diff --git a/rrompy/reduction_methods/standard/rational_interpolant.py b/rrompy/reduction_methods/standard/rational_interpolant.py index 8cd8747..f7d786b 100644 --- a/rrompy/reduction_methods/standard/rational_interpolant.py +++ b/rrompy/reduction_methods/standard/rational_interpolant.py @@ -1,567 +1,616 @@ # 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 . # from copy import deepcopy as copy import numpy as np from rrompy.reduction_methods.base import checkRobustTolerance from .generic_standard_approximant import GenericStandardApproximant from rrompy.utilities.poly_fitting.polynomial import ( polybases as ppb, polyfitname, polyvander as pvP, polyvanderTotal as pvTP, PolynomialInterpolator as PI) from rrompy.utilities.poly_fitting.radial_basis import (polybases as rbpb, RadialBasisInterpolator as RBI) from rrompy.utilities.poly_fitting.moving_least_squares import ( polybases as mlspb, MovingLeastSquaresInterpolator as MLSI) from rrompy.utilities.base.types import (Np1D, Np2D, HFEng, DictAny, Tuple, List, paramVal, sampList) from rrompy.utilities.base import verbosityManager as vbMng from rrompy.utilities.numerical import (multifactorial, customPInv, dot, fullDegreeN, totalDegreeN, degreeTotalToFull, fullDegreeMaxMask, totalDegreeMaxMask, nextDerivativeIndices, hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI) from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert, RROMPyWarning) __all__ = ['RationalInterpolant'] class RationalInterpolant(GenericStandardApproximant): """ ROM rational interpolant computation for parametric problems. Args: HFEngine: HF problem solver. mu0(optional): Default parameter. Defaults to 0. approxParameters(optional): Dictionary containing values for main parameters of approximant. Recognized keys are: - 'POD': whether to compute POD of snapshots; defaults to True; - 'S': total number of samples current approximant relies upon; - 'sampler': sample point generator; - 'polybasis': type of polynomial basis for interpolation; defaults to 'MONOMIAL'; - 'M': degree of rational interpolant numerator; defaults to 0; - 'N': degree of rational interpolant denominator; defaults to 0; - 'polydegreetype': type of polynomial degree; defaults to 'TOTAL'; - 'radialDirectionalWeights': radial basis weights for interpolant numerator; defaults to 0, i.e. identity; - 'nNearestNeighbor': mumber of nearest neighbors considered in numerator if polybasis allows; defaults to -1; - 'interpRcond': tolerance for interpolation; defaults to None; - 'robustTol': tolerance for robust rational denominator - management; defaults to 0. + management; defaults to 0; + - 'centeredLike': whether samples should be managed as if centered; + involves making svd and interpolation problems square; defaults + to False. Defaults to empty dict. approx_state(optional): Whether to approximate state. Defaults to False. verbosity(optional): Verbosity level. Defaults to 10. Attributes: HFEngine: HF problem solver. mu0: Default parameter. mus: Array of snapshot parameters. approxParameters: Dictionary containing values for main parameters of approximant. Recognized keys are in parameterList. parameterListSoft: Recognized keys of soft approximant parameters: - 'POD': whether to compute POD of snapshots; - 'polybasis': type of polynomial basis for interpolation; - 'M': degree of rational interpolant numerator; - 'N': degree of rational interpolant denominator; - 'polydegreetype': type of polynomial degree; - 'radialDirectionalWeights': radial basis weights for interpolant numerator; - 'nNearestNeighbor': mumber of nearest neighbors considered in numerator if polybasis allows; - 'interpRcond': tolerance for interpolation via numpy.polyfit; - 