Make "Erik" branch the default trunk for AHFinderDirect.

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@1526 f88db872-0e4f-0410-b76b-b9085cfa78c5

12 files changed, 2904 insertions, 0 deletions

diff --git a/test/recover2/ADM_BS_phi.x.asc b/test/recover2/ADM_BS_phi.x.asc
new file mode 100644
index 0000000..ba236fd
--- /dev/null
+++ b/test/recover2/ADM_BS_phi.x.asc
@@ -0,0 +1,48 @@
+# iteration 1
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+1	0 0 0 0	0 15 3	0.05	-0.6 0 0	0
+1	0 0 0 0	1 15 3	0.05	-0.4 0 0	0
+1	0 0 0 0	2 15 3	0.05	-0.2 0 0	0
+1	0 0 0 0	3 15 3	0.05	0 0 0	0
+1	0 0 0 0	4 15 3	0.05	0.2 0 0	0
+1	0 0 0 0	5 15 3	0.05	0.4 0 0	0
+1	0 0 0 0	6 15 3	0.05	0.6 0 0	0
+1	0 0 0 0	7 15 3	0.05	0.8 0 0	0.130363851624392
+1	0 0 0 0	8 15 3	0.05	1 0 0	0.104220488796629
+1	0 0 0 0	9 15 3	0.05	1.2 0 0	0.0892505608155271
+1	0 0 0 0	10 15 3	0.05	1.4 0 0	0.0789095857132584
+1	0 0 0 0	11 15 3	0.05	1.6 0 0	0.0710717753323479
+1	0 0 0 0	12 15 3	0.05	1.8 0 0	0.0648365375811699
+1	0 0 0 0	13 15 3	0.05	2 0 0	0.0597142640637997
+1	0 0 0 0	14 15 3	0.05	2.2 0 0	0.0554082209721993
+1	0 0 0 0	15 15 3	0.05	2.4 0 0	0.0517244520929427
+1	0 0 0 0	16 15 3	0.05	2.6 0 0	0.048529132257269
+1	0 0 0 0	17 15 3	0.05	2.8 0 0	0.0457263318069279
+1	0 0 0 0	18 15 3	0.05	3 0 0	0.0432533402490022
+
+
+# iteration 2
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+2	0 0 0 0	0 15 3	0.1	-0.6 0 0	0
+2	0 0 0 0	1 15 3	0.1	-0.4 0 0	0
+2	0 0 0 0	2 15 3	0.1	-0.2 0 0	0
+2	0 0 0 0	3 15 3	0.1	0 0 0	0
+2	0 0 0 0	4 15 3	0.1	0.2 0 0	0
+2	0 0 0 0	5 15 3	0.1	0.4 0 0	0
+2	0 0 0 0	6 15 3	0.1	0.6 0 0	0
+2	0 0 0 0	7 15 3	0.1	0.8 0 0	0.130363851624392
+2	0 0 0 0	8 15 3	0.1	1 0 0	0.104106304221948
+2	0 0 0 0	9 15 3	0.1	1.2 0 0	0.0891363762408464
+2	0 0 0 0	10 15 3	0.1	1.4 0 0	0.0788244977928251
+2	0 0 0 0	11 15 3	0.1	1.6 0 0	0.0710114533838618
+2	0 0 0 0	12 15 3	0.1	1.8 0 0	0.0647929665253498
+2	0 0 0 0	13 15 3	0.1	2 0 0	0.0596821808744584
+2	0 0 0 0	14 15 3	0.1	2.2 0 0	0.0553841224841849
+2	0 0 0 0	15 15 3	0.1	2.4 0 0	0.0517060140340176
+2	0 0 0 0	16 15 3	0.1	2.6 0 0	0.0485148359478545
+2	0 0 0 0	17 15 3	0.1	2.8 0 0	0.0457159177002126
+2	0 0 0 0	18 15 3	0.1	3 0 0	0.0432533402490022
+
+
diff --git a/test/recover2/ADM_BS_phi.y.asc b/test/recover2/ADM_BS_phi.y.asc
new file mode 100644
index 0000000..cf7d80c
--- /dev/null
+++ b/test/recover2/ADM_BS_phi.y.asc
@@ -0,0 +1,72 @@
+# iteration 1
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+1	0 0 0 0	3 0 3	0.05	0 -3 0	0.0432533402490022
+1	0 0 0 0	3 1 3	0.05	0 -2.8 0	0.0457263318065289
+1	0 0 0 0	3 2 3	0.05	0 -2.6 0	0.0485291322573205
+1	0 0 0 0	3 3 3	0.05	0 -2.4 0	0.0517244520929351
+1	0 0 0 0	3 4 3	0.05	0 -2.2 0	0.0554082209725126
+1	0 0 0 0	3 5 3	0.05	0 -2 0	0.059714264063792
+1	0 0 0 0	3 6 3	0.05	0 -1.8 0	0.0648365375817624
+1	0 0 0 0	3 7 3	0.05	0 -1.6 0	0.071071775330888
+1	0 0 0 0	3 8 3	0.05	0 -1.4 0	0.0789095857133257
+1	0 0 0 0	3 9 3	0.05	0 -1.2 0	0.0892505608163802
+1	0 0 0 0	3 10 3	0.05	0 -1 0	0.104220488797482
+1	0 0 0 0	3 11 3	0.05	0 -0.8 0	0.130363851624392
+1	0 0 0 0	3 12 3	0.05	0 -0.6 0	0
+1	0 0 0 0	3 13 3	0.05	0 -0.4 0	0
+1	0 0 0 0	3 14 3	0.05	0 -0.2 0	0
+1	0 0 0 0	3 15 3	0.05	0 0 0	0
+1	0 0 0 0	3 16 3	0.05	0 0.2 0	0
+1	0 0 0 0	3 17 3	0.05	0 0.4 0	0
+1	0 0 0 0	3 18 3	0.05	0 0.6 0	0
+1	0 0 0 0	3 19 3	0.05	0 0.8 0	0.130363851624392
+1	0 0 0 0	3 20 3	0.05	0 1 0	0.104220488796584
+1	0 0 0 0	3 21 3	0.05	0 1.2 0	0.0892505608154827
+1	0 0 0 0	3 22 3	0.05	0 1.4 0	0.0789095857118638
+1	0 0 0 0	3 23 3	0.05	0 1.6 0	0.0710717753325539
+1	0 0 0 0	3 24 3	0.05	0 1.8 0	0.0648365375811426
+1	0 0 0 0	3 25 3	0.05	0 2 0	0.0597142640640769
+1	0 0 0 0	3 26 3	0.05	0 2.2 0	0.0554082209721188
+1	0 0 0 0	3 27 3	0.05	0 2.4 0	0.051724452093734
+1	0 0 0 0	3 28 3	0.05	0 2.6 0	0.048529132256278
+1	0 0 0 0	3 29 3	0.05	0 2.8 0	0.0457263318071654
+1	0 0 0 0	3 30 3	0.05	0 3 0	0.0432533402490022
+
+
+# iteration 2
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+2	0 0 0 0	3 0 3	0.1	0 -3 0	0.0432533402490022
+2	0 0 0 0	3 1 3	0.1	0 -2.8 0	0.0457159176994908
+2	0 0 0 0	3 2 3	0.1	0 -2.6 0	0.0485148359479053
+2	0 0 0 0	3 3 3	0.1	0 -2.4 0	0.0517060140340352
+2	0 0 0 0	3 4 3	0.1	0 -2.2 0	0.0553841224847729
+2	0 0 0 0	3 5 3	0.1	0 -2 0	0.0596821808744254
+2	0 0 0 0	3 6 3	0.1	0 -1.8 0	0.064792966526694
+2	0 0 0 0	3 7 3	0.1	0 -1.6 0	0.0710114533812901
+2	0 0 0 0	3 8 3	0.1	0 -1.4 0	0.0788244977927247
+2	0 0 0 0	3 9 3	0.1	0 -1.2 0	0.0891363762424142
+2	0 0 0 0	3 10 3	0.1	0 -1 0	0.104106304223516
+2	0 0 0 0	3 11 3	0.1	0 -0.8 0	0.130363851624392
+2	0 0 0 0	3 12 3	0.1	0 -0.6 0	0
+2	0 0 0 0	3 13 3	0.1	0 -0.4 0	0
+2	0 0 0 0	3 14 3	0.1	0 -0.2 0	0
+2	0 0 0 0	3 15 3	0.1	0 0 0	0
+2	0 0 0 0	3 16 3	0.1	0 0.2 0	0
+2	0 0 0 0	3 17 3	0.1	0 0.4 0	0
+2	0 0 0 0	3 18 3	0.1	0 0.6 0	0
+2	0 0 0 0	3 19 3	0.1	0 0.8 0	0.130363851624392
+2	0 0 0 0	3 20 3	0.1	0 1 0	0.104106304221705
+2	0 0 0 0	3 21 3	0.1	0 1.2 0	0.0891363762406031
+2	0 0 0 0	3 22 3	0.1	0 1.4 0	0.0788244977903712
+2	0 0 0 0	3 23 3	0.1	0 1.6 0	0.0710114533845545
+2	0 0 0 0	3 24 3	0.1	0 1.8 0	0.0647929665254468
+2	0 0 0 0	3 25 3	0.1	0 2 0	0.0596821808749719
+2	0 0 0 0	3 26 3	0.1	0 2.2 0	0.0553841224841346
+2	0 0 0 0	3 27 3	0.1	0 2.4 0	0.0517060140355346
+2	0 0 0 0	3 28 3	0.1	0 2.6 0	0.0485148359460328
+2	0 0 0 0	3 29 3	0.1	0 2.8 0	0.045715917700652
+2	0 0 0 0	3 30 3	0.1	0 3 0	0.0432533402490022
+
+
diff --git a/test/recover2/ADM_BS_phi.z.asc b/test/recover2/ADM_BS_phi.z.asc
new file mode 100644
index 0000000..403b83a
--- /dev/null
+++ b/test/recover2/ADM_BS_phi.z.asc
@@ -0,0 +1,48 @@
+# iteration 1
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+1	0 0 0 0	3 15 0	0.05	0 0 -0.6	0
+1	0 0 0 0	3 15 1	0.05	0 0 -0.4	0
+1	0 0 0 0	3 15 2	0.05	0 0 -0.2	0
+1	0 0 0 0	3 15 3	0.05	0 0 0	0
+1	0 0 0 0	3 15 4	0.05	0 0 0.2	0
+1	0 0 0 0	3 15 5	0.05	0 0 0.4	0
+1	0 0 0 0	3 15 6	0.05	0 0 0.6	0
+1	0 0 0 0	3 15 7	0.05	0 0 0.8	0.0796160463379387
+1	0 0 0 0	3 15 8	0.05	0 0 1	0.0753458414750121
+1	0 0 0 0	3 15 9	0.05	0 0 1.2	0.070582640321683
+1	0 0 0 0	3 15 10	0.05	0 0 1.4	0.0659345200664271
+1	0 0 0 0	3 15 11	0.05	0 0 1.6	0.0616364211560666
+1	0 0 0 0	3 15 12	0.05	0 0 1.8	0.0577381679321618
+1	0 0 0 0	3 15 13	0.05	0 0 2	0.0542290473265031
+1	0 0 0 0	3 15 14	0.05	0 0 2.2	0.0510759026136498
+1	0 0 0 0	3 15 15	0.05	0 0 2.4	0.0482396956746853
+1	0 0 0 0	3 15 16	0.05	0 0 2.6	0.045682310360457
+1	0 0 0 0	3 15 17	0.05	0 0 2.8	0.043369299549159
+1	0 0 0 0	3 15 18	0.05	0 0 3	0.0412767864358354
+
+
+# iteration 2
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+2	0 0 0 0	3 15 0	0.1	0 0 -0.6	0
+2	0 0 0 0	3 15 1	0.1	0 0 -0.4	0
+2	0 0 0 0	3 15 2	0.1	0 0 -0.2	0
+2	0 0 0 0	3 15 3	0.1	0 0 0	0
+2	0 0 0 0	3 15 4	0.1	0 0 0.2	0
+2	0 0 0 0	3 15 5	0.1	0 0 0.4	0
+2	0 0 0 0	3 15 6	0.1	0 0 0.6	0
+2	0 0 0 0	3 15 7	0.1	0 0 0.8	0.0796079896028402
+2	0 0 0 0	3 15 8	0.1	0 0 1	0.0753234682357545
+2	0 0 0 0	3 15 9	0.1	0 0 1.2	0.0705602670824255
+2	0 0 0 0	3 15 10	0.1	0 0 1.4	0.0659063866573531
+2	0 0 0 0	3 15 11	0.1	0 0 1.6	0.0616106063533713
+2	0 0 0 0	3 15 12	0.1	0 0 1.8	0.0577160977224629
+2	0 0 0 0	3 15 13	0.1	0 0 2	0.0542107222712016
+2	0 0 0 0	3 15 14	0.1	0 0 2.2	0.0510608484355226
+2	0 0 0 0	3 15 15	0.1	0 0 2.4	0.0482273550023926
+2	0 0 0 0	3 15 16	0.1	0 0 2.6	0.045672209279059
+2	0 0 0 0	3 15 17	0.1	0 0 2.8	0.0433616332194261
+2	0 0 0 0	3 15 18	0.1	0 0 3	0.0412767864358354
+
+
diff --git a/test/recover2/BH_diagnostics.ah1.gp b/test/recover2/BH_diagnostics.ah1.gp
new file mode 100644
index 0000000..d84dd2e
--- /dev/null
+++ b/test/recover2/BH_diagnostics.ah1.gp
@@ -0,0 +1,41 @@
+# apparent horizon 1/2
+#
+# column  1 = cctk_iteration
+# column  2 = cctk_time
+# column  3 = centroid_x
+# column  4 = centroid_y
+# column  5 = centroid_z
+# column  6 = min radius
+# column  7 = max radius
+# column  8 = mean radius
+# column  9 = quadrupole_xx
+# column 10 = quadrupole_xy
+# column 11 = quadrupole_xz
+# column 12 = quadrupole_yy
+# column 13 = quadrupole_yz
+# column 14 = quadrupole_zz
+# column 15 = min x
+# column 16 = max x
+# column 17 = min y
+# column 18 = max y
+# column 19 = min z
+# column 20 = max z
+# column 21 = xy-plane circumference
+# column 22 = xz-plane circumference
+# column 23 = yz-plane circumference
+# column 24 = ratio of xz/xy-plane circumferences
+# column 25 = ratio of yz/xy-plane circumferences
+# column 26 = area
+# column 27 = m_irreducible
+# column 28 = areal radius
+# column 29 = expansion Theta_(l)
+# column 30 = inner expansion Theta_(n)
+# column 31 = product of the expansions
+# column 32 = mean curvature
+# column 33 = gradient of the areal radius
+# column 34 = gradient of the expansion Theta_(l)
+# column 35 = gradient of the inner expansion Theta_(n)
+# column 36 = gradient of the product of the expansions
+# column 37 = gradient of the mean curvature
+1       0.050   0.000019        0.000024        0.000000        1.176376382     2.618150327     1.957464086     1.199886145     5.854922778e-06 0.000000000     1.199874876     0.000000000     1.079927681     -1.896954588    1.896253793     -1.896602991    1.896364371     -1.797350075    1.797350075     12.56415138     11.04966423     11.36846649     0.8794596541    0.9048336134    45.22900203     0.9485791509    1.897158302     -5.626879674e-15        -1.469716579    8.253042071e-15 0.7348582893    0.000000000     0.000000000     0.000000000     0.000000000     0.000000000
+2	0.100	0.000019	0.000024	0.000000	1.176438536	2.618207234	1.957468207	1.199888822	5.853386871e-06	0.000000000	1.199877425	0.000000000	1.079938129	-1.896802728	1.896088630	-1.896467806	1.896231804	-1.797215665	1.797215665	12.56254986	11.04882917	11.36752998	0.8795052986	0.9048744170	45.22324503	0.9485187788	1.897037558	-2.249266290e-15	-1.469883991	3.358670001e-15	0.7349419953	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000
diff --git a/test/recover2/BH_diagnostics.ah2.gp b/test/recover2/BH_diagnostics.ah2.gp
new file mode 100644
index 0000000..fab0651
--- /dev/null
+++ b/test/recover2/BH_diagnostics.ah2.gp
@@ -0,0 +1,41 @@
+# apparent horizon 2/2
+#
+# column  1 = cctk_iteration
+# column  2 = cctk_time
+# column  3 = centroid_x
+# column  4 = centroid_y
+# column  5 = centroid_z
+# column  6 = min radius
+# column  7 = max radius
+# column  8 = mean radius
+# column  9 = quadrupole_xx
+# column 10 = quadrupole_xy
+# column 11 = quadrupole_xz
+# column 12 = quadrupole_yy
+# column 13 = quadrupole_yz
+# column 14 = quadrupole_zz
+# column 15 = min x
+# column 16 = max x
+# column 17 = min y
+# column 18 = max y
+# column 19 = min z
+# column 20 = max z
+# column 21 = xy-plane circumference
+# column 22 = xz-plane circumference
+# column 23 = yz-plane circumference
+# column 24 = ratio of xz/xy-plane circumferences
+# column 25 = ratio of yz/xy-plane circumferences
+# column 26 = area
+# column 27 = m_irreducible
+# column 28 = areal radius
+# column 29 = expansion Theta_(l)
+# column 30 = inner expansion Theta_(n)
+# column 31 = product of the expansions
+# column 32 = mean curvature
+# column 33 = gradient of the areal radius
+# column 34 = gradient of the expansion Theta_(l)
+# column 35 = gradient of the inner expansion Theta_(n)
+# column 36 = gradient of the product of the expansions
+# column 37 = gradient of the mean curvature
+1       0.050   0.000000        0.000000        0.000000        1.799782609     1.897391633     1.865208933     1.199938339     1.483362260e-10 0.000000000     1.199938339     -0.000000000    1.079963746     -1.897095303    1.897095303     -1.897095303    1.897095303     -1.799782609    1.799782609     12.56441988     11.61622012     11.61622012     0.9245329455    0.9245329455    45.23086154     0.9485986503    1.897197301     -6.526645613e-17        -1.467342461    1.865090787e-16 0.7336712304    0.000000000     0.000000000     0.000000000     0.000000000     0.000000000
+2	0.100	0.000000	0.000000	0.000000	1.799644021	1.897465641	1.865212809	1.199940613	1.044877168e-10	0.000000000	1.199940613	0.000000000	1.079973796	-1.896947605	1.896947605	-1.896947605	1.896947605	-1.799644021	1.799644021	12.56281687	11.61521159	11.61521159	0.9245706362	0.9245706362	45.22509135	0.9485381411	1.897076282	-1.863312755e-15	-1.467524846	2.882159661e-15	0.7337624228	0.000000000	0.000000000	0.000000000	0.000000000	0.000000000
diff --git a/test/recover2/emask.x.asc b/test/recover2/emask.x.asc
new file mode 100644
index 0000000..5fa4d76
--- /dev/null
+++ b/test/recover2/emask.x.asc
@@ -0,0 +1,48 @@
+# iteration 1
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+1	0 0 0 0	0 15 3	0.05	-0.6 0 0	0
+1	0 0 0 0	1 15 3	0.05	-0.4 0 0	0
+1	0 0 0 0	2 15 3	0.05	-0.2 0 0	0
+1	0 0 0 0	3 15 3	0.05	0 0 0	0
+1	0 0 0 0	4 15 3	0.05	0.2 0 0	0
+1	0 0 0 0	5 15 3	0.05	0.4 0 0	0
+1	0 0 0 0	6 15 3	0.05	0.6 0 0	0
+1	0 0 0 0	7 15 3	0.05	0.8 0 0	0.5
+1	0 0 0 0	8 15 3	0.05	1 0 0	0.5
+1	0 0 0 0	9 15 3	0.05	1.2 0 0	1
+1	0 0 0 0	10 15 3	0.05	1.4 0 0	1
+1	0 0 0 0	11 15 3	0.05	1.6 0 0	1
+1	0 0 0 0	12 15 3	0.05	1.8 0 0	1
+1	0 0 0 0	13 15 3	0.05	2 0 0	1
+1	0 0 0 0	14 15 3	0.05	2.2 0 0	1
+1	0 0 0 0	15 15 3	0.05	2.4 0 0	1
+1	0 0 0 0	16 15 3	0.05	2.6 0 0	1
+1	0 0 0 0	17 15 3	0.05	2.8 0 0	1
+1	0 0 0 0	18 15 3	0.05	3 0 0	1
+
+
+# iteration 2
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+2	0 0 0 0	0 15 3	0.1	-0.6 0 0	0
+2	0 0 0 0	1 15 3	0.1	-0.4 0 0	0
+2	0 0 0 0	2 15 3	0.1	-0.2 0 0	0
+2	0 0 0 0	3 15 3	0.1	0 0 0	0
+2	0 0 0 0	4 15 3	0.1	0.2 0 0	0
+2	0 0 0 0	5 15 3	0.1	0.4 0 0	0
+2	0 0 0 0	6 15 3	0.1	0.6 0 0	0
+2	0 0 0 0	7 15 3	0.1	0.8 0 0	0.5
+2	0 0 0 0	8 15 3	0.1	1 0 0	0.5
+2	0 0 0 0	9 15 3	0.1	1.2 0 0	1
+2	0 0 0 0	10 15 3	0.1	1.4 0 0	1
+2	0 0 0 0	11 15 3	0.1	1.6 0 0	1
+2	0 0 0 0	12 15 3	0.1	1.8 0 0	1
+2	0 0 0 0	13 15 3	0.1	2 0 0	1
+2	0 0 0 0	14 15 3	0.1	2.2 0 0	1
+2	0 0 0 0	15 15 3	0.1	2.4 0 0	1
+2	0 0 0 0	16 15 3	0.1	2.6 0 0	1
+2	0 0 0 0	17 15 3	0.1	2.8 0 0	1
+2	0 0 0 0	18 15 3	0.1	3 0 0	1
+
+
diff --git a/test/recover2/emask.y.asc b/test/recover2/emask.y.asc
new file mode 100644
index 0000000..1ed0cee
--- /dev/null
+++ b/test/recover2/emask.y.asc
@@ -0,0 +1,72 @@
+# iteration 1
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+1	0 0 0 0	3 0 3	0.05	0 -3 0	1
+1	0 0 0 0	3 1 3	0.05	0 -2.8 0	1
+1	0 0 0 0	3 2 3	0.05	0 -2.6 0	1
+1	0 0 0 0	3 3 3	0.05	0 -2.4 0	1
+1	0 0 0 0	3 4 3	0.05	0 -2.2 0	1
+1	0 0 0 0	3 5 3	0.05	0 -2 0	1
+1	0 0 0 0	3 6 3	0.05	0 -1.8 0	1
+1	0 0 0 0	3 7 3	0.05	0 -1.6 0	1
+1	0 0 0 0	3 8 3	0.05	0 -1.4 0	1
+1	0 0 0 0	3 9 3	0.05	0 -1.2 0	1
+1	0 0 0 0	3 10 3	0.05	0 -1 0	0.5
+1	0 0 0 0	3 11 3	0.05	0 -0.8 0	0.5
+1	0 0 0 0	3 12 3	0.05	0 -0.6 0	0
+1	0 0 0 0	3 13 3	0.05	0 -0.4 0	0
+1	0 0 0 0	3 14 3	0.05	0 -0.2 0	0
+1	0 0 0 0	3 15 3	0.05	0 0 0	0
+1	0 0 0 0	3 16 3	0.05	0 0.2 0	0
+1	0 0 0 0	3 17 3	0.05	0 0.4 0	0
+1	0 0 0 0	3 18 3	0.05	0 0.6 0	0
+1	0 0 0 0	3 19 3	0.05	0 0.8 0	0.5
+1	0 0 0 0	3 20 3	0.05	0 1 0	0.5
+1	0 0 0 0	3 21 3	0.05	0 1.2 0	1
+1	0 0 0 0	3 22 3	0.05	0 1.4 0	1
+1	0 0 0 0	3 23 3	0.05	0 1.6 0	1
+1	0 0 0 0	3 24 3	0.05	0 1.8 0	1
+1	0 0 0 0	3 25 3	0.05	0 2 0	1
+1	0 0 0 0	3 26 3	0.05	0 2.2 0	1
+1	0 0 0 0	3 27 3	0.05	0 2.4 0	1
+1	0 0 0 0	3 28 3	0.05	0 2.6 0	1
+1	0 0 0 0	3 29 3	0.05	0 2.8 0	1
+1	0 0 0 0	3 30 3	0.05	0 3 0	1
+
+
+# iteration 2
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+2	0 0 0 0	3 0 3	0.1	0 -3 0	1
+2	0 0 0 0	3 1 3	0.1	0 -2.8 0	1
+2	0 0 0 0	3 2 3	0.1	0 -2.6 0	1
+2	0 0 0 0	3 3 3	0.1	0 -2.4 0	1
+2	0 0 0 0	3 4 3	0.1	0 -2.2 0	1
+2	0 0 0 0	3 5 3	0.1	0 -2 0	1
+2	0 0 0 0	3 6 3	0.1	0 -1.8 0	1
+2	0 0 0 0	3 7 3	0.1	0 -1.6 0	1
+2	0 0 0 0	3 8 3	0.1	0 -1.4 0	1
+2	0 0 0 0	3 9 3	0.1	0 -1.2 0	1
+2	0 0 0 0	3 10 3	0.1	0 -1 0	0.5
+2	0 0 0 0	3 11 3	0.1	0 -0.8 0	0.5
+2	0 0 0 0	3 12 3	0.1	0 -0.6 0	0
+2	0 0 0 0	3 13 3	0.1	0 -0.4 0	0
+2	0 0 0 0	3 14 3	0.1	0 -0.2 0	0
+2	0 0 0 0	3 15 3	0.1	0 0 0	0
+2	0 0 0 0	3 16 3	0.1	0 0.2 0	0
+2	0 0 0 0	3 17 3	0.1	0 0.4 0	0
+2	0 0 0 0	3 18 3	0.1	0 0.6 0	0
+2	0 0 0 0	3 19 3	0.1	0 0.8 0	0.5
+2	0 0 0 0	3 20 3	0.1	0 1 0	0.5
+2	0 0 0 0	3 21 3	0.1	0 1.2 0	1
+2	0 0 0 0	3 22 3	0.1	0 1.4 0	1
+2	0 0 0 0	3 23 3	0.1	0 1.6 0	1
+2	0 0 0 0	3 24 3	0.1	0 1.8 0	1
+2	0 0 0 0	3 25 3	0.1	0 2 0	1
+2	0 0 0 0	3 26 3	0.1	0 2.2 0	1
+2	0 0 0 0	3 27 3	0.1	0 2.4 0	1
+2	0 0 0 0	3 28 3	0.1	0 2.6 0	1
+2	0 0 0 0	3 29 3	0.1	0 2.8 0	1
+2	0 0 0 0	3 30 3	0.1	0 3 0	1
+
+
diff --git a/test/recover2/emask.z.asc b/test/recover2/emask.z.asc
new file mode 100644
index 0000000..7b84cb8
--- /dev/null
+++ b/test/recover2/emask.z.asc
@@ -0,0 +1,48 @@
+# iteration 1
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+1	0 0 0 0	3 15 0	0.05	0 0 -0.6	0
+1	0 0 0 0	3 15 1	0.05	0 0 -0.4	0
+1	0 0 0 0	3 15 2	0.05	0 0 -0.2	0
+1	0 0 0 0	3 15 3	0.05	0 0 0	0
+1	0 0 0 0	3 15 4	0.05	0 0 0.2	0
+1	0 0 0 0	3 15 5	0.05	0 0 0.4	0
+1	0 0 0 0	3 15 6	0.05	0 0 0.6	0
+1	0 0 0 0	3 15 7	0.05	0 0 0.8	0.5
+1	0 0 0 0	3 15 8	0.05	0 0 1	0.5
+1	0 0 0 0	3 15 9	0.05	0 0 1.2	1
+1	0 0 0 0	3 15 10	0.05	0 0 1.4	1
+1	0 0 0 0	3 15 11	0.05	0 0 1.6	1
+1	0 0 0 0	3 15 12	0.05	0 0 1.8	1
+1	0 0 0 0	3 15 13	0.05	0 0 2	1
+1	0 0 0 0	3 15 14	0.05	0 0 2.2	1
