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Update: improved efficiency in gradient computation for G-IMLOP and G…
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…D-IMLOP
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@AyushiSinha
AyushiSinha committed Jan 31, 2019
1 parent 64132c9 commit 4d194ba
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Showing 18 changed files with 17,552 additions and 17,501 deletions.
2 changes: 1 addition & 1 deletion cisstICP/algDirICP_DIMLOP.cpp
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Expand Up @@ -565,7 +565,7 @@ void algDirICP_DIMLOP::CostFunctionGradient(const vctDynamicVector<double> &x, v
for (unsigned int c = 0; c < 3; c++)
{
Jz_a.Column(c) = dRa[c].TransposeRef() * Tssm_Y_t[j];
k_Yn_dRa_Xn.Element(c) = -k*sampleNorms[j] * dRa[c] * matchNorms[j];
k_Yn_dRa_Xn.Element(c) = -k*sampleNorms[j] * dRa[c].TransposeRef() * matchNorms[j];
}

ga += Rat_Tssm_Y_t_x_invMx[j] * Jz_a + k_Yn_dRa_Xn;
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17 changes: 9 additions & 8 deletions cisstICP/algDirICP_GDIMLOP.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -124,8 +124,8 @@ void algDirICP_GDIMLOP::ComputeMatchStatistics(double &Avg, double &StdDev) //go
totalSumSqrMahalDist += sqrMahalDist;

matchAngle = acos(std::fmod( matchNorms[i] * (Freg.Rotation() * sampleNorms[i]), 2 * cmnPI));
axisAngle1 = asin(std::fmod(L[i].Column(0) * (Freg.Rotation() * sampleNorms[i]), 2 * cmnPI));
axisAngle2 = asin(std::fmod(L[i].Column(1) * (Freg.Rotation() * sampleNorms[i]), 2 * cmnPI));
axisAngle1 = asin(std::fmod(R_L[i].Column(0) * matchNorms[i], 2 * cmnPI));
axisAngle2 = asin(std::fmod(R_L[i].Column(1) * matchNorms[i], 2 * cmnPI));

totalSumSqrMatchAngle += (k[i] * matchAngle * matchAngle) + ( (k[i] - 2*B[i]) * axisAngle1 * axisAngle1 ) + ( (k[i] + 2*B[i]) * axisAngle2 * axisAngle2 ) ;

Expand Down Expand Up @@ -1321,6 +1321,7 @@ double algDirICP_GDIMLOP::CostFunctionValue(const vctDynamicVector<double> &x)
UpdateOptimizerCalculations(x);
}
vctDynamicVectorRef<vct3> Yn(matchNorms);
vctDynamicVectorRef<vct3> Xn(sampleNorms);

double f = 0.0;
unsigned int i;
Expand All @@ -1331,11 +1332,11 @@ double algDirICP_GDIMLOP::CostFunctionValue(const vctDynamicVector<double> &x)
{
if (outlierFlags[i]) continue;

double major = RaRL[i].Column(0) * Yn[i];
double minor = RaRL[i].Column(1) * Yn[i];
double major = RaRL[i].Column(0) * Xn[i];
double minor = RaRL[i].Column(1) * Xn[i];
// add extra k[i] * 1.0 to make cost function > 0
f += k[i] * (1.0 - RaXn[i]*Yn[i]) - B[i] * (major*major - minor*minor)
+ (Rat_Tssm_Y_t_x[i] * Rat_Tssm_Y_t_x_invMx[i]) / 2.0;
+ (Rat_Tssm_Y_t_x_invMx[i] * Rat_Tssm_Y_t_x[i]) / 2.0;
}

#ifdef NOREGULARIZER
Expand Down Expand Up @@ -1389,16 +1390,16 @@ void algDirICP_GDIMLOP::CostFunctionGradient(const vctDynamicVector<double> &x,
for (j = 0; j < nSamples; j++)
{
// TODO: vectorize Kent term better
//if (outlierFlags[j]) continue;
if (outlierFlags[j]) continue;

