Geometric Archetypal Analysis
Project description
geom_archetypal
Geometrical Archetypal Analysis
Overview
geom_archetypal is a Python Module for performing Grid Archetypal Analysis (GAA) by using a properly modified version of the PCHA algorithm.
Basic functions are:
fast_archetypal()Archetypal Analysis (AA) with given data rows as archetypesgrid_archetypalFor a data matrix n x d finds the Grid Archetypes and performs AAcloser_grid_archetypalFor a data matrix n x d finds the Closer Grid Archetypes and performs AAarchetypal_pcha()Principal Convex Hull Analysis (PCHA)
Installation
On the terminal of your operating system write and press enter:
$ pip install geom_archetypal
Usage
# Load Module:
from geom_archetypal import *
# Set seed:
seed=20240518
np.random.seed(seed)
# Create random data
n=100
d=2
df = np.random.random((n, d))
# grid_atrchetypal()
BY, A, B, AM, AMDF, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (
grid_archetypal(df, diag_less = 1e-6, verbose = True))
pd.DataFrame(BY)
AMDF
[SSE, varexpl, fin_iters, time_elapsed, diagsum_final]
Fast Archetypal Analysis:
Compute the compositions when the archetypes are already given
|--------|--------------|--------------|-------------------------|
| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |
|--------|--------------|--------------|-------------------------|
| 1 | 2.626019e+01 | 2.078703e+00 | 11.632968|
| 2 | 2.078703e+00 | 8.176473e-01 | 1.542298|
| 3 | 8.176473e-01 | 1.286832e+00 | 0.364605|
| 4 | 8.176473e-01 | 1.563447e-01 | 4.229772|
| 5 | 1.563447e-01 | 1.204240e-01 | 0.298286|
| 6 | 1.204240e-01 | 1.948338e-01 | 0.381914|
| 7 | 1.204240e-01 | 1.339817e-02 | 7.988091|
| 8 | 1.339817e-02 | 6.356475e-03 | 1.107799|
|--------|--------------|--------------|-------------------------|
Time for the 8 A updates was 0 secs
|----------|------------|--------------|-------------------|--------------|
| Iter | VarExpl | SSE | SSE_8 / SSE_0 | muA |
|----------|------------|--------------|-------------------|--------------|
| 8 | 0.999903 | 6.356475e-03 | 0.000242 | 7.4650e-01|
|----------|------------|--------------|-------------------|--------------|
The sum of diagonal elements for the sub-matrix of closer grid points is 4.0
The ideal sum would be 4
#closer_grid_archetypal(
BY, A, B, ADF, imins, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (
closer_grid_archetypal(df, diag_less = 1e-6, verbose = True))
pd.DataFrame(BY)
ADF
[SSE, varexpl, fin_iters, time_elapsed, diagsum_final]
Fast Archetypal Analysis:
Compute the compositions when the archetypes are already given
|--------|--------------|--------------|-------------------------|
| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |
|--------|--------------|--------------|-------------------------|
| 1 | 2.339832e+01 | 2.111296e+00 | 10.082445|
| 2 | 2.111296e+00 | 5.136190e-01 | 3.110626|
| 3 | 5.136190e-01 | 6.213599e-01 | 0.173395|
| 4 | 5.136190e-01 | 1.098227e-01 | 3.676804|
| 5 | 1.098227e-01 | 6.322219e-02 | 0.737090|
| 6 | 6.322219e-02 | 8.338054e-02 | 0.241763|
| 7 | 6.322219e-02 | 1.851679e-02 | 2.414316|
| 8 | 1.851679e-02 | 1.440165e-02 | 0.285741|
| 9 | 1.440165e-02 | 1.325812e-02 | 0.086251|
| 10 | 1.325812e-02 | 1.334901e-02 | 0.006809|
| 11 | 1.325812e-02 | 1.243129e-02 | 0.066512|
|--------|--------------|--------------|-------------------------|
Time for the 11 A updates was 0 secs
|----------|------------|--------------|-------------------|--------------|
| Iter | VarExpl | SSE | SSE_11 / SSE_0 | muA |
|----------|------------|--------------|-------------------|--------------|
| 11 | 0.999799 | 1.243129e-02 | 0.000531 | 5.3748e-01|
|----------|------------|--------------|-------------------|--------------|
The sum of diagonal elements for the sub-matrix of closer grid points is 4.0
The ideal sum would be 4
# fast_archetypal(): we use the imins from closer_grid_archetypal() above
BY, A, B, irows, SSE, varexpl, fin_iters, time_elapsed, diagsum_final = (
fast_archetypal(df, irows = imins, verbose = True, diag_less = 1e-6))
pd.DataFrame(BY)
[SSE,varexpl,fin_iters, time_elapsed, diagsum_final]
Fast Archetypal Analysis:
Compute the compositions when the archetypes are already given
|--------|--------------|--------------|-------------------------|
| Iter | SSE_i | SSE_(i+1) | |SSE_(i+1)-SSE_i|/SSE_i |
|--------|--------------|--------------|-------------------------|
| 1 | 2.240585e+01 | 1.936972e+00 | 10.567465|
| 2 | 1.936972e+00 | 5.236400e-01 | 2.699052|
| 3 | 5.236400e-01 | 5.861317e-01 | 0.106617|
| 4 | 5.236400e-01 | 1.122365e-01 | 3.665504|
| 5 | 1.122365e-01 | 7.476762e-02 | 0.501138|
| 6 | 7.476762e-02 | 8.903380e-02 | 0.160233|
| 7 | 7.476762e-02 | 1.994893e-02 | 2.747951|
| 8 | 1.994893e-02 | 1.549558e-02 | 0.287395|
| 9 | 1.549558e-02 | 1.457414e-02 | 0.063225|
|--------|--------------|--------------|-------------------------|
Time for the 9 A updates was 0 secs
|----------|------------|--------------|-------------------|--------------|
| Iter | VarExpl | SSE | SSE_9 / SSE_0 | muA |
|----------|------------|--------------|-------------------|--------------|
