ANL-CEEESA/powersas.m
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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/getPadeApproxVector.m Normal file
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function [xa,xb]=getPadeApproxVector(xc,m,tag)
% Calculate Pade coefficients by a vector of variables, called by getPadeApproxHelm()
%
% FUNCTION getPadeApproxVector
%
% 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.
% ***************************************************************************************************
%
% INPUT
% xc - HE coefficients in power series
% m - order on the numerator
% tag
% 0 - proceed for computation
% 1 - this variable is ignored, do not compute
%
% OUTPUT
% xa - Pade coeffcients on the numerator
% xb - Pade coeffcients on the denominator
%
N=size(xc,2);
n=N-m;
nD=size(xc,1);
xa=zeros(nD,m);
xb=zeros(nD,n);
txc=xc(tag==0,:);
if size(txc,1)>0
augTxc=[zeros(size(txc,1),n),txc];
nT=2*n-1;
ttxc=augTxc(:,(end-nT):(end-1));
ytxc=-augTxc(:,(end-n+1):end);
tb=solveToepLevinson(ttxc,ytxc);
ta=augTxc(:,(n+1):(n+m));
for k=1:n
ta=ta+augTxc(:,(n+1-k):(n+m-k)).*repmat(tb(:,k),1,m);
end
xa(tag==0,:)=ta;
xb(tag==0,:)=tb;
end
end