+1	0 0 0 0	3 15 15	0.05	0 0 2.4	1
+1	0 0 0 0	3 15 16	0.05	0 0 2.6	1
+1	0 0 0 0	3 15 17	0.05	0 0 2.8	1
+1	0 0 0 0	3 15 18	0.05	0 0 3	1
+
+
+# iteration 2
+# refinement level 0   multigrid level 0   map 0   component 0   time level 0
+# column format: 1:it   2:tl 3:rl 4:c 5:ml      6:ix 7:iy 8:iz  9:time  10:x 11:y 12:z  13:data
+2	0 0 0 0	3 15 0	0.1	0 0 -0.6	0
+2	0 0 0 0	3 15 1	0.1	0 0 -0.4	0
+2	0 0 0 0	3 15 2	0.1	0 0 -0.2	0
+2	0 0 0 0	3 15 3	0.1	0 0 0	0
+2	0 0 0 0	3 15 4	0.1	0 0 0.2	0
+2	0 0 0 0	3 15 5	0.1	0 0 0.4	0
+2	0 0 0 0	3 15 6	0.1	0 0 0.6	0
+2	0 0 0 0	3 15 7	0.1	0 0 0.8	0.5
+2	0 0 0 0	3 15 8	0.1	0 0 1	0.5
+2	0 0 0 0	3 15 9	0.1	0 0 1.2	1
+2	0 0 0 0	3 15 10	0.1	0 0 1.4	1
+2	0 0 0 0	3 15 11	0.1	0 0 1.6	1
+2	0 0 0 0	3 15 12	0.1	0 0 1.8	1
+2	0 0 0 0	3 15 13	0.1	0 0 2	1
+2	0 0 0 0	3 15 14	0.1	0 0 2.2	1
+2	0 0 0 0	3 15 15	0.1	0 0 2.4	1
+2	0 0 0 0	3 15 16	0.1	0 0 2.6	1
+2	0 0 0 0	3 15 17	0.1	0 0 2.8	1
+2	0 0 0 0	3 15 18	0.1	0 0 3	1
+
+
diff --git a/test/recover2/h.ah1.dx b/test/recover2/h.ah1.dx
new file mode 100644
index 0000000..42d895a
--- /dev/null
+++ b/test/recover2/h.ah1.dx
@@ -0,0 +1,15 @@
+# list the size of each patch (N_rho x N_sigma)
+object "+z patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "+x patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "+y patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "-x patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "-y patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+
+# collect all patch sizes into a single OpenDX group
+# for the ImportAHFinderDirectGnuplot macro to read
+object "patchsizes" class group
+member 0 value "+z patch"
+member 1 value "+x patch"
+member 2 value "+y patch"
+member 3 value "-x patch"
+member 4 value "-y patch"
diff --git a/test/recover2/h.ah2.dx b/test/recover2/h.ah2.dx
new file mode 100644
index 0000000..42d895a
--- /dev/null
+++ b/test/recover2/h.ah2.dx
@@ -0,0 +1,15 @@
+# list the size of each patch (N_rho x N_sigma)
+object "+z patch" class array type int rank 1 shape 2 items 1 data follows 19 19
+object "+x patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "+y patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "-x patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+object "-y patch" class array type int rank 1 shape 2 items 1 data follows 10 19
+
+# collect all patch sizes into a single OpenDX group
+# for the ImportAHFinderDirectGnuplot macro to read
+object "patchsizes" class group
+member 0 value "+z patch"
+member 1 value "+x patch"
+member 2 value "+y patch"
+member 3 value "-x patch"
+member 4 value "-y patch"
diff --git a/test/recover2/h.t2.ah1.gp b/test/recover2/h.t2.ah1.gp
new file mode 100644
index 0000000..3c61cd6
--- /dev/null
+++ b/test/recover2/h.t2.ah1.gp
@@ -0,0 +1,1228 @@
+# N_patches = 5
+# origin = 0.4 0.6 0
+
+### +z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-45	2.36780114092420	-0.9670506261	-0.7670506261	1.367050626
+-40	-45	2.35125989303909	-0.7997858628	-0.8298491123	1.429849112
+-35	-45	2.33201651495163	-0.6347451257	-0.8777691888	1.477769189
+-30	-45	2.31071669589907	-0.4733688182	-0.9127191669	1.512719167
+-25	-45	2.28781854776532	-0.3164203416	-0.9363683806	1.536368381
+-20	-45	2.26363192758486	-0.1641957014	-0.9501149496	1.550114950
+-15	-45	2.23835106095368	-0.01668424369	-0.9550867682	1.555086768
+-10	-45	2.21207950797246	0.1263126081	-0.9521583297	1.552158330
+-5	-45	2.18484959587350	0.2650947457	-0.9419741128	1.541974113
+0	-45	2.15663992482467	0.4000000000	-0.9249747154	1.524974715
+5	-45	2.12738474119855	0.5313570417	-0.9014178573	1.501417857
+10	-45	2.09697973073295	0.6594467835	-0.8713958267	1.471395827
+15	-45	2.06529228881559	0.7844681786	-0.8348547763	1.434854776
+20	-45	2.03216382111544	0.9065037643	-0.7916076553	1.391607655
+25	-45	1.99741661629951	1.025482251	-0.7413510154	1.341351015
+30	-45	1.96086166545986	1.141136046	-0.6836852870	1.283685287
+35	-45	1.92231004356450	1.252953200	-0.6181434117	1.218143412
+40	-45	1.88158602334607	1.360123684	-0.5442308497	1.144230850
+45	-45	1.83855702990376	1.461491396	-0.4614913961	1.061491396
+
+-45	-40	2.32683079880043	-1.014993282	-0.5873203408	1.414993282
+-40	-40	2.30879720061965	-0.8484040560	-0.6484040560	1.487790019
+-35	-40	2.28798677937430	-0.6814949463	-0.6960186245	1.544534852
+-30	-40	2.26502843312020	-0.5161626568	-0.7315170850	1.586840270
+-25	-40	2.24039142336830	-0.3536552852	-0.7561687456	1.616218975
+-20	-40	2.21441135024114	-0.1947320020	-0.7710994927	1.634012746
+-15	-40	2.18731557981384	-0.03980127507	-0.7772651612	1.641360704
+-10	-40	2.15924457402934	0.1109663435	-0.7754448330	1.639191321
+-5	-40	2.13026975154564	0.2575484525	-0.7662460504	1.628228639
+0	-40	2.10041209851633	0.4000000000	-0.7501188722	1.609009016
+5	-40	2.06965090261780	0.5383979535	-0.7273682215	1.581895847
+10	-40	2.03793184798257	0.6727948935	-0.6981682872	1.547096720
+15	-40	2.00517839142413	0.8031791395	-0.6625806564	1.504685033
+20	-40	1.97129663163709	0.9294378536	-0.6205698870	1.454618548
+25	-40	1.93618522954822	1.051322004	-0.5720246144	1.396764545
+30	-40	1.89974318346530	1.168411441	-0.5167809061	1.330927657
+35	-40	1.86188198812652	1.280081991	-0.4546537048	1.256887342
+40	-40	1.82254161794474	1.385477784	-0.3854777836	1.174446689
+45	-40	1.78170841729540	1.483493240	-0.3091587778	1.083493240
+
+-45	-35	2.28515211076205	-1.048071812	-0.4139507988	1.448071812
+-40	-35	2.26517881310958	-0.8830991665	-0.4707139835	1.529138041
+-35	-35	2.24246314911873	-0.7157214214	-0.5157214214	1.593415324
+-30	-35	2.21761420366881	-0.5481078142	-0.5498604468	1.642170905
+-25	-35	2.19110624776655	-0.3818545093	-0.5740326619	1.676692406
+-20	-35	2.16329541085500	-0.2180930933	-0.5890902126	1.698196817
+-15	-35	2.13443863797643	-0.05759731389	-0.5957979262	1.707776425
+-10	-35	2.10471134454565	0.09912077303	-0.5948137600	1.706370890
+-5	-35	2.07422375518639	0.2517278886	-0.5866823192	1.694757989
+0	-35	2.04303900322662	0.4000000000	-0.5718390308	1.673559576
+5	-35	2.01118082312383	0.5437656021	-0.5506148831	1.643248352
+10	-35	1.97864319819611	0.6828571421	-0.5232467224	1.604162568
+15	-35	1.94540185762625	0.8170701601	-0.4898919583	1.556527028
+20	-35	1.91142123241542	0.9461280305	-0.4506435081	1.500474432
+25	-35	1.87666174718598	1.069650982	-0.4055478546	1.436071164
+30	-35	1.84109201758570	1.187131380	-0.3546290272	1.363351542
+35	-35	1.80469455442133	1.297912804	-0.2979128037	1.282352381
+40	-35	1.76748357565997	1.401182198	-0.2354613637	1.193162481
+45	-35	1.72951154314330	1.495969456	-0.1674060744	1.095969456
+
+-45	-30	2.24329149146550	-1.068579009	-0.2478844864	1.468579009
+-40	-30	2.22102271071833	-0.9056479302	-0.2983631454	1.556010611
+-35	-30	2.19612974566349	-0.7387204891	-0.3389224552	1.626261397
+-30	-30	2.16920530539174	-0.5700981040	-0.3700981040	1.680259204
+-25	-30	2.14072795914791	-0.4016032520	-0.3924903553	1.719043721
+-20	-30	2.11107323596290	-0.2346447239	-0.4067095264	1.743672048
+-15	-30	2.08052644984856	-0.07029181987	-0.4133380375	1.755152966
+-10	-30	2.04929657300466	0.09065092318	-0.4129066582	1.754405795
+-5	-30	2.01753162285162	0.2475737546	-0.4058827080	1.742239957
+0	-30	1.98533395444008	0.4000000000	-0.3926669772	1.719349640
+5	-30	1.95276779085316	0.5475332823	-0.3735933411	1.686313133
+10	-30	1.91986927726325	0.6898115365	-0.3489345756	1.643602898
+15	-30	1.88665787650554	0.8264688710	-0.3189127060	1.591603495
+20	-30	1.85314256223800	0.9571039079	-0.2837098777	1.530630407
+25	-30	1.81932890985899	1.081254227	-0.2434824184	1.460954404
+30	-30	1.78523017820065	1.198379207	-0.1983792068	1.382833350
+35	-30	1.75087036654072	1.307847983	-0.1485584613	1.296541287
+40	-30	1.71630007841154	1.408942247	-0.09421205349	1.202410548
+45	-30	1.68159436428564	1.500861923	-0.03558292771	1.100861923
+
+-45	-25	2.20155881177710	-1.078441264	-0.08940848370	1.478441264
+-40	-25	2.17673935217441	-0.9176384475	-0.1322430804	1.570300354
+-35	-25	2.14948003231617	-0.7517286150	-0.1670009875	1.644838926
+-30	-25	2.12036269615698	-0.5830485544	-0.1939774063	1.702690043
+-25	-25	2.08987242516347	-0.4135489246	-0.2135489246	1.744661299
+-20	-25	2.05840457219913	-0.2448267515	-0.2261325353	1.771646939
+-15	-25	2.02627134398522	-0.07817100306	-0.2321532848	1.784558478
+-10	-25	1.99371325722761	0.08538365986	-0.2320224630	1.784277930
+-5	-25	1.96091279660194	0.2450024593	-0.2261246350	1.771629997
+0	-25	1.92800679354630	0.4000000000	-0.2148108797	1.747367570
+5	-25	1.89509361302146	0.5497949577	-0.1983952790	1.712164201
+10	-25	1.86224225990066	0.6938696636	-0.1771565877	1.666617681
+15	-25	1.82950372558095	0.8317366646	-0.1513443544	1.611263168
+20	-25	1.79691636379576	0.9629115662	-0.1211852769	1.546586817
+25	-25	1.76451126530674	1.086891805	-0.08689180499	1.473044229
+30	-25	1.73232288853702	1.203144441	-0.04867451047	1.391086977
+35	-25	1.70039063332571	1.311098740	-0.006751993668	1.301183849
+40	-25	1.66877102305551	1.410151655	0.03863465635	1.203851864
+45	-25	1.63753393266612	1.499674342	0.08721343282	1.099674342
+
+-45	-20	2.16010799770576	-1.079222686	0.06160697244	1.479222686
+-40	-20	2.13258130284134	-0.9204326930	0.02724537262	1.573630406
+-35	-20	2.10285382016539	-0.7558675174	-0.0008238245750	1.650749891
+-30	-20	2.07150278259434	-0.5878395262	-0.02274879385	1.710988249
+-25	-20	2.03902229559744	-0.4183535353	-0.03875495659	1.754964820
+-20	-20	2.00582635041313	-0.2491166520	-0.04911665199	1.783433344
+-15	-20	1.97225164791435	-0.08156248593	-0.05413300644	1.797215665
+-10	-20	1.93856629597602	0.08311330553	-0.05411047112	1.797153749
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+-35	40	1.57467207963757	-0.3443224373	1.491965094	1.063002605
+-30	40	1.53756044797758	-0.2219151356	1.503868568	1.077188613
+-25	40	1.50391144819716	-0.1059074944	1.510357753	1.084922123
+-20	40	1.47338380538239	0.004288290764	1.512276659	1.087208986
+-15	40	1.44566199775990	0.1093222415	1.510275555	1.084824163
+-10	40	1.42046399627847	0.2098585461	1.504839539	1.078345771
+-5	40	1.39754873236741	0.3065456478	1.496316269	1.068188134
+0	40	1.37671598896062	0.4000000000	1.484935980	1.054625633
+5	40	1.35780834364029	0.4907969048	1.470828817	1.037813371
+10	40	1.34071164797357	0.5794659088	1.454037070	1.017801746
+15	40	1.32535402440872	0.6664875591	1.434522435	0.9945451102
+20	40	1.31170837332154	0.7522899875	1.412171905	0.9679087858
+25	40	1.29979329368716	0.8372432760	1.386799584	0.9376712313
+30	40	1.28967625382112	0.9216505038	1.358147642	0.9035251763
+35	40	1.28147870155723	1.005734593	1.325887177	0.8650786509
+40	40	1.27537607987457	1.089616511	1.289616511	0.8218529550
+45	40	1.27160433139715	1.173288538	1.248866127	0.7732885377
+
+-45	45	1.61556236910744	-0.5327453687	1.532745369	0.9327453687
+-40	45	1.57247198302766	-0.4023909481	1.556252295	0.9562522951
+-35	45	1.53395441508082	-0.2806349114	1.572047392	0.9720473921
+-30	45	1.49947726234264	-0.1667491333	1.581638294	0.9816382939
+-25	45	1.46853839799945	-0.05986635688	1.586186585	0.9861865848
+-20	45	1.44068480956417	0.04091857574	1.586568105	0.9865681049
+-15	45	1.41552309382464	0.1364907677	1.583429843	0.9834298434
+-10	45	1.39271858390099	0.2276872439	1.577234201	0.9772342012
+-5	45	1.37199452473181	0.3152851205	1.568295504	0.9682955037
+0	45	1.35312746600398	0.4000000000	1.556805607	0.9568056070
+5	45	1.33594416169081	0.4824889215	1.542852688	0.9428526876
+10	45	1.32031986535741	0.5633552949	1.526433914	0.9264339141
+15	45	1.30617628102224	0.6431535809	1.507461518	0.9074615180
+20	45	1.29348323007888	0.7223923772	1.485765776	0.8857657765
+25	45	1.28226017170980	0.8015341475	1.461092758	0.8610927582
+30	45	1.27258091866288	0.8809903763	1.433099770	0.8330997697
+35	45	1.26458242150222	0.9611111621	1.401349788	0.8013497877
+40	45	1.25847170776402	1.042164896	1.365302321	0.7653023213
+45	45	1.25453589585781	1.124306637	1.324306637	0.7243066372
+
+
+### +x patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	-45	1.83855710368077	1.461491439	-0.4614914387	1.061491439
+45	-40	1.78170853158578	1.483493309	-0.3091588361	1.083493309
+45	-35	1.72951164584203	1.495969521	-0.1674061200	1.095969521
+45	-30	1.68159442128726	1.500861961	-0.03558294926	1.100861961
+45	-25	1.63753399996246	1.499674387	0.08721341175	1.099674387
+45	-20	1.59690142182508	1.493543847	0.2019825897	1.093543847
+45	-15	1.55929251654012	1.483313160	0.3097271137	1.083313160
+45	-10	1.52433778672871	1.469587953	0.4114027856	1.069587953
+45	-5	1.49171309695831	1.452787791	0.5078930032	1.052787791
+45	0	1.46113672057138	1.433179683	0.6000000000	1.033179683
+45	5	1.43237452440768	1.410909145	0.6884430900	1.010909145
+45	10	1.40523460608306	1.386016367	0.7738612889	0.9860163666
+45	15	1.37957034623907	1.358451795	0.8568163843	0.9584517946
+45	20	1.35527982646349	1.328083534	0.9377947814	0.9280835344
+45	25	1.33230900482341	1.294702698	1.017206720	0.8947026984
+45	30	1.31065647503188	1.258026072	1.095381584	0.8580260724
+45	35	1.29037968724845	1.217697187	1.172557734	0.8176971867
+45	40	1.27160436703282	1.173288559	1.248866145	0.7732885594
+45	45	1.25453589649598	1.124306638	1.324306638	0.7243066376
+
+50	-45	1.85265029385819	1.526634442	-0.5266344422	0.9453585449
+50	-40	1.79316359383388	1.555515476	-0.3695926099	0.9695926099
+50	-35	1.73785671955745	1.573162492	-0.2214572202	0.9844002140
+50	-30	1.68657678655878	1.581586917	-0.08218952449	0.9914691461
+50	-25	1.63907421986389	1.582428583	0.04862449671	0.9921753875
+50	-20	1.59505351270153	1.576988986	0.1716110429	0.9876110244
+50	-15	1.55420796410954	1.566277012	0.2874970166	0.9786226103
+50	-10	1.51623918584347	1.551053542	0.3970382044	0.9658486023
+50	-5	1.48087536022509	1.531877158	0.5009735802	0.9497577058
+50	0	1.44787301660375	1.509135079	0.6000000000	0.9306748355
+50	5	1.41702857838521	1.483077160	0.6947569733	0.9088096459
+50	10	1.38817546610378	1.453833921	0.7858193535	0.8842716546
+50	15	1.36118931049052	1.421435894	0.8736929229	0.8570864819
+50	20	1.33598906678531	1.385825494	0.9588111361	0.8272058087
+50	25	1.31254069308444	1.346867209	1.041531431	0.7945159255
+50	30	1.29086074165762	1.304355008	1.122129607	0.7588439539
+50	35	1.27102091053359	1.258018985	1.200791361	0.7199634137
+50	40	1.25315299888039	1.207532391	1.277600131	0.6776001314
+50	45	1.23745505170122	1.152521664	1.352521664	0.6314406507
+
+55	-45	1.86481952356807	1.581712401	-0.5817124008	0.8274439310
+55	-40	1.80331006281718	1.617347611	-0.4214759317	0.8523959741
+55	-35	1.74546926420307	1.640268976	-0.2684456863	0.8684456863
+55	-30	1.69133707115326	1.652456142	-0.1231058905	0.8769792316
+55	-25	1.64083121441031	1.655607408	0.01450064997	0.8791857722
+55	-20	1.59379589306142	1.651137084	0.1446233424	0.8760556176
+55	-15	1.55003405597948	1.640191014	0.2676918194	0.8683910967
+55	-10	1.50933358065177	1.623675110	0.3842330626	0.8568265360
+55	-5	1.47148796197692	1.602288795	0.4948133602	0.8418516773
+55	0	1.43630314969611	1.576550661	0.6000000000	0.8238296421
+55	5	1.40361347915485	1.546831508	0.7003347559	0.8030200669
+55	10	1.37328017263025	1.513371350	0.7963174085	0.7795910118
+55	15	1.34520173134708	1.476303513	0.8883946570	0.7536358329
+55	20	1.31931422500717	1.435667716	0.9769522213	0.7251823419
+55	25	1.29559517653709	1.391423668	1.062308449	0.6942023261
+55	30	1.27406588188611	1.343461635	1.144707829	0.6606189489
+55	35	1.25479431893222	1.291612643	1.224313894	0.6243138941
+55	40	1.23789789212233	1.235658866	1.301201046	0.5851346373
+55	45	1.22354625700029	1.175345692	1.375345692	0.5429028986
+
+60	-45	1.87511391705615	1.627550209	-0.6275502088	0.7087264435
+60	-40	1.81208448781005	1.669515471	-0.4652499632	0.7329550987
+60	-35	1.75221960971500	1.697540419	-0.3085475824	0.7491353101
+60	-30	1.69571843810848	1.713497854	-0.1583483397	0.7583483397
+60	-25	1.64264892774743	1.719077146	-0.01509577466	0.7615695451
+60	-20	1.59299025808337	1.715753778	0.1211047892	0.7596507980
+60	-15	1.54665837575355	1.704776508	0.2503861884	0.7533130681
+60	-10	1.50353446340272	1.687178055	0.3730357800	0.7431525963
+60	-5	1.46348622805543	1.663793912	0.4894323597	0.7296517554
+60	0	1.42637574046236	1.635277627	0.6000000000	0.7131878702
+60	5	1.39208013161466	1.602131159	0.7051728485	0.6940507483
+60	10	1.36049052340316	1.564717928	0.8053711957	0.6724502094
+60	15	1.33152620442717	1.523288852	0.9009843407	0.6485311210
+60	20	1.30513380707419	1.477994500	0.9923579109	0.6223804150
+60	25	1.28129443043687	1.428902872	1.079785289	0.5940373503
+60	30	1.26002347008347	1.376009983	1.163499626	0.5634996265
+60	35	1.24137246504201	1.319251753	1.243667007	0.5307302471
+60	40	1.22543089762057	1.258515976	1.320380439	0.4956644299
+60	45	1.21232694867114	1.193654287	1.393654287	0.4582165163
+
+65	-45	1.88361611667965	1.664929094	-0.6649290940	0.5898461235
+65	-40	1.81946750395018	1.712564346	-0.5013722588	0.6120588065
+65	-35	1.75801973069737	1.745283158	-0.3419774081	0.6273158388
