248907385	1.714253382
+35	5	0.815455534260690	0.4665295449	0.05829135528	1.666273240
+40	5	0.802385388289462	0.5146089442	0.05365566506	1.613287058
+45	5	0.788054984446870	0.5561757605	0.04865907397	1.556175760
+
+0	10	0.858087090090081	0.000000000	0.1490052595	1.845050819
+5	10	0.857146658802096	0.07357874016	0.1482925510	1.841008848
+10	10	0.854334938718590	0.1461663447	0.1461663447	1.828950533
+15	10	0.849680694777148	0.2167916261	0.1426621686	1.809077363
+20	10	0.843231799429761	0.2845230265	0.1378384315	1.781720591
+25	10	0.835055212498377	0.3484877738	0.1317752259	1.747334443
+30	10	0.825236827809842	0.4078901456	0.1245726237	1.706486456
+35	10	0.813881035191212	0.4620283263	0.1163484472	1.659844833
+40	10	0.801110148021800	0.5103094050	0.1072355573	1.608163067
+45	10	0.787063318796806	0.5522617437	0.09737864583	1.552261744
+
+0	15	0.853210151696103	0.000000000	0.2208270367	1.824137721
+5	15	0.852326141932660	0.07177217669	0.2198147281	1.820359733
+10	15	0.849680694777150	0.1426621686	0.2167916261	1.809077363
+15	15	0.845293859545753	0.2117992023	0.2117992023	1.790445384
+20	15	0.839199490036572	0.2783357215	0.2049064038	1.764721110
+25	15	0.831446147780659	0.3414600147	0.1962093772	1.732263365
+30	15	0.822098076285902	0.4004098344	0.1858308509	1.693530177
+35	15	0.811236225544831	0.4544869920	0.1739190395	1.649074692
+40	15	0.798959087297527	0.5030725910	0.1606458750	1.599538568
+45	15	0.785383383482418	0.5456424280	0.1462044479	1.545642428
+
+0	20	0.846467112354607	0.000000000	0.2895088031	1.795418899
+5	20	0.845657521365352	0.06928981130	0.2882593908	1.791986167
+10	20	0.843231799429763	0.1378384315	0.2845230265	1.781720591
+15	20	0.839199490036574	0.2049064038	0.2783357215	1.764721110
+20	20	0.833577503653499	0.2697586649	0.2697586649	1.741155841
+25	20	0.826391808215740	0.3316690844	0.2588798880	1.711266647
+30	20	0.817679464247099	0.3899275933	0.2458161796	1.675374403
+35	20	0.807491227353436	0.4438505765	0.2307150230	1.633884316
+40	20	0.795894091856951	0.4927946136	0.2137559883	1.587289751
+45	20	0.782974017098169	0.5361736218	0.1951512387	1.536173622
+
+0	25	0.837941110551597	0.000000000	0.3541292156	1.759432554
+5	25	0.837219778702822	0.06617683710	0.3527173086	1.756404709
+10	25	0.835055212498379	0.1317752259	0.3484877738	1.747334443
+15	25	0.831446147780659	0.1962093772	0.3414600147	1.732263365
+20	25	0.826391808215740	0.2588798880	0.3316690844	1.711266647
+25	25	0.819893990556789	0.3191696614	0.3191696614	1.684461548
+30	25	0.811959994578473	0.3764431908	0.3040413283	1.652018733
+35	25	0.802606233899332	0.4300503155	0.2863947395	1.614175501
+40	25	0.791862533035689	0.4793355335	0.2663781770	1.571249844
+45	25	0.779776825986545	0.5236536178	0.2441836922	1.523653618
+
+0	30	0.827736710560157	0.000000000	0.4138683553	1.716841019
+5	30	0.827112694996977	0.06248907385	0.4123743827	1.714253382
+10	30	0.825236827809844	0.1245726237	0.4078901456	1.706486456
+15	30	0.822098076285902	0.1858308509	0.4004098344	1.693530177
+20	30	0.817679464247098	0.2458161796	0.3899275933	1.675374403
+25	30	0.811959994578471	0.3040413283	0.3764431908	1.652018733
+30	30	0.804917733681416	0.3599701538	0.3599701538	1.623486596
+35	30	0.796533979285098	0.4130127395	0.3405461999	1.589843321
+40	30	0.786798518639227	0.4625264984	0.3182456391	1.551217616
+45	30	0.775715956473751	0.5078252983	0.2931930727	1.507825298
+
+0	35	0.815978279654367	0.000000000	0.4680259138	1.668410276
+5	35	0.815455534260698	0.05829135528	0.4665295449	1.666273240
+10	35	0.813881035191217	0.1163484472	0.4620283263	1.659844833
+15	35	0.811236225544833	0.1739190395	0.4544869920	1.649074692
+20	35	0.807491227353438	0.2307150230	0.4438505765	1.633884316
+25	35	0.802606233899333	0.2863947395	0.4300503155	1.614175501
+30	35	0.796533979285099	0.3405461999	0.4130127395	1.589843321
+35	35	0.789223473538748	0.3926724665	0.3926724665	1.560794400
+40	35	0.780625211356415	0.4421812319	0.3689891168	1.526971072
+45	35	0.770698262192012	0.4883816810	0.3419685346	1.488381681
+
+0	40	0.802807894979750	0.000000000	0.5160349679	1.614986527
+5	40	0.802385388289466	0.05365566506	0.5146089442	1.613287058
+10	40	0.801110148021801	0.1072355573	0.5103094050	1.608163067
+15	40	0.798959087297529	0.1606458750	0.5030725910	1.599538568
+20	40	0.795894091856955	0.2137559883	0.4927946136	1.587289751
+25	40	0.791862533035692	0.2663781770	0.4793355335	1.571249844
+30	40	0.786798518639230	0.3182456391	0.4625264984	1.551217616
+35	40	0.780625211356418	0.3689891168	0.4421812319	1.526971072
+40	40	0.773258835008263	0.4181135812	0.4181135812	1.498288363
+45	40	0.764614948901160	0.4649779504	0.3901628267	1.464977950
+
+0	45	0.788382836575860	0.000000000	0.5574708499	1.557470850
+5	45	0.788054984446870	0.04865907397	0.5561757605	1.556175760
+10	45	0.787063318796807	0.09737864583	0.5522617437	1.552261744
+15	45	0.785383383482422	0.1462044479	0.5456424280	1.545642428
+20	45	0.782974017098176	0.1951512387	0.5361736218	1.536173622
+25	45	0.779776825986553	0.2441836922	0.5236536178	1.523653618
+30	45	0.775715956473759	0.2931930727	0.5078252983	1.507825298
+35	45	0.770698262192019	0.3419685346	0.4883816810	1.488381681
+40	45	0.764614948901165	0.3901628267	0.4649779504	1.464977950
+45	45	0.757345376659998	0.4372535571	0.4372535571	1.437253557
+
+
+### +x patch
+# N_rho = 19
+# N_sigma = 10
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	0	0.788382836672097	0.5574708500	0.000000000	1.557470850
+45	5	0.788054984665087	0.5561757606	0.04865907398	1.556175761
+45	10	0.787063320153356	0.5522617447	0.09737864600	1.552261745
+45	15	0.785383389692179	0.5456424323	0.1462044491	1.545642432
+45	20	0.782974033848673	0.5361736333	0.1951512429	1.536173633
+45	25	0.779776862427512	0.5236536422	0.2441837036	1.523653642
+45	30	0.775716023423619	0.5078253422	0.2931930980	1.507825342
+45	35	0.770698365030330	0.4883817462	0.3419685802	1.488381746
+45	40	0.764615077402988	0.4649780286	0.3901628923	1.464978029
+45	45	0.757345489901898	0.4372536225	0.4372536225	1.437253622
+
+50	0	0.772872903476355	0.5920549929	0.000000000	1.496793126
+50	5	0.772528755093662	0.5904667437	0.05165914627	1.495460427
+50	10	0.771489939501276	0.5856768744	0.1032706349	1.491441249
+50	15	0.769737393320461	0.5776106207	0.1547702993	1.484672859
+50	20	0.767239513579578	0.5661455558	0.2060601306	1.475052527
+50	25	0.763952587412953	0.5511156018	0.2569894257	1.462440898
+50	30	0.759821739072538	0.5323181447	0.3073340242	1.446667959
+50	35	0.754782629470962	0.5095257050	0.3567737396	1.427542831
+50	40	0.748764573037743	0.4825042485	0.4048691369	1.404869137
+50	45	0.741695501533819	0.4510401669	0.4510401669	1.378467638
+
+55	0	0.756457475142239	0.6196536872	0.000000000	1.433886183
+55	5	0.756112559893549	0.6177866771	0.05404933073	1.432578888
+55	10	0.755073470669472	0.6121672662	0.1079416057	1.428644134
+55	15	0.753327340067515	0.6027414650	0.1615040888	1.422044117
+55	20	0.750853220444523	0.5894232210	0.2145325078	1.412718583
+55	25	0.747623010411471	0.5721008853	0.2667750240	1.400589352
+55	30	0.743602949753241	0.5506472348	0.3179163292	1.385567345
+55	35	0.738755849560981	0.5249338844	0.3675626629	1.367562663
+55	40	0.733044351381843	0.4948510013	0.4152292927	1.346498401
+55	45	0.726435429309701	0.4603328871	0.4603328871	1.322328558
+
+60	0	0.739322124030152	0.6402717410	0.000000000	1.369661062
+60	5	0.738992560502725	0.6381572175	0.05583152208	1.368440241
+60	10	0.738001526250593	0.6318041867	0.1114041246	1.364772317
+60	15	0.736342131402123	0.6211856024	0.1664461805	1.358641675
+60	20	0.734003459185750	0.6062609734	0.2206609485	1.350024936
+60	25	0.730971641439320	0.5869836031	0.2737149493	1.338895141
+60	30	0.727231244658014	0.5633108999	0.3252276997	1.325227700
+60	35	0.722767322231418	0.5352181934	0.3747638136	1.309008368
+60	40	0.717568032764615	0.5027159191	0.4218287423	1.290243171
+60	45	0.711627906937504	0.4658698215	0.4658698215	1.268970067
+
+65	0	0.721655307528428	0.6540418248	0.000000000	1.304984712
+65	5	0.721356623999583	0.6517255819	0.05701860015	1.303904630
+65	10	0.720459847750271	0.6447770767	0.1136915952	1.300664489
+65	15	0.718962946746108	0.6331982268	0.1696649535	1.295265182
+65	20	0.716863171292208	0.6169965130	0.2245683654	1.287710199
+65	25	0.714157652011021	0.5961910410	0.2780084482	1.278008448
+65	30	0.710844638096704	0.5708212512	0.3295638030	1.266178321
+65	35	0.706924852116656	0.5409575790	0.3787825747	1.252252662
+65	40	0.702403207535548	0.5067138626	0.4251834153	1.236284555
+65	45	0.697290752622282	0.4682606780	0.4682606780	1.218353540
+
+70	0	0.703644927516054	0.6612099460	0.000000000	1.240660739
+70	5	0.703390878019590	0.6587487623	0.05763304882	1.239764941
+70	10	0.702629139259843	0.6513744691	0.1148548935	1.237080918
+70	15	0.701360954880569	0.6391156503	0.1712505224	1.232619073
+70	20	0.699588837450202	0.6220229680	0.2263978454	1.226397845
+70	25	0.697316929468021	0.6001732703	0.2798653922	1.218445206
+70	30	0.694551698255697	0.5736752101	0.3312115370	1.208800701
+70	35	0.691302658451754	0.5426757567	0.3799856557	1.197517822
+70	40	0.687583264131211	0.5073672593	0.4257316801	1.184666580
+70	45	0.683411823824724	0.4679943201	0.4679943201	1.170336002
+
+75	0	0.685474965522602	0.6621179725	0.000000000	1.177413976
+75	5	0.685276645467391	0.6595754120	0.05770537129	1.176732699
+75	10	0.684682618358995	0.6519639800	0.1149588401	1.174693222
+75	15	0.683695621082637	0.6393327498	0.1713086940	1.171308694
+75	20	0.682320479427537	0.6217650040	0.2263039542	1.166601431
+75	25	0.680564194800462	0.5993800422	0.2794955038	1.160603398
+75	30	0.678436251136610	0.5723356214	0.3304381251	1.153356868
+75	35	0.675948858441476	0.5408305042	0.3786935960	1.144915097
+75	40	0.673117268470366	0.5051069190	0.4238350295	1.135342991
+75	45	0.669960079746157	0.4654524812	0.4654524812	1.124717616
+
