Source code for diamondback.models.DiversityModel

""" **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 classification 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 factory is defined to facilitate construction of an instance, defining
        a state array of a specified order.  A stationary dimension is inferred
        through observation.  An instance, classification, and order are specified.

        Classification 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 from a Factory with constraints.

            obj = DiversityModel.Factory.instance( typ = DiversityModel, classification = '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 - 2021 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

    **Author**

        Larry Turner, Schneider Electric, Analytics & AI, 2018-02-08.

    **Definition**

"""

from diamondback.interfaces.IClear import IClear
from diamondback.interfaces.IEqual import IEqual
from diamondback.interfaces.IS import IS
from typing import Any, Callable, List, Union
import numpy

[docs]class DiversityModel( IClear, IS, IEqual ) : """ Diversity model. """
[docs] class Factory( object ) : """ Factory. """ _distance = { '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 ) ) }
[docs] @classmethod def instance( cls, typ : type, classification : str, order : int ) -> Any : """ Constructs an instance. Arguments : typ : type - derived from DiversityModel. classification : str - in ( 'Chebyshev', 'Euclidean', 'Geometric', 'Manhattan' ). order : int. Returns : instance : typ( ). """ if ( ( not typ ) or ( not issubclass( typ, DiversityModel ) ) ) : raise ValueError( f'Type = {typ}' ) if ( ( not classification ) or ( classification not in DiversityModel.Factory._distance ) ) : raise ValueError( f'Classification = {classification}' ) if ( order <= 0 ) : raise ValueError( f'Order = {order}' ) return typ( DiversityModel.Factory._distance[ classification ], order )
[docs] def __eq__( self, other : Any ) -> bool : """ Equal. Arguments : other : Any. Returns : equal : bool. """ return ( ( super( ).__eq__( other ) ) and ( self._distance == other._distance ) and ( numpy.isclose( self._diversity, other._diversity ) ) )
def __init__( self, distance : Callable[ [ Any, Any ], Any ], order : int ) -> None : """ Initialize. Arguments : distance : Callable[ [ Any, Any ], Any ]. order : int. """ if ( ( not distance ) or ( isinstance( distance, str ) ) ) : raise ValueError( f'Distance = {distance}' ) super( ).__init__( ) self._distance, self._diversity, self._s = distance, 0.0, numpy.zeros( ( 0, order + 1 ) )
[docs] def clear( self ) -> None : """ Clears an instance. """ self._diversity, self._s = 0.0, 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 ( len( x ) == 0 ) ) : 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