+65	-30	1.69959483155734	1.764805748	-0.1879709662	0.6364193723
+65	-25	1.64439165373974	1.772766320	-0.04013144793	0.6401314479
+65	-20	1.59251101615059	1.770657307	0.1011215389	0.6391479989
+65	-15	1.54397704126258	1.759796815	0.2356435417	0.6340836682
+65	-10	1.49876482988683	1.741322780	0.3634886041	0.6254690843
+65	-5	1.45681544751648	1.716192108	0.4848481116	0.6137504594
+65	0	1.41804980451932	1.685189580	0.6000000000	0.5992937434
+65	5	1.38238979244517	1.648950605	0.7092690192	0.5823952318
+65	10	1.34975664772610	1.607967589	0.8129972778	0.5632845378
+65	15	1.32008751751704	1.562614957	0.9115217388	0.5421362579
+65	20	1.29333549858907	1.513160119	1.005157149	0.5190750880
+65	25	1.26947700537737	1.459781150	1.094184066	0.4941840660
+65	30	1.24851421459390	1.402579759	1.178839694	0.4675106196
+65	35	1.23047416604054	1.341591350	1.259309361	0.4390712574
+65	40	1.21541161248317	1.276798264	1.335721100	0.4088577451
+65	45	1.20340895611117	1.208140781	1.408140781	0.3768422353
+
+70	-45	1.89041641440815	1.694540296	-0.6945402958	0.4711741347
+70	-40	1.82546321959612	1.747008165	-0.5302740541	0.4902708772
+70	-35	1.76280964995537	1.783813658	-0.3689567550	0.5036669814
+70	-30	1.70287154129959	1.806511843	-0.2120499913	0.5119284451
+70	-25	1.64595188738118	1.816653297	-0.06059628127	0.5156196323
+70	-20	1.59225501945511	1.815716118	0.08472147296	0.5152785270
+70	-15	1.54190209395873	1.805059339	0.2235154848	0.5113997767
+70	-10	1.49495428669766	1.785901894	0.3556281035	0.5044270370
+70	-5	1.45142350074719	1.759305991	0.4810761355	0.4947469201
+70	0	1.41128715681329	1.726176127	0.6000000000	0.4826886356
+70	5	1.37450776533321	1.687271868	0.7126216953	0.4685286432
+70	10	1.34103505920293	1.643210609	0.8192115730	0.4524916564
+70	15	1.31082090442204	1.594486447	0.9200616787	0.4347575118
+70	20	1.28382097328065	1.541479237	1.015464465	0.4154644652
+70	25	1.26000313631314	1.484471309	1.105697276	0.3947152762
+70	30	1.23935153432982	1.423660663	1.191010759	0.3725820113
+70	35	1.22186575766357	1.359170222	1.271618220	0.3491094106
+70	40	1.20756491471146	1.291061393	1.347689286	0.3243198240
+70	45	1.19648701381318	1.219343633	1.419343633	0.2982166940
+
+75	-45	1.89560358188232	1.716964126	-0.7169641257	0.3528794739
+75	-40	1.83009047990760	1.773299137	-0.5523347994	0.3679743947
+75	-35	1.76655590596355	1.813431371	-0.3896953004	0.3787277943
+75	-30	1.70548106695150	1.838760922	-0.2306690056	0.3855148272
+75	-25	1.64724730452264	1.850748021	-0.07649491238	0.3887267607
+75	-20	1.59214081766713	1.850839410	0.07193763999	0.3887512483
+75	-15	1.54036330883740	1.840413950	0.2140422454	0.3859577546
+75	-10	1.49204878001560	1.820748877	0.3494836402	0.3806885142
+75	-5	1.44727076249696	1.792991014	0.4781290779	0.3732508173
+75	0	1.40605689195242	1.758146665	0.6000000000	0.3639143021
+75	5	1.36840577969094	1.717083855	0.7152299062	0.3529115553
+75	10	1.33428978707439	1.670528646	0.8240284800	0.3404371246
+75	15	1.30367208586776	1.619080880	0.9266517374	0.3266517374
+75	20	1.27650861591858	1.563219350	1.023377219	0.3116836855
+75	25	1.25275745565764	1.503316663	1.114485010	0.2956328090
+75	30	1.23238285901597	1.439650532	1.200242515	0.2785735205
+75	35	1.21535951580160	1.372416022	1.280893029	0.2605580877
+75	40	1.20167437782538	1.301735955	1.356646307	0.2416194208
+75	45	1.19132678662913	1.227670223	1.427670223	0.2217735679
+
+80	-45	1.89925173714658	1.732655266	-0.7326552655	0.2349830793
+80	-40	1.83337359316774	1.791806245	-0.5678641067	0.2454129929
+80	-35	1.76924035796933	1.834391586	-0.4043718014	0.2529219375
+80	-30	1.70737624663940	1.861687304	-0.2439055581	0.2577349090
+80	-25	1.64821630045007	1.875074692	-0.08783862522	0.2600954668
+80	-20	1.59210544449680	1.875966169	0.06279224779	0.2602526582
+80	-15	1.53930540678781	1.865747271	0.2072542024	0.2584507908
+80	-10	1.49000560593100	1.845733852	0.3450781150	0.2549218850
+80	-5	1.44432734981270	1.817134476	0.4760167987	0.2498790434
+80	0	1.40233722059248	1.781032567	0.6000000000	0.2435133028
+80	5	1.36406208510749	1.738380394	0.7170931120	0.2359925740
+80	10	1.32949193789180	1.689989442	0.8274599435	0.2274599435
+80	15	1.29859703988388	1.636541533	0.9313303052	0.2180356350
+80	20	1.27133233411578	1.578592486	1.028972583	0.2078176546
+80	25	1.24764692855188	1.516584279	1.120671800	0.1968839346
+80	30	1.22748910284337	1.450855217	1.206711543	0.1852941276
+80	35	1.21081232895664	1.381652385	1.287360400	0.1730918012
+80	40	1.19757831956371	1.309142027	1.362860739	0.1603062686
+80	45	1.18775737025889	1.233418279	1.433418279	0.1469541288
+
+85	-45	1.90141766701521	1.741939887	-0.7419398871	0.1174045273
+85	-40	1.83533411681296	1.802800546	-0.5770894209	0.1227291450
+85	-35	1.77085382618272	1.846887618	-0.4131216173	0.1265862640
+85	-30	1.70852534395794	1.875397504	-0.2518211463	0.1290805558
+85	-25	1.64881497807079	1.889658326	-0.09463908554	0.1303282161
+85	-20	1.59210275361291	1.891056753	0.05729972443	0.1304505625
+85	-15	1.53868735601227	1.880979037	0.2031728629	0.1295688767
+85	-10	1.48879288589414	1.860762843	0.3424280983	0.1278001889
+85	-5	1.44257082295207	1.831654181	0.4747464890	0.1252535110
+85	0	1.40011240382768	1.794784553	0.6000000000	0.1220278365
+85	5	1.36146237751187	1.751159523	0.7182111409	0.1182111409
+85	10	1.32662171612369	1.701644929	0.8295151203	0.1138791752
+85	15	1.29556538945438	1.646975336	0.9341260344	0.1090962056
+85	20	1.26824633505670	1.587754533	1.032307295	0.1039150567
+85	25	1.24460763317992	1.524468269	1.124348165	0.09837822600
+85	30	1.22458696449154	1.457492391	1.210543517	0.09251859599
+85	35	1.20812406101435	1.387105609	1.291178789	0.08636055053
+85	40	1.19516468453354	1.313499976	1.366517493	0.07992089206
+85	45	1.18566116146766	1.236789325	1.436789325	0.07320957965
+
+90	-45	1.90213490743581	1.745012492	-0.7450124918	0.000000000
+90	-40	1.83598514961913	1.806446222	-0.5801485057	0.000000000
+90	-35	1.77139125527095	1.851038768	-0.4160282836	0.000000000
+90	-30	1.70890957096503	1.879959101	-0.2544547855	0.000000000
+90	-25	1.64901670086095	1.894516677	-0.09690457170	0.000000000
+90	-20	1.59210426616875	1.896088630	0.05546827070	0.000000000
+90	-15	1.53848342293054	1.886060872	0.2018111896	0.000000000
+90	-10	1.48839011494307	1.865778125	0.3415437689	0.000000000
+90	-5	1.44198613066850	1.836498938	0.4743226277	0.000000000
+90	0	1.39937115520189	1.799371155	0.6000000000	0.000000000
+90	5	1.36059605531513	1.755418577	0.7185837598	0.000000000
+90	10	1.32566556678831	1.705525728	0.8301994099	0.000000000
+90	15	1.29455620320659	1.650445270	0.9350558003	0.000000000
+90	20	1.26722010568657	1.590797382	1.033414802	0.000000000
+90	25	1.24359821704181	1.527082748	1.125567317	0.000000000
+90	30	1.22362459487473	1.459689984	1.211812297	0.000000000
+90	35	1.20723410637523	1.388908286	1.292441037	0.000000000
+90	40	1.19436704328397	1.314938237	1.367724337	0.000000000
+90	45	1.18496964630267	1.237900072	1.437900072	0.000000000
+
+
+### +y patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	45	1.25453593314896	1.124306659	1.324306659	0.7243066587
+40	45	1.25847179665140	1.042164941	1.365302375	0.7653023754
+35	45	1.26458247455989	0.9611111856	1.401349821	0.8013498213
+30	45	1.27258097801434	0.8809903987	1.433099809	0.8330998085
+25	45	1.28226019564128	0.8015341550	1.461092774	0.8610927742
+20	45	1.29348323725399	0.7223923790	1.485765781	0.8857657814
+15	45	1.30617628949730	0.6431535825	1.507461524	0.9074615239
+10	45	1.32031986988007	0.5633552955	1.526433917	0.9264339173
+5	45	1.33594416470411	0.4824889217	1.542852690	0.9428526897
+0	45	1.35312747000108	0.4000000000	1.556805610	0.9568056098
+-5	45	1.37199453288963	0.3152851200	1.568295509	0.9682955095
+-10	45	1.39271860314216	0.2276872415	1.577234215	0.9772342147
+-15	45	1.41552311974411	0.1364907628	1.583429861	0.9834298614
+-20	45	1.44068485444865	0.04091856455	1.586568136	0.9865681356
+-25	45	1.46853847138171	-0.05986637986	1.586186634	0.9861866341
+-30	45	1.49947735422727	-0.1667491680	1.581638354	0.9816383541
+-35	45	1.53395458947413	-0.2806349888	1.572047503	0.9720475026
+-40	45	1.57247212216943	-0.4023910191	1.556252380	0.9562523797
+-45	45	1.61556257171606	-0.5327454857	1.532745486	0.9327454857
+
+45	50	1.23745507716645	1.152521679	1.352521679	0.6314406637
+40	50	1.23947181920476	1.070202496	1.398716232	0.6702024959
+35	50	1.24402374184178	0.9880302290	1.439794199	0.7046710030
+30	50	1.25084326938723	0.9059432704	1.476319450	0.7353193273
+25	50	1.25972903946348	0.8237658824	1.508768868	0.7625476216
+20	50	1.27054034880511	0.7412333509	1.537530926	0.7866818545
+15	50	1.28319492438818	0.6580106726	1.562908939	0.8079765356
+10	50	1.29766314686891	0.5737034927	1.585121460	0.8266150541
+5	50	1.31396538670640	0.4878651178	1.604302892	0.8427101867
+0	50	1.33217041917687	0.4000000000	1.620501747	0.8563026394
+-5	50	1.35239315243702	0.3095652101	1.633674379	0.8673557899
+-10	50	1.37479611053976	0.2159715896	1.643676978	0.8757489677
+-15	50	1.39958844910452	0.1185862021	1.650250592	0.8812648841
+-20	50	1.42702681317282	0.01673854612	1.653002190	0.8835737495
+-25	50	1.45741572093148	-0.09026658884	1.651380093	0.8822126480
+-30	50	1.49110175214138	-0.2031234411	1.644640443	0.8765574107
+-35	50	1.52846954968746	-0.3224832366	1.631812994	0.8657939029
+-40	50	1.56992067900889	-0.4488815487	1.611657635	0.8488815487
+-45	50	1.61584828872881	-0.5826303116	1.582630312	0.8245247320
+
+45	55	1.22354629667482	1.175345718	1.375345718	0.5429029162
+40	55	1.22377029464923	1.093198540	1.426121850	0.5784567468
+35	55	1.22680730997176	1.010389159	1.471726061	0.6103891590
+30	55	1.23242591785390	0.9269052846	1.512626724	0.6390281115
+25	55	1.24044729182761	0.8426299773	1.549223049	0.6646531347
+20	55	1.25074164579137	0.7573597803	1.581837927	0.6874903178
+15	55	1.26323077555022	0.6708210953	1.610718087	0.7077124237
+10	55	1.27788486415052	0.5826801623	1.636030683	0.7254364943
+5	55	1.29471968345956	0.4925506811	1.657859125	0.7407209337
+0	55	1.31379689538845	0.4000000000	1.676199413	0.7535629413
+-5	55	1.33522102144956	0.3045541545	1.690951006	0.7638921184
+-10	55	1.35914054051316	0.2057039241	1.701907803	0.7715641500
+-15	55	1.38574335499944	0.1029137190	1.708741095	0.7763488726
+-20	55	1.41525709091258	-0.004364854069	1.710983306	0.7779188855
+-25	55	1.44794473216123	-0.1166714846	1.708005574	0.7758338556
+-30	55	1.48409466580381	-0.2345024970	1.698990562	0.7695214762
+-35	55	1.52401227800232	-0.3582613546	1.682909442	0.7582613546
+-40	55	1.56799399142215	-0.4881823245	1.658494476	0.7411658113
+-45	55	1.61629787931661	-0.6242273975	1.624227397	0.7171717446
+
+45	60	1.21232697197081	1.193654302	1.393654302	0.4582165251
+40	60	1.21094315328632	1.111863690	1.448366110	0.4898044017
+35	60	1.21257804902638	1.028736746	1.497929130	0.5184196249
+30	60	1.21704573849957	0.9442794006	1.542719575	0.5442794006
+25	60	1.22419889944104	0.8584056627	1.583054116	0.5675665586
+20	60	1.23393024889089	0.7709522288	1.619182872	0.5884255057
+15	60	1.24617524036845	0.6816912141	1.651285923	0.6069602107
+10	60	1.26091124761864	0.5903393269	1.679467964	0.6232311198
+5	60	1.27815529249820	0.4965657291	1.703751335	0.6372511302
+0	60	1.29796455171107	0.4000000000	1.724070275	0.6489822759
+-5	60	1.32043335937349	0.3002401266	1.740260570	0.6583297472
+-10	60	1.34569353610744	0.1968624656	1.752050206	0.6651364964
+-15	60	1.37390867289127	0.08943533010	1.759043127	0.6691738614
+-20	60	1.40527134965582	-0.02246191769	1.760704579	0.6701331014
+-25	60	1.43999600718485	-0.1392116627	1.756343142	0.6676150245
+-30	60	1.47830774138762	-0.2611193203	1.745092253	0.6611193203
+-35	60	1.52042680555544	-0.3883601409	1.725894964	0.6500357604
+-40	60	1.56654812887056	-0.5209092334	1.697496887	0.6336401234
+-45	60	1.61681013142320	-0.6584506874	1.658450687	0.6110967893
+
+45	65	1.20340896741194	1.208140789	1.408140789	0.3768422388
+40	65	1.20063781789213	1.126778127	1.466140444	0.4038879223
+35	65	1.20103255859640	1.043534038	1.519061854	0.4285655808
+30	65	1.20445351371466	0.9584121470	1.567198210	0.4510119323
+25	65	1.21078970212628	0.8713381775	1.610787984	0.4713381775
+20	65	1.21996235787624	0.7821718893	1.650008636	0.4896270681
+15	65	1.23192670824472	0.6907170511	1.684970805	0.5059301953
+10	65	1.24667324674071	0.5967302835	1.715712880	0.5202654602
+5	65	1.26422336308674	0.4999287232	1.742190533	0.5326121927
+0	65	1.28463345770582	0.4000000000	1.764273306	0.5429095589
+-5	65	1.30798875777581	0.2966119039	1.781731346	0.5510503766
+-10	65	1.33440384539292	0.1894254590	1.794227566	0.5568774597
+-15	65	1.36401575949363	0.07811182552	1.801303022	0.5601767987
+-20	65	1.39697940401513	-0.03762518953	1.802365326	0.5606721596
+-25	65	1.43345826489738	-0.1580189565	1.796675514	0.5580189565
+-30	65	1.47361321605595	-0.2832007300	1.783338376	0.5517997470
+-35	65	1.51758359767676	-0.4131475654	1.761295075	0.5415207867
+-40	65	1.56547264960960	-0.5476223920	1.729332390	0.5266163421
+-45	65	1.61731558300850	-0.6860968522	1.686096852	0.5064552797
+
+45	70	1.19648702690860	1.219343642	1.419343642	0.2982166973
+40	70	1.19256916392280	1.138404351	1.479996038	0.3202923641
+35	70	1.19191847751917	1.055157215	1.535661470	0.3405529245
+30	70	1.19443767373663	0.9695926434	1.586563398	0.3590797111
+25	70	1.20005190476689	0.8816360865	1.632871921	0.3759346349
+20	70	1.20871235925274	0.7911581477	1.674698178	0.3911581477
+15	70	1.22039681467590	0.6979829296	1.712087433	0.4047667235
+10	70	1.23511020507068	0.6018966238	1.745012652	0.4167505232
+5	70	1.25288234078573	0.5026561921	1.773365645	0.4270701687
+0	70	1.27377095985675	0.4000000000	1.796953172	0.4356553263
+-5	70	1.29785343340249	0.2936590556	1.815482557	0.4423994710
+-10	70	1.32522802708746	0.1833723150	1.828556652	0.4471580523
+-15	70	1.35600548539216	0.06890565250	1.835660927	0.4497437971
+-20	70	1.39030378106625	-0.04992396048	1.836155922	0.4499239605
+-25	70	1.42823749387753	-0.1732174704	1.829268832	0.4474172648
+-30	70	1.46990771959437	-0.3009563093	1.814091942	0.4418933284
+-35	70	1.51538219022342	-0.4329542612	1.789581968	0.4329724275
+-40	70	1.56468515642353	-0.5688078161	1.754580195	0.4202328242
+-45	70	1.61776956545668	-0.7078341659	1.707834166	0.4032186609
+
+45	75	1.19132678836086	1.227670225	1.427670225	0.2217735683
+40	75	1.18651302158554	1.147099807	1.490358879	0.2385709427
+35	75	1.18503319260069	1.063903009	1.548151759	0.2540564981
+30	75	1.18682539722227	0.9780533667	1.601217801	0.2682755011
+25	75	1.19184655087641	0.8894699938	1.649671789	0.2812587082
+20	75	1.20007514497410	0.7980266734	1.693569298	0.2930210101
+15	75	1.21150985368606	0.7035593098	1.732898767	0.3035593098
+10	75	1.22617136816253	0.6058752983	1.767576836	0.3128512703
+5	75	1.24409828223512	0.5047622938	1.797438498	0.3208526785
+0	75	1.26535070610725	0.4000000000	1.822234926	0.3274968615
+-5	75	1.29000010081701	0.2913724329	1.841618773	0.3326907476
+-10	75	1.31813039954986	0.1786846960	1.855141460	0.3363141407
+-15	75	1.34982880844753	0.06178310467	1.862242637	0.3382168953
+-20	75	1.38518045051446	-0.05942020305	1.862246634	0.3382179662
+-25	75	1.42425716933605	-0.1849168648	1.854358265	0.3361042840
+-30	75	1.46710903782158	-0.3145678889	1.837667889	0.3316321114
+-35	75	1.51374540830848	-0.4480607444	1.811156262	0.3245283422
+-40	75	1.56412669788084	-0.5848680403	1.773720025	0.3144973329
+-45	75	1.61814335942214	-0.7241995821	1.724199582	0.3012283701
+
+45	80	1.18775737177606	1.233418280	1.433418280	0.1469541289
+40	80	1.18230255025539	1.153130031	1.497545421	0.1582614741
+35	80	1.18022286472721	1.069995210	1.556852323	0.1687188811
+30	80	1.18148279463991	0.9839719858	1.611469150	0.1783493012
+25	80	1.18606384008063	0.8949717588	1.661470362	0.1871658641
+20	80	1.19396640249399	0.8028677934	1.706870165	0.1951710743
+15	80	1.20520544668287	0.7075019241	1.747612804	0.2023551008
+10	80	1.21981559018379	0.6086956508	1.783571850	0.2086956508
+5	80	1.23784336698532	0.5062583101	1.814538042	0.2141558259
+0	80	1.25935127545454	0.4000000000	1.840218900	0.2186840540
+-5	80	1.28440654823073	0.2897446374	1.860224561	0.2222115919
+-10	80	1.31308192312348	0.1753476110	1.874067010	0.2246523890
+-15	80	1.34544601231566	0.05671642230	1.881151753	0.2259016205
+-20	80	1.38155813409937	-0.06616494047	1.880777648	0.2258356556
+-25	80	1.42145704199194	-0.1932067638	1.872136010	0.2243119017
+-30	80	1.46515403094324	-0.3241822842	1.854320510	0.2211705484
+-35	80	1.51261524137642	-0.4586894867	1.826335679	0.2162360676
+-40	80	1.56375467498930	-0.5961161017	1.787124943	0.2093221569
+-45	80	1.61841942565501	-0.7356025782	1.735602578	0.2002373739
+
+45	85	1.18566116177574	1.236789325	1.436789325	0.07320957967
+40	85	1.17982171438206	1.156677297	1.501772887	0.07889490470
+35	85	1.17737961524696	1.073589611	1.561985660	0.08416283976
+30	85	1.17831547719936	0.9874738961	1.617534636	0.08902274542
+25	85	1.18262624076705	0.8982356549	1.668469810	0.09347899570
