ForwardSolution Solves the potential distribution in 2D EIT
Function [U,p,r]=ForwardSolution(NNode,NElement,A,C,T,MeasPattern,style,p,r);
computes the internal voltages for the injected currents (U.Current)
and for the "measurement field" (U.MeasField) and the voltages
on the electrodes (U.Electrode).
INPUT
NNode = the number of nodes
NElement = the number of elements
A = the system matrix
C = the reference matrix
T = current patterns
MeasPattern = measurement pattern, default \sum_{l=1}^L=0.
style = 'comp' for complex reconstruction and 'real' for real
p = the permutation vector (optional)
r = reversed permutation (optional)
OUTPUT
U = potential data structure, includes potetial correspondign to the actual
current injections (U.Current), for the measurement pattern (U.MeasField)
and voltages on the electrodes (U.Electrode)
p = the permutation vector (optional)
r = reversed permutation (optional)0001 function [U,p,r]=ForwardSolution(NNode,NElement,A,C,T,MeasPattern,style,p,r); 0002 0003 %ForwardSolution Solves the potential distribution in 2D EIT 0004 % Function [U,p,r]=ForwardSolution(NNode,NElement,A,C,T,MeasPattern,style,p,r); 0005 % computes the internal voltages for the injected currents (U.Current) 0006 % and for the "measurement field" (U.MeasField) and the voltages 0007 % on the electrodes (U.Electrode). 0008 % 0009 % INPUT 0010 % 0011 % NNode = the number of nodes 0012 % NElement = the number of elements 0013 % A = the system matrix 0014 % C = the reference matrix 0015 % T = current patterns 0016 % MeasPattern = measurement pattern, default \sum_{l=1}^L=0. 0017 % style = 'comp' for complex reconstruction and 'real' for real 0018 % p = the permutation vector (optional) 0019 % r = reversed permutation (optional) 0020 % 0021 % OUTPUT 0022 % 0023 % U = potential data structure, includes potetial correspondign to the actual 0024 % current injections (U.Current), for the measurement pattern (U.MeasField) 0025 % and voltages on the electrodes (U.Electrode) 0026 % p = the permutation vector (optional) 0027 % r = reversed permutation (optional) 0028 0029 % M. Vauhkonen 13.8.1999 0030 % University of Kuopio, Department of Applied Physics, 0031 % PO Box 1627, FIN-70211, Kuopio, Finland, email:Marko.Vauhkonen@uku.fi 0032 % Ordering added 15.11.1999, modified 28.3.2000 by M. Vauhkonen 0033 0034 L=max(size(A))-NNode+1; % The number of electrodes 0035 0036 if style=='comp' 0037 II1=sparse([zeros(L,NNode),C,zeros(L,NNode+L-1);zeros(L,2*NNode+L-1),C]); 0038 if ~isempty(MeasPattern) 0039 II1=MeasPattern'*II1; 0040 II1=II1'; 0041 else 0042 MeasPattern=eye(2*max(size(C))); 0043 II1=II1'; 0044 end 0045 II=sparse([[zeros(NNode,size(T,2));C'*T];zeros(NNode+L-1,size(T,2))]); 0046 A=[real(A),-imag(A);imag(A),real(A)]; 0047 UU=A'\II1;%Voltages for the "measurement field" and for the current patterns. 0048 UU=full([UU,A\II]); 0049 U.MeasField=[UU(1:NNode,1:size(II1,2));UU(NNode+L:2*NNode+L-1,1:size(II1,2))]; %The "measurement field" data 0050 U.Electrode=MeasPattern'*[C,zeros(size(C));zeros(size(C)),C]* ... 0051 [UU(NNode+1:NNode+L-1,size(II1,2)+1:size(UU,2));UU(2*NNode+L:size(UU,1), ... 0052 size(II1,2)+1:size(UU,2))];%Voltages on the electrodes 0053 U.Current=[UU(1:NNode,size(II1,2)+1:size(UU,2));UU(NNode+L:2*NNode+L-1,size(II1,2)+1:size(UU,2))]; 0054 0055 elseif style=='real' 0056 II1=sparse([zeros(L,NNode),C]); 0057 if ~isempty(MeasPattern) 0058 II1=MeasPattern'*II1; 0059 II1=II1'; 0060 else 0061 MeasPattern=eye(max(size(C))); 0062 II1=II1'; 0063 end 0064 II=[zeros(NNode,size(T,2));C'*T]; 0065 0066 if nargin<8 0067 p=symmmd(A); 0068 r(p)=1:max(size(p)); 0069 end 0070 0071 R=chol(A(p,p)); 0072 UU=R\(R'\[II1(p,:),II(p,:)]); 0073 UU=full(UU(r,:)); 0074 U.MeasField=UU(1:NNode,1:size(II1,2)); %The "measurement field" data 0075 U.Electrode=MeasPattern'*C*UU(NNode+1:size(A,1),size(II1,2)+1:size(UU,2));%Voltages on the electrodes 0076 U.Current=UU(1:NNode,size(II1,2)+1:size(UU,2)); 0077 end 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092