'robustTol': tolerance for robust rational denominator - management. + management; + - 'centeredLike': whether samples should be managed as if centered; + involves making svd and interpolation problems square. parameterListCritical: Recognized keys of critical approximant parameters: - 'S': total number of samples current approximant relies upon; - 'sampler': sample point generator. approx_state: Whether to approximate state. verbosity: Verbosity level. POD: Whether to compute POD of snapshots. S: Number of solution snapshots over which current approximant is based upon. sampler: Sample point generator. polybasis: type of polynomial basis for interpolation. M: Numerator degree of approximant. N: Denominator degree of approximant. polydegreetype: Type of polynomial degree. radialDirectionalWeights: Radial basis weights for interpolant numerator. nNearestNeighbor: Number of nearest neighbors considered in numerator if polybasis allows. interpRcond: Tolerance for interpolation via numpy.polyfit. robustTol: Tolerance for robust rational denominator management. + centeredLike: Whether samples should be managed as if centered; + involves making svd and interpolation problems square. muBounds: list of bounds for parameter values. samplingEngine: Sampling engine. uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as sampleList. lastSolvedHF: Parameter(s) corresponding to last computed high fidelity solution(s) as parameterList. uApproxReduced: Reduced approximate solution(s) with parameter(s) lastSolvedApprox as sampleList. lastSolvedApproxReduced: Parameter(s) corresponding to last computed reduced approximate solution(s) as parameterList. uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as sampleList. lastSolvedApprox: Parameter(s) corresponding to last computed approximate solution(s) as parameterList. Q: Numpy 1D vector containing complex coefficients of approximant denominator. P: Numpy 2D vector whose columns are FE dofs of coefficients of approximant numerator. """ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None, approxParameters : DictAny = {}, approx_state : bool = False, verbosity : int = 10, timestamp : bool = True): self._preInit() self._addParametersToList(["polybasis", "M", "N", "polydegreetype", "radialDirectionalWeights", "nNearestNeighbor", "interpRcond", - "robustTol"], - ["MONOMIAL", 0, 0, "TOTAL", 1, -1, -1, 0]) + "robustTol", "centeredLike"], + ["MONOMIAL", 0, 0, "TOTAL", 1, -1, -1, 0, + False]) super().__init__(HFEngine = HFEngine, mu0 = mu0, approxParameters = approxParameters, approx_state = approx_state, verbosity = verbosity, timestamp = timestamp) self.catchInstability = False self._postInit() @property def tModelType(self): from rrompy.reduction_methods.trained_model import TrainedModelRational return TrainedModelRational @property def polybasis(self): """Value of polybasis.""" return self._polybasis @polybasis.setter def polybasis(self, polybasis): try: polybasis = polybasis.upper().strip().replace(" ","") if polybasis not in ppb + rbpb + mlspb: raise RROMPyException("Prescribed polybasis not recognized.") self._polybasis = polybasis except: RROMPyWarning(("Prescribed polybasis not recognized. Overriding " "to 'MONOMIAL'.")) self._polybasis = "MONOMIAL" self._approxParameters["polybasis"] = self.polybasis @property def polybasis0(self): if "_" in self.polybasis: return self.polybasis.split("_")[0] return self.polybasis @property def interpRcond(self): """Value of interpRcond.""" return self._interpRcond @interpRcond.setter def interpRcond(self, interpRcond): self._interpRcond = interpRcond self._approxParameters["interpRcond"] = self.interpRcond @property def radialDirectionalWeights(self): """Value