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Fixing small bug in GDIMLOP gradient computation
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@AyushiSinha
AyushiSinha committed Nov 6, 2018
1 parent 0f16b12 commit 64132c9
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Showing 11 changed files with 8,759 additions and 8,701 deletions.
6 changes: 6 additions & 0 deletions cisstICP/algDirICP_DIMLOP.cpp
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Expand Up @@ -342,6 +342,12 @@ double algDirICP_DIMLOP::ICP_EvaluateErrorFunction()
costFuncValue = /*logExp +*/ k*(nSamples - sumNormProducts) /*- nlogkappa*/ + (nklog2PI + expCost + logCost + ssmCost) / 2.0;
// ^ add logExp back if you can make sure it is stable - can be unstable if k is big => exp(k) blows up

#if 0
std::fstream dist_file("distance_DIMLOP.csv", std::ios::in | std::ios::out | std::ios::app);
dist_file << expCost / nSamples << "\n";
dist_file.close();
#endif

//-- Test for algorithm-specific termination --//

// remove last iteration from monitoring variable
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20 changes: 15 additions & 5 deletions cisstICP/algDirICP_GDIMLOP.cpp
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Expand Up @@ -123,9 +123,9 @@ void algDirICP_GDIMLOP::ComputeMatchStatistics(double &Avg, double &StdDev) //go
sqrMahalDist = residual*invM[i]*residual;
totalSumSqrMahalDist += sqrMahalDist;

matchAngle = acos(std::fmod(matchNorms[i] * (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));
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));

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

Expand Down Expand Up @@ -170,6 +170,7 @@ double algDirICP_GDIMLOP::ICP_EvaluateErrorFunction()
double Error = 0.0;
double nklog2PI = 0.0;
double logCost = 0.0;
double expCost = 0.0;
double ssmCost = 0.0;
double normCost = 0.0; // for debugging only
double normCost1 = 0.0; // for debugging only
Expand All @@ -180,6 +181,9 @@ double algDirICP_GDIMLOP::ICP_EvaluateErrorFunction()

if (outlierFlags[i]) continue; // skip outliers

vct3 residual = samplePtsXfmd.Element(i) - Tssm_Y.Element(i); // matchPts.Element(s);
expCost += residual * inv_Mi[i] * residual;

Error += MatchError(samplePtsXfmd[i], sampleNormsXfmd[i],
Tssm_Y[i], matchNorms[i],
k[i], B[i], R_L[i], inv_Mi[i]);
Expand All @@ -197,6 +201,12 @@ double algDirICP_GDIMLOP::ICP_EvaluateErrorFunction()
prevCostFuncValue = costFuncValue;
costFuncValue = Error;

#if 0
fstream dist_file("distance_GDIMLOP.csv", ios::in | ios::out | ios::app);
dist_file << expCost / nSamples << "\n";
dist_file.close();
#endif

//-- Test for algorithm-specific termination --//

// remove last iteration from monitoring variable
Expand Down Expand Up @@ -1379,14 +1389,14 @@ 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] * Yn[j])
-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)));

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6 changes: 6 additions & 0 deletions cisstICP/algICP_DIMLP.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -388,6 +388,12 @@ double algICP_DIMLP::ICP_EvaluateErrorFunction()

prevCostFuncValue = costFuncValue;
costFuncValue = nklog2PI + (logCost + expCost + ssmCost) / 2.0;

#if 0
std::fstream dist_file("distance_DIMLP.csv", std::ios::in | std::ios::out | std::ios::app);
dist_file << expCost / nSamples << "\n";
dist_file.close();
#endif

//-- Test for algorithm-specific termination --//

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2 changes: 1 addition & 1 deletion cisstICP/cisstICP.cpp
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Expand Up @@ -266,8 +266,8 @@ cisstICP::ReturnType cisstICP::IterateICP()
Freg2 = Freg;

pAlgorithm->ReturnScale(scale);

pAlgorithm->ReturnShapeParam(sp);

prevShapeNorm = ShapeNorm;
ShapeNorm = sp.Norm();

