conjugate_gradient_versus_svd_or_lu_decomposition
— Alan Coelho 2017/08/28 16:43
TOPAS uses the Conjugate Gradient (CG) routine as described at:
Coelho, A. A. (2005). J. Appl. Cryst. 38, 455-461. "A bound constrained conjugate gradient solution method as applied to crystallographic refinement problems"
The routine uses min/max limits during the solution to the normal equations. Newton methods such as LU-Decomposition, SVD or Cholsky Decomposition cannot use min/max limits and hence struggle to solve the normal equations due to ill-conditioning. The following are outputs comparing CG with SVD:
Use of TOPAS Conjugate Gradient routine on PAWLEY1.INP:
TOPAS-32 Version 6 (c) 1992-2017 Alan A. Coelho
Maximum number of threads 8
Time 0.01, INP file pre-processed
Loading xyz's for p-1 from file C:\c\t5\sg\p-1.sg
Number of hkls generated for C:\c\t5\sg\p-1.sg 530
Number of independent parameters : 551
0 Time 0.02 Rwp 92.483 0.000 MC 0.00 0
Sparse matrix methods invoked - 83.0% of the A matrix elements are zero
1 Time 0.03 Rwp 67.173 -25.310 MC 1.00 2
2 Time 0.05 Rwp 37.184 -29.990 MC 1.15 1
3 Time 0.06 Rwp 21.833 -15.351 MC 0.47 1
4 Time 0.07 Rwp 14.298 -7.535 MC 0.16 1
5 Time 0.08 Rwp 10.961 -3.337 MC 0.06 1
6 Time 0.10 Rwp 8.309 -2.653 MC 0.02 1
7 Time 0.11 Rwp 5.847 -2.462 MC 0.00 1
8 Time 0.13 Rwp 4.554 -1.292 MC 0.00 1
9 Time 0.14 Rwp 4.136 -0.418 MC 0.00 1
10 Time 0.16 Rwp 3.966 -0.170 MC 0.00 1
11 Time 0.17 Rwp 3.908 -0.059 MC 0.00 1
12 Time 0.18 Rwp 3.894 -0.014 MC 0.00 1
13 Time 0.19 Rwp 3.891 -0.002 MC 0.00 1
14 Time 0.20 Rwp 3.888 -0.004 MC 0.00 1
15 Time 0.21 Rwp 3.888 -0.000 MC 0.00 1
--- 0.213 seconds ---
*** Parameter(s) close to limit(s).
Check for LIMIT_MIN and LIMIT_MAX in Grid/Text
Errors calculated
File C:\c\t5\test_examples\peak-intensity-extraction\pawley1.out updated
with parameters from last iteration
Process Times (secs)
0.01 = Peak buffer derivatives
0.01 = Ycalc calculation and Penalties
0.10 = A and Y matrix dot products and derivatives
0.06 = Ycalc derivatives
0.04 = A and Y matrix dot products
0.07 = Solution to the normal equations
Using Cholsky Decomposition on PAWLEY1.INP:
