#!/usr/bin/env python3
"``naginterface.library.mv.discrim_group`` Python Example."
# NAG Copyright 2017-2019.
# pylint: disable=invalid-name
from naginterfaces.library import mv
[docs]def main():
"""
Example for :func:`naginterfaces.library.mv.discrim_group`.
Discriminant analysis.
>>> main()
naginterfaces.library.mv.discrim_group Python Example Results.
Discriminant analysis for diagnosis of Cushing's syndrome.
Obs Posterior Allocated Atypicality
probabilities to group index
1 0.094 0.905 0.002 2 0.596 0.254 0.975
2 0.005 0.168 0.827 3 0.952 0.836 0.018
3 0.019 0.920 0.062 2 0.954 0.797 0.912
4 0.697 0.303 0.000 1 0.207 0.860 0.993
5 0.317 0.013 0.670 3 0.991 1.000 0.984
6 0.032 0.366 0.601 3 0.981 0.978 0.887
"""
print('naginterfaces.library.mv.discrim_group Python Example Results.')
print('Discriminant analysis for diagnosis of Cushing\'s syndrome.')
# The observations:
x = [
[1.1314, 2.4596],
[1.0986, 0.2624],
[0.6419, -2.3026],
[1.3350, -3.2189],
[1.4110, 0.0953],
[0.6419, -0.9163],
[2.1163, 0.0000],
[1.3350, -1.6094],
[1.3610, -0.5108],
[2.0541, 0.1823],
[2.2083, -0.5108],
[2.7344, 1.2809],
[2.0412, 0.4700],
[1.8718, -0.9163],
[1.7405, -0.9163],
[2.6101, 0.4700],
[2.3224, 1.8563],
[2.2192, 2.0669],
[2.2618, 1.1314],
[3.9853, 0.9163],
[2.7600, 2.0281],
]
# The inclusions:
isx = [1]*len(x[0])
# The groupings:
ing = [
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
2,
2,
2,
2,
2,
3,
3,
3,
3,
3,
]
# The number of groups:
ng = 3
d = mv.discrim(
x, isx, ing, ng,
)
# For the grouping computation:
# Predictive approach:
typ = 'Predictive'
# Assuming unequal within-group var-covar matrices:
equal = 'Unequal'
# The form of the prior probabilities:
priors = 'Equal'
# The observations:
x_g = [
[1.6292, -0.9163],
[2.5572, 1.6094],
[2.5649, -0.2231],
[0.9555, -2.3026],
[3.4012, -2.3026],
[3.0204, -0.2231],
]
# No priors need to be input:
prior = [0.]*ng
# Require atypicality indices:
atiq = True
dg = mv.discrim_group(
typ, equal, priors, d.nig, d.gmn, d.gc, d.det, isx,
x_g, prior, atiq,
)
print(
' Obs Posterior Allocated'
' Atypicality'
)
print(' probabilities to group index')
for i, ig in enumerate(dg.iag):
print(
'{:6d}'.format(i+1) + ' '*5 +
''.join(['{:6.3f}']*ng).format(*dg.p[i, :]) +
'{:6d}'.format(ig) + ' '*5 +
''.join(['{:6.3f}']*ng).format(*dg.ati[i, :])
)
if __name__ == '__main__':
import doctest
import sys
sys.exit(
doctest.testmod(
None, verbose=True, report=False,
optionflags=doctest.REPORT_NDIFF,
).failed
)