| 9 | 0.999764 | 1.457414e-02 | 0.000650 | 8.9580e-01|
|----------|------------|--------------|-------------------|--------------|
# archetypal_pcha()
BY, A, B, SSE, varexpl, BY0, converges, iterations, total_time = (
archetypal_pcha(df, kappas = 3, conv_crit=1E-6, maxiter=2000, verbose=True))
pd.DataFrame(BY0)
pd.DataFrame(BY)
[SSE, varexpl, converges, iterations, total_time]
PCHA Archetypal Analysis:
Principal Convex Hull Analysis / Archetypal Analysis
The mumber of Archetypes will be kappas = 3
To stop algorithm press control C
|----------|------------|------------|-------------|------------|------------|------------|------------|
Iter | VarExpl | SSE | |dSSE|/SSE | muC | mualpha | muS | Time(s)
|----------|------------|------------|-------------|------------|------------|------------|------------|
| 1 | 0.969057 | 1.9137e+00 | 7.0437e-01 | 1.548e+00 | 1.000e+00 | 1.154e+00 | 0.004 |
| 2 | 0.973296 | 1.6515e+00 | 1.5874e-01 | 2.396e+00 | 1.000e+00 | 8.929e-01 | 0.004 |
| 3 | 0.974737 | 1.5623e+00 | 5.7068e-02 | 7.418e+00 | 1.000e+00 | 1.382e+00 | 0.003 |
| 4 | 0.975468 | 1.5171e+00 | 2.9789e-02 | 1.148e+01 | 1.000e+00 | 1.070e+00 | 0.004 |
| 5 | 0.975934 | 1.4883e+00 | 1.9357e-02 | 1.777e+01 | 1.000e+00 | 1.656e+00 | 0.003 |
| 6 | 0.976253 | 1.4686e+00 | 1.3440e-02 | 1.376e+01 | 1.000e+00 | 1.282e+00 | 0.004 |
| 7 | 0.976555 | 1.4499e+00 | 1.2862e-02 | 2.129e+01 | 1.000e+00 | 1.984e+00 | 0.002 |
| 8 | 0.976821 | 1.4335e+00 | 1.1475e-02 | 3.296e+01 | 1.000e+00 | 1.535e+00 | 0.002 |
| 9 | 0.977052 | 1.4192e+00 | 1.0097e-02 | 2.551e+01 | 1.000e+00 | 1.188e+00 | 0.002 |
| 10 | 0.977240 | 1.4075e+00 | 8.2598e-03 | 1.975e+01 | 1.000e+00 | 9.197e-01 | 0.002 |
| 11 | 0.977397 | 1.3978e+00 | 6.9319e-03 | 1.528e+01 | 1.000e+00 | 1.424e+00 | 0.002 |
| 12 | 0.977546 | 1.3886e+00 | 6.6443e-03 | 5.914e+00 | 1.000e+00 | 2.204e+00 | 0.002 |
| 13 | 0.977713 | 1.3783e+00 | 7.4633e-03 | 4.577e+00 | 1.000e+00 | 8.528e-01 | 0.002 |
| 14 | 0.977873 | 1.3684e+00 | 7.2652e-03 | 7.085e+00 | 1.000e+00 | 1.320e+00 | 0.002 |
| 15 | 0.978040 | 1.3581e+00 | 7.6022e-03 | 5.484e+00 | 1.000e+00 | 1.022e+00 | 0.002 |
| 16 | 0.978221 | 1.3469e+00 | 8.2898e-03 | 4.244e+00 | 1.000e+00 | 1.582e+00 | 0.002 |
| 17 | 0.978424 | 1.3344e+00 | 9.4027e-03 | 6.570e+00 | 1.000e+00 | 1.224e+00 | 0.002 |
| 18 | 0.978628 | 1.3217e+00 | 9.5674e-03 | 5.085e+00 | 1.000e+00 | 9.474e-01 | 0.002 |
| 19 | 0.978841 | 1.3086e+00 | 1.0053e-02 | 3.935e+00 | 1.000e+00 | 1.467e+00 | 0.002 |
| 20 | 0.979046 | 1.2959e+00 | 9.7856e-03 | 6.092e+00 | 1.000e+00 | 5.675e-01 | 0.002 |