TOPAS-32 Version 6 (c) 1992-2017 Alan A. Coelho
Maximum number of threads 8
Loading C:\c\t5\topas.inc
Time 0.02, INP file pre-processed
Loading xyz's for p-1 from file C:\c\t5\sg\p-1.sg
Number of hkls generated for C:\c\t5\sg\p-1.sg 530
Number of independent parameters : 551
0 Time 0.04 Rwp 92.483 0.000 MC 0.00 0
Loading C:\c\t5\topas.inc
Loading C:\c\t5\interface.inc
1 Time 0.18 Rwp 61.400 -31.083 MC 1.00 2
2 Time 0.26 Rwp 31.414 -29.986 MC 0.47 1
3 Time 0.33 Rwp 18.986 -12.428 MC 0.16 1
4 Time 0.40 Rwp 16.034 -2.952 MC 0.06 1
5 Time 0.47 Rwp 15.974 -0.060 MC 0.03 1
6 Time 0.54 Rwp 10.716 -5.258 MC 1.60 1
7 Time 0.61 Rwp 8.807 -1.909 MC 0.56 1
8 Time 0.68 Rwp 7.804 -1.003 MC 0.17 1
9 Time 0.74 Rwp 7.694 -0.109 MC 0.05 1
10 Time 0.82 Rwp 6.206 -1.488 MC 1.61 1
11 Time 0.88 Rwp 5.753 -0.453 MC 0.52 1
12 Time 0.99 Rwp 5.414 -0.339 MC 2.50 2
13 Time 1.06 Rwp 5.303 -0.111 MC 0.74 1
14 Time 1.16 Rwp 5.144 -0.159 MC 3.09 2
15 Time 1.23 Rwp 5.097 -0.046 MC 0.89 1
16 Time 1.33 Rwp 4.998 -0.100 MC 3.72 2
17 Time 1.40 Rwp 4.967 -0.030 MC 1.05 1
18 Time 1.51 Rwp 4.900 -0.068 MC 4.15 2
19 Time 1.58 Rwp 4.879 -0.021 MC 1.18 1
20 Time 1.69 Rwp 4.828 -0.050 MC 4.78 2
21 Time 1.76 Rwp 4.811 -0.017 MC 1.35 1
22 Time 1.87 Rwp 4.774 -0.038 MC 5.30 2
23 Time 1.93 Rwp 4.760 -0.014 MC 1.49 1
24 Time 2.03 Rwp 4.730 -0.029 MC 5.80 2
25 Time 2.09 Rwp 4.718 -0.012 MC 1.64 1
26 Time 2.20 Rwp 4.695 -0.023 MC 6.20 2
27 Time 2.26 Rwp 4.685 -0.010 MC 1.76 1
28 Time 2.36 Rwp 4.665 -0.019 MC 6.68 2
29 Time 2.43 Rwp 4.656 -0.009 MC 1.86 1
30 Time 2.52 Rwp 4.639 -0.016 MC 7.02 2
31 Time 2.59 Rwp 4.631 -0.008 MC 1.96 1
32 Time 2.69 Rwp 4.617 -0.014 MC 7.37 2
33 Time 2.75 Rwp 4.609 -0.008 MC 2.08 1
34 Time 2.85 Rwp 4.597 -0.012 MC 7.86 2
35 Time 2.92 Rwp 4.590 -0.007 MC 2.20 1
36 Time 3.03 Rwp 4.580 -0.011 MC 8.18 2
37 Time 3.10 Rwp 4.573 -0.006 MC 2.29 1
38 Time 3.20 Rwp 4.564 -0.009 MC 8.47 2
39 Time 3.26 Rwp 4.558 -0.006 MC 2.38 1
40 Time 3.36 Rwp 4.550 -0.008 MC 8.78 2
41 Time 3.42 Rwp 4.544 -0.006 MC 2.54 1
42 Time 3.52 Rwp 4.537 -0.007 MC 9.03 2
43 Time 3.58 Rwp 4.532 -0.005 MC 2.57 1
44 Time 3.68 Rwp 4.525 -0.007 MC 9.24 2
45 Time 3.75 Rwp 4.520 -0.005 MC 2.58 1
46 Time 3.85 Rwp 4.513 -0.006 MC 9.23 2
47 Time 3.91 Rwp 4.509 -0.005 MC 2.57 1
48 Time 4.01 Rwp 4.502 -0.006 MC 9.06 2
49 Time 4.08 Rwp 4.498 -0.004 MC 2.53 1
50 Time 4.18 Rwp 4.492 -0.006 MC 9.08 2
51 Time 4.24 Rwp 4.488 -0.004 MC 2.51 1
52 Time 4.34 Rwp 4.482 -0.006 MC 8.92 2
53 Time 4.41 Rwp 4.478 -0.004 MC 2.46 1
54 Time 4.50 Rwp 4.473 -0.005 MC 8.92 2
55 Time 4.57 Rwp 4.469 -0.004 MC 2.45 1
56 Time 4.67 Rwp 4.464 -0.005 MC 8.94 2
57 Time 4.73 Rwp 4.460 -0.004 MC 2.46 1
58 Time 4.84 Rwp 4.455 -0.005 MC 8.81 2
59 Time 4.90 Rwp 4.452 -0.003 MC 2.34 1
60 Time 5.00 Rwp 4.446 -0.005 MC 8.74 2
61 Time 5.06 Rwp 4.443 -0.003 MC 2.40 1
62 Time 5.16 Rwp 4.438 -0.005 MC 8.75 2
63 Time 5.22 Rwp 4.435 -0.003 MC 2.39 1
64 Time 5.32 Rwp 4.430 -0.005 MC 8.82 2
65 Time 5.39 Rwp 4.427 -0.003 MC 2.53 1
66 Time 5.49 Rwp 4.423 -0.005 MC 8.48 2
67 Time 5.57 Rwp 4.420 -0.002 MC 2.38 1
68 Time 5.67 Rwp 4.415 -0.005 MC 8.95 2
69 Time 5.73 Rwp 4.413 -0.002 MC 2.38 1
70 Time 5.83 Rwp 4.408 -0.005 MC 9.00 2
71 Time 5.89 Rwp 4.406 -0.002 MC 2.46 1
72 Time 5.99 Rwp 4.401 -0.004 MC 9.36 2
73 Time 6.05 Rwp 4.399 -0.002 MC 2.54 1
74 Time 6.16 Rwp 4.395 -0.004 MC 9.29 2
75 Time 6.22 Rwp 4.393 -0.002 MC 2.55 1
76 Time 6.32 Rwp 4.389 -0.004 MC 9.13 2
77 Time 6.38 Rwp 4.387 -0.002 MC 2.54 1
78 Time 6.48 Rwp 4.383 -0.004 MC 9.21 2
79 Time 6.55 Rwp 4.381 -0.002 MC 2.57 1
80 Time 6.65 Rwp 4.377 -0.004 MC 9.36 2
81 Time 6.72 Rwp 4.375 -0.002 MC 2.65 1
82 Time 6.83 Rwp 4.371 -0.004 MC 9.50 2
83 Time 6.90 Rwp 4.369 -0.002 MC 2.65 1
84 Time 7.00 Rwp 4.366 -0.004 MC 9.63 2
85 Time 7.06 Rwp 4.364 -0.002 MC 2.62 1
86 Time 7.16 Rwp 4.361 -0.003 MC 9.65 2
87 Time 7.22 Rwp 4.359 -0.002 MC 2.63 1
88 Time 7.32 Rwp 4.355 -0.003 MC 9.58 2
89 Time 7.38 Rwp 4.354 -0.002 MC 2.63 1
90 Time 7.48 Rwp 4.350 -0.003 MC 9.55 2
91 Time 7.56 Rwp 4.349 -0.002 MC 2.64 1
92 Time 7.66 Rwp 4.346 -0.003 MC 9.44 2
93 Time 7.74 Rwp 4.344 -0.002 MC 2.65 1
94 Time 7.84 Rwp 4.341 -0.003 MC 9.85 2
95 Time 7.92 Rwp 4.339 -0.001 MC 2.64 1
