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106 lines
4.8 KiB
106 lines
4.8 KiB
function flucTag=getFluctuationTagPade(coeffA,coeffB,maxTime,rateThreshold)
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% Determine steady state from the fluctuation bounds using Pade approximation
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%
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% FUNCTION getFluctuationTagPade
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%
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% Author: Rui Yao <ruiyao@ieee.org>
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%
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% Copyright (C) 2021, UChicago Argonne, LLC. All rights reserved.
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%
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% OPEN SOURCE LICENSE
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%
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% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
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%
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% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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% 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
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% 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
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%
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%
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% ******************************************************************************************************
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% DISCLAIMER
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%
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
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% WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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% PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
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% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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% CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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% ***************************************************************************************************
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%
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% INPUT
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% coeffA - Pade coefficients on the numerator
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% coeffB - Pade coefficients on the denomenator
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% maxTime - maximum time considered
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% rateThreshold - the threshold of fluctuation rate
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%
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% OUTPUT
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% flucTag
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% 1 - lower than threshold, entered steady state
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% 0 - Not entered steady state yet
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%
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if nargin<4
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rateThreshold=0.0005;
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end
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NA=size(coeffA,2);
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timePwrA=maxTime.^(1:(NA-1));
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coeffAx=coeffA(:,2:NA);
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constA=coeffA(:,1);
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fluctuationPosA=sum(coeffAx.*(coeffAx>0).*repmat(timePwrA,size(coeffA,1),1),2);
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fluctuationNegA=sum(-coeffAx.*(coeffAx<0).*repmat(timePwrA,size(coeffA,1),1),2);
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NB=size(coeffB,2);
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timePwrB=maxTime.^(1:(NB-1));
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coeffBx=coeffB(:,2:NB);
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constB=coeffB(:,1);
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constTotal=constA./constB;
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fluctuationPosB=sum(coeffBx.*(coeffBx>0).*repmat(timePwrB,size(coeffB,1),1),2);
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fluctuationNegB=sum(-coeffBx.*(coeffBx<0).*repmat(timePwrB,size(coeffB,1),1),2);
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denSgn=(constB+fluctuationPosB).*(constB-fluctuationNegB); % if the denomenator will change sign, then fluctuation is too big.
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totalFluctuation=max(abs([(constA+fluctuationPosA)./(constB+fluctuationPosB)-constTotal,...
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(constA+fluctuationPosA)./(constB-fluctuationNegB)-constTotal,...
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(constA-fluctuationNegA)./(constB+fluctuationPosB)-constTotal,...
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(constA-fluctuationNegA)./(constB-fluctuationNegB)-constTotal]),[],2);
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% Special: check if the coefficients on Num/Den can be directly eliminated
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totalFlucRes=zeros(size(coeffA,1),1);
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if NA>NB
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regA=coeffA(:,1:NB);
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res=coeffA(:,(NB+1):end);
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regB=coeffB;
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flucResPos=sum(res.*(res>0).*repmat(timePwrA(NB:end),size(res,1),1),2);
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flucResNeg=sum(-res.*(res<0).*repmat(timePwrA(NB:end),size(res,1),1),2);
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flucResNum=max([flucResPos,flucResNeg],[],2);
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flucRes=abs([flucResNum./(constB-fluctuationNegB),flucResNum./(constB+fluctuationPosB)]);
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flucRes(all(regB(:,2:end)>=0,2),1)=0;
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flucRes(all(regB(:,2:end)<=0,2),2)=0;
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totalFlucRes=max(flucRes,[],2);
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elseif NB>NA
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regA=coeffA;
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regB=coeffB(:,1:NA);
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res=coeffB(:,(NA+1):end);
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flucResPos=sum(res.*(res>0).*repmat(timePwrB(NA:end),size(res,1),1),2);
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flucResNeg=sum(-res.*(res<0).*repmat(timePwrB(NA:end),size(res,1),1),2);
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flucResNum=max([flucResPos,flucResNeg],[],2);
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flucRes=abs([flucResNum./(constB-fluctuationNegB),flucResNum./(constB+fluctuationPosB)]);
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flucRes(all(regB(:,2:end)>=0,2),1)=0;
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flucRes(all(regB(:,2:end)<=0,2),2)=0;
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totalFlucRes=max(flucRes,[],2);
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else
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regA=coeffA;
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regB=coeffB;
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end
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ratioAB=regA./regB;
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ratioAB(isnan(ratioAB))=0;
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ratioAB=ratioAB./repmat(mean(ratioAB,2),1,size(ratioAB,2));
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flucRatioAB=max(ratioAB,[],2)-min(ratioAB,[],2);
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eachFlucTag1=(totalFluctuation/maxTime)<rateThreshold;
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eachFlucTag2=(flucRatioAB<rateThreshold)&((totalFlucRes/maxTime)<rateThreshold);
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eachFlucTag=eachFlucTag1|eachFlucTag2;
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flucTag=all(eachFlucTag);
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end |