+80	0	0.667322241034252	0.6571841167	0.000000000	1.115879291
+80	5	0.667187381303029	0.6546260029	0.05727235411	1.115428227
+80	10	0.666783689130184	0.6469718956	0.1140786010	1.114078601
+80	15	0.666113817164709	0.6342825182	0.1699554885	1.111841121
+80	20	0.665182381878737	0.6166593394	0.2244456442	1.108733679
+80	25	0.663995756462838	0.5942444178	0.2771007229	1.104781324
+80	30	0.662562286267469	0.5672205429	0.3274849332	1.100016286
+80	35	0.660892252328253	0.5358109099	0.3751788382	1.094477920
+80	40	0.658997891704586	0.5002784945	0.4197835002	1.088212596
+80	45	0.656893454477817	0.4609249548	0.4609249548	1.081273506
+
+85	0	0.649353600708708	0.6468826142	0.000000000	1.056594895
+85	5	0.649286131280836	0.6443726644	0.05637530322	1.056375303
+85	10	0.649084219080226	0.6368636755	0.1122962490	1.055718352
+85	15	0.648749453574726	0.6244181688	0.1673123441	1.054629511
+85	20	0.648284376830692	0.6071397060	0.2209807810	1.053117841
+85	25	0.647692592722345	0.5851721851	0.2728702713	1.051195932
+85	30	0.646978678217142	0.5586986055	0.3225647903	1.048879794
+85	35	0.646148188652678	0.5279395735	0.3696672691	1.046188728
+85	40	0.645207620575531	0.4931514073	0.4138031640	1.043145158
+85	45	0.644164352267156	0.4546238594	0.4546238594	1.039774434
+
+90	0	0.631723370380533	0.6317233704	0.000000000	1.000000000
+90	5	0.631723387728183	0.6293194895	0.05505832107	1.000000000
+90	10	0.631723428577022	0.6221261302	0.1096976222	1.000000000
+90	15	0.631723455713195	0.6101980009	0.1635020616	1.000000000
+90	20	0.631723499656663	0.5936259110	0.2160621619	1.000000000
+90	25	0.631723525842059	0.5725359507	0.2669778984	1.000000000
+90	30	0.631723544708017	0.5470886379	0.3158617724	1.000000000
+90	35	0.631723561090522	0.5174776465	0.3623417489	1.000000000
+90	40	0.631723576974829	0.4839283357	0.4060640880	1.000000000
+90	45	0.631723570673165	0.4466960207	0.4466960207	1.000000000
+
+95	0	0.614571834607572	0.6122332032	0.000000000	0.9464365353
+95	5	0.614635716976011	0.6099844668	0.05336672577	0.9466332742
+95	10	0.614826962034995	0.6032513922	0.1063694966	0.9472223419
+95	15	0.615144310515167	0.5920733834	0.1586455849	0.9482002910
+95	20	0.615585677085302	0.5765162949	0.2098347709	0.9495613599
+95	25	0.616148188172034	0.5566726958	0.2595807411	0.9512974498
+95	30	0.616828126384022	0.5326620887	0.3075326003	0.9533981058
+95	35	0.617620951055870	0.5046312088	0.3533465764	0.9558504900
+95	40	0.618521312337959	0.4727542668	0.3966879309	0.9586393610
+95	45	0.619523069000361	0.4372330876	0.4372330876	0.9617470615
+
+100	0	0.598023539185519	0.5889382179	0.000000000	0.8961543022
+100	5	0.598144447343870	0.5868829653	0.05134560628	0.8965166987
+100	10	0.598506668264735	0.5807235540	0.1023972309	0.8976027691
+100	15	0.599108626081834	0.5704792758	0.1528594613	0.8994091117
+100	20	0.599947623733875	0.5561832595	0.2024341513	0.9019298851
+100	25	0.601019846403171	0.5378839929	0.2508194251	0.9051565396
+100	30	0.602320197258837	0.5156472024	0.2977090511	0.9090774857
+100	35	0.603842241061102	0.4895582593	0.3427923836	0.9136776703
+100	40	0.605578060671123	0.4597248099	0.3857549184	0.9189381123
+100	45	0.607518114661440	0.4262795703	0.4262795703	0.9248354104
+
+105	0	0.582186690224495	0.5623491598	0.000000000	0.8493189968
+105	5	0.582355201363813	0.5605140265	0.04903862307	0.8498107192
+105	10	0.582860540320213	0.5550076305	0.09786281975	0.8512861536
+105	15	0.583702059014912	0.5458274574	0.1462540264	0.8537459736
+105	20	0.584878520925079	0.5329709526	0.1939855625	0.8571908637
+105	25	0.586387920489467	0.5164380072	0.2408189977	0.8616208530
+105	30	0.588227181516859	0.4962343461	0.2865010333	0.8670344077
+105	35	0.590391791966972	0.4723758115	0.3307611041	0.8734272828
+105	40	0.592875383091923	0.4448934415	0.3733099227	0.8807911616
+105	45	0.595669306244035	0.4138392196	0.4138392196	0.8891121153
+
+110	0	0.567153120802155	0.5329496025	0.000000000	0.8060222083
+110	5	0.567357989529798	0.5313494745	0.04648705539	0.8066046073
+110	10	0.567973156533265	0.5265412330	0.09284342583	0.8083546641
+110	15	0.569000227444905	0.5185018468	0.1389321511	0.8112807613
+110	20	0.570441624615616	0.5071947599	0.1846037956	0.8153962044
+110	25	0.572300204332661	0.4925727037	0.2296904239	0.8207181977
+110	30	0.574578742651722	0.4745817795	0.2739999182	0.8272663585
+110	35	0.577279213540306	0.4531668296	0.3173108302	0.8350607629
+110	40	0.580401941405293	0.4282782285	0.3593681036	0.8441194728
+110	45	0.583944604328841	0.3998800555	0.3998800555	0.8544555625
+
+115	0	0.552998720661852	0.5011870468	0.000000000	0.7662926419
+115	5	0.553227715217220	0.4998258041	0.04372909160	0.7669273998
+115	10	0.553916383287523	0.4957286481	0.08741033578	0.7688379350
+115	15	0.555069695365734	0.4888557171	0.1309884946	0.7720428354
+115	20	0.556695616498432	0.4791420008	0.1743934263	0.7765724157
+115	25	0.558804642053158	0.4664996872	0.2175323767	0.7824676233
+115	30	0.561409081976454	0.4508217653	0.2602820675	0.7897783584
+115	35	0.564522030243011	0.4319871764	0.3024806773	0.7985610714
+115	40	0.568156075128795	0.4098679452	0.3439200417	0.8088754383
+115	45	0.572321721516149	0.3843386082	0.3843386082	0.8207799637
+
+120	0	0.539784321692906	0.4674669352	0.000000000	0.7301078392
+120	5	0.540025048090083	0.4663387705	0.04079935578	0.7307591853
+120	10	0.540750246479173	0.4629370774	0.08162829712	0.7327231537
+120	15	0.541968906705171	0.4572104018	0.1225091579	0.7360294514
+120	20	0.543695758414210	0.4490735236	0.1634493956	0.7407272803
+120	25	0.545950863526249	0.4384085330	0.2044332563	0.7468847155
+120	30	0.548758897036150	0.4250668139	0.2454124394	0.7545875606
+120	35	0.552148141401147	0.4088725675	0.2862956539	0.7639373131
+120	40	0.556148838167921	0.3896283859	0.3269370349	0.7750479465
+120	45	0.560791136277064	0.3671239759	0.3671239759	0.7880408737
+
+125	0	0.527557113335237	0.4321494879	0.000000000	0.6974056710
+125	5	0.527797765631197	0.4312405918	0.03772866304	0.6980420868
+125	10	0.528524083760427	0.4284949161	0.07555521481	0.6999646296
+125	15	0.529749151907052	0.4238552923	0.1135716833	0.7032133293
+125	20	0.531494743778791	0.4172258109	0.1518577761	0.7078553420
+125	25	0.533791182747736	0.4084711197	0.1904732113	0.7139854428
+125	30	0.536676979662555	0.3974159798	0.2294482229	0.7217263352
+125	35	0.540198220146772	0.3838458270	0.2687717416	0.7312282584
+125	40	0.544407167806141	0.3675090485	0.3083767071	0.7426673939
+125	45	0.549360052747731	0.3481224744	0.3481224744	0.7562420192
+
+130	0	0.516352069872154	0.3955486338	0.000000000	0.6680952873
+130	5	0.516582092249686	0.3948390838	0.03454394375	0.6686906704
+130	10	0.517277664865283	0.3926915316	0.06924211212	0.6704926807
+130	15	0.518455405495554	0.3890487212	0.1042452907	0.6735493615
+130	20	0.520143335724352	0.3838134411	0.1396966681	0.6779422831
+130	25	0.522381283068656	0.3768459980	0.1757261748	0.6837886621
+130	30	0.525221289550047	0.3679610730	0.2124424246	0.6912439993
+130	35	0.528727804847013	0.3569244932	0.2499212207	0.7005047894
+130	40	0.532977355276478	0.3434508623	0.2881894919	0.7118105081
+130	45	0.538057157237820	0.3272035350	0.3272035350	0.7254436345
+
+135	0	0.506193826667313	0.3579330874	0.000000000	0.6420669126
+135	5	0.506404413576282	0.3573987417	0.03126833826	0.6426012583
+135	10	0.507042449652714	0.3557784243	0.06273333536	0.6442215757
+135	15	0.508126994689015	0.3530194972	0.09459128918	0.6469805028
+135	20	0.509690588373251	0.3490315679	0.1270371015	0.6509684321
+135	25	0.511780371653196	0.3436824925	0.1602617782	0.6563175075
+135	30	0.514459538811272	0.3367928255	0.1944474285	0.6632071745
+135	35	0.517808937344632	0.3281289341	0.2297583531	0.6718710659
+135	40	0.521928616823929	0.3173954405	0.2663263971	0.6826045595
+135	45	0.526938524534182	0.3042280990	0.3042280990	0.6957719010
+
+
+### +y patch
+# N_rho = 19
+# N_sigma = 10
+# ghosted_gfn=-1
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	45	0.757345489901900	0.4372536225	0.4372536225	1.437253622
+40	45	0.764615077402987	0.3901628923	0.4649780286	1.464978029
+35	45	0.770698365030328	0.3419685802	0.4883817462	1.488381746
+30	45	0.775716023423616	0.2931930980	0.5078253422	1.507825342
+25	45	0.779776862427510	0.2441837036	0.5236536422	1.523653642
+20	45	0.782974033848674	0.1951512429	0.5361736333	1.536173633
+15	45	0.785383389692182	0.1462044491	0.5456424323	1.545642432
+10	45	0.787063320153362	0.09737864600	0.5522617447	1.552261745
+5	45	0.788054984665095	0.04865907398	0.5561757606	1.556175761
+0	45	0.788382836672106	0.000000000	0.5574708500	1.557470850
+
+45	50	0.741695501533819	0.4510401669	0.4510401669	1.378467638
+40	50	0.748764573037744	0.4048691369	0.4825042485	1.404869137
+35	50	0.754782629470964	0.3567737396	0.5095257050	1.427542831
+30	50	0.759821739072541	0.3073340242	0.5323181447	1.446667959
+25	50	0.763952587412957	0.2569894257	0.5511156018	1.462440898
+20	50	0.767239513579581	0.2060601306	0.5661455558	1.475052527
+15	50	0.769737393320464	0.1547702993	0.5776106207	1.484672859
+10	50	0.771489939501277	0.1032706349	0.5856768744	1.491441249
+5	50	0.772528755093662	0.05165914627	0.5904667437	1.495460427
+0	50	0.772872903476355	0.000000000	0.5920549929	1.496793126
+
+45	55	0.726435429309702	0.4603328871	0.4603328871	1.322328558
+40	55	0.733044351381843	0.4152292927	0.4948510013	1.346498401
+35	55	0.738755849560981	0.3675626629	0.5249338844	1.367562663
+30	55	0.743602949753243	0.3179163292	0.5506472348	1.385567345
+25	55	0.747623010411475	0.2667750240	0.5721008853	1.400589352
+20	55	0.750853220444526	0.2145325078	0.5894232210	1.412718583
+15	55	0.753327340067515	0.1615040888	0.6027414650	1.422044117
+10	55	0.755073470669470	0.1079416057	0.6121672662	1.428644134
+5	55	0.756112559893544	0.05404933073	0.6177866771	1.432578888
+0	55	0.756457475142235	0.000000000	0.6196536872	1.433886183
+
+45	60	0.711627906937506	0.4658698215	0.4658698215	1.268970067