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34 changes: 23 additions & 11 deletions test_data/LastRun_GDIMLOP/testing/SaveIterations.csv
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@@ -1,11 +1,23 @@
0 ,, 14203.449 ,, 0.0000 ,, 9.79,17.14 ,, 0.412 ,, 1
1 ,, 12272.397 ,, 0.1360 ,, 11.16,5.64 ,, 0.017 ,, 1
2 ,, 5969.421 ,, 0.5136 ,, 3.31,5.16 ,, 0.335 ,, 0
3 ,, 3576.106 ,, 0.4009 ,, 2.33,2.90 ,, 0.245 ,, 2
4 ,, 2991.064 ,, 0.1636 ,, 0.10,0.01 ,, 0.192 ,, 0
5 ,, 2968.171 ,, 0.0077 ,, 0.06,0.02 ,, 0.180 ,, 1
6 ,, 2982.149 ,, 0.0047 ,, 0.04,0.00 ,, 0.182 ,, 0
7 ,, 2732.537 ,, 0.0837 ,, 0.83,1.71 ,, 0.177 ,, 1
8 ,, 2397.390 ,, 0.1227 ,, 0.35,1.24 ,, 0.166 ,, 0
9 ,, 2239.295 ,, 0.0659 ,, 0.00,0.00 ,, 0.149 ,, 2
10 ,, 2271.129 ,, 0.0142 ,, 0.00,0.00 ,, 0.146 ,, 0
0 ,, 14203.449 ,, 0.0000 ,, 9.79,17.14 ,, 0.414 ,, 1
1 ,, 8282.150 ,, 0.4169 ,, 1.83,7.74 ,, 0.012 ,, 1
2 ,, 4641.101 ,, 0.4396 ,, 1.20,3.91 ,, 0.286 ,, 0
3 ,, 3400.229 ,, 0.2674 ,, 1.21,1.99 ,, 0.218 ,, 3
4 ,, 2913.685 ,, 0.1431 ,, 1.40,1.49 ,, 0.189 ,, 0
5 ,, 2591.538 ,, 0.1106 ,, 1.12,0.96 ,, 0.163 ,, 0
6 ,, 2362.595 ,, 0.0883 ,, 1.24,0.86 ,, 0.153 ,, 0
7 ,, 2215.975 ,, 0.0621 ,, 0.89,0.58 ,, 0.145 ,, 1
8 ,, 2125.634 ,, 0.0408 ,, 0.87,0.49 ,, 0.136 ,, 0
9 ,, 2051.776 ,, 0.0347 ,, 0.63,0.37 ,, 0.134 ,, 1
10 ,, 2029.641 ,, 0.0108 ,, 0.45,0.26 ,, 0.126 ,, 0
11 ,, 2015.425 ,, 0.0070 ,, 0.27,0.18 ,, 0.125 ,, 0
12 ,, 2011.845 ,, 0.0018 ,, 0.09,0.08 ,, 0.126 ,, 0
13 ,, 2009.463 ,, 0.0012 ,, 0.10,0.06 ,, 0.127 ,, 0
14 ,, 2008.184 ,, 0.0006 ,, 0.08,0.02 ,, 0.127 ,, 0
15 ,, 2008.882 ,, 0.0003 ,, 0.05,0.01 ,, 0.125 ,, 0
16 ,, 2008.954 ,, 0.0000 ,, 0.04,0.00 ,, 0.127 ,, 0
17 ,, 2008.967 ,, 0.0000 ,, 0.04,0.00 ,, 0.126 ,, 0
18 ,, 2008.321 ,, 0.0003 ,, 0.06,0.01 ,, 0.126 ,, 0
19 ,, 2008.232 ,, 0.0000 ,, 0.04,0.01 ,, 0.126 ,, 0
20 ,, 2008.353 ,, 0.0001 ,, 0.01,0.00 ,, 0.128 ,, 0
21 ,, 2008.353 ,, 0.0000 ,, 0.00,0.00 ,, 0.127 ,, 0
22 ,, 2008.353 ,, 0.0000 ,, 0.00,0.00 ,, 0.129 ,, 0
70 changes: 41 additions & 29 deletions test_data/LastRun_GDIMLOP/testing/SaveIterations.txt
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@@ -1,45 +1,57 @@
iter=0 E=14203.449 tolE=0.0000 (dAng/dPos)= 9.79/17.14 t=0.4121 NOut=1/
iter=1 E=12272.397 tolE=0.1360 (dAng/dPos)= 11.16/5.64 t=0.0171 NOut=1/
