function fluctuation=calcFluctuationHEpade(coeffsa,coeffsb,maxTime)
% Calculate the bounds of rate of system state fluctuation using Pad'e of HE coefficients
% Author: Rui Yao <ruiyao@ieee.org>
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Nvec=size(coeffsa,1);
Nnum=max([size(coeffsa,2)-1,size(coeffsb,2)]);
Nden=size(coeffsb,2);
timePwrnum=maxTime.^(1:Nnum);
coeffNum=zeros(Nvec,Nnum);
coeffNum(:,1:(size(coeffsa,2)-1))=coeffsa(:,2:end);
coeffNum(:,1:size(coeffsb,2))=coeffNum(:,1:size(coeffsb,2))-coeffsb;

fluctuationNumPos=sum(coeffNum.*(coeffNum>0).*repmat(timePwrnum,Nvec,1),2);
fluctuationNumNeg=sum(-coeffNum.*(coeffNum<0).*repmat(timePwrnum,Nvec,1),2);
fluctuationNum=max([fluctuationNumPos,fluctuationNumNeg],[],2);

timePwrDen=maxTime.^(1:Nden);
denMin=1+sum(coeffsb.*(coeffsb<0).*repmat(timePwrDen,Nvec,1),2);
denMin(denMin<1e-6)=1e-6;

fluctuation=fluctuationNum./denMin;
end