+40	60	0.717568032764614	0.4218287423	0.5027159191	1.290243171
+35	60	0.722767322231416	0.3747638136	0.5352181934	1.309008368
+30	60	0.727231244658014	0.3252276997	0.5633108999	1.325227700
+25	60	0.730971641439322	0.2737149493	0.5869836031	1.338895141
+20	60	0.734003459185752	0.2206609485	0.6062609734	1.350024936
+15	60	0.736342131402121	0.1664461805	0.6211856024	1.358641675
+10	60	0.738001526250586	0.1114041246	0.6318041867	1.364772317
+5	60	0.738992560502716	0.05583152208	0.6381572175	1.368440241
+0	60	0.739322124030144	0.000000000	0.6402717410	1.369661062
+
+45	65	0.697290752622285	0.4682606780	0.4682606780	1.218353540
+40	65	0.702403207535547	0.4251834153	0.5067138626	1.236284555
+35	65	0.706924852116654	0.3787825747	0.5409575790	1.252252662
+30	65	0.710844638096703	0.3295638030	0.5708212512	1.266178321
+25	65	0.714157652011022	0.2780084482	0.5961910410	1.278008448
+20	65	0.716863171292208	0.2245683654	0.6169965130	1.287710199
+15	65	0.718962946746103	0.1696649535	0.6331982268	1.295265182
+10	65	0.720459847750262	0.1136915952	0.6447770767	1.300664489
+5	65	0.721356623999573	0.05701860015	0.6517255819	1.303904630
+0	65	0.721655307528419	0.000000000	0.6540418248	1.304984712
+
+45	70	0.683411823824728	0.4679943201	0.4679943201	1.170336002
+40	70	0.687583264131210	0.4257316801	0.5073672593	1.184666580
+35	70	0.691302658451752	0.3799856557	0.5426757567	1.197517822
+30	70	0.694551698255696	0.3312115370	0.5736752101	1.208800701
+25	70	0.697316929468021	0.2798653922	0.6001732703	1.218445206
+20	70	0.699588837450200	0.2263978454	0.6220229680	1.226397845
+15	70	0.701360954880562	0.1712505224	0.6391156503	1.232619073
+10	70	0.702629139259834	0.1148548935	0.6513744691	1.237080918
+5	70	0.703390878019580	0.05763304882	0.6587487623	1.239764941
+0	70	0.703644927516045	0.000000000	0.6612099460	1.240660739
+
+45	75	0.669960079746160	0.4654524812	0.4654524812	1.124717616
+40	75	0.673117268470366	0.4238350295	0.5051069190	1.135342991
+35	75	0.675948858441475	0.3786935960	0.5408305042	1.144915097
+30	75	0.678436251136611	0.3304381251	0.5723356214	1.153356868
+25	75	0.680564194800462	0.2794955038	0.5993800422	1.160603398
+20	75	0.682320479427535	0.2263039542	0.6217650040	1.166601431
+15	75	0.683695621082631	0.1713086940	0.6393327498	1.171308694
+10	75	0.684682618358988	0.1149588401	0.6519639800	1.174693222
+5	75	0.685276645467382	0.05770537129	0.6595754120	1.176732699
+0	75	0.685474965522595	0.000000000	0.6621179725	1.177413976
+
+45	80	0.656893454477817	0.4609249548	0.4609249548	1.081273506
+40	80	0.658997891704585	0.4197835002	0.5002784945	1.088212596
+35	80	0.660892252328253	0.3751788382	0.5358109099	1.094477920
+30	80	0.662562286267470	0.3274849332	0.5672205429	1.100016286
+25	80	0.663995756462839	0.2771007229	0.5942444178	1.104781324
+20	80	0.665182381878736	0.2244456442	0.6166593394	1.108733679
+15	80	0.666113817164706	0.1699554885	0.6342825182	1.111841121
+10	80	0.666783689130181	0.1140786010	0.6469718956	1.114078601
+5	80	0.667187381303025	0.05727235411	0.6546260029	1.115428227
+0	80	0.667322241034249	0.000000000	0.6571841167	1.115879291
+
+45	85	0.644164352267155	0.4546238594	0.4546238594	1.039774434
+40	85	0.645207620575531	0.4138031640	0.4931514073	1.043145158
+35	85	0.646148188652679	0.3696672691	0.5279395735	1.046188728
+30	85	0.646978678217144	0.3225647903	0.5586986055	1.048879794
+25	85	0.647692592722347	0.2728702713	0.5851721851	1.051195932
+20	85	0.648284376830692	0.2209807810	0.6071397060	1.053117841
+15	85	0.648749453574726	0.1673123441	0.6244181688	1.054629511
+10	85	0.649084219080226	0.1122962490	0.6368636755	1.055718352
+5	85	0.649286131280837	0.05637530322	0.6443726644	1.056375303
+0	85	0.649353600708710	0.000000000	0.6468826142	1.056594895
+
+45	90	0.631723570673163	0.4466960207	0.4466960207	1.000000000
+40	90	0.631723576974829	0.4060640880	0.4839283357	1.000000000
+35	90	0.631723561090523	0.3623417489	0.5174776465	1.000000000
+30	90	0.631723544708018	0.3158617724	0.5470886379	1.000000000
+25	90	0.631723525842061	0.2669778984	0.5725359507	1.000000000
+20	90	0.631723499656665	0.2160621619	0.5936259110	1.000000000
+15	90	0.631723455713198	0.1635020616	0.6101980009	1.000000000
+10	90	0.631723428577027	0.1096976222	0.6221261302	1.000000000
+5	90	0.631723387728189	0.05505832107	0.6293194895	1.000000000
+0	90	0.631723370380539	0.000000000	0.6317233704	1.000000000
+
+45	95	0.619523069000359	0.4372330876	0.4372330876	0.9617470615
+40	95	0.618521312337959	0.3966879309	0.4727542668	0.9586393610
+35	95	0.617620951055870	0.3533465764	0.5046312088	0.9558504900
+30	95	0.616828126384023	0.3075326003	0.5326620887	0.9533981058
+25	95	0.616148188172037	0.2595807411	0.5566726958	0.9512974498
+20	95	0.615585677085306	0.2098347709	0.5765162949	0.9495613599
+15	95	0.615144310515173	0.1586455849	0.5920733834	0.9482002910
+10	95	0.614826962035002	0.1063694966	0.6032513922	0.9472223419
+5	95	0.614635716976021	0.05336672577	0.6099844668	0.9466332742
+0	95	0.614571834607582	0.000000000	0.6122332032	0.9464365353
+
+45	100	0.607518114661439	0.4262795703	0.4262795703	0.9248354104
+40	100	0.605578060671122	0.3857549184	0.4597248099	0.9189381123
+35	100	0.603842241061103	0.3427923836	0.4895582593	0.9136776703
+30	100	0.602320197258838	0.2977090511	0.5156472024	0.9090774857
+25	100	0.601019846403175	0.2508194251	0.5378839929	0.9051565396
+20	100	0.599947623733881	0.2024341513	0.5561832595	0.9019298851
+15	100	0.599108626081841	0.1528594613	0.5704792758	0.8994091117
+10	100	0.598506668264744	0.1023972309	0.5807235540	0.8976027691
+5	100	0.598144447343882	0.05134560628	0.5868829653	0.8965166987
+0	100	0.598023539185530	0.000000000	0.5889382179	0.8961543022
+
+45	105	0.595669306244036	0.4138392196	0.4138392196	0.8891121153
+40	105	0.592875383091923	0.3733099227	0.4448934415	0.8807911616
+35	105	0.590391791966972	0.3307611041	0.4723758115	0.8734272828
+30	105	0.588227181516861	0.2865010333	0.4962343461	0.8670344077
+25	105	0.586387920489471	0.2408189977	0.5164380072	0.8616208530
+20	105	0.584878520925085	0.1939855625	0.5329709526	0.8571908637
+15	105	0.583702059014920	0.1462540264	0.5458274574	0.8537459736
+10	105	0.582860540320222	0.09786281975	0.5550076305	0.8512861536
+5	105	0.582355201363824	0.04903862307	0.5605140265	0.8498107192
+0	105	0.582186690224506	0.000000000	0.5623491598	0.8493189968
+
+45	110	0.583944604328845	0.3998800555	0.3998800555	0.8544555625
+40	110	0.580401941405293	0.3593681036	0.4282782285	0.8441194728
+35	110	0.577279213540307	0.3173108302	0.4531668296	0.8350607629
+30	110	0.574578742651724	0.2739999182	0.4745817795	0.8272663585
+25	110	0.572300204332666	0.2296904239	0.4925727037	0.8207181977
+20	110	0.570441624615623	0.1846037956	0.5071947599	0.8153962044
+15	110	0.569000227444913	0.1389321511	0.5185018468	0.8112807613
+10	110	0.567973156533273	0.09284342583	0.5265412330	0.8083546641
+5	110	0.567357989529807	0.04648705539	0.5313494745	0.8066046073
+0	110	0.567153120802165	0.000000000	0.5329496025	0.8060222083
+
+45	115	0.572321721516154	0.3843386082	0.3843386082	0.8207799637
+40	115	0.568156075128795	0.3439200417	0.4098679452	0.8088754383
+35	115	0.564522030243012	0.3024806773	0.4319871764	0.7985610714
+30	115	0.561409081976457	0.2602820675	0.4508217653	0.7897783584
+25	115	0.558804642053163	0.2175323767	0.4664996872	0.7824676233
+20	115	0.556695616498438	0.1743934263	0.4791420008	0.7765724157
+15	115	0.555069695365740	0.1309884946	0.4888557171	0.7720428354
+10	115	0.553916383287529	0.08741033578	0.4957286481	0.7688379350
+5	115	0.553227715217227	0.04372909160	0.4998258041	0.7669273998
+0	115	0.552998720661859	0.000000000	0.5011870468	0.7662926419
+
+45	120	0.560791136277069	0.3671239759	0.3671239759	0.7880408737
+40	120	0.556148838167922	0.3269370349	0.3896283859	0.7750479465
+35	120	0.552148141401149	0.2862956539	0.4088725675	0.7639373131
+30	120	0.548758897036154	0.2454124394	0.4250668139	0.7545875606
+25	120	0.545950863526253	0.2044332563	0.4384085330	0.7468847155
+20	120	0.543695758414214	0.1634493956	0.4490735236	0.7407272803
+15	120	0.541968906705174	0.1225091579	0.4572104018	0.7360294514
+10	120	0.540750246479175	0.08162829712	0.4629370774	0.7327231537
+5	120	0.540025048090087	0.04079935578	0.4663387705	0.7307591853
+0	120	0.539784321692910	0.000000000	0.4674669352	0.7301078392
+
+45	125	0.549360052747735	0.3481224744	0.3481224744	0.7562420192
+40	125	0.544407167806143	0.3083767071	0.3675090485	0.7426673939
+35	125	0.540198220146775	0.2687717416	0.3838458270	0.7312282584
+30	125	0.536676979662559	0.2294482229	0.3974159798	0.7217263352
+25	125	0.533791182747740	0.1904732113	0.4084711197	0.7139854428
+20	125	0.531494743778792	0.1518577761	0.4172258109	0.7078553420
+15	125	0.529749151907051	0.1135716833	0.4238552923	0.7032133293
+10	125	0.528524083760426	0.07555521481	0.4284949161	0.6999646296
+5	125	0.527797765631199	0.03772866304	0.4312405918	0.6980420868
+0	125	0.527557113335240	0.000000000	0.4321494879	0.6974056710
+
+45	130	0.538057157237822	0.3272035350	0.3272035350	0.7254436345
+40	130	0.532977355276480	0.2881894919	0.3434508623	0.7118105081
+35	130	0.528727804847016	0.2499212207	0.3569244932	0.7005047894
+30	130	0.525221289550050	0.2124424246	0.3679610730	0.6912439993
+25	130	0.522381283068657	0.1757261748	0.3768459980	0.6837886621
+20	130	0.520143335724350	0.1396966681	0.3838134411	0.6779422831
+15	130	0.518455405495551	0.1042452907	0.3890487212	0.6735493615
+10	130	0.517277664865281	0.06924211212	0.3926915316	0.6704926807
+5	130	0.516582092249686	0.03454394375	0.3948390838	0.6686906704
+0	130	0.516352069872155	0.000000000	0.3955486338	0.6680952873
+
+45	135	0.526938524534184	0.3042280990	0.3042280990	0.6957719010
+40	135	0.521928616823930	0.2663263971	0.3173954405	0.6826045595
+35	135	0.517808937344634	0.2297583531	0.3281289341	0.6718710659
