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45 lines
2.6 KiB
45 lines
2.6 KiB
function fluctuation=calcFluctuationHEpade(coeffsa,coeffsb,maxTime)
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% Calculate the bounds of rate of system state fluctuation using Pad'e of HE coefficients
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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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Nvec=size(coeffsa,1);
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Nnum=max([size(coeffsa,2)-1,size(coeffsb,2)]);
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Nden=size(coeffsb,2);
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timePwrnum=maxTime.^(1:Nnum);
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coeffNum=zeros(Nvec,Nnum);
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coeffNum(:,1:(size(coeffsa,2)-1))=coeffsa(:,2:end);
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coeffNum(:,1:size(coeffsb,2))=coeffNum(:,1:size(coeffsb,2))-coeffsb;
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fluctuationNumPos=sum(coeffNum.*(coeffNum>0).*repmat(timePwrnum,Nvec,1),2);
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fluctuationNumNeg=sum(-coeffNum.*(coeffNum<0).*repmat(timePwrnum,Nvec,1),2);
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fluctuationNum=max([fluctuationNumPos,fluctuationNumNeg],[],2);
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timePwrDen=maxTime.^(1:Nden);
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denMin=1+sum(coeffsb.*(coeffsb<0).*repmat(timePwrDen,Nvec,1),2);
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denMin(denMin<1e-6)=1e-6;
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fluctuation=fluctuationNum./denMin;
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end |