| 21 | 0.979247 | 1.2835e+00 | 9.6734e-03 | 4.715e+00 | 1.000e+00 | 8.785e-01 | 0.002 |
| 22 | 0.979447 | 1.2710e+00 | 9.7607e-03 | 7.298e+00 | 1.000e+00 | 1.360e+00 | 0.002 |
| 23 | 0.979640 | 1.2592e+00 | 9.4451e-03 | 5.649e+00 | 1.000e+00 | 1.052e+00 | 0.002 |
| 24 | 0.979829 | 1.2474e+00 | 9.4144e-03 | 8.744e+00 | 1.000e+00 | 8.146e-01 | 0.002 |
| 25 | 0.979933 | 1.2410e+00 | 5.1822e-03 | 6.767e+00 | 1.000e+00 | 1.261e+00 | 0.002 |
| 26 | 0.980005 | 1.2366e+00 | 3.5570e-03 | 1.048e+01 | 1.000e+00 | 1.952e+00 | 0.002 |
| 27 | 0.980053 | 1.2336e+00 | 2.4384e-03 | 1.622e+01 | 1.000e+00 | 7.553e-01 | 0.002 |
| 28 | 0.980086 | 1.2315e+00 | 1.6616e-03 | 1.255e+01 | 1.000e+00 | 1.169e+00 | 0.002 |
| 29 | 0.980109 | 1.2301e+00 | 1.1472e-03 | 1.943e+01 | 1.000e+00 | 9.049e-01 | 0.002 |
| 30 | 0.980124 | 1.2292e+00 | 7.7082e-04 | 1.504e+01 | 1.000e+00 | 1.401e+00 | 0.002 |
| 31 | 0.980135 | 1.2285e+00 | 5.2532e-04 | 2.327e+01 | 1.000e+00 | 1.084e+00 | 0.002 |
| 32 | 0.980142 | 1.2281e+00 | 3.7454e-04 | 1.801e+01 | 1.000e+00 | 1.678e+00 | 0.002 |
| 33 | 0.980147 | 1.2277e+00 | 2.5874e-04 | 1.394e+01 | 1.000e+00 | 1.299e+00 | 0.002 |
| 34 | 0.980151 | 1.2275e+00 | 1.7650e-04 | 1.079e+01 | 1.000e+00 | 2.011e+00 | 0.002 |
| 35 | 0.980154 | 1.2274e+00 | 1.2759e-04 | 1.670e+01 | 1.000e+00 | 1.556e+00 | 0.002 |
| 36 | 0.980155 | 1.2273e+00 | 9.8252e-05 | 1.293e+01 | 1.000e+00 | 1.204e+00 | 0.002 |
| 37 | 0.980157 | 1.2272e+00 | 7.7710e-05 | 1.001e+01 | 1.000e+00 | 9.321e-01 | 0.002 |
| 38 | 0.980158 | 1.2271e+00 | 5.6505e-05 | 1.549e+01 | 1.000e+00 | 1.443e+00 | 0.002 |
| 39 | 0.980159 | 1.2270e+00 | 4.9600e-05 | 1.199e+01 | 1.000e+00 | 1.117e+00 | 0.002 |
| 40 | 0.980160 | 1.2270e+00 | 4.1790e-05 | 9.278e+00 | 1.000e+00 | 1.729e+00 | 0.002 |
| 41 | 0.980161 | 1.2269e+00 | 3.7995e-05 | 1.436e+01 | 1.000e+00 | 1.338e+00 | 0.002 |
| 42 | 0.980161 | 1.2269e+00 | 3.6791e-05 | 1.112e+01 | 1.000e+00 | 2.071e+00 | 0.002 |
| 43 | 0.980162 | 1.2268e+00 | 3.3335e-05 | 1.721e+01 | 1.000e+00 | 1.603e+00 | 0.002 |
| 44 | 0.980163 | 1.2268e+00 | 3.1141e-05 | 1.332e+01 | 1.000e+00 | 1.241e+00 | 0.002 |
| 45 | 0.980163 | 1.2268e+00 | 3.3211e-05 | 1.031e+01 | 1.000e+00 | 9.602e-01 | 0.002 |
| 46 | 0.980164 | 1.2267e+00 | 3.3546e-05 | 7.977e+00 | 1.000e+00 | 1.486e+00 | 0.002 |
| 47 | 0.980165 | 1.2267e+00 | 3.1603e-05 | 1.235e+01 | 1.000e+00 | 1.150e+00 | 0.002 |
| 48 | 0.980165 | 1.2266e+00 | 3.0910e-05 | 1.911e+01 | 1.000e+00 | 1.781e+00 | 0.002 |
| 49 | 0.980166 | 1.2266e+00 | 3.1031e-05 | 1.479e+01 | 1.000e+00 | 1.378e+00 | 0.002 |