+30	135	0.514459538811272	0.1944474285	0.3367928255	0.6632071745
+25	135	0.511780371653194	0.1602617782	0.3436824925	0.6563175075
+20	135	0.509690588373248	0.1270371015	0.3490315679	0.6509684321
+15	135	0.508126994689012	0.09459128918	0.3530194972	0.6469805028
+10	135	0.507042449652711	0.06273333536	0.3557784243	0.6442215757
+5	135	0.506404413576281	0.03126833826	0.3573987417	0.6426012583
+0	135	0.506193826667312	0.000000000	0.3579330874	0.6420669126
+
+
+### -z patch
+# N_rho = 10
+# N_sigma = 10
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = 180 - drho = 180 - dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+135	45	0.526938568911584	0.3042281246	0.3042281246	0.6957718754
+140	45	0.521928667147711	0.2663264227	0.3173954711	0.6826045289
+145	45	0.517808973757666	0.2297583693	0.3281289571	0.6718710429
+150	45	0.514459562616494	0.1944474375	0.3367928411	0.6632071589
+155	45	0.511780385964118	0.1602617827	0.3436825021	0.6563174979
+160	45	0.509690595720473	0.1270371033	0.3490315729	0.6509684271
+165	45	0.508126998140241	0.09459128982	0.3530194996	0.6469805004
+170	45	0.507042451084253	0.06273333553	0.3557784253	0.6442215747
+175	45	0.506404414128971	0.03126833829	0.3573987421	0.6426012579
+180	45	0.506193827001395	4.383416101e-17	0.3579330877	0.6420669123
+
+135	40	0.521928667147712	0.3173954711	0.2663264227	0.6826045289
+140	40	0.516094229548639	0.2790605122	0.2790605122	0.6674286320
+145	40	0.511224096070916	0.2416474961	0.2895803227	0.6548916101
+150	40	0.507213009870998	0.2051584042	0.2981696735	0.6446552204
+155	40	0.503969369007678	0.1695325087	0.3050661147	0.6364363618
+160	40	0.501416546042881	0.1346671504	0.3104626301	0.6300050452
+165	40	0.499493007924457	0.1004325411	0.3145107749	0.6251806540
+170	40	0.498151837212729	0.06668195382	0.3173241136	0.6218278476
+175	40	0.497360116054381	0.03325856651	0.3189813373	0.6198528453
+180	40	0.497098359024173	4.663448099e-17	0.3195286660	0.6192005644
+
+135	35	0.517808973757667	0.3281289571	0.2297583693	0.6718710429
+140	35	0.511224096070916	0.2895803227	0.2416474961	0.6548916101
+145	35	0.505654512228904	0.2515847680	0.2515847680	0.6406997151
+150	35	0.501013678631811	0.2142009115	0.2597818013	0.6289931383
+155	35	0.497223201537385	0.1774246240	0.2664207997	0.6195116659
+160	35	0.494215222276499	0.1412063345	0.2716533677	0.6120387844
+165	35	0.491933736345380	0.1054645247	0.2756009619	0.6064010356
+170	35	0.490335151318638	0.07009591204	0.2783560735	0.6024663284
+175	35	0.489388389141943	0.03498303864	0.2799835588	0.6001420386
+180	35	0.489074863102279	4.906261739e-17	0.2805218171	0.5993733261
+
+135	30	0.514459562616496	0.3367928411	0.1944474375	0.6632071589
+140	30	0.507213009870999	0.2981696735	0.2051584042	0.6446552204
+145	30	0.501013678631811	0.2597818013	0.2142009115	0.6289931383
+150	30	0.495795298692308	0.2217263982	0.2217263982	0.6159586130
+155	30	0.491495197897123	0.1840421373	0.2278683947	0.6053203629
+160	30	0.488057316682977	0.1467230012	0.2327403625	0.5968818672
+165	30	0.485434114687618	0.1097297721	0.2364347991	0.5904829154
+170	30	0.483587808608437	0.07299941069	0.2390231446	0.5859997693
+175	30	0.482491044372331	0.03645261243	0.2405560303	0.5833447334
+180	30	0.482127297804471	5.113322740e-17	0.2410636489	0.5824655122
+
+135	25	0.511780385964119	0.3436825021	0.1602617827	0.6563174979
+140	25	0.503969369007680	0.3050661147	0.1695325087	0.6364363618
+145	25	0.497223201537387	0.2664207997	0.1774246240	0.6195116659
+150	25	0.491495197897124	0.2278683947	0.1840421373	0.6053203629
+155	25	0.486739074258395	0.1894785757	0.1894785757	0.5936618832
+160	25	0.482911916820506	0.1512795525	0.1938147882	0.5843628454
+165	25	0.479976304310402	0.1132675303	0.1971176562	0.5772798220
+170	25	0.477901870887848	0.07541492590	0.1994394581	0.5723007018
+175	25	0.476666299561735	0.03767740426	0.2008175853	0.5693452986
+180	25	0.476255967748112	5.285997993e-17	0.2012744692	0.5683655078
+
+135	20	0.509690595720475	0.3490315729	0.1270371033	0.6509684271
+140	20	0.501416546042884	0.3104626301	0.1346671504	0.6300050452
+145	20	0.494215222276501	0.2716533677	0.1412063345	0.6120387844
+150	20	0.488057316682980	0.2327403625	0.1467230012	0.5968818672
+155	20	0.482911916820507	0.1938147882	0.1512795525	0.5843628454
+160	20	0.478749056294757	0.1549306521	0.1549306521	0.5743315316
+165	20	0.475541801804128	0.1161125115	0.1577220578	0.5666622075
+170	20	0.473267774757798	0.07736246166	0.1596898738	0.5612556777
+175	20	0.471910246328712	0.03866644722	0.1608601079	0.5580404859
+180	20	0.471458896204563	5.425509187e-17	0.1612484393	0.5569735542
+
+135	15	0.508126998140243	0.3530194996	0.09459128982	0.6469805004
+140	15	0.499493007924460	0.3145107749	0.1004325411	0.6251806540
+145	15	0.491933736345383	0.2756009619	0.1054645247	0.6064010356
+150	15	0.485434114687620	0.2364347991	0.1097297721	0.5904829154
+155	15	0.479976304310405	0.1971176562	0.1132675303	0.5772798220
+160	15	0.475541801804129	0.1577220578	0.1161125115	0.5666622075
+165	15	0.472113256970270	0.1182940229	0.1182940229	0.5585206962
+170	15	0.469675752429430	0.07885898997	0.1198353343	0.5527684439
+175	15	0.468217965359857	0.03942742207	0.1207533122	0.5493425036
+180	15	0.467732834494599	5.532895757e-17	0.1210581656	0.5482047754
+
+135	10	0.507042451084256	0.3557784253	0.06273333553	0.6442215747
+140	10	0.498151837212732	0.3173241136	0.06668195382	0.6218278476
+145	10	0.490335151318640	0.2783560735	0.07009591204	0.6024663284
+150	10	0.483587808608439	0.2390231446	0.07299941069	0.5859997693
+155	10	0.477901870887851	0.1994394581	0.07541492590	0.5723007018
+160	10	0.473267774757801	0.1596898738	0.07736246166	0.5612556777
+165	10	0.469675752429431	0.1198353343	0.07885898997	0.5527684439
+170	10	0.467116990831690	0.07991805088	0.07991805088	0.5467622110
+175	10	0.465584647647193	0.03996647652	0.08054950035	0.5431810831
+180	10	0.465074364608535	5.608990599e-17	0.08075931589	0.5419911600
+
+135	5	0.506404414128974	0.3573987421	0.03126833829	0.6426012579
+140	5	0.497360116054383	0.3189813373	0.03325856651	0.6198528453
+145	5	0.489388389141944	0.2799835588	0.03498303864	0.6001420386
+150	5	0.482491044372333	0.2405560303	0.03645261243	0.5833447334
+155	5	0.476666299561738	0.2008175853	0.03767740426	0.5693452986
+160	5	0.471910246328715	0.1608601079	0.03866644722	0.5580404859
+165	5	0.468217965359859	0.1207533122	0.03942742207	0.5493425036
+170	5	0.465584647647194	0.08054950035	0.03996647652	0.5431810831
+175	5	0.464006388978063	0.04028809429	0.04028809429	0.5395049751
+180	5	0.463480604485610	5.654401492e-17	0.04039499633	0.5382830791
+
+135	0	0.506193827001399	0.3579330877	4.383416101e-17	0.6420669123
+140	0	0.497098359024174	0.3195286660	4.663448099e-17	0.6192005644
+145	0	0.489074863102279	0.2805218171	4.906261739e-17	0.5993733261
+150	0	0.482127297804472	0.2410636489	5.113322740e-17	0.5824655122
+155	0	0.476255967748114	0.2012744692	5.285997993e-17	0.5683655078
+160	0	0.471458896204566	0.1612484393	5.425509187e-17	0.5569735542
+165	0	0.467732834494601	0.1210581656	5.532895757e-17	0.5482047754
+170	0	0.465074364608537	0.08075931589	5.608990599e-17	0.5419911600
+175	0	0.463480604485612	0.04039499633	5.654401492e-17	0.5382830791
+180	0	0.462949586763618	5.669497296e-17	5.669497296e-17	0.5370504132
+
+
diff --git a/test/misner1.2-025-init-mask/h.t0.ah2.gp b/test/misner1.2-025-init-mask/h.t0.ah2.gp
new file mode 100644
index 0000000..87fbbca
--- /dev/null
+++ b/test/misner1.2-025-init-mask/h.t0.ah2.gp
@@ -0,0 +1,845 @@
+# N_patches = 3
+
+### +z patch
+# N_rho = 16
+# N_sigma = 16
+# ghosted_gfn=-1
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+0	0	1.93684729839377	0.000000000	0.000000000	1.936847298
+3	0	1.93277963294637	0.1011538703	0.000000000	1.930130826
+6	0	1.92056873611684	0.2007540986	0.000000000	1.910047660
+9	0	1.90019000018873	0.2972552062	0.000000000	1.876795508
+12	0	1.87159850470054	0.3891272096	0.000000000	1.830699587
+15	0	1.83472297531187	0.4748612485	0.000000000	1.772206306
+18	0	1.78945592165328	0.5529722905	0.000000000	1.701873715
+21	0	1.73563885505988	0.6219973376	0.000000000	1.620358463
+24	0	1.67304069776031	0.6804869571	0.000000000	1.528398730
+27	0	1.60132565333811	0.7269866336	0.000000000	1.426791604
+30	0	1.52000692272622	0.7600034614	0.000000000	1.316364609
+33	0	1.42838234941703	0.7779527844	0.000000000	1.197942236
+36	0	1.32545825997317	0.7790848177	0.000000000	1.072318258
+39	0	1.20992818800746	0.7614324804	0.000000000	0.9402908050
+42	0	1.08053734870585	0.7230206113	0.000000000	0.8029957394
+45	0	0.938273177410541	0.6634593264	0.000000000	0.6634593264
+
+0	3	1.93277963294637	0.000000000	0.1011538703	1.930130826
+3	3	1.92872552381501	0.1008037357	0.1008037357	1.923449859
+6	3	1.91655494905433	0.2000629858	0.09975674886	1.903472160
+9	3	1.89624248841642	0.2962410762	0.09802311960	1.870392544
+12	3	1.86774180979787	0.3878161310	0.09561964136	1.824531447
+15	3	1.83097969898215	0.4732863859	0.09256937192	1.766328839
+18	3	1.78584621589627	0.5511726155	0.08890114423	1.696334885
+21	3	1.73217996813738	0.6200161175	0.08464889876	1.615197208
+24	3	1.66974648806975	0.6783700477	0.07985080230	1.523644073
+27	3	1.59820625808587	0.7247807010	0.07454808596	1.422462218
+30	3	1.51706844109747	0.7577541612	0.06878357031	1.312468707
+33	3	1.42562685946020	0.7757031259	0.06259994284	1.194478066
+36	3	1.32288468562843	0.7768741456	0.05603835589	1.069275529
+39	3	1.20753613895756	0.7592976108	0.04914038801	0.9376544605
+42	3	1.07834073810856	0.7210041769	0.04196585744	0.8007562621
+45	3	0.936352731565143	0.6616472060	0.03467546073	0.6616472060
+
+0	6	1.92056873611685	0.000000000	0.2007540986	1.910047660
+3	6	1.91655494905433	0.09975674886	0.2000629858	1.903472160
+6	6	1.90450455570855	0.1979962001	0.1979962001	1.883808008
+9	6	1.88438957684007	0.2932078227	0.1945733048	1.851241335