of radialDirectionalWeights.""" return self._radialDirectionalWeights @radialDirectionalWeights.setter def radialDirectionalWeights(self, radialDirectionalWeights): self._radialDirectionalWeights = radialDirectionalWeights self._approxParameters["radialDirectionalWeights"] = ( self.radialDirectionalWeights) @property def nNearestNeighbor(self): """Value of nNearestNeighbor.""" return self._nNearestNeighbor @nNearestNeighbor.setter def nNearestNeighbor(self, nNearestNeighbor): self._nNearestNeighbor = nNearestNeighbor self._approxParameters["nNearestNeighbor"] = self.nNearestNeighbor @property def M(self): """Value of M.""" return self._M @M.setter def M(self, M): if M < 0: raise RROMPyException("M must be non-negative.") self._M = M self._approxParameters["M"] = self.M @property def N(self): """Value of N.""" return self._N @N.setter def N(self, N): if N < 0: raise RROMPyException("N must be non-negative.") self._N = N self._approxParameters["N"] = self.N @property def polydegreetype(self): """Value of polydegreetype.""" return self._polydegreetype @polydegreetype.setter def polydegreetype(self, polydegreetype): try: polydegreetype = polydegreetype.upper().strip().replace(" ","") if polydegreetype not in ["TOTAL", "FULL"]: raise RROMPyException(("Prescribed polydegreetype not " "recognized.")) self._polydegreetype = polydegreetype except: RROMPyWarning(("Prescribed polydegreetype not recognized. " "Overriding to 'TOTAL'.")) self._polydegreetype = "TOTAL" self._approxParameters["polydegreetype"] = self.polydegreetype @property def robustTol(self): """Value of tolerance for robust rational denominator management.""" return self._robustTol @robustTol.setter def robustTol(self, robustTol): if robustTol < 0.: RROMPyWarning(("Overriding prescribed negative robustness " "tolerance to 0.")) robustTol = 0. self._robustTol = robustTol self._approxParameters["robustTol"] = self.robustTol + @property + def centeredLike(self): + """Whether samples should be managed as if centered.""" + return self._centeredLike + @centeredLike.setter + def centeredLike(self, centeredLike): + if centeredLike and not hasattr(self, "_centeredLike"): + RROMPyWarning(("Centered-like method is unstable for more than " + "one parameter.")) + self._centeredLike = centeredLike + self._approxParameters["centeredLike"] = self.centeredLike + def resetSamples(self): """Reset samples.""" super().resetSamples() self._musUniqueCN = None self._derIdxs = None self._reorder = None def _setupInterpolationIndices(self): """Setup parameters for polyvander.""" if self._musUniqueCN is None or len(self._reorder) != len(self.mus): self._musUniqueCN, musIdxsTo, musIdxs, musCount = ( self.trainedModel.centerNormalize(self.mus).unique( return_index = True, return_inverse = True, return_counts = True)) + if self.centeredLike and len(self._musUniqueCN) > 1: + raise RROMPyException(("Cannot apply centered-like method " + "with more than one distinct sample " + "point.")) self._musUnique = self.mus[musIdxsTo] self._derIdxs = [None] * len(self._musUniqueCN) self._reorder = np.empty(len(musIdxs), dtype = int) filled = 0 for j, cnt in enumerate(musCount): self._derIdxs[j] = nextDerivativeIndices([], self.mus.shape[1], cnt) jIdx = np.nonzero(musIdxs == j)[0] self._reorder[jIdx] = np.arange(filled, filled + cnt) filled += cnt def _setupDenominator(self): """Compute rational denominator.""" RROMPyAssert(self._mode, message = "Cannot setup denominator.") vbMng(self, "INIT", "Starting computation of denominator.", 7) while self.N > 0: invD, fitinv = self._computeInterpolantInverseBlocks() + if self.centeredLike: + if self.polydegreetype == "TOTAL": + Seff = totalDegreeN(self.N, self.npar) + else: + Seff = fullDegreeN(self.N, self.npar) + else: + Seff = self.S + idxSamplesEff = list(range(self.S - Seff, self.S)) if self.POD: - ev, eV = self.findeveVGQR(self.samplingEngine.RPOD, invD) + ev, eV = self.findeveVGQR( + self.samplingEngine.RPOD[:, idxSamplesEff], invD) else: - ev, eV = self.findeveVGExplicit(self.samplingEngine.samples, - invD) + ev, eV = self.findeveVGExplicit( + self.samplingEngine.samples(idxSamplesEff), invD) nevBad = checkRobustTolerance(ev, self.robustTol) if nevBad <= 1: break if self.catchInstability: raise RROMPyException(("Instability in denominator " "computation: eigenproblem is poorly " "conditioned.")) RROMPyWarning(("Smallest {} eigenvalues below tolerance. Reducing " "N by 1.").format(nevBad)) self.N = self.N - 1 if self.N <= 0: self._N = 0 eV = np.ones((1, 1)) q = PI() q.npar = self.npar q.polybasis = self.polybasis0 if self.polydegreetype == "TOTAL": q.coeffs = degreeTotalToFull(tuple([self.N + 1] * self.npar), self.npar, eV[:, 0]) else: q.coeffs = eV[:, 0].reshape([self.N + 1] * self.npar) vbMng(self, "DEL", "Done computing denominator.", 7) return q, fitinv def _setupNumerator(self): """Compute rational numerator.""" RROMPyAssert(self._mode, message = "Cannot setup numerator.") vbMng(self, "INIT", "Starting computation of numerator.", 7) Qevaldiag = np.zeros((len(self.mus), len(self.mus)), dtype = np.complex) verb = self.trainedModel.verbosity self.trainedModel.verbosity = 0 self._setupInterpolationIndices() idxGlob = 0 for j, derIdxs in enumerate(self._derIdxs): nder = len(derIdxs) idxLoc = np.arange(len(self.mus))[(self._reorder >= idxGlob) * (self._reorder < idxGlob + nder)] idxGlob += nder Qval = [0] * nder for der in range(nder): derIdx = hashI(der, self.npar) Qval[der] = (self.trainedModel.getQVal( self._musUnique[j], derIdx, scl = np.power(self.scaleFactor, -1.)) / multifactorial(derIdx)) for derU, derUIdx in enumerate(derIdxs): for derQ, derQIdx in enumerate(derIdxs): diffIdx = [x - y for (x, y) in zip(derUIdx, derQIdx)] if all([x >= 0 for x in diffIdx]): diffj = hashD(diffIdx) Qevaldiag[idxLoc[derU], idxLoc[derQ]] = Qval[diffj] if self.POD: Qevaldiag = Qevaldiag.dot(self.samplingEngine.RPOD.T) self.trainedModel.verbosity = verb cfun = totalDegreeN if self.polydegreetype == "TOTAL" else fullDegreeN M = copy(self.M) while len(self.mus) < cfun(M, self.npar): M -= 1 if M < self.M: RROMPyWarning(("M too large compared to S. Reducing M by " "{}").format(self.M - M)) self.M = M while self.M >= 0: + if self.centeredLike: + Seff = cfun(self.M, self.npar) + derIdxsEff = [self._derIdxs[0][: Seff]] + reorder = self._reorder[: Seff] + QevaldiagEff = Qevaldiag[: Seff, : Seff] + else: + derIdxsEff = self._derIdxs + reorder = self._reorder + QevaldiagEff = Qevaldiag if self.polybasis in ppb: p = PI() wellCond, msg = p.setupByInterpolation( - self._musUniqueCN, Qevaldiag, self.M, + self._musUniqueCN, QevaldiagEff, self.M, self.polybasis, self.verbosity >= 5, self.polydegreetype == "TOTAL", - {"derIdxs": self._derIdxs, - "reorder": self._reorder, + {"derIdxs": derIdxsEff, + "reorder": reorder, "scl": np.power(self.scaleFactor, -1.)}, {"rcond": self.interpRcond}) elif self.polybasis in rbpb: p = RBI() wellCond, msg = p.setupByInterpolation( - self._musUniqueCN, Qevaldiag, self.M, self.polybasis, - self.radialDirectionalWeights, self.verbosity >= 5, - self.polydegreetype == "TOTAL", - {"derIdxs": self._derIdxs, "reorder": self._reorder, + self._musUniqueCN, QevaldiagEff, self.M, + self.polybasis, self.radialDirectionalWeights, + self.verbosity >= 5, self.polydegreetype == "TOTAL", + {"derIdxs": derIdxs, "reorder": reorder, "scl": np.power(self.scaleFactor, -1.), "nNearestNeighbor": self.nNearestNeighbor}, {"rcond": self.interpRcond}) else:# if