| 50 | 0.980167 | 1.2266e+00 | 3.1274e-05 | 1.145e+01 | 1.000e+00 | 1.067e+00 | 0.002 |
| 51 | 0.980167 | 1.2265e+00 | 3.0282e-05 | 1.772e+01 | 1.000e+00 | 1.651e+00 | 0.002 |
| 52 | 0.980168 | 1.2265e+00 | 3.0849e-05 | 1.372e+01 | 1.000e+00 | 1.278e+00 | 0.002 |
| 53 | 0.980168 | 1.2265e+00 | 3.1283e-05 | 1.062e+01 | 1.000e+00 | 9.890e-01 | 0.002 |
| 54 | 0.980169 | 1.2264e+00 | 3.0494e-05 | 1.643e+01 | 1.000e+00 | 1.531e+00 | 0.002 |
| 55 | 0.980170 | 1.2264e+00 | 3.1566e-05 | 1.272e+01 | 1.000e+00 | 1.185e+00 | 0.002 |
| 56 | 0.980170 | 1.2263e+00 | 3.0652e-05 | 9.844e+00 | 1.000e+00 | 1.834e+00 | 0.002 |
| 57 | 0.980171 | 1.2263e+00 | 2.6192e-05 | 3.048e+01 | 1.000e+00 | 1.420e+00 | 0.002 |
| 58 | 0.980171 | 1.2263e+00 | 1.1450e-05 | 2.359e+01 | 1.000e+00 | 1.099e+00 | 0.002 |
| 59 | 0.980171 | 1.2263e+00 | 9.3466e-06 | 1.826e+01 | 1.000e+00 | 1.701e+00 | 0.002 |
| 60 | 0.980171 | 1.2263e+00 | 8.4407e-06 | 2.826e+01 | 1.000e+00 | 1.316e+00 | 0.002 |
| 61 | 0.980171 | 1.2263e+00 | 8.4114e-06 | 2.187e+01 | 1.000e+00 | 1.019e+00 | 0.002 |
| 62 | 0.980172 | 1.2263e+00 | 9.1324e-06 | 1.693e+01 | 1.000e+00 | 1.577e+00 | 0.002 |
| 63 | 0.980172 | 1.2262e+00 | 8.8070e-06 | 1.310e+01 | 1.000e+00 | 1.221e+00 | 0.002 |
| 64 | 0.980172 | 1.2262e+00 | 8.6021e-06 | 2.028e+01 | 1.000e+00 | 9.447e-01 | 0.002 |
| 65 | 0.980172 | 1.2262e+00 | 8.4549e-06 | 1.570e+01 | 1.000e+00 | 1.462e+00 | 0.002 |
| 66 | 0.980172 | 1.2262e+00 | 8.9234e-06 | 1.215e+01 | 1.000e+00 | 1.132e+00 | 0.002 |
| 67 | 0.980172 | 1.2262e+00 | 8.7704e-06 | 1.881e+01 | 1.000e+00 | 8.759e-01 | 0.002 |
| 68 | 0.980173 | 1.2262e+00 | 8.6715e-06 | 1.455e+01 | 1.000e+00 | 1.356e+00 | 0.002 |
| 69 | 0.980173 | 1.2262e+00 | 8.0681e-06 | 2.253e+01 | 1.000e+00 | 1.049e+00 | 0.002 |
| 70 | 0.980173 | 1.2262e+00 | 8.8384e-06 | 1.744e+01 | 1.000e+00 | 1.624e+00 | 0.002 |
| 71 | 0.980173 | 1.2262e+00 | 8.6672e-06 | 2.699e+01 | 1.000e+00 | 1.257e+00 | 0.002 |
| 72 | 0.980173 | 1.2261e+00 | 8.1818e-06 | 2.089e+01 | 1.000e+00 | 9.731e-01 | 0.002 |
| 73 | 0.980174 | 1.2261e+00 | 8.9279e-06 | 1.617e+01 | 1.000e+00 | 1.506e+00 | 0.002 |
| 74 | 0.980174 | 1.2261e+00 | 8.5495e-06 | 2.503e+01 | 1.000e+00 | 1.166e+00 | 0.002 |
| 75 | 0.980174 | 1.2261e+00 | 8.5998e-06 | 1.937e+01 | 1.000e+00 | 9.023e-01 | 0.002 |
| 76 | 0.980174 | 1.2261e+00 | 8.6971e-06 | 1.499e+01 | 1.000e+00 | 1.397e+00 | 0.002 |
| 77 | 0.980174 | 1.2261e+00 | 8.5365e-06 | 2.321e+01 | 1.000e+00 | 1.081e+00 | 0.002 |
| 78 | 0.980174 | 1.2261e+00 | 8.5858e-06 | 1.796e+01 | 1.000e+00 | 1.673e+00 | 0.002 |
