""" **Description**
A diversity model realizes the selection and retention of a state as a
finite collection of observations extracted from an incident signal, to
maximize a minimum distance between any members of a state, according to
a specified style or distance metric.
.. math::
d_{k} = \min(\ d_{u,v}\ )\quad\quad u, v \\in [\ 0,\ M\ ),\ u \\neq v
.. math::
d_{k} \geq d_{n}\qquad \longrightarrow\qquad d_{n} = d_{k}
A diversity model is an opportunistic unsupervised learning model which
typically improves condition and numerical accuracy and reduces storage
relative to alternative approaches including generalized linear inverse.
A state array of a specified order is defined. A stationary dimension is
inferred. A style and order are specified.
Style is in ( 'Chebyshev', 'Euclidean', 'Geometric', 'Manhattan' ).
* | 'Chebyshev' distance is an L-infinity norm, a maximum absolute difference
| in any dimension.
.. math::
d_{u,v} = \max(\ |\ \\vec{x_{u}} - \\vec{x_{v}}\ |\ )
* | 'Euclidean' distance is an L-2 norm, a square root of a sum of squared
| differences in each dimension.
.. math::
d_{u,v} = \matrix{\sum_{i=0}^{N}(\ |\ \\vec{x_{u,i}} - \\vec{x_{v,i}}\ )^2|}^{0.5}
* | 'Geometric' distance is a ordered root of a product of absolute differences
| in each dimension.
.. math::
d_{u,v} = \prod_{i=0}^{N}{(\ |\ \\vec{x_{u,i}} - \\vec{x_{v,i}}\ |\ )}^{\\frac{1}{N}}
* | 'Manhattan' distance is an L-1 norm, a sum of absolute differences in each
| dimension.
.. math::
d_{u,v} = \sum_{i=0}^{N}{\ (\ |\ \\vec{x_{u}} - \\vec{x_{v}}\ |\ )\ }
**Example**
::
from diamondback import DiversityModel
# Create an instance.
obj = DiversityModel( style = 'Euclidean', order = 4 )
# Model an incident signal and extract a state.
x = numpy.random.rand( 2, 32 )
y = obj.model( x )
s = obj.s
**License**
`BSD-3C. <https://github.com/larryturner/diamondback/blob/master/license>`_
© 2018 - 2022 Larry Turner, Schneider Electric Industries SAS. All rights reserved.
**Author**
Larry Turner, Schneider Electric, Analytics & AI, 2018-02-08.
"""
from typing import List, Union
import numpy
[docs]class DiversityModel( object ) :
""" Diversity model.
"""
__distance = dict( Chebyshev = lambda x, y : max( abs( x - y ) ),
Euclidean = lambda x, y : sum( ( x - y ) ** 2 ) ** 0.5,
Geometric = lambda x, y : numpy.prod( abs( x - y ) ) ** ( 1.0 / len( x ) ),
Manhattan = lambda x, y : sum( abs( x - y ) ) )
@property
def s( self ) :
""" s : Union[ List, numpy.ndarray ] - state.
"""
return self._s
@s.setter
def s( self, s : Union[ List, numpy.ndarray ] ) :
self._s = s
def __init__( self, style : str, order : int ) -> None :
""" Initialize.
Arguments :
style : str - in ( 'Chebyshev', 'Euclidean', 'Geometric', 'Manhattan' ).
order : int.
"""
if ( ( not style ) or ( style not in DiversityModel.__distance ) ) :
raise ValueError( f'style = {style}' )
if ( order <= 0 ) :
raise ValueError( f'Order = {order}' )
super( ).__init__( )
self._distance = DiversityModel.__distance[ style ]
self._diversity = 0.0
self._s = numpy.zeros( ( 0, order + 1 ) )
[docs] def clear( self ) -> None :
""" Clears an instance.
"""
self._diversity = 0.0
self.s = numpy.zeros( ( 0, self.s.shape[ 1 ] ) )
[docs] def model( self, x : Union[ List, numpy.ndarray ] ) -> numpy.ndarray :
""" Models an incident signal and produces a reference signal.
Arguments :
x : Union[ List, numpy.ndarray ] - incident signal.
Returns :
y : numpy.ndarray - diversity.
"""
if ( ( not numpy.isscalar( x ) ) and ( not isinstance( x, numpy.ndarray ) ) ) :
x = numpy.array( list( x ) )
if ( ( len( x.shape ) > 2 ) or ( not len( x ) ) ) :
raise ValueError( f'X = {x}' )
if ( len( x.shape ) < 2 ) :
rows, cols = 1, x.shape[ 0 ]
else :
rows, cols = x.shape
if ( not self.s.shape[ 0 ] ) :
self.s = numpy.zeros( ( rows, self.s.shape[ 1 ] ) ) + numpy.finfo( float ).max
if ( ( rows != self.s.shape[ 0 ] ) or ( cols <= 0 ) ) :
raise ValueError( f'Rows = {rows} Colums = {cols}' )
cc = 0
for jj in range( 0, self.s.shape[ 1 ] ) :
if ( numpy.isclose( self.s[ 0, jj ], numpy.finfo( float ).max ) ) :
break
cc += 1
y = numpy.zeros( cols )
for jj in range( 0, cols ) :
if ( cc < self.s.shape[ 1 ] ) :
self.s[ :, cc ] = x[ :, jj ]
cc += 1
else :
v, ii = self._diversity, -1
for kk in range( 0, cc ) :
u, s = float( 'inf' ), numpy.array( self.s )
s[ :, kk ] = x[ :, jj ]
for uu in range( 0, cc - 1 ) :
for vv in range( uu + 1, cc ) :
d = self._distance( s[ :, uu ], s[ :, vv ] )
if ( d < u ) :
u = d
if ( u > v ) :
v, ii = u, kk
if ( v > self._diversity ) :
self._diversity, self.s[ :, ii ] = v, x[ :, jj ]
y[ jj ] = self._diversity
return y