//--- Kent term ---// (orientations)
for (unsigned int i = 0; i < 3; i++)
{
// rotational effect
ga[i] +=
-k[j] * (Xn[j] * dRa[i].TransposeRef() * Yn[j])
- 2.0 * B[j] * ((dRa[i] * L[j].Column(0) * Yn[j]) * (Yn[j] * RaRL[j].Column(0))
- (dRa[i] * L[j].Column(1) * Yn[j]) * (Yn[j] * RaRL[j].Column(1)));
- 2.0 * B[j] * ((dRa[i] * L[j].Column(0) * Xn[j]) * (Yn[j] * RaRL[j].Column(0))
- (dRa[i] * L[j].Column(1) * Xn[j]) * (Yn[j] * RaRL[j].Column(1)));

//--- Gaussian term ---// (positions)
// rotational effect
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37 changes: 29 additions & 8 deletions test_data/LastRun_DIMLOP/testing/SaveIterations.csv
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@@ -1,8 +1,29 @@
0 ,, 14412.337 ,, 0.0000 ,, 9.79,17.14 ,, 0.067 ,, 0
1 ,, 7028.713 ,, 0.5123 ,, 13.69,5.61 ,, 0.090 ,, 0
2 ,, 4138.705 ,, 0.4112 ,, 7.10,5.19 ,, 0.094 ,, 0
3 ,, 2973.684 ,, 0.2815 ,, 0.39,2.30 ,, 0.084 ,, 0
4 ,, 2648.381 ,, 0.1094 ,, 2.69,1.52 ,, 0.077 ,, 0
5 ,, 2319.708 ,, 0.1241 ,, 0.91,1.50 ,, 0.076 ,, 0
6 ,, 2275.653 ,, 0.0190 ,, 0.00,0.00 ,, 0.083 ,, 0
7 ,, 2275.464 ,, 0.0001 ,, 0.00,0.00 ,, 0.092 ,, 0
0 ,, 14412.337 ,, 0.0000 ,, 9.79,17.14 ,, 0.079 ,, 0
1 ,, 6235.271 ,, 0.5674 ,, 2.27,7.84 ,, 0.042 ,, 0
2 ,, 3292.586 ,, 0.4719 ,, 2.73,3.96 ,, 0.073 ,, 0
3 ,, 2767.617 ,, 0.1594 ,, 1.52,1.64 ,, 0.059 ,, 1
4 ,, 2502.065 ,, 0.0959 ,, 1.87,1.30 ,, 0.057 ,, 0
5 ,, 2292.684 ,, 0.0837 ,, 2.17,1.15 ,, 0.053 ,, 0
6 ,, 2190.084 ,, 0.0448 ,, 1.01,0.79 ,, 0.051 ,, 0
7 ,, 2125.749 ,, 0.0294 ,, 0.77,0.61 ,, 0.056 ,, 0
8 ,, 2090.104 ,, 0.0168 ,, 0.61,0.54 ,, 0.050 ,, 0
9 ,, 2063.502 ,, 0.0127 ,, 0.39,0.40 ,, 0.047 ,, 0
10 ,, 2038.152 ,, 0.0123 ,, 0.30,0.28 ,, 0.043 ,, 0
11 ,, 2034.001 ,, 0.0020 ,, 0.23,0.19 ,, 0.053 ,, 0
12 ,, 2031.077 ,, 0.0014 ,, 0.16,0.12 ,, 0.051 ,, 0
13 ,, 2028.263 ,, 0.0014 ,, 0.15,0.08 ,, 0.044 ,, 0
14 ,, 2028.860 ,, 0.0003 ,, 0.18,0.07 ,, 0.046 ,, 0
15 ,, 2029.043 ,, 0.0001 ,, 0.04,0.04 ,, 0.043 ,, 0
16 ,, 2029.136 ,, 0.0000 ,, 0.04,0.03 ,, 0.044 ,, 0
17 ,, 2028.511 ,, 0.0003 ,, 0.05,0.02 ,, 0.042 ,, 0
18 ,, 2027.156 ,, 0.0007 ,, 0.03,0.01 ,, 0.043 ,, 0
19 ,, 2026.533 ,, 0.0003 ,, 0.03,0.01 ,, 0.046 ,, 0
20 ,, 2026.052 ,, 0.0002 ,, 0.02,0.02 ,, 0.043 ,, 0
21 ,, 2027.364 ,, 0.0006 ,, 0.01,0.01 ,, 0.046 ,, 0
22 ,, 2027.483 ,, 0.0001 ,, 0.02,0.01 ,, 0.043 ,, 0
23 ,, 2027.822 ,, 0.0002 ,, 0.01,0.01 ,, 0.046 ,, 0
24 ,, 2027.833 ,, 0.0000 ,, 0.00,0.00 ,, 0.041 ,, 0
25 ,, 2027.615 ,, 0.0001 ,, 0.00,0.01 ,, 0.043 ,, 0
26 ,, 2027.612 ,, 0.0000 ,, 0.00,0.00 ,, 0.041 ,, 0
27 ,, 2027.614 ,, 0.0000 ,, 0.00,0.00 ,, 0.043 ,, 0
28 ,, 2027.615 ,, 0.0000 ,, 0.00,0.00 ,, 0.040 ,, 0
73 changes: 48 additions & 25 deletions test_data/LastRun_DIMLOP/testing/SaveIterations.txt