+12	6	1.85615956757203	0.3838938480	0.1898265055	1.806078556
+15	6	1.81973553020060	0.4685736322	0.1838000437	1.748740603
+18	6	1.77500032413135	0.5457852953	0.1765493036	1.679754418
+21	6	1.72178387290061	0.6140829891	0.1681395418	1.599740880
+24	6	1.65984171835457	0.6720277232	0.1586442254	1.509398979
+27	6	1.58882325655122	0.7181683516	0.1481428169	1.409484752
+30	6	1.50822570767852	0.7510081543	0.1367179370	1.300784280
+33	6	1.41733090763928	0.7689521242	0.1244520788	1.184082435
+36	6	1.31513297862429	0.7702362689	0.1114251278	1.060139275
+39	6	1.20032896320393	0.7528841066	0.09771902758	0.9297344425
+42	6	1.07172372329458	0.7149455881	0.08345565502	0.7940275176
+45	6	0.930579457315630	0.6562092707	0.06897037357	0.6562092707
+
+0	9	1.90019000018873	0.000000000	0.2972552062	1.876795508
+3	9	1.89624248841642	0.09802311960	0.2962410762	1.870392544
+6	9	1.88438957684007	0.1945733048	0.2932078227	1.851241335
+9	9	1.86459921399960	0.2881827268	0.2881827268	1.819514128
+12	9	1.83681426440602	0.3773930611	0.2812107436	1.775494758
+15	9	1.80094643540510	0.4607583499	0.2723536978	1.719573572
+18	9	1.75686678748713	0.5368453020	0.2616890995	1.652239948
+21	9	1.70439117537207	0.6042294669	0.2493084457	1.574071577
+24	9	1.64325889163142	0.6614851783	0.2353149363	1.485720036
+27	9	1.57310115146338	0.7071659821	0.2198204003	1.387891386
+30	9	1.49339570931659	0.7397711729	0.2029413502	1.281321257
+33	9	1.40340499947345	0.7576938326	0.1847944417	1.166746186
+36	9	1.30210921918213	0.7591537878	0.1654936128	1.044885548
+39	9	1.18821291103471	0.7421656165	0.1451590560	0.9164982095
+42	9	1.06060561486446	0.7048182321	0.1239801642	0.7827799492
+45	9	0.920920451762803	0.6471432443	0.1024974206	0.6471432443
+
+0	12	1.87159850470055	0.000000000	0.3891272096	1.830699587
+3	12	1.86774180979788	0.09561964136	0.3878161310	1.824531447
+6	12	1.85615956757203	0.1898265055	0.3838938480	1.806078556
+9	12	1.83681426440602	0.2812107436	0.3773930611	1.775494758
+12	12	1.80963978331709	0.3683677317	0.3683677317	1.733033922
+15	12	1.77453538946721	0.4498989609	0.3568921980	1.679045780
+18	12	1.73135628363373	0.5244105366	0.3430598448	1.613969675
+21	12	1.67989937502816	0.5905078727	0.3269812006	1.538325602
+24	12	1.61988192580287	0.6467843692	0.3087812313	1.452701478
+27	12	1.55091049607481	0.6918010685	0.2885957053	1.357736045
+30	12	1.47243640228218	0.7240530493	0.2665664759	1.254096669
+33	12	1.38369643770333	0.7419187972	0.2428362560	1.142454762
+36	12	1.28365375237456	0.7435984119	0.2175464142	1.023475410
+39	12	1.17102993182310	0.7270996313	0.1908531056	0.8978932673
+42	12	1.04485547233192	0.6905823395	0.1630243762	0.7669693887
+45	12	0.907331121379211	0.6344538073	0.1348573198	0.6344538073
+
+0	15	1.83472297531188	0.000000000	0.4748612485	1.772206306
+3	15	1.83097969898215	0.09256937192	0.4732863859	1.766328839
+6	15	1.81973553020060	0.1838000437	0.4685736322	1.748740603
+9	15	1.80094643540510	0.2723536978	0.4607583499	1.719573572
+12	15	1.77453538946721	0.3568921980	0.4498989609	1.679045780
+15	15	1.74038654643836	0.4360761385	0.4360761385	1.627458305
+18	15	1.69833586778477	0.5085611906	0.4193915048	1.565190404
+21	15	1.64815700460016	0.5729908990	0.3999657031	1.492692325
+24	15	1.58954022240662	0.6279838343	0.3779355797	1.410474785
+27	15	1.52206174836567	0.6721121765	0.3534502842	1.319094418
+30	15	1.44514060032060	0.7038679753	0.3266662642	1.219135095
+33	15	1.35798315740586	0.7216144281	0.2977421349	1.111188775
+36	15	1.25953602745270	0.7235318972	0.2668388705	0.9958562222
+39	15	1.14855605524381	0.7076303894	0.2341476043	0.8738507558
+42	15	1.02430017969469	0.6721936424	0.2000365778	0.7465466716
+45	15	0.889772502240671	0.6181664123	0.1656371910	0.6181664123
+
+0	18	1.78945592165328	0.000000000	0.5529722905	1.701873715
+3	18	1.78584621589627	0.08890114423	0.5511726155	1.696334885
+6	18	1.77500032413135	0.1765493036	0.5457852953	1.679754418
+9	18	1.75686678748713	0.2616890995	0.5368453020	1.652239948
+12	18	1.73135628363373	0.3430598448	0.5244105366	1.613969675
+15	18	1.69833586778477	0.4193915048	0.5085611906	1.565190404
+18	18	1.65761953881833	0.4893985910	0.4893985910	1.506213987
+21	18	1.60895429063005	0.5517707773	0.4670434763	1.437412018
+24	18	1.55199930884133	0.6051582257	0.4416333299	1.359207629
+27	18	1.48629600065062	0.6481489189	0.4133186086	1.272063877
+30	18	1.41122679159269	0.6792348370	0.3822580307	1.176469248
+33	18	1.32596557370708	0.6967660862	0.3486146874	1.072925684
+36	18	1.22944872980498	0.6989084453	0.3125613587	0.9619649481
+39	18	1.12050211595786	0.6836949759	0.2743274191	0.8442929817
+42	18	0.998742456874516	0.6496196766	0.2344216792	0.7214757427
+45	18	0.868239258728531	0.5983486113	0.1944152490	0.5983486113
+
+0	21	1.73563885505988	0.000000000	0.6219973376	1.620358463
+3	21	1.73217996813739	0.08464889876	0.6200161175	1.615197208
+6	21	1.72178387290061	0.1681395418	0.6140829891	1.599740880
+9	21	1.70439117537208	0.2493084457	0.6042294669	1.574071577
+12	21	1.67989937502816	0.3269812006	0.5905078727	1.538325602
+15	21	1.64815700460016	0.3999657031	0.5729908990	1.492692325
+18	21	1.60895429063006	0.4670434763	0.5517707773	1.437412018
+21	21	1.56200920935960	0.5269578814	0.5269578814	1.372772214
+24	21	1.50694700370730	0.5783973920	0.4986784636	1.299101812
+27	21	1.44327136740337	0.6199716070	0.4670714739	1.216762789
+30	21	1.37032627038196	0.6501776374	0.4322849138	1.126140702
+33	21	1.28725569556510	0.6673587963	0.3944749693	1.027642429
+36	21	1.19300213186514	0.6696793396	0.3538207381	0.9217345356
+39	21	1.08652299280236	0.6552363913	0.3106034137	0.8091495565
+42	21	0.967997438055734	0.6228687402	0.2655440182	0.6917658180
+45	21	0.842801243803528	0.5751400198	0.2207755687	0.5751400198
+
+0	24	1.67304069776032	0.000000000	0.6804869571	1.528398730
+3	24	1.66974648806975	0.07985080230	0.6783700477	1.523644073
+6	24	1.65984171835457	0.1586442254	0.6720277232	1.509398979
+9	24	1.64325889163143	0.2353149363	0.6614851783	1.485720036
+12	24	1.61988192580287	0.3087812313	0.6467843692	1.452701478
+15	24	1.58954022240663	0.3779355797	0.6279838343	1.410474785
+18	24	1.55199930884133	0.4416333299	0.6051582257	1.359207629
+21	24	1.50694700370730	0.4986784636	0.5783973920	1.299101812
+24	24	1.45397346596152	0.5478047695	0.5478047695	1.230389657
+27	24	1.39254413221871	0.5876506319	0.5134952896	1.153329304
+30	24	1.32196665937157	0.6167264796	0.4755939927	1.068201597
+33	24	1.24136581673142	0.6333811864	0.4342411081	0.9753214976
+36	24	1.14972514747399	0.6358036585	0.3896234784	0.8751086605
+39	24	1.04624898341028	0.6222313392	0.3421100315	0.7683917114
+42	24	0.931961603987716	0.5920388986	0.2927493519	0.6575258100
+45	24	0.813660234157721	0.5487906028	0.2443373186	0.5487906028
+
+0	27	1.60132565333812	0.000000000	0.7269866336	1.426791604
+3	27	1.59820625808588	0.07454808596	0.7247807010	1.422462218
+6	27	1.58882325655122	0.1481428169	0.7181683516	1.409484752
+9	27	1.57310115146339	0.2198204003	0.7071659821	1.387891386
+12	27	1.55091049607482	0.2885957053	0.6918010685	1.357736045
+15	27	1.52206174836567	0.3534502842	0.6721121765	1.319094418
+18	27	1.48629600065062	0.4133186086	0.6481489189	1.272063877
+21	27	1.44327136740337	0.4670714739	0.6199716070	1.216762789
+24	27	1.39254413221872	0.5134952896	0.5876506319	1.153329304
+27	27	1.33354479596592	0.5512662282	0.5512662282	1.081920891
+30	27	1.26555434029040	0.5789208138	0.5109114928	1.002720263
+33	27	1.18770375253271	0.5948355158	0.4667081764	0.9159663700
+36	27	1.09909007658420	0.5972741296	0.4188693127	0.8220773135
+39	27	0.999367588565548	0.5847477258	0.3679300105	0.7221033039
+42	27	0.890731453500958	0.5573949229	0.3154216159	0.6190497770
+45	27	0.781218160419923	0.5197027228	0.2648017635	0.5197027228
+
+0	30	1.52000692272623	0.000000000	0.7600034614	1.316364609
+3	30	1.51706844109748	0.06878357031	0.7577541612	1.312468707
+6	30	1.50822570767853	0.1367179370	0.7510081543	1.300784280
+9	30	1.49339570931660	0.2029413502	0.7397711729	1.281321257
+12	30	1.47243640228219	0.2665664759	0.7240530493	1.254096669
+15	30	1.44514060032061	0.3266662642	0.7038679753	1.219135095
+18	30	1.41122679159270	0.3822580307	0.6792348370	1.176469248
+21	30	1.37032627038196	0.4322849138	0.6501776374	1.126140702
+24	30	1.32196665937158	0.4755939927	0.6167264796	1.068201597
+27	30	1.26555434029040	0.5109114928	0.5789208138	1.002720263
+30	30	1.20036706501466	0.5368204711	0.5368204711	0.9298003304
+33	30	1.12559871233211	0.5517654795	0.4905423827	0.8496443301
+36	30	1.04060645889610	0.5541806297	0.4403821159	0.7627641994
+39	30	0.945806735199348	0.5430566082	0.3871820956	0.6706190614
+42	30	0.844782662303204	0.5194740808	0.3330932399	0.5769344152
+45	30	0.746140861480309	0.4884638538	0.2820147375	0.4884638538
+
+0	33	1.42838234941704	0.000000000	0.7779527844	1.197942236
+3	33	1.42562685946021	0.06259994284	0.7757031259	1.194478066
+6	33	1.41733090763929	0.1244520788	0.7689521242	1.184082435
+9	33	1.40340499947346	0.1847944417	0.7576938326	1.166746186
+12	33	1.38369643770334	0.2428362560	0.7419187972	1.142454762
+15	33	1.35798315740587	0.2977421349	0.7216144281	1.111188775
+18	33	1.32596557370709	0.3486146874	0.6967660862	1.072925684
+21	33	1.28725569556511	0.3944749693	0.6673587963	1.027642429
+24	33	1.24136581673142	0.4342411081	0.6333811864	0.9753214976
+27	33	1.18770375253271	0.4667081764	0.5948355158	0.9159663700
+30	33	1.12559871233211	0.4905423827	0.5517654795	0.8496443301
+33	33	1.05443281688578	0.5043352974	0.5043352974	0.7766082545
+36	33	0.974089835351112	0.5068598989	0.4530480383	0.6976328011
+39	33	0.886082931364081	0.4978231774	0.3992300888	0.6147604262
+42	33	0.795183110839353	0.4791957619	0.3456152473	0.5322008102
+45	33	0.709381543599367	0.4558447991	0.2960290739	0.4558447991
+
+0	36	1.32545825997317	0.000000000	0.7790848177	1.072318258