96 Time 8.02 Rwp 4.336 -0.003 MC 10.16 2
97 Time 8.09 Rwp 4.335 -0.002 MC 2.72 1
98 Time 8.19 Rwp 4.332 -0.003 MC 9.83 2
99 Time 8.25 Rwp 4.330 -0.001 MC 2.70 1
100 Time 8.38 Rwp 4.327 -0.003 MC 9.96 2
101 Time 8.45 Rwp 4.326 -0.002 MC 2.86 1
102 Time 8.56 Rwp 4.323 -0.003 MC 9.99 2
103 Time 8.64 Rwp 4.322 -0.001 MC 2.72 1
104 Time 8.74 Rwp 4.319 -0.003 MC 10.20 2
105 Time 8.81 Rwp 4.317 -0.002 MC 2.91 1
106 Time 8.90 Rwp 4.315 -0.003 MC 10.09 2
107 Time 8.97 Rwp 4.314 -0.001 MC 2.73 1
108 Time 9.07 Rwp 4.311 -0.003 MC 10.33 2
109 Time 9.13 Rwp 4.310 -0.001 MC 2.80 1
110 Time 9.25 Rwp 4.307 -0.003 MC 10.90 2
111 Time 9.31 Rwp 4.306 -0.001 MC 2.71 1
112 Time 9.41 Rwp 4.303 -0.003 MC 11.08 2
113 Time 9.48 Rwp 4.302 -0.001 MC 3.04 1
114 Time 9.58 Rwp 4.299 -0.002 MC 10.32 2
115 Time 9.64 Rwp 4.298 -0.001 MC 2.80 1
116 Time 9.74 Rwp 4.296 -0.002 MC 10.59 2
117 Time 9.80 Rwp 4.295 -0.001 MC 2.90 1
118 Time 9.90 Rwp 4.292 -0.002 MC 10.43 2
119 Time 9.96 Rwp 4.291 -0.001 MC 2.82 1
120 Time 10.06 Rwp 4.289 -0.002 MC 10.48 2
121 Time 10.12 Rwp 4.288 -0.001 MC 2.82 1
122 Time 10.22 Rwp 4.286 -0.002 MC 10.43 2
123 Time 10.29 Rwp 4.285 -0.001 MC 2.79 1
124 Time 10.38 Rwp 4.282 -0.002 MC 10.64 2
125 Time 10.47 Rwp 4.281 -0.001 MC 2.86 1
126 Time 10.57 Rwp 4.279 -0.002 MC 10.38 2
127 Time 10.63 Rwp 4.278 -0.001 MC 2.82 1
--- 10.649 seconds ---
*** Parameter(s) close to limit(s).
Check for LIMIT_MIN and LIMIT_MAX in Grid/Text
Errors calculated
File C:\c\t5\test_examples\peak-intensity-extraction\pawley1.out updated
with parameters from last iteration
Process Times (secs)
0.07 = Peak buffer derivatives
0.20 = Ycalc calculation and Penalties
1.37 = A and Y matrix dot products and derivatives
0.58 = Ycalc derivatives
0.79 = A and Y matrix dot products
6.37 = Solution to the normal equations
SVD convergence behavior on PAWLEY1.INP: 0 Time 0.02 Rwp 92.483 0.000 MC 0.00 0 1 Time 2.77 Rwp 61.400 -31.083 MC 1.00 2 2 Time 4.14 Rwp 31.414 -29.986 MC 0.47 1 3 Time 5.50 Rwp 18.986 -12.428 MC 0.16 1 4 Time 6.78 Rwp 16.034 -2.952 MC 0.06 1 5 Time 8.07 Rwp 15.974 -0.060 MC 0.03 1 6 Time 9.48 Rwp 10.716 -5.258 MC 1.60 1 7 Time 10.84 Rwp 8.807 -1.909 MC 0.56 1 8 Time 12.16 Rwp 7.804 -1.003 MC 0.17 1 9 Time 13.46 Rwp 7.694 -0.109 MC 0.05 1 10 Time 14.84 Rwp 6.206 -1.488 MC 1.61 1 11 Time 16.19 Rwp 5.753 -0.453 MC 0.52 1 12 Time 18.93 Rwp 5.414 -0.339 MC 2.50 2 13 Time 20.37 Rwp 5.303 -0.111 MC 0.74 1 14 Time 23.12 Rwp 5.144 -0.159 MC 3.09 2 15 Time 24.54 Rwp 5.097 -0.046 MC 0.89 1 16 Time 27.31 Rwp 4.998 -0.100 MC 3.72 2 17 Time 28.73 Rwp 4.967 -0.030 MC 1.05 1 18 Time 31.48 Rwp 4.900 -0.068 MC 4.15 2 19 Time 32.87 Rwp 4.879 -0.021 MC 1.18 1 20 Time 35.67 Rwp 4.828 -0.050 MC 4.78 2 21 Time 37.10 Rwp 4.811 -0.017 MC 1.35 1 22 Time 39.94 Rwp 4.774 -0.038 MC 5.30 2 23 Time 41.34 Rwp 4.760 -0.014 MC 1.49 1 24 Time 44.12 Rwp 4.730 -0.029 MC 5.80 2 25 Time 45.57 Rwp 4.718 -0.012 MC 1.64 1 26 Time 48.36 Rwp 4.695 -0.023 MC 6.20 2 27 Time 49.82 Rwp 4.685 -0.010 MC 1.76 1 28 Time 52.63 Rwp 4.665 -0.019 MC 6.68 2 29 Time 54.04 Rwp 4.656 -0.009 MC 1.86 1 30 Time 56.93 Rwp 4.639 -0.016 MC 7.02 2 31 Time 58.33 Rwp 4.631 -0.008 MC 1.96 1 32 Time 61.20 Rwp 4.617 -0.014 MC 7.37 2 33 Time 62.63 Rwp 4.609 -0.008 MC 2.08 1 34 Time 65.53 Rwp 4.597 -0.012 MC 7.86 2 35 Time 66.96 Rwp 4.590 -0.007 MC 2.20 1 36 Time 69.81 Rwp 4.580 -0.011 MC 8.18 2 37 Time 71.28 Rwp 4.573 -0.006 MC 2.29 1 38 Time 74.16 Rwp 4.564 -0.009 MC 8.47 2 39 Time 75.58 Rwp 4.558 -0.006 MC 2.38 1 40 Time 78.43 Rwp 4.550 -0.008 MC 8.78 2 41 Time 79.86 Rwp 4.544 -0.006 MC 2.54 1 42 Time 82.68 Rwp 4.537 -0.007 MC 9.03 2 43 Time 84.13 Rwp 4.532 -0.005 MC 2.57 1 44 Time 87.03 Rwp 4.525 -0.007 MC 9.24 2 45 Time 88.46 Rwp 4.520 -0.005 MC 2.58 1 46 Time 91.31 Rwp 4.513 -0.006 MC 9.23 2 47 Time 92.73 Rwp 4.509 -0.005 MC 2.57 1 48 Time 95.57 Rwp 4.502 -0.006 MC 9.06 2 49 Time 97.04 Rwp 4.498 -0.004 MC 2.53 1
A few points to note:
- Convergence of the CG routine is fast.
- The SVD routine does try and minimize on the residual (A x – b)^2
- The SVD refinement was truncated at 50 iterations to minimize on waiting time.
- On a problem with 551 independent parameters, SVD is 100s of times slower over the whole refinement. Note, the CG routine is threaded.