iter=2 E=5969.421 tolE=0.5136 (dAng/dPos)= 3.31/5.16 t=0.3351 NOut=0/
iter=3 E=3576.106 tolE=0.4009 (dAng/dPos)= 2.33/2.90 t=0.2450 NOut=2/
iter=4 E=2991.064 tolE=0.1636 (dAng/dPos)= 0.10/0.01 t=0.1918 NOut=0/
iter=5 E=2968.171 tolE=0.0077 (dAng/dPos)= 0.06/0.02 t=0.1803 NOut=1/
iter=6 E=2982.149 tolE=0.0047 (dAng/dPos)= 0.04/0.00 t=0.1823 NOut=0/
iter=7 E=2732.537 tolE=0.0837 (dAng/dPos)= 0.83/1.71 t=0.1771 NOut=1/
iter=8 E=2397.390 tolE=0.1227 (dAng/dPos)= 0.35/1.24 t=0.1655 NOut=0/
iter=9 E=2239.295 tolE=0.0659 (dAng/dPos)= 0.00/0.00 t=0.1493 NOut=2/
iter=10 E=2271.129 tolE=0.0142 (dAng/dPos)= 0.00/0.00 t=0.1456 NOut=0/
iter=0 E=14203.449 tolE=0.0000 (dAng/dPos)= 9.79/17.14 t=0.4140 NOut=1/
iter=1 E=8282.150 tolE=0.4169 (dAng/dPos)= 1.83/7.74 t=0.0120 NOut=1/
iter=2 E=4641.101 tolE=0.4396 (dAng/dPos)= 1.20/3.91 t=0.2856 NOut=0/
iter=3 E=3400.229 tolE=0.2674 (dAng/dPos)= 1.21/1.99 t=0.2176 NOut=3/
iter=4 E=2913.685 tolE=0.1431 (dAng/dPos)= 1.40/1.49 t=0.1888 NOut=0/
iter=5 E=2591.538 tolE=0.1106 (dAng/dPos)= 1.12/0.96 t=0.1627 NOut=0/
iter=6 E=2362.595 tolE=0.0883 (dAng/dPos)= 1.24/0.86 t=0.1532 NOut=0/
iter=7 E=2215.975 tolE=0.0621 (dAng/dPos)= 0.89/0.58 t=0.1450 NOut=1/
iter=8 E=2125.634 tolE=0.0408 (dAng/dPos)= 0.87/0.49 t=0.1355 NOut=0/
iter=9 E=2051.776 tolE=0.0347 (dAng/dPos)= 0.63/0.37 t=0.1339 NOut=1/
iter=10 E=2029.641 tolE=0.0108 (dAng/dPos)= 0.45/0.26 t=0.1260 NOut=0/
iter=11 E=2015.425 tolE=0.0070 (dAng/dPos)= 0.27/0.18 t=0.1254 NOut=0/
iter=12 E=2011.845 tolE=0.0018 (dAng/dPos)= 0.09/0.08 t=0.1256 NOut=0/
iter=13 E=2009.463 tolE=0.0012 (dAng/dPos)= 0.10/0.06 t=0.1268 NOut=0/
iter=14 E=2008.184 tolE=0.0006 (dAng/dPos)= 0.08/0.02 t=0.1269 NOut=0/
iter=15 E=2008.882 tolE=0.0003 (dAng/dPos)= 0.05/0.01 t=0.1254 NOut=0/
iter=16 E=2008.954 tolE=0.0000 (dAng/dPos)= 0.04/0.00 t=0.1272 NOut=0/
iter=17 E=2008.967 tolE=0.0000 (dAng/dPos)= 0.04/0.00 t=0.1264 NOut=0/
iter=18 E=2008.321 tolE=0.0003 (dAng/dPos)= 0.06/0.01 t=0.1259 NOut=0/
iter=19 E=2008.232 tolE=0.0000 (dAng/dPos)= 0.04/0.01 t=0.1262 NOut=0/
iter=20 E=2008.353 tolE=0.0001 (dAng/dPos)= 0.01/0.00 t=0.1279 NOut=0/
iter=21 E=2008.353 tolE=0.0000 (dAng/dPos)= 0.00/0.00 t=0.1275 NOut=0/
iter=22 E=2008.353 tolE=0.0000 (dAng/dPos)= 0.00/0.00 t=0.1288 NOut=0/