+20	85	1.19032622285903	0.8057466566	1.714779777	0.09753059281
+15	85	1.20144120293575	0.7098514270	1.756381268	0.1011702517
+10	85	1.21601479505099	0.6103793256	1.793120444	0.1043845131
+5	85	1.23409914611648	0.5071526253	1.824760112	0.1071526253
+0	85	1.25575856314322	0.4000000000	1.850980023	0.1094465703
+-5	85	1.28105773189384	0.2887701206	1.871363339	0.1112298794
+-10	85	1.31006229831383	0.1733497784	1.885397281	0.1124576902
+-15	85	1.34282897690858	0.05368469664	1.892466308	0.1130761499
+-20	85	1.37940059059480	-0.07019646122	1.891854160	0.1130225939
+-25	85	1.41979502328051	-0.1981539043	1.882745187	0.1122256621
+-30	85	1.46399940815547	-0.3299076121	1.864237069	0.1106064115
+-35	85	1.51195335283331	-0.4650022963	1.835351305	0.1080792347
+-40	85	1.56354278878113	-0.6027763659	1.795062337	0.1045544067
+-45	85	1.61858928992674	-0.7423316227	1.742331623	0.09994106698
+
+45	90	1.18496964645972	1.237900073	1.437900073	0.000000000
+40	90	1.17900195506956	1.157847849	1.503167896	0.000000000
+35	90	1.17643853591678	1.074777423	1.563682032	0.000000000
+30	90	1.17726549831596	0.9886327492	1.619541829	0.000000000
+25	90	1.18148502743236	0.8993171486	1.670789081	0.000000000
+20	90	1.18911621807103	0.8067016993	1.717403735	0.000000000
+15	90	1.20018868595747	0.7106316896	1.759293248	0.000000000
+10	90	1.21474913007631	0.6109389728	1.796294361	0.000000000
+5	90	1.23285167660568	0.5074501036	1.828160304	0.000000000
+0	90	1.25456129773949	0.4000000000	1.854561298	0.000000000
+-5	90	1.27994182401713	0.2884457197	1.875071259	0.000000000
+-10	90	1.30905648904261	0.1726847262	1.889168980	0.000000000
+-15	90	1.34195791078883	0.05267573496	1.896231804	0.000000000
+-20	90	1.37868321319610	-0.07153743018	1.895538442	0.000000000
+-25	90	1.41924316175037	-0.1997980780	1.886271129	0.000000000
+-30	90	1.46361670377104	-0.3318083519	1.867529247	0.000000000
+-35	90	1.51173450126016	-0.4670952879	1.838340407	0.000000000
+-40	90	1.56347310503035	-0.6049811400	1.797689884	0.000000000
+-45	90	1.61864565527610	-0.7445553192	1.744555319	0.000000000
+
+
+### -x patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-90	45	1.61864564809350	-0.7445553141	1.744555314	1.401676002e-16
+-90	40	1.67698609100679	-0.8846458762	1.677945881	1.573237460e-16
+-90	35	1.73814785541947	-1.023807369	1.596960653	1.743661137e-16
+-90	30	1.80170377980948	-1.160321243	1.500851890	1.910842416e-16
+-90	25	1.86713980525775	-1.292203345	1.389087379	2.072351410e-16
+-90	20	1.93386960323120	-1.417242996	1.261422359	2.225480818e-16
+-90	15	2.00123408540714	-1.533043688	1.117957495	2.367295765e-16
+-90	10	2.06852973197637	-1.637104117	0.9591964184	2.494733037e-16
+-90	5	2.13501350535426	-1.726889134	0.7860786878	2.604687971e-16
+-90	-2.84217e-14	2.19992588910757	-1.799925889	0.6000000000	2.694132198e-16
+-90	-5	2.26251705016845	-1.853907490	0.4028086460	2.760240593e-16
+-90	-10	2.32205417657879	-1.886776956	0.1967795238	2.800494080e-16
+-90	-15	2.37782515501177	-1.896802728	-0.01542643604	2.812772109e-16
+-90	-20	2.42915271615398	-1.882656882	-0.2308191601	2.795448444e-16
+-90	-25	2.47540576585471	-1.843479522	-0.4461516819	2.747470015e-16
+-90	-30	2.51600384653883	-1.778923247	-0.6580019233	2.668411380e-16
+-90	-35	2.55042375266283	-1.689184831	-0.8628629672	2.558513516e-16
+-90	-40	2.57819900965373	-1.575015025	-1.057234379	2.418695828e-16
+-90	-45	2.59894183102243	-1.437729393	-1.237729393	2.250569418e-16
+
+-85	45	1.61858927901529	-0.7423316150	1.742331615	0.09994106630
+-85	40	1.67676995815122	-0.8816052356	1.675394480	0.1121259292
+-85	35	1.73771455208029	-1.019810959	1.594162336	0.1242173633
+-85	30	1.80099567208534	-1.155250280	1.497924168	0.1360667685
+-85	25	1.86610576228187	-1.285974487	1.386182815	0.1475036546
+-85	20	1.93246627082131	-1.409818415	1.258720033	0.1583385944
+-85	15	1.99943363604850	-1.524445073	1.115653503	0.1683671275
+-85	10	2.06632308124082	-1.627419669	0.9574887888	0.1773762372
+-85	5	2.13241180594968	-1.716274799	0.7851500538	0.1851500538
+-85	-2.84217e-14	2.19696301335206	-1.788602906	0.6000000000	0.1914779432
+-85	-5	2.25924577831613	-1.842148957	0.4038373844	0.1961626156
+-85	-10	2.31854539913691	-1.874893306	0.1988749320	0.1990273750
+-85	-15	2.37416538883663	-1.885122548	-0.01229674143	0.1999223177
+-85	-20	2.42543914330383	-1.871503774	-0.2267597606	0.1987308293
+-85	-25	2.47173947541886	-1.833147648	-0.4413338499	0.1953751032
+-85	-30	2.51248402594472	-1.769656233	-0.6526516101	0.1898203241
+-85	-35	2.54714152772978	-1.681158526	-0.8572428881	0.1820777780
+-85	-40	2.57523363347546	-1.568327791	-1.051623123	0.1722063678
+-85	-45	2.59635329554735	-1.432395958	-1.232395958	0.1603138735
+
+-80	45	1.61841940063980	-0.7356025607	1.735602561	0.2002373708
+-80	40	1.67611989982868	-0.8724270451	1.667693064	0.2243632190
+-80	35	1.73641425452939	-1.007778194	1.585736904	0.2482292785
+-80	30	1.79887611031947	-1.140020471	1.489131233	0.2715471598
+-80	25	1.86301496777139	-1.267309217	1.377479057	0.2939916002
+-80	20	1.92827877344088	-1.387616670	1.250639258	0.3152050501
+-80	15	1.99406911582024	-1.498779379	1.108776401	0.3348060350
+-80	10	2.05975404450823	-1.598553654	0.9523989317	0.3523989317
+-80	5	2.12467092447190	-1.684668976	0.7823849026	0.3675833863
+-80	-2.84217e-14	2.18814882495910	-1.754905928	0.6000000000	0.3799680559
+-80	-5	2.24951274916086	-1.807160358	0.4068984901	0.3891819219
+-80	-10	2.30810014771510	-1.839520780	0.2051120626	0.3948879374
+-80	-15	2.36325998777891	-1.850327883	-0.002973539045	0.3967935213
+-80	-20	2.41435709167199	-1.838237046	-0.2146516619	0.3946615804
+-80	-25	2.46077847457346	-1.802278942	-0.4269395361	0.3883211965
+-80	-30	2.50193862436822	-1.741913318	-0.6366342307	0.3776771083
+-80	-35	2.53728548096555	-1.657075473	-0.8403797526	0.3627179072
+-80	-40	2.56630677314225	-1.548212741	-1.034744592	0.3435224704
+-80	-45	2.58854103294485	-1.416311535	-1.216311535	0.3202647290
+
+-75	45	1.61814331018596	-0.7241995479	1.724199548	0.3012283610
+-75	40	1.67504054933300	-0.8569497334	1.654706058	0.3367986660
+-75	35	1.73425426823584	-0.9875866475	1.571598630	0.3718027216
+-75	30	1.79536292577561	-1.114586159	1.474446727	0.4058321382
+-75	25	1.85790553057203	-1.236276936	1.363008466	0.4384390836
+-75	20	1.92137797101537	-1.350856992	1.237259829	0.4691407170
+-75	15	1.98525243142957	-1.456435608	1.097430422	0.4974304220
+-75	10	2.04897644495659	-1.551062875	0.9440250259	0.5227857218
+-75	5	2.11198646655539	-1.632776621	0.7778449098	0.5446808540
+-75	-2.84217e-14	2.17370565577693	-1.699638432	0.6000000000	0.5625964222
+-75	-5	2.23355672221675	-1.749787396	0.4119179739	0.5760337967
+-75	-10	2.29095686569620	-1.781479880	0.2153462393	0.5845257721
+-75	-15	2.34532584179684	-1.793144981	0.01234857355	0.5876514265
+-75	-20	2.39608092885610	-1.783430387	-0.1947036694	0.5850484089
+-75	-25	2.44263764747289	-1.751256660	-0.4031474550	0.5764274846
+-75	-30	2.48441309746751	-1.695875790	-0.6100544517	0.5615882254
+-75	-35	2.52083254850763	-1.616932378	-0.8122712550	0.5404354018
+-75	-40	2.55133108424869	-1.514517787	-1.006471169	0.5129934950
+-75	-45	2.57536887998873	-1.389228749	-1.189228749	0.4794223983
+
+-70	45	1.61776947772419	-0.7078341059	1.707834106	0.4032186390
+-70	40	1.67353721216239	-0.8349020590	1.636205862	0.4494675917
+-70	35	1.73124701931746	-0.9590368485	1.551607846	0.4946489601
+-70	30	1.79049047832667	-1.078881995	1.453832918	0.5382690263
+-70	25	1.85084940176328	-1.193006410	1.342831088	0.5798069162
+-70	20	1.91188805601583	-1.299910318	1.218716757	0.6187167566
+-70	15	1.97316910025423	-1.398051694	1.081786499	0.6544372961
+-70	10	2.03424619350730	-1.485854088	0.9325269573	0.6863947541
+-70	5	2.09467534791887	-1.561732567	0.7716293605	0.7140122621
+-70	-2.84217e-14	2.15400334914439	-1.624101052	0.6000000000	0.7367125342
+-70	-5	2.21176946549890	-1.671395071	0.4187764136	0.7539261494
+-70	-10	2.26750380467076	-1.702096262	0.2293437130	0.7651004688
+-70	-15	2.32071741659216	-1.714755335	0.03335301585	0.7697079946
+-70	-20	2.37090049516274	-1.708030437	-0.1672603320	0.7672603320
+-70	-25	2.41751523498760	-1.680729670	-0.3702601798	0.7573236655
+-70	-30	2.45999987310106	-1.631873146	-0.5731025078	0.7395413449
+-70	-35	2.49775951028475	-1.560752669	-0.7729337991	0.7136556081
+-70	-40	2.53017563797718	-1.467015016	-0.9666116114	0.6795378928
+-70	-45	2.55661960889354	-1.350750300	-1.150750300	0.6372209968
+
+-65	45	1.61731541879742	-0.6860967419	1.686096742	0.5064552283
+-65	40	1.67162292401815	-0.8059092265	1.611877987	0.5623247074
+-65	35	1.72741422790781	-0.9218630182	1.525578450	0.6163948484
+-65	30	1.78430995513868	-1.032833543	1.427246832	0.6681412538
+-65	25	1.84194887216010	-1.137690470	1.317036842	0.7170368421
+-65	20	1.89998306191376	-1.235295229	1.195198788	0.7625506886
+-65	15	1.95807792887839	-1.324499820	1.062078334	0.8041474728
+-65	10	2.01591240995214	-1.404145109	0.9181194598	0.8412866808
+-65	5	2.07317196870968	-1.473053027	0.7638709060	0.8734189704
+-65	-2.84217e-14	2.12953917738045	-1.530017939	0.6000000000	0.8999821455
+-65	-5	2.18468993275338	-1.573806395	0.4273143164	0.9204010379
+-65	-10	2.23827852612568	-1.603152139	0.2467902315	0.9340851828
+-65	-15	2.28993036790899	-1.616765753	0.05960924522	0.9404333152
+-65	-20	2.33923078057729	-1.613351072	-0.1327998614	0.9388410236
+-65	-25	2.38571336128058	-1.591634380	-0.3287143636	0.9287143636
+-65	-30	2.42885377759558	-1.550414026	-0.5260720627	0.9094929967
+-65	-35	2.46806288270200	-1.488626942	-0.7224308218	0.8806812066
+-65	-40	2.50268442127542	-1.405437214	-0.9149417003	0.8418891992
+-65	-45	2.53200360416813	-1.300349130	-1.100349130	0.7928858208
+
+-60	45	1.61680989782411	-0.6584505344	1.658450534	0.6110967010
+-60	40	1.66932116290174	-0.7694979213	1.581325274	0.6752099397
+-60	35	1.72279361528901	-0.8757501039	1.493289840	0.7365546659
+-60	30	1.77689799805474	-0.9763792709	1.394652943	0.7946529425
+-60	25	1.83134534328292	-1.070603820	1.285753823	0.8490535113
+-60	20	1.88588581334072	-1.157675178	1.166947399	0.8993241834
+-60	15	1.94030292767568	-1.236858997	1.038595046	0.9450409828
+-60	10	1.99440003863962	-1.307408792	0.9010622371	0.9857729256
+-60	5	2.04800078147804	-1.368551607	0.7547282164	1.021073746
+-60	-2.84217e-14	2.10092225303199	-1.419452043	0.6000000000	1.050461127
+-60	-5	2.15297530188825	-1.459202381	0.4373408685	1.073410995
+-60	-10	2.20394948391251	-1.486804379	0.2673054807	1.089347016
+-60	-15	2.25359660512338	-1.501156684	0.09058660189	1.097633323
+-60	-20	2.30161663832770	-1.501054179	-0.09192713496	1.097574142
+-60	-25	2.34763928788829	-1.485197304	-0.2790819402	1.088419171
+-60	-30	2.39121112500968	-1.452224173	-0.4693821248	1.069382125
+-60	-35	2.43178234559377	-1.400765079	-0.6609092825	1.039672203
+-60	-40	2.46869409700689	-1.329524958	-0.8512437547	0.9985417003
+-60	-45	2.50117592252576	-1.237403999	-1.037403999	0.9453556395
+
+-55	45	1.61629755121710	-0.6242271896	1.624227190	0.7171715990
+-55	40	1.66667305479767	-0.7251090448	1.544078584	0.7878098345
+-55	35	1.71744737340574	-0.8203576073	1.454503596	0.8545035959
+-55	30	1.76836064748120	-0.9094930581	1.356036170	0.9169169105
+-55	25	1.81921638659003	-0.9921124561	1.249152699	0.9747676358
+-55	20	1.86987008807648	-1.067856593	1.134256108	1.027804251
+-55	15	1.92022202507066	-1.136380501	1.011671915	1.075785209
+-55	10	1.97020064666261	-1.197317865	0.8816502363	1.118454010
+-55	5	2.01975259974535	-1.250251978	0.7443783400	1.155518875
+-55	-2.84217e-14	2.06882613413063	-1.294683157	0.6000000000	1.186629921
+-55	-5	2.11736112301288	-1.330003655	0.4486442923	1.211361601
+-55	-10	2.16527716683892	-1.355473944	0.2904625797	1.229196089
+-55	-15	2.21245413938462	-1.370197069	0.1256771250	1.239505332
+-55	-20	2.25871712049863	-1.373103297	-0.04535682222	1.241540294
+-55	-25	2.30381767980989	-1.362942172	-0.2220734359	1.234425399
+-55	-30	2.34741115038847	-1.338287159	-0.4036005591	1.217161772
+-55	-35	2.38903334250666	-1.297562941	-0.5886463676	1.188646368
+-55	-40	2.42807496617587	-1.239103181	-0.7753708746	1.147712403
+-55	-45	2.46376258101707	-1.161254994	-0.9612549943	1.093202516
+
+-50	45	1.61584776117642	-0.5826299908	1.582629991	0.8245244628
+-50	40	1.66374352209459	-0.6721171202	1.499613080	0.8996130801
+-50	35	1.71146537995184	-0.7553466790	1.408982454	0.9694509722
+-50	30	1.75884169955808	-0.8322144817	1.311419363	1.033950717
+-50	25	1.80577999286882	-0.9026901720	1.207454403	1.093086843
+-50	20	1.85224701315187	-0.9667719091	1.097464292	1.146857805
+-50	15	1.89825319579372	-1.024448411	0.9816798013	1.195254136
+-50	10	1.94383704005728	-1.075664612	0.8601994855	1.238229631
+-50	5	1.98905476130740	-1.120293815	0.7330084740	1.275677979
+-50	-2.84217e-14	2.03396809254102	-1.158109955	0.6000000000	1.307409488
+-50	-5	2.07862873991057	-1.188757875	0.4610016968	1.333126147
+-50	-10	2.12307280359046	-1.211731508	0.3158082495	1.352403314
+-50	-15	2.16730362257502	-1.226343739	0.1642225084	1.364664432
+-50	-20	2.21127737767004	-1.231700190	0.006109699647	1.369159027
+-50	-25	2.25488250682339	-1.226672846	-0.1585300055	1.364940585
+-50	-30	2.29791345726638	-1.209878956	-0.3294640489	1.350848839
+-50	-35	2.34003961149513	-1.179673785	-0.5060994918	1.325503690
+-50	-40	2.38076759496348	-1.134167775	-0.6873196143	1.287319614
+-50	-45	2.41940329395345	-1.071288505	-0.8712885047	1.234557642
+
+-45	45	1.61556226658466	-0.5327453095	1.532745310	0.9327453095
+-45	40	1.66063583595222	-0.6098665328	1.447378635	1.009866533
+-45	35	1.70497573570273	-0.6804214266	1.356519227	1.080421427
+-45	30	1.74852260200100	-0.7446767397	1.260879424	1.144676740
+-45	25	1.79129362014386	-0.8029305738	1.160935739	1.202930574
+-45	20	1.83336166568924	-0.8554697128	1.056953605	1.255469713
+-45	15	1.87483557606993	-0.9025356244	0.9490133687	1.302535624
+-45	10	1.91584695512168	-0.9442996959	0.8370363065	1.344299696
+-45	5	1.95653963176089	-0.9808426303	0.7208080763	1.380842630
+-45	-2.84217e-14	1.99706246175111	-1.012136409	0.6000000000	1.412136409
+-45	-5	2.03755894459176	-1.038022623	0.4741893226	1.438022623
+-45	-10	2.07816268369499	-1.058192397	0.3428813373	1.458192397
+-45	-15	2.11898570375467	-1.072158093	0.2055364278	1.472158093
+-45	-20	2.16010799349570	-1.079222683	0.06160697349	1.479222683
+-45	-25	2.20155875377918	-1.078441225	-0.08940846554	1.478441225
+-45	-30	2.24329137907486	-1.068578936	-0.2478844439	1.468578936
+-45	-35	2.28515188556691	-1.048071670	-0.4139506989	1.448071670
+-45	-40	2.32683028548632	-1.014992970	-0.5873200789	1.414992970
+-45	-45	2.36780077389597	-0.9670504142	-0.7670504142	1.367050414
+
+
+### -y patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-90	2.59894184123571	-1.437729400	-1.237729400	2.250569427e-16
+-40	-90	2.61234701688614	-1.279184295	-1.401173916	2.450731231e-16
+-35	-90	2.61820723435607	-1.101741975	-1.544709808	2.626512002e-16
+-30	-90	2.61642716302921	-0.9082135815	-1.665892390	2.774917863e-16
+-25	-90	2.60702606300246	-0.7017768231	-1.762768022	2.893556295e-16
+-20	-90	2.59013511043930	-0.4858783817	-1.833930850	2.980705625e-16
+-15	-90	2.56600453986324	-0.2641308447	-1.878570055	3.035372885e-16
+-10	-90	2.53497984559546	-0.04019463061	-1.896467806	3.057291307e-16
+-5	-90	2.49749069773218	0.1823293432	-1.887986992	3.046905306e-16
+-2.84217e-14	-90	2.45404604800721	0.4000000000	-1.854046048	3.005339638e-16
+5	-90	2.40521878890097	0.6096286300	-1.796066205	2.934334809e-16
+10	-90	2.35163414636902	0.8083569841	-1.715907540	2.836168755e-16
+15	-90	2.29395607173564	0.9937195200	-1.615791414	2.713561863e-16
+20	-90	2.23287923219811	1.163689675	-1.498220138	2.569578575e-16
+25	-90	2.16912691816512	1.316712648	-1.365896617	2.407528999e-16
+30	-90	2.10344068935238	1.451720345	-1.221633072	2.230857111e-16
+35	-90	2.03655811716862	1.568121747	-1.068250745	2.043017935e-16
+40	-90	1.96921632857131	1.665787857	-0.9085072258	1.847388546e-16
+45	-90	1.90213490278970	1.745012488	-0.7450124885	1.647165239e-16
+
+-45	-85	2.59635331139603	-1.432395970	-1.232395970	0.1603138744
+-40	-85	2.60926406619282	-1.273448502	-1.394338264	0.1744819894
+-35	-85	2.61466059999611	-1.095871165	-1.536325422	0.1869042561
+-30	-85	2.61247410158357	-0.9025037596	-1.656002689	0.1973746601
+-25	-85	2.60274500645934	-0.6965259506	-1.751507490	0.2057302475
+-20	-85	2.58562118498538	-0.4813610343	-1.821519540	0.2118555083
+-15	-85	2.56136537517781	-0.2605755775	-1.865301618	0.2156859437
+-10	-85	2.53032924023630	-0.03776519922	-1.882689816	0.2172072139
+-5	-85	2.49294270589804	0.1835462761	-1.874077385	0.2164537239
+-2.84217e-14	-85	2.44970675109414	0.4000000000	-1.840384877	0.2135060114
+5	-85	2.40118073703155	0.6084863446	-1.783009824	0.2084863446
+10	-85	2.34797185794800	0.8062160575	-1.703765742	0.2015533858
+15	-85	2.29072306365475	0.9907769838	-1.604809719	0.1928958557
+20	-85	2.23010727318116	1.160176960	-1.488569033	0.1827261134
+25	-85	2.16682549090758	1.312874821	-1.357666371	0.1712736144