- The Solution to the normal equations for CG took 0.07s; for LU decomposition its 6.37s.
Using the CG routine without limits
The following INP file is used:
r_wp 0
process_times
xdd alvo4.xdd
CuKa1(0.001)
Radius(200.5)
Simple_Axial_Model(@, 1)
LP_Factor(27)
Zero_Error(@, 0)
bkg @ 0 0 0 0 0 0 0 0
hkl_Is
a @ 6.54
b @ 7.75
c @ 9.12
al @ 96.1
be @ 107.2
ga @ 101.4
PV_Peak_Type(, 0, @, 0.05, @, 0.05, @, 0.05, @, 0.05, @, .05)
macro VV(v)
{
#m_unique i v min = -1e40; max = 1e40; update = Max(Val+Change,0);
= i;
}
space_group "p-1"
load hkl_m_d_th2 prm I
{
0 0 1 2 8.58454 10.29625 VV(1)
0 1 0 2 7.48537 11.81320 VV(1)
0 1 -1 2 6.21484 14.23967 VV(1)
1 0 0 2 6.06127 14.60239 VV(1)
1 0 -1 2 5.94891 14.87973 VV(1)
1 -1 0 2 5.39088 16.43013 VV(1)
0 1 1 2 5.20274 17.02859 VV(1)
1 -1 -1 2 4.94022 17.94077 VV(1)
1 1 -1 2 4.41793 20.08252 VV(1)
1 0 1 2 4.33066 20.49155 VV(1)
0 0 2 2 4.29227 20.67682 VV(1)
1 -1 1 2 4.26461 20.81240 VV(1)
1 1 0 2 4.23626 20.95326 VV(1)
1 0 -2 2 4.20949 21.08801 VV(1)
0 1 -2 2 4.04647 21.94796 VV(1)
0 2 0 2 3.74269 23.75433 VV(1)
1 1 -2 2 3.67893 24.17217 VV(1)
0 2 -1 2 3.67841 24.17564 VV(1)
1 -1 -2 2 3.65936 24.30337 VV(1)
1 -2 0 2 3.59687 24.73228 VV(1)
0 1 2 2 3.46733 25.67175 VV(1)
1 1 1 2 3.38351 26.31901 VV(1)
1 -2 -1 2 3.34477 26.62939 VV(1)
1 -2 1 2 3.29076 27.07465 VV(1)
0 2 1 2 3.22729 27.61759 VV(1)
2 0 -1 2 3.20450 27.81798 VV(1)
2 -1 -1 2 3.17113 28.11671 VV(1)
1 -1 2 2 3.12045 28.58292 VV(1)
0 2 -2 2 3.10742 28.70539 VV(1)
2 -1 0 2 3.08006 28.96593 VV(1)
1 0 2 2 3.06338 29.12706 VV(1)
2 0 0 2 3.03063 29.44889 VV(1)
1 2 -1 2 3.01639 29.59110 VV(1)
1 0 -3 2 2.99141 29.84393 VV(1)
2 0 -2 2 2.97446 30.01803 VV(1)
1 2 0 2 2.88769 30.94216 VV(1)
2 -1 -2 2 2.87939 31.03365 VV(1)
0 0 3 2 2.86151 31.23245 VV(1)
0 1 -3 2 2.84677 31.39836 VV(1)
1 1 -3 2 2.84354 31.43496 VV(1)
1 2 -2 2 2.80572 31.86981 VV(1)
1 -2 -2 2 2.78839 32.07327 VV(1)
2 1 -1 2 2.76272 32.37944 VV(1)
1 -2 2 2 2.72639 32.82297 VV(1)
1 -1 -3 2 2.71643 32.94678 VV(1)
2 -2 -1 2 2.69977 33.15596 VV(1)
2 -2 0 2 2.69544 33.21076 VV(1)
2 -1 1 2 2.68688 33.31959 VV(1)
2 1 -2 2 2.66184 33.64236 VV(1)
1 1 2 2 2.61607 34.24898 VV(1)
2 0 1 2 2.60370 34.41676 VV(1)
0 2 2 2 2.60137 34.44849 VV(1)
2 1 0 2 2.59905 34.48019 VV(1)
2 0 -3 2 2.53337 35.40325 VV(1)
1 -3 0 2 2.53286 35.41063 VV(1)
0 1 3 2 2.52738 35.49006 VV(1)
1 2 1 2 2.52316 35.55128 VV(1)
0 3 -1 2 2.51883 35.61446 VV(1)
0 3 0 2 2.49512 35.96437 VV(1)
0 2 -3 2 2.49721 35.93325 VV(1)
2 -2 -2 2 2.47011 36.34125 VV(1)
2 -2 1 2 2.46020 36.49280 VV(1)
1 -3 1 2 2.45887 36.51316 VV(1)
2 -1 -3 2 2.43306 36.91444 VV(1)
1 2 -3 2 2.41617 37.18181 VV(1)
1 -3 -1 2 2.40082 37.42835 VV(1)
1 -1 3 2 2.37322 37.88022 VV(1)
2 1 -3 2 2.36761 37.97335 VV(1)
0 3 -2 2 2.34567 38.34228 VV(1)
1 0 3 2 2.31286 38.90808 VV(1)
0 3 1 2 2.28950 39.32133 VV(1)
2 1 1 2 2.28101 39.47363 VV(1)
1 0 -4 2 2.26918 39.68803 VV(1)
1 -2 -3 2 2.26465 39.77089 VV(1)
2 -1 2 2 2.24302 40.17080 VV(1)
2 2 -1 2 2.23414 40.33737 VV(1)
1 1 -4 2 2.23270 40.36449 VV(1)
1 -3 2 2 2.22465 40.51696 VV(1)
1 -2 3 2 2.21481 40.70495 VV(1)
1 3 -1 2 2.21255 40.74827 VV(1)
2 2 -2 2 2.20896 40.81743 VV(1)
2 -3 0 2 2.20561 40.88230 VV(1)
2 -3 -1 2 2.17882 41.40781 VV(1)
3 -1 -1 2 2.17007 41.58250 VV(1)
2 0 2 2 2.16533 41.67785 VV(1)
0 1 -4 2 2.16750 41.63424 VV(1)
1 3 -2 2 2.15230 41.94204 VV(1)
0 0 4 2 2.14613 42.06819 VV(1)
2 -2 -3 2 2.14308 42.13106 VV(1)
1 -3 -2 2 2.14055 42.18324 VV(1)
1 3 0 2 2.13290 42.34165 VV(1)
2 -2 2 2 2.13231 42.35412 VV(1)
3 0 -1 2 2.12744 42.45570 VV(1)
3 -1 -2 2 2.12723 42.46010 VV(1)
1 2 2 2 2.12541 42.49828 VV(1)
2 2 0 2 2.11813 42.65137 VV(1)
1 -1 -4 2 2.11524 42.71249 VV(1)
3 0 -2 2 2.11260 42.76840 VV(1)
2 0 -4 2 2.10475 42.93597 VV(1)
0 2 3 2 2.10039 43.02952 VV(1)
2 -3 1 2 2.09604 43.12333 VV(1)
3 -1 0 2 2.08131 43.44394 VV(1)
1 1 3 2 2.07603 43.55996 VV(1)
0 3 -3 2 2.07161 43.65768 VV(1)
2 2 -3 2 2.05555 44.01651 VV(1)
3 -2 -1 2 2.04359 44.28769 VV(1)
2 -3 -2 2 2.02914 44.62011 VV(1)
2 1 -4 2 2.02948 44.61227 VV(1)
1 2 -4 2 2.02987 44.60318 VV(1)
3 0 0 2 2.02042 44.82299 VV(1)
2 -1 -4 2 2.02289 44.76545 VV(1)
0 2 -4 2 2.02323 44.75736 VV(1)