Termination Condition satisfied for 2 iterations:
reached min dAngle & dTrans & dShape (0.001/0.001/0.001)
E: 2271.13
dE/E: 0.0142165
E: 2008.35
dE/E: 7.83073e-008
dAng: 0 0 (deg)
dPos: 2.22045e-016 2.48253e-016
dShp: 2.05678 2.05678
iter: 10
runtime: 2.23908
dPos: 0.00028833 0.000993712
dShp: 1.20346 1.20342
iter: 22
runtime: 3.5725

translation:
0.190937 -1.97464 1.58262
0.0767001 0.105207 -0.00390863
rotation:
0.999992 -0.00133809 0.00365433
0.00133419 0.999999 0.00107016
-0.00365576 -0.00106528 0.999993
0.999951 -0.00884721 0.00435264
0.00884335 0.999960 0.000905164
-0.00436048 -0.000866628 0.999990
scale:
1
shape parameters:
1.52723 0.609591 1.23544
0.936340 0.660749 0.367271

WARNING: best iteration (9) is not the final iteration
WARNING: best iteration (14) is not the final iteration

Sum square mahalanobis distance = 1121.13 over 300 samples
Sum square match angle = 1410.33 over 300 samples
Sum square mahalanobis distance = 1121.13 over 300 inliers
Sum square match angle = 1410.33 over 300 inliers
Sum square mahalanobis distance = 543.896 over 300 samples
Sum square match angle = 497.148 over 300 samples
Sum square mahalanobis distance = 543.896 over 300 inliers
Sum square match angle = 497.148 over 300 inliers

Starting Offset: dAng: 9.78918 dPos: 17.1429 dShp: 1.08435 0.542175 0.271088
Registration Error: dAng: 0.231213 dPos: 2.53779 dShp: -0.442875 -0.0674153 -0.964351
Registration Error: dAng: 0.567218 dPos: 0.130256 dShp: 0.148011 -0.118574 -0.0961832

Average Match Error (Mahalanobis): 1.73403 (+/-2.59692)
Average Match Error (Mahalanobis): 1.20849 (+/-1.80926)