+3	36	1.32288468562843	0.05603835589	0.7768741456	1.069275529
+6	36	1.31513297862430	0.1114251278	0.7702362689	1.060139275
+9	36	1.30210921918213	0.1654936128	0.7591537878	1.044885548
+12	36	1.28365375237457	0.2175464142	0.7435984119	1.023475410
+15	36	1.25953602745271	0.2668388705	0.7235318972	0.9958562222
+18	36	1.22944872980499	0.3125613587	0.6989084453	0.9619649481
+21	36	1.19300213186515	0.3538207381	0.6696793396	0.9217345356
+24	36	1.14972514747400	0.3896234784	0.6358036585	0.8751086605
+27	36	1.09909007658420	0.4188693127	0.5972741296	0.8220773135
+30	36	1.04060645889611	0.4403821159	0.5541806297	0.7627641994
+33	36	0.974089835351112	0.4530480383	0.5068598989	0.6976328011
+36	36	0.900277694008040	0.4561993850	0.4561993850	0.6279045856
+39	36	0.821801138055317	0.4503477427	0.4040543825	0.5561331469
+42	36	0.743721207927512	0.4378954380	0.3533409923	0.4863321536
+45	36	0.672113945303939	0.4227329011	0.3071334306	0.4227329011
+
+0	39	1.20992818800747	0.000000000	0.7614324804	0.9402908050
+3	39	1.20753613895756	0.04914038801	0.7592976108	0.9376544605
+6	39	1.20032896320394	0.09771902758	0.7528841066	0.9297344425
+9	39	1.18821291103472	0.1451590560	0.7421656165	0.9164982095
+12	39	1.17102993182311	0.1908531056	0.7270996313	0.8978932673
+15	39	1.14855605524382	0.2341476043	0.7076303894	0.8738507558
+18	39	1.12050211595786	0.2743274191	0.6836949759	0.8442929817
+21	39	1.08652299280236	0.3106034137	0.6552363913	0.8091495565
+24	39	1.04624898341028	0.3421100315	0.6222313392	0.7683917114
+27	39	0.999367588565548	0.3679300105	0.5847477258	0.7221033039
+30	39	0.945806735199347	0.3871820956	0.5430566082	0.6706190614
+33	39	0.886082931364080	0.3992300888	0.4978231774	0.6147604262
+36	39	0.821801138055317	0.4040543825	0.4503477427	0.5561331469
+39	39	0.756005552838451	0.4026680875	0.4026680875	0.4972536763
+42	39	0.692736540576127	0.3971613183	0.3571895264	0.4410923305
+45	39	0.635551456285669	0.3899932662	0.3158103200	0.3899932662
+
+0	42	1.08053734870586	0.000000000	0.7230206113	0.8029957394
+3	42	1.07834073810857	0.04196585744	0.7210041769	0.8007562621
+6	42	1.07172372329459	0.08345565502	0.7149455881	0.7940275176
+9	42	1.06060561486447	0.1239801642	0.7048182321	0.7827799492
+12	42	1.04485547233193	0.1630243762	0.6905823395	0.7669693887
+15	42	1.02430017969469	0.2000365778	0.6721936424	0.7465466716
+18	42	0.998742456874519	0.2344216792	0.6496196766	0.7214757427
+21	42	0.967997438055736	0.2655440182	0.6228687402	0.6917658180
+24	42	0.931961603987717	0.2927493519	0.5920388986	0.6575258100
+27	42	0.890731453500959	0.3154216159	0.5573949229	0.6190497770
+30	42	0.844782662303205	0.3330932399	0.5194740808	0.5769344152
+33	42	0.795183110839355	0.3456152473	0.4791957619	0.5322008102
+36	42	0.743721207927514	0.3533409923	0.4378954380	0.4863321536
+39	42	0.692736540576128	0.3571895264	0.3971613183	0.4410923305
+42	42	0.644539512165942	0.3584394391	0.3584394391	0.3980873268
+45	42	0.600712048927379	0.3583083887	0.3226223223	0.3583083887
+
+0	45	0.938273177410550	0.000000000	0.6634593264	0.6634593264
+3	45	0.936352731565153	0.03467546073	0.6616472060	0.6616472060
+6	45	0.930579457315639	0.06897037357	0.6562092707	0.6562092707
+9	45	0.920920451762809	0.1024974206	0.6471432443	0.6471432443
+12	45	0.907331121379215	0.1348573198	0.6344538073	0.6344538073
+15	45	0.889772502240674	0.1656371910	0.6181664123	0.6181664123
+18	45	0.868239258728532	0.1944152490	0.5983486113	0.5983486113
+21	45	0.842801243803529	0.2207755687	0.5751400198	0.5751400198
+24	45	0.813660234157723	0.2443373186	0.5487906028	0.5487906028
+27	45	0.781218160419926	0.2648017635	0.5197027228	0.5197027228
+30	45	0.746140861480313	0.2820147375	0.4884638538	0.4884638538
+33	45	0.709381543599372	0.2960290739	0.4558447991	0.4558447991
+36	45	0.672113945303944	0.3071334306	0.4227329011	0.4227329011
+39	45	0.635551456285669	0.3158103200	0.3899932662	0.3899932662
+42	45	0.600712048927376	0.3226223223	0.3583083887	0.3583083887
+45	45	0.568254552376758	0.3280819188	0.3280819188	0.3280819188
+
+
+### +x patch
+# N_rho = 16
+# N_sigma = 16
+# ghosted_gfn=-1
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	0	0.938212827517983	0.6634166525	0.000000000	0.6634166525
+45	3	0.936288762967978	0.6616020044	0.03467309182	0.6616020044
+45	6	0.930505368774322	0.6561570263	0.06896488246	0.6561570263
+45	9	0.920832300625956	0.6470812993	0.1024876094	0.6470812993
+45	12	0.907230207373212	0.6343832429	0.1348423209	0.6343832429
+45	15	0.889668802632320	0.6180943674	0.1656178866	0.6180943674
+45	18	0.868154360410446	0.5982901035	0.1943962387	0.5982901035
+45	21	0.842767961418568	0.5751173074	0.2207668503	0.5751173074
+45	24	0.813714827113485	0.5488274242	0.2443537125	0.5488274242
+45	27	0.781382049616536	0.5198117496	0.2648573153	0.5198117496
+45	30	0.746395302157393	0.4886304244	0.2821109070	0.4886304244
+45	33	0.709652562232288	0.4560189543	0.2961421715	0.4560189543
+45	36	0.672295999452495	0.4228474059	0.3072166232	0.4228474059
+45	39	0.635577647331625	0.3900093378	0.3158233345	0.3900093378
+45	42	0.600616675043636	0.3582515008	0.3225711002	0.3582515008
+45	45	0.568152329683595	0.3280229005	0.3280229005	0.3280229005
+
+48	0	0.794188312977937	0.5901969352	0.000000000	0.5314157074
+48	3	0.792421343427665	0.5884377085	0.03083871355	0.5298316926
+48	6	0.787138508525215	0.5831816749	0.06129486396	0.5250991386
+48	9	0.778396960760305	0.5744958587	0.09099120504	0.5172783946
+48	12	0.766301434483985	0.5624986023	0.1195627688	0.5064760164
+48	15	0.751017310550517	0.5473683248	0.1466669006	0.4928526534
+48	18	0.732786490730909	0.5293533623	0.1719973337	0.4766319083
+48	21	0.711943136934512	0.5087801962	0.1953024191	0.4581077463
+48	24	0.688924896142434	0.4860563981	0.2164062511	0.4376471466
+48	27	0.664273470709191	0.4616636612	0.2352293845	0.4156838276
+48	30	0.638616896031835	0.4361359222	0.2518031921	0.3926985482
+48	33	0.612626221956430	0.4100189846	0.2662694420	0.3691827520
+48	36	0.586945270237397	0.3838136580	0.2788569453	0.3455873699
+48	39	0.562107492298968	0.3579157288	0.2898344424	0.3222687697
+48	42	0.538474372285700	0.3325782507	0.2994548019	0.2994548019
+48	45	0.516233175836196	0.3079190400	0.3079190400	0.2772515490
+
+51	0	0.672846718941537	0.5229001103	0.000000000	0.4234361603
+51	3	0.671524950125335	0.5214405967	0.02732754370	0.4222542695
+51	6	0.667587899272836	0.5170911328	0.05434846808	0.4187321431
+51	9	0.661120599901927	0.5099387832	0.08076636878	0.4129402846
+51	12	0.652265382504476	0.5001278614	0.1063054586	0.4049955567
+51	15	0.641221864336391	0.4878579571	0.1307211456	0.3950595842
+51	18	0.628245081576348	0.4733796622	0.1538103760	0.3833352921
+51	21	0.613640329960914	0.4569869245	0.1754208448	0.3700607148
+51	24	0.597753147545879	0.4390050278	0.1954576314	0.3554992620
+51	27	0.580953398716386	0.4197738384	0.2138854537	0.3399261519
+51	30	0.563613443138302	0.3996270106	0.2307247622	0.3236115724
+51	33	0.546082557056363	0.3788696674	0.2460408388	0.3068026073
+51	36	0.528662736738869	0.3577591437	0.2599272327	0.2897076423
+51	39	0.511593512613858	0.3364945587	0.2724879209	0.2724879209
+51	42	0.495051858677831	0.3152187957	0.2838242785	0.2552591478
+51	45	0.479165113552487	0.2940299575	0.2940299575	0.2381007649
+
+54	0	0.585692279860313	0.4738350079	0.000000000	0.3442612845
+54	3	0.584795223087312	0.4726846021	0.02477235030	0.3434254658
+54	6	0.582125377572509	0.4692559504	0.04932078781	0.3409344045
+54	9	0.577746040797494	0.4636158625	0.07342953890	0.3368366407
+54	12	0.571760404762955	0.4558727100	0.09689873580	0.3312109112
+54	15	0.564307960756272	0.4461719091	0.1195514027	0.3241628668
+54	18	0.555559248438053	0.4346895569	0.1412391988	0.3158204496
+54	21	0.545708867766882	0.4216243176	0.1618464118	0.3063279976
+54	24	0.534966899395540	0.4071878986	0.1812917328	0.2958393252
+54	27	0.523549110787875	0.3915946979	0.1995274645	0.2845102018
+54	30	0.511666800751756	0.3750516003	0.2165361424	0.2724909378
+54	33	0.499517596680334	0.3577492009	0.2323250475	0.2599200088
+54	36	0.487278828893518	0.3398558169	0.2469197044	0.2469197044
+54	39	0.475104706301720	0.3215151004	0.2603577948	0.2335943939
+54	42	0.463127111549976	0.3028468237	0.2726845049	0.2200310969
+54	45	0.451458420513191	0.2839493648	0.2839493648	0.2063012893
+
+57	0	0.525189078707048	0.4404606229	0.000000000	0.2860384730
+57	3	0.524582249007829	0.4395273462	0.02303465215	0.2854323960
+57	6	0.522774934478898	0.4367424812	0.04590348450	0.2836238836
+57	9	0.519806121707575	0.4321502419	0.06844587420	0.2806416485
+57	12	0.515739019114163	0.4258220822	0.09051127768	0.2765320935
+57	15	0.510658473894189	0.4178534624	0.1119634978	0.2713572113
+57	18	0.504667498952738	0.4083595625	0.1326840650	0.2651918006
+57	21	0.497883072928610	0.3974701934	0.1525745123	0.2581201617
+57	24	0.490431455930673	0.3853242418	0.1715574056	0.2502324884
+57	27	0.482443321349527	0.3720640411	0.1895760978	0.2416212134
+57	30	0.474049104587343	0.3578301303	0.2065933221	0.2323776037
+57	33	0.465375014018398	0.3427568561	0.2225889050	0.2225889050
+57	36	0.456540094702668	0.3269691701	0.2375570074	0.2123362618
+57	39	0.447654501485579	0.3105807170	0.2515033056	0.2016934759
+57	42	0.438818864853110	0.2936930529	0.2644424126	0.1907264986
+57	45	0.430124587990059	0.2763957678	0.2763957678	0.1794935103
+
+60	0	0.481919235535716	0.4173543005	0.000000000	0.2409596178
+60	3	0.481499308991599	0.4165618098	0.02183107939	0.2405020730
+60	6	0.480247474964577	0.4141942169	0.04353356642	0.2391351427
+60	9	0.478187271377460	0.4102807528	0.06498208741	0.2368757031
+60	12	0.475356948239611	0.4048688041	0.08605752092	0.2337511130
+60	15	0.471808056132075	0.3980220051	0.1066496748	0.2297981118
+60	18	0.467603578634334	0.3898177343	0.1266594598	0.2250613738
+60	21	0.462815714477774	0.3803441741	0.1460004494	0.2195918113
+60	24	0.457523440467191	0.3696971223	0.1645997637	0.2134447331