+30	-85	2.10159718868339	1.447795359	-1.214834798	0.1587774710
+35	-85	2.03514063644800	1.564322511	-1.062824873	0.1454783258
+40	-85	1.96817793927548	1.662288653	-0.9043370376	0.1316124369
+45	-85	1.90141766027113	1.741939882	-0.7419398824	0.1174045268
+
+-45	-80	2.58854106426170	-1.416311557	-1.216311557	0.3202647328
+-40	-80	2.59998382584200	-1.256196969	-1.373778688	0.3480304366
+-35	-80	2.60401188377333	-1.078259353	-1.511173148	0.3722567870
+-30	-80	2.60063097835212	-0.8854149410	-1.626403987	0.3925750928
+-25	-80	2.58994260596299	-0.6808427031	-1.717874657	0.4087038399
+-20	-80	2.57214811312277	-0.4678934621	-1.784517690	0.4204548046
+-15	-80	2.54754002055384	-0.2499916344	-1.825801804	0.4277343079
+-10	-80	2.51648586800163	-0.03054020640	-1.841714845	0.4305402064
+-5	-80	2.47941310178084	0.1871635029	-1.832732294	0.4289563402
+-2.84217e-14	-80	2.43679982549560	0.4000000000	-1.799779361	0.4231458490
+5	-80	2.38916601140505	0.6050895530	-1.744184318	0.4133429430
+10	-80	2.33706711268853	0.7998438338	-1.667627065	0.3998438338
+15	-80	2.28108724773432	0.9820075903	-1.572081897	0.3829966428
+20	-80	2.22183397926025	1.149690570	-1.459757912	0.3631908936
+25	-80	2.15994414377710	1.301394441	-1.333046616	0.3408482734
+30	-80	2.09607323469451	1.436026978	-1.194451364	0.3164101910
+35	-80	2.03088310843939	1.552902553	-1.046515483	0.2903251039
+40	-80	1.96505110326009	1.651743049	-0.8917692756	0.2630391723
+45	-80	1.89925172602482	1.732655258	-0.7326552577	0.2349830779
+
+-45	-75	2.57536892393365	-1.389228779	-1.189228779	0.4794224065
+-40	-75	2.58441712253089	-1.227304125	-1.339345537	0.5196460704
+-35	-75	2.58623826734217	-1.048914156	-1.469263863	0.5544575811
+-30	-75	2.58094931488232	-0.8570732344	-1.577314711	0.5834097184
+-25	-75	2.56875288570168	-0.6549407205	-1.662327676	0.6061888738
+-20	-75	2.54992565641456	-0.4457290618	-1.723621500	0.6226125045
+-15	-75	2.52480265716259	-0.2326216411	-1.760976107	0.6326216411
+-10	-75	2.49376767462247	-0.01870588169	-1.774599055	0.6362718990
+-5	-75	2.45723742271986	0.1930824015	-1.765078974	0.6337210010
+-2.84217e-14	-75	2.41565184999555	0.4000000000	-1.733340509	0.6252167051
+5	-75	2.36946878769132	0.5995268291	-1.680602093	0.6110854890
+10	-75	2.31916768103902	0.7893903825	-1.608342597	0.5917236155
+15	-75	2.26523833620735	0.9675844762	-1.518254103	0.5675844762
+20	-75	2.20818885395350	1.132385857	-1.412213605	0.5391710105
+25	-75	2.14855563924473	1.282373251	-1.292255543	0.5070283446
+30	-75	2.08689348892072	1.416439158	-1.160524264	0.4717310548
+35	-75	2.02377612354782	1.533800358	-1.019234721	0.4338726359
+40	-75	1.95980783082842	1.634012629	-0.8706389833	0.3940565279
+45	-75	1.89560353640986	1.716964094	-0.7169640941	0.3528794655
+
+-45	-70	2.55661972041193	-1.350750376	-1.150750376	0.6372210246
+-40	-70	2.56243077492519	-1.186583060	-1.290816061	0.6882007648
+-35	-70	2.56131502600104	-1.007868113	-1.410644040	0.7318145822
+-30	-70	2.55353636864847	-0.8177073464	-1.509130993	0.7676609015
+-25	-70	2.53941810211378	-0.6191854134	-1.585650172	0.7955116053
+-20	-70	2.51931507415637	-0.4152896017	-1.639989771	0.8152896017
+-15	-70	2.49360925389182	-0.2088617913	-1.672303140	0.8270507062
+-10	-70	2.46269325184500	-0.002562824747	-1.683047229	0.8309612349
+-5	-70	2.42695907043719	0.2011446339	-1.672927236	0.8272778584
+-2.84217e-14	-70	2.38679308344985	0.4000000000	-1.642851848	0.8163313125
+5	-70	2.34257545997020	0.5919413090	-1.593899200	0.7985140060
+10	-70	2.29468313279818	0.7750991412	-1.527292940	0.7742713098
+15	-70	2.24349241862753	0.9477910425	-1.444384003	0.7440949243
+20	-70	2.18939245026995	1.108521501	-1.346646826	0.7085215013
+25	-70	2.13278987615286	1.255986783	-1.235669580	0.6681290870
+30	-70	2.07411034688226	1.389082998	-1.113142005	0.6235326970
+35	-70	2.01381497294351	1.506925879	-0.9808539877	0.5753837963
+40	-70	1.95240629377004	1.608873536	-0.8406793794	0.5243644112
+45	-70	1.89041631613435	1.694540228	-0.6945402285	0.4711741102
+
+-45	-65	2.53200366498430	-1.300349171	-1.100349171	0.7928858398
+-40	-65	2.53386326452337	-1.133815087	-1.227929640	0.8523775896
+-35	-65	2.52924516975086	-0.9552133505	-1.335445245	0.9025129398
+-30	-65	2.51857965680144	-0.7676710288	-1.422465548	0.9430911736
+-25	-65	2.50230053514755	-0.5740996076	-1.488963350	0.9740996076
+-20	-65	2.48083887299727	-0.3771607648	-1.535231652	0.9956748715
+-15	-65	2.45460658541891	-0.1792519825	-1.561797829	1.008062883
+-10	-65	2.42398611609243	0.01748479244	-1.569351542	1.011585237
+-5	-65	2.38932817196578	0.2111389802	-1.558691335	1.006614301
+-2.84217e-14	-65	2.35095091543867	0.4000000000	-1.530685122	0.9935547893
+5	-65	2.30914351421315	0.5825229385	-1.486246734	0.9728328287
+10	-65	2.26417336318950	0.7572960828	-1.426326778	0.9448916947
+15	-65	2.21629439062822	0.9230137193	-1.351913773	0.9101923406
+20	-65	2.16576146671170	1.078457943	-1.264047877	0.8692198004
+25	-65	2.11283759421470	1.222488843	-1.163833015	0.8224888428
+30	-65	2.05780891126506	1.354047192	-1.052458209	0.7705539175
+35	-65	2.00100271084572	1.472171896	-0.9312201556	0.7140196849
+40	-65	1.94279569204641	1.576026104	-0.8015333342	0.6535457269
+45	-65	1.88361594516363	1.664928979	-0.6649289788	0.5898460698
+
+-45	-60	2.50117598097370	-1.237404037	-1.037404037	0.9453556616
+-40	-60	2.49855150024165	-1.068795694	-1.150442546	1.010618475
+-35	-60	2.49008853228810	-0.8911417629	-1.243941535	1.064600142
+-30	-60	2.47635909151671	-0.7074614531	-1.318179504	1.107461453
+-25	-60	2.45789741976135	-0.5203684926	-1.373736602	1.139537358
+-20	-60	2.43517454155819	-0.3320781904	-1.411368298	1.161264028
+-15	-60	2.40860261096954	-0.1444516725	-1.431921304	1.173130312
+-10	-60	2.37853184656568	0.04095161207	-1.436264595	1.175637912
+-5	-60	2.34525341414664	0.2228140921	-1.425244195	1.169275281
+-2.84217e-14	-60	2.30900513393545	0.4000000000	-1.399657103	1.154502567
+5	-60	2.26997959172313	0.5714989060	-1.360241466	1.131745938
+10	-60	2.22833340615389	0.7363753647	-1.307679490	1.101399267
+15	-60	2.18420032701314	0.8937267425	-1.242613288	1.063833278
+20	-60	2.13769994321149	1.042649420	-1.165664769	1.019407030
+25	-60	2.08895744820061	1.182217599	-1.077471054	0.9684883645
+30	-60	2.03811677515936	1.311473531	-0.9787184656	0.9114735311
+35	-60	1.98536319771320	1.429435422	-0.8701861460	0.8488123672
+40	-60	1.93092628617672	1.535112170	-0.7527740066	0.7810244369
+45	-60	1.87511358227490	1.627549990	-0.6275499896	0.7087263170
+
+-45	-55	2.46376246218477	-1.161254919	-0.9612549190	1.093202463
+-40	-55	2.45636466256620	-0.9913954311	-1.058200504	1.161084493
+-35	-55	2.44397762561219	-0.8159835007	-1.136604413	1.215983501
+-30	-55	2.42727621144600	-0.6377456725	-1.197428230	1.258572796
+-25	-55	2.40683589075226	-0.4588335213	-1.241774430	1.289624340
+-20	-55	2.38313017110203	-0.2809039079	-1.270768112	1.309925934
+-15	-55	2.35653524914505	-0.1052120876	-1.285477179	1.320225334
+-10	-55	2.32734069545364	0.06729477125	-1.286865115	1.321197177
+-5	-55	2.29576082266315	0.2358917143	-1.275766288	1.313425695
+-2.84217e-14	-55	2.26194581266058	0.4000000000	-1.252877537	1.297398818
+5	-55	2.22599332725111	0.5591210832	-1.218762303	1.273511075
+10	-55	2.18795557512971	0.7127794145	-1.173860207	1.242070289
+15	-55	2.14785466866196	0.8604735454	-1.118510667	1.203314123
+20	-55	2.10569742808895	1.001636295	-1.052982136	1.157430552
+25	-55	2.06148187794471	1.135600523	-0.9775004125	1.104577680
+30	-55	2.01522050009858	1.261577411	-0.8922958499	1.044916803
+35	-55	1.96695182090540	1.378642740	-0.7976466790	0.9786427404
+40	-55	1.91676298714979	1.485740771	-0.6939354646	0.9060233663
+45	-55	1.86481896841500	1.581712049	-0.5817120490	0.8274436847
+
+-45	-50	2.41940313041112	-1.071288405	-0.8712884053	1.234557558
+-40	-50	2.40724577831399	-0.9016367971	-0.9512303292	1.301636797
+-35	-50	2.39115796380041	-0.7302623236	-1.014181885	1.354459424
+-30	-50	2.37184473462643	-0.5593679010	-1.061673948	1.394309997
+-25	-50	2.34985937748476	-0.3904796996	-1.095189186	1.422432621
+-20	-50	2.32562006072251	-0.2245997044	-1.116073584	1.439956711
+-15	-50	2.29942933635174	-0.06234387182	-1.125490820	1.447858711
+-10	-50	2.27149186005411	0.09594106854	-1.124403890	1.446946668
+-5	-50	2.24193206936336	0.2500815718	-1.113575475	1.437860549
+-2.84217e-14	-50	2.21081260943645	0.4000000000	-1.093580714	1.421082953
+5	-50	2.17814175131871	0.5456527574	-1.064818635	1.396948702
+10	-50	2.14388365512493	0.6869774639	-1.027530074	1.365659885
+15	-50	2.10797093584947	0.8238475298	-0.9818205159	1.327305011
+20	-50	2.07031478443349	0.9560314964	-0.9276839807	1.281879065
+25	-50	2.03081372868980	1.083154508	-0.8650295695	1.229305771
+30	-50	1.98936358819243	1.204661259	-0.7937141833	1.169465057
+35	-50	1.94587557139857	1.319784422	-0.7135882884	1.102231448
+40	-50	1.90030220136429	1.427524191	-0.6245556461	1.027524191
+45	-50	1.85264987644196	1.526634188	-0.5266341884	0.9453583319
+
+-45	-45	2.36780064480585	-0.9670503397	-0.7670503397	1.367050340
+-40	-45	2.35125928310199	-0.7997855516	-0.8298487414	1.429848741
+-35	-45	2.33201609584795	-0.6347449398	-0.8777689232	1.477768923
+-30	-45	2.31071647604195	-0.4733687351	-0.9127190230	1.512719023
+-25	-45	2.28781845711032	-0.3164203132	-0.9363683197	1.536368320
+-20	-45	2.26363189736417	-0.1641956938	-0.9501149289	1.550114929
+-15	-45	2.23835107063425	-0.01668424550	-0.9550867749	1.555086775
+-10	-45	2.21207952366980	0.1263126062	-0.9521583407	1.552158341
+-5	-45	2.18484959414901	0.2650947458	-0.9419741116	1.541974112
+-2.84217e-14	-45	2.15663991271126	0.4000000000	-0.9249747069	1.524974707
+5	-45	2.12738471690751	0.5313570402	-0.9014178402	1.501417840
+10	-45	2.09697967989888	0.6594467773	-0.8713957910	1.471395791
+15	-45	2.06529219068318	0.7844681603	-0.8348547081	1.434854708
+20	-45	2.03216369209095	0.9065037321	-0.7916075669	1.391607567
+25	-45	1.99741641774621	1.025482189	-0.7413508821	1.341350882
+30	-45	1.96086129924802	1.141135908	-0.6836850473	1.283685047
+35	-45	1.92230952684000	1.252952970	-0.6181430843	1.218143084
+40	-45	1.88158570675291	1.360123522	-0.5442306572	1.144230657
+45	-45	1.83855661111634	1.461491154	-0.4614911543	1.061491154
+
+
diff --git a/test/recover2/h.t2.ah2.gp b/test/recover2/h.t2.ah2.gp
new file mode 100644
index 0000000..8202058
--- /dev/null
+++ b/test/recover2/h.t2.ah2.gp
@@ -0,0 +1,1228 @@
+# N_patches = 5
+# origin = 0 0 0
+
+### +z patch
+# N_rho = 19
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = dsigma = dnu
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-45	1.86338407450618	-1.075825297	-1.075825297	1.075825297
+-40	-45	1.85977403351066	-0.9489936013	-1.130966534	1.130966534
+-35	-45	1.85663472569950	-0.8238122330	-1.176525799	1.176525799
+-30	-45	1.85396392723581	-0.7007324987	-1.213704290	1.213704290
+-25	-45	1.85174826198128	-0.5798668446	-1.243528461	1.243528461
+-20	-45	1.84996698710866	-0.4610923751	-1.266840889	1.266840889
+-15	-45	1.84860052917144	-0.3441295366	-1.284308915	1.284308915
+-10	-45	1.84763131910966	-0.2285963931	-1.296434568	1.296434568
+-5	-45	1.84704675609212	-0.1140473527	-1.303567206	1.303567206
+0	-45	1.84683872919875	0.000000000	-1.305912189	1.305912189
+5	-45	1.84700629821872	0.1140448546	-1.303538652	1.303538652
+10	-45	1.84755321643850	0.2285867300	-1.296379766	1.296379766
+15	-45	1.84849073562048	0.3441090978	-1.284232636	1.284232636
+20	-45	1.84983467368504	0.4610593968	-1.266750282	1.266750282
+25	-45	1.85160534554668	0.5798220910	-1.243432487	1.243432487
+30	-45	1.85382660879841	0.7006805972	-1.213614394	1.213614394
+35	-45	1.85652069429419	0.8237616359	-1.176453538	1.176453538
+40	-45	1.85970549083907	0.9489586257	-1.130924851	1.130924851
+45	-45	1.86338407335912	1.075825296	-1.075825296	1.075825296
+
+-45	-40	1.85970549135094	-1.130924852	-0.9489586260	1.130924852
+-40	-40	1.85522820909427	-1.003151953	-1.003151953	1.195509944
+-35	-40	1.85125402687834	-0.8750583231	-1.048633549	1.249712800
+-30	-40	1.84781428546337	-0.7474071497	-1.086254042	1.294547157
+-25	-40	1.84491955011765	-0.6206207340	-1.116779062	1.330925459
+-20	-40	1.84256667244733	-0.4948644099	-1.140864018	1.359628792
+-15	-40	1.84074754303340	-0.3701171994	-1.159045126	1.381296193
+-10	-40	1.83945194977038	-0.2462266338	-1.171736037	1.396420632
+-5	-40	1.83867180023273	-0.1229523365	-1.179230040	1.405351637
+0	-40	1.83840133063409	0.000000000	-1.181701597	1.408297124
+5	-40	1.83864054564745	0.1229502465	-1.179209995	1.405327748
+10	-40	1.83939249287280	0.2462186749	-1.171698163	1.396375495
+15	-40	1.84066587241123	0.3701007779	-1.158993701	1.381234907
+20	-40	1.84247239846176	0.4948390904	-1.140805646	1.359559227
+25	-40	1.84482387945157	0.6205885510	-1.116721150	1.330856442
+30	-40	1.84773297194859	0.7473742598	-1.086206241	1.294490190
+35	-40	1.85120405350914	0.8750347015	-1.048605242	1.249679065
+40	-40	1.85522820858527	1.003151953	-1.003151953	1.195509944
+45	-40	1.85977403303049	1.130966533	-0.9489936010	1.130966533
+
+-45	-35	1.85652069461174	-1.176453539	-0.8237616360	1.176453539
+-40	-35	1.85120405387108	-1.048605243	-0.8750347016	1.249679065
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+-5	20	1.81092377752012	-0.1483798863	0.6172898268	1.695989861
+0	20	1.81037654250634	0.000000000	0.6191852445	1.701197478
+5	20	1.81092830886901	0.1483802575	0.6172913715	1.695994104
+10	20	1.81256945621721	0.2962906890	0.6115966544	1.680347998
+15	20	1.81527424816090	0.4432334893	0.6020686066	1.654169902
+20	20	1.81900027964327	0.5886568253	0.5886568253	1.617321335
+25	20	1.82368380488619	0.7319282835	0.5712968770	1.569625269
+30	20	1.82923786835573	0.8723104233	0.5499175216	1.510885973
+35	20	1.83554848176420	1.008938827	0.5244497970	1.440913975
+40	20	1.84247239861832	1.140805646	0.4948390904	1.359559227
+45	20	1.84983467383226	1.266750282	0.4610593968	1.266750282
+
+-45	25	1.85174826185566	-1.243528461	0.5798668446	1.243528461
+-40	25	1.84491954996427	-1.116779062	0.6206207340	1.330925459
+-35	25	1.83856984399232	-0.9851375533	0.6560586118	1.406922233
+-30	25	1.83284419235033	-0.8497484119	0.6863150727	1.471807423
+-25	25	1.82785503195644	-0.7115503691	0.7115503691	1.525924691
+-20	25	1.82368380477473	-0.5712968770	0.7319282835	1.569625269
+-15	25	1.82039047003100	-0.4295860668	0.7476017038	1.603237028
+-10	25	1.81801558160319	-0.2868905077	0.7586997762	1.627036921
+-5	25	1.81658313738434	-0.1435892097	0.7653191329	1.641232177
+0	25	1.81610727983751	0.000000000	0.7675201017	1.645952170
+5	25	1.81659208103485	0.1435899166	0.7653229008	1.641240257
+10	25	1.81803094087651	0.2868929315	0.7587061860	1.627050666
+15	25	1.82040820692924	0.4295902525	0.7476089881	1.603252649
+20	25	1.82369701368260	0.5713010149	0.7319335848	1.569636638
+25	25	1.82785503209149	0.7115503692	0.7115503692	1.525924691
+30	25	1.83282210760771	0.8497381729	0.6863068030	1.471789689
+35	25	1.83851541826873	0.9851083911	0.6560391910	1.406880585
+40	25	1.84482387965228	1.116721150	0.6205885510	1.330856442
+45	25	1.85160534573097	1.243432487	0.5798220911	1.243432487
+
+-45	30	1.85396392705378	-1.213704290	0.7007324987	1.213704290
+-40	30	1.84781428523832	-1.086254042	0.7474071496	1.294547157
+-35	30	1.84217405956607	-0.9551900794	0.7875939909	1.364152808
+-30	30	1.83715094712062	-0.8215988805	0.8215988805	1.423051005
+-25	30	1.83282210743832	-0.6863068030	0.8497381729	1.471789689
+-20	30	1.82923786821996	-0.5499175216	0.8723104232	1.510885973
+-15	30	1.82642967024764	-0.4128546088	0.8895780478	1.540794376
+-10	30	1.82441740570973	-0.2754027151	0.9017555399	1.561886411
+-5	30	1.82321026300664	-0.1377450999	0.9089997182	1.574433696
+0	30	1.82281260812772	0.000000000	0.9114063041	1.578602025
+5	30	1.82322534748747	0.1377462395	0.9090072389	1.574446722
+10	30	1.82444466180812	0.2754068295	0.9017690118	1.561909745
+15	30	1.82646404870519	0.4128623798	0.8895947921	1.540823378
+20	30	1.82927108217566	0.5499275066	0.8723262620	1.510913407
+25	30	1.83284419250522	0.6863150728	0.8497484120	1.471807423
+30	30	1.83715094732458	0.8215988806	0.8215988806	1.423051005
+35	30	1.84213914468674	0.9551719756	0.7875790636	1.364126953
+40	30	1.84773297221175	1.086206241	0.7473742599	1.294490190
+45	30	1.85382660903278	1.213614394	0.7006805973	1.213614394
+
+-45	35	1.85663472542622	-1.176525798	0.8238122329	1.176525798
+-40	35	1.85125402654060	-1.048633549	0.8750583229	1.249712800
+-35	35	1.84639895941458	-0.9186625306	0.9186625306	1.311986062
+-30	35	1.84213914443870	-0.7875790634	0.9551719755	1.364126953
+-25	35	1.83851541807387	-0.6560391909	0.9851083910	1.406880585
+-20	35	1.83554848161184	-0.5244497969	1.008938827	1.440913975
+-15	35	1.83324516624037	-0.3930251490	1.027057292	1.466789825
+-10	35	1.83160722942802	-0.2618376001	1.039776560	1.484954821
+-5	35	1.83063131355517	-0.1308593489	1.047320863	1.495729203
+0	35	1.83031402001902	0.000000000	1.049824993	1.499305471
+5	35	1.83065383886063	0.1308609591	1.047333750	1.495747607
+10	35	1.83164919220373	0.2618435989	1.039800381	1.484988842