2 changes: 1 addition & 1 deletion test_data/LastRun_GDIMLOP/testing/SaveRegXfm.txt
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@@ -1 +1 @@
0.999992 -0.00133809 0.00365433 0.00133419 0.999999 0.00107016 -0.00365576 -0.00106528 0.999993 0.190937 -1.97464 1.58262
0.999951 -0.00884721 0.00435264 0.00884335 0.999960 0.000905164 -0.00436048 -0.000866628 0.999990 0.0767001 0.105207 -0.00390863
32 changes: 22 additions & 10 deletions test_data/LastRun_GDIMLOP/testing/SaveTrackRegPath.csv
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@@ -1,11 +1,23 @@
0, , 14203.4, , 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, , 12272.4, , 0.999727, -0.012207, -0.0199272, , 0.012496, 0.999818, 0.0144442, , 0.0197473, -0.0146892, 0.999697, , 8.08817, -5.46323, 7.44066, ,1, ,2.14757,2.85919,-0.404878,
2, , 5969.42, , 0.999462, -0.00358285, 0.0326072, , 0.00384888, 0.99996, -0.00809966, , -0.0325768, 0.0082208, 0.999435, , 3.71648, -4.78073, 4.96276, ,1, ,2.68085,2.64634,0.272604,
3, , 3576.11, , 0.999979, -0.00470731, -0.00434612, , 0.00474599, 0.999949, 0.00893118, , 0.00430386, -0.00895163, 0.999951, , 1.31243, -3.8364, 3.51992, ,1, ,2.37993,1.96562,0.40782,
4, , 2991.06, , 0.999988, -0.00410301, -0.00269652, , 0.00412637, 0.999953, 0.00871761, , 0.00266063, -0.00872863, 0.999958, , 1.30979, -3.83349, 3.51675, ,1, ,2.3788,1.96326,0.407546,
5, , 2968.17, , 0.999991, -0.00377085, -0.00168563, , 0.00378482, 0.999958, 0.00835791, , 0.00165405, -0.00836422, 0.999964, , 1.30034, -3.82388, 3.50494, ,1, ,2.37343,1.95334,0.41462,
6, , 2982.15, , 0.999993, -0.00352476, -0.00108257, , 0.00353344, 0.999961, 0.00811995, , 0.00105391, -0.00812372, 0.999966, , 1.30028, -3.82382, 3.50486, ,1, ,2.37341,1.95333,0.414631,
7, , 2732.54, , 0.999962, 3.08988e-006, 0.00871979, , 1.44091e-005, 0.999998, -0.00200675, , -0.00871978, 0.0020068, 0.99996, , 0.412842, -2.90609, 2.3694, ,1, ,1.86365,0.989762,1.07076,
8, , 2397.39, , 0.999992, -0.00133809, 0.00365433, , 0.00133419, 0.999999, 0.00107016, , -0.00365576, -0.00106528, 0.999993, , 0.190937, -1.97464, 1.58262, ,1, ,1.52723,0.609591,1.23544,
9, , 2239.29, , 0.999992, -0.00133809, 0.00365433, , 0.00133419, 0.999999, 0.00107016, , -0.00365576, -0.00106528, 0.999993, , 0.190937, -1.97464, 1.58262, ,1, ,1.52723,0.609591,1.23544,
10, , 2271.13, , 0.999992, -0.00133809, 0.00365433, , 0.00133419, 0.999999, 0.00107016, , -0.00365576, -0.00106528, 0.999993, , 0.190937, -1.97464, 1.58262, ,1, ,1.52723,0.609591,1.23544,
1, , 8282.15, , 0.989334, 0.0323767, 0.142025, , -0.0325603, 0.999469, -0.0010317, , -0.141983, -0.00360366, 0.989863, , 5.41043, -5.58814, 6.61319, ,1, ,2.27542,3,1.30257,
2, , 4641.1, , 0.991006, 0.0181011, 0.132587, , -0.0199521, 0.999721, 0.0126454, , -0.132322, -0.0151771, 0.991091, , 2.19418, -4.89119, 4.58894, ,1, ,2.45789,2.91429,0.617919,
3, , 3400.23, , 0.993026, 0.0205063, 0.116094, , -0.0235717, 0.999407, 0.0250936, , -0.115511, -0.0276552, 0.992921, , 0.93934, -3.78476, 3.46124, ,1, ,2.15573,1.75268,0.964921,
4, , 2913.69, , 0.995421, 0.024042, 0.0925149, , -0.0268813, 0.999201, 0.0295675, , -0.0917301, -0.031919, 0.995272, , 0.328263, -2.87119, 2.43146, ,1, ,1.71982,1.00575,1.27998,
5, , 2591.54, , 0.997076, 0.0222143, 0.073115, , -0.0243514, 0.999298, 0.0284693, , -0.0724313, -0.0301666, 0.996917, , 0.156855, -2.20846, 1.75486, ,1, ,1.42299,0.765443,1.30417,