| 79 | 0.980175 | 1.2261e+00 | 8.4775e-06 | 2.780e+01 | 1.000e+00 | 1.295e+00 | 0.002 |
| 80 | 0.980175 | 1.2261e+00 | 8.5313e-06 | 2.152e+01 | 1.000e+00 | 1.002e+00 | 0.002 |
| 81 | 0.980175 | 1.2261e+00 | 8.6361e-06 | 1.665e+01 | 1.000e+00 | 1.552e+00 | 0.002 |
| 82 | 0.980175 | 1.2260e+00 | 8.1931e-06 | 2.578e+01 | 1.000e+00 | 1.201e+00 | 0.002 |
| 83 | 0.980175 | 1.2260e+00 | 8.6973e-06 | 1.995e+01 | 1.000e+00 | 9.294e-01 | 0.002 |
| 84 | 0.980175 | 1.2260e+00 | 8.5786e-06 | 1.544e+01 | 1.000e+00 | 1.439e+00 | 0.002 |
| 85 | 0.980176 | 1.2260e+00 | 8.3171e-06 | 2.391e+01 | 1.000e+00 | 1.114e+00 | 0.002 |
| 86 | 0.980176 | 1.2260e+00 | 8.7468e-06 | 1.850e+01 | 1.000e+00 | 8.618e-01 | 0.002 |
| 87 | 0.980176 | 1.2260e+00 | 8.7327e-06 | 1.432e+01 | 1.000e+00 | 1.334e+00 | 0.002 |
| 88 | 0.980176 | 1.2260e+00 | 8.2775e-06 | 2.217e+01 | 1.000e+00 | 1.032e+00 | 0.002 |
| 89 | 0.980176 | 1.2260e+00 | 8.7811e-06 | 1.716e+01 | 1.000e+00 | 1.598e+00 | 0.002 |
| 90 | 0.980176 | 1.2260e+00 | 8.6705e-06 | 1.328e+01 | 1.000e+00 | 2.474e+00 | 0.002 |
| 91 | 0.980177 | 1.2259e+00 | 8.4991e-06 | 2.055e+01 | 1.000e+00 | 9.574e-01 | 0.002 |
| 92 | 0.980177 | 1.2259e+00 | 8.6603e-06 | 1.591e+01 | 1.000e+00 | 1.482e+00 | 0.002 |
| 93 | 0.980177 | 1.2259e+00 | 8.0501e-06 | 2.462e+01 | 1.000e+00 | 1.147e+00 | 0.002 |
| 94 | 0.980177 | 1.2259e+00 | 8.5048e-06 | 1.906e+01 | 1.000e+00 | 8.877e-01 | 0.002 |
| 95 | 0.980177 | 1.2259e+00 | 8.3868e-06 | 2.950e+01 | 1.000e+00 | 1.374e+00 | 0.002 |
| 96 | 0.980177 | 1.2259e+00 | 9.5861e-06 | 1.142e+01 | 1.000e+00 | 2.127e+00 | 0.002 |
| 97 | 0.980178 | 1.2259e+00 | 8.7613e-06 | 1.767e+01 | 1.000e+00 | 1.646e+00 | 0.002 |
| 98 | 0.980178 | 1.2259e+00 | 8.9700e-06 | 1.368e+01 | 1.000e+00 | 1.274e+00 | 0.002 |
| 99 | 0.980178 | 1.2259e+00 | 7.8132e-06 | 2.117e+01 | 1.000e+00 | 1.972e+00 | 0.002 |
| 100 | 0.980178 | 1.2259e+00 | 9.5240e-06 | 1.639e+01 | 1.000e+00 | 1.527e+00 | 0.002 |
|----------|------------|------------|-------------|------------|------------|------------|------------|
Iter | VarExpl | SSE | |dSSE|/SSE | muC | mualpha | muS | Time(s)
|----------|------------|------------|-------------|------------|------------|------------|------------|
| 101 | 0.980178 | 1.2258e+00 | 8.5607e-06 | 2.536e+01 | 1.000e+00 | 1.181e+00 | 0.002 |
| 102 | 0.980178 | 1.2258e+00 | 8.7858e-06 | 1.963e+01 | 1.000e+00 | 1.829e+00 | 0.002 |
| 103 | 0.980179 | 1.2258e+00 | 8.7585e-06 | 1.519e+01 | 1.000e+00 | 1.415e+00 | 0.002 |