self.polybasis in mlspb: p = MLSI() wellCond, msg = p.setupByInterpolation( - self._musUniqueCN, Qevaldiag, self.M, self.polybasis, - self.radialDirectionalWeights, self.verbosity >= 5, - self.polydegreetype == "TOTAL", - {"derIdxs": self._derIdxs, "reorder": self._reorder, + self._musUniqueCN, QevaldiagEff, self.M, + self.polybasis, self.radialDirectionalWeights, + self.verbosity >= 5, self.polydegreetype == "TOTAL", + {"derIdxs": derIdxs, "reorder": reorder, "scl": np.power(self.scaleFactor, -1.), "nNearestNeighbor": self.nNearestNeighbor}) vbMng(self, "MAIN", msg, 5) if wellCond: break if self.catchInstability: raise RROMPyException(("Instability in numerator computation: " "polyfit is poorly conditioned.")) RROMPyWarning("Polyfit is poorly conditioned. Reducing M by 1.") self.M = self.M - 1 if self.M < 0: raise RROMPyException(("Instability in computation of numerator. " "Aborting.")) vbMng(self, "DEL", "Done computing numerator.", 7) return p def setupApprox(self): """ Compute rational interpolant. SVD-based robust eigenvalue management. """ if self.checkComputedApprox(): return RROMPyAssert(self._mode, message = "Cannot setup approximant.") vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5) self.computeSnapshots() pMat = self.samplingEngine.samples.data pMatEff = dot(self.HFEngine.C, pMat) if self.approx_state else pMat if self.trainedModel is None: self.trainedModel = self.tModelType() self.trainedModel.verbosity = self.verbosity self.trainedModel.timestamp = self.timestamp datadict = {"mu0": self.mu0, "projMat": pMatEff, "scaleFactor": self.scaleFactor, "rescalingExp": self.HFEngine.rescalingExp} self.trainedModel.data = self.initializeModelData(datadict)[0] else: self.trainedModel = self.trainedModel self.trainedModel.data.projMat = copy(pMatEff) if self.N > 0: Q = self._setupDenominator()[0] else: Q = PI() Q.coeffs = np.ones(tuple([1] * self.npar), dtype = np.complex) Q.npar = self.npar Q.polybasis = self.polybasis self.trainedModel.data.mus = copy(self.mus) self.trainedModel.data.Q = Q self.trainedModel.data.P = self._setupNumerator() self.trainedModel.data.approxParameters = copy(self.approxParameters) vbMng(self, "DEL", "Done setting up approximant.", 5) def _computeInterpolantInverseBlocks(self) -> Tuple[List[Np2D], Np2D]: """ Compute inverse factors for minimal interpolant target functional. """ RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.") self._setupInterpolationIndices() cfun = totalDegreeN if self.polydegreetype == "TOTAL" else fullDegreeN N = copy(self.N) while len(self.mus) < cfun(N, self.npar): N -= 1 if N < self.N: RROMPyWarning(("N too large compared to S. Reducing N by " "{}").format(self.N - N)) self.N = N while self.N >= 0: + if self.centeredLike: + Seff = cfun(self.N, self.npar) + #derIdxsEff = [self._derIdxs[0][- Seff :]] + derIdxsEff = [self._derIdxs[0][: Seff]] + reorder = self._reorder[: Seff] + else: + Seff = len(self.mus) + derIdxsEff = self._derIdxs + reorder = self._reorder if self.polydegreetype == "TOTAL": TE, _, argIdxs = pvTP(self._musUniqueCN, self.N, - self.polybasis0, self._derIdxs, - self._reorder, + self.polybasis0, derIdxsEff, reorder, scl = np.power(self.scaleFactor, -1.)) TE = TE[:, argIdxs] idxsB = totalDegreeMaxMask(self.N, self.npar) else: #if self.polydegreetype == "FULL": TE = pvP(self._musUniqueCN, [self.N] * self.npar, - self.polybasis0, self._derIdxs, self._reorder, + self.polybasis0, derIdxsEff, reorder, scl = np.power(self.scaleFactor, -1.)) idxsB = fullDegreeMaxMask(self.N, self.npar) fitOut = customPInv(TE, rcond = self.interpRcond, full = True) vbMng(self, "MAIN", ("Fitting {} samples with degree {} through {}... " "Conditioning of pseudoinverse system: {:.4e}.").format( TE.shape[0], self.N, polyfitname(self.polybasis0), fitOut[1][1][0] / fitOut[1][1][-1]), 5) if fitOut[1][0] == TE.shape[1]: fitinv = fitOut[0][idxsB, :] break if self.catchInstability: raise RROMPyException(("Instability in denominator " "computation: polyfit is poorly " "conditioned.")) RROMPyWarning("Polyfit is poorly conditioned. Reducing N by 1.") self.N = self.N - 1 if self.polydegreetype == "TOTAL": TN, _, argIdxs = pvTP(self._musUniqueCN, self.N, self.polybasis0, - self._derIdxs, self._reorder, + derIdxsEff, reorder, scl = np.power(self.scaleFactor, -1.)) TN = TN[:, argIdxs] else: #if self.polydegreetype == "FULL": - TN = pvP(self._musUniqueCN, [self.N] * self.npar, - self.polybasis0, self._derIdxs, self._reorder, + TN = pvP(self._musUniqueCN, [self.N] * self.npar, self.polybasis0, + derIdxsEff, reorder, scl = np.power(self.scaleFactor, -1.)) invD = [None] * (len(idxsB)) for k in range(len(idxsB)): pseudoInv = np.diag(fitinv[k, :]) idxGlob = 0 - for j, derIdxs in enumerate(self._derIdxs): + for j, derIdxs in enumerate(derIdxsEff): nder = len(derIdxs) idxGlob += nder if nder > 1: - idxLoc = np.arange(len(self.mus))[ - (self._reorder >= idxGlob - nder) - * (self._reorder < idxGlob)] + idxLoc = np.arange(Seff)[(reorder >= idxGlob - nder) + * (reorder < idxGlob)] invLoc = fitinv[k, idxLoc] pseudoInv[np.ix_(idxLoc, idxLoc)] = 0. for diffj, diffjIdx in enumerate(derIdxs): for derQ, derQIdx in enumerate(derIdxs): derUIdx = [x - y for (x, y) in zip(diffjIdx, derQIdx)] if all([x >= 0 for x in derUIdx]): derU = hashD(derUIdx) pseudoInv[idxLoc[derU], idxLoc[derQ]] = ( invLoc[diffj]) invD[k] = dot(pseudoInv, TN) return invD, fitinv def findeveVGExplicit(self, sampleE:sampList, invD:List[Np2D]) -> Tuple[Np1D, Np2D]: """ Compute explicitly eigenvalues and eigenvectors of rational denominator matrix. """ RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.") nEnd = invD[0].shape[1] eWidth = len(invD) vbMng(self, "INIT", "Building gramian matrix.", 10) gramian = self.HFEngine.innerProduct(sampleE, sampleE, is_state = self.approx_state) G = np.zeros((nEnd, nEnd), dtype = np.complex) for k in range(eWidth): G += dot(dot(gramian, invD[k]).T, invD[k].conj()).T vbMng(self, "DEL", "Done building gramian.", 10) vbMng(self, "INIT", "Solving eigenvalue problem for gramian matrix.", 7) ev, eV = np.linalg.eigh(G) vbMng(self, "MAIN", ("Solved eigenvalue problem of size {} with condition number " "{:.4e}.").format(nEnd, ev[-1] / ev[0]), 5) vbMng(self, "DEL", "Done solving eigenvalue problem.", 7) return ev, eV def findeveVGQR(self, RPODE:Np2D, invD:List[Np2D]) -> Tuple[Np1D, Np2D]: """ Compute eigenvalues and eigenvectors of rational denominator matrix through SVD of R factor. """ RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.") nEnd = invD[0].shape[1] S = RPODE.shape[0] eWidth = len(invD) vbMng(self, "INIT", "Building half-gramian matrix stack.", 10) Rstack = np.zeros((S * eWidth, nEnd), dtype = np.complex) for k in range(eWidth): Rstack[k * S : (k + 1) * S, :] = dot(RPODE, invD[k]) vbMng(self, "DEL", "Done building half-gramian.", 10) vbMng(self, "INIT", "Solving svd for square root of gramian matrix.", 7) _, s, eV = np.linalg.svd(Rstack, full_matrices = False) ev = s[::-1] eV = eV[::-1, :].T.conj() vbMng(self, "MAIN", ("Solved svd problem of size {} x {} with condition number " "{:.4e}.").format(*Rstack.shape, s[0] / s[-1]), 5) vbMng(self, "DEL", "Done solving svd.", 7) return ev, eV def getResidues(self, *args, **kwargs) -> Np1D: """ Obtain approximant residues. Returns: Matrix with residues as columns. """ return self.trainedModel.getResidues(*args, **kwargs)