6, , 2362.6, , 0.998494, 0.0170053, 0.052153, , -0.0184753, 0.999442, 0.0278354, , -0.0516505, -0.028757, 0.998251, , 0.088227, -1.55043, 1.20365, ,1, ,1.23818,0.541633,1.23526,
7, , 2215.98, , 0.999199, 0.0102904, 0.038663, , -0.0112337, 0.999643, 0.0242598, , -0.0383995, -0.0246747, 0.998958, , 0.0964779, -1.07922, 0.868509, ,1, ,1.13755,0.534559,1.0321,
8, , 2125.63, , 0.999657, 0.00398079, 0.0258738, , -0.00447699, 0.999807, 0.0191483, , -0.0257926, -0.0192575, 0.999482, , 0.0894086, -0.676133, 0.583668, ,1, ,1.12947,0.52388,0.819896,
9, , 2051.78, , 0.999845, 0.000543903, 0.0176202, , -0.000771233, 0.999917, 0.0128974, , -0.0176117, -0.012909, 0.999762, , 0.0881926, -0.373386, 0.366621, ,1, ,1.09985,0.559781,0.694376,
10, , 2029.64, , 0.999928, -0.00161803, 0.0118611, , 0.00152365, 0.999967, 0.00796164, , -0.0118736, -0.00794299, 0.999898, , 0.0645173, -0.170053, 0.211245, ,1, ,1.02837,0.584871,0.538944,
11, , 2015.42, , 0.999961, -0.00340054, 0.00810673, , 0.00335236, 0.999977, 0.00594917, , -0.00812678, -0.00592176, 0.999949, , 0.0714201, -0.0245489, 0.107894, ,1, ,1.00431,0.598947,0.47962,
12, , 2011.84, , 0.999967, -0.00411469, 0.00703017, , 0.00407817, 0.999978, 0.00520095, , -0.00705142, -0.00517211, 0.999962, , 0.0702158, 0.0430402, 0.066335, ,1, ,0.985,0.615719,0.453135,
13, , 2009.46, , 0.999967, -0.00542639, 0.00602492, , 0.00539909, 0.999975, 0.00453786, , -0.0060494, -0.00450518, 0.999972, , 0.0729312, 0.0888385, 0.0316239, ,1, ,0.96998,0.644246,0.421112,
14, , 2008.18, , 0.999965, -0.00649141, 0.00526229, , 0.00647117, 0.999972, 0.00385527, , -0.00528717, -0.00382108, 0.999979, , 0.0740343, 0.108078, 0.0200242, ,1, ,0.959967,0.6673,0.395221,
15, , 2008.88, , 0.999963, -0.0068415, 0.00514529, , 0.00682573, 0.999972, 0.00307624, , -0.00516619, -0.00304101, 0.999982, , 0.0716829, 0.113301, 0.0109241, ,1, ,0.948157,0.666224,0.38261,
16, , 2008.95, , 0.999962, -0.00725161, 0.00490548, , 0.0072388, 0.99997, 0.00262268, , -0.00492435, -0.00258707, 0.999985, , 0.0722217, 0.115801, 0.00751152, ,1, ,0.945892,0.668297,0.376659,
17, , 2008.97, , 0.999961, -0.00759918, 0.00446318, , 0.00758974, 0.999969, 0.0021289, , -0.00447922, -0.00209495, 0.999988, , 0.0731815, 0.117114, 0.00310775, ,1, ,0.943791,0.672447,0.373123,
18, , 2008.32, , 0.999955, -0.00825876, 0.00456739, , 0.00825278, 0.999965, 0.00132814, , -0.0045782, -0.00129039, 0.999989, , 0.0748479, 0.114585, -0.00292776, ,1, ,0.93535,0.667721,0.370871,
19, , 2008.23, , 0.999952, -0.00876356, 0.00431588, , 0.00875947, 0.999961, 0.000966743, , -0.00432418, -0.000928892, 0.99999, , 0.0758933, 0.10974, -0.00521919, ,1, ,0.934674,0.664005,0.368692,
20, , 2008.35, , 0.999951, -0.00884604, 0.00435111, , 0.00884213, 0.99996, 0.00091777, , -0.00435905, -0.000879252, 0.99999, , 0.0766804, 0.10646, -0.00417962, ,1, ,0.935992,0.661487,0.367581,
21, , 2008.35, , 0.999951, -0.00884746, 0.00435265, , 0.00884359, 0.99996, 0.000907517, , -0.00436051, -0.00086898, 0.99999, , 0.0767028, 0.10549, -0.00396411, ,1, ,0.936268,0.660908,0.36733,
22, , 2008.35, , 0.999951, -0.00884721, 0.00435264, , 0.00884335, 0.99996, 0.000905164, , -0.00436048, -0.000866628, 0.99999, , 0.0767001, 0.105207, -0.00390863, ,1, ,0.93634,0.660749,0.367271,
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