+15	35	1.83330095588122	0.3930371096	1.027088548	1.466834462
+20	35	1.83560889596110	0.5244670584	1.008972035	1.440961400
+25	35	1.83856984415582	0.6560586118	0.9851375534	1.406922233
+30	35	1.84217405979551	0.7875939910	0.9551900795	1.364152808
+35	35	1.84639895972316	0.9186625308	0.9186625308	1.311986062
+40	35	1.85120405387125	1.048605243	0.8750347016	1.249679065
+45	35	1.85652069461189	1.176453539	0.8237616360	1.176453539
+
+-45	40	1.85977403303055	-1.130966533	0.9489936010	1.130966533
+-40	40	1.85522820858535	-1.003151953	1.003151953	1.195509944
+-35	40	1.85120405350926	-0.8750347015	1.048605242	1.249679065
+-30	40	1.84773297194873	-0.7473742598	1.086206241	1.294490190
+-25	40	1.84482387945176	-0.6205885510	1.116721150	1.330856442
+-20	40	1.84247239846198	-0.4948390904	1.140805646	1.359559227
+-15	40	1.84066587241150	-0.3701007779	1.158993701	1.381234907
+-10	40	1.83939249287314	-0.2462186749	1.171698163	1.396375495
+-5	40	1.83864054564789	-0.1229502465	1.179209995	1.405327748
+0	40	1.83840133063466	0.000000000	1.181701597	1.408297124
+5	40	1.83867180023319	0.1229523365	1.179230040	1.405351637
+10	40	1.83945194977077	0.2462266338	1.171736037	1.396420632
+15	40	1.84074754303373	0.3701171994	1.159045126	1.381296193
+20	40	1.84256667244761	0.4948644099	1.140864018	1.359628792
+25	40	1.84491955011790	0.6206207340	1.116779062	1.330925459
+30	40	1.84781428546360	0.7474071497	1.086254042	1.294547157
+35	40	1.85125402687855	0.8750583231	1.048633549	1.249712800
+40	40	1.85522820909446	1.003151953	1.003151953	1.195509944
+45	40	1.85970549135111	1.130924852	0.9489586260	1.130924852
+
+-45	45	1.86338407335920	-1.075825296	1.075825296	1.075825296
+-40	45	1.85970549083917	-0.9489586257	1.130924851	1.130924851
+-35	45	1.85652069429432	-0.8237616359	1.176453538	1.176453538
+-30	45	1.85382660879857	-0.7006805972	1.213614394	1.213614394
+-25	45	1.85160534554687	-0.5798220910	1.243432487	1.243432487
+-20	45	1.84983467368527	-0.4610593968	1.266750282	1.266750282
+-15	45	1.84849073562075	-0.3441090978	1.284232636	1.284232636
+-10	45	1.84755321643883	-0.2285867300	1.296379766	1.296379766
+-5	45	1.84700629821910	-0.1140448546	1.303538652	1.303538652
+0	45	1.84683872919920	0.000000000	1.305912189	1.305912189
+5	45	1.84704675609253	0.1140473527	1.303567206	1.303567206
+10	45	1.84763131911001	0.2285963931	1.296434568	1.296434568
+15	45	1.84860052917175	0.3441295366	1.284308915	1.284308915
+20	45	1.84996698710895	0.4610923751	1.266840889	1.266840889
+25	45	1.85174826198154	0.5798668446	1.243528461	1.243528461
+30	45	1.85396392723604	0.7007324987	1.213704290	1.213704290
+35	45	1.85663472569971	0.8238122330	1.176525799	1.176525799
+40	45	1.85977403351085	0.9489936013	1.130966534	1.130966534
+45	45	1.86338407450635	1.075825297	1.075825297	1.075825297
+
+
+### +x patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = drho = dnu
+# dpy = dsigma = dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	-45	1.86338394519520	1.075825222	-1.075825222	1.075825222
+45	-40	1.85977391284639	1.130966460	-0.9489935397	1.130966460
+45	-35	1.85663469922808	1.176525782	-0.8238122213	1.176525782
+45	-30	1.85396384235652	1.213704235	-0.7007324667	1.213704235
+45	-25	1.85174823070994	1.243528440	-0.5798668349	1.243528440
+45	-20	1.84996697036535	1.266840877	-0.4610923709	1.266840877
+45	-15	1.84860052648869	1.284308913	-0.3441295361	1.284308913
+45	-10	1.84763131916241	1.296434568	-0.2285963931	1.296434568
+45	-5	1.84704675664033	1.303567206	-0.1140473527	1.303567206
+45	0	1.84683872964863	1.305912189	0.000000000	1.305912189
+45	5	1.84700629899394	1.303538653	0.1140448546	1.303538653
+45	10	1.84755321758801	1.296379767	0.2285867301	1.296379767
+45	15	1.84849073251853	1.284232634	0.3441090972	1.284232634
+45	20	1.84983466843334	1.266750278	0.4610593955	1.266750278
+45	25	1.85160530765092	1.243432461	0.5798220791	1.243432461
+45	30	1.85382654806771	1.213614355	0.7006805743	1.213614355
+45	35	1.85652064612480	1.176453508	0.8237616145	1.176453508
+45	40	1.85970535409978	1.130924768	0.9489585560	1.130924768
+45	45	1.86338397897839	1.075825242	1.075825242	1.075825242
+
+50	-45	1.87071350516659	1.137619050	-1.137619050	0.9545757249
+50	-40	1.86753406879208	1.203439846	-1.009805931	1.009805931
+50	-35	1.86469833981794	1.258788556	-0.8814132359	1.056249013
+50	-30	1.86223189492981	1.304647888	-0.7532388095	1.094729562
+50	-25	1.86014712079929	1.341910633	-0.6257432046	1.125996717
+50	-20	1.85844359025549	1.371344359	-0.4991285278	1.150694546
+50	-15	1.85711842432933	1.393580895	-0.3734088755	1.169353215
+50	-10	1.85616663086768	1.409109588	-0.2484640391	1.182383336
+50	-5	1.85558502018345	1.418278915	-0.1240833268	1.190077314
+50	0	1.85537111104318	1.421296730	0.000000000	1.192609562
+50	5	1.85552654431567	1.418234220	0.1240794165	1.190039811
+50	10	1.85605434448367	1.409024346	0.2484490086	1.182311809
+50	15	1.85696137839996	1.393463048	0.3733772984	1.169254330
+50	20	1.85825655304349	1.371206345	0.4990782945	1.150578738
+50	25	1.85994728326322	1.341766470	0.6256759804	1.125875750
+50	30	1.86204257609358	1.304515255	0.7531622335	1.094618269
+50	35	1.86454470582432	1.258684843	0.8813406155	1.056161988
+50	40	1.86744356231023	1.203381523	1.009756992	1.009756992
+50	45	1.87071349820314	1.137619045	1.137619045	0.9545757214
+
+55	-45	1.87713951241262	1.189519421	-1.189519421	0.8329104654
+55	-40	1.87449966735577	1.265405068	-1.061800926	0.8860461675
+55	-35	1.87209093848978	1.330241877	-0.9314453902	0.9314453902
+55	-30	1.86995251855518	1.384723102	-0.7994702559	0.9695935546
+55	-25	1.86810829317549	1.429525835	-0.6665988444	1.000964766
+55	-20	1.86657560088832	1.465270406	-0.5333148128	1.025993383
+55	-15	1.86536473509919	1.492488873	-0.3999111884	1.045051960
+55	-10	1.86448238793741	1.511607983	-0.2665372717	1.058439305
+55	-5	1.86393451169931	1.522939797	-0.1332399675	1.066373926
+55	0	1.86372388297437	1.526673229	0.000000000	1.068988103
+55	5	1.86385475194315	1.522874629	0.1332342660	1.066328295
+55	10	1.86433000102226	1.511484437	0.2665154873	1.058352797
+55	15	1.86515229832361	1.492318902	0.3998656445	1.044932944
+55	20	1.86632447534655	1.465073271	0.5332430616	1.025855348
+55	25	1.86784398907291	1.429323583	0.6665045326	1.000823147
+55	30	1.86970506392171	1.384539859	0.7993644604	0.9694652463
+55	35	1.87189455769093	1.330102336	0.9313476823	0.9313476823
+55	40	1.87438659004625	1.265328734	1.061736874	0.8859927176
+55	45	1.87713946829880	1.189519393	1.189519393	0.8329104458
+
+60	-45	1.88263655510030	1.232474931	-1.232474931	0.7115697334
+60	-40	1.88058391432841	1.317505000	-1.105517960	0.7606618664
+60	-35	1.87867151065318	1.391179625	-0.9741144601	0.8031979307
+60	-30	1.87693629096544	1.453868599	-0.8393914272	0.8393914272
+60	-25	1.87540964274484	1.505988259	-0.7022538581	0.8694827265
+60	-20	1.87411975787294	1.547956831	-0.5634102105	0.8937132932
+60	-15	1.87308306383821	1.580151646	-0.4234003576	0.9123009785
+60	-10	1.87231474420204	1.602891393	-0.2826329997	0.9254297770
+60	-5	1.87182686649129	1.616416577	-0.1414181260	0.9332385456
+60	0	1.87162736027442	1.620876840	0.000000000	0.9358136801
+60	5	1.87172284706838	1.616326751	0.1414102672	0.9331866845
+60	10	1.87211708748425	1.602722178	0.2826031626	0.9253320812
+60	15	1.87280947503798	1.579920844	0.4233385143	0.9121677247
+60	20	1.87379950260125	1.547692312	0.5633139332	0.8935605727
+60	25	1.87507835351008	1.505722227	0.7021298057	0.8693291333
+60	30	1.87662914497895	1.453630685	0.8392540673	0.8392540673
+60	35	1.87843097564530	1.391001505	0.9739897397	0.8030950936
+60	40	1.88044886772584	1.317410389	1.105438571	0.7606072425
+60	45	1.88263658017198	1.232474948	1.232474948	0.7115697429
+
+65	-45	1.88721437039500	1.267345476	-1.267345476	0.5909729009
+65	-40	1.88574097002596	1.360374042	-1.141489357	0.6343528339
+65	-35	1.88433821984269	1.441945404	-1.009661042	0.6723901845
+65	-30	1.88303721052187	1.512113335	-0.8730190411	0.7051100282
+65	-25	1.88187115960239	1.571018280	-0.7325778548	0.7325778548
+65	-20	1.88086465608213	1.618840220	-0.5892096542	0.7548775921
+65	-15	1.88003806463106	1.655769291	-0.4436620445	0.7720979007
+65	-10	1.87941113410003	1.681983001	-0.2965789842	0.7843215544
+65	-5	1.87900074872535	1.697624747	-0.1485229203	0.7916154203
+65	0	1.87881878933733	1.702788099	0.000000000	0.7940231309
+65	5	1.87887205795223	1.697508479	0.1485127481	0.7915612034
+65	10	1.87916749883469	1.681764959	0.2965405375	0.7842198798
+65	15	1.87970210024901	1.655473404	0.4435827617	0.7719599262
+65	20	1.88047308520188	1.618503199	0.5890869886	0.7547204366
+65	25	1.88147001649455	1.570683398	0.7324216972	0.7324216972
+65	30	1.88267275873053	1.511820674	0.8728500729	0.7049735579
+65	35	1.88405595273481	1.441729406	1.009509798	0.6722894628
+65	40	1.88558474144676	1.360261339	1.141394788	0.6343002795
+65	45	1.88721438052219	1.267345483	1.267345483	0.5909729041
+
+70	-45	1.89089770764524	1.294869881	-1.294869881	0.4712940940
+70	-40	1.88995088788590	1.394593575	-1.170202954	0.5075905501
+70	-35	1.88902701678737	1.482894870	-1.038334166	0.5397295932
+70	-30	1.88814917143381	1.559544632	-0.9004035131	0.5676278251
+70	-25	1.88734177389323	1.624415007	-0.7574771577	0.5912387106
+70	-20	1.88662460629926	1.677447915	-0.6105411108	0.6105411108
+70	-15	1.88601859938535	1.718635740	-0.4605070586	0.6255322529
+70	-10	1.88554349994344	1.747998806	-0.3082193517	0.6362195348
+70	-5	1.88521785251255	1.765568713	-0.1544672470	0.6426144580
+70	0	1.88505508602501	1.771372354	0.000000000	0.6447268107
+70	5	1.88506600087535	1.765426499	0.1544548049	0.6425626963
+70	10	1.88525682908391	1.747733047	0.3081724912	0.6361228064
+70	15	1.88562525154781	1.718277302	0.4604110153	0.6254017920
+70	20	1.88616736878219	1.677041374	0.6103931416	0.6103931416
+70	25	1.88687595557680	1.624014082	0.7572902033	0.5910927858
+70	30	1.88773147910999	1.559199633	0.9002043278	0.5675022557
+70	35	1.88870812256299	1.482644537	1.038158881	0.5396384793
+70	40	1.88977621919895	1.394464687	1.170094804	0.5075436387
+70	45	1.89089770819352	1.294869881	1.294869881	0.4712940941
+
+75	-45	1.89371946609289	1.315655143	-1.315655143	0.3525287330
+75	-40	1.89321244383849	1.420665833	-1.192080176	0.3806662625
+75	-35	1.89269878791241	1.514359004	-1.060365590	0.4057712721
+75	-30	1.89219208540587	1.596272209	-0.9216081893	0.4277198492
+75	-25	1.89170492014599	1.666044414	-0.7768892690	0.4464152552
+75	-20	1.89125224307001	1.723404901	-0.6272680857	0.4617849516
+75	-15	1.89084947818579	1.768158167	-0.4737765530	0.4737765530
+75	-10	1.89051671160334	1.800175390	-0.3174194913	0.4823555420
+75	-5	1.89027201389041	1.819377547	-0.1591749100	0.4875007445
+75	0	1.89012918870040	1.825724598	0.000000000	0.4892014317
+75	5	1.89010043848267	1.819212407	0.1591604621	0.4874564952
+75	10	1.89019309734601	1.799867240	0.3173651561	0.4822729735
+75	15	1.89040694253061	1.767744346	0.4736656701	0.4736656701
+75	20	1.89073948528267	1.722937650	0.6270980203	0.4616597521
+75	25	1.89118504744021	1.665586556	0.7766757666	0.4462925727
+75	30	1.89172908859227	1.595881620	0.9213826828	0.4276151913
+75	35	1.89235011894888	1.514080032	1.060170252	0.4056965218
+75	40	1.89302296441289	1.420523647	1.191960868	0.3806281641
+75	45	1.89371946197438	1.315655140	1.315655140	0.3525287322
+
+80	-45	1.89571003745605	1.330170147	-1.330170147	0.2345448859
+80	-40	1.89553259965541	1.438994278	-1.207459568	0.2537335163
+80	-35	1.89533248232792	1.536619348	-1.075952451	0.2709474502
+80	-30	1.89511295274615	1.622408972	-0.9366982569	0.2860744756
+80	-25	1.89487754652728	1.695824700	-0.7907760445	0.2990196492
+80	-20	1.89463453191464	1.756426674	-0.6392870282	0.3097054123
+80	-15	1.89439518023069	1.803868520	-0.4833451131	0.3180706897
+80	-10	1.89417863220230	1.837897897	-0.3240709871	0.3240709871
+80	-5	1.89400123851655	1.858342192	-0.1625838747	0.3276758678
+80	0	1.89387591766260	1.865103687	0.000000000	0.3288681018
+80	5	1.89381518853238	1.858159644	0.1625679039	0.3276436798
+80	10	1.89382789413867	1.837557581	0.3240109801	0.3240109801
+80	15	1.89391632739693	1.803412550	0.4832229363	0.3179902899
+80	20	1.89407987192084	1.755912475	0.6390998750	0.3096147451
+80	25	1.89431703563362	1.695323070	0.7905421304	0.2989311982
+80	30	1.89461582500208	1.621983381	0.9364525414	0.2859994323
+80	35	1.89496057481285	1.536317828	1.075741324	0.2708942841
+80	40	1.89533220597023	1.438842149	1.207331916	0.2537066918
+80	45	1.89571003354047	1.330170145	1.330170145	0.2345448855
+
+85	-45	1.89689427867493	1.338747472	-1.338747472	0.1171252271
+85	-40	1.89692010943756	1.449872555	-1.216587526	0.1268474121
+85	-35	1.89691542927617	1.549887070	-1.085242610	0.1355975483
+85	-30	1.89687651039300	1.638048203	-0.9457275710	0.1433106481
+85	-25	1.89680185417921	1.713707549	-0.7991149541	0.1499299832
+85	-20	1.89669269323541	1.776315280	-0.6465258885	0.1554074498
+85	-15	1.89655928832847	1.825429018	-0.4891222312	0.1597043451
+85	-10	1.89641921388467	1.860714643	-0.3280941949	0.1627914373
+85	-5	1.89628672988173	1.881936597	-0.1646481177	0.1646481177
+85	0	1.89617346594891	1.888957953	0.000000000	0.1652624068
+85	5	1.89609190745776	1.881743249	0.1646312020	0.1646312020
+85	10	1.89605218089542	1.860354520	0.3280306956	0.1627599306
+85	15	1.89605858403549	1.824947092	0.4889930996	0.1596621821
+85	20	1.89611209178345	1.775771527	0.6463279788	0.1553598776
+85	25	1.89621457007244	1.713176954	0.7988675336	0.1498835621
+85	30	1.89635810511244	1.637600534	0.9454691091	0.1432714821
+85	35	1.89652899390913	1.549571330	1.085021526	0.1355699247
+85	40	1.89671310667372	1.449714337	1.216454765	0.1268335698
+85	45	1.89689427555732	1.338747469	1.338747469	0.1171252269
+
+90	-45	1.89728648384518	1.341584139	-1.341584139	0.000000000
+90	-40	1.89738103488980	1.453478198	-1.219613020	0.000000000
+90	-35	1.89744282852728	1.554294172	-1.088328496	0.000000000
+90	-30	1.89746564130228	1.643253448	-0.9487328207	0.000000000
+90	-25	1.89744614565938	1.719670217	-0.8018953918	0.000000000
+90	-20	1.89738318437130	1.782956977	-0.6489432687	0.000000000
+90	-15	1.89728653602291	1.832638065	-0.4910538895	0.000000000
+90	-10	1.89717318215456	1.868350859	-0.3294406658	0.000000000
+90	-5	1.89705651405948	1.889837641	-0.1653393695	0.000000000
+90	0	1.89694760485563	1.896947605	0.000000000	0.000000000
+90	5	1.89685877007339	1.889640650	0.1653221350	0.000000000
+90	10	1.89680074227129	1.867984077	0.3293759923	0.000000000
+90	15	1.89677857502036	1.832147412	0.4909224196	0.000000000
+90	20	1.89679387577454	1.782403208	0.6487417133	0.000000000
+90	25	1.89684982451163	1.719129767	0.8016433756	0.000000000
+90	30	1.89694005020999	1.642798273	0.9484700251	0.000000000
+90	35	1.89705147100976	1.553973591	1.088104022	0.000000000
+90	40	1.89717182258600	1.453317932	1.219478541	0.000000000
+90	45	1.89728648176908	1.341584137	1.341584137	0.000000000
+
+
+### +y patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = 90 - dsigma = 90 - dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+45	45	1.86338394555680	1.075825223	1.075825223	1.075825223
+40	45	1.85977391316397	0.9489935399	1.130966460	1.130966460
+35	45	1.85663469946787	0.8238122214	1.176525782	1.176525782
+30	45	1.85396384253110	0.7007324667	1.213704235	1.213704235
+25	45	1.85174823083385	0.5798668349	1.243528440	1.243528440
+20	45	1.84996697044838	0.4610923709	1.266840877	1.266840877
+15	45	1.84860052653659	0.3441295361	1.284308913	1.284308913
+10	45	1.84763131917894	0.2285963931	1.296434568	1.296434568
+5	45	1.84704675662883	0.1140473527	1.303567206	1.303567206
+0	45	1.84683872961156	0.000000000	1.305912189	1.305912189
+-5	45	1.84700629893176	-0.1140448546	1.303538653	1.303538653
+-10	45	1.84755321750004	-0.2285867301	1.296379767	1.296379767
+-15	45	1.84849073240289	-0.3441090972	1.284232634	1.284232634
+-20	45	1.84983466828704	-0.4610593955	1.266750278	1.266750278
+-25	45	1.85160530746921	-0.5798220791	1.243432461	1.243432461
+-30	45	1.85382654784244	-0.7006805742	1.213614354	1.213614354
+-35	45	1.85652064584448	-0.8237616144	1.176453508	1.176453508
+-40	45	1.85970535375840	-0.9489585558	1.130924768	1.130924768
+-45	45	1.86338397861656	-1.075825242	1.075825242	1.075825242
+
+45	50	1.87071350542383	1.137619050	1.137619050	0.9545757250
+40	50	1.86753406904451	1.009805931	1.203439846	1.009805931
+35	50	1.86469834003075	0.8814132360	1.258788556	1.056249013
+30	50	1.86223189509498	0.7532388096	1.304647888	1.094729562
+25	50	1.86014712091991	0.6257432046	1.341910633	1.125996717
+20	50	1.85844359033700	0.4991285278	1.371344360	1.150694546
+15	50	1.85711842437619	0.3734088755	1.393580895	1.169353215
+10	50	1.85616663088296	0.2484640391	1.409109588	1.182383336
+5	50	1.85558502016984	0.1240833268	1.418278915	1.190077314
+0	50	1.85537111100295	0.000000000	1.421296730	1.192609562
+-5	50	1.85552654424983	-0.1240794165	1.418234220	1.190039811
+-10	50	1.85605434439181	-0.2484490086	1.409024346	1.182311809