0 3 2 2 2.00780 45.12036 VV(1)
3 -2 0 2 1.99039 45.53706 VV(1)
3 -2 -2 2 1.98570 45.65067 VV(1)
3 0 -3 2 1.98297 45.71699 VV(1)
1 3 -3 2 1.98182 45.74513 VV(1)
3 -1 -3 2 1.97346 45.94984 VV(1)
0 1 4 2 1.97232 45.97795 VV(1)
1 3 1 2 1.95182 46.48914 VV(1)
3 1 -2 2 1.95060 46.51995 VV(1)
2 1 2 2 1.94811 46.58276 VV(1)
3 1 -1 2 1.94170 46.74562 VV(1)
1 -3 3 2 1.93943 46.80366 VV(1)
1 -4 0 2 1.92397 47.20255 VV(1)
2 2 1 2 1.91538 47.42716 VV(1)
1 -4 1 2 1.90990 47.57172 VV(1)
3 -1 1 2 1.90179 47.78707 VV(1)
2 -3 2 2 1.90068 47.81661 VV(1)
0 4 -1 2 1.89996 47.83609 VV(1)
1 -1 4 2 1.89136 48.06709 VV(1)
0 4 0 2 1.87134 48.61434 VV(1)
2 -1 3 2 1.86941 48.66780 VV(1)
3 1 -3 2 1.86485 48.79473 VV(1)
1 -2 -4 2 1.86180 48.87980 VV(1)
1 -3 -3 2 1.85649 49.02865 VV(1)
3 -2 1 2 1.84890 49.24346 VV(1)
1 -4 -1 2 1.84650 49.31167 VV(1)
3 1 0 2 1.84181 49.44567 VV(1)
1 0 4 2 1.84284 49.41615 VV(1)
3 -2 -3 2 1.84140 49.45740 VV(1)
3 0 1 2 1.83761 49.56613 VV(1)
2 2 -4 2 1.83946 49.51292 VV(1)
0 4 -2 2 1.83920 49.52041 VV(1)
2 -2 -4 2 1.82968 49.79561 VV(1)
1 -2 4 2 1.82476 49.93920 VV(1)
2 -2 3 2 1.82030 50.06993 VV(1)
3 -3 -1 2 1.81896 50.10930 VV(1)
2 -3 -3 2 1.81898 50.10880 VV(1)
1 0 -5 2 1.81429 50.24730 VV(1)
2 3 -2 2 1.81239 50.30348 VV(1)
2 3 -1 2 1.80962 50.38595 VV(1)
1 1 -5 2 1.81169 50.32438 VV(1)
2 0 3 2 1.80719 50.45859 VV(1)
1 -4 2 2 1.80988 50.37810 VV(1)
2 -4 0 2 1.79843 50.72150 VV(1)
3 -3 0 2 1.79696 50.76605 VV(1)
3 0 -4 2 1.79114 50.94287 VV(1)
0 3 -4 2 1.79195 50.91820 VV(1)
1 2 3 2 1.78799 51.03886 VV(1)
3 -1 -4 2 1.76863 51.63845 VV(1)
2 -4 -1 2 1.76834 51.64754 VV(1)
0 4 1 2 1.76437 51.77233 VV(1)
1 3 -4 2 1.76643 51.70760 VV(1)
3 -3 -2 2 1.76245 51.83302 VV(1)
2 0 -5 2 1.76009 51.90776 VV(1)
2 -4 1 2 1.75221 52.15866 VV(1)
0 1 -5 2 1.74222 52.48059 VV(1)
2 3 -3 2 1.73909 52.58219 VV(1)
1 3 2 2 1.73470 52.72538 VV(1)
0 3 3 2 1.73425 52.74030 VV(1)
0 2 4 2 1.73366 52.75943 VV(1)
2 3 0 2 1.73177 52.82164 VV(1)
1 4 -1 2 1.72945 52.89782 VV(1)
2 1 -5 2 1.72947 52.89714 VV(1)
3 2 -2 2 1.72188 53.14873 VV(1)
1 -1 -5 2 1.71847 53.26243 VV(1)
0 0 5 2 1.71691 53.31475 VV(1)
3 1 -4 2 1.71646 53.32974 VV(1)
1 4 -2 2 1.71396 53.41368 VV(1)
1 2 -5 2 1.71187 53.48409 VV(1)
0 4 -3 2 1.71155 53.49493 VV(1)
1 -4 -2 2 1.70604 53.68154 VV(1)
3 -3 1 2 1.70431 53.74038 VV(1)
1 1 4 2 1.70234 53.80743 VV(1)
3 2 -1 2 1.70196 53.82040 VV(1)
2 -1 -5 2 1.69769 53.96700 VV(1)
3 -1 2 2 1.69209 54.16016 VV(1)
2 2 2 2 1.69175 54.17175 VV(1)
3 1 1 2 1.68675 54.34575 VV(1)
2 -3 3 2 1.68277 54.48465 VV(1)
1 4 0 2 1.67741 54.67336 VV(1)
0 2 -5 2 1.67750 54.67019 VV(1)
3 2 -3 2 1.67487 54.76335 VV(1)
1 -3 4 2 1.67413 54.78958 VV(1)
2 -4 -2 2 1.67238 54.85149 VV(1)
3 -2 2 2 1.66717 55.03764 VV(1)
2 1 3 2 1.66221 55.21571 VV(1)
3 -2 -4 2 1.65893 55.33419 VV(1)
1 -4 3 2 1.65850 55.34988 VV(1)
3 -3 -3 2 1.64674 55.77951 VV(1)
2 -4 2 2 1.64538 55.82953 VV(1)
3 0 2 2 1.63421 56.24482 VV(1)
1 4 -3 2 1.63601 56.17753 VV(1)
4 -1 -2 2 1.63125 56.35621 VV(1)
4 -1 -1 2 1.62287 56.67349 VV(1)
3 2 0 2 1.62157 56.72279 VV(1)
2 2 -5 2 1.61891 56.82439 VV(1)
0 4 2 2 1.61365 57.02691 VV(1)
0 1 5 2 1.61224 57.08135 VV(1)
2 3 -4 2 1.61377 57.02193 VV(1)
2 3 1 2 1.60405 57.39957 VV(1)
2 -3 -4 2 1.60388 57.40635 VV(1)
1 -3 -4 2 1.60297 57.44183 VV(1)
4 0 -2 2 1.60225 57.47019 VV(1)
4 -2 -1 2 1.58883 58.00145 VV(1)
3 0 -5 2 1.58863 58.00937 VV(1)
4 -2 -2 2 1.58556 58.13241 VV(1)
4 0 -1 2 1.58322 58.22656 VV(1)
4 -1 -3 2 1.58302 58.23478 VV(1)
2 -1 4 2 1.57981 58.36433 VV(1)
3 -4 -1 2 1.57970 58.36891 VV(1)
3 -4 0 2 1.57593 58.52211 VV(1)
3 2 -4 2 1.57559 58.53596 VV(1)
1 4 1 2 1.57405 58.59869 VV(1)
3 -3 2 2 1.56942 58.78873 VV(1)
2 -2 -5 2 1.56782 58.85447 VV(1)
4 0 -3 2 1.56700 58.88828 VV(1)
1 -1 5 2 1.56427 59.00139 VV(1)
1 -2 -5 2 1.56338 59.03818 VV(1)
4 -1 0 2 1.56036 59.16385 VV(1)
3 -1 -5 2 1.56222 59.08613 VV(1)
2 -2 4 2 1.56023 59.16932 VV(1)
1 3 -5 2 1.55511 59.38332 VV(1)
0 4 -4 2 1.55371 59.44242 VV(1)
0 3 -5 2 1.54863 59.65705 VV(1)
3 1 -5 2 1.54594 59.77131 VV(1)
1 -5 1 2 1.54563 59.78450 VV(1)
1 -5 0 2 1.54282 59.90486 VV(1)
1 -4 -3 2 1.54121 59.97386 VV(1)
4 -2 0 2 1.54003 60.02439 VV(1)
2 -4 -3 2 1.53858 60.08652 VV(1)