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@@ -1,40 +1,63 @@
iter=0 E=14412.337 tolE=0.0000 (dAng/dPos)= 9.79/17.14 t=0.0667 NOut=0/
iter=1 E=7028.713 tolE=0.5123 (dAng/dPos)= 13.69/5.61 t=0.0895 NOut=0/
iter=2 E=4138.705 tolE=0.4112 (dAng/dPos)= 7.10/5.19 t=0.0944 NOut=0/
iter=3 E=2973.684 tolE=0.2815 (dAng/dPos)= 0.39/2.30 t=0.0838 NOut=0/
iter=4 E=2648.381 tolE=0.1094 (dAng/dPos)= 2.69/1.52 t=0.0770 NOut=0/
iter=5 E=2319.708 tolE=0.1241 (dAng/dPos)= 0.91/1.50 t=0.0757 NOut=0/
iter=6 E=2275.653 tolE=0.0190 (dAng/dPos)= 0.00/0.00 t=0.0832 NOut=0/
iter=7 E=2275.464 tolE=0.0001 (dAng/dPos)= 0.00/0.00 t=0.0916 NOut=0/
iter=0 E=14412.337 tolE=0.0000 (dAng/dPos)= 9.79/17.14 t=0.0788 NOut=0/
iter=1 E=6235.271 tolE=0.5674 (dAng/dPos)= 2.27/7.84 t=0.0424 NOut=0/
iter=2 E=3292.586 tolE=0.4719 (dAng/dPos)= 2.73/3.96 t=0.0725 NOut=0/
iter=3 E=2767.617 tolE=0.1594 (dAng/dPos)= 1.52/1.64 t=0.0590 NOut=1/
iter=4 E=2502.065 tolE=0.0959 (dAng/dPos)= 1.87/1.30 t=0.0566 NOut=0/
iter=5 E=2292.684 tolE=0.0837 (dAng/dPos)= 2.17/1.15 t=0.0533 NOut=0/
iter=6 E=2190.084 tolE=0.0448 (dAng/dPos)= 1.01/0.79 t=0.0513 NOut=0/
iter=7 E=2125.749 tolE=0.0294 (dAng/dPos)= 0.77/0.61 t=0.0561 NOut=0/
iter=8 E=2090.104 tolE=0.0168 (dAng/dPos)= 0.61/0.54 t=0.0498 NOut=0/
iter=9 E=2063.502 tolE=0.0127 (dAng/dPos)= 0.39/0.40 t=0.0471 NOut=0/
iter=10 E=2038.152 tolE=0.0123 (dAng/dPos)= 0.30/0.28 t=0.0430 NOut=0/
iter=11 E=2034.001 tolE=0.0020 (dAng/dPos)= 0.23/0.19 t=0.0529 NOut=0/
iter=12 E=2031.077 tolE=0.0014 (dAng/dPos)= 0.16/0.12 t=0.0506 NOut=0/
iter=13 E=2028.263 tolE=0.0014 (dAng/dPos)= 0.15/0.08 t=0.0442 NOut=0/
iter=14 E=2028.860 tolE=0.0003 (dAng/dPos)= 0.18/0.07 t=0.0456 NOut=0/
iter=15 E=2029.043 tolE=0.0001 (dAng/dPos)= 0.04/0.04 t=0.0428 NOut=0/
iter=16 E=2029.136 tolE=0.0000 (dAng/dPos)= 0.04/0.03 t=0.0444 NOut=0/
iter=17 E=2028.511 tolE=0.0003 (dAng/dPos)= 0.05/0.02 t=0.0418 NOut=0/
iter=18 E=2027.156 tolE=0.0007 (dAng/dPos)= 0.03/0.01 t=0.0425 NOut=0/
iter=19 E=2026.533 tolE=0.0003 (dAng/dPos)= 0.03/0.01 t=0.0456 NOut=0/
iter=20 E=2026.052 tolE=0.0002 (dAng/dPos)= 0.02/0.02 t=0.0426 NOut=0/
iter=21 E=2027.364 tolE=0.0006 (dAng/dPos)= 0.01/0.01 t=0.0464 NOut=0/
iter=22 E=2027.483 tolE=0.0001 (dAng/dPos)= 0.02/0.01 t=0.0433 NOut=0/
iter=23 E=2027.822 tolE=0.0002 (dAng/dPos)= 0.01/0.01 t=0.0455 NOut=0/
iter=24 E=2027.833 tolE=0.0000 (dAng/dPos)= 0.00/0.00 t=0.0411 NOut=0/
iter=25 E=2027.615 tolE=0.0001 (dAng/dPos)= 0.00/0.01 t=0.0430 NOut=0/
iter=26 E=2027.612 tolE=0.0000 (dAng/dPos)= 0.00/0.00 t=0.0413 NOut=0/
iter=27 E=2027.614 tolE=0.0000 (dAng/dPos)= 0.00/0.00 t=0.0432 NOut=0/
iter=28 E=2027.615 tolE=0.0000 (dAng/dPos)= 0.00/0.00 t=0.0398 NOut=0/