+-15	50	1.85696137828058	-0.3733772984	1.393463048	1.169254330
+-20	50	1.85825655289451	-0.4990782945	1.371206345	1.150578738
+-25	50	1.85994728308168	-0.6256759803	1.341766470	1.125875750
+-30	50	1.86204257587588	-0.7531622334	1.304515255	1.094618269
+-35	50	1.86454470557095	-0.8813406154	1.258684843	1.056161988
+-40	50	1.86744356203534	-1.009756992	1.203381523	1.009756992
+-45	50	1.87071349794559	-1.137619045	1.137619045	0.9545757212
+
+45	55	1.87713951261612	1.189519421	1.189519421	0.8329104655
+40	55	1.87449966755671	1.061800926	1.265405068	0.8860461676
+35	55	1.87209093866783	0.9314453903	1.330241877	0.9314453903
+30	55	1.86995251870024	0.7994702560	1.384723103	0.9695935547
+25	55	1.86810829328458	0.6665988445	1.429525835	1.000964766
+20	55	1.86657560096290	0.5333148128	1.465270406	1.025993384
+15	55	1.86536473514147	0.3999111884	1.492488874	1.045051960
+10	55	1.86448238794975	0.2665372717	1.511607983	1.058439305
+5	55	1.86393451168388	0.1332399675	1.522939797	1.066373926
+0	55	1.86372388293253	0.000000000	1.526673229	1.068988103
+-5	55	1.86385475187579	-0.1332342660	1.522874629	1.066328295
+-10	55	1.86433000092997	-0.2665154872	1.511484437	1.058352797
+-15	55	1.86515229820569	-0.3998656445	1.492318902	1.044932944
+-20	55	1.86632447520210	-0.5332430616	1.465073271	1.025855348
+-25	55	1.86784398890158	-0.6665045325	1.429323582	1.000823147
+-30	55	1.86970506372449	-0.7993644603	1.384539859	0.9694652462
+-35	55	1.87189455747366	-0.9313476822	1.330102336	0.9313476822
+-40	55	1.87438658982468	-1.061736874	1.265328734	0.8859927175
+-45	55	1.87713946809518	-1.189519393	1.189519393	0.8329104457
+
+45	60	1.88263655527178	1.232474932	1.232474932	0.7115697335
+40	60	1.88058391449578	1.105517960	1.317505000	0.7606618665
+35	60	1.87867151080306	0.9741144602	1.391179625	0.8031979308
+30	60	1.87693629108992	0.8393914273	1.453868599	0.8393914273
+25	60	1.87540964284059	0.7022538581	1.505988259	0.8694827266
+20	60	1.87411975793885	0.5634102105	1.547956831	0.8937132932
+15	60	1.87308306387453	0.4234003576	1.580151647	0.9123009785
+10	60	1.87231474421009	0.2826329997	1.602891393	0.9254297770
+5	60	1.87182686647280	0.1414181260	1.616416576	0.9332385456
+0	60	1.87162736023089	0.000000000	1.620876840	0.9358136801
+-5	60	1.87172284700081	-0.1414102672	1.616326750	0.9331866845
+-10	60	1.87211708739328	-0.2826031626	1.602722178	0.9253320811
+-15	60	1.87280947492454	-0.4233385143	1.579920844	0.9121677247
+-20	60	1.87379950246560	-0.5633139332	1.547692312	0.8935605727
+-25	60	1.87507835335273	-0.7021298056	1.505722227	0.8693291332
+-30	60	1.87662914480360	-0.8392540673	1.453630685	0.8392540673
+-35	60	1.87843097545895	-0.9739897396	1.391001505	0.8030950935
+-40	60	1.88044886754051	-1.105438571	1.317410388	0.7606072424
+-45	60	1.88263658000051	-1.232474948	1.232474948	0.7115697428
+
+45	65	1.88721437054582	1.267345476	1.267345476	0.5909729010
+40	65	1.88574097017119	1.141489357	1.360374043	0.6343528340
+35	65	1.88433821997289	1.009661042	1.441945404	0.6723901845
+30	65	1.88303721063027	0.8730190411	1.512113335	0.7051100282
+25	65	1.88187115968623	0.7325778549	1.571018280	0.7325778549
+20	65	1.88086465613910	0.5892096542	1.618840220	0.7548775921
+15	65	1.88003806466115	0.4436620445	1.655769291	0.7720979007
+10	65	1.87941113410501	0.2965789842	1.681983001	0.7843215544
+5	65	1.87900074870564	0.1485229203	1.697624747	0.7916154203
+0	65	1.87881878929369	0.000000000	1.702788099	0.7940231309
+-5	65	1.87887205788596	-0.1485127481	1.697508479	0.7915612034
+-10	65	1.87916749874660	-0.2965405375	1.681764959	0.7842198797
+-15	65	1.87970210014115	-0.4435827617	1.655473404	0.7719599261
+-20	65	1.88047308507539	-0.5890869886	1.618503199	0.7547204366
+-25	65	1.88147001634992	-0.7324216971	1.570683398	0.7324216971
+-30	65	1.88267275857319	-0.8728500728	1.511820674	0.7049735578
+-35	65	1.88405595257144	-1.009509798	1.441729406	0.6722894628
+-40	65	1.88558474128553	-1.141394788	1.360261339	0.6343002795
+-45	65	1.88721438037142	-1.267345483	1.267345483	0.5909729040
+
+45	70	1.89089770778195	1.294869881	1.294869881	0.4712940940
+40	70	1.88995088801574	1.170202954	1.394593575	0.5075905501
+35	70	1.88902701690296	1.038334166	1.482894870	0.5397295932
+30	70	1.88814917152949	0.9004035132	1.559544632	0.5676278251
+25	70	1.88734177396717	0.7574771577	1.624415007	0.5912387106
+20	70	1.88662460634912	0.6105411108	1.677447916	0.6105411108
+15	70	1.88601859941080	0.4605070586	1.718635740	0.6255322529
+10	70	1.88554349994559	0.3082193517	1.747998806	0.6362195348
+5	70	1.88521785249149	0.1544672470	1.765568713	0.6426144580
+0	70	1.88505508598108	0.000000000	1.771372354	0.6447268107
+-5	70	1.88506600081010	-0.1544548049	1.765426499	0.6425626963
+-10	70	1.88525682899896	-0.3081724912	1.747733047	0.6361228064
+-15	70	1.88562525144483	-0.4604110153	1.718277301	0.6254017919
+-20	70	1.88616736866289	-0.6103931416	1.677041373	0.6103931416
+-25	70	1.88687595544362	-0.7572902033	1.624014082	0.5910927858
+-30	70	1.88773147896741	-0.9002043277	1.559199633	0.5675022556
+-35	70	1.88870812241634	-1.038158881	1.482644536	0.5396384793
+-40	70	1.88977621905429	-1.170094804	1.394464687	0.5075436387
+-45	70	1.89089770805686	-1.294869881	1.294869881	0.4712940941
+
+45	75	1.89371946621960	1.315655143	1.315655143	0.3525287330
+40	75	1.89321244395762	1.192080176	1.420665833	0.3806662626
+35	75	1.89269878801716	1.060365590	1.514359004	0.4057712721
+30	75	1.89219208549180	0.9216081894	1.596272209	0.4277198492
+25	75	1.89170492021250	0.7768892690	1.666044414	0.4464152552
+20	75	1.89125224311538	0.6272680857	1.723404901	0.4617849516
+15	75	1.89084947820713	0.4737765530	1.768158167	0.4737765530
+10	75	1.89051671160268	0.3174194913	1.800175390	0.4823555420
+5	75	1.89027201386843	0.1591749100	1.819377547	0.4875007445
+0	75	1.89012918865653	0.000000000	1.825724598	0.4892014317
+-5	75	1.89010043841806	-0.1591604621	1.819212406	0.4874564952
+-10	75	1.89019309726289	-0.3173651561	1.799867240	0.4822729734
+-15	75	1.89040694243141	-0.4736656700	1.767744346	0.4736656700
+-20	75	1.89073948516940	-0.6270980202	1.722937650	0.4616597520
+-25	75	1.89118504731665	-0.7766757665	1.665586556	0.4462925727
+-30	75	1.89172908846100	-0.9213826828	1.595881620	0.4276151912
+-35	75	1.89235011881399	-1.060170252	1.514080032	0.4056965217
+-40	75	1.89302296427970	-1.191960868	1.420523647	0.3806281641
+-45	75	1.89371946184773	-1.315655140	1.315655140	0.3525287322
+
+45	80	1.89571003757581	1.330170148	1.330170148	0.2345448860
+40	80	1.89553259976724	1.207459568	1.438994278	0.2537335163
+35	80	1.89533248242683	1.075952451	1.536619348	0.2709474502
+30	80	1.89511295282694	0.9366982570	1.622408972	0.2860744756
+25	80	1.89487754658932	0.7907760445	1.695824700	0.2990196492
+20	80	1.89463453195672	0.6392870282	1.756426674	0.3097054123
+15	80	1.89439518024965	0.4833451131	1.803868520	0.3180706897
+10	80	1.89417863219976	0.3240709871	1.837897897	0.3240709871
+5	80	1.89400123849362	0.1625838747	1.858342192	0.3276758678
+0	80	1.89387591761938	0.000000000	1.865103687	0.3288681018
+-5	80	1.89381518846947	-0.1625679039	1.858159644	0.3276436798
+-10	80	1.89382789405794	-0.3240109801	1.837557581	0.3240109801
+-15	80	1.89391632730148	-0.4832229363	1.803412550	0.3179902899
+-20	80	1.89407987181286	-0.6390998749	1.755912475	0.3096147451
+-25	80	1.89431703551691	-0.7905421304	1.695323069	0.2989311982
+-30	80	1.89461582487941	-0.9364525413	1.621983380	0.2859994322
+-35	80	1.89496057468672	-1.075741324	1.536317828	0.2708942841
+-40	80	1.89533220584477	-1.207331916	1.438842149	0.2537066918
+-45	80	1.89571003342075	-1.330170145	1.330170145	0.2345448854
+
+45	85	1.89689427879084	1.338747472	1.338747472	0.1171252271
+40	85	1.89692010954531	1.216587526	1.449872555	0.1268474121
+35	85	1.89691542937283	1.085242610	1.549887070	0.1355975484
+30	85	1.89687651047256	0.9457275710	1.638048203	0.1433106481
+25	85	1.89680185423892	0.7991149541	1.713707549	0.1499299832
+20	85	1.89669269327514	0.6465258885	1.776315280	0.1554074498
+15	85	1.89655928834741	0.4891222312	1.825429018	0.1597043451
+10	85	1.89641921388204	0.3280941949	1.860714643	0.1627914373
+5	85	1.89628672985817	0.1646481177	1.881936597	0.1646481177
+0	85	1.89617346590587	0.000000000	1.888957953	0.1652624068
+-5	85	1.89609190739703	-0.1646312020	1.881743249	0.1646312020
+-10	85	1.89605218081865	-0.3280306956	1.860354520	0.1627599306
+-15	85	1.89605858394462	-0.4889930996	1.824947092	0.1596621821
+-20	85	1.89611209167959	-0.6463279787	1.775771527	0.1553598776
+-25	85	1.89621456995918	-0.7988675336	1.713176954	0.1498835621
+-30	85	1.89635810499466	-0.9454691091	1.637600534	0.1432714821
+-35	85	1.89652899378854	-1.085021526	1.549571330	0.1355699247
+-40	85	1.89671310655297	-1.216454765	1.449714337	0.1268335698
+-45	85	1.89689427544146	-1.338747469	1.338747469	0.1171252269
+
+45	90	1.89728648395996	1.341584139	1.341584139	0.000000000
+40	90	1.89738103499617	1.219613020	1.453478198	0.000000000
+35	90	1.89744282862298	1.088328496	1.554294172	0.000000000
+30	90	1.89746564138154	0.9487328207	1.643253448	0.000000000
+25	90	1.89744614571777	0.8018953918	1.719670217	0.000000000
+20	90	1.89738318440989	0.6489432687	1.782956977	0.000000000
+15	90	1.89728653604155	0.4910538895	1.832638065	0.000000000
+10	90	1.89717318215177	0.3294406658	1.868350859	0.000000000
+5	90	1.89705651403587	0.1653393695	1.889837641	0.000000000
+0	90	1.89694760481255	0.000000000	1.896947605	0.000000000
+-5	90	1.89685877001345	-0.1653221350	1.889640650	0.000000000
+-10	90	1.89680074219697	-0.3293759923	1.867984077	0.000000000
+-15	90	1.89677857493240	-0.4909224195	1.832147412	0.000000000
+-20	90	1.89679387567256	-0.6487417132	1.782403208	0.000000000
+-25	90	1.89684982439958	-0.8016433756	1.719129767	0.000000000
+-30	90	1.89694005009317	-0.9484700250	1.642798273	0.000000000
+-35	90	1.89705147089080	-1.088104022	1.553973591	0.000000000
+-40	90	1.89717182246692	-1.219478541	1.453317932	0.000000000
+-45	90	1.89728648165435	-1.341584137	1.341584137	0.000000000
+
+
+### -x patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = drho = dnu
+# dpy = 180 - dsigma = 180 - dphi
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-90	45	1.89728648384523	-1.341584139	1.341584139	1.642966721e-16
+-90	40	1.89738103488983	-1.453478198	1.219613020	1.779997423e-16
+-90	35	1.89744282852730	-1.554294172	1.088328496	1.903461383e-16
+-90	30	1.89746564130230	-1.643253448	0.9487328207	2.012405075e-16
+-90	25	1.89744614565937	-1.719670217	0.8018953918	2.105988627e-16
+-90	20	1.89738318437129	-1.782956977	0.6489432687	2.183492555e-16
+-90	15	1.89728653602288	-1.832638065	0.4910538895	2.244334340e-16
+-90	10	1.89717318215452	-1.868350859	0.3294406658	2.288069899e-16
+-90	5	1.89705651405942	-1.889837641	0.1653393695	2.314383618e-16
+-90	-2.84217e-14	1.89694760485557	-1.896947605	-6.101048817e-16	2.323090812e-16
+-90	-5	1.89685877007331	-1.889640650	-0.1653221350	2.314142373e-16
+-90	-10	1.89680074227120	-1.867984077	-0.3293759923	2.287620721e-16
+-90	-15	1.89677857502027	-1.832147412	-0.4909224196	2.243733464e-16
+-90	-20	1.89679387577443	-1.782403208	-0.6487417133	2.182814384e-16
+-90	-25	1.89684982451151	-1.719129767	-0.8016433756	2.105326766e-16
+-90	-30	1.89694005020987	-1.642798273	-0.9484700251	2.011847647e-16
+-90	-35	1.89705147100962	-1.553973591	-1.088104022	1.903068784e-16
+-90	-40	1.89717182258586	-1.453317932	-1.219478541	1.779801154e-16
+-90	-45	1.89728648176893	-1.341584137	-1.341584137	1.642966719e-16
+
+-85	45	1.89689427867498	-1.338747472	1.338747472	0.1171252271
+-85	40	1.89692010943760	-1.449872555	1.216587526	0.1268474121
+-85	35	1.89691542927619	-1.549887070	1.085242610	0.1355975483
+-85	30	1.89687651039301	-1.638048203	0.9457275710	0.1433106481
+-85	25	1.89680185417921	-1.713707549	0.7991149541	0.1499299832
+-85	20	1.89669269323539	-1.776315280	0.6465258885	0.1554074498
+-85	15	1.89655928832844	-1.825429018	0.4891222312	0.1597043451
+-85	10	1.89641921388463	-1.860714643	0.3280941949	0.1627914373
+-85	5	1.89628672988168	-1.881936597	0.1646481177	0.1646481177
+-85	-2.84217e-14	1.89617346594885	-1.888957953	-6.075352138e-16	0.1652624068
+-85	-5	1.89609190745768	-1.881743249	-0.1646312020	0.1646312020
+-85	-10	1.89605218089533	-1.860354520	-0.3280306956	0.1627599306
+-85	-15	1.89605858403539	-1.824947092	-0.4889930996	0.1596621821
+-85	-20	1.89611209178334	-1.775771527	-0.6463279788	0.1553598776
+-85	-25	1.89621457007232	-1.713176954	-0.7988675336	0.1498835621
+-85	-30	1.89635810511231	-1.637600534	-0.9454691091	0.1432714821
+-85	-35	1.89652899390900	-1.549571330	-1.085021526	0.1355699247
+-85	-40	1.89671310667358	-1.449714337	-1.216454765	0.1268335698
+-85	-45	1.89689427555717	-1.338747469	-1.338747469	0.1171252269
+
+-80	45	1.89571003745610	-1.330170147	1.330170147	0.2345448859
+-80	40	1.89553259965544	-1.438994278	1.207459568	0.2537335163
+-80	35	1.89533248232794	-1.536619348	1.075952451	0.2709474502
+-80	30	1.89511295274616	-1.622408972	0.9366982569	0.2860744756
+-80	25	1.89487754652728	-1.695824700	0.7907760445	0.2990196492
+-80	20	1.89463453191462	-1.756426674	0.6392870282	0.3097054123
+-80	15	1.89439518023066	-1.803868520	0.4833451131	0.3180706897
+-80	10	1.89417863220226	-1.837897897	0.3240709871	0.3240709871
+-80	5	1.89400123851650	-1.858342192	0.1625838747	0.3276758678
+-80	-2.84217e-14	1.89387591766253	-1.865103687	-5.998630966e-16	0.3288681018
+-80	-5	1.89381518853230	-1.858159644	-0.1625679039	0.3276436798
+-80	-10	1.89382789413858	-1.837557581	-0.3240109801	0.3240109801
+-80	-15	1.89391632739684	-1.803412550	-0.4832229363	0.3179902899
+-80	-20	1.89407987192073	-1.755912475	-0.6390998750	0.3096147451
+-80	-25	1.89431703563351	-1.695323070	-0.7905421304	0.2989311982
+-80	-30	1.89461582500196	-1.621983381	-0.9364525414	0.2859994323
+-80	-35	1.89496057481271	-1.536317828	-1.075741324	0.2708942841
+-80	-40	1.89533220597009	-1.438842149	-1.207331916	0.2537066918
+-80	-45	1.89571003354032	-1.330170145	-1.330170145	0.2345448855
+
+-75	45	1.89371946609294	-1.315655143	1.315655143	0.3525287330
+-75	40	1.89321244383853	-1.420665833	1.192080176	0.3806662625
+-75	35	1.89269878791243	-1.514359004	1.060365590	0.4057712721
+-75	30	1.89219208540589	-1.596272209	0.9216081893	0.4277198492
+-75	25	1.89170492014599	-1.666044414	0.7768892690	0.4464152552
+-75	20	1.89125224307000	-1.723404901	0.6272680857	0.4617849516
+-75	15	1.89084947818576	-1.768158167	0.4737765530	0.4737765530
+-75	10	1.89051671160330	-1.800175390	0.3174194913	0.4823555420
+-75	5	1.89027201389036	-1.819377547	0.1591749100	0.4875007445
+-75	-2.84217e-14	1.89012918870034	-1.825724598	-5.871978157e-16	0.4892014317
+-75	-5	1.89010043848260	-1.819212407	-0.1591604621	0.4874564952
+-75	-10	1.89019309734592	-1.799867240	-0.3173651561	0.4822729735
+-75	-15	1.89040694253052	-1.767744346	-0.4736656701	0.4736656701
+-75	-20	1.89073948528256	-1.722937650	-0.6270980203	0.4616597521
+-75	-25	1.89118504744009	-1.665586556	-0.7766757666	0.4462925727
+-75	-30	1.89172908859215	-1.595881620	-0.9213826828	0.4276151913
+-75	-35	1.89235011894875	-1.514080032	-1.060170252	0.4056965218
+-75	-40	1.89302296441275	-1.420523647	-1.191960868	0.3806281641
+-75	-45	1.89371946197423	-1.315655140	-1.315655140	0.3525287322
+
+-70	45	1.89089770764530	-1.294869881	1.294869881	0.4712940940
+-70	40	1.88995088788594	-1.394593575	1.170202954	0.5075905501
+-70	35	1.88902701678740	-1.482894870	1.038334166	0.5397295932
+-70	30	1.88814917143383	-1.559544632	0.9004035131	0.5676278251
+-70	25	1.88734177389324	-1.624415007	0.7574771577	0.5912387106
+-70	20	1.88662460629924	-1.677447915	0.6105411108	0.6105411108
+-70	15	1.88601859938533	-1.718635740	0.4605070586	0.6255322529
+-70	10	1.88554349994340	-1.747998806	0.3082193517	0.6362195348
+-70	5	1.88521785251250	-1.765568713	0.1544672470	0.6426144580
+-70	-2.84217e-14	1.88505508602495	-1.771372354	-5.697168007e-16	0.6447268107
+-70	-5	1.88506600087528	-1.765426499	-0.1544548049	0.6425626963
+-70	-10	1.88525682908382	-1.747733047	-0.3081724912	0.6361228064
+-70	-15	1.88562525154772	-1.718277302	-0.4604110153	0.6254017920
+-70	-20	1.88616736878208	-1.677041374	-0.6103931416	0.6103931416
+-70	-25	1.88687595557669	-1.624014082	-0.7572902033	0.5910927858
+-70	-30	1.88773147910986	-1.559199633	-0.9002043278	0.5675022557
+-70	-35	1.88870812256285	-1.482644537	-1.038158881	0.5396384793
+-70	-40	1.88977621919881	-1.394464687	-1.170094804	0.5075436387
+-70	-45	1.89089770819337	-1.294869881	-1.294869881	0.4712940941
+
+-65	45	1.88721437039506	-1.267345476	1.267345476	0.5909729009
+-65	40	1.88574097002601	-1.360374042	1.141489357	0.6343528339
+-65	35	1.88433821984272	-1.441945404	1.009661042	0.6723901845
+-65	30	1.88303721052188	-1.512113335	0.8730190411	0.7051100282
+-65	25	1.88187115960239	-1.571018280	0.7325778548	0.7325778548
+-65	20	1.88086465608212	-1.618840220	0.5892096542	0.7548775921
+-65	15	1.88003806463104	-1.655769291	0.4436620445	0.7720979007
+-65	10	1.87941113410000	-1.681983001	0.2965789842	0.7843215544