1 -2 5 2 1.53587 60.20384 VV(1)
2 0 4 2 1.53169 60.38498 VV(1)
3 -4 -2 2 1.53222 60.36189 VV(1)
4 -2 -3 2 1.53115 60.40858 VV(1)
1 3 3 2 1.52628 60.62173 VV(1)
1 0 5 2 1.52655 60.60950 VV(1)
1 2 4 2 1.52256 60.78538 VV(1)
3 -4 1 2 1.52197 60.81150 VV(1)
0 5 -1 2 1.52124 60.84365 VV(1)
3 1 2 2 1.51566 61.09166 VV(1)
4 0 0 2 1.51532 61.10679 VV(1)
1 4 -4 2 1.51800 60.98731 VV(1)
1 1 -6 2 1.51467 61.13586 VV(1)
4 1 -2 2 1.50936 61.37406 VV(1)
2 4 -2 2 1.50820 61.42645 VV(1)
2 -4 3 2 1.50725 61.46924 VV(1)
1 0 -6 2 1.50664 61.49659 VV(1)
3 2 1 2 1.50326 61.65004 VV(1)
3 -3 -4 2 1.50289 61.66692 VV(1)
0 3 4 2 1.50066 61.76876 VV(1)
1 -5 2 2 1.50042 61.77965 VV(1)
0 5 -2 2 1.49873 61.85686 VV(1)
2 4 -1 2 1.49724 61.92545 VV(1)
0 5 0 2 1.49707 61.93282 VV(1)
3 3 -2 2 1.49498 62.02941 VV(1)
2 0 -6 2 1.49571 61.99578 VV(1)
4 -3 -1 2 1.49358 62.09372 VV(1)
3 -1 3 2 1.49207 62.16359 VV(1)
2 -5 0 2 1.49321 62.11064 VV(1)
1 -5 -1 2 1.49272 62.13340 VV(1)
4 -1 -4 2 1.49165 62.18326 VV(1)
1 -4 4 2 1.49243 62.14716 VV(1)
4 1 -3 2 1.48882 62.31452 VV(1)
4 0 -4 2 1.48723 62.38862 VV(1)
2 2 3 2 1.48517 62.48496 VV(1)
4 1 -1 2 1.48430 62.52546 VV(1)
3 -2 3 2 1.48385 62.54682 VV(1)
2 1 -6 2 1.48576 62.45704 VV(1)
4 -3 -2 2 1.48179 62.64331 VV(1)
2 -3 4 2 1.47988 62.73350 VV(1)
3 -2 -5 2 1.47611 62.91204 VV(1)
2 -5 1 2 1.47523 62.95369 VV(1)
3 3 -1 2 1.47298 63.06120 VV(1)
2 4 -3 2 1.47393 63.01569 VV(1)
3 3 -3 2 1.47264 63.07707 VV(1)
2 -5 -1 2 1.46705 63.34518 VV(1)
2 3 -5 2 1.46731 63.33286 VV(1)
0 2 5 2 1.46507 63.44112 VV(1)
4 -3 0 2 1.46137 63.62026 VV(1)
1 2 -6 2 1.46345 63.51918 VV(1)
4 -1 1 2 1.46037 63.66919 VV(1)
2 3 2 2 1.45709 63.82915 VV(1)
0 4 3 2 1.45248 64.05578 VV(1)
4 -2 1 2 1.45205 64.07730 VV(1)
0 1 -6 2 1.45372 63.99480 VV(1)
1 -3 5 2 1.45114 64.12210 VV(1)
3 2 -5 2 1.44897 64.22964 VV(1)
2 -1 -6 2 1.44837 64.25922 VV(1)
3 -4 -3 2 1.44593 64.38095 VV(1)
1 4 2 2 1.44495 64.42992 VV(1)
3 0 3 2 1.44355 64.49980 VV(1)
2 4 0 2 1.44385 64.48501 VV(1)
1 -1 -6 2 1.44205 64.57506 VV(1)
4 -2 -4 2 1.43969 64.69361 VV(1)
1 1 5 2 1.43554 64.90364 VV(1)
0 5 -3 2 1.43530 64.91572 VV(1)
2 1 4 2 1.43222 65.07294 VV(1)
0 5 1 2 1.43240 65.06360 VV(1)
3 -4 2 2 1.43163 65.10271 VV(1)
0 0 6 2 1.43076 65.14755 VV(1)
4 -3 -3 2 1.42896 65.23964 VV(1)
4 1 -4 2 1.42787 65.29543 VV(1)
0 2 -6 2 1.42339 65.52709 VV(1)
3 -3 3 2 1.42154 65.62299 VV(1)
4 1 0 2 1.41993 65.70637 VV(1)
2 2 -6 2 1.42177 65.61092 VV(1)
1 -5 3 2 1.41855 65.77839 VV(1)
4 0 1 2 1.41534 65.94654 VV(1)
2 -5 2 2 1.41757 65.82979 VV(1)
1 5 -1 2 1.41408 66.01281 VV(1)
3 3 0 2 1.41209 66.11813 VV(1)
1 5 -2 2 1.41331 66.05337 VV(1)
2 -3 -5 2 1.41086 66.18301 VV(1)
3 3 -4 2 1.41150 66.14908 VV(1)
1 -5 -2 2 1.40776 66.34772 VV(1)
2 -5 -2 2 1.40316 66.59322 VV(1)
3 0 -6 2 1.40316 66.59303 VV(1)
2 4 -4 2 1.40286 66.60924 VV(1)
2 -4 -4 2 1.39419 67.07791 VV(1)
4 -3 1 2 1.39297 67.14481 VV(1)
1 -3 -5 2 1.39299 67.14358 VV(1)
0 4 -5 2 1.39446 67.06368 VV(1)
1 4 -5 2 1.38481 67.59329 VV(1)
4 2 -2 2 1.38136 67.78515 VV(1)
4 0 -5 2 1.38130 67.78834 VV(1)
1 -4 -4 2 1.37940 67.89464 VV(1)
3 1 -6 2 1.38070 67.82171 VV(1)
1 5 0 2 1.37792 67.97737 VV(1)
4 -1 -5 2 1.37756 67.99769 VV(1)
3 -1 -6 2 1.37759 67.99610 VV(1)
1 5 -3 2 1.37579 68.09726 VV(1)
4 2 -3 2 1.37265 68.27406 VV(1)
3 2 2 2 1.37118 68.35747 VV(1)
3 -5 0 2 1.37192 68.31576 VV(1)
1 3 -6 2 1.36889 68.48760 VV(1)
3 -5 -1 2 1.36729 68.57940 VV(1)
4 -4 -1 2 1.36576 68.66649 VV(1)
2 -4 4 2 1.36320 68.81395 VV(1)
0 1 6 2 1.36145 68.91493 VV(1)
2 4 1 2 1.36029 68.98160 VV(1)
2 -1 5 2 1.35790 69.12062 VV(1)
2 -2 -6 2 1.35821 69.10205 VV(1)
4 2 -1 2 1.35515 69.28084 VV(1)
3 -3 -5 2 1.35601 69.23063 VV(1)
3 1 3 2 1.35298 69.40742 VV(1)
2 -2 5 2 1.35218 69.45477 VV(1)
4 -4 -2 2 1.34988 69.58975 VV(1)
4 -4 0 2 1.34772 69.71770 VV(1)
0 3 -6 2 1.34882 69.65246 VV(1)
4 -3 -4 2 1.34696 69.76247 VV(1)
1 3 4 2 1.34429 69.92169 VV(1)
4 -1 2 2 1.34327 69.98200 VV(1)
4 -2 2 2 1.34344 69.97205 VV(1)
0 5 -4 2 1.34502 69.87805 VV(1)
3 -5 1 2 1.34251 70.02778 VV(1)
0 5 2 2 1.34144 70.09199 VV(1)
1 -2 -6 2 1.33999 70.17880 VV(1)
4 1 -5 2 1.33996 70.18070 VV(1)
3 -4 -4 2 1.33893 70.24221 VV(1)
1 -4 5 2 1.33450 70.51049 VV(1)
2 -5 3 2 1.33284 70.61097 VV(1)