Termination Condition satisfied for 2 iterations:
reached min dAngle & dTrans & dShape (0.001/0.001/0.001)
E: 2275.46
dE/E: 8.28864e-005
E: 2027.62
dE/E: 4.98889e-007
dAng: 0 0 (deg)
dPos: 1.33342e-015 4.44089e-016
dShp: 2.28192 2.28192
iter: 7
runtime: 0.689578
dPos: 0.000147074 0.000464109
dShp: 1.07863 1.07861
iter: 28
runtime: 1.61503

translation:
0.267757 -2.97805 2.21367
0.119811 0.0422813 -0.0834769
rotation:
0.999985 -0.00458533 0.00305651
0.00450636 0.999668 0.0253593
-0.00317178 -0.0253452 0.999674
0.999977 -0.00587323 -0.00339458
0.00587123 0.999983 -0.000600097
0.00339804 0.000580153 0.999994
scale:
1
shape parameters:
1.58031 0.531220 1.55808
0.835535 0.626634 0.269460

Sum square mahalanobis distance = 1584.44 over 300 samples
Sum square match angle = 989.916 over 300 samples
Sum square mahalanobis distance = 1584.44 over 300 inliers
Sum square match angle = 989.916 over 300 inliers
WARNING: best iteration (20) is not the final iteration