| 104 | 0.980179 | 1.2258e+00 | 8.6764e-06 | 2.352e+01 | 1.000e+00 | 2.191e+00 | 0.002 |
| 105 | 0.980179 | 1.2258e+00 | 9.0183e-06 | 1.820e+01 | 1.000e+00 | 1.696e+00 | 0.002 |
| 106 | 0.980179 | 1.2258e+00 | 8.8824e-06 | 1.409e+01 | 1.000e+00 | 1.313e+00 | 0.002 |
| 107 | 0.980179 | 1.2258e+00 | 8.6711e-06 | 2.181e+01 | 1.000e+00 | 1.016e+00 | 0.002 |
| 108 | 0.980180 | 1.2258e+00 | 8.7784e-06 | 1.688e+01 | 1.000e+00 | 1.572e+00 | 0.002 |
| 109 | 0.980180 | 1.2258e+00 | 8.8722e-06 | 1.306e+01 | 1.000e+00 | 2.434e+00 | 0.002 |
| 110 | 0.980180 | 1.2257e+00 | 8.7731e-06 | 2.022e+01 | 1.000e+00 | 9.419e-01 | 0.002 |
| 111 | 0.980180 | 1.2257e+00 | 8.7979e-06 | 1.565e+01 | 1.000e+00 | 1.458e+00 | 0.002 |
| 112 | 0.980180 | 1.2257e+00 | 8.4729e-06 | 2.423e+01 | 1.000e+00 | 1.128e+00 | 0.002 |
| 113 | 0.980180 | 1.2257e+00 | 8.9500e-06 | 1.875e+01 | 1.000e+00 | 8.734e-01 | 0.002 |
| 114 | 0.980181 | 1.2257e+00 | 8.9462e-06 | 1.451e+01 | 1.000e+00 | 1.352e+00 | 0.002 |
| 115 | 0.980181 | 1.2257e+00 | 8.9787e-06 | 2.246e+01 | 1.000e+00 | 2.093e+00 | 0.002 |
| 116 | 0.980181 | 1.2257e+00 | 8.9491e-06 | 1.739e+01 | 1.000e+00 | 1.620e+00 | 0.002 |
| 117 | 0.980181 | 1.2257e+00 | 8.9754e-06 | 1.346e+01 | 1.000e+00 | 1.254e+00 | 0.002 |
| 118 | 0.980181 | 1.2257e+00 | 8.8896e-06 | 2.083e+01 | 1.000e+00 | 9.703e-01 | 0.002 |
| 119 | 0.980181 | 1.2256e+00 | 8.8829e-06 | 1.612e+01 | 1.000e+00 | 1.502e+00 | 0.002 |
| 120 | 0.980182 | 1.2256e+00 | 9.2186e-06 | 1.248e+01 | 1.000e+00 | 1.162e+00 | 0.002 |
| 121 | 0.980182 | 1.2256e+00 | 8.8778e-06 | 1.931e+01 | 1.000e+00 | 1.799e+00 | 0.002 |
| 122 | 0.980182 | 1.2256e+00 | 9.2538e-06 | 1.495e+01 | 1.000e+00 | 1.393e+00 | 0.002 |
| 123 | 0.980182 | 1.2256e+00 | 9.0276e-06 | 2.314e+01 | 1.000e+00 | 1.078e+00 | 0.002 |
| 124 | 0.980182 | 1.2256e+00 | 9.1088e-06 | 1.791e+01 | 1.000e+00 | 1.668e+00 | 0.002 |
| 125 | 0.980183 | 1.2256e+00 | 9.0611e-06 | 2.772e+01 | 1.000e+00 | 1.291e+00 | 0.002 |
| 126 | 0.980183 | 1.2256e+00 | 9.1043e-06 | 2.146e+01 | 1.000e+00 | 9.995e-01 | 0.002 |
| 127 | 0.980183 | 1.2256e+00 | 2.6405e-06 | 1.661e+01 | 1.000e+00 | 1.547e+00 | 0.002 |
| 128 | 0.980183 | 1.2256e+00 | 9.1533e-07 | 2.571e+01 | 1.000e+00 | 2.395e+00 | 0.001 |
|----------|------------|------------|-------------|------------|------------|------------|------------|
| 128 | 0.980183 | 1.2256e+00 | 9.1533e-07 | 2.571e+01 | 1.000e+00 | 2.395e+00 | 0.001 |
|----------|------------|------------|-------------|------------|------------|------------|------------|
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