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First release of PowerSAS.m

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Rui Yao
2021-12-22 23:37:28 -06:00
commit 985517593c
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internal/calcFluctuationHEpade.m Normal file
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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>
%
% Copyright (C) 2021, UChicago Argonne, LLC. All rights reserved.
%
% OPEN SOURCE LICENSE
%
% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
%
% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
% 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.
% 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.
%
%
% ******************************************************************************************************
% DISCLAIMER
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
% WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
% PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
% CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
% ***************************************************************************************************
%
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