Sum square mahalanobis distance = 513.498 over 300 samples
Sum square match angle = 529.748 over 300 samples
Sum square mahalanobis distance = 513.498 over 300 inliers
Sum square match angle = 529.748 over 300 inliers

Starting Offset: dAng: 9.78918 dPos: 17.1429 dShp: 1.08435 0.542175 0.271088
Registration Error: dAng: 1.48666 dPos: 3.72032 dShp: -0.495960 0.0109551 -1.28699
Registration Error: dAng: 0.390146 dPos: 0.152023 dShp: 0.248816 -0.0844582 0.00162732

Average Match Error (Mahalanobis): 2.03957 (+/-3.07267)
Average Match Error (Mahalanobis): 1.16594 (+/-1.75245)

2 changes: 1 addition & 1 deletion test_data/LastRun_DIMLOP/testing/SaveRegXfm.txt
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@@ -1 +1 @@
0.999985 -0.00458533 0.00305651 0.00450636 0.999668 0.0253593 -0.00317178 -0.0253452 0.999674 0.267757 -2.97805 2.21367
0.999977 -0.00587323 -0.00339458 0.00587123 0.999983 -0.000600097 0.00339804 0.000580153 0.999994 0.119811 0.0422813 -0.0834769
35 changes: 28 additions & 7 deletions test_data/LastRun_DIMLOP/testing/SaveTrackRegPath.csv
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@@ -1,8 +1,29 @@
0, , 14412.3, , 0.985637, 0.0339246, 0.165436, , -0.0306238, 0.999279, -0.0224628, , -0.166079, 0.0170739, 0.985965, , 12.1827, -6.2197, 10.3334, ,1, ,0,0,0,
1, , 7028.71, , 0.997796, -0.0247214, -0.061576, , 0.0261343, 0.999411, 0.0222473, , 0.0609898, -0.0238075, 0.997854, , 6.83002, -6.23556, 8.50365, ,1, ,2.92522,3,-0.438764,
2, , 4138.71, , 0.997991, -0.0185441, 0.0605812, , 0.0160311, 0.999001, 0.0417086, , -0.0612941, -0.0406537, 0.997291, , 2.95152, -5.767, 5.80329, ,1, ,2.83713,3,0.0889155,
3, , 2973.68, , 0.998131, -0.0170053, 0.0587053, , 0.0149537, 0.999268, 0.0352116, , -0.0592611, -0.034268, 0.997654, , 1.42992, -4.91486, 4.28257, ,1, ,2.34392,2.30503,0.73218,
4, , 2648.38, , 0.999788, -0.0167628, 0.0119863, , 0.0163934, 0.999407, 0.0302833, , -0.0124868, -0.0300804, 0.999469, , 0.70006, -3.94132, 3.30518, ,1, ,1.99539,1.5394,1.02977,
5, , 2319.71, , 0.999985, -0.00458533, 0.00305651, , 0.00450636, 0.999668, 0.0253593, , -0.00317178, -0.0253452, 0.999674, , 0.267757, -2.97805, 2.21367, ,1, ,1.58031,0.53122,1.55808,
6, , 2275.65, , 0.999985, -0.00458533, 0.00305651, , 0.00450636, 0.999668, 0.0253593, , -0.00317178, -0.0253452, 0.999674, , 0.267757, -2.97805, 2.21367, ,1, ,1.58031,0.53122,1.55808,
7, , 2275.46, , 0.999985, -0.00458533, 0.00305651, , 0.00450636, 0.999668, 0.0253593, , -0.00317178, -0.0253452, 0.999674, , 0.267757, -2.97805, 2.21367, ,1, ,1.58031,0.53122,1.55808,
1, , 6235.27, , 0.99, 0.0331743, 0.137109, , -0.0341296, 0.999407, 0.00462125, , -0.136874, -0.0092545, 0.990545, , 5.36528, -5.55827, 6.50334, ,1, ,2.09227,3,1.51768,