+60	27	0.451810009073615	0.3579767670	0.1823982731	0.2066779828
+60	30	0.445760543032629	0.3452846319	0.1993501752	0.1993501752
+60	33	0.439459895213028	0.3317208914	0.2154220657	0.1915191460
+60	36	0.432990903570143	0.3173821930	0.2305916608	0.1832406945
+60	39	0.426433109182418	0.3023600496	0.2448463405	0.1745676561
+60	42	0.419861954842286	0.2867397997	0.2581816753	0.1655493006
+60	45	0.413348396465529	0.2706000450	0.2706000450	0.1562310088
+
+63	0	0.449820039474448	0.4007925899	0.000000000	0.2042140245
+63	3	0.449524260912691	0.4000930881	0.02096799025	0.2038576106
+63	6	0.448641840686103	0.3980013704	0.04183162967	0.2027918271
+63	9	0.447187369647320	0.3945375652	0.06248861145	0.2010269302
+63	12	0.445184655655387	0.3897344528	0.08284061526	0.1985796223
+63	15	0.442665985762120	0.3836363614	0.1027950532	0.1954724895
+63	18	0.439671146730194	0.3762977115	0.1222665381	0.1917332606
+63	21	0.436246256670827	0.3677812946	0.1411780118	0.1873939294
+63	24	0.432442468267537	0.3581563839	0.1594614959	0.1824897925
+63	27	0.428314614154499	0.3474967847	0.1770584554	0.1770584554
+63	30	0.423919868824532	0.3358789337	0.1939197928	0.1711388647
+63	33	0.419316502505551	0.3233801475	0.2100055233	0.1647704150
+63	36	0.414562786905486	0.3100770987	0.2252841992	0.1579921731
+63	39	0.409716098619708	0.2960445705	0.2397321663	0.1508422428
+63	42	0.404832237911134	0.2813545044	0.2533327336	0.1433572803
+63	45	0.399964933885660	0.2660753112	0.2660753112	0.1355721426
+
+66	0	0.425335786581742	0.3885635758	0.000000000	0.1729996500
+66	3	0.425126309210625	0.3879278598	0.02033043765	0.1727166110
+66	6	0.424501002890626	0.3860255911	0.04057292455	0.1718696664
+66	9	0.423469163362643	0.3828712711	0.06064085198	0.1704652727
+66	12	0.422046015323474	0.3784886173	0.08045023912	0.1685139895
+66	15	0.420252321924902	0.3729099114	0.09992090962	0.1660301896
+66	18	0.418113862322416	0.3661751318	0.1189775126	0.1630316725
+66	21	0.415660800766146	0.3583309156	0.1375503511	0.1595392025
+66	24	0.412926975382865	0.3494294027	0.1555759936	0.1555759936
+66	27	0.409949139032045	0.3395270169	0.1729976559	0.1511671673
+66	30	0.406766188461286	0.3286832456	0.1897653603	0.1463392093
+66	33	0.403418417407279	0.3169594730	0.2058358885	0.1411194494
+66	36	0.399946826444757	0.3044179144	0.2211725611	0.1355355878
+66	39	0.396392514086851	0.2911206865	0.2357448837	0.1296152805
+66	42	0.392796164333799	0.2771290309	0.2495281002	0.1233857941
+66	45	0.389197618966089	0.2625026847	0.2625026847	0.1168737252
+
+69	0	0.406334955994691	0.3793463615	0.000000000	0.1456174250
+69	3	0.406187760423221	0.3787558733	0.01984975421	0.1453907578
+69	6	0.405748191528991	0.3769880640	0.03962304217	0.1447121594
+69	9	0.405022259112559	0.3740538177	0.05924430457	0.1435858078
+69	12	0.404019835389953	0.3699710028	0.07863976427	0.1420185620
+69	15	0.402754443559631	0.3647640760	0.09773823959	0.1400198100
+69	18	0.401242972614816	0.3584635526	0.1164718686	0.1376012657
+69	21	0.399505328561253	0.3511053656	0.1347767224	0.1347767224
+69	24	0.397564035418215	0.3427301409	0.1525932901	0.1315617748
+69	27	0.395443800318920	0.3333824201	0.1698668275	0.1279735210
+69	30	0.393171061029513	0.3231098638	0.1865475669	0.1240302561
+69	33	0.390773533871314	0.3119624678	0.2025907954	0.1197511717
+69	36	0.388279778650521	0.2999918205	0.2179568157	0.1151560707
+69	39	0.385718794458759	0.2872504250	0.2326108077	0.1102651072
+69	42	0.383119657839333	0.2737911001	0.2465226139	0.1050985565
+69	45	0.380511197298748	0.2596664625	0.2596664625	0.09967661605
+
+72	0	0.391483749441901	0.3723231709	0.000000000	0.1209751316
+72	3	0.391382621226284	0.3717654901	0.01948340375	0.1207939301
+72	6	0.391080536314201	0.3700952895	0.03889858237	0.1202512490
+72	9	0.390581370148453	0.3673210441	0.05817793799	0.1193498421
+72	12	0.389891503025650	0.3634567122	0.07725510907	0.1180942445
+72	15	0.389019703685773	0.3585214908	0.09606554393	0.1164906939
+72	18	0.387976971006568	0.3525394860	0.1145470227	0.1145470227
+72	21	0.386776338830093	0.3455393115	0.1326401144	0.1122725281
+72	24	0.385432649105340	0.3375536278	0.1502885579	0.1096778222
+72	27	0.383962300244506	0.3286186414	0.1674395610	0.1067746691
+72	30	0.382382979883324	0.3187735802	0.1840440123	0.1035758148
+72	33	0.380713392068819	0.3080601674	0.2000566119	0.1000948160
+72	36	0.378972985106553	0.2965221071	0.2154359213	0.09634587297
+72	39	0.377181690319648	0.2842045985	0.2301443460	0.09234367180
+72	42	0.375359677730518	0.2711538900	0.2441480592	0.08810323956
+72	45	0.373527125799583	0.2574168753	0.2574168753	0.08363981293
+
+75	0	0.379914205580655	0.3669689429	0.000000000	0.09832903191
+75	3	0.379847518365577	0.3664353168	0.01920406120	0.09818604721
+75	6	0.379648274467650	0.3648367256	0.03834588504	0.09775770599
+75	9	0.379318914157746	0.3621800001	0.05736367661	0.09704583854
+75	12	0.378863461345132	0.3584764214	0.07619651558	0.09605346762
+75	15	0.378287459104971	0.3537415686	0.09478476764	0.09478476764
+75	18	0.377597882018527	0.3479951126	0.1130704663	0.09324500939
+75	21	0.376803026954090	0.3412605625	0.1309976565	0.09144049213
+75	24	0.375912384301146	0.3335649719	0.1485126939	0.08937846483
+75	27	0.374936492994624	0.3249386142	0.1655644934	0.08706703925
+75	30	0.373886784653600	0.3154146390	0.1821047267	0.08451509780
+75	33	0.372775421361448	0.3050287197	0.1980879667	0.08173219911
+75	36	0.371615129142370	0.2938187003	0.2134717813	0.07872848348
+75	39	0.370419035265762	0.2818242544	0.2282167814	0.07551458138
+75	42	0.369200510513803	0.2690865605	0.2422866273	0.07210152658
+75	45	0.367973016636321	0.2556479987	0.2556479987	0.06850067481
+
+78	0	0.371045372906375	0.3629371413	0.000000000	0.07714467085
+78	3	0.371004302564629	0.3624210870	0.01899368434	0.07703498013
+78	6	0.370881579694039	0.3608748298	0.03792947301	0.07670631301
+78	9	0.370678661759614	0.3583040669	0.05674978910	0.07615988048
+78	12	0.370397954578171	0.3547182294	0.07539768721	0.07539768721
+78	15	0.370042777419928	0.3501303877	0.09381715464	0.07442251135
+78	18	0.369617315392609	0.3445571222	0.1119533955	0.07323787718
+78	21	0.369126559806520	0.3380183633	0.1297530928	0.07184802108
+78	24	0.368576236792971	0.3305372049	0.1471646452	0.07025785177
+78	27	0.367972725930246	0.3221396946	0.1641383727	0.06847290585
+78	30	0.367322972693702	0.3128546100	0.1806266933	0.06649930021
+78	33	0.366634395368126	0.3027132248	0.1965842668	0.06434368224
+78	36	0.365914787353825	0.2917490690	0.2119681061	0.06201317897
+78	39	0.365172221636713	0.2799976929	0.2267376610	0.05951534687
+78	42	0.364414954861796	0.2674964362	0.2408548730	0.05685812273
+78	45	0.363651333943383	0.2542842055	0.2542842055	0.05404977641
+
+81	0	0.364483245462494	0.3599958519	0.000000000	0.05701774152
+81	3	0.364460724955908	0.3594923258	0.01884019446	0.05693799082
+81	6	0.364393427339315	0.3579833932	0.03762557078	0.05669899937
+81	9	0.364282140822009	0.3554739789	0.05630154720	0.05630154720
+81	12	0.364128167207545	0.3519722515	0.07481401159	0.05574692807
+81	15	0.363933303980693	0.3474895639	0.09310954803	0.05503694010
+81	18	0.363699819933053	0.3420403732	0.1111356541	0.05417387307
+81	21	0.363430424535483	0.3356421399	0.1288409462	0.05316049248
+81	24	0.363128230479965	0.3283152097	0.1461753492	0.05200002074
+81	27	0.362796710833057	0.3200826782	0.1630902705	0.05069611585
+81	30	0.362439653315490	0.3109702468	0.1795387557	0.04925284850
+81	33	0.362061110504537	0.3010060674	0.1954756258	0.04767467752
+81	36	0.361665346812745	0.2902205811	0.2108575947	0.04596642431
+81	39	0.361256787568828	0.2786463570	0.2256433708	0.04413324730
+81	42	0.360839965833710	0.2663179283	0.2397937397	0.04218061603
+81	45	0.360419471574957	0.2532716324	0.2532716324	0.04011428575
+
+84	0	0.359962806625814	0.3579908927	0.000000000	0.03762635901
+84	3	0.359952877520452	0.3574957670	0.01873555925	0.03757431920
+84	6	0.359923208389700	0.3560118669	0.03741835501	0.03741835501
+84	9	0.359874152250342	0.3535436165	0.05599580783	0.03715893145
+84	12	0.359806292056155	0.3500983643	0.07441570456	0.03679682085
+84	15	0.359720432439633	0.3456863458	0.09262637719	0.03633309902
+84	18	0.359617588641470	0.3403206327	0.1105768766	0.03576913985
+84	21	0.359498972592839	0.3340170690	0.1282171399	0.03510660860
+84	24	0.359365975142596	0.3267941938	0.1454981493	0.03434745382
+84	27	0.359220146056019	0.3186731540	0.1623720820	0.03349389815
+84	30	0.359063173191093	0.3096776092	0.1787924510	0.03254842829
+84	33	0.358896858958926	0.2998336269	0.1947142340	0.03151378407
+84	36	0.358723095138523	0.2891695731	0.2100939927	0.03039294684
+84	39	0.358543840127760	0.2777159991	0.2248899819	0.02918912771
+84	42	0.358361093581443	0.2655055248	0.2390622483	0.02790575514
+84	45	0.358176873982769	0.2525727206	0.2525727206	0.02654646265
+
+87	0	0.357313838606538	0.3568241524	0.000000000	0.01870036142
+87	3	0.357311220681848	0.3563338632	0.01867466646	0.01867466646
+87	6	0.357303402769256	0.3548643781	0.03729774908	0.01859765400
+87	9	0.357290491917614	0.3524198388	0.05581781892	0.01846954113
+87	12	0.357272664461909	0.3490071315	0.07418375587	0.01829068872
+87	15	0.357250162742763	0.3446358610	0.09234490064	0.01806160014
+87	18	0.357223290922354	0.3393183157	0.1102512041	0.01778291940
+87	21	0.357192409753371	0.3330694232	0.1278533727	0.01745542882
+87	24	0.357157929091570	0.3259066965	0.1451030100	0.01708004622
+87	27	0.357120300001075	0.3178501720	0.1619527518	0.01665782166
+87	30	0.357080007153911	0.3089223416	0.1783563971	0.01618993390
+87	33	0.357037559425537	0.2991480769	0.1942690327	0.01567768639
+87	36	0.356993479928462	0.2885545476	0.2096471505	0.01512250304
+87	39	0.356948298816824	0.2771711370	0.2244487612	0.01452592377
+87	42	0.356902543554136	0.2650293517	0.2386335001	0.01388959977
+87	45	0.356856732633042	0.2521627290	0.2521627290	0.01321528864
