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82 lines
3.2 KiB
82 lines
3.2 KiB
function x=solveToepLevinson(ct,y)
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% Solving Toeplitz matrix equations with Levinson algorithm (vector)
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%
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% FUNCTION solveToepLevinson
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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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% ct - D*(2N-1)
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% y - D*N
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%
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% OUTPUT
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% x - solution to the equations
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%
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% overheadTag=tic;
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D=size(ct,1); % The dimension of the variables
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N=round((size(ct,2)+1)/2); % The size of the Toep matrix
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f=zeros(D,N);
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b=zeros(D,N);
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temp=zeros(D,N);
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x=zeros(D,N);
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epsf=zeros(D,1);
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epsb=zeros(D,1);
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epsx=zeros(D,1);
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alphaf=zeros(D,1);
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betaf=zeros(D,1);
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alphab=zeros(D,1);
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betab=zeros(D,1);
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% oh=toc(overheadTag);
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% disp(sprintf('Overhead=%10.8f s.',oh));
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% mainTag=tic;
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f(:,1)=1./ct(:,N);
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b(:,end)=f(:,1);
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x(:,1)=y(:,1).*f(:,1);
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for k=2:N
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epsf(:)=sum(f(:,1:(k-1)).*ct(:,((N+k-1):-1:(N+1))),2);
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epsb(:)=sum(b(:,(N-k+2):N).*ct(:,((N-1):-1:(N-k+1))),2);
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epsx(:)=sum(x(:,1:(k-1)).*ct(:,((N+k-1):-1:(N+1))),2);
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alphaf(:)=1./(1-epsf.*epsb);
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betaf(:)=-epsf.*alphaf;
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alphab(:)=-epsb.*alphaf;
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betab(:)=alphaf;
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temp(:,1:(k-1))=f(:,1:(k-1));
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f(:,1:k)=repmat(alphaf,1,k).*temp(:,1:k)+repmat(betaf,1,k).*b(:,(N-k+1):N);
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b(:,(N-k+1):N)=repmat(alphab,1,k).*temp(:,1:k)+repmat(betab,1,k).*b(:,(N-k+1):N);
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x(:,1:k)=x(:,1:k)+repmat((y(:,k)-epsx),1,k).*b(:,(N-k+1):N);
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end
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% mn=toc(mainTag);
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% disp(sprintf('Main=%10.8f s.',mn));
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% disp(sprintf('xxxxx/=%10.8f ',oh/(oh+mn)));
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end |