2, , 3292.59, , 0.991131, -0.000497267, 0.132886, , -0.00518178, 0.999088, 0.0423869, , -0.132786, -0.0426995, 0.990224, , 2.11785, -4.87907, 4.69042, ,1, ,2.11332,2.89983,0.579822,
3, , 2767.62, , 0.994112, 0.00374466, 0.108293, , -0.00923141, 0.998696, 0.0502088, , -0.107964, -0.0509129, 0.99285, , 1.12422, -4.06305, 3.629, ,1, ,1.93489,1.99883,0.777722,
4, , 2502.06, , 0.997078, 0.00710079, 0.0760587, , -0.0108272, 0.998755, 0.0486948, , -0.0756182, -0.049376, 0.995914, , 0.637187, -3.20259, 2.75752, ,1, ,1.63234,1.17954,1.07536,
5, , 2292.68, , 0.99917, 0.0103464, 0.0394026, , -0.01191, 0.999142, 0.0396572, , -0.0389585, -0.0400935, 0.998436, , 0.212629, -2.49687, 1.92725, ,1, ,1.39099,0.650194,1.34059,
6, , 2190.08, , 0.999719, 0.00592918, 0.0229534, , -0.00674168, 0.999348, 0.0354838, , -0.0227281, -0.0356285, 0.999107, , 0.14166, -1.89166, 1.42676, ,1, ,1.28995,0.384922,1.32439,
7, , 2125.75, , 0.999924, 0.00552767, 0.0110436, , -0.00584734, 0.999559, 0.0291273, , -0.0108777, -0.0291896, 0.999515, , 0.13773, -1.42903, 1.02266, ,1, ,1.19098,0.322296,1.14363,
8, , 2090.1, , 0.999989, 0.00320739, 0.00350593, , -0.00328401, 0.999751, 0.0220709, , -0.00343427, -0.0220822, 0.99975, , 0.135219, -0.984741, 0.708708, ,1, ,1.19424,0.286079,0.896006,
9, , 2063.5, , 1, 0.000298261, 0.000792606, , -0.000311263, 0.999865, 0.0164551, , -0.00078759, -0.0164553, 0.999864, , 0.127283, -0.65702, 0.478949, ,1, ,1.08192,0.348343,0.699146,
10, , 2038.15, , 1, -9.60657e-005, -0.000409497, , 0.000100747, 0.999934, 0.0114479, , 0.000408371, -0.0114479, 0.999934, , 0.124747, -0.428065, 0.311586, ,1, ,1.01423,0.420987,0.571786,
11, , 2034, , 0.999999, -0.000797352, -0.000949899, , 0.000804417, 0.999972, 0.00746106, , 0.000943923, -0.00746182, 0.999972, , 0.120025, -0.28555, 0.189399, ,1, ,0.971714,0.496433,0.487282,
12, , 2031.08, , 0.999996, -0.00263504, -0.00118746, , 0.00264147, 0.999982, 0.00545105, , 0.00117307, -0.00545416, 0.999984, , 0.122367, -0.193923, 0.11067, ,1, ,0.9392,0.543569,0.41553,
13, , 2028.26, , 0.999988, -0.00472369, -0.00145122, , 0.00472949, 0.999981, 0.00402306, , 0.00143219, -0.00402987, 0.999991, , 0.114877, -0.128422, 0.0666599, ,1, ,0.91733,0.579317,0.38038,
14, , 2028.86, , 0.999978, -0.00571124, -0.00326208, , 0.00571684, 0.999982, 0.00170997, , 0.00325226, -0.00172858, 0.999993, , 0.117341, -0.080543, 0.0202078, ,1, ,0.900027,0.615899,0.32515,
15, , 2029.04, , 0.999976, -0.00613126, -0.00310881, , 0.00613483, 0.999981, 0.00113961, , 0.00310176, -0.00115866, 0.999995, , 0.118793, -0.0478281, -0.00485474, ,1, ,0.882491,0.630337,0.300047,