+-65	5	1.87900074872530	-1.697624747	0.1485229203	0.7916154203
+-65	-2.84217e-14	1.87881878933727	-1.702788099	-5.476584220e-16	0.7940231309
+-65	-5	1.87887205795216	-1.697508479	-0.1485127481	0.7915612034
+-65	-10	1.87916749883460	-1.681764959	-0.2965405375	0.7842198798
+-65	-15	1.87970210024891	-1.655473404	-0.4435827617	0.7719599262
+-65	-20	1.88047308520177	-1.618503199	-0.5890869886	0.7547204366
+-65	-25	1.88147001649443	-1.570683398	-0.7324216972	0.7324216972
+-65	-30	1.88267275873040	-1.511820674	-0.8728500729	0.7049735579
+-65	-35	1.88405595273468	-1.441729406	-1.009509798	0.6722894628
+-65	-40	1.88558474144661	-1.360261339	-1.141394788	0.6343002795
+-65	-45	1.88721438052204	-1.267345483	-1.267345483	0.5909729041
+
+-60	45	1.88263655510036	-1.232474931	1.232474931	0.7115697334
+-60	40	1.88058391432845	-1.317505000	1.105517960	0.7606618664
+-60	35	1.87867151065322	-1.391179625	0.9741144601	0.8031979307
+-60	30	1.87693629096546	-1.453868599	0.8393914272	0.8393914272
+-60	25	1.87540964274485	-1.505988259	0.7022538581	0.8694827265
+-60	20	1.87411975787293	-1.547956831	0.5634102105	0.8937132932
+-60	15	1.87308306383820	-1.580151646	0.4234003576	0.9123009785
+-60	10	1.87231474420200	-1.602891393	0.2826329997	0.9254297770
+-60	5	1.87182686649124	-1.616416577	0.1414181260	0.9332385456
+-60	-2.84217e-14	1.87162736027436	-1.620876840	-5.213137519e-16	0.9358136801
+-60	-5	1.87172284706831	-1.616326751	-0.1414102672	0.9331866845
+-60	-10	1.87211708748416	-1.602722178	-0.2826031626	0.9253320812
+-60	-15	1.87280947503788	-1.579920844	-0.4233385143	0.9121677247
+-60	-20	1.87379950260114	-1.547692312	-0.5633139332	0.8935605727
+-60	-25	1.87507835350996	-1.505722227	-0.7021298057	0.8693291333
+-60	-30	1.87662914497882	-1.453630685	-0.8392540673	0.8392540673
+-60	-35	1.87843097564516	-1.391001505	-0.9739897397	0.8030950936
+-60	-40	1.88044886772568	-1.317410389	-1.105438571	0.7606072425
+-60	-45	1.88263658017182	-1.232474948	-1.232474948	0.7115697429
+
+-55	45	1.87713951241269	-1.189519421	1.189519421	0.8329104654
+-55	40	1.87449966735582	-1.265405068	1.061800926	0.8860461675
+-55	35	1.87209093848981	-1.330241877	0.9314453902	0.9314453902
+-55	30	1.86995251855521	-1.384723102	0.7994702559	0.9695935546
+-55	25	1.86810829317550	-1.429525835	0.6665988444	1.000964766
+-55	20	1.86657560088832	-1.465270406	0.5333148128	1.025993383
+-55	15	1.86536473509917	-1.492488873	0.3999111884	1.045051960
+-55	10	1.86448238793738	-1.511607983	0.2665372717	1.058439305
+-55	5	1.86393451169926	-1.522939797	0.1332399675	1.066373926
+-55	-2.84217e-14	1.86372388297431	-1.526673229	-4.910155596e-16	1.068988103
+-55	-5	1.86385475194308	-1.522874629	-0.1332342660	1.066328295
+-55	-10	1.86433000102217	-1.511484437	-0.2665154873	1.058352797
+-55	-15	1.86515229832351	-1.492318902	-0.3998656445	1.044932944
+-55	-20	1.86632447534644	-1.465073271	-0.5332430616	1.025855348
+-55	-25	1.86784398907279	-1.429323583	-0.6665045326	1.000823147
+-55	-30	1.86970506392157	-1.384539859	-0.7993644604	0.9694652463
+-55	-35	1.87189455769078	-1.330102336	-0.9313476823	0.9313476823
+-55	-40	1.87438659004609	-1.265328734	-1.061736874	0.8859927176
+-55	-45	1.87713946829864	-1.189519393	-1.189519393	0.8329104458
+
+-50	45	1.87071350516666	-1.137619050	1.137619050	0.9545757249
+-50	40	1.86753406879214	-1.203439846	1.009805931	1.009805931
+-50	35	1.86469833981798	-1.258788556	0.8814132359	1.056249013
+-50	30	1.86223189492984	-1.304647888	0.7532388095	1.094729562
+-50	25	1.86014712079930	-1.341910633	0.6257432046	1.125996717
+-50	20	1.85844359025549	-1.371344359	0.4991285278	1.150694546
+-50	15	1.85711842432932	-1.393580895	0.3734088755	1.169353215
+-50	10	1.85616663086765	-1.409109588	0.2484640391	1.182383336
+-50	5	1.85558502018341	-1.418278915	0.1240833268	1.190077314
+-50	-2.84217e-14	1.85537111104312	-1.421296730	-4.571238925e-16	1.192609562
+-50	-5	1.85552654431559	-1.418234220	-0.1240794165	1.190039811
+-50	-10	1.85605434448358	-1.409024346	-0.2484490086	1.182311809
+-50	-15	1.85696137839986	-1.393463048	-0.3733772984	1.169254330
+-50	-20	1.85825655304338	-1.371206345	-0.4990782945	1.150578738
+-50	-25	1.85994728326310	-1.341766470	-0.6256759804	1.125875750
+-50	-30	1.86204257609344	-1.304515255	-0.7531622335	1.094618269
+-50	-35	1.86454470582417	-1.258684843	-0.8813406155	1.056161988
+-50	-40	1.86744356231007	-1.203381523	-1.009756992	1.009756992
+-50	-45	1.87071349820297	-1.137619045	-1.137619045	0.9545757214
+
+-45	45	1.86338394519528	-1.075825222	1.075825222	1.075825222
+-45	40	1.85977391284645	-1.130966460	0.9489935397	1.130966460
+-45	35	1.85663469922813	-1.176525782	0.8238122213	1.176525782
+-45	30	1.85396384235655	-1.213704235	0.7007324667	1.213704235
+-45	25	1.85174823070996	-1.243528440	0.5798668349	1.243528440
+-45	20	1.84996697036536	-1.266840877	0.4610923709	1.266840877
+-45	15	1.84860052648868	-1.284308913	0.3441295361	1.284308913
+-45	10	1.84763131916239	-1.296434568	0.2285963931	1.296434568
+-45	5	1.84704675664029	-1.303567206	0.1140473527	1.303567206
+-45	-2.84217e-14	1.84683872964858	-1.305912189	-4.200133941e-16	1.305912189
+-45	-5	1.84700629899387	-1.303538653	-0.1140448546	1.303538653
+-45	-10	1.84755321758792	-1.296379767	-0.2285867301	1.296379767
+-45	-15	1.84849073251843	-1.284232634	-0.3441090972	1.284232634
+-45	-20	1.84983466843322	-1.266750278	-0.4610593955	1.266750278
+-45	-25	1.85160530765079	-1.243432461	-0.5798220791	1.243432461
+-45	-30	1.85382654806757	-1.213614355	-0.7006805743	1.213614355
+-45	-35	1.85652064612465	-1.176453508	-0.8237616145	1.176453508
+-45	-40	1.85970535409961	-1.130924768	-0.9489585560	1.130924768
+-45	-45	1.86338397897821	-1.075825242	-1.075825242	1.075825242
+
+
+### -y patch
+# N_rho = 10
+# N_sigma = 19
+# ghosted_gfn=-3
+# dpx = 90 + dsigma = 90 + dphi
+# dpy = drho = dmu
+#
+# dpx	dpy	gridfn	global_x	global_y	global_z
+-45	-90	1.89728648395981	-1.341584139	-1.341584139	1.642966721e-16
+-40	-90	1.89738103499602	-1.219613020	-1.453478198	1.779997423e-16
+-35	-90	1.89744282862283	-1.088328496	-1.554294172	1.903461383e-16
+-30	-90	1.89746564138138	-0.9487328207	-1.643253448	2.012405076e-16
+-25	-90	1.89744614571761	-0.8018953918	-1.719670217	2.105988627e-16
+-20	-90	1.89738318440972	-0.6489432687	-1.782956977	2.183492555e-16
+-15	-90	1.89728653604139	-0.4910538895	-1.832638065	2.244334340e-16
+-10	-90	1.89717318215161	-0.3294406658	-1.868350859	2.288069899e-16
+-5	-90	1.89705651403572	-0.1653393695	-1.889837641	2.314383618e-16
+-2.84217e-14	-90	1.89694760481240	-6.101048817e-16	-1.896947605	2.323090812e-16
+5	-90	1.89685877001330	0.1653221350	-1.889640650	2.314142373e-16
+10	-90	1.89680074219683	0.3293759923	-1.867984077	2.287620721e-16
+15	-90	1.89677857493227	0.4909224195	-1.832147412	2.243733464e-16
+20	-90	1.89679387567245	0.6487417132	-1.782403208	2.182814384e-16
+25	-90	1.89684982439948	0.8016433756	-1.719129767	2.105326766e-16
+30	-90	1.89694005009308	0.9484700250	-1.642798273	2.011847646e-16
+35	-90	1.89705147089072	1.088104022	-1.553973591	1.903068784e-16
+40	-90	1.89717182246686	1.219478541	-1.453317932	1.779801154e-16
+45	-90	1.89728648165430	1.341584137	-1.341584137	1.642966719e-16
+
+-45	-85	1.89689427879069	-1.338747472	-1.338747472	0.1171252271
+-40	-85	1.89692010954515	-1.216587526	-1.449872555	0.1268474121
+-35	-85	1.89691542937267	-1.085242610	-1.549887070	0.1355975484
+-30	-85	1.89687651047240	-0.9457275710	-1.638048203	0.1433106481
+-25	-85	1.89680185423875	-0.7991149541	-1.713707549	0.1499299832
+-20	-85	1.89669269327497	-0.6465258885	-1.776315280	0.1554074498
+-15	-85	1.89655928834724	-0.4891222312	-1.825429018	0.1597043451
+-10	-85	1.89641921388187	-0.3280941949	-1.860714643	0.1627914373
+-5	-85	1.89628672985801	-0.1646481177	-1.881936597	0.1646481177
+-2.84217e-14	-85	1.89617346590572	-6.075352138e-16	-1.888957953	0.1652624068
+5	-85	1.89609190739688	0.1646312020	-1.881743249	0.1646312020
+10	-85	1.89605218081851	0.3280306956	-1.860354520	0.1627599306
+15	-85	1.89605858394450	0.4889930996	-1.824947092	0.1596621821
+20	-85	1.89611209167948	0.6463279787	-1.775771527	0.1553598776
+25	-85	1.89621456995908	0.7988675336	-1.713176954	0.1498835621
+30	-85	1.89635810499457	0.9454691091	-1.637600534	0.1432714821
+35	-85	1.89652899378847	1.085021526	-1.549571330	0.1355699247
+40	-85	1.89671310655290	1.216454765	-1.449714337	0.1268335698
+45	-85	1.89689427544141	1.338747469	-1.338747469	0.1171252269
+
+-45	-80	1.89571003757566	-1.330170148	-1.330170148	0.2345448860
+-40	-80	1.89553259976708	-1.207459568	-1.438994278	0.2537335163
+-35	-80	1.89533248242667	-1.075952451	-1.536619348	0.2709474502
+-30	-80	1.89511295282677	-0.9366982570	-1.622408972	0.2860744756
+-25	-80	1.89487754658915	-0.7907760445	-1.695824700	0.2990196492
+-20	-80	1.89463453195655	-0.6392870282	-1.756426674	0.3097054123
+-15	-80	1.89439518024948	-0.4833451131	-1.803868520	0.3180706897
+-10	-80	1.89417863219959	-0.3240709871	-1.837897897	0.3240709871
+-5	-80	1.89400123849346	-0.1625838747	-1.858342192	0.3276758678
+-2.84217e-14	-80	1.89387591761923	-5.998630966e-16	-1.865103687	0.3288681018
+5	-80	1.89381518846932	0.1625679039	-1.858159644	0.3276436798
+10	-80	1.89382789405780	0.3240109801	-1.837557581	0.3240109801
+15	-80	1.89391632730135	0.4832229363	-1.803412550	0.3179902899
+20	-80	1.89407987181274	0.6390998749	-1.755912475	0.3096147451
+25	-80	1.89431703551680	0.7905421304	-1.695323069	0.2989311982
+30	-80	1.89461582487932	0.9364525413	-1.621983380	0.2859994322
+35	-80	1.89496057468664	1.075741324	-1.536317828	0.2708942841
+40	-80	1.89533220584471	1.207331916	-1.438842149	0.2537066918
+45	-80	1.89571003342070	1.330170145	-1.330170145	0.2345448854
+
+-45	-75	1.89371946621945	-1.315655143	-1.315655143	0.3525287330
+-40	-75	1.89321244395746	-1.192080176	-1.420665833	0.3806662626
+-35	-75	1.89269878801699	-1.060365590	-1.514359004	0.4057712721
+-30	-75	1.89219208549163	-0.9216081894	-1.596272209	0.4277198492
+-25	-75	1.89170492021233	-0.7768892690	-1.666044414	0.4464152552
+-20	-75	1.89125224311520	-0.6272680857	-1.723404901	0.4617849516
+-15	-75	1.89084947820695	-0.4737765530	-1.768158167	0.4737765530
+-10	-75	1.89051671160250	-0.3174194913	-1.800175390	0.4823555420
+-5	-75	1.89027201386825	-0.1591749100	-1.819377547	0.4875007445
+-2.84217e-14	-75	1.89012918865636	-5.871978157e-16	-1.825724598	0.4892014317
+5	-75	1.89010043841790	0.1591604621	-1.819212406	0.4874564952
+10	-75	1.89019309726275	0.3173651561	-1.799867240	0.4822729734
+15	-75	1.89040694243127	0.4736656700	-1.767744346	0.4736656700
+20	-75	1.89073948516927	0.6270980202	-1.722937650	0.4616597520
+25	-75	1.89118504731654	0.7766757665	-1.665586556	0.4462925727
+30	-75	1.89172908846090	0.9213826828	-1.595881620	0.4276151912
+35	-75	1.89235011881391	1.060170252	-1.514080032	0.4056965217
+40	-75	1.89302296427963	1.191960868	-1.420523647	0.3806281641
+45	-75	1.89371946184768	1.315655140	-1.315655140	0.3525287322
+
+-45	-70	1.89089770778180	-1.294869881	-1.294869881	0.4712940940
+-40	-70	1.88995088801558	-1.170202954	-1.394593575	0.5075905501
+-35	-70	1.88902701690280	-1.038334166	-1.482894870	0.5397295932
+-30	-70	1.88814917152931	-0.9004035132	-1.559544632	0.5676278251
+-25	-70	1.88734177396699	-0.7574771577	-1.624415007	0.5912387106
+-20	-70	1.88662460634893	-0.6105411108	-1.677447916	0.6105411108
+-15	-70	1.88601859941061	-0.4605070586	-1.718635740	0.6255322529
+-10	-70	1.88554349994540	-0.3082193517	-1.747998806	0.6362195348
+-5	-70	1.88521785249130	-0.1544672470	-1.765568713	0.6426144580
+-2.84217e-14	-70	1.88505508598090	-5.697168007e-16	-1.771372354	0.6447268107
+5	-70	1.88506600080993	0.1544548049	-1.765426499	0.6425626963
+10	-70	1.88525682899880	0.3081724912	-1.747733047	0.6361228064
+15	-70	1.88562525144469	0.4604110153	-1.718277301	0.6254017919
+20	-70	1.88616736866275	0.6103931416	-1.677041373	0.6103931416
+25	-70	1.88687595544350	0.7572902033	-1.624014082	0.5910927858
+30	-70	1.88773147896731	0.9002043277	-1.559199633	0.5675022556
+35	-70	1.88870812241625	1.038158881	-1.482644536	0.5396384793
+40	-70	1.88977621905422	1.170094804	-1.394464687	0.5075436387
+45	-70	1.89089770805681	1.294869881	-1.294869881	0.4712940941
+
+-45	-65	1.88721437054566	-1.267345476	-1.267345476	0.5909729010
+-40	-65	1.88574097017103	-1.141489357	-1.360374043	0.6343528340
+-35	-65	1.88433821997272	-1.009661042	-1.441945404	0.6723901845
+-30	-65	1.88303721063009	-0.8730190411	-1.512113335	0.7051100282
+-25	-65	1.88187115968604	-0.7325778549	-1.571018280	0.7325778549
+-20	-65	1.88086465613890	-0.5892096542	-1.618840220	0.7548775921
+-15	-65	1.88003806466095	-0.4436620445	-1.655769291	0.7720979007
+-10	-65	1.87941113410481	-0.2965789842	-1.681983001	0.7843215544
+-5	-65	1.87900074870543	-0.1485229203	-1.697624747	0.7916154203
+-2.84217e-14	-65	1.87881878929349	-5.476584220e-16	-1.702788099	0.7940231309
+5	-65	1.87887205788577	0.1485127481	-1.697508479	0.7915612034
+10	-65	1.87916749874643	0.2965405375	-1.681764959	0.7842198797
+15	-65	1.87970210014099	0.4435827617	-1.655473404	0.7719599261
+20	-65	1.88047308507524	0.5890869886	-1.618503199	0.7547204366
+25	-65	1.88147001634980	0.7324216971	-1.570683398	0.7324216971
+30	-65	1.88267275857308	0.8728500728	-1.511820674	0.7049735578
+35	-65	1.88405595257135	1.009509798	-1.441729406	0.6722894628
+40	-65	1.88558474128546	1.141394788	-1.360261339	0.6343002795
+45	-65	1.88721438037136	1.267345483	-1.267345483	0.5909729040
+
+-45	-60	1.88263655527162	-1.232474932	-1.232474932	0.7115697335
+-40	-60	1.88058391449561	-1.105517960	-1.317505000	0.7606618665
+-35	-60	1.87867151080288	-0.9741144602	-1.391179625	0.8031979308
+-30	-60	1.87693629108973	-0.8393914273	-1.453868599	0.8393914273
+-25	-60	1.87540964284038	-0.7022538581	-1.505988259	0.8694827266
+-20	-60	1.87411975793863	-0.5634102105	-1.547956831	0.8937132932
+-15	-60	1.87308306387431	-0.4234003576	-1.580151647	0.9123009785
+-10	-60	1.87231474420986	-0.2826329997	-1.602891393	0.9254297770
+-5	-60	1.87182686647257	-0.1414181260	-1.616416576	0.9332385456
+-2.84217e-14	-60	1.87162736023066	-5.213137519e-16	-1.620876840	0.9358136801
+5	-60	1.87172284700059	0.1414102672	-1.616326750	0.9331866845
+10	-60	1.87211708739308	0.2826031626	-1.602722178	0.9253320811
+15	-60	1.87280947492436	0.4233385143	-1.579920844	0.9121677247
+20	-60	1.87379950246544	0.5633139332	-1.547692312	0.8935605727
+25	-60	1.87507835335259	0.7021298056	-1.505722227	0.8693291332
+30	-60	1.87662914480349	0.8392540673	-1.453630685	0.8392540673
+35	-60	1.87843097545885	0.9739897396	-1.391001505	0.8030950935
+40	-60	1.88044886754043	1.105438571	-1.317410388	0.7606072424
+45	-60	1.88263658000045	1.232474948	-1.232474948	0.7115697428
+
+-45	-55	1.87713951261596	-1.189519421	-1.189519421	0.8329104655
+-40	-55	1.87449966755653	-1.061800926	-1.265405068	0.8860461676
+-35	-55	1.87209093866764	-0.9314453903	-1.330241877	0.9314453903
+-30	-55	1.86995251870003	-0.7994702560	-1.384723103	0.9695935547
+-25	-55	1.86810829328436	-0.6665988445	-1.429525835	1.000964766
+-20	-55	1.86657560096267	-0.5333148128	-1.465270406	1.025993384
+-15	-55	1.86536473514123	-0.3999111884	-1.492488874	1.045051960
+-10	-55	1.86448238794949	-0.2665372717	-1.511607983	1.058439305
+-5	-55	1.86393451168362	-0.1332399675	-1.522939797	1.066373926
+-2.84217e-14	-55	1.86372388293226	-4.910155595e-16	-1.526673229	1.068988103
+5	-55	1.86385475187554	0.1332342660	-1.522874629	1.066328295
+10	-55	1.86433000092974	0.2665154872	-1.511484437	1.058352797
+15	-55	1.86515229820548	0.3998656445	-1.492318902	1.044932944
+20	-55	1.86632447520192	0.5332430616	-1.465073271	1.025855348
+25	-55	1.86784398890143	0.6665045325	-1.429323582	1.000823147
+30	-55	1.86970506372436	0.7993644603	-1.384539859	0.9694652462
+35	-55	1.87189455747355	0.9313476822	-1.330102336	0.9313476822
+40	-55	1.87438658982459	1.061736874	-1.265328734	0.8859927175
+45	-55	1.87713946809511	1.189519393	-1.189519393	0.8329104457
+
+-45	-50	1.87071350542366	-1.137619050	-1.137619050	0.9545757250
+-40	-50	1.86753406904433	-1.009805931	-1.203439846	1.009805931
+-35	-50	1.86469834003054	-0.8814132360	-1.258788556	1.056249013
+-30	-50	1.86223189509476	-0.7532388096	-1.304647888	1.094729562
+-25	-50	1.86014712091967	-0.6257432046	-1.341910633	1.125996717
+-20	-50	1.85844359033674	-0.4991285278	-1.371344360	1.150694546
+-15	-50	1.85711842437592	-0.3734088755	-1.393580895	1.169353215
+-10	-50	1.85616663088267	-0.2484640391	-1.409109588	1.182383336
+-5	-50	1.85558502016953	-0.1240833268	-1.418278915	1.190077314
+-2.84217e-14	-50	1.85537111100264	-4.571238925e-16	-1.421296730	1.192609562
+5	-50	1.85552654424953	0.1240794165	-1.418234220	1.190039811
+10	-50	1.85605434439155	0.2484490086	-1.409024346	1.182311809
+15	-50	1.85696137828035	0.3733772984	-1.393463048	1.169254330
+20	-50	1.85825655289431	0.4990782945	-1.371206345	1.150578738
+25	-50	1.85994728308151	0.6256759803	-1.341766470	1.125875750
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