4 1 1 2 1.33014 70.77582 VV(1)
4 2 -4 2 1.33092 70.72834 VV(1)
1 -1 6 2 1.33044 70.75743 VV(1)
4 -2 -5 2 1.32978 70.79802 VV(1)
3 -5 -2 2 1.32961 70.80858 VV(1)
3 3 1 2 1.32540 71.06717 VV(1)
3 3 -5 2 1.32468 71.11204 VV(1)
3 -4 3 2 1.32309 71.21034 VV(1)
2 0 5 2 1.32056 71.36747 VV(1)
2 3 -6 2 1.32211 71.27122 VV(1)
1 -2 6 2 1.31914 71.45648 VV(1)
3 -2 4 2 1.31796 71.53034 VV(1)
3 -1 4 2 1.31734 71.56858 VV(1)
1 2 5 2 1.31638 71.62923 VV(1)
1 -5 4 2 1.31667 71.61117 VV(1)
3 2 -6 2 1.31657 71.61740 VV(1)
2 -5 -3 2 1.31497 71.71812 VV(1)
2 3 3 2 1.31250 71.87355 VV(1)
1 5 1 2 1.31259 71.86803 VV(1)
1 4 3 2 1.31144 71.94114 VV(1)
3 -2 -6 2 1.31118 71.95763 VV(1)
0 3 5 2 1.30995 72.03553 VV(1)
2 2 4 2 1.30803 72.15765 VV(1)
5 -1 -2 2 1.30738 72.19939 VV(1)
2 4 -5 2 1.30959 72.05844 VV(1)
1 5 -4 2 1.30952 72.06293 VV(1)
1 -5 -3 2 1.30461 72.37720 VV(1)
2 -3 5 2 1.30496 72.35418 VV(1)
4 -4 -3 2 1.30342 72.45367 VV(1)
4 0 2 2 1.30185 72.55484 VV(1)
4 -3 2 2 1.30230 72.52545 VV(1)
0 4 4 2 1.30069 72.63006 VV(1)
1 0 6 2 1.30088 72.61734 VV(1)
4 2 0 2 1.29953 72.70522 VV(1)
4 -4 1 2 1.29953 72.70513 VV(1)
3 4 -2 2 1.29828 72.78626 VV(1)
1 1 -7 2 1.29725 72.85314 VV(1)
5 -1 -3 2 1.29557 72.96301 VV(1)
5 -2 -2 2 1.29492 73.00537 VV(1)
2 0 -7 2 1.29278 73.14578 VV(1)
1 -6 1 2 1.29237 73.17309 VV(1)
2 1 -7 2 1.29227 73.17960 VV(1)
5 -1 -1 2 1.28941 73.36848 VV(1)
3 4 -3 2 1.28946 73.36530 VV(1)
1 0 -7 2 1.28628 73.57617 VV(1)
3 -5 2 2 1.28511 73.65436 VV(1)
1 -6 0 2 1.28482 73.67373 VV(1)
5 -2 -1 2 1.28325 73.77857 VV(1)
5 0 -2 2 1.28096 73.93251 VV(1)
3 -3 4 2 1.27946 74.03345 VV(1)
2 5 -2 2 1.27983 74.00864 VV(1)
3 0 4 2 1.27779 74.14661 VV(1)
3 4 -1 2 1.27799 74.13336 VV(1)
5 -2 -3 2 1.27764 74.15671 VV(1)
5 0 -3 2 1.27554 74.29936 VV(1)
1 -6 2 2 1.27122 74.59445 VV(1)
1 -3 6 2 1.26990 74.68520 VV(1)
1 2 -7 2 1.27027 74.66014 VV(1)
2 5 -1 2 1.26745 74.85470 VV(1)
0 6 -1 2 1.26703 74.88391 VV(1)
3 -5 -3 2 1.26639 74.92801 VV(1)
4 0 -6 2 1.26669 74.90740 VV(1)
2 -6 0 2 1.26643 74.92511 VV(1)
0 2 6 2 1.26369 75.11588 VV(1)
4 2 -5 2 1.26442 75.06512 VV(1)
2 5 -3 2 1.26424 75.07760 VV(1)
2 4 2 2 1.26158 75.26305 VV(1)
2 -6 1 2 1.26091 75.31028 VV(1)
5 0 -1 2 1.25850 75.47980 VV(1)
0 6 -2 2 1.25942 75.41504 VV(1)
4 -1 -6 2 1.25826 75.49667 VV(1)
5 -1 -4 2 1.25627 75.63691 VV(1)
2 -4 -5 2 1.25627 75.63726 VV(1)
2 -1 -7 2 1.25634 75.63235 VV(1)
2 2 -7 2 1.25492 75.73256 VV(1)
3 4 -4 2 1.25322 75.85399 VV(1)
1 4 -6 2 1.25384 75.80945 VV(1)
2 1 5 2 1.24978 76.09968 VV(1)
4 -3 -5 2 1.25024 76.06652 VV(1)
1 -6 -1 2 1.25002 76.08244 VV(1)
0 6 0 2 1.24756 76.25924 VV(1)
5 -3 -2 2 1.24672 76.31999 VV(1)
0 4 -6 2 1.24861 76.18398 VV(1)
2 -3 -6 2 1.24692 76.30525 VV(1)
5 -1 0 2 1.24511 76.43672 VV(1)
5 -2 0 2 1.24486 76.45482 VV(1)
4 3 -2 2 1.24526 76.42531 VV(1)
0 1 -7 2 1.24604 76.36896 VV(1)
2 -6 -1 2 1.24499 76.44540 VV(1)
4 3 -3 2 1.24416 76.50517 VV(1)
5 0 -4 2 1.24326 76.57064 VV(1)
3 2 3 2 1.24191 76.66954 VV(1)
3 0 -7 2 1.24349 76.55381 VV(1)
5 -3 -1 2 1.24155 76.69553 VV(1)
0 5 -5 2 1.24297 76.59214 VV(1)
1 -1 -7 2 1.24008 76.80303 VV(1)
0 5 3 2 1.23920 76.86752 VV(1)
4 1 -6 2 1.23981 76.82279 VV(1)
1 1 6 2 1.23790 76.96323 VV(1)
4 -4 -4 2 1.23505 77.17303 VV(1)
5 -2 -4 2 1.23467 77.20133 VV(1)
2 -5 4 2 1.23529 77.15550 VV(1)
1 -4 -5 2 1.23348 77.28978 VV(1)
3 4 0 2 1.23240 77.36997 VV(1)
3 1 -7 2 1.23293 77.33086 VV(1)
4 -5 -1 2 1.23126 77.45502 VV(1)
0 2 -7 2 1.23191 77.40623 VV(1)
4 1 2 2 1.22946 77.58971 VV(1)
4 -2 3 2 1.22999 77.54972 VV(1)
4 -4 2 2 1.23010 77.54187 VV(1)
1 5 2 2 1.22971 77.57074 VV(1)
2 5 0 2 1.22940 77.59406 VV(1)
2 -6 2 2 1.22944 77.59145 VV(1)
3 3 2 2 1.22708 77.76862 VV(1)
2 -4 5 2 1.22793 77.70424 VV(1)
3 -4 -5 2 1.22680 77.78990 VV(1)
5 -3 -3 2 1.22615 77.83861 VV(1)
0 0 7 2 1.22636 77.82252 VV(1)
4 2 1 2 1.22453 77.96074 VV(1)
4 -1 3 2 1.22476 77.94380 VV(1)
3 3 -6 2 1.22631 77.82653 VV(1)
0 6 -3 2 1.22614 77.83964 VV(1)
1 5 -5 2 1.22618 77.83628 VV(1)
1 -6 3 2 1.22533 77.90044 VV(1)
1 -3 -6 2 1.22291 78.08360 VV(1)
4 -5 0 2 1.22301 78.07600 VV(1)
5 1 -2 2 1.22214 78.14275 VV(1)
5 1 -3 2 1.22244 78.11934 VV(1)
2 5 -4 2 1.22356 78.03452 VV(1)
4 3 -1 2 1.22090 78.23715 VV(1)
3 -1 -7 2 1.22053 78.26509 VV(1)