16, , 2029.14, , 0.999979, -0.00580751, -0.00299397, , 0.00580924, 0.999983, 0.00057183, , 0.0029906, -0.00058921, 0.999995, , 0.119972, -0.0207745, -0.022248, ,1, ,0.866881,0.631794,0.285388,
17, , 2028.51, , 0.999982, -0.00551152, -0.00255664, , 0.00551127, 0.999985, -0.000106962, , 0.00255719, 9.28696e-005, 0.999997, , 0.120943, -0.00664482, -0.0353609, ,1, ,0.860651,0.643142,0.279333,
18, , 2027.16, , 0.999983, -0.00532719, -0.00250669, , 0.00532594, 0.999986, -0.000508367, , 0.00250936, 0.000495008, 0.999997, , 0.120402, -0.000374218, -0.0433733, ,1, ,0.855611,0.648578,0.277247,
19, , 2026.53, , 0.999981, -0.00542948, -0.00292285, , 0.00542738, 0.999985, -0.000726621, , 0.00292676, 0.000710744, 0.999995, , 0.119892, 0.00389293, -0.0526571, ,1, ,0.850045,0.647519,0.270725,
20, , 2026.05, , 0.999979, -0.00557579, -0.00315789, , 0.00557304, 0.999984, -0.000880291, , 0.00316275, 0.000862674, 0.999995, , 0.116399, 0.0119617, -0.0652418, ,1, ,0.84377,0.645413,0.270322,
21, , 2027.36, , 0.999979, -0.00561624, -0.00327159, , 0.00561319, 0.999984, -0.000940707, , 0.00327682, 0.000922324, 0.999994, , 0.115881, 0.0187381, -0.0717685, ,1, ,0.843903,0.640913,0.267714,
22, , 2027.48, , 0.999978, -0.00575765, -0.00342883, , 0.00575518, 0.999983, -0.000732253, , 0.00343299, 0.000712503, 0.999994, , 0.118122, 0.0262072, -0.0761914, ,1, ,0.838883,0.640555,0.26752,
23, , 2027.82, , 0.999977, -0.00583809, -0.00342081, , 0.00583614, 0.999983, -0.000579508, , 0.00342413, 0.00055953, 0.999994, , 0.118743, 0.0331672, -0.0795785, ,1, ,0.834261,0.631883,0.2694,
24, , 2027.83, , 0.999977, -0.00583721, -0.00342254, , 0.00583534, 0.999983, -0.000556585, , 0.00342573, 0.000536601, 0.999994, , 0.118804, 0.0353889, -0.0805428, ,1, ,0.833589,0.630814,0.26952,
25, , 2027.61, , 0.999977, -0.00587362, -0.00339375, , 0.00587162, 0.999983, -0.000597693, , 0.00339721, 0.000577752, 0.999994, , 0.119835, 0.0403203, -0.0826428, ,1, ,0.83558,0.627114,0.270053,
26, , 2027.61, , 0.999977, -0.00587358, -0.00339419, , 0.00587158, 0.999983, -0.000600661, , 0.00339766, 0.000580718, 0.999994, , 0.119836, 0.0417151, -0.0832486, ,1, ,0.835608,0.626621,0.269702,
27, , 2027.61, , 0.999977, -0.00587332, -0.00339448, , 0.00587132, 0.999983, -0.000600356, , 0.00339795, 0.000580412, 0.999994, , 0.119817, 0.0421436, -0.0834258, ,1, ,0.835557,0.626608,0.269524,
28, , 2027.62, , 0.999977, -0.00587323, -0.00339458, , 0.00587123, 0.999983, -0.000600097, , 0.00339804, 0.000580153, 0.999994, , 0.119811, 0.0422813, -0.0834769, ,1, ,0.835535,0.626634,0.26946,
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