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point_matching.py
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Thu, Jun 6, 05:43

point_matching.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
import numpy as np
from scipy.optimize import linear_sum_assignment as LSA
from .point_distances import distanceMatrix, chordalMetricAngleMatrix
from rrompy.utilities.base.types import Tuple, List, ListAny, Np1D, Np2D, HFEng
from rrompy.utilities.exception_manager import RROMPyAssert
__all__ = ['pointMatching', 'rationalFunctionMatching']
def pointMatching(distMatrix:Np2D) -> Tuple[Np1D, Np1D]:
return LSA(distMatrix)
def rationalFunctionMatching(poles:List[Np1D], coeffs:List[Np2D],
featPts:Np2D, matchingWeight:float, supps:ListAny,
projMat:Np2D, HFEngine : HFEng = None,
is_state : bool = True, root : int = None,
projMapping : Np2D = None) \
-> Tuple[List[Np1D], List[Np2D]]:
"""
Match poles and residues of a set of rational functions.
Args:
poles: List of (lists of) poles.
coeffs: List of (lists of) residues.
featPts: Marginal parameters corresponding to rational models.
matchingWeight: Matching weight in distance computation.
supps: Support indices for projection matrix.
projMat: Projection matrix for residues.
HFEngine(optional): Engine for distance evaluation. Defaults to None,
i.e. Euclidean metric.
is_state(optional): Whether residues are of system state. Defaults to
True.
root(optional): Root of search tree. Defaults to None, i.e.
automatically chosen.
projMapping(optional): Mapping for projection based on projMap. Should
be assigned for nonlinear outputs. Defaults to None
Returns:
Matched list of (lists of) poles and list of (lists of) residues.
"""
M, N = len(featPts), len(poles[0])
RROMPyAssert(len(poles), M, "Number of rational functions to be matched")
RROMPyAssert(len(coeffs), M, "Number of rational functions to be matched")
if M <= 1: return poles, coeffs
featDist = distanceMatrix(featPts).flatten()
free = list(range(M))
if root is None: #start from sample points closest to each other
root = np.argpartition(featDist, M)[M] % M
fixed = [free.pop(root)]
featDist = featDist.reshape(M, M)
for j in range(M - 1, 0, -1):
#find closest point
idx = np.argmin(featDist[np.ix_(fixed, free)].flatten())
Ifix = fixed[idx // j]
fixed += [free.pop(idx % j)]
Ifree = fixed[-1]
plsfix, plsfree = poles[Ifix], poles[Ifree]
resfix, resfree = None, None
if matchingWeight != 0:
resfix, resfree = coeffs[Ifix][: N].T, coeffs[Ifree][: N].T
if projMapping is not None:
resfix = resfix[projMapping[0]] * resfix[projMapping[1]].conj()
resfree = (resfree[projMapping[0]]
* resfree[projMapping[1]].conj())
if isinstance(projMat, (np.ndarray,)):
suppfix, suppfree = supps[Ifix], supps[Ifree]
resfix = projMat[:, suppfix : suppfix + len(resfix)].dot(
resfix)
resfree = projMat[:, suppfree : suppfree + len(resfree)].dot(
resfree)
#build assignment distance matrix
distj = chordalMetricAngleMatrix(plsfix, plsfree, matchingWeight,
resfix, resfree, HFEngine, is_state)
reordering = pointMatching(distj)[1]
poles[Ifree] = poles[Ifree][reordering]
coeffs[Ifree][: N] = coeffs[Ifree][reordering]
return poles, coeffs

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