3 -3 -6 2 1.21979 78.32199 VV(1)
4 3 -4 2 1.21779 78.47497 VV(1)
2 -5 -4 2 1.21637 78.58457 VV(1)
4 -2 -6 2 1.21653 78.57217 VV(1)
4 -5 -2 2 1.21461 78.72073 VV(1)
5 0 0 2 1.21225 78.90324 VV(1)
5 -3 0 2 1.21156 78.95700 VV(1)
3 -4 4 2 1.21115 78.98941 VV(1)
1 3 -7 2 1.21183 78.93593 VV(1)
3 1 4 2 1.20878 79.17414 VV(1)
3 -5 3 2 1.20973 79.10024 VV(1)
1 -5 5 2 1.20925 79.13741 VV(1)
2 4 -6 2 1.20809 79.22882 VV(1)
0 6 1 2 1.20453 79.50926 VV(1)
4 -3 3 2 1.20297 79.63291 VV(1)
2 -6 -2 2 1.20041 79.83661 VV(1)
5 1 -1 2 1.19781 80.04542 VV(1)
5 1 -4 2 1.19868 79.97561 VV(1)
3 -6 0 2 1.19896 79.95315 VV(1)
1 -5 -4 2 1.19725 80.08967 VV(1)
1 6 -2 2 1.19818 80.01569 VV(1)
5 -1 -5 2 1.19641 80.15774 VV(1)
3 4 -5 2 1.19596 80.19403 VV(1)
1 -6 -2 2 1.19411 80.34368 VV(1)
1 6 -1 2 1.19391 80.35942 VV(1)
1 -4 6 2 1.19420 80.33659 VV(1)
}
The CG routine in this case is used to solve the normal equations but the limits on the intensity parameter is set to the very large values of -1e40 and 1e40. The macro VV limits the intensity to a positive value after the solution to the normal equations; this is performed using:
#m_unique i v min = -1e40; max = 1e40; update = Max(Val+Change,0);
Thus convergence output is as follows:
TOPAS-32 Version 6 (c) 1992-2017 Alan A. Coelho
Maximum number of threads 8
Time 0.01, INP file pre-processed
Number of independent parameters : 551
0 Time 0.03 Rwp 92.483 0.000 MC 0.00 0
Sparse matrix methods invoked - 83.0% of the A matrix elements are zero
1 Time 0.04 Rwp 37.725 -54.758 MC 0.00 1
2 Time 0.05 Rwp 27.737 -9.988 MC 0.05 1
3 Time 0.07 Rwp 19.533 -8.204 MC 1.27 2
4 Time 0.08 Rwp 14.885 -4.647 MC 0.48 1
5 Time 0.09 Rwp 13.575 -1.311 MC 0.15 1
6 Time 0.10 Rwp 12.636 -0.939 MC 1.63 2
7 Time 0.11 Rwp 12.187 -0.449 MC 0.48 1
8 Time 0.12 Rwp 11.871 -0.316 MC 2.34 2
9 Time 0.13 Rwp 11.660 -0.211 MC 0.66 1
10 Time 0.14 Rwp 11.484 -0.176 MC 2.73 2
11 Time 0.15 Rwp 11.352 -0.132 MC 0.75 1
12 Time 0.16 Rwp 11.228 -0.124 MC 3.00 2
13 Time 0.17 Rwp 11.121 -0.107 MC 0.82 1
14 Time 0.18 Rwp 11.022 -0.099 MC 3.14 2
15 Time 0.19 Rwp 10.915 -0.107 MC 0.85 1
16 Time 0.20 Rwp 10.871 -0.044 MC 0.22 1
17 Time 0.21 Rwp 10.455 -0.416 MC 0.83 1
18 Time 0.21 Rwp 10.133 -0.322 MC 0.22 1
19 Time 0.22 Rwp 9.835 -0.297 MC 0.06 1
20 Time 0.24 Rwp 8.753 -1.082 MC 1.24 2
21 Time 0.24 Rwp 8.026 -0.727 MC 0.38 1
22 Time 0.25 Rwp 7.176 -0.850 MC 0.10 1
23 Time 0.27 Rwp 6.769 -0.407 MC 0.03 1
24 Time 0.27 Rwp 5.443 -1.326 MC 0.28 1
25 Time 0.29 Rwp 5.159 -0.284 MC 0.09 1
26 Time 0.30 Rwp 4.742 -0.417 MC 1.31 2
27 Time 0.31 Rwp 4.645 -0.097 MC 0.39 1
28 Time 0.32 Rwp 4.482 -0.164 MC 2.08 2
29 Time 0.33 Rwp 4.455 -0.027 MC 0.59 1
30 Time 0.34 Rwp 4.362 -0.093 MC 2.71 2
31 Time 0.35 Rwp 4.351 -0.011 MC 0.76 1
32 Time 0.36 Rwp 4.290 -0.061 MC 3.45 2
33 Time 0.36 Rwp 4.282 -0.008 MC 0.96 1
34 Time 0.37 Rwp 4.240 -0.042 MC 3.99 2
35 Time 0.38 Rwp 4.235 -0.005 MC 1.11 1
36 Time 0.39 Rwp 4.205 -0.031 MC 4.71 2
37 Time 0.41 Rwp 4.200 -0.004 MC 1.30 1
38 Time 0.42 Rwp 4.178 -0.023 MC 5.14 2
39 Time 0.42 Rwp 4.175 -0.003 MC 1.40 1
40 Time 0.43 Rwp 4.157 -0.018 MC 5.73 2
41 Time 0.44 Rwp 4.154 -0.003 MC 1.57 1
42 Time 0.45 Rwp 4.139 -0.014 MC 5.86 2
43 Time 0.46 Rwp 4.138 -0.001 MC 1.59 1
44 Time 0.47 Rwp 4.130 -0.009 MC 2.12 1
45 Time 0.47 Rwp 4.118 -0.012 MC 6.46 2
46 Time 0.48 Rwp 4.118 -0.000 MC 1.65 1
--- 0.483 seconds ---
*** Parameter(s) close to limit(s).
Check for LIMIT_MIN and LIMIT_MAX in Grid/Text
File C:\c\t5\test_examples\peak-intensity-extraction\pawley1.out updated
with parameters from last iteration
Process Times (secs)
0.02 = Peak buffer derivatives
0.04 = Ycalc calculation and Penalties
0.22 = A and Y matrix dot products and derivatives
0.15 = Ycalc derivatives
0.07 = A and Y matrix dot products
0.13 = Solution to the normal equations
As can be seen, not having min/max limits on the intensity parameters leads to slow convergence.
Removing the 'update' attribute by changing the VV macro to:
#m_unique i v min = -1e40; max = 1e40;
results in fast convergence but many of the intensities become negative.
conjugate_gradient_versus_svd_or_lu_decomposition.txt · Last modified: 2022/11/03 15:08 by 127.0.0.1