Metadata-Version: 2.1
Name: geom_archetypal
Version: 1.0.2
Summary: Geometric Archetypal Analysis
Author-email: Demetris Christopoulos <dchristop@econ.uoa.gr>
Maintainer-email: Demetris Christopoulos <dchristop@econ.uoa.gr>
License: Copyright (c) 2024 Demetris Christopoulos
        
        Permission is hereby granted, free of charge, to any person obtaining a copy
        of this software and associated documentation files (the "Software"), to deal
        in the Software without restriction, including without limitation the rights
        to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
        copies of the Software, and to permit persons to whom the Software is
        furnished to do so, subject to the following conditions:
        
        The above copyright notice and this permission notice shall be included in all
        copies or substantial portions of the Software.
        
        THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
        IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
        FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
        AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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        SOFTWARE.
Project-URL: Homepage, https://github.com/dchristop/geom_archetypal
Project-URL: Issues, https://github.com/dchristop/geom_archetypal/issues
Project-URL: Funding, https://www.insead.edu/hoffmann-institute
Keywords: geometrical archetypal analysis,convex hull,grid archetypal
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Requires-Python: >=3.8
Description-Content-Type: text/markdown
License-File: LICENSE

# 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 archetypes
-   `grid_archetypal` For a data matrix n x d finds the Grid Archetypes and performs AA
-   `closer_grid_archetypal` For a data matrix n x d finds the Closer Grid Archetypes and performs AA
-   `archetypal_pcha()` Principal Convex Hull Analysis (PCHA)

Installation
------------
On the terminal of your operating system write and press enter:

```python
$ pip install geom_archetypal
```

Usage
-----
```python
# 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 | 
|----------|------------|------------|-------------|------------|------------|------------|------------|

```


Contact
-------

Please send comments, suggestions or bug reports to
<dchristop@econ.uoa.gr> or <dem.christop@gmail.com>

GitHub repository:

https://github.com/dchristop/geom_archetypal

https://github.com/dchristop/geom_archetypal/issues