+
+90	0	0.356441076061109	0.3564410761	0.000000000	0.000000000
+90	3	0.356440856411725	0.3559523666	0.01865467306	0.000000000
+90	6	0.356440206673631	0.3544875899	0.03725814705	0.000000000
+90	9	0.356439154250766	0.3520507968	0.05575936841	0.000000000
+90	12	0.356437743763832	0.3486487239	0.07410757398	0.000000000
+90	15	0.356436035308584	0.3442907719	0.09225243430	0.000000000
+90	18	0.356434102404428	0.3389889757	0.1101441950	0.000000000
+90	21	0.356432029459276	0.3327579661	0.1277338155	0.000000000
+90	24	0.356429907481979	0.3256149229	0.1449731041	0.000000000
+90	27	0.356427829980860	0.3175795219	0.1618148487	0.000000000
+90	30	0.356425889510761	0.3086738749	0.1782129448	0.000000000
+90	33	0.356424172731179	0.2989224634	0.1941225175	0.000000000
+90	36	0.356422755281138	0.2883520662	0.2095000391	0.000000000
+90	39	0.356421699554656	0.2769916844	0.2243034433	0.000000000
+90	42	0.356421049992375	0.2648724590	0.2384922333	0.000000000
+90	45	0.356420831881345	0.2520275872	0.2520275872	0.000000000
+
+
+### +y patch
+# N_rho = 16
+# N_sigma = 16
+# ghosted_gfn=-1
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	45	0.568152329683595	0.3280229005	0.3280229005	0.3280229005
+42	45	0.600616675043636	0.3225711002	0.3582515008	0.3582515008
+39	45	0.635577647331625	0.3158233345	0.3900093378	0.3900093378
+36	45	0.672295999452497	0.3072166232	0.4228474059	0.4228474059
+33	45	0.709652562232293	0.2961421715	0.4560189543	0.4560189543
+30	45	0.746395302157398	0.2821109070	0.4886304244	0.4886304244
+27	45	0.781382049616540	0.2648573153	0.5198117496	0.5198117496
+24	45	0.813714827113488	0.2443537125	0.5488274242	0.5488274242
+21	45	0.842767961418569	0.2207668503	0.5751173074	0.5751173074
+18	45	0.868154360410446	0.1943962387	0.5982901035	0.5982901035
+15	45	0.889668802632318	0.1656178866	0.6180943674	0.6180943674
+12	45	0.907230207373209	0.1348423209	0.6343832429	0.6343832429
+9	45	0.920832300625955	0.1024876094	0.6470812993	0.6470812993
+6	45	0.930505368774323	0.06896488246	0.6561570263	0.6561570263
+3	45	0.936288762967983	0.03467309182	0.6616020044	0.6616020044
+0	45	0.938212827517988	0.000000000	0.6634166525	0.6634166525
+
+45	48	0.516233175836197	0.3079190400	0.3079190400	0.2772515490
+42	48	0.538474372285699	0.2994548019	0.3325782507	0.2994548019
+39	48	0.562107492298967	0.2898344424	0.3579157288	0.3222687697
+36	48	0.586945270237397	0.2788569453	0.3838136580	0.3455873699
+33	48	0.612626221956432	0.2662694420	0.4100189846	0.3691827520
+30	48	0.638616896031839	0.2518031921	0.4361359222	0.3926985482
+27	48	0.664273470709196	0.2352293845	0.4616636612	0.4156838276
+24	48	0.688924896142439	0.2164062511	0.4860563981	0.4376471466
+21	48	0.711943136934516	0.1953024191	0.5087801962	0.4581077463
+18	48	0.732786490730913	0.1719973337	0.5293533623	0.4766319083
+15	48	0.751017310550520	0.1466669006	0.5473683248	0.4928526534
+12	48	0.766301434483987	0.1195627688	0.5624986023	0.5064760164
+9	48	0.778396960760308	0.09099120504	0.5744958587	0.5172783946
+6	48	0.787138508525219	0.06129486396	0.5831816749	0.5250991386
+3	48	0.792421343427670	0.03083871355	0.5884377085	0.5298316926
+0	48	0.794188312977941	0.000000000	0.5901969352	0.5314157074
+
+45	51	0.479165113552487	0.2940299575	0.2940299575	0.2381007649
+42	51	0.495051858677830	0.2838242785	0.3152187957	0.2552591478
+39	51	0.511593512613857	0.2724879209	0.3364945587	0.2724879209
+36	51	0.528662736738868	0.2599272327	0.3577591437	0.2897076423
+33	51	0.546082557056362	0.2460408388	0.3788696674	0.3068026073
+30	51	0.563613443138302	0.2307247622	0.3996270106	0.3236115724
+27	51	0.580953398716387	0.2138854537	0.4197738384	0.3399261519
+24	51	0.597753147545881	0.1954576314	0.4390050278	0.3554992620
+21	51	0.613640329960916	0.1754208448	0.4569869245	0.3700607148
+18	51	0.628245081576350	0.1538103760	0.4733796622	0.3833352921
+15	51	0.641221864336394	0.1307211456	0.4878579571	0.3950595842
+12	51	0.652265382504481	0.1063054586	0.5001278614	0.4049955567
+9	51	0.661120599901931	0.08076636878	0.5099387832	0.4129402846
+6	51	0.667587899272840	0.05434846808	0.5170911328	0.4187321431
+3	51	0.671524950125339	0.02732754370	0.5214405967	0.4222542695
+0	51	0.672846718941540	0.000000000	0.5229001103	0.4234361603
+
+45	54	0.451458420513191	0.2839493648	0.2839493648	0.2063012893
+42	54	0.463127111549975	0.2726845049	0.3028468237	0.2200310969
+39	54	0.475104706301718	0.2603577948	0.3215151004	0.2335943939
+36	54	0.487278828893517	0.2469197044	0.3398558169	0.2469197044
+33	54	0.499517596680332	0.2323250475	0.3577492009	0.2599200088
+30	54	0.511666800751754	0.2165361424	0.3750516003	0.2724909378
+27	54	0.523549110787874	0.1995274645	0.3915946979	0.2845102018
+24	54	0.534966899395539	0.1812917328	0.4071878986	0.2958393252
+21	54	0.545708867766881	0.1618464118	0.4216243176	0.3063279976
+18	54	0.555559248438053	0.1412391988	0.4346895569	0.3158204496
+15	54	0.564307960756273	0.1195514027	0.4461719091	0.3241628668
+12	54	0.571760404762956	0.09689873580	0.4558727100	0.3312109112
+9	54	0.577746040797496	0.07342953890	0.4636158625	0.3368366407
+6	54	0.582125377572510	0.04932078781	0.4692559504	0.3409344045
+3	54	0.584795223087313	0.02477235030	0.4726846021	0.3434254658
+0	54	0.585692279860314	0.000000000	0.4738350079	0.3442612845
+
+45	57	0.430124587990059	0.2763957678	0.2763957678	0.1794935103
+42	57	0.438818864853110	0.2644424126	0.2936930529	0.1907264986
+39	57	0.447654501485578	0.2515033056	0.3105807170	0.2016934759
+36	57	0.456540094702667	0.2375570074	0.3269691701	0.2123362618
+33	57	0.465375014018397	0.2225889050	0.3427568561	0.2225889050
+30	57	0.474049104587342	0.2065933221	0.3578301303	0.2323776037
+27	57	0.482443321349526	0.1895760978	0.3720640411	0.2416212134
+24	57	0.490431455930673	0.1715574056	0.3853242418	0.2502324884
+21	57	0.497883072928610	0.1525745123	0.3974701934	0.2581201617
+18	57	0.504667498952738	0.1326840650	0.4083595625	0.2651918006
+15	57	0.510658473894189	0.1119634978	0.4178534624	0.2713572113
+12	57	0.515739019114164	0.09051127768	0.4258220822	0.2765320935
+9	57	0.519806121707576	0.06844587420	0.4321502419	0.2806416485
+6	57	0.522774934478899	0.04590348450	0.4367424812	0.2836238836
+3	57	0.524582249007829	0.02303465215	0.4395273462	0.2854323960
+0	57	0.525189078707048	0.000000000	0.4404606229	0.2860384730
+
+45	60	0.413348396465529	0.2706000450	0.2706000450	0.1562310088
+42	60	0.419861954842286	0.2581816753	0.2867397997	0.1655493006
+39	60	0.426433109182417	0.2448463405	0.3023600496	0.1745676561
+36	60	0.432990903570142	0.2305916608	0.3173821930	0.1832406945
+33	60	0.439459895213027	0.2154220657	0.3317208914	0.1915191460
+30	60	0.445760543032628	0.1993501752	0.3452846319	0.1993501752
+27	60	0.451810009073615	0.1823982731	0.3579767670	0.2066779828
+24	60	0.457523440467190	0.1645997637	0.3696971223	0.2134447331
+21	60	0.462815714477773	0.1460004494	0.3803441741	0.2195918113
+18	60	0.467603578634334	0.1266594598	0.3898177343	0.2250613738
+15	60	0.471808056132074	0.1066496748	0.3980220051	0.2297981118
+12	60	0.475356948239611	0.08605752092	0.4048688041	0.2337511130
+9	60	0.478187271377459	0.06498208741	0.4102807528	0.2368757031
+6	60	0.480247474964576	0.04353356642	0.4141942169	0.2391351427
+3	60	0.481499308991599	0.02183107939	0.4165618098	0.2405020730
+0	60	0.481919235535716	0.000000000	0.4173543005	0.2409596178
+
+45	63	0.399964933885660	0.2660753112	0.2660753112	0.1355721426
+42	63	0.404832237911134	0.2533327336	0.2813545044	0.1433572803
+39	63	0.409716098619708	0.2397321663	0.2960445705	0.1508422428
+36	63	0.414562786905486	0.2252841992	0.3100770987	0.1579921731
+33	63	0.419316502505550	0.2100055233	0.3233801475	0.1647704150
+30	63	0.423919868824531	0.1939197928	0.3358789337	0.1711388647
+27	63	0.428314614154499	0.1770584554	0.3474967847	0.1770584554
+24	63	0.432442468267536	0.1594614959	0.3581563839	0.1824897925
+21	63	0.436246256670827	0.1411780118	0.3677812946	0.1873939294
+18	63	0.439671146730194	0.1222665381	0.3762977115	0.1917332606
+15	63	0.442665985762119	0.1027950532	0.3836363614	0.1954724895
+12	63	0.445184655655387	0.08284061526	0.3897344528	0.1985796223
+9	63	0.447187369647319	0.06248861145	0.3945375652	0.2010269302
+6	63	0.448641840686103	0.04183162967	0.3980013704	0.2027918271
+3	63	0.449524260912690	0.02096799025	0.4000930881	0.2038576106
+0	63	0.449820039474447	0.000000000	0.4007925899	0.2042140245
+
+45	66	0.389197618966089	0.2625026847	0.2625026847	0.1168737252
+42	66	0.392796164333799	0.2495281002	0.2771290309	0.1233857941
+39	66	0.396392514086851	0.2357448837	0.2911206865	0.1296152805
+36	66	0.399946826444756	0.2211725611	0.3044179144	0.1355355878
+33	66	0.403418417407279	0.2058358885	0.3169594730	0.1411194494
+30	66	0.406766188461286	0.1897653603	0.3286832456	0.1463392093
+27	66	0.409949139032045	0.1729976559	0.3395270169	0.1511671673
+24	66	0.412926975382864	0.1555759936	0.3494294027	0.1555759936
+21	66	0.415660800766146	0.1375503511	0.3583309156	0.1595392025
+18	66	0.418113862322416	0.1189775126	0.3661751318	0.1630316725
+15	66	0.420252321924902	0.09992090962	0.3729099114	0.1660301896
+12	66	0.422046015323474	0.08045023912	0.3784886173	0.1685139895
+9	66	0.423469163362642	0.06064085198	0.3828712711	0.1704652727
+6	66	0.424501002890626	0.04057292455	0.3860255911	0.1718696664
+3	66	0.425126309210624	0.02033043765	0.3879278598	0.1727166110
+0	66	0.425335786581741	0.000000000	0.3885635758	0.1729996500
+
+45	69	0.380511197298748	0.2596664625	0.2596664625	0.09967661605
+42	69	0.383119657839333	0.2465226139	0.2737911001	0.1050985565
+39	69	0.385718794458759	0.2326108077	0.2872504250	0.1102651072
+36	69	0.388279778650521	0.2179568157	0.2999918205	0.1151560707
+33	69	0.390773533871314	0.2025907954	0.3119624678	0.1197511717
+30	69	0.393171061029513	0.1865475669	0.3231098638	0.1240302561
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