function [J]=JacobianNode(Node,Element,Agrad,U,U0,rho,style);%JacobianNode Computes the Jacobian for 2D EIT when node basis is used% Function [J]=JacobianNode(g,H,Agrad,U,U0,rho,style);% computes the Jacobian for 2D EIT when node basis% is used.%% INPUT%% Node = nodal data structure% Element = element data structure% Agrad = \int_{Element(ii) \nabla\phi_i\cdot\nabla\phi_j% U = voltages corresponding to the injected currents% U0 = voltages corresponding to the measurement field% rho = resistivity or admittivity vector% style = either 'real' for reconstructing resistivity or 'comp'% for reconstructin admittivity%% OUTPUT%% J = Jacobian% M. Vauhkonen 13.8.1999,% University of Kuopio, Department of Applied Physics, PO Box 1627,% FIN-70211 Kuopio, Finland, email: Marko.Vauhkonen@uku.fiNNode=max(size(Node));NElement=max(size(Element));if nargin<3mE=max(size(Element(1).Topology));if mE==3 Agrad=sparse(NNode^2,NNode); H=reshape([Element.Topology],3,NElement)'; mH=max(max(H)); else H=reshape([Element.Topology],6,NElement)'; mH=max(max(H(:,1:2:6)));  Agrad=sparse(NNode^2,mH); clear Hendg=reshape([Node.Coordinate],2,NNode)';      %Nodesfor jj=1:mHAa=sparse(NNode,NNode);El=Node(jj).ElementConnection; for ii=1:max(size(El))   ind=Element(El(ii)).Topology; % Indices of the element   gg=g(ind,:);   if max(size(gg))==3    indsig=ind;    I=find(jj==indsig);    anis=grinprodgausnode(gg,I);    Aa(ind,ind)=Aa(ind,ind)+anis;   else     indsig=ind(1:2:6);     I=find(jj==indsig);     anis=grinprodgaus2ndnode(gg,I);     Aa(ind,ind)=Aa(ind,ind)+anis;            end   end   Agrad(:,jj)=Aa(:);endJ=Agrad;elseif style=='comp'  J=zeros(size(U,2)*size(U0,2),2*size(Agrad,2)); for ii=1:size(Agrad,2);    Agrad1=reshape(Agrad(:,ii),NNode,NNode);    AgU1=Agrad1*U(1:NNode,:);    AgU2=Agrad1*U(NNode+1:2*NNode,:);    JJ=-U0.'*[AgU1;AgU2];    JJ=JJ(:);    J(:,ii)=JJ;    JJ=-U0.'*[-AgU2;AgU1];    J(:,ii+size(Agrad,2))=JJ(:); endelseif style=='real'  J=zeros(size(U,2)*size(U0,2),size(Agrad,2));   for ii=1:size(Agrad,2);    JJ=-U0.'*reshape(Agrad(:,ii),NNode,NNode)*U;    JJ=JJ(:);    J(:,ii)=JJ;   end endend